TSTP Solution File: ALG193+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG193+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:39:45 EDT 2023
% Result : Unsatisfiable 22.95s 3.84s
% Output : Proof 252.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG193+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:05:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 7.29/1.77 Prover 1: Preprocessing ...
% 7.29/1.79 Prover 2: Preprocessing ...
% 7.29/1.79 Prover 3: Preprocessing ...
% 7.29/1.79 Prover 6: Preprocessing ...
% 7.96/1.80 Prover 5: Preprocessing ...
% 7.96/1.81 Prover 4: Preprocessing ...
% 7.96/1.82 Prover 0: Preprocessing ...
% 13.24/2.57 Prover 2: Constructing countermodel ...
% 13.24/2.57 Prover 3: Constructing countermodel ...
% 14.82/2.76 Prover 4: Constructing countermodel ...
% 14.82/2.78 Prover 1: Constructing countermodel ...
% 15.47/2.84 Prover 6: Constructing countermodel ...
% 15.47/2.87 Prover 0: Constructing countermodel ...
% 18.06/3.17 Prover 5: Constructing countermodel ...
% 22.95/3.84 Prover 6: proved (3188ms)
% 22.95/3.84
% 22.95/3.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.95/3.84
% 22.95/3.85 Prover 2: proved (3198ms)
% 22.95/3.85
% 22.95/3.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.95/3.85
% 22.95/3.85 Prover 0: stopped
% 23.37/3.86 Prover 5: stopped
% 23.37/3.86 Prover 3: stopped
% 23.37/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.37/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.37/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.37/3.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.37/3.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.68/4.43 Prover 7: Preprocessing ...
% 26.68/4.46 Prover 8: Preprocessing ...
% 26.68/4.46 Prover 11: Preprocessing ...
% 26.68/4.46 Prover 13: Preprocessing ...
% 27.14/4.47 Prover 10: Preprocessing ...
% 30.24/4.81 Prover 8: Constructing countermodel ...
% 31.14/4.93 Prover 13: Constructing countermodel ...
% 31.14/4.94 Prover 10: Constructing countermodel ...
% 31.14/5.00 Prover 11: Constructing countermodel ...
% 31.64/5.07 Prover 7: Constructing countermodel ...
% 63.98/9.38 Prover 13: stopped
% 65.32/9.40 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.11/9.59 Prover 16: Preprocessing ...
% 69.86/10.01 Prover 16: Constructing countermodel ...
% 109.08/15.27 Prover 16: stopped
% 109.08/15.29 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 111.39/15.51 Prover 19: Preprocessing ...
% 112.82/15.78 Prover 19: Constructing countermodel ...
% 114.81/15.99 Prover 1: stopped
% 136.92/19.03 Prover 19: stopped
% 180.23/26.82 Prover 7: stopped
% 184.52/27.97 Prover 4: stopped
% 221.67/39.60 Prover 8: stopped
% 223.09/40.25 Prover 11: stopped
% 239.15/55.11 Prover 10: Found proof (size 4495134)
% 239.15/55.11 Prover 10: proved (51249ms)
% 239.15/55.11
% 239.15/55.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 239.15/55.11
% 243.47/57.53 % SZS output start Proof for theBenchmark
% 243.47/57.55 Assumptions after simplification:
% 243.47/57.55 ---------------------------------
% 243.47/57.55
% 243.47/57.55 (ax1)
% 243.75/57.61 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.61 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 243.75/57.61 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 243.75/57.61 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 243.75/57.61 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 243.75/57.61 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) =
% 243.75/57.61 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) =
% 243.75/57.61 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) =
% 243.75/57.61 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) =
% 243.75/57.61 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6
% 243.75/57.61 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 243.75/57.61 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) &
% 243.75/57.61 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 243.75/57.61 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 243.75/57.61 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 |
% 243.75/57.61 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 =
% 243.75/57.61 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) &
% 243.75/57.61 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 =
% 243.75/57.61 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 |
% 243.75/57.61 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 =
% 243.75/57.61 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 |
% 243.75/57.61 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 =
% 243.75/57.61 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 |
% 243.75/57.61 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12
% 243.75/57.61 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 |
% 243.75/57.61 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 =
% 243.75/57.61 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 =
% 243.75/57.61 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2
% 243.75/57.61 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) &
% 243.75/57.61 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4
% 243.75/57.61 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 =
% 243.75/57.61 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 =
% 243.75/57.61 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1
% 243.75/57.61 | v0 = e0))
% 243.75/57.61
% 243.75/57.61 (ax10)
% 243.75/57.61 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.62 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e1,
% 243.75/57.62 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 243.75/57.62 e0) = v1 & $i(v1))))
% 243.75/57.62
% 243.75/57.62 (ax100)
% 243.75/57.62 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.62 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.62 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 243.75/57.62 e3) = v1 & $i(v1))))
% 243.75/57.62
% 243.75/57.62 (ax101)
% 243.75/57.62 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.62 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.62 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 243.75/57.62 e3) = v1 & $i(v1))))
% 243.75/57.62
% 243.75/57.62 (ax102)
% 243.75/57.62 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.62 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.62 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 243.75/57.62 e3) = v1 & $i(v1))))
% 243.75/57.62
% 243.75/57.62 (ax103)
% 243.75/57.63 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.63 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.63 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 243.75/57.63 e4) = v1 & $i(v1))))
% 243.75/57.63
% 243.75/57.63 (ax104)
% 243.75/57.63 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.63 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.63 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 243.75/57.63 e4) = v1 & $i(v1))))
% 243.75/57.63
% 243.75/57.63 (ax105)
% 243.75/57.63 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.63 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.63 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 243.75/57.63 e4) = v1 & $i(v1))))
% 243.75/57.63
% 243.75/57.63 (ax106)
% 243.75/57.63 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.63 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.63 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 243.75/57.63 e4) = v1 & $i(v1))))
% 243.75/57.63
% 243.75/57.63 (ax107)
% 243.75/57.64 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.64 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.64 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 243.75/57.64 e4) = v1 & $i(v1))))
% 243.75/57.64
% 243.75/57.64 (ax108)
% 243.75/57.64 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.64 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.64 v1) = v2 & op(e0, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 243.75/57.64 e4) = v1 & $i(v1))))
% 243.75/57.64
% 243.75/57.64 (ax109)
% 243.75/57.64 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.64 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.64 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 243.75/57.64 e4) = v1 & $i(v1))))
% 243.75/57.64
% 243.75/57.64 (ax11)
% 243.75/57.64 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.64 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e1,
% 243.75/57.64 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 243.75/57.64 e0) = v1 & $i(v1))))
% 243.75/57.64
% 243.75/57.64 (ax110)
% 243.75/57.64 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.64 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.64 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 243.75/57.64 e4) = v1 & $i(v1))))
% 243.75/57.64
% 243.75/57.64 (ax111)
% 243.75/57.65 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.65 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.65 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 243.75/57.65 e4) = v1 & $i(v1))))
% 243.75/57.65
% 243.75/57.65 (ax112)
% 243.75/57.65 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.65 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.65 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 243.75/57.65 e4) = v1 & $i(v1))))
% 243.75/57.65
% 243.75/57.65 (ax113)
% 243.75/57.65 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.65 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.65 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 243.75/57.65 e4) = v1 & $i(v1))))
% 243.75/57.65
% 243.75/57.65 (ax114)
% 243.75/57.65 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.65 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.65 v1) = v2 & op(e1, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 243.75/57.65 e4) = v1 & $i(v1))))
% 243.75/57.65
% 243.75/57.65 (ax115)
% 243.75/57.65 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.65 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.65 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 243.75/57.65 e4) = v1 & $i(v1))))
% 243.75/57.65
% 243.75/57.65 (ax116)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.66 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax117)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4,
% 243.75/57.66 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax118)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.66 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax119)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.66 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax12)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e1,
% 243.75/57.66 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 243.75/57.66 e0) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax120)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.66 v1) = v2 & op(e2, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax121)
% 243.75/57.66 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.66 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.66 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 243.75/57.66 e4) = v1 & $i(v1))))
% 243.75/57.66
% 243.75/57.66 (ax122)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.67 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 243.75/57.67 e4) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax123)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4,
% 243.75/57.67 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 243.75/57.67 e4) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax124)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.67 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 243.75/57.67 e4) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax125)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4,
% 243.75/57.67 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 243.75/57.67 e4) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax126)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4,
% 243.75/57.67 v1) = v2 & op(e3, e4) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 243.75/57.67 e4) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax13)
% 243.75/57.67 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.67 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e2,
% 243.75/57.67 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 243.75/57.67 e0) = v1 & $i(v1))))
% 243.75/57.67
% 243.75/57.67 (ax14)
% 243.75/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.68 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e2,
% 243.75/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 243.75/57.68 e0) = v1 & $i(v1))))
% 243.75/57.68
% 243.75/57.68 (ax15)
% 243.75/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.68 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e2,
% 243.75/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 243.75/57.68 e0) = v1 & $i(v1))))
% 243.75/57.68
% 243.75/57.68 (ax16)
% 243.75/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.68 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e2,
% 243.75/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 243.75/57.68 e0) = v1 & $i(v1))))
% 243.75/57.68
% 243.75/57.68 (ax17)
% 243.75/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.68 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e2,
% 243.75/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 243.75/57.68 e0) = v1 & $i(v1))))
% 243.75/57.68
% 243.75/57.68 (ax18)
% 243.75/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 243.75/57.68 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e2,
% 243.75/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 243.75/57.68 e0) = v1 & $i(v1))))
% 243.75/57.68
% 243.75/57.68 (ax19)
% 244.18/57.68 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.68 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.68 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 244.18/57.68 e0) = v1 & $i(v1))))
% 244.18/57.68
% 244.18/57.68 (ax2)
% 244.18/57.71 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.71 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 244.18/57.71 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 244.18/57.71 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 244.18/57.71 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 244.18/57.71 [v23: $i] : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4,
% 244.18/57.71 e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) =
% 244.18/57.71 e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) |
% 244.18/57.71 (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12 = e4 &
% 244.18/57.71 op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 = e3 & op(e4,
% 244.18/57.71 e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) =
% 244.18/57.71 e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) &
% 244.18/57.71 ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 &
% 244.18/57.71 op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & op(e0, e4)
% 244.18/57.71 = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) |
% 244.18/57.71 (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 &
% 244.18/57.71 op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 & op(e3,
% 244.18/57.71 e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) =
% 244.18/57.71 e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) |
% 244.18/57.71 (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 &
% 244.18/57.71 op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & op(e4,
% 244.18/57.71 e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) =
% 244.18/57.71 e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) &
% 244.18/57.71 ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 &
% 244.18/57.71 op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 & op(e4, e0)
% 244.18/57.71 = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) |
% 244.18/57.71 (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 &
% 244.18/57.71 op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & op(e3,
% 244.18/57.71 e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) =
% 244.18/57.71 e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) |
% 244.18/57.71 (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 &
% 244.18/57.71 op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 & op(e4,
% 244.18/57.71 e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) =
% 244.18/57.71 e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) &
% 244.18/57.71 ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 &
% 244.18/57.71 op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3)
% 244.18/57.71 = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) |
% 244.18/57.71 (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 &
% 244.18/57.71 op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 & op(e3,
% 244.18/57.71 e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) =
% 244.18/57.71 e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) |
% 244.18/57.71 (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 &
% 244.18/57.71 op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & op(e3,
% 244.18/57.71 e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) =
% 244.18/57.71 e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) &
% 244.18/57.71 ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 &
% 244.18/57.71 op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 & op(e3, e0)
% 244.18/57.71 = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) |
% 244.18/57.71 (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 &
% 244.18/57.71 op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & op(e3,
% 244.18/57.71 e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) =
% 244.18/57.71 e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) |
% 244.18/57.71 (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 244.18/57.71 op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 & op(e4,
% 244.18/57.71 e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) =
% 244.18/57.71 e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) &
% 244.18/57.71 ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 &
% 244.18/57.71 op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & op(e0, e2)
% 244.18/57.71 = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) |
% 244.18/57.71 (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 244.18/57.71 op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 & op(e2,
% 244.18/57.71 e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) =
% 244.18/57.71 e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) |
% 244.18/57.71 (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 &
% 244.18/57.71 op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & op(e2,
% 244.18/57.71 e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) =
% 244.18/57.71 e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) &
% 244.18/57.71 ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 &
% 244.18/57.71 op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 & op(e2, e0)
% 244.18/57.71 = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) |
% 244.18/57.71 (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 &
% 244.18/57.71 op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & op(e3,
% 244.18/57.71 e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4)
% 244.18/57.71 | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3
% 244.18/57.71 & op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 & op(e1,
% 244.18/57.71 e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) =
% 244.18/57.71 e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9
% 244.18/57.71 = e2 & op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 &
% 244.18/57.71 op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & op(e2, e1)
% 244.18/57.71 = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) &
% 244.18/57.71 ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 &
% 244.18/57.71 op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) =
% 244.18/57.71 e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) |
% 244.18/57.71 (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 &
% 244.18/57.71 op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & op(e1,
% 244.18/57.71 e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3)
% 244.18/57.71 | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2
% 244.18/57.71 & op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 & op(e1,
% 244.18/57.71 e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) =
% 244.18/57.71 e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9
% 244.18/57.71 = e1 & op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 &
% 244.18/57.71 op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & op(e1, e2)
% 244.18/57.71 = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) &
% 244.18/57.71 ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 &
% 244.18/57.71 op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) =
% 244.18/57.71 e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6
% 244.18/57.71 = e3 & op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 &
% 244.18/57.71 op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & op(e3, e0)
% 244.18/57.71 = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0
% 244.18/57.71 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 &
% 244.18/57.71 op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) =
% 244.18/57.71 e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3
% 244.18/57.71 = e4 & op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 &
% 244.18/57.71 op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4)
% 244.18/57.71 = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 244.18/57.71 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 &
% 244.18/57.71 op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) =
% 244.18/57.71 e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4
% 244.18/57.71 = e1 & op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 &
% 244.18/57.71 op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) =
% 244.18/57.71 e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) |
% 244.18/57.71 (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 &
% 244.18/57.71 op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 & op(e0,
% 244.18/57.71 e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) =
% 244.18/57.71 e0)))))
% 244.18/57.71
% 244.18/57.71 (ax20)
% 244.18/57.71 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.71 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e3,
% 244.18/57.71 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 244.18/57.71 e0) = v1 & $i(v1))))
% 244.18/57.71
% 244.18/57.71 (ax21)
% 244.18/57.71 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.71 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax22)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e3,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax23)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e3,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax24)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e3,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax25)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax26)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e4,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax27)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax28)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e4,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax29)
% 244.18/57.72 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.72 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e4,
% 244.18/57.72 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.18/57.72 e0) = v1 & $i(v1))))
% 244.18/57.72
% 244.18/57.72 (ax3)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 244.18/57.73 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 244.18/57.73 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 244.18/57.73 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 244.18/57.73 [v23: $i] : ? [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22,
% 244.18/57.73 v23) = e3 & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 &
% 244.18/57.73 op(v18, v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) =
% 244.18/57.73 e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 & op(v11,
% 244.18/57.73 v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7) = e4 & op(v7,
% 244.18/57.73 v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4, v3) = e2 & op(v3,
% 244.18/57.73 v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 & op(v0, v0) = e0 & op(e4,
% 244.18/57.73 e4) = v24 & op(e4, e3) = v22 & op(e4, e2) = v19 & op(e4, e1) = v14 &
% 244.18/57.73 op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3, e3) = v21 & op(e3, e2) = v17 &
% 244.18/57.73 op(e3, e1) = v12 & op(e3, e0) = v5 & op(e2, e4) = v20 & op(e2, e3) = v18 &
% 244.18/57.73 op(e2, e2) = v16 & op(e2, e1) = v10 & op(e2, e0) = v3 & op(e1, e4) = v15 &
% 244.18/57.73 op(e1, e3) = v13 & op(e1, e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 &
% 244.18/57.73 op(e0, e4) = v8 & op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 &
% 244.18/57.73 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19)
% 244.18/57.73 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 244.18/57.73 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 244.18/57.73 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.18/57.73
% 244.18/57.73 (ax30)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e4,
% 244.18/57.73 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.18/57.73 e0) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax31)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e1,
% 244.18/57.73 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 244.18/57.73 e1) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax32)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1,
% 244.18/57.73 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 244.18/57.73 e1) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax33)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e1,
% 244.18/57.73 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 244.18/57.73 e1) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax34)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1,
% 244.18/57.73 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 244.18/57.73 e1) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax35)
% 244.18/57.73 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.73 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1,
% 244.18/57.73 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.18/57.73 e1) = v1 & $i(v1))))
% 244.18/57.73
% 244.18/57.73 (ax36)
% 244.18/57.74 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.74 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1,
% 244.18/57.74 v1) = v2 & op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.18/57.74 e1) = v1 & $i(v1))))
% 244.18/57.74
% 244.18/57.74 (ax37)
% 244.18/57.74 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.74 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.74 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 244.18/57.74 e1) = v1 & $i(v1))))
% 244.18/57.74
% 244.18/57.74 (ax38)
% 244.18/57.74 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.74 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.74 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 244.18/57.74 e1) = v1 & $i(v1))))
% 244.18/57.74
% 244.18/57.74 (ax39)
% 244.18/57.74 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.74 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.74 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 244.18/57.74 e1) = v1 & $i(v1))))
% 244.18/57.74
% 244.18/57.74 (ax4)
% 244.18/57.74 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.74 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 244.18/57.74 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 244.18/57.74 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 244.18/57.74 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 244.18/57.74 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) &
% 244.18/57.74 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 =
% 244.18/57.74 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) &
% 244.18/57.74 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 =
% 244.18/57.74 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) &
% 244.18/57.74 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 =
% 244.18/57.74 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~
% 244.18/57.74 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 =
% 244.18/57.74 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) &
% 244.18/57.74 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 =
% 244.18/57.74 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) &
% 244.18/57.74 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 =
% 244.18/57.74 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) &
% 244.18/57.74 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 =
% 244.18/57.74 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) &
% 244.18/57.74 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 =
% 244.18/57.74 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~
% 244.18/57.74 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~
% 244.18/57.74 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~
% 244.18/57.74 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~
% 244.18/57.74 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~
% 244.18/57.74 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) &
% 244.18/57.74 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 &
% 244.18/57.74 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 &
% 244.18/57.74 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 &
% 244.18/57.74 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 &
% 244.18/57.74 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 &
% 244.18/57.74 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 &
% 244.18/57.74 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19)
% 244.18/57.74 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 244.18/57.74 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 244.18/57.74 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.18/57.74
% 244.18/57.74 (ax40)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e2,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax41)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax42)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e2,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax43)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax44)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax45)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax46)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax47)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax48)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e3,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax49)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.75 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.75 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.18/57.75 e1) = v1 & $i(v1))))
% 244.18/57.75
% 244.18/57.75 (ax5)
% 244.18/57.75 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~
% 244.18/57.75 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4)
% 244.18/57.75 & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 244.18/57.75
% 244.18/57.75 (ax50)
% 244.18/57.75 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e4,
% 244.18/57.76 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.18/57.76 e1) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax51)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.76 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 244.18/57.76 e1) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax52)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e4,
% 244.18/57.76 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4,
% 244.18/57.76 e1) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax53)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e4,
% 244.18/57.76 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.18/57.76 e1) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax54)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e4,
% 244.18/57.76 e1) = v1 & op(e1, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.18/57.76 e1) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax55)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.76 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 244.18/57.76 e2) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax56)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.76 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 244.18/57.76 e2) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax57)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.76 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 244.18/57.76 e2) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax58)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2,
% 244.18/57.76 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0,
% 244.18/57.76 e2) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax59)
% 244.18/57.76 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.76 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.76 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.18/57.76 e2) = v1 & $i(v1))))
% 244.18/57.76
% 244.18/57.76 (ax6)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 244.18/57.77 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ?
% 244.18/57.77 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ?
% 244.18/57.77 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ?
% 244.18/57.77 [v23: $i] : ? [v24: $i] : (op(v24, e4) = e4 & op(v23, e3) = e4 & op(v22, e2)
% 244.18/57.77 = e4 & op(v21, e1) = e4 & op(v20, e0) = e4 & op(v19, e4) = e3 & op(v18, e3)
% 244.18/57.77 = e3 & op(v17, e2) = e3 & op(v16, e1) = e3 & op(v15, e0) = e3 & op(v14, e4)
% 244.18/57.77 = e2 & op(v13, e3) = e2 & op(v12, e2) = e2 & op(v11, e1) = e2 & op(v10, e0)
% 244.18/57.77 = e2 & op(v9, e4) = e1 & op(v8, e3) = e1 & op(v7, e2) = e1 & op(v6, e1) = e1
% 244.18/57.77 & op(v5, e0) = e1 & op(v4, e4) = e0 & op(v3, e3) = e0 & op(v2, e2) = e0 &
% 244.18/57.77 op(v1, e1) = e0 & op(v0, e0) = e0 & op(e4, e4) = v24 & op(e4, e3) = v23 &
% 244.18/57.77 op(e4, e2) = v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 &
% 244.18/57.77 op(e3, e3) = v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 &
% 244.18/57.77 op(e2, e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 &
% 244.18/57.77 op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 &
% 244.18/57.77 op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 &
% 244.18/57.77 op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) &
% 244.18/57.77 $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 244.18/57.77 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 244.18/57.77 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.18/57.77
% 244.18/57.77 (ax60)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2,
% 244.18/57.77 v1) = v2 & op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax61)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax62)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax63)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax64)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax65)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax66)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2,
% 244.18/57.77 v1) = v2 & op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax67)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.77 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax68)
% 244.18/57.77 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.77 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e3,
% 244.18/57.77 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3,
% 244.18/57.77 e2) = v1 & $i(v1))))
% 244.18/57.77
% 244.18/57.77 (ax69)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e3,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax7)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e1,
% 244.18/57.78 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 244.18/57.78 e0) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax70)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e3,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax71)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e3,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax72)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e3,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax73)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax74)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e4,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax75)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e4,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax76)
% 244.18/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.18/57.78 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e4,
% 244.18/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 244.18/57.78 e2) = v1 & $i(v1))))
% 244.18/57.78
% 244.18/57.78 (ax77)
% 244.65/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.78 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e4,
% 244.65/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.65/57.78 e2) = v1 & $i(v1))))
% 244.65/57.78
% 244.65/57.78 (ax78)
% 244.65/57.78 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.78 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e4,
% 244.65/57.78 e2) = v1 & op(e2, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4,
% 244.65/57.78 e2) = v1 & $i(v1))))
% 244.65/57.78
% 244.65/57.78 (ax79)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax8)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e1,
% 244.65/57.79 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 244.65/57.79 e0) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax80)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax81)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax82)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax83)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax84)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3,
% 244.65/57.79 v1) = v2 & op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax85)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.65/57.79 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax86)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3,
% 244.65/57.79 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax87)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.65/57.79 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax88)
% 244.65/57.79 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.79 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3,
% 244.65/57.79 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1,
% 244.65/57.79 e3) = v1 & $i(v1))))
% 244.65/57.79
% 244.65/57.79 (ax89)
% 244.65/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.80 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3,
% 244.65/57.80 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 244.65/57.80 e3) = v1 & $i(v1))))
% 244.65/57.80
% 244.65/57.80 (ax9)
% 244.65/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.80 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e1,
% 244.65/57.80 e0) = v1 & op(e0, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1,
% 244.65/57.80 e0) = v1 & $i(v1))))
% 244.65/57.80
% 244.65/57.80 (ax90)
% 244.65/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.65/57.80 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3,
% 244.65/57.80 v1) = v2 & op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1,
% 244.65/57.80 e3) = v1 & $i(v1))))
% 244.65/57.80
% 244.65/57.80 (ax91)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax92)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax93)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax94)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax95)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax96)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3,
% 244.71/57.80 v1) = v2 & op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax97)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e4,
% 244.71/57.80 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax98)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e4,
% 244.71/57.80 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (ax99)
% 244.71/57.80 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ?
% 244.71/57.80 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e4,
% 244.71/57.80 e3) = v1 & op(e3, v1) = v2 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4,
% 244.71/57.80 e3) = v1 & $i(v1))))
% 244.71/57.80
% 244.71/57.80 (function-axioms)
% 244.71/57.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 244.71/57.81 v2) = v1) | ~ (op(v3, v2) = v0))
% 244.71/57.81
% 244.71/57.81 Those formulas are unsatisfiable:
% 244.71/57.81 ---------------------------------
% 244.71/57.81
% 244.71/57.81 Begin of proof
% 244.71/57.81 |
% 244.71/57.81 | ALPHA: (ax1) implies:
% 244.77/57.82 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 244.77/57.82 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 244.77/57.82 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 244.77/57.82 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 244.77/57.82 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 244.77/57.82 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 &
% 244.77/57.82 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) =
% 244.77/57.82 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2,
% 244.77/57.82 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11
% 244.77/57.82 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) =
% 244.77/57.82 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3)
% 244.77/57.82 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24)
% 244.77/57.82 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17)
% 244.77/57.82 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10)
% 244.77/57.82 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 244.77/57.82 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1
% 244.77/57.82 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 =
% 244.77/57.82 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21
% 244.77/57.82 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20
% 244.77/57.82 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19
% 244.77/57.82 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18
% 244.77/57.82 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17
% 244.77/57.82 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) &
% 244.77/57.82 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 |
% 244.77/57.82 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 |
% 244.77/57.82 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 |
% 244.77/57.82 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 |
% 244.77/57.82 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0)
% 244.77/57.82 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 =
% 244.77/57.82 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 |
% 244.77/57.82 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 =
% 244.77/57.82 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4
% 244.77/57.82 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3
% 244.77/57.82 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1
% 244.77/57.82 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) &
% 244.77/57.82 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 244.77/57.82 |
% 244.77/57.82 | ALPHA: (ax2) implies:
% 244.77/57.83 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 244.77/57.83 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 244.77/57.83 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 244.77/57.83 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 244.77/57.83 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 244.77/57.83 | [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, e3) =
% 244.77/57.83 | e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) = e4)
% 244.77/57.83 | | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) |
% 244.77/57.83 | (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12
% 244.77/57.83 | = e4 & op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 =
% 244.77/57.83 | e3 & op(e4, e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3
% 244.77/57.83 | & op(e4, e2) = e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 &
% 244.77/57.83 | op(e4, e0) = e3)) & ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 &
% 244.77/57.83 | op(e3, e4) = e3) | (v18 = e3 & op(e2, e4) = e3) | (v12 = e3 &
% 244.77/57.83 | op(e1, e4) = e3) | (v4 = e3 & op(e0, e4) = e3)) & ((v24 = e2 &
% 244.77/57.83 | op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) | (v20 = e2 &
% 244.77/57.83 | op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 &
% 244.77/57.83 | op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 &
% 244.77/57.83 | op(e3, e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 &
% 244.77/57.83 | op(e1, e4) = e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 &
% 244.77/57.83 | op(e4, e4) = e1) | (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 &
% 244.77/57.83 | op(e4, e2) = e1) | (v15 = e1 & op(e4, e1) = e1) | (v8 = e1 &
% 244.77/57.83 | op(e4, e0) = e1)) & ((v24 = e1 & op(e4, e4) = e1) | (v22 = e1 &
% 244.77/57.83 | op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) = e1) | (v12 = e1 &
% 244.77/57.83 | op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) & ((v24 = e0 &
% 244.77/57.83 | op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 &
% 244.77/57.83 | op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 &
% 244.77/57.83 | op(e4, e0) = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 &
% 244.77/57.83 | op(e3, e4) = e0) | (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 &
% 244.77/57.83 | op(e1, e4) = e0) | (v4 = e0 & op(e0, e4) = e0)) & ((v23 = e4 &
% 244.77/57.83 | op(e4, e3) = e4) | (v21 = e4 & op(e3, e3) = e4) | (v17 = e4 &
% 244.77/57.83 | op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) = e4) | (v3 = e4 &
% 244.77/57.83 | op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) | (v21 = e3 &
% 244.77/57.83 | op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 &
% 244.77/57.83 | op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 &
% 244.77/57.83 | op(e4, e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 &
% 244.77/57.83 | op(e2, e3) = e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 &
% 244.77/57.83 | op(e0, e3) = e2)) & ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 &
% 244.77/57.83 | op(e3, e3) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v11 = e1 &
% 244.77/57.83 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v23 = e0 &
% 244.77/57.83 | op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) | (v17 = e0 &
% 244.77/57.83 | op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 &
% 244.77/57.83 | op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 &
% 244.77/57.83 | op(e3, e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 &
% 244.77/57.83 | op(e3, e1) = e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 &
% 244.77/57.83 | op(e3, e4) = e3) | (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 &
% 244.77/57.83 | op(e3, e2) = e3) | (v14 = e3 & op(e3, e1) = e3) | (v7 = e3 &
% 244.77/57.83 | op(e3, e0) = e3)) & ((v22 = e2 & op(e3, e4) = e2) | (v21 = e2 &
% 244.77/57.83 | op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v14 = e2 &
% 244.77/57.83 | op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) & ((v22 = e1 &
% 244.77/57.83 | op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 &
% 244.77/57.83 | op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 &
% 244.77/57.83 | op(e3, e0) = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 &
% 244.77/57.83 | op(e3, e3) = e0) | (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 &
% 244.77/57.83 | op(e3, e1) = e0) | (v7 = e0 & op(e3, e0) = e0)) & ((v20 = e4 &
% 244.77/57.83 | op(e4, e2) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v16 = e4 &
% 244.77/57.83 | op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) = e4) | (v2 = e4 &
% 244.77/57.83 | op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) | (v19 = e3 &
% 244.77/57.83 | op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 244.77/57.83 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 &
% 244.77/57.83 | op(e4, e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 &
% 244.77/57.83 | op(e2, e2) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 &
% 244.77/57.83 | op(e0, e2) = e2)) & ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 &
% 244.77/57.83 | op(e3, e2) = e1) | (v16 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 244.77/57.83 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v20 = e0 &
% 244.77/57.83 | op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) | (v16 = e0 &
% 244.77/57.83 | op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 244.77/57.83 | op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 &
% 244.77/57.83 | op(e2, e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 &
% 244.77/57.83 | op(e2, e1) = e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 &
% 244.77/57.83 | op(e2, e4) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 &
% 244.77/57.83 | op(e2, e2) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v6 = e3 &
% 244.77/57.83 | op(e2, e0) = e3)) & ((v18 = e2 & op(e2, e4) = e2) | (v17 = e2 &
% 244.77/57.83 | op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) = e2) | (v13 = e2 &
% 244.77/57.83 | op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) & ((v18 = e1 &
% 244.77/57.83 | op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 &
% 244.77/57.83 | op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 &
% 244.77/57.83 | op(e2, e0) = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 &
% 244.77/57.83 | op(e2, e3) = e0) | (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 &
% 244.77/57.83 | op(e2, e1) = e0) | (v6 = e0 & op(e2, e0) = e0)) & ((v15 = e4 &
% 244.77/57.83 | op(e4, e1) = e4) | (v14 = e4 & op(e3, e1) = e4) | (v13 = e4 &
% 244.77/57.83 | op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v1 = e4 &
% 244.77/57.83 | op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3 &
% 244.77/57.83 | op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 &
% 244.77/57.83 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 &
% 244.77/57.83 | op(e4, e1) = e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 &
% 244.77/57.83 | op(e2, e1) = e2) | (v9 = e2 & op(e1, e1) = e2) | (v1 = e2 &
% 244.77/57.83 | op(e0, e1) = e2)) & ((v15 = e1 & op(e4, e1) = e1) | (v14 = e1 &
% 244.77/57.83 | op(e3, e1) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v9 = e1 &
% 244.77/57.83 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v15 = e0 &
% 244.77/57.83 | op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 &
% 244.77/57.83 | op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 &
% 244.77/57.83 | op(e0, e1) = e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 &
% 244.77/57.83 | op(e1, e3) = e4) | (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 &
% 244.77/57.83 | op(e1, e1) = e4) | (v5 = e4 & op(e1, e0) = e4)) & ((v12 = e3 &
% 244.77/57.83 | op(e1, e4) = e3) | (v11 = e3 & op(e1, e3) = e3) | (v10 = e3 &
% 244.77/57.83 | op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3) | (v5 = e3 &
% 244.77/57.83 | op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2 &
% 244.77/57.83 | op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 &
% 244.77/57.83 | op(e1, e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 &
% 244.77/57.83 | op(e1, e4) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 &
% 244.77/57.83 | op(e1, e2) = e1) | (v9 = e1 & op(e1, e1) = e1) | (v5 = e1 &
% 244.77/57.83 | op(e1, e0) = e1)) & ((v12 = e0 & op(e1, e4) = e0) | (v11 = e0 &
% 244.77/57.83 | op(e1, e3) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v9 = e0 &
% 244.77/57.83 | op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) & ((v8 = e4 &
% 244.77/57.83 | op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 &
% 244.77/57.83 | op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 &
% 244.77/57.83 | op(e0, e0) = e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 &
% 244.77/57.83 | op(e3, e0) = e3) | (v6 = e3 & op(e2, e0) = e3) | (v5 = e3 &
% 244.77/57.83 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v8 = e2 &
% 244.77/57.83 | op(e4, e0) = e2) | (v7 = e2 & op(e3, e0) = e2) | (v6 = e2 &
% 244.77/57.83 | op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0 = e2 &
% 244.77/57.83 | op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 &
% 244.77/57.83 | op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 &
% 244.77/57.83 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 &
% 244.77/57.83 | op(e0, e4) = e4) | (v3 = e4 & op(e0, e3) = e4) | (v2 = e4 &
% 244.77/57.83 | op(e0, e2) = e4) | (v1 = e4 & op(e0, e1) = e4) | (v0 = e4 &
% 244.77/57.83 | op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4) = e3) | (v3 = e3 &
% 244.77/57.83 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 244.77/57.83 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 &
% 244.77/57.83 | op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 &
% 244.77/57.83 | op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 &
% 244.77/57.83 | op(e0, e0) = e2)) & ((v4 = e1 & op(e0, e4) = e1) | (v3 = e1 &
% 244.77/57.83 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 244.77/57.83 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 244.77/57.83 | op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) | (v7 = e0 &
% 244.77/57.83 | op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 &
% 244.77/57.83 | op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 &
% 244.77/57.83 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 244.77/57.83 | op(e0, e1) = e0)))))
% 244.77/57.83 |
% 244.77/57.83 | ALPHA: (ax3) implies:
% 244.77/57.84 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 244.77/57.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 244.77/57.84 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 244.77/57.84 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 244.77/57.84 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 244.77/57.84 | [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22, v23) = e3
% 244.77/57.84 | & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 & op(v18,
% 244.77/57.84 | v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) =
% 244.77/57.84 | e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 &
% 244.77/57.84 | op(v11, v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7)
% 244.77/57.84 | = e4 & op(v7, v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4,
% 244.77/57.84 | v3) = e2 & op(v3, v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 &
% 244.77/57.84 | op(v0, v0) = e0 & op(e4, e4) = v24 & op(e4, e3) = v22 & op(e4, e2) =
% 244.77/57.84 | v19 & op(e4, e1) = v14 & op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3,
% 244.77/57.84 | e3) = v21 & op(e3, e2) = v17 & op(e3, e1) = v12 & op(e3, e0) = v5 &
% 244.77/57.84 | op(e2, e4) = v20 & op(e2, e3) = v18 & op(e2, e2) = v16 & op(e2, e1) =
% 244.77/57.84 | v10 & op(e2, e0) = v3 & op(e1, e4) = v15 & op(e1, e3) = v13 & op(e1,
% 244.77/57.84 | e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 & op(e0, e4) = v8 &
% 244.77/57.84 | op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0
% 244.77/57.84 | & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18)
% 244.77/57.84 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11)
% 244.77/57.84 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 244.77/57.84 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.77/57.84 |
% 244.77/57.84 | ALPHA: (ax4) implies:
% 244.77/57.84 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 244.77/57.84 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 244.77/57.84 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 244.77/57.84 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 244.77/57.84 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ?
% 244.77/57.84 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24
% 244.77/57.84 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24
% 244.77/57.84 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23
% 244.77/57.84 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 =
% 244.77/57.84 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 =
% 244.77/57.84 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 =
% 244.77/57.84 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 =
% 244.77/57.84 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 =
% 244.77/57.84 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 =
% 244.77/57.84 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 =
% 244.77/57.84 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 =
% 244.77/57.84 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 =
% 244.77/57.84 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 =
% 244.77/57.84 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 =
% 244.77/57.84 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 =
% 244.77/57.84 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 =
% 244.77/57.84 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 =
% 244.77/57.84 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 =
% 244.77/57.84 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8)
% 244.77/57.84 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8
% 244.77/57.84 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) &
% 244.77/57.84 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 =
% 244.77/57.84 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) &
% 244.77/57.84 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 244.77/57.84 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4,
% 244.77/57.84 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 &
% 244.77/57.84 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) =
% 244.77/57.84 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2,
% 244.77/57.84 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 &
% 244.77/57.84 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) =
% 244.77/57.84 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0,
% 244.77/57.84 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 244.77/57.84 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) &
% 244.77/57.84 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 244.77/57.84 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.77/57.84 |
% 244.77/57.84 | ALPHA: (ax5) implies:
% 244.77/57.84 | (5) ~ (e1 = e0)
% 244.77/57.84 | (6) ~ (e2 = e0)
% 244.77/57.84 | (7) ~ (e2 = e1)
% 244.77/57.84 | (8) ~ (e3 = e0)
% 244.77/57.84 | (9) ~ (e3 = e1)
% 244.77/57.84 | (10) ~ (e3 = e2)
% 244.77/57.84 | (11) ~ (e4 = e0)
% 244.77/57.84 | (12) ~ (e4 = e1)
% 244.77/57.84 | (13) ~ (e4 = e2)
% 244.77/57.84 | (14) ~ (e4 = e3)
% 244.77/57.84 |
% 244.77/57.84 | ALPHA: (ax6) implies:
% 244.77/57.85 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 244.77/57.85 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 244.77/57.85 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 244.77/57.85 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 244.77/57.85 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i]
% 244.77/57.85 | : ? [v24: $i] : (op(v24, e4) = e4 & op(v23, e3) = e4 & op(v22, e2) =
% 244.77/57.85 | e4 & op(v21, e1) = e4 & op(v20, e0) = e4 & op(v19, e4) = e3 &
% 244.77/57.85 | op(v18, e3) = e3 & op(v17, e2) = e3 & op(v16, e1) = e3 & op(v15, e0)
% 244.77/57.85 | = e3 & op(v14, e4) = e2 & op(v13, e3) = e2 & op(v12, e2) = e2 &
% 244.77/57.85 | op(v11, e1) = e2 & op(v10, e0) = e2 & op(v9, e4) = e1 & op(v8, e3) =
% 244.77/57.85 | e1 & op(v7, e2) = e1 & op(v6, e1) = e1 & op(v5, e0) = e1 & op(v4,
% 244.77/57.85 | e4) = e0 & op(v3, e3) = e0 & op(v2, e2) = e0 & op(v1, e1) = e0 &
% 244.77/57.85 | op(v0, e0) = e0 & op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) =
% 244.77/57.85 | v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 &
% 244.77/57.85 | op(e3, e3) = v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0)
% 244.77/57.85 | = v15 & op(e2, e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 244.77/57.85 | op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) =
% 244.77/57.85 | v8 & op(e1, e2) = v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0,
% 244.77/57.85 | e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 &
% 244.77/57.85 | op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 244.77/57.85 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13)
% 244.77/57.85 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 244.77/57.85 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax7) implies:
% 244.77/57.85 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax8) implies:
% 244.77/57.85 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax9) implies:
% 244.77/57.85 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax10) implies:
% 244.77/57.85 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax11) implies:
% 244.77/57.85 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax12) implies:
% 244.77/57.85 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e1, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax13) implies:
% 244.77/57.85 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax14) implies:
% 244.77/57.85 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax15) implies:
% 244.77/57.85 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax16) implies:
% 244.77/57.85 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.85 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.85 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.85 |
% 244.77/57.85 | ALPHA: (ax17) implies:
% 244.77/57.86 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax18) implies:
% 244.77/57.86 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e2, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax19) implies:
% 244.77/57.86 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax20) implies:
% 244.77/57.86 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax21) implies:
% 244.77/57.86 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e4) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax22) implies:
% 244.77/57.86 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax23) implies:
% 244.77/57.86 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax24) implies:
% 244.77/57.86 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e3, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax25) implies:
% 244.77/57.86 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax26) implies:
% 244.77/57.86 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax27) implies:
% 244.77/57.86 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax28) implies:
% 244.77/57.86 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax29) implies:
% 244.77/57.86 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax30) implies:
% 244.77/57.86 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e4, e0) = v1 & op(e0, v1) = v2 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e0) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax31) implies:
% 244.77/57.86 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax32) implies:
% 244.77/57.86 | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.86 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.86 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.86 |
% 244.77/57.86 | ALPHA: (ax33) implies:
% 244.77/57.87 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax34) implies:
% 244.77/57.87 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax35) implies:
% 244.77/57.87 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax36) implies:
% 244.77/57.87 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, v1) = v2 & op(e0, e1) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax37) implies:
% 244.77/57.87 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax38) implies:
% 244.77/57.87 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax39) implies:
% 244.77/57.87 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax40) implies:
% 244.77/57.87 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax41) implies:
% 244.77/57.87 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax42) implies:
% 244.77/57.87 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e2, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax43) implies:
% 244.77/57.87 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax44) implies:
% 244.77/57.87 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax45) implies:
% 244.77/57.87 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e4) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax46) implies:
% 244.77/57.87 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax47) implies:
% 244.77/57.87 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax48) implies:
% 244.77/57.87 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e3, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax49) implies:
% 244.77/57.87 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax50) implies:
% 244.77/57.87 | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax51) implies:
% 244.77/57.87 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax52) implies:
% 244.77/57.87 | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax53) implies:
% 244.77/57.87 | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax54) implies:
% 244.77/57.87 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e4, e1) = v1 & op(e1, v1) = v2 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e1) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax55) implies:
% 244.77/57.87 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax56) implies:
% 244.77/57.87 | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.87 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.87 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.87 |
% 244.77/57.87 | ALPHA: (ax57) implies:
% 244.77/57.88 | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax58) implies:
% 244.77/57.88 | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax59) implies:
% 244.77/57.88 | (68) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax60) implies:
% 244.77/57.88 | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, v1) = v2 & op(e0, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax61) implies:
% 244.77/57.88 | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax62) implies:
% 244.77/57.88 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax63) implies:
% 244.77/57.88 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax64) implies:
% 244.77/57.88 | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax65) implies:
% 244.77/57.88 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax66) implies:
% 244.77/57.88 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, v1) = v2 & op(e1, e2) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax67) implies:
% 244.77/57.88 | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax68) implies:
% 244.77/57.88 | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax69) implies:
% 244.77/57.88 | (78) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e4) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax70) implies:
% 244.77/57.88 | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax71) implies:
% 244.77/57.88 | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax72) implies:
% 244.77/57.88 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e3, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e3, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax73) implies:
% 244.77/57.88 | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax74) implies:
% 244.77/57.88 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax75) implies:
% 244.77/57.88 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax76) implies:
% 244.77/57.88 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax77) implies:
% 244.77/57.88 | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax78) implies:
% 244.77/57.88 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e4, e2) = v1 & op(e2, v1) = v2 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e4, e2) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax79) implies:
% 244.77/57.88 | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax80) implies:
% 244.77/57.88 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax81) implies:
% 244.77/57.88 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.88 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.88 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.88 |
% 244.77/57.88 | ALPHA: (ax82) implies:
% 244.77/57.89 | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax83) implies:
% 244.77/57.89 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax84) implies:
% 244.77/57.89 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, v1) = v2 & op(e0, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e0, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax85) implies:
% 244.77/57.89 | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax86) implies:
% 244.77/57.89 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax87) implies:
% 244.77/57.89 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax88) implies:
% 244.77/57.89 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax89) implies:
% 244.77/57.89 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax90) implies:
% 244.77/57.89 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, v1) = v2 & op(e1, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e1, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax91) implies:
% 244.77/57.89 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax92) implies:
% 244.77/57.89 | (101) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax93) implies:
% 244.77/57.89 | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e4) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax94) implies:
% 244.77/57.89 | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax95) implies:
% 244.77/57.89 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax96) implies:
% 244.77/57.89 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, v1) = v2 & op(e2, e3) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e4) & op(e2, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax97) implies:
% 244.77/57.89 | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax98) implies:
% 244.77/57.89 | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax99) implies:
% 244.77/57.89 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax100) implies:
% 244.77/57.89 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax101) implies:
% 244.77/57.89 | (110) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax102) implies:
% 244.77/57.89 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e4, e3) = v1 & op(e3, v1) = v2 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e4, e3) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax103) implies:
% 244.77/57.89 | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax104) implies:
% 244.77/57.89 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax105) implies:
% 244.77/57.89 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax106) implies:
% 244.77/57.89 | (115) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax107) implies:
% 244.77/57.89 | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax108) implies:
% 244.77/57.89 | (117) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) &
% 244.77/57.89 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e0, e4) = v1 &
% 244.77/57.89 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e4) = v1 & $i(v1))))
% 244.77/57.89 |
% 244.77/57.89 | ALPHA: (ax109) implies:
% 244.77/57.90 | (118) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax110) implies:
% 244.77/57.90 | (119) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax111) implies:
% 244.77/57.90 | (120) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax112) implies:
% 244.77/57.90 | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax113) implies:
% 244.77/57.90 | (122) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax114) implies:
% 244.77/57.90 | (123) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e1, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax115) implies:
% 244.77/57.90 | (124) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax116) implies:
% 244.77/57.90 | (125) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax117) implies:
% 244.77/57.90 | (126) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e3) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax118) implies:
% 244.77/57.90 | (127) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax119) implies:
% 244.77/57.90 | (128) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax120) implies:
% 244.77/57.90 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e2, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax121) implies:
% 244.77/57.90 | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax122) implies:
% 244.77/57.90 | (131) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax123) implies:
% 244.77/57.90 | (132) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e2) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax124) implies:
% 244.77/57.90 | (133) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax125) implies:
% 244.77/57.90 | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e1) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (ax126) implies:
% 244.77/57.90 | (135) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) &
% 244.77/57.90 | ( ~ (v0 = e4) | ( ~ (v2 = e0) & op(e4, v1) = v2 & op(e3, e4) = v1 &
% 244.77/57.90 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e4) = v1 & $i(v1))))
% 244.77/57.90 |
% 244.77/57.90 | DELTA: instantiating (129) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 244.77/57.90 | (136) op(e1, e2) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e4) | ( ~
% 244.77/57.90 | (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2, e4) = all_4_1
% 244.77/57.90 | & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e2, e4) =
% 244.77/57.90 | all_4_1 & $i(all_4_1)))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (136) implies:
% 244.77/57.90 | (137) op(e1, e2) = all_4_2
% 244.77/57.90 | (138) ~ (all_4_2 = e4) | ( ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 &
% 244.77/57.90 | op(e2, e4) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 244.77/57.90 | e3) & op(e2, e4) = all_4_1 & $i(all_4_1))
% 244.77/57.90 |
% 244.77/57.90 | DELTA: instantiating (49) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 244.77/57.90 | (139) op(e4, e2) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e1) | ( ~
% 244.77/57.90 | (all_6_0 = e0) & op(e2, e1) = all_6_1 & op(e1, all_6_1) = all_6_0
% 244.77/57.90 | & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e3) & op(e2, e1) =
% 244.77/57.90 | all_6_1 & $i(all_6_1)))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (139) implies:
% 244.77/57.90 | (140) op(e4, e2) = all_6_2
% 244.77/57.90 | (141) ~ (all_6_2 = e1) | ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_1 &
% 244.77/57.90 | op(e1, all_6_1) = all_6_0 & $i(all_6_0) & $i(all_6_1)) | ( ~
% 244.77/57.90 | (all_6_1 = e3) & op(e2, e1) = all_6_1 & $i(all_6_1))
% 244.77/57.90 |
% 244.77/57.90 | DELTA: instantiating (51) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 244.77/57.90 | (142) op(e3, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | ( ~
% 244.77/57.90 | (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0
% 244.77/57.90 | & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 244.77/57.90 | all_8_1 & $i(all_8_1)))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (142) implies:
% 244.77/57.90 | (143) op(e3, e2) = all_8_2
% 244.77/57.90 | (144) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 &
% 244.77/57.90 | op(e1, all_8_1) = all_8_0 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 244.77/57.90 | (all_8_1 = e4) & op(e2, e1) = all_8_1 & $i(all_8_1))
% 244.77/57.90 |
% 244.77/57.90 | DELTA: instantiating (131) with fresh symbols all_10_0, all_10_1, all_10_2
% 244.77/57.90 | gives:
% 244.77/57.90 | (145) op(e2, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e4) | ( ~
% 244.77/57.90 | (all_10_0 = e1) & op(e4, all_10_1) = all_10_0 & op(e3, e4) =
% 244.77/57.90 | all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) &
% 244.77/57.90 | op(e3, e4) = all_10_1 & $i(all_10_1)))
% 244.77/57.90 |
% 244.77/57.90 | ALPHA: (145) implies:
% 244.77/57.90 | (146) op(e2, e3) = all_10_2
% 244.77/57.91 | (147) ~ (all_10_2 = e4) | ( ~ (all_10_0 = e1) & op(e4, all_10_1) =
% 244.77/57.91 | all_10_0 & op(e3, e4) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | (
% 244.77/57.91 | ~ (all_10_1 = e0) & op(e3, e4) = all_10_1 & $i(all_10_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (84) with fresh symbols all_12_0, all_12_1, all_12_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (148) op(e0, e4) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e2) | ( ~
% 244.77/57.91 | (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2, all_12_1) =
% 244.77/57.91 | all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) &
% 244.77/57.91 | op(e4, e2) = all_12_1 & $i(all_12_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (148) implies:
% 244.77/57.91 | (149) op(e0, e4) = all_12_2
% 244.77/57.91 | (150) ~ (all_12_2 = e2) | ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 &
% 244.77/57.91 | op(e2, all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 244.77/57.91 | (all_12_1 = e1) & op(e4, e2) = all_12_1 & $i(all_12_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (86) with fresh symbols all_14_0, all_14_1, all_14_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (151) op(e0, e4) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e2) | ( ~
% 244.77/57.91 | (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2, all_14_1) =
% 244.77/57.91 | all_14_0 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) &
% 244.77/57.91 | op(e4, e2) = all_14_1 & $i(all_14_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (151) implies:
% 244.77/57.91 | (152) op(e0, e4) = all_14_2
% 244.77/57.91 | (153) ~ (all_14_2 = e2) | ( ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 &
% 244.77/57.91 | op(e2, all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 244.77/57.91 | (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (82) with fresh symbols all_16_0, all_16_1, all_16_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (154) op(e1, e4) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | ( ~
% 244.77/57.91 | (all_16_0 = e3) & op(e4, e2) = all_16_1 & op(e2, all_16_1) =
% 244.77/57.91 | all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e0) &
% 244.77/57.91 | op(e4, e2) = all_16_1 & $i(all_16_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (154) implies:
% 244.77/57.91 | (155) op(e1, e4) = all_16_2
% 244.77/57.91 | (156) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 &
% 244.77/57.91 | op(e2, all_16_1) = all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 244.77/57.91 | (all_16_1 = e0) & op(e4, e2) = all_16_1 & $i(all_16_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (108) with fresh symbols all_18_0, all_18_1, all_18_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (157) op(e0, e4) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e3) | ( ~
% 244.77/57.91 | (all_18_0 = e2) & op(e4, e3) = all_18_1 & op(e3, all_18_1) =
% 244.77/57.91 | all_18_0 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) &
% 244.77/57.91 | op(e4, e3) = all_18_1 & $i(all_18_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (157) implies:
% 244.77/57.91 | (158) op(e0, e4) = all_18_2
% 244.77/57.91 | (159) ~ (all_18_2 = e3) | ( ~ (all_18_0 = e2) & op(e4, e3) = all_18_1 &
% 244.77/57.91 | op(e3, all_18_1) = all_18_0 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 244.77/57.91 | (all_18_1 = e1) & op(e4, e3) = all_18_1 & $i(all_18_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (120) with fresh symbols all_20_0, all_20_1, all_20_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (160) op(e0, e1) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e4) | ( ~
% 244.77/57.91 | (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4) =
% 244.77/57.91 | all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e2) &
% 244.77/57.91 | op(e1, e4) = all_20_1 & $i(all_20_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (160) implies:
% 244.77/57.91 | (161) op(e0, e1) = all_20_2
% 244.77/57.91 | (162) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) =
% 244.77/57.91 | all_20_0 & op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | (
% 244.77/57.91 | ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (56) with fresh symbols all_22_0, all_22_1, all_22_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (163) op(e0, e3) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e1) | ( ~
% 244.77/57.91 | (all_22_0 = e2) & op(e3, e1) = all_22_1 & op(e1, all_22_1) =
% 244.77/57.91 | all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e4) &
% 244.77/57.91 | op(e3, e1) = all_22_1 & $i(all_22_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (163) implies:
% 244.77/57.91 | (164) op(e0, e3) = all_22_2
% 244.77/57.91 | (165) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 244.77/57.91 | op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 244.77/57.91 | (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (106) with fresh symbols all_24_0, all_24_1, all_24_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (166) op(e1, e4) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e3) | ( ~
% 244.77/57.91 | (all_24_0 = e2) & op(e4, e3) = all_24_1 & op(e3, all_24_1) =
% 244.77/57.91 | all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e0) &
% 244.77/57.91 | op(e4, e3) = all_24_1 & $i(all_24_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (166) implies:
% 244.77/57.91 | (167) op(e1, e4) = all_24_2
% 244.77/57.91 | (168) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 244.77/57.91 | op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 244.77/57.91 | (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (97) with fresh symbols all_26_0, all_26_1, all_26_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (169) op(e4, e1) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e3) | ( ~
% 244.77/57.91 | (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 & op(e1, e3) =
% 244.77/57.91 | all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e2) &
% 244.77/57.91 | op(e1, e3) = all_26_1 & $i(all_26_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (169) implies:
% 244.77/57.91 | (170) op(e4, e1) = all_26_2
% 244.77/57.91 | (171) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) =
% 244.77/57.91 | all_26_0 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | (
% 244.77/57.91 | ~ (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (104) with fresh symbols all_28_0, all_28_1, all_28_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (172) op(e0, e2) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | ( ~
% 244.77/57.91 | (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 244.77/57.91 | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) &
% 244.77/57.91 | op(e2, e3) = all_28_1 & $i(all_28_1)))
% 244.77/57.91 |
% 244.77/57.91 | ALPHA: (172) implies:
% 244.77/57.91 | (173) op(e0, e2) = all_28_2
% 244.77/57.91 | (174) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) =
% 244.77/57.91 | all_28_0 & op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | (
% 244.77/57.91 | ~ (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 244.77/57.91 |
% 244.77/57.91 | DELTA: instantiating (65) with fresh symbols all_30_0, all_30_1, all_30_2
% 244.77/57.91 | gives:
% 244.77/57.91 | (175) op(e4, e0) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e2) | ( ~
% 244.77/57.91 | (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 & op(e0, e2) =
% 244.77/57.91 | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e1) &
% 244.77/57.91 | op(e0, e2) = all_30_1 & $i(all_30_1)))
% 244.77/57.91 |
% 245.19/57.91 | ALPHA: (175) implies:
% 245.19/57.91 | (176) op(e4, e0) = all_30_2
% 245.19/57.91 | (177) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) =
% 245.19/57.91 | all_30_0 & op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | (
% 245.19/57.91 | ~ (all_30_1 = e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 245.19/57.91 |
% 245.19/57.91 | DELTA: instantiating (72) with fresh symbols all_32_0, all_32_1, all_32_2
% 245.19/57.91 | gives:
% 245.19/57.91 | (178) op(e0, e1) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | ( ~
% 245.19/57.91 | (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) =
% 245.19/57.91 | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 245.19/57.91 | op(e1, e2) = all_32_1 & $i(all_32_1)))
% 245.19/57.91 |
% 245.19/57.91 | ALPHA: (178) implies:
% 245.19/57.91 | (179) op(e0, e1) = all_32_2
% 245.19/57.91 | (180) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) =
% 245.19/57.91 | all_32_0 & op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | (
% 245.19/57.91 | ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 245.19/57.91 |
% 245.19/57.91 | DELTA: instantiating (66) with fresh symbols all_34_0, all_34_1, all_34_2
% 245.19/57.91 | gives:
% 245.19/57.91 | (181) op(e1, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e2) | ( ~
% 245.19/57.91 | (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) =
% 245.19/57.91 | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e3) &
% 245.19/57.91 | op(e0, e2) = all_34_1 & $i(all_34_1)))
% 245.19/57.91 |
% 245.19/57.91 | ALPHA: (181) implies:
% 245.19/57.91 | (182) op(e1, e0) = all_34_2
% 245.19/57.91 | (183) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) =
% 245.19/57.91 | all_34_0 & op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | (
% 245.19/57.91 | ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 245.19/57.91 |
% 245.19/57.91 | DELTA: instantiating (121) with fresh symbols all_36_0, all_36_1, all_36_2
% 245.19/57.91 | gives:
% 245.19/57.91 | (184) op(e3, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e4) | ( ~
% 245.19/57.91 | (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 & op(e1, e4) =
% 245.19/57.91 | all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) &
% 245.19/57.91 | op(e1, e4) = all_36_1 & $i(all_36_1)))
% 245.19/57.91 |
% 245.19/57.91 | ALPHA: (184) implies:
% 245.19/57.91 | (185) op(e3, e1) = all_36_2
% 245.19/57.91 | (186) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) =
% 245.19/57.91 | all_36_0 & op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | (
% 245.19/57.91 | ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 245.19/57.91 |
% 245.19/57.91 | DELTA: instantiating (123) with fresh symbols all_38_0, all_38_1, all_38_2
% 245.19/57.91 | gives:
% 245.19/57.91 | (187) op(e2, e1) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e4) | ( ~
% 245.19/57.91 | (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1, e4) =
% 245.19/57.91 | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 245.19/57.91 | op(e1, e4) = all_38_1 & $i(all_38_1)))
% 245.19/57.91 |
% 245.19/57.91 | ALPHA: (187) implies:
% 245.19/57.91 | (188) op(e2, e1) = all_38_2
% 245.19/57.91 | (189) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) =
% 245.19/57.91 | all_38_0 & op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | (
% 245.19/57.91 | ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 245.19/57.91 |
% 245.19/57.91 | DELTA: instantiating (117) with fresh symbols all_40_0, all_40_1, all_40_2
% 245.19/57.91 | gives:
% 245.19/57.91 | (190) op(e2, e0) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e4) | ( ~
% 245.19/57.91 | (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 245.19/57.91 | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 245.19/57.91 | op(e0, e4) = all_40_1 & $i(all_40_1)))
% 245.19/57.91 |
% 245.19/57.91 | ALPHA: (190) implies:
% 245.19/57.91 | (191) op(e2, e0) = all_40_2
% 245.19/57.92 | (192) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) =
% 245.19/57.92 | all_40_0 & op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | (
% 245.19/57.92 | ~ (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (110) with fresh symbols all_42_0, all_42_1, all_42_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (193) op(e0, e4) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e3) | ( ~
% 245.19/57.92 | (all_42_0 = e1) & op(e4, e3) = all_42_1 & op(e3, all_42_1) =
% 245.19/57.92 | all_42_0 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) &
% 245.19/57.92 | op(e4, e3) = all_42_1 & $i(all_42_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (193) implies:
% 245.19/57.92 | (194) op(e0, e4) = all_42_2
% 245.19/57.92 | (195) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(e4, e3) = all_42_1 &
% 245.19/57.92 | op(e3, all_42_1) = all_42_0 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 245.19/57.92 | (all_42_1 = e2) & op(e4, e3) = all_42_1 & $i(all_42_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (73) with fresh symbols all_44_0, all_44_1, all_44_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (196) op(e4, e1) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e2) | ( ~
% 245.19/57.92 | (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 & op(e1, e2) =
% 245.19/57.92 | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e3) &
% 245.19/57.92 | op(e1, e2) = all_44_1 & $i(all_44_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (196) implies:
% 245.19/57.92 | (197) op(e4, e1) = all_44_2
% 245.19/57.92 | (198) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) =
% 245.19/57.92 | all_44_0 & op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | (
% 245.19/57.92 | ~ (all_44_1 = e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (75) with fresh symbols all_46_0, all_46_1, all_46_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (199) op(e3, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e2) | ( ~
% 245.19/57.92 | (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 245.19/57.92 | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 245.19/57.92 | op(e1, e2) = all_46_1 & $i(all_46_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (199) implies:
% 245.19/57.92 | (200) op(e3, e1) = all_46_2
% 245.19/57.92 | (201) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) =
% 245.19/57.92 | all_46_0 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | (
% 245.19/57.92 | ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (45) with fresh symbols all_48_0, all_48_1, all_48_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (202) op(e3, e0) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e1) | ( ~
% 245.19/57.92 | (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 & op(e0, e1) =
% 245.19/57.92 | all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e4) &
% 245.19/57.92 | op(e0, e1) = all_48_1 & $i(all_48_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (202) implies:
% 245.19/57.92 | (203) op(e3, e0) = all_48_2
% 245.19/57.92 | (204) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) =
% 245.19/57.92 | all_48_0 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 245.19/57.92 | ~ (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (105) with fresh symbols all_50_0, all_50_1, all_50_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (205) op(e1, e2) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e3) | ( ~
% 245.19/57.92 | (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 & op(e2, e3) =
% 245.19/57.92 | all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e4) &
% 245.19/57.92 | op(e2, e3) = all_50_1 & $i(all_50_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (205) implies:
% 245.19/57.92 | (206) op(e1, e2) = all_50_2
% 245.19/57.92 | (207) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) =
% 245.19/57.92 | all_50_0 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 245.19/57.92 | ~ (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (119) with fresh symbols all_52_0, all_52_1, all_52_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (208) op(e3, e1) = all_52_2 & $i(all_52_2) & ( ~ (all_52_2 = e4) | ( ~
% 245.19/57.92 | (all_52_0 = e2) & op(e4, all_52_1) = all_52_0 & op(e1, e4) =
% 245.19/57.92 | all_52_1 & $i(all_52_0) & $i(all_52_1)) | ( ~ (all_52_1 = e0) &
% 245.19/57.92 | op(e1, e4) = all_52_1 & $i(all_52_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (208) implies:
% 245.19/57.92 | (209) op(e3, e1) = all_52_2
% 245.19/57.92 | (210) ~ (all_52_2 = e4) | ( ~ (all_52_0 = e2) & op(e4, all_52_1) =
% 245.19/57.92 | all_52_0 & op(e1, e4) = all_52_1 & $i(all_52_0) & $i(all_52_1)) | (
% 245.19/57.92 | ~ (all_52_1 = e0) & op(e1, e4) = all_52_1 & $i(all_52_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (67) with fresh symbols all_54_0, all_54_1, all_54_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (211) op(e4, e0) = all_54_2 & $i(all_54_2) & ( ~ (all_54_2 = e2) | ( ~
% 245.19/57.92 | (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0, e2) =
% 245.19/57.92 | all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 = e3) &
% 245.19/57.92 | op(e0, e2) = all_54_1 & $i(all_54_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (211) implies:
% 245.19/57.92 | (212) op(e4, e0) = all_54_2
% 245.19/57.92 | (213) ~ (all_54_2 = e2) | ( ~ (all_54_0 = e1) & op(e2, all_54_1) =
% 245.19/57.92 | all_54_0 & op(e0, e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)) | (
% 245.19/57.92 | ~ (all_54_1 = e3) & op(e0, e2) = all_54_1 & $i(all_54_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (22) with fresh symbols all_56_0, all_56_1, all_56_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (214) op(e3, e2) = all_56_2 & $i(all_56_2) & ( ~ (all_56_2 = e0) | ( ~
% 245.19/57.92 | (all_56_0 = e4) & op(e2, e0) = all_56_1 & op(e0, all_56_1) =
% 245.19/57.92 | all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~ (all_56_1 = e1) &
% 245.19/57.92 | op(e2, e0) = all_56_1 & $i(all_56_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (214) implies:
% 245.19/57.92 | (215) op(e3, e2) = all_56_2
% 245.19/57.92 | (216) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 245.19/57.92 | op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 245.19/57.92 | (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (98) with fresh symbols all_58_0, all_58_1, all_58_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (217) op(e0, e1) = all_58_2 & $i(all_58_2) & ( ~ (all_58_2 = e3) | ( ~
% 245.19/57.92 | (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 & op(e1, e3) =
% 245.19/57.92 | all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 = e4) &
% 245.19/57.92 | op(e1, e3) = all_58_1 & $i(all_58_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (217) implies:
% 245.19/57.92 | (218) op(e0, e1) = all_58_2
% 245.19/57.92 | (219) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) =
% 245.19/57.92 | all_58_0 & op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | (
% 245.19/57.92 | ~ (all_58_1 = e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (122) with fresh symbols all_60_0, all_60_1, all_60_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (220) op(e0, e1) = all_60_2 & $i(all_60_2) & ( ~ (all_60_2 = e4) | ( ~
% 245.19/57.92 | (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 245.19/57.92 | all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 = e3) &
% 245.19/57.92 | op(e1, e4) = all_60_1 & $i(all_60_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (220) implies:
% 245.19/57.92 | (221) op(e0, e1) = all_60_2
% 245.19/57.92 | (222) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) =
% 245.19/57.92 | all_60_0 & op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | (
% 245.19/57.92 | ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (130) with fresh symbols all_62_0, all_62_1, all_62_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (223) op(e1, e3) = all_62_2 & $i(all_62_2) & ( ~ (all_62_2 = e4) | ( ~
% 245.19/57.92 | (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 & op(e3, e4) =
% 245.19/57.92 | all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 = e0) &
% 245.19/57.92 | op(e3, e4) = all_62_1 & $i(all_62_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (223) implies:
% 245.19/57.92 | (224) op(e1, e3) = all_62_2
% 245.19/57.92 | (225) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) =
% 245.19/57.92 | all_62_0 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | (
% 245.19/57.92 | ~ (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (109) with fresh symbols all_64_0, all_64_1, all_64_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (226) op(e2, e4) = all_64_2 & $i(all_64_2) & ( ~ (all_64_2 = e3) | ( ~
% 245.19/57.92 | (all_64_0 = e0) & op(e4, e3) = all_64_1 & op(e3, all_64_1) =
% 245.19/57.92 | all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~ (all_64_1 = e1) &
% 245.19/57.92 | op(e4, e3) = all_64_1 & $i(all_64_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (226) implies:
% 245.19/57.92 | (227) op(e2, e4) = all_64_2
% 245.19/57.92 | (228) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 245.19/57.92 | op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 245.19/57.92 | (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (111) with fresh symbols all_66_0, all_66_1, all_66_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (229) op(e1, e4) = all_66_2 & $i(all_66_2) & ( ~ (all_66_2 = e3) | ( ~
% 245.19/57.92 | (all_66_0 = e0) & op(e4, e3) = all_66_1 & op(e3, all_66_1) =
% 245.19/57.92 | all_66_0 & $i(all_66_0) & $i(all_66_1)) | ( ~ (all_66_1 = e2) &
% 245.19/57.92 | op(e4, e3) = all_66_1 & $i(all_66_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (229) implies:
% 245.19/57.92 | (230) op(e1, e4) = all_66_2
% 245.19/57.92 | (231) ~ (all_66_2 = e3) | ( ~ (all_66_0 = e0) & op(e4, e3) = all_66_1 &
% 245.19/57.92 | op(e3, all_66_1) = all_66_0 & $i(all_66_0) & $i(all_66_1)) | ( ~
% 245.19/57.92 | (all_66_1 = e2) & op(e4, e3) = all_66_1 & $i(all_66_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (132) with fresh symbols all_68_0, all_68_1, all_68_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (232) op(e0, e3) = all_68_2 & $i(all_68_2) & ( ~ (all_68_2 = e4) | ( ~
% 245.19/57.92 | (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 & op(e3, e4) =
% 245.19/57.92 | all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 = e1) &
% 245.19/57.92 | op(e3, e4) = all_68_1 & $i(all_68_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (232) implies:
% 245.19/57.92 | (233) op(e0, e3) = all_68_2
% 245.19/57.92 | (234) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) =
% 245.19/57.92 | all_68_0 & op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | (
% 245.19/57.92 | ~ (all_68_1 = e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 245.19/57.92 |
% 245.19/57.92 | DELTA: instantiating (81) with fresh symbols all_70_0, all_70_1, all_70_2
% 245.19/57.92 | gives:
% 245.19/57.92 | (235) op(e1, e3) = all_70_2 & $i(all_70_2) & ( ~ (all_70_2 = e2) | ( ~
% 245.19/57.92 | (all_70_0 = e0) & op(e3, e2) = all_70_1 & op(e2, all_70_1) =
% 245.19/57.92 | all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~ (all_70_1 = e4) &
% 245.19/57.92 | op(e3, e2) = all_70_1 & $i(all_70_1)))
% 245.19/57.92 |
% 245.19/57.92 | ALPHA: (235) implies:
% 245.19/57.92 | (236) op(e1, e3) = all_70_2
% 245.19/57.93 | (237) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 245.19/57.93 | op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 245.19/57.93 | (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (54) with fresh symbols all_72_0, all_72_1, all_72_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (238) op(e0, e3) = all_72_2 & $i(all_72_2) & ( ~ (all_72_2 = e1) | ( ~
% 245.19/57.93 | (all_72_0 = e4) & op(e3, e1) = all_72_1 & op(e1, all_72_1) =
% 245.19/57.93 | all_72_0 & $i(all_72_0) & $i(all_72_1)) | ( ~ (all_72_1 = e2) &
% 245.19/57.93 | op(e3, e1) = all_72_1 & $i(all_72_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (238) implies:
% 245.19/57.93 | (239) op(e0, e3) = all_72_2
% 245.19/57.93 | (240) ~ (all_72_2 = e1) | ( ~ (all_72_0 = e4) & op(e3, e1) = all_72_1 &
% 245.19/57.93 | op(e1, all_72_1) = all_72_0 & $i(all_72_0) & $i(all_72_1)) | ( ~
% 245.19/57.93 | (all_72_1 = e2) & op(e3, e1) = all_72_1 & $i(all_72_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (21) with fresh symbols all_74_0, all_74_1, all_74_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (241) op(e3, e1) = all_74_2 & $i(all_74_2) & ( ~ (all_74_2 = e0) | ( ~
% 245.19/57.93 | (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0, all_74_1) =
% 245.19/57.93 | all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 = e4) &
% 245.19/57.93 | op(e1, e0) = all_74_1 & $i(all_74_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (241) implies:
% 245.19/57.93 | (242) op(e3, e1) = all_74_2
% 245.19/57.93 | (243) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 &
% 245.19/57.93 | op(e0, all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~
% 245.19/57.93 | (all_74_1 = e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (112) with fresh symbols all_76_0, all_76_1, all_76_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (244) op(e2, e0) = all_76_2 & $i(all_76_2) & ( ~ (all_76_2 = e4) | ( ~
% 245.19/57.93 | (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0, e4) =
% 245.19/57.93 | all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 = e1) &
% 245.19/57.93 | op(e0, e4) = all_76_1 & $i(all_76_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (244) implies:
% 245.19/57.93 | (245) op(e2, e0) = all_76_2
% 245.19/57.93 | (246) ~ (all_76_2 = e4) | ( ~ (all_76_0 = e3) & op(e4, all_76_1) =
% 245.19/57.93 | all_76_0 & op(e0, e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | (
% 245.19/57.93 | ~ (all_76_1 = e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (52) with fresh symbols all_78_0, all_78_1, all_78_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (247) op(e2, e3) = all_78_2 & $i(all_78_2) & ( ~ (all_78_2 = e1) | ( ~
% 245.19/57.93 | (all_78_0 = e4) & op(e3, e1) = all_78_1 & op(e1, all_78_1) =
% 245.19/57.93 | all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~ (all_78_1 = e0) &
% 245.19/57.93 | op(e3, e1) = all_78_1 & $i(all_78_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (247) implies:
% 245.19/57.93 | (248) op(e2, e3) = all_78_2
% 245.19/57.93 | (249) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 245.19/57.93 | op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 245.19/57.93 | (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (23) with fresh symbols all_80_0, all_80_1, all_80_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (250) op(e4, e2) = all_80_2 & $i(all_80_2) & ( ~ (all_80_2 = e0) | ( ~
% 245.19/57.93 | (all_80_0 = e3) & op(e2, e0) = all_80_1 & op(e0, all_80_1) =
% 245.19/57.93 | all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~ (all_80_1 = e1) &
% 245.19/57.93 | op(e2, e0) = all_80_1 & $i(all_80_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (250) implies:
% 245.19/57.93 | (251) op(e4, e2) = all_80_2
% 245.19/57.93 | (252) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 245.19/57.93 | op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 245.19/57.93 | (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (50) with fresh symbols all_82_0, all_82_1, all_82_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (253) op(e0, e2) = all_82_2 & $i(all_82_2) & ( ~ (all_82_2 = e1) | ( ~
% 245.19/57.93 | (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1, all_82_1) =
% 245.19/57.93 | all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 = e4) &
% 245.19/57.93 | op(e2, e1) = all_82_1 & $i(all_82_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (253) implies:
% 245.19/57.93 | (254) op(e0, e2) = all_82_2
% 245.19/57.93 | (255) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 245.19/57.93 | op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 245.19/57.93 | (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (53) with fresh symbols all_84_0, all_84_1, all_84_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (256) op(e4, e3) = all_84_2 & $i(all_84_2) & ( ~ (all_84_2 = e1) | ( ~
% 245.19/57.93 | (all_84_0 = e2) & op(e3, e1) = all_84_1 & op(e1, all_84_1) =
% 245.19/57.93 | all_84_0 & $i(all_84_0) & $i(all_84_1)) | ( ~ (all_84_1 = e0) &
% 245.19/57.93 | op(e3, e1) = all_84_1 & $i(all_84_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (256) implies:
% 245.19/57.93 | (257) op(e4, e3) = all_84_2
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (93) with fresh symbols all_86_0, all_86_1, all_86_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (258) op(e2, e0) = all_86_2 & $i(all_86_2) & ( ~ (all_86_2 = e3) | ( ~
% 245.19/57.93 | (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 & op(e0, e3) =
% 245.19/57.93 | all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 = e4) &
% 245.19/57.93 | op(e0, e3) = all_86_1 & $i(all_86_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (258) implies:
% 245.19/57.93 | (259) op(e2, e0) = all_86_2
% 245.19/57.93 | (260) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) =
% 245.19/57.93 | all_86_0 & op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | (
% 245.19/57.93 | ~ (all_86_1 = e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (95) with fresh symbols all_88_0, all_88_1, all_88_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (261) op(e4, e1) = all_88_2 & $i(all_88_2) & ( ~ (all_88_2 = e3) | ( ~
% 245.19/57.93 | (all_88_0 = e2) & op(e3, all_88_1) = all_88_0 & op(e1, e3) =
% 245.19/57.93 | all_88_1 & $i(all_88_0) & $i(all_88_1)) | ( ~ (all_88_1 = e0) &
% 245.19/57.93 | op(e1, e3) = all_88_1 & $i(all_88_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (261) implies:
% 245.19/57.93 | (262) op(e4, e1) = all_88_2
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (78) with fresh symbols all_90_0, all_90_1, all_90_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (263) op(e0, e3) = all_90_2 & $i(all_90_2) & ( ~ (all_90_2 = e2) | ( ~
% 245.19/57.93 | (all_90_0 = e4) & op(e3, e2) = all_90_1 & op(e2, all_90_1) =
% 245.19/57.93 | all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~ (all_90_1 = e1) &
% 245.19/57.93 | op(e3, e2) = all_90_1 & $i(all_90_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (263) implies:
% 245.19/57.93 | (264) op(e0, e3) = all_90_2
% 245.19/57.93 | (265) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 245.19/57.93 | op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 245.19/57.93 | (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (96) with fresh symbols all_92_0, all_92_1, all_92_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (266) op(e0, e1) = all_92_2 & $i(all_92_2) & ( ~ (all_92_2 = e3) | ( ~
% 245.19/57.93 | (all_92_0 = e4) & op(e3, all_92_1) = all_92_0 & op(e1, e3) =
% 245.19/57.93 | all_92_1 & $i(all_92_0) & $i(all_92_1)) | ( ~ (all_92_1 = e2) &
% 245.19/57.93 | op(e1, e3) = all_92_1 & $i(all_92_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (266) implies:
% 245.19/57.93 | (267) op(e0, e1) = all_92_2
% 245.19/57.93 | (268) ~ (all_92_2 = e3) | ( ~ (all_92_0 = e4) & op(e3, all_92_1) =
% 245.19/57.93 | all_92_0 & op(e1, e3) = all_92_1 & $i(all_92_0) & $i(all_92_1)) | (
% 245.19/57.93 | ~ (all_92_1 = e2) & op(e1, e3) = all_92_1 & $i(all_92_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (94) with fresh symbols all_94_0, all_94_1, all_94_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (269) op(e2, e1) = all_94_2 & $i(all_94_2) & ( ~ (all_94_2 = e3) | ( ~
% 245.19/57.93 | (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 & op(e1, e3) =
% 245.19/57.93 | all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 = e0) &
% 245.19/57.93 | op(e1, e3) = all_94_1 & $i(all_94_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (269) implies:
% 245.19/57.93 | (270) op(e2, e1) = all_94_2
% 245.19/57.93 | (271) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) =
% 245.19/57.93 | all_94_0 & op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | (
% 245.19/57.93 | ~ (all_94_1 = e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (92) with fresh symbols all_96_0, all_96_1, all_96_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (272) op(e1, e0) = all_96_2 & $i(all_96_2) & ( ~ (all_96_2 = e3) | ( ~
% 245.19/57.93 | (all_96_0 = e2) & op(e3, all_96_1) = all_96_0 & op(e0, e3) =
% 245.19/57.93 | all_96_1 & $i(all_96_0) & $i(all_96_1)) | ( ~ (all_96_1 = e4) &
% 245.19/57.93 | op(e0, e3) = all_96_1 & $i(all_96_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (272) implies:
% 245.19/57.93 | (273) op(e1, e0) = all_96_2
% 245.19/57.93 | (274) ~ (all_96_2 = e3) | ( ~ (all_96_0 = e2) & op(e3, all_96_1) =
% 245.19/57.93 | all_96_0 & op(e0, e3) = all_96_1 & $i(all_96_0) & $i(all_96_1)) | (
% 245.19/57.93 | ~ (all_96_1 = e4) & op(e0, e3) = all_96_1 & $i(all_96_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (55) with fresh symbols all_98_0, all_98_1, all_98_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (275) op(e4, e3) = all_98_2 & $i(all_98_2) & ( ~ (all_98_2 = e1) | ( ~
% 245.19/57.93 | (all_98_0 = e0) & op(e3, e1) = all_98_1 & op(e1, all_98_1) =
% 245.19/57.93 | all_98_0 & $i(all_98_0) & $i(all_98_1)) | ( ~ (all_98_1 = e2) &
% 245.19/57.93 | op(e3, e1) = all_98_1 & $i(all_98_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (275) implies:
% 245.19/57.93 | (276) op(e4, e3) = all_98_2
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (83) with fresh symbols all_100_0, all_100_1, all_100_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (277) op(e3, e4) = all_100_2 & $i(all_100_2) & ( ~ (all_100_2 = e2) | ( ~
% 245.19/57.93 | (all_100_0 = e1) & op(e4, e2) = all_100_1 & op(e2, all_100_1) =
% 245.19/57.93 | all_100_0 & $i(all_100_0) & $i(all_100_1)) | ( ~ (all_100_1 = e0)
% 245.19/57.93 | & op(e4, e2) = all_100_1 & $i(all_100_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (277) implies:
% 245.19/57.93 | (278) op(e3, e4) = all_100_2
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (133) with fresh symbols all_102_0, all_102_1, all_102_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (279) op(e2, e3) = all_102_2 & $i(all_102_2) & ( ~ (all_102_2 = e4) | ( ~
% 245.19/57.93 | (all_102_0 = e0) & op(e4, all_102_1) = all_102_0 & op(e3, e4) =
% 245.19/57.93 | all_102_1 & $i(all_102_0) & $i(all_102_1)) | ( ~ (all_102_1 = e1)
% 245.19/57.93 | & op(e3, e4) = all_102_1 & $i(all_102_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (279) implies:
% 245.19/57.93 | (280) op(e2, e3) = all_102_2
% 245.19/57.93 | (281) ~ (all_102_2 = e4) | ( ~ (all_102_0 = e0) & op(e4, all_102_1) =
% 245.19/57.93 | all_102_0 & op(e3, e4) = all_102_1 & $i(all_102_0) & $i(all_102_1))
% 245.19/57.93 | | ( ~ (all_102_1 = e1) & op(e3, e4) = all_102_1 & $i(all_102_1))
% 245.19/57.93 |
% 245.19/57.93 | DELTA: instantiating (134) with fresh symbols all_104_0, all_104_1, all_104_2
% 245.19/57.93 | gives:
% 245.19/57.93 | (282) op(e0, e3) = all_104_2 & $i(all_104_2) & ( ~ (all_104_2 = e4) | ( ~
% 245.19/57.93 | (all_104_0 = e1) & op(e4, all_104_1) = all_104_0 & op(e3, e4) =
% 245.19/57.93 | all_104_1 & $i(all_104_0) & $i(all_104_1)) | ( ~ (all_104_1 = e2)
% 245.19/57.93 | & op(e3, e4) = all_104_1 & $i(all_104_1)))
% 245.19/57.93 |
% 245.19/57.93 | ALPHA: (282) implies:
% 245.19/57.93 | (283) op(e0, e3) = all_104_2
% 245.19/57.93 | (284) ~ (all_104_2 = e4) | ( ~ (all_104_0 = e1) & op(e4, all_104_1) =
% 245.19/57.93 | all_104_0 & op(e3, e4) = all_104_1 & $i(all_104_0) & $i(all_104_1))
% 245.19/57.93 | | ( ~ (all_104_1 = e2) & op(e3, e4) = all_104_1 & $i(all_104_1))
% 245.19/57.93 |
% 245.19/57.94 | DELTA: instantiating (18) with fresh symbols all_106_0, all_106_1, all_106_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (285) op(e2, e1) = all_106_2 & $i(all_106_2) & ( ~ (all_106_2 = e0) | ( ~
% 245.19/57.94 | (all_106_0 = e4) & op(e1, e0) = all_106_1 & op(e0, all_106_1) =
% 245.19/57.94 | all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~ (all_106_1 = e3)
% 245.19/57.94 | & op(e1, e0) = all_106_1 & $i(all_106_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (285) implies:
% 245.19/57.94 | (286) op(e2, e1) = all_106_2
% 245.19/57.94 | (287) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 245.19/57.94 | op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | (
% 245.19/57.94 | ~ (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (48) with fresh symbols all_108_0, all_108_1, all_108_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (288) op(e0, e2) = all_108_2 & $i(all_108_2) & ( ~ (all_108_2 = e1) | ( ~
% 245.19/57.94 | (all_108_0 = e4) & op(e2, e1) = all_108_1 & op(e1, all_108_1) =
% 245.19/57.94 | all_108_0 & $i(all_108_0) & $i(all_108_1)) | ( ~ (all_108_1 = e3)
% 245.19/57.94 | & op(e2, e1) = all_108_1 & $i(all_108_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (288) implies:
% 245.19/57.94 | (289) op(e0, e2) = all_108_2
% 245.19/57.94 | (290) ~ (all_108_2 = e1) | ( ~ (all_108_0 = e4) & op(e2, e1) = all_108_1 &
% 245.19/57.94 | op(e1, all_108_1) = all_108_0 & $i(all_108_0) & $i(all_108_1)) | (
% 245.19/57.94 | ~ (all_108_1 = e3) & op(e2, e1) = all_108_1 & $i(all_108_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (116) with fresh symbols all_110_0, all_110_1, all_110_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (291) op(e1, e0) = all_110_2 & $i(all_110_2) & ( ~ (all_110_2 = e4) | ( ~
% 245.19/57.94 | (all_110_0 = e2) & op(e4, all_110_1) = all_110_0 & op(e0, e4) =
% 245.19/57.94 | all_110_1 & $i(all_110_0) & $i(all_110_1)) | ( ~ (all_110_1 = e3)
% 245.19/57.94 | & op(e0, e4) = all_110_1 & $i(all_110_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (291) implies:
% 245.19/57.94 | (292) op(e1, e0) = all_110_2
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (32) with fresh symbols all_112_0, all_112_1, all_112_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (293) op(e1, e3) = all_112_2 & $i(all_112_2) & ( ~ (all_112_2 = e0) | ( ~
% 245.19/57.94 | (all_112_0 = e2) & op(e3, e0) = all_112_1 & op(e0, all_112_1) =
% 245.19/57.94 | all_112_0 & $i(all_112_0) & $i(all_112_1)) | ( ~ (all_112_1 = e4)
% 245.19/57.94 | & op(e3, e0) = all_112_1 & $i(all_112_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (293) implies:
% 245.19/57.94 | (294) op(e1, e3) = all_112_2
% 245.19/57.94 | (295) ~ (all_112_2 = e0) | ( ~ (all_112_0 = e2) & op(e3, e0) = all_112_1 &
% 245.19/57.94 | op(e0, all_112_1) = all_112_0 & $i(all_112_0) & $i(all_112_1)) | (
% 245.19/57.94 | ~ (all_112_1 = e4) & op(e3, e0) = all_112_1 & $i(all_112_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (30) with fresh symbols all_114_0, all_114_1, all_114_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (296) op(e1, e3) = all_114_2 & $i(all_114_2) & ( ~ (all_114_2 = e0) | ( ~
% 245.19/57.94 | (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0, all_114_1) =
% 245.19/57.94 | all_114_0 & $i(all_114_0) & $i(all_114_1)) | ( ~ (all_114_1 = e2)
% 245.19/57.94 | & op(e3, e0) = all_114_1 & $i(all_114_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (296) implies:
% 245.19/57.94 | (297) op(e1, e3) = all_114_2
% 245.19/57.94 | (298) ~ (all_114_2 = e0) | ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 &
% 245.19/57.94 | op(e0, all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1)) | (
% 245.19/57.94 | ~ (all_114_1 = e2) & op(e3, e0) = all_114_1 & $i(all_114_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (42) with fresh symbols all_116_0, all_116_1, all_116_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (299) op(e2, e0) = all_116_2 & $i(all_116_2) & ( ~ (all_116_2 = e1) | ( ~
% 245.19/57.94 | (all_116_0 = e4) & op(e1, all_116_1) = all_116_0 & op(e0, e1) =
% 245.19/57.94 | all_116_1 & $i(all_116_0) & $i(all_116_1)) | ( ~ (all_116_1 = e3)
% 245.19/57.94 | & op(e0, e1) = all_116_1 & $i(all_116_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (299) implies:
% 245.19/57.94 | (300) op(e2, e0) = all_116_2
% 245.19/57.94 | (301) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 245.19/57.94 | all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1))
% 245.19/57.94 | | ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (80) with fresh symbols all_118_0, all_118_1, all_118_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (302) op(e0, e3) = all_118_2 & $i(all_118_2) & ( ~ (all_118_2 = e2) | ( ~
% 245.19/57.94 | (all_118_0 = e1) & op(e3, e2) = all_118_1 & op(e2, all_118_1) =
% 245.19/57.94 | all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~ (all_118_1 = e4)
% 245.19/57.94 | & op(e3, e2) = all_118_1 & $i(all_118_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (302) implies:
% 245.19/57.94 | (303) op(e0, e3) = all_118_2
% 245.19/57.94 | (304) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 245.19/57.94 | op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | (
% 245.19/57.94 | ~ (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (58) with fresh symbols all_120_0, all_120_1, all_120_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (305) op(e2, e4) = all_120_2 & $i(all_120_2) & ( ~ (all_120_2 = e1) | ( ~
% 245.19/57.94 | (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1, all_120_1) =
% 245.19/57.94 | all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~ (all_120_1 = e0)
% 245.19/57.94 | & op(e4, e1) = all_120_1 & $i(all_120_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (305) implies:
% 245.19/57.94 | (306) op(e2, e4) = all_120_2
% 245.19/57.94 | (307) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 245.19/57.94 | op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | (
% 245.19/57.94 | ~ (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (16) with fresh symbols all_122_0, all_122_1, all_122_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (308) op(e3, e1) = all_122_2 & $i(all_122_2) & ( ~ (all_122_2 = e0) | ( ~
% 245.19/57.94 | (all_122_0 = e4) & op(e1, e0) = all_122_1 & op(e0, all_122_1) =
% 245.19/57.94 | all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~ (all_122_1 = e2)
% 245.19/57.94 | & op(e1, e0) = all_122_1 & $i(all_122_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (308) implies:
% 245.19/57.94 | (309) op(e3, e1) = all_122_2
% 245.19/57.94 | (310) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 245.19/57.94 | op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | (
% 245.19/57.94 | ~ (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (33) with fresh symbols all_124_0, all_124_1, all_124_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (311) op(e2, e3) = all_124_2 & $i(all_124_2) & ( ~ (all_124_2 = e0) | ( ~
% 245.19/57.94 | (all_124_0 = e1) & op(e3, e0) = all_124_1 & op(e0, all_124_1) =
% 245.19/57.94 | all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~ (all_124_1 = e4)
% 245.19/57.94 | & op(e3, e0) = all_124_1 & $i(all_124_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (311) implies:
% 245.19/57.94 | (312) op(e2, e3) = all_124_2
% 245.19/57.94 | (313) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 245.19/57.94 | op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | (
% 245.19/57.94 | ~ (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (40) with fresh symbols all_126_0, all_126_1, all_126_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (314) op(e3, e0) = all_126_2 & $i(all_126_2) & ( ~ (all_126_2 = e1) | ( ~
% 245.19/57.94 | (all_126_0 = e4) & op(e1, all_126_1) = all_126_0 & op(e0, e1) =
% 245.19/57.94 | all_126_1 & $i(all_126_0) & $i(all_126_1)) | ( ~ (all_126_1 = e2)
% 245.19/57.94 | & op(e0, e1) = all_126_1 & $i(all_126_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (314) implies:
% 245.19/57.94 | (315) op(e3, e0) = all_126_2
% 245.19/57.94 | (316) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 245.19/57.94 | all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1))
% 245.19/57.94 | | ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (89) with fresh symbols all_128_0, all_128_1, all_128_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (317) op(e4, e0) = all_128_2 & $i(all_128_2) & ( ~ (all_128_2 = e3) | ( ~
% 245.19/57.94 | (all_128_0 = e2) & op(e3, all_128_1) = all_128_0 & op(e0, e3) =
% 245.19/57.94 | all_128_1 & $i(all_128_0) & $i(all_128_1)) | ( ~ (all_128_1 = e1)
% 245.19/57.94 | & op(e0, e3) = all_128_1 & $i(all_128_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (317) implies:
% 245.19/57.94 | (318) op(e4, e0) = all_128_2
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (76) with fresh symbols all_130_0, all_130_1, all_130_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (319) op(e1, e3) = all_130_2 & $i(all_130_2) & ( ~ (all_130_2 = e2) | ( ~
% 245.19/57.94 | (all_130_0 = e4) & op(e3, e2) = all_130_1 & op(e2, all_130_1) =
% 245.19/57.94 | all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~ (all_130_1 = e0)
% 245.19/57.94 | & op(e3, e2) = all_130_1 & $i(all_130_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (319) implies:
% 245.19/57.94 | (320) op(e1, e3) = all_130_2
% 245.19/57.94 | (321) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 245.19/57.94 | op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | (
% 245.19/57.94 | ~ (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (91) with fresh symbols all_132_0, all_132_1, all_132_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (322) op(e4, e0) = all_132_2 & $i(all_132_2) & ( ~ (all_132_2 = e3) | ( ~
% 245.19/57.94 | (all_132_0 = e1) & op(e3, all_132_1) = all_132_0 & op(e0, e3) =
% 245.19/57.94 | all_132_1 & $i(all_132_0) & $i(all_132_1)) | ( ~ (all_132_1 = e2)
% 245.19/57.94 | & op(e0, e3) = all_132_1 & $i(all_132_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (322) implies:
% 245.19/57.94 | (323) op(e4, e0) = all_132_2
% 245.19/57.94 | (324) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 245.19/57.94 | all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1))
% 245.19/57.94 | | ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (34) with fresh symbols all_134_0, all_134_1, all_134_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (325) op(e2, e4) = all_134_2 & $i(all_134_2) & ( ~ (all_134_2 = e0) | ( ~
% 245.19/57.94 | (all_134_0 = e3) & op(e4, e0) = all_134_1 & op(e0, all_134_1) =
% 245.19/57.94 | all_134_0 & $i(all_134_0) & $i(all_134_1)) | ( ~ (all_134_1 = e1)
% 245.19/57.94 | & op(e4, e0) = all_134_1 & $i(all_134_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (325) implies:
% 245.19/57.94 | (326) op(e2, e4) = all_134_2
% 245.19/57.94 | (327) ~ (all_134_2 = e0) | ( ~ (all_134_0 = e3) & op(e4, e0) = all_134_1 &
% 245.19/57.94 | op(e0, all_134_1) = all_134_0 & $i(all_134_0) & $i(all_134_1)) | (
% 245.19/57.94 | ~ (all_134_1 = e1) & op(e4, e0) = all_134_1 & $i(all_134_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (35) with fresh symbols all_136_0, all_136_1, all_136_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (328) op(e3, e4) = all_136_2 & $i(all_136_2) & ( ~ (all_136_2 = e0) | ( ~
% 245.19/57.94 | (all_136_0 = e2) & op(e4, e0) = all_136_1 & op(e0, all_136_1) =
% 245.19/57.94 | all_136_0 & $i(all_136_0) & $i(all_136_1)) | ( ~ (all_136_1 = e1)
% 245.19/57.94 | & op(e4, e0) = all_136_1 & $i(all_136_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (328) implies:
% 245.19/57.94 | (329) op(e3, e4) = all_136_2
% 245.19/57.94 | (330) ~ (all_136_2 = e0) | ( ~ (all_136_0 = e2) & op(e4, e0) = all_136_1 &
% 245.19/57.94 | op(e0, all_136_1) = all_136_0 & $i(all_136_0) & $i(all_136_1)) | (
% 245.19/57.94 | ~ (all_136_1 = e1) & op(e4, e0) = all_136_1 & $i(all_136_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (28) with fresh symbols all_138_0, all_138_1, all_138_2
% 245.19/57.94 | gives:
% 245.19/57.94 | (331) op(e2, e3) = all_138_2 & $i(all_138_2) & ( ~ (all_138_2 = e0) | ( ~
% 245.19/57.94 | (all_138_0 = e4) & op(e3, e0) = all_138_1 & op(e0, all_138_1) =
% 245.19/57.94 | all_138_0 & $i(all_138_0) & $i(all_138_1)) | ( ~ (all_138_1 = e1)
% 245.19/57.94 | & op(e3, e0) = all_138_1 & $i(all_138_1)))
% 245.19/57.94 |
% 245.19/57.94 | ALPHA: (331) implies:
% 245.19/57.94 | (332) op(e2, e3) = all_138_2
% 245.19/57.94 | (333) ~ (all_138_2 = e0) | ( ~ (all_138_0 = e4) & op(e3, e0) = all_138_1 &
% 245.19/57.94 | op(e0, all_138_1) = all_138_0 & $i(all_138_0) & $i(all_138_1)) | (
% 245.19/57.94 | ~ (all_138_1 = e1) & op(e3, e0) = all_138_1 & $i(all_138_1))
% 245.19/57.94 |
% 245.19/57.94 | DELTA: instantiating (29) with fresh symbols all_140_0, all_140_1, all_140_2
% 245.19/57.94 | gives:
% 245.19/57.95 | (334) op(e4, e3) = all_140_2 & $i(all_140_2) & ( ~ (all_140_2 = e0) | ( ~
% 245.19/57.95 | (all_140_0 = e2) & op(e3, e0) = all_140_1 & op(e0, all_140_1) =
% 245.19/57.95 | all_140_0 & $i(all_140_0) & $i(all_140_1)) | ( ~ (all_140_1 = e1)
% 245.19/57.95 | & op(e3, e0) = all_140_1 & $i(all_140_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (334) implies:
% 245.19/57.95 | (335) op(e4, e3) = all_140_2
% 245.19/57.95 | (336) ~ (all_140_2 = e0) | ( ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 &
% 245.19/57.95 | op(e0, all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1)) | (
% 245.19/57.95 | ~ (all_140_1 = e1) & op(e3, e0) = all_140_1 & $i(all_140_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (31) with fresh symbols all_142_0, all_142_1, all_142_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (337) op(e4, e3) = all_142_2 & $i(all_142_2) & ( ~ (all_142_2 = e0) | ( ~
% 245.19/57.95 | (all_142_0 = e1) & op(e3, e0) = all_142_1 & op(e0, all_142_1) =
% 245.19/57.95 | all_142_0 & $i(all_142_0) & $i(all_142_1)) | ( ~ (all_142_1 = e2)
% 245.19/57.95 | & op(e3, e0) = all_142_1 & $i(all_142_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (337) implies:
% 245.19/57.95 | (338) op(e4, e3) = all_142_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (36) with fresh symbols all_144_0, all_144_1, all_144_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (339) op(e1, e4) = all_144_2 & $i(all_144_2) & ( ~ (all_144_2 = e0) | ( ~
% 245.19/57.95 | (all_144_0 = e3) & op(e4, e0) = all_144_1 & op(e0, all_144_1) =
% 245.19/57.95 | all_144_0 & $i(all_144_0) & $i(all_144_1)) | ( ~ (all_144_1 = e2)
% 245.19/57.95 | & op(e4, e0) = all_144_1 & $i(all_144_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (339) implies:
% 245.19/57.95 | (340) op(e1, e4) = all_144_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (37) with fresh symbols all_146_0, all_146_1, all_146_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (341) op(e3, e4) = all_146_2 & $i(all_146_2) & ( ~ (all_146_2 = e0) | ( ~
% 245.19/57.95 | (all_146_0 = e1) & op(e4, e0) = all_146_1 & op(e0, all_146_1) =
% 245.19/57.95 | all_146_0 & $i(all_146_0) & $i(all_146_1)) | ( ~ (all_146_1 = e2)
% 245.19/57.95 | & op(e4, e0) = all_146_1 & $i(all_146_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (341) implies:
% 245.19/57.95 | (342) op(e3, e4) = all_146_2
% 245.19/57.95 | (343) ~ (all_146_2 = e0) | ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 245.19/57.95 | op(e0, all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)) | (
% 245.19/57.95 | ~ (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (39) with fresh symbols all_148_0, all_148_1, all_148_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (344) op(e2, e4) = all_148_2 & $i(all_148_2) & ( ~ (all_148_2 = e0) | ( ~
% 245.19/57.95 | (all_148_0 = e1) & op(e4, e0) = all_148_1 & op(e0, all_148_1) =
% 245.19/57.95 | all_148_0 & $i(all_148_0) & $i(all_148_1)) | ( ~ (all_148_1 = e3)
% 245.19/57.95 | & op(e4, e0) = all_148_1 & $i(all_148_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (344) implies:
% 245.19/57.95 | (345) op(e2, e4) = all_148_2
% 245.19/57.95 | (346) ~ (all_148_2 = e0) | ( ~ (all_148_0 = e1) & op(e4, e0) = all_148_1 &
% 245.19/57.95 | op(e0, all_148_1) = all_148_0 & $i(all_148_0) & $i(all_148_1)) | (
% 245.19/57.95 | ~ (all_148_1 = e3) & op(e4, e0) = all_148_1 & $i(all_148_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (26) with fresh symbols all_150_0, all_150_1, all_150_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (347) op(e1, e2) = all_150_2 & $i(all_150_2) & ( ~ (all_150_2 = e0) | ( ~
% 245.19/57.95 | (all_150_0 = e3) & op(e2, e0) = all_150_1 & op(e0, all_150_1) =
% 245.19/57.95 | all_150_0 & $i(all_150_0) & $i(all_150_1)) | ( ~ (all_150_1 = e4)
% 245.19/57.95 | & op(e2, e0) = all_150_1 & $i(all_150_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (347) implies:
% 245.19/57.95 | (348) op(e1, e2) = all_150_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (38) with fresh symbols all_152_0, all_152_1, all_152_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (349) op(e1, e4) = all_152_2 & $i(all_152_2) & ( ~ (all_152_2 = e0) | ( ~
% 245.19/57.95 | (all_152_0 = e2) & op(e4, e0) = all_152_1 & op(e0, all_152_1) =
% 245.19/57.95 | all_152_0 & $i(all_152_0) & $i(all_152_1)) | ( ~ (all_152_1 = e3)
% 245.19/57.95 | & op(e4, e0) = all_152_1 & $i(all_152_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (349) implies:
% 245.19/57.95 | (350) op(e1, e4) = all_152_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (125) with fresh symbols all_154_0, all_154_1, all_154_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (351) op(e3, e2) = all_154_2 & $i(all_154_2) & ( ~ (all_154_2 = e4) | ( ~
% 245.19/57.95 | (all_154_0 = e1) & op(e4, all_154_1) = all_154_0 & op(e2, e4) =
% 245.19/57.95 | all_154_1 & $i(all_154_0) & $i(all_154_1)) | ( ~ (all_154_1 = e0)
% 245.19/57.95 | & op(e2, e4) = all_154_1 & $i(all_154_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (351) implies:
% 245.19/57.95 | (352) op(e3, e2) = all_154_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (127) with fresh symbols all_156_0, all_156_1, all_156_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (353) op(e3, e2) = all_156_2 & $i(all_156_2) & ( ~ (all_156_2 = e4) | ( ~
% 245.19/57.95 | (all_156_0 = e0) & op(e4, all_156_1) = all_156_0 & op(e2, e4) =
% 245.19/57.95 | all_156_1 & $i(all_156_0) & $i(all_156_1)) | ( ~ (all_156_1 = e1)
% 245.19/57.95 | & op(e2, e4) = all_156_1 & $i(all_156_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (353) implies:
% 245.19/57.95 | (354) op(e3, e2) = all_156_2
% 245.19/57.95 | (355) ~ (all_156_2 = e4) | ( ~ (all_156_0 = e0) & op(e4, all_156_1) =
% 245.19/57.95 | all_156_0 & op(e2, e4) = all_156_1 & $i(all_156_0) & $i(all_156_1))
% 245.19/57.95 | | ( ~ (all_156_1 = e1) & op(e2, e4) = all_156_1 & $i(all_156_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (126) with fresh symbols all_158_0, all_158_1, all_158_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (356) op(e0, e2) = all_158_2 & $i(all_158_2) & ( ~ (all_158_2 = e4) | ( ~
% 245.19/57.95 | (all_158_0 = e3) & op(e4, all_158_1) = all_158_0 & op(e2, e4) =
% 245.19/57.95 | all_158_1 & $i(all_158_0) & $i(all_158_1)) | ( ~ (all_158_1 = e1)
% 245.19/57.95 | & op(e2, e4) = all_158_1 & $i(all_158_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (356) implies:
% 245.19/57.95 | (357) op(e0, e2) = all_158_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (124) with fresh symbols all_160_0, all_160_1, all_160_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (358) op(e1, e2) = all_160_2 & $i(all_160_2) & ( ~ (all_160_2 = e4) | ( ~
% 245.19/57.95 | (all_160_0 = e3) & op(e4, all_160_1) = all_160_0 & op(e2, e4) =
% 245.19/57.95 | all_160_1 & $i(all_160_0) & $i(all_160_1)) | ( ~ (all_160_1 = e0)
% 245.19/57.95 | & op(e2, e4) = all_160_1 & $i(all_160_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (358) implies:
% 245.19/57.95 | (359) op(e1, e2) = all_160_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (128) with fresh symbols all_162_0, all_162_1, all_162_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (360) op(e0, e2) = all_162_2 & $i(all_162_2) & ( ~ (all_162_2 = e4) | ( ~
% 245.19/57.95 | (all_162_0 = e1) & op(e4, all_162_1) = all_162_0 & op(e2, e4) =
% 245.19/57.95 | all_162_1 & $i(all_162_0) & $i(all_162_1)) | ( ~ (all_162_1 = e3)
% 245.19/57.95 | & op(e2, e4) = all_162_1 & $i(all_162_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (360) implies:
% 245.19/57.95 | (361) op(e0, e2) = all_162_2
% 245.19/57.95 | (362) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 245.19/57.95 | all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1))
% 245.19/57.95 | | ( ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (114) with fresh symbols all_164_0, all_164_1, all_164_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (363) op(e1, e0) = all_164_2 & $i(all_164_2) & ( ~ (all_164_2 = e4) | ( ~
% 245.19/57.95 | (all_164_0 = e3) & op(e4, all_164_1) = all_164_0 & op(e0, e4) =
% 245.19/57.95 | all_164_1 & $i(all_164_0) & $i(all_164_1)) | ( ~ (all_164_1 = e2)
% 245.19/57.95 | & op(e0, e4) = all_164_1 & $i(all_164_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (363) implies:
% 245.19/57.95 | (364) op(e1, e0) = all_164_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (135) with fresh symbols all_166_0, all_166_1, all_166_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (365) op(e1, e3) = all_166_2 & $i(all_166_2) & ( ~ (all_166_2 = e4) | ( ~
% 245.19/57.95 | (all_166_0 = e0) & op(e4, all_166_1) = all_166_0 & op(e3, e4) =
% 245.19/57.95 | all_166_1 & $i(all_166_0) & $i(all_166_1)) | ( ~ (all_166_1 = e2)
% 245.19/57.95 | & op(e3, e4) = all_166_1 & $i(all_166_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (365) implies:
% 245.19/57.95 | (366) op(e1, e3) = all_166_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (85) with fresh symbols all_168_0, all_168_1, all_168_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (367) op(e3, e4) = all_168_2 & $i(all_168_2) & ( ~ (all_168_2 = e2) | ( ~
% 245.19/57.95 | (all_168_0 = e0) & op(e4, e2) = all_168_1 & op(e2, all_168_1) =
% 245.19/57.95 | all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~ (all_168_1 = e1)
% 245.19/57.95 | & op(e4, e2) = all_168_1 & $i(all_168_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (367) implies:
% 245.19/57.95 | (368) op(e3, e4) = all_168_2
% 245.19/57.95 | (369) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 245.19/57.95 | op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | (
% 245.19/57.95 | ~ (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (87) with fresh symbols all_170_0, all_170_1, all_170_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (370) op(e1, e4) = all_170_2 & $i(all_170_2) & ( ~ (all_170_2 = e2) | ( ~
% 245.19/57.95 | (all_170_0 = e0) & op(e4, e2) = all_170_1 & op(e2, all_170_1) =
% 245.19/57.95 | all_170_0 & $i(all_170_0) & $i(all_170_1)) | ( ~ (all_170_1 = e3)
% 245.19/57.95 | & op(e4, e2) = all_170_1 & $i(all_170_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (370) implies:
% 245.19/57.95 | (371) op(e1, e4) = all_170_2
% 245.19/57.95 | (372) ~ (all_170_2 = e2) | ( ~ (all_170_0 = e0) & op(e4, e2) = all_170_1 &
% 245.19/57.95 | op(e2, all_170_1) = all_170_0 & $i(all_170_0) & $i(all_170_1)) | (
% 245.19/57.95 | ~ (all_170_1 = e3) & op(e4, e2) = all_170_1 & $i(all_170_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (57) with fresh symbols all_172_0, all_172_1, all_172_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (373) op(e2, e3) = all_172_2 & $i(all_172_2) & ( ~ (all_172_2 = e1) | ( ~
% 245.19/57.95 | (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 245.19/57.95 | all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4)
% 245.19/57.95 | & op(e3, e1) = all_172_1 & $i(all_172_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (373) implies:
% 245.19/57.95 | (374) op(e2, e3) = all_172_2
% 245.19/57.95 | (375) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 245.19/57.95 | op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | (
% 245.19/57.95 | ~ (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (44) with fresh symbols all_174_0, all_174_1, all_174_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (376) op(e2, e0) = all_174_2 & $i(all_174_2) & ( ~ (all_174_2 = e1) | ( ~
% 245.19/57.95 | (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0, e1) =
% 245.19/57.95 | all_174_1 & $i(all_174_0) & $i(all_174_1)) | ( ~ (all_174_1 = e4)
% 245.19/57.95 | & op(e0, e1) = all_174_1 & $i(all_174_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (376) implies:
% 245.19/57.95 | (377) op(e2, e0) = all_174_2
% 245.19/57.95 | (378) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 245.19/57.95 | all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1))
% 245.19/57.95 | | ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (59) with fresh symbols all_176_0, all_176_1, all_176_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (379) op(e3, e4) = all_176_2 & $i(all_176_2) & ( ~ (all_176_2 = e1) | ( ~
% 245.19/57.95 | (all_176_0 = e2) & op(e4, e1) = all_176_1 & op(e1, all_176_1) =
% 245.19/57.95 | all_176_0 & $i(all_176_0) & $i(all_176_1)) | ( ~ (all_176_1 = e0)
% 245.19/57.95 | & op(e4, e1) = all_176_1 & $i(all_176_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (379) implies:
% 245.19/57.95 | (380) op(e3, e4) = all_176_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (88) with fresh symbols all_178_0, all_178_1, all_178_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (381) op(e2, e0) = all_178_2 & $i(all_178_2) & ( ~ (all_178_2 = e3) | ( ~
% 245.19/57.95 | (all_178_0 = e4) & op(e3, all_178_1) = all_178_0 & op(e0, e3) =
% 245.19/57.95 | all_178_1 & $i(all_178_0) & $i(all_178_1)) | ( ~ (all_178_1 = e1)
% 245.19/57.95 | & op(e0, e3) = all_178_1 & $i(all_178_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (381) implies:
% 245.19/57.95 | (382) op(e2, e0) = all_178_2
% 245.19/57.95 | (383) ~ (all_178_2 = e3) | ( ~ (all_178_0 = e4) & op(e3, all_178_1) =
% 245.19/57.95 | all_178_0 & op(e0, e3) = all_178_1 & $i(all_178_0) & $i(all_178_1))
% 245.19/57.95 | | ( ~ (all_178_1 = e1) & op(e0, e3) = all_178_1 & $i(all_178_1))
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (24) with fresh symbols all_180_0, all_180_1, all_180_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (384) op(e1, e2) = all_180_2 & $i(all_180_2) & ( ~ (all_180_2 = e0) | ( ~
% 245.19/57.95 | (all_180_0 = e4) & op(e2, e0) = all_180_1 & op(e0, all_180_1) =
% 245.19/57.95 | all_180_0 & $i(all_180_0) & $i(all_180_1)) | ( ~ (all_180_1 = e3)
% 245.19/57.95 | & op(e2, e0) = all_180_1 & $i(all_180_1)))
% 245.19/57.95 |
% 245.19/57.95 | ALPHA: (384) implies:
% 245.19/57.95 | (385) op(e1, e2) = all_180_2
% 245.19/57.95 |
% 245.19/57.95 | DELTA: instantiating (77) with fresh symbols all_182_0, all_182_1, all_182_2
% 245.19/57.95 | gives:
% 245.19/57.95 | (386) op(e4, e3) = all_182_2 & $i(all_182_2) & ( ~ (all_182_2 = e2) | ( ~
% 245.19/57.95 | (all_182_0 = e1) & op(e3, e2) = all_182_1 & op(e2, all_182_1) =
% 245.19/57.95 | all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~ (all_182_1 = e0)
% 245.19/57.95 | & op(e3, e2) = all_182_1 & $i(all_182_1)))
% 245.19/57.95 |
% 245.19/57.96 | ALPHA: (386) implies:
% 245.19/57.96 | (387) op(e4, e3) = all_182_2
% 245.19/57.96 | (388) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 245.19/57.96 | op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | (
% 245.19/57.96 | ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (79) with fresh symbols all_184_0, all_184_1, all_184_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (389) op(e4, e3) = all_184_2 & $i(all_184_2) & ( ~ (all_184_2 = e2) | ( ~
% 245.19/57.96 | (all_184_0 = e0) & op(e3, e2) = all_184_1 & op(e2, all_184_1) =
% 245.19/57.96 | all_184_0 & $i(all_184_0) & $i(all_184_1)) | ( ~ (all_184_1 = e1)
% 245.19/57.96 | & op(e3, e2) = all_184_1 & $i(all_184_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (389) implies:
% 245.19/57.96 | (390) op(e4, e3) = all_184_2
% 245.19/57.96 | (391) ~ (all_184_2 = e2) | ( ~ (all_184_0 = e0) & op(e3, e2) = all_184_1 &
% 245.19/57.96 | op(e2, all_184_1) = all_184_0 & $i(all_184_0) & $i(all_184_1)) | (
% 245.19/57.96 | ~ (all_184_1 = e1) & op(e3, e2) = all_184_1 & $i(all_184_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (107) with fresh symbols all_186_0, all_186_1, all_186_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (392) op(e2, e4) = all_186_2 & $i(all_186_2) & ( ~ (all_186_2 = e3) | ( ~
% 245.19/57.96 | (all_186_0 = e1) & op(e4, e3) = all_186_1 & op(e3, all_186_1) =
% 245.19/57.96 | all_186_0 & $i(all_186_0) & $i(all_186_1)) | ( ~ (all_186_1 = e0)
% 245.19/57.96 | & op(e4, e3) = all_186_1 & $i(all_186_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (392) implies:
% 245.19/57.96 | (393) op(e2, e4) = all_186_2
% 245.19/57.96 | (394) ~ (all_186_2 = e3) | ( ~ (all_186_0 = e1) & op(e4, e3) = all_186_1 &
% 245.19/57.96 | op(e3, all_186_1) = all_186_0 & $i(all_186_0) & $i(all_186_1)) | (
% 245.19/57.96 | ~ (all_186_1 = e0) & op(e4, e3) = all_186_1 & $i(all_186_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (99) with fresh symbols all_188_0, all_188_1, all_188_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (395) op(e2, e1) = all_188_2 & $i(all_188_2) & ( ~ (all_188_2 = e3) | ( ~
% 245.19/57.96 | (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 & op(e1, e3) =
% 245.19/57.96 | all_188_1 & $i(all_188_0) & $i(all_188_1)) | ( ~ (all_188_1 = e4)
% 245.19/57.96 | & op(e1, e3) = all_188_1 & $i(all_188_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (395) implies:
% 245.19/57.96 | (396) op(e2, e1) = all_188_2
% 245.19/57.96 | (397) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 245.19/57.96 | all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1))
% 245.19/57.96 | | ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (20) with fresh symbols all_190_0, all_190_1, all_190_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (398) op(e2, e1) = all_190_2 & $i(all_190_2) & ( ~ (all_190_2 = e0) | ( ~
% 245.19/57.96 | (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0, all_190_1) =
% 245.19/57.96 | all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~ (all_190_1 = e4)
% 245.19/57.96 | & op(e1, e0) = all_190_1 & $i(all_190_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (398) implies:
% 245.19/57.96 | (399) op(e2, e1) = all_190_2
% 245.19/57.96 | (400) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 245.19/57.96 | op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | (
% 245.19/57.96 | ~ (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (100) with fresh symbols all_192_0, all_192_1, all_192_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (401) op(e1, e2) = all_192_2 & $i(all_192_2) & ( ~ (all_192_2 = e3) | ( ~
% 245.19/57.96 | (all_192_0 = e4) & op(e3, all_192_1) = all_192_0 & op(e2, e3) =
% 245.19/57.96 | all_192_1 & $i(all_192_0) & $i(all_192_1)) | ( ~ (all_192_1 = e0)
% 245.19/57.96 | & op(e2, e3) = all_192_1 & $i(all_192_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (401) implies:
% 245.19/57.96 | (402) op(e1, e2) = all_192_2
% 245.19/57.96 | (403) ~ (all_192_2 = e3) | ( ~ (all_192_0 = e4) & op(e3, all_192_1) =
% 245.19/57.96 | all_192_0 & op(e2, e3) = all_192_1 & $i(all_192_0) & $i(all_192_1))
% 245.19/57.96 | | ( ~ (all_192_1 = e0) & op(e2, e3) = all_192_1 & $i(all_192_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (101) with fresh symbols all_194_0, all_194_1, all_194_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (404) op(e4, e2) = all_194_2 & $i(all_194_2) & ( ~ (all_194_2 = e3) | ( ~
% 245.19/57.96 | (all_194_0 = e1) & op(e3, all_194_1) = all_194_0 & op(e2, e3) =
% 245.19/57.96 | all_194_1 & $i(all_194_0) & $i(all_194_1)) | ( ~ (all_194_1 = e0)
% 245.19/57.96 | & op(e2, e3) = all_194_1 & $i(all_194_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (404) implies:
% 245.19/57.96 | (405) op(e4, e2) = all_194_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (103) with fresh symbols all_196_0, all_196_1, all_196_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (406) op(e4, e2) = all_196_2 & $i(all_196_2) & ( ~ (all_196_2 = e3) | ( ~
% 245.19/57.96 | (all_196_0 = e0) & op(e3, all_196_1) = all_196_0 & op(e2, e3) =
% 245.19/57.96 | all_196_1 & $i(all_196_0) & $i(all_196_1)) | ( ~ (all_196_1 = e1)
% 245.19/57.96 | & op(e2, e3) = all_196_1 & $i(all_196_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (406) implies:
% 245.19/57.96 | (407) op(e4, e2) = all_196_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (68) with fresh symbols all_198_0, all_198_1, all_198_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (408) op(e1, e0) = all_198_2 & $i(all_198_2) & ( ~ (all_198_2 = e2) | ( ~
% 245.19/57.96 | (all_198_0 = e3) & op(e2, all_198_1) = all_198_0 & op(e0, e2) =
% 245.19/57.96 | all_198_1 & $i(all_198_0) & $i(all_198_1)) | ( ~ (all_198_1 = e4)
% 245.19/57.96 | & op(e0, e2) = all_198_1 & $i(all_198_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (408) implies:
% 245.19/57.96 | (409) op(e1, e0) = all_198_2
% 245.19/57.96 | (410) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 245.19/57.96 | all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1))
% 245.19/57.96 | | ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (69) with fresh symbols all_200_0, all_200_1, all_200_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (411) op(e3, e0) = all_200_2 & $i(all_200_2) & ( ~ (all_200_2 = e2) | ( ~
% 245.19/57.96 | (all_200_0 = e1) & op(e2, all_200_1) = all_200_0 & op(e0, e2) =
% 245.19/57.96 | all_200_1 & $i(all_200_0) & $i(all_200_1)) | ( ~ (all_200_1 = e4)
% 245.19/57.96 | & op(e0, e2) = all_200_1 & $i(all_200_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (411) implies:
% 245.19/57.96 | (412) op(e3, e0) = all_200_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (71) with fresh symbols all_202_0, all_202_1, all_202_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (413) op(e4, e1) = all_202_2 & $i(all_202_2) & ( ~ (all_202_2 = e2) | ( ~
% 245.19/57.96 | (all_202_0 = e3) & op(e2, all_202_1) = all_202_0 & op(e1, e2) =
% 245.19/57.96 | all_202_1 & $i(all_202_0) & $i(all_202_1)) | ( ~ (all_202_1 = e0)
% 245.19/57.96 | & op(e1, e2) = all_202_1 & $i(all_202_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (413) implies:
% 245.19/57.96 | (414) op(e4, e1) = all_202_2
% 245.19/57.96 | (415) ~ (all_202_2 = e2) | ( ~ (all_202_0 = e3) & op(e2, all_202_1) =
% 245.19/57.96 | all_202_0 & op(e1, e2) = all_202_1 & $i(all_202_0) & $i(all_202_1))
% 245.19/57.96 | | ( ~ (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (70) with fresh symbols all_204_0, all_204_1, all_204_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (416) op(e3, e1) = all_204_2 & $i(all_204_2) & ( ~ (all_204_2 = e2) | ( ~
% 245.19/57.96 | (all_204_0 = e4) & op(e2, all_204_1) = all_204_0 & op(e1, e2) =
% 245.19/57.96 | all_204_1 & $i(all_204_0) & $i(all_204_1)) | ( ~ (all_204_1 = e0)
% 245.19/57.96 | & op(e1, e2) = all_204_1 & $i(all_204_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (416) implies:
% 245.19/57.96 | (417) op(e3, e1) = all_204_2
% 245.19/57.96 | (418) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 245.19/57.96 | all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1))
% 245.19/57.96 | | ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (102) with fresh symbols all_206_0, all_206_1, all_206_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (419) op(e0, e2) = all_206_2 & $i(all_206_2) & ( ~ (all_206_2 = e3) | ( ~
% 245.19/57.96 | (all_206_0 = e4) & op(e3, all_206_1) = all_206_0 & op(e2, e3) =
% 245.19/57.96 | all_206_1 & $i(all_206_0) & $i(all_206_1)) | ( ~ (all_206_1 = e1)
% 245.19/57.96 | & op(e2, e3) = all_206_1 & $i(all_206_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (419) implies:
% 245.19/57.96 | (420) op(e0, e2) = all_206_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (61) with fresh symbols all_208_0, all_208_1, all_208_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (421) op(e3, e4) = all_208_2 & $i(all_208_2) & ( ~ (all_208_2 = e1) | ( ~
% 245.19/57.96 | (all_208_0 = e0) & op(e4, e1) = all_208_1 & op(e1, all_208_1) =
% 245.19/57.96 | all_208_0 & $i(all_208_0) & $i(all_208_1)) | ( ~ (all_208_1 = e2)
% 245.19/57.96 | & op(e4, e1) = all_208_1 & $i(all_208_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (421) implies:
% 245.19/57.96 | (422) op(e3, e4) = all_208_2
% 245.19/57.96 | (423) ~ (all_208_2 = e1) | ( ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 &
% 245.19/57.96 | op(e1, all_208_1) = all_208_0 & $i(all_208_0) & $i(all_208_1)) | (
% 245.19/57.96 | ~ (all_208_1 = e2) & op(e4, e1) = all_208_1 & $i(all_208_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (62) with fresh symbols all_210_0, all_210_1, all_210_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (424) op(e0, e4) = all_210_2 & $i(all_210_2) & ( ~ (all_210_2 = e1) | ( ~
% 245.19/57.96 | (all_210_0 = e2) & op(e4, e1) = all_210_1 & op(e1, all_210_1) =
% 245.19/57.96 | all_210_0 & $i(all_210_0) & $i(all_210_1)) | ( ~ (all_210_1 = e3)
% 245.19/57.96 | & op(e4, e1) = all_210_1 & $i(all_210_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (424) implies:
% 245.19/57.96 | (425) op(e0, e4) = all_210_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (60) with fresh symbols all_212_0, all_212_1, all_212_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (426) op(e0, e4) = all_212_2 & $i(all_212_2) & ( ~ (all_212_2 = e1) | ( ~
% 245.19/57.96 | (all_212_0 = e3) & op(e4, e1) = all_212_1 & op(e1, all_212_1) =
% 245.19/57.96 | all_212_0 & $i(all_212_0) & $i(all_212_1)) | ( ~ (all_212_1 = e2)
% 245.19/57.96 | & op(e4, e1) = all_212_1 & $i(all_212_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (426) implies:
% 245.19/57.96 | (427) op(e0, e4) = all_212_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (47) with fresh symbols all_214_0, all_214_1, all_214_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (428) op(e4, e2) = all_214_2 & $i(all_214_2) & ( ~ (all_214_2 = e1) | ( ~
% 245.19/57.96 | (all_214_0 = e3) & op(e2, e1) = all_214_1 & op(e1, all_214_1) =
% 245.19/57.96 | all_214_0 & $i(all_214_0) & $i(all_214_1)) | ( ~ (all_214_1 = e0)
% 245.19/57.96 | & op(e2, e1) = all_214_1 & $i(all_214_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (428) implies:
% 245.19/57.96 | (429) op(e4, e2) = all_214_2
% 245.19/57.96 | (430) ~ (all_214_2 = e1) | ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 &
% 245.19/57.96 | op(e1, all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)) | (
% 245.19/57.96 | ~ (all_214_1 = e0) & op(e2, e1) = all_214_1 & $i(all_214_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (17) with fresh symbols all_216_0, all_216_1, all_216_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (431) op(e4, e1) = all_216_2 & $i(all_216_2) & ( ~ (all_216_2 = e0) | ( ~
% 245.19/57.96 | (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0, all_216_1) =
% 245.19/57.96 | all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~ (all_216_1 = e2)
% 245.19/57.96 | & op(e1, e0) = all_216_1 & $i(all_216_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (431) implies:
% 245.19/57.96 | (432) op(e4, e1) = all_216_2
% 245.19/57.96 | (433) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 245.19/57.96 | op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | (
% 245.19/57.96 | ~ (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (25) with fresh symbols all_218_0, all_218_1, all_218_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (434) op(e4, e2) = all_218_2 & $i(all_218_2) & ( ~ (all_218_2 = e0) | ( ~
% 245.19/57.96 | (all_218_0 = e1) & op(e2, e0) = all_218_1 & op(e0, all_218_1) =
% 245.19/57.96 | all_218_0 & $i(all_218_0) & $i(all_218_1)) | ( ~ (all_218_1 = e3)
% 245.19/57.96 | & op(e2, e0) = all_218_1 & $i(all_218_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (434) implies:
% 245.19/57.96 | (435) op(e4, e2) = all_218_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (27) with fresh symbols all_220_0, all_220_1, all_220_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (436) op(e3, e2) = all_220_2 & $i(all_220_2) & ( ~ (all_220_2 = e0) | ( ~
% 245.19/57.96 | (all_220_0 = e1) & op(e2, e0) = all_220_1 & op(e0, all_220_1) =
% 245.19/57.96 | all_220_0 & $i(all_220_0) & $i(all_220_1)) | ( ~ (all_220_1 = e4)
% 245.19/57.96 | & op(e2, e0) = all_220_1 & $i(all_220_1)))
% 245.19/57.96 |
% 245.19/57.96 | ALPHA: (436) implies:
% 245.19/57.96 | (437) op(e3, e2) = all_220_2
% 245.19/57.96 |
% 245.19/57.96 | DELTA: instantiating (19) with fresh symbols all_222_0, all_222_1, all_222_2
% 245.19/57.96 | gives:
% 245.19/57.96 | (438) op(e4, e1) = all_222_2 & $i(all_222_2) & ( ~ (all_222_2 = e0) | ( ~
% 245.19/57.96 | (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0, all_222_1) =
% 245.19/57.96 | all_222_0 & $i(all_222_0) & $i(all_222_1)) | ( ~ (all_222_1 = e3)
% 245.19/57.97 | & op(e1, e0) = all_222_1 & $i(all_222_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (438) implies:
% 245.19/57.97 | (439) op(e4, e1) = all_222_2
% 245.19/57.97 | (440) ~ (all_222_2 = e0) | ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 &
% 245.19/57.97 | op(e0, all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | (
% 245.19/57.97 | ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (63) with fresh symbols all_224_0, all_224_1, all_224_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (441) op(e2, e4) = all_224_2 & $i(all_224_2) & ( ~ (all_224_2 = e1) | ( ~
% 245.19/57.97 | (all_224_0 = e0) & op(e4, e1) = all_224_1 & op(e1, all_224_1) =
% 245.19/57.97 | all_224_0 & $i(all_224_0) & $i(all_224_1)) | ( ~ (all_224_1 = e3)
% 245.19/57.97 | & op(e4, e1) = all_224_1 & $i(all_224_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (441) implies:
% 245.19/57.97 | (442) op(e2, e4) = all_224_2
% 245.19/57.97 | (443) ~ (all_224_2 = e1) | ( ~ (all_224_0 = e0) & op(e4, e1) = all_224_1 &
% 245.19/57.97 | op(e1, all_224_1) = all_224_0 & $i(all_224_0) & $i(all_224_1)) | (
% 245.19/57.97 | ~ (all_224_1 = e3) & op(e4, e1) = all_224_1 & $i(all_224_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (64) with fresh symbols all_226_0, all_226_1, all_226_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (444) op(e3, e0) = all_226_2 & $i(all_226_2) & ( ~ (all_226_2 = e2) | ( ~
% 245.19/57.97 | (all_226_0 = e4) & op(e2, all_226_1) = all_226_0 & op(e0, e2) =
% 245.19/57.97 | all_226_1 & $i(all_226_0) & $i(all_226_1)) | ( ~ (all_226_1 = e1)
% 245.19/57.97 | & op(e0, e2) = all_226_1 & $i(all_226_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (444) implies:
% 245.19/57.97 | (445) op(e3, e0) = all_226_2
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (113) with fresh symbols all_228_0, all_228_1, all_228_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (446) op(e3, e0) = all_228_2 & $i(all_228_2) & ( ~ (all_228_2 = e4) | ( ~
% 245.19/57.97 | (all_228_0 = e2) & op(e4, all_228_1) = all_228_0 & op(e0, e4) =
% 245.19/57.97 | all_228_1 & $i(all_228_0) & $i(all_228_1)) | ( ~ (all_228_1 = e1)
% 245.19/57.97 | & op(e0, e4) = all_228_1 & $i(all_228_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (446) implies:
% 245.19/57.97 | (447) op(e3, e0) = all_228_2
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (74) with fresh symbols all_230_0, all_230_1, all_230_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (448) op(e0, e1) = all_230_2 & $i(all_230_2) & ( ~ (all_230_2 = e2) | ( ~
% 245.19/57.97 | (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1, e2) =
% 245.19/57.97 | all_230_1 & $i(all_230_0) & $i(all_230_1)) | ( ~ (all_230_1 = e4)
% 245.19/57.97 | & op(e1, e2) = all_230_1 & $i(all_230_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (448) implies:
% 245.19/57.97 | (449) op(e0, e1) = all_230_2
% 245.19/57.97 | (450) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 245.19/57.97 | all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1))
% 245.19/57.97 | | ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (90) with fresh symbols all_232_0, all_232_1, all_232_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (451) op(e1, e0) = all_232_2 & $i(all_232_2) & ( ~ (all_232_2 = e3) | ( ~
% 245.19/57.97 | (all_232_0 = e4) & op(e3, all_232_1) = all_232_0 & op(e0, e3) =
% 245.19/57.97 | all_232_1 & $i(all_232_0) & $i(all_232_1)) | ( ~ (all_232_1 = e2)
% 245.19/57.97 | & op(e0, e3) = all_232_1 & $i(all_232_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (451) implies:
% 245.19/57.97 | (452) op(e1, e0) = all_232_2
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (46) with fresh symbols all_234_0, all_234_1, all_234_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (453) op(e3, e2) = all_234_2 & $i(all_234_2) & ( ~ (all_234_2 = e1) | ( ~
% 245.19/57.97 | (all_234_0 = e4) & op(e2, e1) = all_234_1 & op(e1, all_234_1) =
% 245.19/57.97 | all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~ (all_234_1 = e0)
% 245.19/57.97 | & op(e2, e1) = all_234_1 & $i(all_234_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (453) implies:
% 245.19/57.97 | (454) op(e3, e2) = all_234_2
% 245.19/57.97 | (455) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 245.19/57.97 | op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | (
% 245.19/57.97 | ~ (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (41) with fresh symbols all_236_0, all_236_1, all_236_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (456) op(e4, e0) = all_236_2 & $i(all_236_2) & ( ~ (all_236_2 = e1) | ( ~
% 245.19/57.97 | (all_236_0 = e3) & op(e1, all_236_1) = all_236_0 & op(e0, e1) =
% 245.19/57.97 | all_236_1 & $i(all_236_0) & $i(all_236_1)) | ( ~ (all_236_1 = e2)
% 245.19/57.97 | & op(e0, e1) = all_236_1 & $i(all_236_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (456) implies:
% 245.19/57.97 | (457) op(e4, e0) = all_236_2
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (43) with fresh symbols all_238_0, all_238_1, all_238_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (458) op(e4, e0) = all_238_2 & $i(all_238_2) & ( ~ (all_238_2 = e1) | ( ~
% 245.19/57.97 | (all_238_0 = e2) & op(e1, all_238_1) = all_238_0 & op(e0, e1) =
% 245.19/57.97 | all_238_1 & $i(all_238_0) & $i(all_238_1)) | ( ~ (all_238_1 = e3)
% 245.19/57.97 | & op(e0, e1) = all_238_1 & $i(all_238_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (458) implies:
% 245.19/57.97 | (459) op(e4, e0) = all_238_2
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (115) with fresh symbols all_240_0, all_240_1, all_240_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (460) op(e3, e0) = all_240_2 & $i(all_240_2) & ( ~ (all_240_2 = e4) | ( ~
% 245.19/57.97 | (all_240_0 = e1) & op(e4, all_240_1) = all_240_0 & op(e0, e4) =
% 245.19/57.97 | all_240_1 & $i(all_240_0) & $i(all_240_1)) | ( ~ (all_240_1 = e2)
% 245.19/57.97 | & op(e0, e4) = all_240_1 & $i(all_240_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (460) implies:
% 245.19/57.97 | (461) op(e3, e0) = all_240_2
% 245.19/57.97 | (462) ~ (all_240_2 = e4) | ( ~ (all_240_0 = e1) & op(e4, all_240_1) =
% 245.19/57.97 | all_240_0 & op(e0, e4) = all_240_1 & $i(all_240_0) & $i(all_240_1))
% 245.19/57.97 | | ( ~ (all_240_1 = e2) & op(e0, e4) = all_240_1 & $i(all_240_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (118) with fresh symbols all_242_0, all_242_1, all_242_2
% 245.19/57.97 | gives:
% 245.19/57.97 | (463) op(e2, e1) = all_242_2 & $i(all_242_2) & ( ~ (all_242_2 = e4) | ( ~
% 245.19/57.97 | (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 245.19/57.97 | all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0)
% 245.19/57.97 | & op(e1, e4) = all_242_1 & $i(all_242_1)))
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (463) implies:
% 245.19/57.97 | (464) op(e2, e1) = all_242_2
% 245.19/57.97 | (465) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 245.19/57.97 | all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1))
% 245.19/57.97 | | ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (3) with fresh symbols all_244_0, all_244_1, all_244_2,
% 245.19/57.97 | all_244_3, all_244_4, all_244_5, all_244_6, all_244_7, all_244_8,
% 245.19/57.97 | all_244_9, all_244_10, all_244_11, all_244_12, all_244_13, all_244_14,
% 245.19/57.97 | all_244_15, all_244_16, all_244_17, all_244_18, all_244_19, all_244_20,
% 245.19/57.97 | all_244_21, all_244_22, all_244_23, all_244_24 gives:
% 245.19/57.97 | (466) op(all_244_0, all_244_0) = e4 & op(all_244_1, all_244_2) = e4 &
% 245.19/57.97 | op(all_244_2, all_244_1) = e3 & op(all_244_3, all_244_3) = e3 &
% 245.19/57.97 | op(all_244_4, all_244_5) = e4 & op(all_244_5, all_244_4) = e2 &
% 245.19/57.97 | op(all_244_6, all_244_7) = e3 & op(all_244_7, all_244_6) = e2 &
% 245.19/57.97 | op(all_244_8, all_244_8) = e2 & op(all_244_9, all_244_10) = e4 &
% 245.19/57.97 | op(all_244_10, all_244_9) = e1 & op(all_244_11, all_244_12) = e3 &
% 245.19/57.97 | op(all_244_12, all_244_11) = e1 & op(all_244_13, all_244_14) = e2 &
% 245.19/57.97 | op(all_244_14, all_244_13) = e1 & op(all_244_15, all_244_15) = e1 &
% 245.19/57.97 | op(all_244_16, all_244_17) = e4 & op(all_244_17, all_244_16) = e0 &
% 245.19/57.97 | op(all_244_18, all_244_19) = e3 & op(all_244_19, all_244_18) = e0 &
% 245.19/57.97 | op(all_244_20, all_244_21) = e2 & op(all_244_21, all_244_20) = e0 &
% 245.19/57.97 | op(all_244_22, all_244_23) = e1 & op(all_244_23, all_244_22) = e0 &
% 245.19/57.97 | op(all_244_24, all_244_24) = e0 & op(e4, e4) = all_244_0 & op(e4, e3)
% 245.19/57.97 | = all_244_2 & op(e4, e2) = all_244_5 & op(e4, e1) = all_244_10 &
% 245.19/57.97 | op(e4, e0) = all_244_17 & op(e3, e4) = all_244_1 & op(e3, e3) =
% 245.19/57.97 | all_244_3 & op(e3, e2) = all_244_7 & op(e3, e1) = all_244_12 & op(e3,
% 245.19/57.97 | e0) = all_244_19 & op(e2, e4) = all_244_4 & op(e2, e3) = all_244_6
% 245.19/57.97 | & op(e2, e2) = all_244_8 & op(e2, e1) = all_244_14 & op(e2, e0) =
% 245.19/57.97 | all_244_21 & op(e1, e4) = all_244_9 & op(e1, e3) = all_244_11 &
% 245.19/57.97 | op(e1, e2) = all_244_13 & op(e1, e1) = all_244_15 & op(e1, e0) =
% 245.19/57.97 | all_244_23 & op(e0, e4) = all_244_16 & op(e0, e3) = all_244_18 &
% 245.19/57.97 | op(e0, e2) = all_244_20 & op(e0, e1) = all_244_22 & op(e0, e0) =
% 245.19/57.97 | all_244_24 & $i(all_244_0) & $i(all_244_1) & $i(all_244_2) &
% 245.19/57.97 | $i(all_244_3) & $i(all_244_4) & $i(all_244_5) & $i(all_244_6) &
% 245.19/57.97 | $i(all_244_7) & $i(all_244_8) & $i(all_244_9) & $i(all_244_10) &
% 245.19/57.97 | $i(all_244_11) & $i(all_244_12) & $i(all_244_13) & $i(all_244_14) &
% 245.19/57.97 | $i(all_244_15) & $i(all_244_16) & $i(all_244_17) & $i(all_244_18) &
% 245.19/57.97 | $i(all_244_19) & $i(all_244_20) & $i(all_244_21) & $i(all_244_22) &
% 245.19/57.97 | $i(all_244_23) & $i(all_244_24)
% 245.19/57.97 |
% 245.19/57.97 | ALPHA: (466) implies:
% 245.19/57.97 | (467) op(e0, e0) = all_244_24
% 245.19/57.97 | (468) op(e0, e1) = all_244_22
% 245.19/57.97 | (469) op(e0, e2) = all_244_20
% 245.19/57.97 | (470) op(e0, e3) = all_244_18
% 245.19/57.97 | (471) op(e0, e4) = all_244_16
% 245.19/57.97 | (472) op(e1, e0) = all_244_23
% 245.19/57.97 | (473) op(e1, e1) = all_244_15
% 245.19/57.97 | (474) op(e1, e2) = all_244_13
% 245.19/57.97 | (475) op(e1, e3) = all_244_11
% 245.19/57.97 | (476) op(e1, e4) = all_244_9
% 245.19/57.97 | (477) op(e2, e0) = all_244_21
% 245.19/57.97 | (478) op(e2, e1) = all_244_14
% 245.19/57.97 | (479) op(e2, e2) = all_244_8
% 245.19/57.97 | (480) op(e2, e3) = all_244_6
% 245.19/57.97 | (481) op(e2, e4) = all_244_4
% 245.19/57.97 | (482) op(e3, e0) = all_244_19
% 245.19/57.97 | (483) op(e3, e1) = all_244_12
% 245.19/57.97 | (484) op(e3, e2) = all_244_7
% 245.19/57.97 | (485) op(e3, e3) = all_244_3
% 245.19/57.97 | (486) op(e3, e4) = all_244_1
% 245.19/57.97 | (487) op(e4, e0) = all_244_17
% 245.19/57.97 | (488) op(e4, e1) = all_244_10
% 245.19/57.97 | (489) op(e4, e2) = all_244_5
% 245.19/57.97 | (490) op(e4, e3) = all_244_2
% 245.19/57.97 | (491) op(e4, e4) = all_244_0
% 245.19/57.97 | (492) op(all_244_24, all_244_24) = e0
% 245.19/57.97 | (493) op(all_244_23, all_244_22) = e0
% 245.19/57.97 | (494) op(all_244_22, all_244_23) = e1
% 245.19/57.97 | (495) op(all_244_21, all_244_20) = e0
% 245.19/57.97 | (496) op(all_244_20, all_244_21) = e2
% 245.19/57.97 | (497) op(all_244_19, all_244_18) = e0
% 245.19/57.97 | (498) op(all_244_18, all_244_19) = e3
% 245.19/57.97 | (499) op(all_244_17, all_244_16) = e0
% 245.19/57.97 | (500) op(all_244_16, all_244_17) = e4
% 245.19/57.97 | (501) op(all_244_15, all_244_15) = e1
% 245.19/57.97 | (502) op(all_244_14, all_244_13) = e1
% 245.19/57.97 | (503) op(all_244_13, all_244_14) = e2
% 245.19/57.97 | (504) op(all_244_12, all_244_11) = e1
% 245.19/57.97 | (505) op(all_244_11, all_244_12) = e3
% 245.19/57.97 | (506) op(all_244_10, all_244_9) = e1
% 245.19/57.97 | (507) op(all_244_9, all_244_10) = e4
% 245.19/57.97 | (508) op(all_244_8, all_244_8) = e2
% 245.19/57.97 | (509) op(all_244_7, all_244_6) = e2
% 245.19/57.97 | (510) op(all_244_6, all_244_7) = e3
% 245.19/57.97 | (511) op(all_244_5, all_244_4) = e2
% 245.19/57.97 | (512) op(all_244_4, all_244_5) = e4
% 245.19/57.97 | (513) op(all_244_3, all_244_3) = e3
% 245.19/57.97 | (514) op(all_244_2, all_244_1) = e3
% 245.19/57.97 | (515) op(all_244_1, all_244_2) = e4
% 245.19/57.97 |
% 245.19/57.97 | DELTA: instantiating (15) with fresh symbols all_246_0, all_246_1, all_246_2,
% 245.19/57.97 | all_246_3, all_246_4, all_246_5, all_246_6, all_246_7, all_246_8,
% 245.19/57.97 | all_246_9, all_246_10, all_246_11, all_246_12, all_246_13, all_246_14,
% 245.19/57.97 | all_246_15, all_246_16, all_246_17, all_246_18, all_246_19, all_246_20,
% 245.19/57.97 | all_246_21, all_246_22, all_246_23, all_246_24 gives:
% 245.19/57.98 | (516) op(all_246_0, e4) = e4 & op(all_246_1, e3) = e4 & op(all_246_2, e2) =
% 245.19/57.98 | e4 & op(all_246_3, e1) = e4 & op(all_246_4, e0) = e4 & op(all_246_5,
% 245.19/57.98 | e4) = e3 & op(all_246_6, e3) = e3 & op(all_246_7, e2) = e3 &
% 245.19/57.98 | op(all_246_8, e1) = e3 & op(all_246_9, e0) = e3 & op(all_246_10, e4)
% 245.19/57.98 | = e2 & op(all_246_11, e3) = e2 & op(all_246_12, e2) = e2 &
% 245.19/57.98 | op(all_246_13, e1) = e2 & op(all_246_14, e0) = e2 & op(all_246_15,
% 245.19/57.98 | e4) = e1 & op(all_246_16, e3) = e1 & op(all_246_17, e2) = e1 &
% 245.19/57.98 | op(all_246_18, e1) = e1 & op(all_246_19, e0) = e1 & op(all_246_20,
% 245.19/57.98 | e4) = e0 & op(all_246_21, e3) = e0 & op(all_246_22, e2) = e0 &
% 245.19/57.98 | op(all_246_23, e1) = e0 & op(all_246_24, e0) = e0 & op(e4, e4) =
% 245.19/57.98 | all_246_0 & op(e4, e3) = all_246_1 & op(e4, e2) = all_246_2 & op(e4,
% 245.19/57.98 | e1) = all_246_3 & op(e4, e0) = all_246_4 & op(e3, e4) = all_246_5 &
% 245.19/57.98 | op(e3, e3) = all_246_6 & op(e3, e2) = all_246_7 & op(e3, e1) =
% 245.19/57.98 | all_246_8 & op(e3, e0) = all_246_9 & op(e2, e4) = all_246_10 & op(e2,
% 245.19/57.98 | e3) = all_246_11 & op(e2, e2) = all_246_12 & op(e2, e1) =
% 245.19/57.98 | all_246_13 & op(e2, e0) = all_246_14 & op(e1, e4) = all_246_15 &
% 245.19/57.98 | op(e1, e3) = all_246_16 & op(e1, e2) = all_246_17 & op(e1, e1) =
% 245.19/57.98 | all_246_18 & op(e1, e0) = all_246_19 & op(e0, e4) = all_246_20 &
% 245.19/57.98 | op(e0, e3) = all_246_21 & op(e0, e2) = all_246_22 & op(e0, e1) =
% 245.19/57.98 | all_246_23 & op(e0, e0) = all_246_24 & $i(all_246_0) & $i(all_246_1)
% 245.19/57.98 | & $i(all_246_2) & $i(all_246_3) & $i(all_246_4) & $i(all_246_5) &
% 245.19/57.98 | $i(all_246_6) & $i(all_246_7) & $i(all_246_8) & $i(all_246_9) &
% 245.19/57.98 | $i(all_246_10) & $i(all_246_11) & $i(all_246_12) & $i(all_246_13) &
% 245.19/57.98 | $i(all_246_14) & $i(all_246_15) & $i(all_246_16) & $i(all_246_17) &
% 245.19/57.98 | $i(all_246_18) & $i(all_246_19) & $i(all_246_20) & $i(all_246_21) &
% 245.19/57.98 | $i(all_246_22) & $i(all_246_23) & $i(all_246_24)
% 245.19/57.98 |
% 245.19/57.98 | ALPHA: (516) implies:
% 245.19/57.98 | (517) op(e0, e0) = all_246_24
% 245.19/57.98 | (518) op(e0, e1) = all_246_23
% 245.19/57.98 | (519) op(e0, e2) = all_246_22
% 245.19/57.98 | (520) op(e0, e3) = all_246_21
% 245.19/57.98 | (521) op(e0, e4) = all_246_20
% 245.19/57.98 | (522) op(e1, e0) = all_246_19
% 245.19/57.98 | (523) op(e1, e1) = all_246_18
% 245.19/57.98 | (524) op(e1, e2) = all_246_17
% 245.19/57.98 | (525) op(e1, e3) = all_246_16
% 245.19/57.98 | (526) op(e1, e4) = all_246_15
% 245.19/57.98 | (527) op(e2, e0) = all_246_14
% 245.19/57.98 | (528) op(e2, e1) = all_246_13
% 245.19/57.98 | (529) op(e2, e2) = all_246_12
% 245.19/57.98 | (530) op(e2, e3) = all_246_11
% 245.19/57.98 | (531) op(e2, e4) = all_246_10
% 245.19/57.98 | (532) op(e3, e0) = all_246_9
% 245.19/57.98 | (533) op(e3, e1) = all_246_8
% 245.19/57.98 | (534) op(e3, e2) = all_246_7
% 245.19/57.98 | (535) op(e3, e3) = all_246_6
% 245.19/57.98 | (536) op(e3, e4) = all_246_5
% 245.19/57.98 | (537) op(e4, e0) = all_246_4
% 245.19/57.98 | (538) op(e4, e1) = all_246_3
% 245.19/57.98 | (539) op(e4, e2) = all_246_2
% 245.19/57.98 | (540) op(e4, e3) = all_246_1
% 245.19/57.98 | (541) op(e4, e4) = all_246_0
% 245.19/57.98 | (542) op(all_246_23, e1) = e0
% 245.19/57.98 | (543) op(all_246_22, e2) = e0
% 245.19/57.98 | (544) op(all_246_21, e3) = e0
% 245.19/57.98 | (545) op(all_246_20, e4) = e0
% 245.19/57.98 | (546) op(all_246_19, e0) = e1
% 245.19/57.98 | (547) op(all_246_17, e2) = e1
% 245.19/57.98 | (548) op(all_246_16, e3) = e1
% 245.19/57.98 | (549) op(all_246_15, e4) = e1
% 245.19/57.98 | (550) op(all_246_14, e0) = e2
% 245.19/57.98 | (551) op(all_246_13, e1) = e2
% 245.19/57.98 | (552) op(all_246_11, e3) = e2
% 245.19/57.98 | (553) op(all_246_10, e4) = e2
% 245.19/57.98 | (554) op(all_246_9, e0) = e3
% 245.19/57.98 | (555) op(all_246_8, e1) = e3
% 245.19/57.98 | (556) op(all_246_7, e2) = e3
% 245.19/57.98 | (557) op(all_246_5, e4) = e3
% 245.19/57.98 | (558) op(all_246_4, e0) = e4
% 245.19/57.98 | (559) op(all_246_3, e1) = e4
% 245.19/57.98 | (560) op(all_246_2, e2) = e4
% 245.19/57.98 | (561) op(all_246_1, e3) = e4
% 245.19/57.98 |
% 245.19/57.98 | DELTA: instantiating (4) with fresh symbols all_248_0, all_248_1, all_248_2,
% 245.19/57.98 | all_248_3, all_248_4, all_248_5, all_248_6, all_248_7, all_248_8,
% 245.19/57.98 | all_248_9, all_248_10, all_248_11, all_248_12, all_248_13, all_248_14,
% 245.19/57.98 | all_248_15, all_248_16, all_248_17, all_248_18, all_248_19, all_248_20,
% 245.19/57.98 | all_248_21, all_248_22, all_248_23, all_248_24 gives:
% 245.19/57.98 | (562) ~ (all_248_0 = all_248_1) & ~ (all_248_0 = all_248_2) & ~
% 245.19/57.98 | (all_248_0 = all_248_3) & ~ (all_248_0 = all_248_4) & ~ (all_248_0
% 245.19/57.98 | = all_248_5) & ~ (all_248_0 = all_248_10) & ~ (all_248_0 =
% 245.19/57.98 | all_248_15) & ~ (all_248_0 = all_248_20) & ~ (all_248_1 =
% 245.19/57.98 | all_248_2) & ~ (all_248_1 = all_248_3) & ~ (all_248_1 =
% 245.19/57.98 | all_248_4) & ~ (all_248_1 = all_248_6) & ~ (all_248_1 =
% 245.19/57.98 | all_248_11) & ~ (all_248_1 = all_248_16) & ~ (all_248_1 =
% 245.19/57.98 | all_248_21) & ~ (all_248_2 = all_248_3) & ~ (all_248_2 =
% 245.19/57.98 | all_248_4) & ~ (all_248_2 = all_248_7) & ~ (all_248_2 =
% 245.19/57.98 | all_248_12) & ~ (all_248_2 = all_248_17) & ~ (all_248_2 =
% 245.19/57.98 | all_248_22) & ~ (all_248_3 = all_248_4) & ~ (all_248_3 =
% 245.19/57.98 | all_248_8) & ~ (all_248_3 = all_248_13) & ~ (all_248_3 =
% 245.19/57.98 | all_248_18) & ~ (all_248_3 = all_248_23) & ~ (all_248_4 =
% 245.19/57.98 | all_248_9) & ~ (all_248_4 = all_248_14) & ~ (all_248_4 =
% 245.19/57.98 | all_248_19) & ~ (all_248_4 = all_248_24) & ~ (all_248_5 =
% 245.19/57.98 | all_248_6) & ~ (all_248_5 = all_248_7) & ~ (all_248_5 =
% 245.19/57.98 | all_248_8) & ~ (all_248_5 = all_248_9) & ~ (all_248_5 =
% 245.19/57.98 | all_248_10) & ~ (all_248_5 = all_248_15) & ~ (all_248_5 =
% 245.19/57.98 | all_248_20) & ~ (all_248_6 = all_248_7) & ~ (all_248_6 =
% 245.19/57.98 | all_248_8) & ~ (all_248_6 = all_248_9) & ~ (all_248_6 =
% 245.19/57.98 | all_248_11) & ~ (all_248_6 = all_248_16) & ~ (all_248_6 =
% 245.19/57.98 | all_248_21) & ~ (all_248_7 = all_248_8) & ~ (all_248_7 =
% 245.19/57.98 | all_248_9) & ~ (all_248_7 = all_248_12) & ~ (all_248_7 =
% 245.19/57.98 | all_248_17) & ~ (all_248_7 = all_248_22) & ~ (all_248_8 =
% 245.19/57.98 | all_248_9) & ~ (all_248_8 = all_248_13) & ~ (all_248_8 =
% 245.19/57.98 | all_248_18) & ~ (all_248_8 = all_248_23) & ~ (all_248_9 =
% 245.19/57.98 | all_248_14) & ~ (all_248_9 = all_248_19) & ~ (all_248_9 =
% 245.19/57.98 | all_248_24) & ~ (all_248_10 = all_248_11) & ~ (all_248_10 =
% 245.19/57.98 | all_248_12) & ~ (all_248_10 = all_248_13) & ~ (all_248_10 =
% 245.19/57.98 | all_248_14) & ~ (all_248_10 = all_248_15) & ~ (all_248_10 =
% 245.19/57.98 | all_248_20) & ~ (all_248_11 = all_248_12) & ~ (all_248_11 =
% 245.19/57.98 | all_248_13) & ~ (all_248_11 = all_248_14) & ~ (all_248_11 =
% 245.19/57.98 | all_248_16) & ~ (all_248_11 = all_248_21) & ~ (all_248_12 =
% 245.19/57.98 | all_248_13) & ~ (all_248_12 = all_248_14) & ~ (all_248_12 =
% 245.19/57.98 | all_248_17) & ~ (all_248_12 = all_248_22) & ~ (all_248_13 =
% 245.19/57.98 | all_248_14) & ~ (all_248_13 = all_248_18) & ~ (all_248_13 =
% 245.19/57.98 | all_248_23) & ~ (all_248_14 = all_248_19) & ~ (all_248_14 =
% 245.19/57.98 | all_248_24) & ~ (all_248_15 = all_248_16) & ~ (all_248_15 =
% 245.19/57.98 | all_248_17) & ~ (all_248_15 = all_248_18) & ~ (all_248_15 =
% 245.19/57.98 | all_248_19) & ~ (all_248_15 = all_248_20) & ~ (all_248_16 =
% 245.19/57.98 | all_248_17) & ~ (all_248_16 = all_248_18) & ~ (all_248_16 =
% 245.19/57.98 | all_248_19) & ~ (all_248_16 = all_248_21) & ~ (all_248_17 =
% 245.19/57.98 | all_248_18) & ~ (all_248_17 = all_248_19) & ~ (all_248_17 =
% 245.19/57.98 | all_248_22) & ~ (all_248_18 = all_248_19) & ~ (all_248_18 =
% 245.19/57.98 | all_248_23) & ~ (all_248_19 = all_248_24) & ~ (all_248_20 =
% 245.19/57.98 | all_248_21) & ~ (all_248_20 = all_248_22) & ~ (all_248_20 =
% 245.19/57.98 | all_248_23) & ~ (all_248_20 = all_248_24) & ~ (all_248_21 =
% 245.19/57.98 | all_248_22) & ~ (all_248_21 = all_248_23) & ~ (all_248_21 =
% 245.19/57.98 | all_248_24) & ~ (all_248_22 = all_248_23) & ~ (all_248_22 =
% 245.19/57.98 | all_248_24) & ~ (all_248_23 = all_248_24) & op(e4, e4) = all_248_0
% 245.19/57.98 | & op(e4, e3) = all_248_5 & op(e4, e2) = all_248_10 & op(e4, e1) =
% 245.19/57.98 | all_248_15 & op(e4, e0) = all_248_20 & op(e3, e4) = all_248_1 &
% 245.19/57.98 | op(e3, e3) = all_248_6 & op(e3, e2) = all_248_11 & op(e3, e1) =
% 245.19/57.98 | all_248_16 & op(e3, e0) = all_248_21 & op(e2, e4) = all_248_2 &
% 245.19/57.98 | op(e2, e3) = all_248_7 & op(e2, e2) = all_248_12 & op(e2, e1) =
% 245.19/57.98 | all_248_17 & op(e2, e0) = all_248_22 & op(e1, e4) = all_248_3 &
% 245.19/57.98 | op(e1, e3) = all_248_8 & op(e1, e2) = all_248_13 & op(e1, e1) =
% 245.19/57.98 | all_248_18 & op(e1, e0) = all_248_23 & op(e0, e4) = all_248_4 &
% 245.19/57.98 | op(e0, e3) = all_248_9 & op(e0, e2) = all_248_14 & op(e0, e1) =
% 245.19/57.98 | all_248_19 & op(e0, e0) = all_248_24 & $i(all_248_0) & $i(all_248_1)
% 245.19/57.98 | & $i(all_248_2) & $i(all_248_3) & $i(all_248_4) & $i(all_248_5) &
% 245.19/57.98 | $i(all_248_6) & $i(all_248_7) & $i(all_248_8) & $i(all_248_9) &
% 245.19/57.98 | $i(all_248_10) & $i(all_248_11) & $i(all_248_12) & $i(all_248_13) &
% 245.19/57.98 | $i(all_248_14) & $i(all_248_15) & $i(all_248_16) & $i(all_248_17) &
% 245.19/57.98 | $i(all_248_18) & $i(all_248_19) & $i(all_248_20) & $i(all_248_21) &
% 245.19/57.98 | $i(all_248_22) & $i(all_248_23) & $i(all_248_24)
% 245.19/57.98 |
% 245.19/57.98 | ALPHA: (562) implies:
% 245.19/57.98 | (563) ~ (all_248_23 = all_248_24)
% 245.19/57.98 | (564) ~ (all_248_22 = all_248_24)
% 245.19/57.98 | (565) ~ (all_248_22 = all_248_23)
% 245.19/57.98 | (566) ~ (all_248_21 = all_248_24)
% 245.19/57.98 | (567) ~ (all_248_21 = all_248_23)
% 245.19/57.98 | (568) ~ (all_248_21 = all_248_22)
% 245.19/57.98 | (569) ~ (all_248_20 = all_248_24)
% 245.19/57.98 | (570) ~ (all_248_20 = all_248_23)
% 245.19/57.98 | (571) ~ (all_248_20 = all_248_22)
% 245.19/57.98 | (572) ~ (all_248_20 = all_248_21)
% 245.19/57.98 | (573) ~ (all_248_19 = all_248_24)
% 245.19/57.98 | (574) ~ (all_248_18 = all_248_23)
% 245.19/57.98 | (575) ~ (all_248_18 = all_248_19)
% 245.19/57.98 | (576) ~ (all_248_17 = all_248_22)
% 245.19/57.98 | (577) ~ (all_248_17 = all_248_19)
% 245.19/57.98 | (578) ~ (all_248_17 = all_248_18)
% 245.19/57.98 | (579) ~ (all_248_16 = all_248_21)
% 245.19/57.98 | (580) ~ (all_248_16 = all_248_19)
% 245.19/57.98 | (581) ~ (all_248_16 = all_248_18)
% 245.19/57.98 | (582) ~ (all_248_16 = all_248_17)
% 245.19/57.98 | (583) ~ (all_248_15 = all_248_20)
% 245.19/57.98 | (584) ~ (all_248_15 = all_248_19)
% 245.19/57.98 | (585) ~ (all_248_15 = all_248_18)
% 245.19/57.98 | (586) ~ (all_248_15 = all_248_17)
% 245.19/57.98 | (587) ~ (all_248_15 = all_248_16)
% 245.19/57.98 | (588) ~ (all_248_14 = all_248_24)
% 245.19/57.98 | (589) ~ (all_248_14 = all_248_19)
% 245.19/57.98 | (590) ~ (all_248_13 = all_248_23)
% 245.19/57.98 | (591) ~ (all_248_13 = all_248_18)
% 245.19/57.98 | (592) ~ (all_248_13 = all_248_14)
% 245.19/57.98 | (593) ~ (all_248_12 = all_248_22)
% 245.19/57.98 | (594) ~ (all_248_12 = all_248_17)
% 245.19/57.98 | (595) ~ (all_248_12 = all_248_14)
% 245.19/57.98 | (596) ~ (all_248_12 = all_248_13)
% 245.19/57.98 | (597) ~ (all_248_11 = all_248_21)
% 245.19/57.98 | (598) ~ (all_248_11 = all_248_16)
% 245.19/57.98 | (599) ~ (all_248_11 = all_248_14)
% 245.19/57.98 | (600) ~ (all_248_11 = all_248_13)
% 245.19/57.98 | (601) ~ (all_248_11 = all_248_12)
% 245.19/57.98 | (602) ~ (all_248_10 = all_248_20)
% 245.19/57.98 | (603) ~ (all_248_10 = all_248_15)
% 245.19/57.98 | (604) ~ (all_248_10 = all_248_14)
% 245.19/57.98 | (605) ~ (all_248_10 = all_248_13)
% 245.19/57.98 | (606) ~ (all_248_10 = all_248_12)
% 245.19/57.98 | (607) ~ (all_248_10 = all_248_11)
% 245.19/57.98 | (608) ~ (all_248_9 = all_248_24)
% 245.19/57.98 | (609) ~ (all_248_9 = all_248_19)
% 245.19/57.98 | (610) ~ (all_248_9 = all_248_14)
% 245.19/57.98 | (611) ~ (all_248_8 = all_248_23)
% 245.19/57.98 | (612) ~ (all_248_8 = all_248_18)
% 245.19/57.98 | (613) ~ (all_248_8 = all_248_13)
% 245.19/57.98 | (614) ~ (all_248_8 = all_248_9)
% 245.19/57.98 | (615) ~ (all_248_7 = all_248_22)
% 245.19/57.98 | (616) ~ (all_248_7 = all_248_17)
% 245.19/57.98 | (617) ~ (all_248_7 = all_248_12)
% 245.19/57.98 | (618) ~ (all_248_7 = all_248_9)
% 245.19/57.98 | (619) ~ (all_248_7 = all_248_8)
% 245.19/57.98 | (620) ~ (all_248_6 = all_248_21)
% 245.19/57.98 | (621) ~ (all_248_6 = all_248_16)
% 245.19/57.98 | (622) ~ (all_248_6 = all_248_11)
% 245.19/57.98 | (623) ~ (all_248_6 = all_248_9)
% 245.19/57.98 | (624) ~ (all_248_6 = all_248_8)
% 245.19/57.98 | (625) ~ (all_248_6 = all_248_7)
% 245.19/57.98 | (626) ~ (all_248_5 = all_248_20)
% 245.19/57.98 | (627) ~ (all_248_5 = all_248_15)
% 245.19/57.98 | (628) ~ (all_248_5 = all_248_10)
% 245.19/57.98 | (629) ~ (all_248_5 = all_248_9)
% 245.19/57.98 | (630) ~ (all_248_5 = all_248_8)
% 245.19/57.98 | (631) ~ (all_248_5 = all_248_7)
% 245.19/57.98 | (632) ~ (all_248_5 = all_248_6)
% 245.19/57.98 | (633) ~ (all_248_4 = all_248_24)
% 245.19/57.98 | (634) ~ (all_248_4 = all_248_19)
% 245.19/57.98 | (635) ~ (all_248_4 = all_248_14)
% 245.19/57.98 | (636) ~ (all_248_4 = all_248_9)
% 245.19/57.98 | (637) ~ (all_248_3 = all_248_23)
% 245.19/57.98 | (638) ~ (all_248_3 = all_248_18)
% 245.19/57.98 | (639) ~ (all_248_3 = all_248_13)
% 245.19/57.98 | (640) ~ (all_248_3 = all_248_8)
% 245.19/57.98 | (641) ~ (all_248_3 = all_248_4)
% 245.19/57.98 | (642) ~ (all_248_2 = all_248_22)
% 245.19/57.98 | (643) ~ (all_248_2 = all_248_17)
% 245.19/57.98 | (644) ~ (all_248_2 = all_248_12)
% 245.19/57.98 | (645) ~ (all_248_2 = all_248_7)
% 245.19/57.98 | (646) ~ (all_248_2 = all_248_4)
% 245.19/57.98 | (647) ~ (all_248_2 = all_248_3)
% 245.19/57.98 | (648) ~ (all_248_1 = all_248_21)
% 245.19/57.98 | (649) ~ (all_248_1 = all_248_16)
% 245.19/57.98 | (650) ~ (all_248_1 = all_248_11)
% 245.19/57.98 | (651) ~ (all_248_1 = all_248_6)
% 245.19/57.99 | (652) ~ (all_248_1 = all_248_4)
% 245.19/57.99 | (653) ~ (all_248_1 = all_248_3)
% 245.19/57.99 | (654) ~ (all_248_1 = all_248_2)
% 245.19/57.99 | (655) ~ (all_248_0 = all_248_20)
% 245.19/57.99 | (656) ~ (all_248_0 = all_248_15)
% 245.19/57.99 | (657) ~ (all_248_0 = all_248_10)
% 245.19/57.99 | (658) ~ (all_248_0 = all_248_5)
% 245.19/57.99 | (659) ~ (all_248_0 = all_248_4)
% 245.19/57.99 | (660) ~ (all_248_0 = all_248_3)
% 245.19/57.99 | (661) ~ (all_248_0 = all_248_2)
% 245.19/57.99 | (662) ~ (all_248_0 = all_248_1)
% 245.19/57.99 | (663) op(e0, e0) = all_248_24
% 245.19/57.99 | (664) op(e0, e1) = all_248_19
% 245.19/57.99 | (665) op(e0, e2) = all_248_14
% 245.19/57.99 | (666) op(e0, e3) = all_248_9
% 245.19/57.99 | (667) op(e0, e4) = all_248_4
% 245.19/57.99 | (668) op(e1, e0) = all_248_23
% 245.19/57.99 | (669) op(e1, e1) = all_248_18
% 245.19/57.99 | (670) op(e1, e2) = all_248_13
% 245.19/57.99 | (671) op(e1, e3) = all_248_8
% 245.19/57.99 | (672) op(e1, e4) = all_248_3
% 245.19/57.99 | (673) op(e2, e0) = all_248_22
% 245.19/57.99 | (674) op(e2, e1) = all_248_17
% 245.19/57.99 | (675) op(e2, e2) = all_248_12
% 245.19/57.99 | (676) op(e2, e3) = all_248_7
% 245.19/57.99 | (677) op(e2, e4) = all_248_2
% 245.19/57.99 | (678) op(e3, e0) = all_248_21
% 245.19/57.99 | (679) op(e3, e1) = all_248_16
% 245.19/57.99 | (680) op(e3, e2) = all_248_11
% 245.19/57.99 | (681) op(e3, e3) = all_248_6
% 245.19/57.99 | (682) op(e3, e4) = all_248_1
% 245.19/57.99 | (683) op(e4, e0) = all_248_20
% 245.19/57.99 | (684) op(e4, e1) = all_248_15
% 245.19/57.99 | (685) op(e4, e2) = all_248_10
% 245.19/57.99 | (686) op(e4, e3) = all_248_5
% 245.19/57.99 | (687) op(e4, e4) = all_248_0
% 245.19/57.99 |
% 245.19/57.99 | DELTA: instantiating (1) with fresh symbols all_250_0, all_250_1, all_250_2,
% 245.19/57.99 | all_250_3, all_250_4, all_250_5, all_250_6, all_250_7, all_250_8,
% 245.19/57.99 | all_250_9, all_250_10, all_250_11, all_250_12, all_250_13, all_250_14,
% 245.19/57.99 | all_250_15, all_250_16, all_250_17, all_250_18, all_250_19, all_250_20,
% 245.19/57.99 | all_250_21, all_250_22, all_250_23, all_250_24 gives:
% 245.19/57.99 | (688) op(e4, e4) = all_250_0 & op(e4, e3) = all_250_1 & op(e4, e2) =
% 245.19/57.99 | all_250_2 & op(e4, e1) = all_250_3 & op(e4, e0) = all_250_4 & op(e3,
% 245.19/57.99 | e4) = all_250_5 & op(e3, e3) = all_250_6 & op(e3, e2) = all_250_7 &
% 245.19/57.99 | op(e3, e1) = all_250_8 & op(e3, e0) = all_250_9 & op(e2, e4) =
% 245.19/57.99 | all_250_10 & op(e2, e3) = all_250_11 & op(e2, e2) = all_250_12 &
% 245.19/57.99 | op(e2, e1) = all_250_13 & op(e2, e0) = all_250_14 & op(e1, e4) =
% 245.19/57.99 | all_250_15 & op(e1, e3) = all_250_16 & op(e1, e2) = all_250_17 &
% 245.19/57.99 | op(e1, e1) = all_250_18 & op(e1, e0) = all_250_19 & op(e0, e4) =
% 245.19/57.99 | all_250_20 & op(e0, e3) = all_250_21 & op(e0, e2) = all_250_22 &
% 245.19/57.99 | op(e0, e1) = all_250_23 & op(e0, e0) = all_250_24 & $i(all_250_0) &
% 245.19/57.99 | $i(all_250_1) & $i(all_250_2) & $i(all_250_3) & $i(all_250_4) &
% 245.19/57.99 | $i(all_250_5) & $i(all_250_6) & $i(all_250_7) & $i(all_250_8) &
% 245.19/57.99 | $i(all_250_9) & $i(all_250_10) & $i(all_250_11) & $i(all_250_12) &
% 245.19/57.99 | $i(all_250_13) & $i(all_250_14) & $i(all_250_15) & $i(all_250_16) &
% 245.19/57.99 | $i(all_250_17) & $i(all_250_18) & $i(all_250_19) & $i(all_250_20) &
% 245.19/57.99 | $i(all_250_21) & $i(all_250_22) & $i(all_250_23) & $i(all_250_24) &
% 245.19/57.99 | (all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 245.19/57.99 | all_250_0 = e0) & (all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2
% 245.19/57.99 | | all_250_1 = e1 | all_250_1 = e0) & (all_250_2 = e4 | all_250_2 =
% 245.19/57.99 | e3 | all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0) & (all_250_3
% 245.19/57.99 | = e4 | all_250_3 = e3 | all_250_3 = e2 | all_250_3 = e1 | all_250_3
% 245.19/57.99 | = e0) & (all_250_4 = e4 | all_250_4 = e3 | all_250_4 = e2 |
% 245.19/57.99 | all_250_4 = e1 | all_250_4 = e0) & (all_250_5 = e4 | all_250_5 = e3
% 245.19/57.99 | | all_250_5 = e2 | all_250_5 = e1 | all_250_5 = e0) & (all_250_6 =
% 245.19/57.99 | e4 | all_250_6 = e3 | all_250_6 = e2 | all_250_6 = e1 | all_250_6 =
% 245.19/57.99 | e0) & (all_250_7 = e4 | all_250_7 = e3 | all_250_7 = e2 | all_250_7
% 245.19/57.99 | = e1 | all_250_7 = e0) & (all_250_8 = e4 | all_250_8 = e3 |
% 245.19/57.99 | all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0) & (all_250_9 = e4
% 245.19/57.99 | | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | all_250_9 =
% 245.19/57.99 | e0) & (all_250_10 = e4 | all_250_10 = e3 | all_250_10 = e2 |
% 245.19/57.99 | all_250_10 = e1 | all_250_10 = e0) & (all_250_11 = e4 | all_250_11
% 245.19/57.99 | = e3 | all_250_11 = e2 | all_250_11 = e1 | all_250_11 = e0) &
% 245.19/57.99 | (all_250_12 = e4 | all_250_12 = e3 | all_250_12 = e2 | all_250_12 =
% 245.19/57.99 | e1 | all_250_12 = e0) & (all_250_13 = e4 | all_250_13 = e3 |
% 245.19/57.99 | all_250_13 = e2 | all_250_13 = e1 | all_250_13 = e0) & (all_250_14
% 245.19/57.99 | = e4 | all_250_14 = e3 | all_250_14 = e2 | all_250_14 = e1 |
% 245.19/57.99 | all_250_14 = e0) & (all_250_15 = e4 | all_250_15 = e3 | all_250_15
% 245.19/57.99 | = e2 | all_250_15 = e1 | all_250_15 = e0) & (all_250_16 = e4 |
% 245.19/57.99 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 | all_250_16 =
% 245.19/57.99 | e0) & (all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 |
% 245.19/57.99 | all_250_17 = e1 | all_250_17 = e0) & (all_250_18 = e4 | all_250_18
% 245.19/57.99 | = e3 | all_250_18 = e2 | all_250_18 = e1 | all_250_18 = e0) &
% 245.19/57.99 | (all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 =
% 245.19/57.99 | e1 | all_250_19 = e0) & (all_250_20 = e4 | all_250_20 = e3 |
% 245.19/57.99 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0) & (all_250_21
% 245.19/57.99 | = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 245.19/57.99 | all_250_21 = e0) & (all_250_22 = e4 | all_250_22 = e3 | all_250_22
% 245.19/57.99 | = e2 | all_250_22 = e1 | all_250_22 = e0) & (all_250_23 = e4 |
% 245.19/57.99 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 =
% 245.19/57.99 | e0) & (all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 |
% 245.19/57.99 | all_250_24 = e1 | all_250_24 = e0)
% 245.19/57.99 |
% 245.19/57.99 | ALPHA: (688) implies:
% 245.19/57.99 | (689) op(e0, e0) = all_250_24
% 245.19/57.99 | (690) op(e0, e1) = all_250_23
% 245.19/57.99 | (691) op(e0, e2) = all_250_22
% 245.19/57.99 | (692) op(e0, e3) = all_250_21
% 245.19/57.99 | (693) op(e0, e4) = all_250_20
% 245.19/57.99 | (694) op(e1, e0) = all_250_19
% 245.19/57.99 | (695) op(e1, e1) = all_250_18
% 245.19/57.99 | (696) op(e1, e2) = all_250_17
% 245.19/57.99 | (697) op(e1, e3) = all_250_16
% 245.19/57.99 | (698) op(e1, e4) = all_250_15
% 245.19/57.99 | (699) op(e2, e0) = all_250_14
% 245.19/57.99 | (700) op(e2, e1) = all_250_13
% 245.19/57.99 | (701) op(e2, e2) = all_250_12
% 245.19/57.99 | (702) op(e2, e3) = all_250_11
% 245.19/57.99 | (703) op(e2, e4) = all_250_10
% 245.19/57.99 | (704) op(e3, e0) = all_250_9
% 245.19/57.99 | (705) op(e3, e1) = all_250_8
% 245.19/57.99 | (706) op(e3, e2) = all_250_7
% 245.19/57.99 | (707) op(e3, e3) = all_250_6
% 245.19/57.99 | (708) op(e3, e4) = all_250_5
% 245.19/57.99 | (709) op(e4, e0) = all_250_4
% 245.19/57.99 | (710) op(e4, e1) = all_250_3
% 245.19/57.99 | (711) op(e4, e2) = all_250_2
% 245.19/57.99 | (712) op(e4, e3) = all_250_1
% 245.19/57.99 | (713) op(e4, e4) = all_250_0
% 245.19/57.99 | (714) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1
% 245.19/57.99 | | all_250_24 = e0
% 245.19/57.99 | (715) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1
% 245.19/57.99 | | all_250_23 = e0
% 245.19/57.99 | (716) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1
% 245.19/57.99 | | all_250_22 = e0
% 245.19/57.99 | (717) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1
% 245.19/57.99 | | all_250_21 = e0
% 245.19/57.99 | (718) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1
% 245.19/57.99 | | all_250_20 = e0
% 245.19/57.99 | (719) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1
% 245.19/57.99 | | all_250_18 = e0
% 245.19/57.99 | (720) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1
% 245.19/57.99 | | all_250_17 = e0
% 245.19/57.99 | (721) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1
% 245.19/57.99 | | all_250_16 = e0
% 245.19/57.99 | (722) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1
% 245.19/57.99 | | all_250_15 = e0
% 245.19/57.99 | (723) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1
% 245.19/57.99 | | all_250_13 = e0
% 245.19/57.99 | (724) all_250_12 = e4 | all_250_12 = e3 | all_250_12 = e2 | all_250_12 = e1
% 245.19/57.99 | | all_250_12 = e0
% 245.19/57.99 | (725) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1
% 245.19/57.99 | | all_250_11 = e0
% 245.19/57.99 | (726) all_250_10 = e4 | all_250_10 = e3 | all_250_10 = e2 | all_250_10 = e1
% 245.19/57.99 | | all_250_10 = e0
% 245.19/57.99 | (727) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 |
% 245.19/57.99 | all_250_9 = e0
% 245.19/57.99 | (728) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 245.19/57.99 | all_250_8 = e0
% 245.19/57.99 | (729) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 245.19/57.99 | all_250_2 = e0
% 245.19/57.99 | (730) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 245.19/57.99 | all_250_1 = e0
% 245.19/57.99 | (731) all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 245.19/57.99 | all_250_0 = e0
% 245.19/57.99 |
% 245.19/57.99 | DELTA: instantiating (2) with fresh symbols all_252_0, all_252_1, all_252_2,
% 245.19/57.99 | all_252_3, all_252_4, all_252_5, all_252_6, all_252_7, all_252_8,
% 245.19/57.99 | all_252_9, all_252_10, all_252_11, all_252_12, all_252_13, all_252_14,
% 245.19/57.99 | all_252_15, all_252_16, all_252_17, all_252_18, all_252_19, all_252_20,
% 245.19/57.99 | all_252_21, all_252_22, all_252_23, all_252_24 gives:
% 245.57/58.00 | (732) ((all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) =
% 245.57/58.00 | e4) | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 &
% 245.57/58.00 | op(e4, e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4)) &
% 245.57/58.00 | ((all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 245.57/58.00 | e4) | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 &
% 245.57/58.00 | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)) &
% 245.57/58.00 | ((all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) =
% 245.57/58.00 | e3) | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 &
% 245.57/58.00 | op(e4, e1) = e3) | (all_252_16 = e3 & op(e4, e0) = e3)) &
% 245.57/58.00 | ((all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 245.57/58.00 | e3) | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 245.57/58.00 | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)) &
% 245.57/58.00 | ((all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) =
% 245.57/58.00 | e2) | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 &
% 245.57/58.00 | op(e4, e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2)) &
% 245.57/58.00 | ((all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 245.57/58.00 | e2) | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 245.57/58.00 | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)) &
% 245.57/58.00 | ((all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) =
% 245.57/58.00 | e1) | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 &
% 245.57/58.00 | op(e4, e1) = e1) | (all_252_16 = e1 & op(e4, e0) = e1)) &
% 245.57/58.00 | ((all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 245.57/58.00 | e1) | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 245.57/58.00 | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)) &
% 245.57/58.00 | ((all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) =
% 245.57/58.00 | e0) | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 &
% 245.57/58.00 | op(e4, e1) = e0) | (all_252_16 = e0 & op(e4, e0) = e0)) &
% 245.57/58.00 | ((all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) =
% 245.57/58.00 | e0) | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 &
% 245.57/58.00 | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)) &
% 245.57/58.00 | ((all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 245.57/58.00 | e4) | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 245.57/58.00 | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)) &
% 245.57/58.00 | ((all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 245.57/58.00 | e3) | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 245.57/58.00 | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)) &
% 245.57/58.00 | ((all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 245.57/58.00 | e2) | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 &
% 245.57/58.00 | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)) &
% 245.57/58.00 | ((all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 245.57/58.00 | e1) | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 &
% 245.57/58.00 | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)) &
% 245.57/58.00 | ((all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 245.57/58.00 | e0) | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 245.57/58.00 | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)) &
% 245.57/58.00 | ((all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 245.57/58.00 | e4) | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 &
% 245.57/58.00 | op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)) &
% 245.57/58.00 | ((all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 245.57/58.00 | e3) | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 &
% 245.57/58.00 | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)) &
% 245.57/58.00 | ((all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 245.57/58.00 | e2) | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 &
% 245.57/58.00 | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)) &
% 245.57/58.00 | ((all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 245.57/58.00 | e1) | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 &
% 245.57/58.00 | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)) &
% 245.57/58.00 | ((all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 245.57/58.00 | e0) | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 &
% 245.57/58.00 | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)) &
% 245.57/58.00 | ((all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) =
% 245.57/58.00 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 &
% 245.57/58.00 | op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)) &
% 245.57/58.00 | ((all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) =
% 245.57/58.00 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 &
% 245.57/58.00 | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)) &
% 245.57/58.00 | ((all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) =
% 245.57/58.00 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 &
% 245.57/58.00 | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)) &
% 245.57/58.00 | ((all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 245.57/58.00 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 245.57/58.00 | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)) &
% 245.57/58.00 | ((all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 245.57/58.00 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 &
% 245.57/58.00 | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0)) &
% 245.57/58.00 | ((all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 245.57/58.00 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 245.57/58.00 | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)) &
% 245.57/58.00 | ((all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 245.57/58.00 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 245.57/58.00 | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)) &
% 245.57/58.00 | ((all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 245.57/58.00 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 &
% 245.57/58.00 | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)) &
% 245.57/58.00 | ((all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) =
% 245.57/58.00 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 &
% 245.57/58.00 | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)) &
% 245.57/58.00 | ((all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 245.57/58.00 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 245.57/58.00 | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)) &
% 245.57/58.00 | ((all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 245.57/58.00 | e4) | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 &
% 245.57/58.00 | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)) &
% 245.57/58.00 | ((all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 245.57/58.00 | e3) | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 &
% 245.57/58.00 | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)) &
% 245.57/58.00 | ((all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 245.57/58.00 | e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 &
% 245.57/58.00 | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)) &
% 245.57/58.00 | ((all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 245.57/58.00 | e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 &
% 245.57/58.00 | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)) &
% 245.57/58.00 | ((all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 245.57/58.00 | e0) | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 &
% 245.57/58.00 | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)) &
% 245.57/58.00 | ((all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 245.57/58.00 | = e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 245.57/58.00 | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)) &
% 245.57/58.00 | ((all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 245.57/58.00 | = e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 245.57/58.00 | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)) &
% 245.57/58.00 | ((all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 245.57/58.00 | = e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 245.57/58.00 | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)) &
% 245.57/58.00 | ((all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3)
% 245.57/58.00 | = e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 &
% 245.57/58.00 | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)) &
% 245.57/58.00 | ((all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3)
% 245.57/58.00 | = e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 &
% 245.57/58.00 | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 245.57/58.00 | ((all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0)
% 245.57/58.00 | = e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 &
% 245.57/58.00 | op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)) &
% 245.57/58.00 | ((all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0)
% 245.57/58.00 | = e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 245.57/58.00 | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)) &
% 245.57/58.00 | ((all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0)
% 245.57/58.00 | = e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 &
% 245.57/58.00 | op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)) &
% 245.57/58.00 | ((all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0)
% 245.57/58.00 | = e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 &
% 245.57/58.00 | op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)) &
% 245.57/58.00 | ((all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3)
% 245.57/58.00 | = e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 245.57/58.00 | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)) &
% 245.57/58.00 | ((all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 245.57/58.00 | = e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 245.57/58.00 | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)) &
% 245.57/58.00 | ((all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 245.57/58.00 | = e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 245.57/58.00 | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)) &
% 245.57/58.00 | ((all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3)
% 245.57/58.00 | = e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 &
% 245.57/58.00 | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)) &
% 245.57/58.00 | ((all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4,
% 245.57/58.00 | e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0) |
% 245.57/58.00 | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 245.57/58.00 | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 245.57/58.00 | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 245.57/58.00 | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))))
% 245.57/58.00 |
% 245.57/58.00 | ALPHA: (732) implies:
% 245.57/58.00 | (733) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0)
% 245.57/58.00 | = e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0
% 245.57/58.00 | & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 245.57/58.00 | ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0,
% 245.57/58.00 | e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 245.57/58.00 | = e0 & op(e0, e1) = e0)))
% 245.57/58.00 | (734) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 245.57/58.00 | e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 &
% 245.57/58.00 | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 245.57/58.00 | (735) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 245.57/58.00 | e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 245.57/58.00 | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 245.57/58.00 | (736) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 245.57/58.00 | e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 245.57/58.00 | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 245.57/58.00 | (737) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) =
% 245.57/58.00 | e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 245.57/58.00 | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 245.57/58.00 | (738) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 245.57/58.00 | e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 &
% 245.57/58.00 | op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 245.57/58.00 | (739) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 245.57/58.00 | e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 &
% 245.57/58.00 | op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 245.57/58.00 | (740) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 245.57/58.00 | e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 245.57/58.00 | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 245.57/58.00 | (741) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 245.57/58.00 | e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 &
% 245.57/58.00 | op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 245.57/58.00 | (742) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 245.57/58.00 | e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 &
% 245.57/58.00 | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 245.57/58.00 | (743) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 245.57/58.00 | e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 &
% 245.57/58.00 | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 245.57/58.00 | (744) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 245.57/58.00 | e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 245.57/58.00 | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 245.57/58.00 | (745) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 245.57/58.00 | e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 245.57/58.00 | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 245.57/58.00 | (746) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 245.57/58.00 | e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 245.57/58.00 | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 245.57/58.00 | (747) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 245.57/58.00 | e0) | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 &
% 245.57/58.00 | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 245.57/58.01 | (748) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 245.57/58.01 | e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 &
% 245.57/58.01 | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 245.57/58.01 | (749) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 245.57/58.01 | e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 &
% 245.57/58.01 | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 245.57/58.01 | (750) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 245.57/58.01 | e3) | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 &
% 245.57/58.01 | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 245.57/58.01 | (751) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 245.57/58.01 | e4) | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 &
% 245.57/58.01 | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 245.57/58.01 | (752) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 245.57/58.01 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 245.57/58.01 | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 245.57/58.01 | (753) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) =
% 245.57/58.01 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 &
% 245.57/58.01 | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 245.57/58.01 | (754) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 245.57/58.01 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 &
% 245.57/58.01 | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 245.57/58.01 | (755) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 245.57/58.01 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 245.57/58.01 | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 245.57/58.01 | (756) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 245.57/58.01 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 245.57/58.01 | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 245.57/58.01 | (757) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 245.57/58.01 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 &
% 245.57/58.01 | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 245.57/58.01 | (758) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 245.57/58.01 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 245.57/58.01 | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 245.57/58.01 | (759) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) =
% 245.57/58.01 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 &
% 245.57/58.01 | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 245.57/58.01 | (760) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) =
% 245.57/58.01 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 &
% 245.57/58.01 | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 245.57/58.01 | (761) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) =
% 245.57/58.01 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 &
% 245.57/58.01 | op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 245.57/58.01 | (762) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 245.57/58.01 | e0) | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 &
% 245.57/58.01 | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 245.57/58.01 | (763) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 245.57/58.01 | e1) | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 &
% 245.57/58.01 | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 245.57/58.01 | (764) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 245.57/58.01 | e2) | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 &
% 245.57/58.01 | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 245.57/58.01 | (765) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 245.57/58.01 | e3) | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 &
% 245.57/58.01 | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 245.57/58.01 | (766) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 245.57/58.01 | e4) | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 &
% 245.57/58.01 | op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 245.57/58.01 | (767) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 245.57/58.01 | e0) | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 245.57/58.01 | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 245.57/58.01 | (768) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 245.57/58.01 | e1) | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 &
% 245.57/58.01 | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 245.57/58.01 | (769) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 245.57/58.01 | e2) | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 &
% 245.57/58.01 | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 245.57/58.01 | (770) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 245.57/58.01 | e3) | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 245.57/58.01 | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 245.57/58.01 | (771) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 245.57/58.01 | e4) | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 245.57/58.01 | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 245.57/58.01 | (772) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) =
% 245.57/58.01 | e0) | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 &
% 245.57/58.01 | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)
% 245.57/58.01 | (773) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) =
% 245.57/58.01 | e0) | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4,
% 245.57/58.01 | e1) = e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 245.57/58.01 | (774) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 245.57/58.01 | e1) | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 245.57/58.01 | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 245.57/58.01 | (775) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) =
% 245.57/58.01 | e1) | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4,
% 245.57/58.01 | e1) = e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 245.57/58.01 | (776) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 245.57/58.01 | e2) | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 245.57/58.01 | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 245.57/58.01 | (777) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) =
% 245.57/58.01 | e2) | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4,
% 245.57/58.01 | e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2)
% 245.57/58.01 | (778) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 245.57/58.01 | e3) | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 245.57/58.01 | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 245.57/58.01 | (779) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) =
% 245.57/58.01 | e3) | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4,
% 245.57/58.01 | e1) = e3) | (all_252_16 = e3 & op(e4, e0) = e3)
% 245.57/58.01 | (780) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 245.57/58.01 | e4) | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 &
% 245.57/58.01 | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 245.57/58.01 | (781) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) =
% 245.57/58.01 | e4) | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4,
% 245.57/58.01 | e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_248_24, all_250_24, e0,
% 245.57/58.01 | e0, simplifying with (663), (689) gives:
% 245.57/58.01 | (782) all_250_24 = all_248_24
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_246_24, all_250_24, e0,
% 245.57/58.01 | e0, simplifying with (517), (689) gives:
% 245.57/58.01 | (783) all_250_24 = all_246_24
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_244_24, all_250_24, e0,
% 245.57/58.01 | e0, simplifying with (467), (689) gives:
% 245.57/58.01 | (784) all_250_24 = all_244_24
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_58_2, all_60_2, e1, e0,
% 245.57/58.01 | simplifying with (218), (221) gives:
% 245.57/58.01 | (785) all_60_2 = all_58_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_60_2, e1, e0,
% 245.57/58.01 | simplifying with (161), (221) gives:
% 245.57/58.01 | (786) all_60_2 = all_20_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_92_2, all_244_22, e1,
% 245.57/58.01 | e0, simplifying with (267), (468) gives:
% 245.57/58.01 | (787) all_244_22 = all_92_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_60_2, all_244_22, e1,
% 245.57/58.01 | e0, simplifying with (221), (468) gives:
% 245.57/58.01 | (788) all_244_22 = all_60_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_244_22, all_246_23, e1,
% 245.57/58.01 | e0, simplifying with (468), (518) gives:
% 245.57/58.01 | (789) all_246_23 = all_244_22
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_244_22, all_248_19, e1,
% 245.57/58.01 | e0, simplifying with (468), (664) gives:
% 245.57/58.01 | (790) all_248_19 = all_244_22
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_230_2, all_248_19, e1,
% 245.57/58.01 | e0, simplifying with (449), (664) gives:
% 245.57/58.01 | (791) all_248_19 = all_230_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_246_23, all_250_23, e1,
% 245.57/58.01 | e0, simplifying with (518), (690) gives:
% 245.57/58.01 | (792) all_250_23 = all_246_23
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_250_23, e1,
% 245.57/58.01 | e0, simplifying with (179), (690) gives:
% 245.57/58.01 | (793) all_250_23 = all_32_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_162_2, all_206_2, e2,
% 245.57/58.01 | e0, simplifying with (361), (420) gives:
% 245.57/58.01 | (794) all_206_2 = all_162_2
% 245.57/58.01 |
% 245.57/58.01 | GROUND_INST: instantiating (function-axioms) with all_158_2, all_206_2, e2,
% 245.57/58.01 | e0, simplifying with (357), (420) gives:
% 245.57/58.01 | (795) all_206_2 = all_158_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_108_2, all_206_2, e2,
% 245.57/58.02 | e0, simplifying with (289), (420) gives:
% 245.57/58.02 | (796) all_206_2 = all_108_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_162_2, all_244_20, e2,
% 245.57/58.02 | e0, simplifying with (361), (469) gives:
% 245.57/58.02 | (797) all_244_20 = all_162_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_22, all_248_14, e2,
% 245.57/58.02 | e0, simplifying with (519), (665) gives:
% 245.57/58.02 | (798) all_248_14 = all_246_22
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_20, all_248_14, e2,
% 245.57/58.02 | e0, simplifying with (469), (665) gives:
% 245.57/58.02 | (799) all_248_14 = all_244_20
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_248_14, e2,
% 245.57/58.02 | e0, simplifying with (173), (665) gives:
% 245.57/58.02 | (800) all_248_14 = all_28_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_158_2, all_250_22, e2,
% 245.57/58.02 | e0, simplifying with (357), (691) gives:
% 245.57/58.02 | (801) all_250_22 = all_158_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_82_2, all_250_22, e2,
% 245.57/58.02 | e0, simplifying with (254), (691) gives:
% 245.57/58.02 | (802) all_250_22 = all_82_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_68_2, all_72_2, e3, e0,
% 245.57/58.02 | simplifying with (233), (239) gives:
% 245.57/58.02 | (803) all_72_2 = all_68_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_18, all_246_21, e3,
% 245.57/58.02 | e0, simplifying with (470), (520) gives:
% 245.57/58.02 | (804) all_246_21 = all_244_18
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_104_2, all_246_21, e3,
% 245.57/58.02 | e0, simplifying with (283), (520) gives:
% 245.57/58.02 | (805) all_246_21 = all_104_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_21, all_248_9, e3,
% 245.57/58.02 | e0, simplifying with (520), (666) gives:
% 245.57/58.02 | (806) all_248_9 = all_246_21
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_248_9, e3, e0,
% 245.57/58.02 | simplifying with (164), (666) gives:
% 245.57/58.02 | (807) all_248_9 = all_22_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_118_2, all_250_21, e3,
% 245.57/58.02 | e0, simplifying with (303), (692) gives:
% 245.57/58.02 | (808) all_250_21 = all_118_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_104_2, all_250_21, e3,
% 245.57/58.02 | e0, simplifying with (283), (692) gives:
% 245.57/58.02 | (809) all_250_21 = all_104_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_90_2, all_250_21, e3,
% 245.57/58.02 | e0, simplifying with (264), (692) gives:
% 245.57/58.02 | (810) all_250_21 = all_90_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_72_2, all_250_21, e3,
% 245.57/58.02 | e0, simplifying with (239), (692) gives:
% 245.57/58.02 | (811) all_250_21 = all_72_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_210_2, e4, e0,
% 245.57/58.02 | simplifying with (149), (425) gives:
% 245.57/58.02 | (812) all_210_2 = all_12_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_212_2, e4, e0,
% 245.57/58.02 | simplifying with (194), (427) gives:
% 245.57/58.02 | (813) all_212_2 = all_42_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_212_2, all_244_16, e4,
% 245.57/58.02 | e0, simplifying with (427), (471) gives:
% 245.57/58.02 | (814) all_244_16 = all_212_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_16, all_246_20, e4,
% 245.57/58.02 | e0, simplifying with (471), (521) gives:
% 245.57/58.02 | (815) all_246_20 = all_244_16
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_20, all_248_4, e4,
% 245.57/58.02 | e0, simplifying with (521), (667) gives:
% 245.57/58.02 | (816) all_248_4 = all_246_20
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_248_4, e4, e0,
% 245.57/58.02 | simplifying with (152), (667) gives:
% 245.57/58.02 | (817) all_248_4 = all_14_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_210_2, all_250_20, e4,
% 245.57/58.02 | e0, simplifying with (425), (693) gives:
% 245.57/58.02 | (818) all_250_20 = all_210_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_250_20, e4,
% 245.57/58.02 | e0, simplifying with (194), (693) gives:
% 245.57/58.02 | (819) all_250_20 = all_42_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_250_20, e4,
% 245.57/58.02 | e0, simplifying with (158), (693) gives:
% 245.57/58.02 | (820) all_250_20 = all_18_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_164_2, all_198_2, e0,
% 245.57/58.02 | e1, simplifying with (364), (409) gives:
% 245.57/58.02 | (821) all_198_2 = all_164_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_96_2, all_198_2, e0, e1,
% 245.57/58.02 | simplifying with (273), (409) gives:
% 245.57/58.02 | (822) all_198_2 = all_96_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_198_2, all_232_2, e0,
% 245.57/58.02 | e1, simplifying with (409), (452) gives:
% 245.57/58.02 | (823) all_232_2 = all_198_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_110_2, all_232_2, e0,
% 245.57/58.02 | e1, simplifying with (292), (452) gives:
% 245.57/58.02 | (824) all_232_2 = all_110_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_164_2, all_244_23, e0,
% 245.57/58.02 | e1, simplifying with (364), (472) gives:
% 245.57/58.02 | (825) all_244_23 = all_164_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_23, all_246_19, e0,
% 245.57/58.02 | e1, simplifying with (472), (522) gives:
% 245.57/58.02 | (826) all_246_19 = all_244_23
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_19, all_248_23, e0,
% 245.57/58.02 | e1, simplifying with (522), (668) gives:
% 245.57/58.02 | (827) all_248_23 = all_246_19
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_248_23, all_250_19, e0,
% 245.57/58.02 | e1, simplifying with (668), (694) gives:
% 245.57/58.02 | (828) all_250_19 = all_248_23
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_250_19, e0,
% 245.57/58.02 | e1, simplifying with (182), (694) gives:
% 245.57/58.02 | (829) all_250_19 = all_34_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_15, all_248_18, e1,
% 245.57/58.02 | e1, simplifying with (473), (669) gives:
% 245.57/58.02 | (830) all_248_18 = all_244_15
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_248_18, all_250_18, e1,
% 245.57/58.02 | e1, simplifying with (669), (695) gives:
% 245.57/58.02 | (831) all_250_18 = all_248_18
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_18, all_250_18, e1,
% 245.57/58.02 | e1, simplifying with (523), (695) gives:
% 245.57/58.02 | (832) all_250_18 = all_246_18
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_150_2, all_180_2, e2,
% 245.57/58.02 | e1, simplifying with (348), (385) gives:
% 245.57/58.02 | (833) all_180_2 = all_150_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_180_2, all_192_2, e2,
% 245.57/58.02 | e1, simplifying with (385), (402) gives:
% 245.57/58.02 | (834) all_192_2 = all_180_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_160_2, all_246_17, e2,
% 245.57/58.02 | e1, simplifying with (359), (524) gives:
% 245.57/58.02 | (835) all_246_17 = all_160_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_17, all_248_13, e2,
% 245.57/58.02 | e1, simplifying with (524), (670) gives:
% 245.57/58.02 | (836) all_248_13 = all_246_17
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_13, all_248_13, e2,
% 245.57/58.02 | e1, simplifying with (474), (670) gives:
% 245.57/58.02 | (837) all_248_13 = all_244_13
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_150_2, all_248_13, e2,
% 245.57/58.02 | e1, simplifying with (348), (670) gives:
% 245.57/58.02 | (838) all_248_13 = all_150_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_248_13, e2,
% 245.57/58.02 | e1, simplifying with (206), (670) gives:
% 245.57/58.02 | (839) all_248_13 = all_50_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_192_2, all_250_17, e2,
% 245.57/58.02 | e1, simplifying with (402), (696) gives:
% 245.57/58.02 | (840) all_250_17 = all_192_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_250_17, e2, e1,
% 245.57/58.02 | simplifying with (137), (696) gives:
% 245.57/58.02 | (841) all_250_17 = all_4_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_112_2, all_130_2, e3,
% 245.57/58.02 | e1, simplifying with (294), (320) gives:
% 245.57/58.02 | (842) all_130_2 = all_112_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_70_2, all_130_2, e3, e1,
% 245.57/58.02 | simplifying with (236), (320) gives:
% 245.57/58.02 | (843) all_130_2 = all_70_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_62_2, all_130_2, e3, e1,
% 245.57/58.02 | simplifying with (224), (320) gives:
% 245.57/58.02 | (844) all_130_2 = all_62_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_130_2, all_166_2, e3,
% 245.57/58.02 | e1, simplifying with (320), (366) gives:
% 245.57/58.02 | (845) all_166_2 = all_130_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_166_2, all_246_16, e3,
% 245.57/58.02 | e1, simplifying with (366), (525) gives:
% 245.57/58.02 | (846) all_246_16 = all_166_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_114_2, all_246_16, e3,
% 245.57/58.02 | e1, simplifying with (297), (525) gives:
% 245.57/58.02 | (847) all_246_16 = all_114_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_248_8, all_250_16, e3,
% 245.57/58.02 | e1, simplifying with (671), (697) gives:
% 245.57/58.02 | (848) all_250_16 = all_248_8
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_16, all_250_16, e3,
% 245.57/58.02 | e1, simplifying with (525), (697) gives:
% 245.57/58.02 | (849) all_250_16 = all_246_16
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_11, all_250_16, e3,
% 245.57/58.02 | e1, simplifying with (475), (697) gives:
% 245.57/58.02 | (850) all_250_16 = all_244_11
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_152_2, e4, e1,
% 245.57/58.02 | simplifying with (155), (350) gives:
% 245.57/58.02 | (851) all_152_2 = all_16_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_170_2, all_246_15, e4,
% 245.57/58.02 | e1, simplifying with (371), (526) gives:
% 245.57/58.02 | (852) all_246_15 = all_170_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_246_15, all_248_3, e4,
% 245.57/58.02 | e1, simplifying with (526), (672) gives:
% 245.57/58.02 | (853) all_248_3 = all_246_15
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_66_2, all_248_3, e4, e1,
% 245.57/58.02 | simplifying with (230), (672) gives:
% 245.57/58.02 | (854) all_248_3 = all_66_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_244_9, all_250_15, e4,
% 245.57/58.02 | e1, simplifying with (476), (698) gives:
% 245.57/58.02 | (855) all_250_15 = all_244_9
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_170_2, all_250_15, e4,
% 245.57/58.02 | e1, simplifying with (371), (698) gives:
% 245.57/58.02 | (856) all_250_15 = all_170_2
% 245.57/58.02 |
% 245.57/58.02 | GROUND_INST: instantiating (function-axioms) with all_152_2, all_250_15, e4,
% 245.57/58.02 | e1, simplifying with (350), (698) gives:
% 245.57/58.02 | (857) all_250_15 = all_152_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_144_2, all_250_15, e4,
% 245.57/58.03 | e1, simplifying with (340), (698) gives:
% 245.57/58.03 | (858) all_250_15 = all_144_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_250_15, e4,
% 245.57/58.03 | e1, simplifying with (167), (698) gives:
% 245.57/58.03 | (859) all_250_15 = all_24_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_76_2, all_116_2, e0, e2,
% 245.57/58.03 | simplifying with (245), (300) gives:
% 245.57/58.03 | (860) all_116_2 = all_76_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_116_2, all_174_2, e0,
% 245.57/58.03 | e2, simplifying with (300), (377) gives:
% 245.57/58.03 | (861) all_174_2 = all_116_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_174_2, all_178_2, e0,
% 245.57/58.03 | e2, simplifying with (377), (382) gives:
% 245.57/58.03 | (862) all_178_2 = all_174_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_116_2, all_244_21, e0,
% 245.57/58.03 | e2, simplifying with (300), (477) gives:
% 245.57/58.03 | (863) all_244_21 = all_116_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_21, all_246_14, e0,
% 245.57/58.03 | e2, simplifying with (477), (527) gives:
% 245.57/58.03 | (864) all_246_14 = all_244_21
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_246_14, e0,
% 245.57/58.03 | e2, simplifying with (191), (527) gives:
% 245.57/58.03 | (865) all_246_14 = all_40_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_178_2, all_248_22, e0,
% 245.57/58.03 | e2, simplifying with (382), (673) gives:
% 245.57/58.03 | (866) all_248_22 = all_178_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_248_22, all_250_14, e0,
% 245.57/58.03 | e2, simplifying with (673), (699) gives:
% 245.57/58.03 | (867) all_250_14 = all_248_22
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_86_2, all_250_14, e0,
% 245.57/58.03 | e2, simplifying with (259), (699) gives:
% 245.57/58.03 | (868) all_250_14 = all_86_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_190_2, all_242_2, e1,
% 245.57/58.03 | e2, simplifying with (399), (464) gives:
% 245.57/58.03 | (869) all_242_2 = all_190_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_188_2, all_242_2, e1,
% 245.57/58.03 | e2, simplifying with (396), (464) gives:
% 245.57/58.03 | (870) all_242_2 = all_188_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_242_2, e1, e2,
% 245.57/58.03 | simplifying with (188), (464) gives:
% 245.57/58.03 | (871) all_242_2 = all_38_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_188_2, all_244_14, e1,
% 245.57/58.03 | e2, simplifying with (396), (478) gives:
% 245.57/58.03 | (872) all_244_14 = all_188_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_14, all_246_13, e1,
% 245.57/58.03 | e2, simplifying with (478), (528) gives:
% 245.57/58.03 | (873) all_246_13 = all_244_14
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_13, all_248_17, e1,
% 245.57/58.03 | e2, simplifying with (528), (674) gives:
% 245.57/58.03 | (874) all_248_17 = all_246_13
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_94_2, all_248_17, e1,
% 245.57/58.03 | e2, simplifying with (270), (674) gives:
% 245.57/58.03 | (875) all_248_17 = all_94_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_14, all_250_13, e1,
% 245.57/58.03 | e2, simplifying with (478), (700) gives:
% 245.57/58.03 | (876) all_250_13 = all_244_14
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_106_2, all_250_13, e1,
% 245.57/58.03 | e2, simplifying with (286), (700) gives:
% 245.57/58.03 | (877) all_250_13 = all_106_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_12, all_248_12, e2,
% 245.57/58.03 | e2, simplifying with (529), (675) gives:
% 245.57/58.03 | (878) all_248_12 = all_246_12
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_248_12, all_250_12, e2,
% 245.57/58.03 | e2, simplifying with (675), (701) gives:
% 245.57/58.03 | (879) all_250_12 = all_248_12
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_8, all_250_12, e2,
% 245.57/58.03 | e2, simplifying with (479), (701) gives:
% 245.57/58.03 | (880) all_250_12 = all_244_8
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_124_2, e3, e2,
% 245.57/58.03 | simplifying with (146), (312) gives:
% 245.57/58.03 | (881) all_124_2 = all_10_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_124_2, all_172_2, e3,
% 245.57/58.03 | e2, simplifying with (312), (374) gives:
% 245.57/58.03 | (882) all_172_2 = all_124_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_102_2, all_172_2, e3,
% 245.57/58.03 | e2, simplifying with (280), (374) gives:
% 245.57/58.03 | (883) all_172_2 = all_102_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_124_2, all_244_6, e3,
% 245.57/58.03 | e2, simplifying with (312), (480) gives:
% 245.57/58.03 | (884) all_244_6 = all_124_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_78_2, all_244_6, e3, e2,
% 245.57/58.03 | simplifying with (248), (480) gives:
% 245.57/58.03 | (885) all_244_6 = all_78_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_172_2, all_248_7, e3,
% 245.57/58.03 | e2, simplifying with (374), (676) gives:
% 245.57/58.03 | (886) all_248_7 = all_172_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_138_2, all_248_7, e3,
% 245.57/58.03 | e2, simplifying with (332), (676) gives:
% 245.57/58.03 | (887) all_248_7 = all_138_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_248_7, all_250_11, e3,
% 245.57/58.03 | e2, simplifying with (676), (702) gives:
% 245.57/58.03 | (888) all_250_11 = all_248_7
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_11, all_250_11, e3,
% 245.57/58.03 | e2, simplifying with (530), (702) gives:
% 245.57/58.03 | (889) all_250_11 = all_246_11
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_120_2, all_148_2, e4,
% 245.57/58.03 | e2, simplifying with (306), (345) gives:
% 245.57/58.03 | (890) all_148_2 = all_120_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_64_2, all_148_2, e4, e2,
% 245.57/58.03 | simplifying with (227), (345) gives:
% 245.57/58.03 | (891) all_148_2 = all_64_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_134_2, all_244_4, e4,
% 245.57/58.03 | e2, simplifying with (326), (481) gives:
% 245.57/58.03 | (892) all_244_4 = all_134_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_10, all_248_2, e4,
% 245.57/58.03 | e2, simplifying with (531), (677) gives:
% 245.57/58.03 | (893) all_248_2 = all_246_10
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_4, all_248_2, e4,
% 245.57/58.03 | e2, simplifying with (481), (677) gives:
% 245.57/58.03 | (894) all_248_2 = all_244_4
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_224_2, all_248_2, e4,
% 245.57/58.03 | e2, simplifying with (442), (677) gives:
% 245.57/58.03 | (895) all_248_2 = all_224_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_148_2, all_248_2, e4,
% 245.57/58.03 | e2, simplifying with (345), (677) gives:
% 245.57/58.03 | (896) all_248_2 = all_148_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_10, all_250_10, e4,
% 245.57/58.03 | e2, simplifying with (531), (703) gives:
% 245.57/58.03 | (897) all_250_10 = all_246_10
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_186_2, all_250_10, e4,
% 245.57/58.03 | e2, simplifying with (393), (703) gives:
% 245.57/58.03 | (898) all_250_10 = all_186_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_226_2, all_228_2, e0,
% 245.57/58.03 | e3, simplifying with (445), (447) gives:
% 245.57/58.03 | (899) all_228_2 = all_226_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_226_2, all_244_19, e0,
% 245.57/58.03 | e3, simplifying with (445), (482) gives:
% 245.57/58.03 | (900) all_244_19 = all_226_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_200_2, all_244_19, e0,
% 245.57/58.03 | e3, simplifying with (412), (482) gives:
% 245.57/58.03 | (901) all_244_19 = all_200_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_126_2, all_244_19, e0,
% 245.57/58.03 | e3, simplifying with (315), (482) gives:
% 245.57/58.03 | (902) all_244_19 = all_126_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_228_2, all_248_21, e0,
% 245.57/58.03 | e3, simplifying with (447), (678) gives:
% 245.57/58.03 | (903) all_248_21 = all_228_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_248_21, e0,
% 245.57/58.03 | e3, simplifying with (203), (678) gives:
% 245.57/58.03 | (904) all_248_21 = all_48_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_9, all_250_9, e0,
% 245.57/58.03 | e3, simplifying with (532), (704) gives:
% 245.57/58.03 | (905) all_250_9 = all_246_9
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_19, all_250_9, e0,
% 245.57/58.03 | e3, simplifying with (482), (704) gives:
% 245.57/58.03 | (906) all_250_9 = all_244_19
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_240_2, all_250_9, e0,
% 245.57/58.03 | e3, simplifying with (461), (704) gives:
% 245.57/58.03 | (907) all_250_9 = all_240_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_74_2, e1, e3,
% 245.57/58.03 | simplifying with (209), (242) gives:
% 245.57/58.03 | (908) all_74_2 = all_52_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_122_2, e1, e3,
% 245.57/58.03 | simplifying with (209), (309) gives:
% 245.57/58.03 | (909) all_122_2 = all_52_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_122_2, all_204_2, e1,
% 245.57/58.03 | e3, simplifying with (309), (417) gives:
% 245.57/58.03 | (910) all_204_2 = all_122_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_74_2, all_244_12, e1,
% 245.57/58.03 | e3, simplifying with (242), (483) gives:
% 245.57/58.03 | (911) all_244_12 = all_74_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_204_2, all_246_8, e1,
% 245.57/58.03 | e3, simplifying with (417), (533) gives:
% 245.57/58.03 | (912) all_246_8 = all_204_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_8, all_248_16, e1,
% 245.57/58.03 | e3, simplifying with (533), (679) gives:
% 245.57/58.03 | (913) all_248_16 = all_246_8
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_248_16, e1,
% 245.57/58.03 | e3, simplifying with (200), (679) gives:
% 245.57/58.03 | (914) all_248_16 = all_46_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_244_12, all_250_8, e1,
% 245.57/58.03 | e3, simplifying with (483), (705) gives:
% 245.57/58.03 | (915) all_250_8 = all_244_12
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_250_8, e1, e3,
% 245.57/58.03 | simplifying with (185), (705) gives:
% 245.57/58.03 | (916) all_250_8 = all_36_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_154_2, all_156_2, e2,
% 245.57/58.03 | e3, simplifying with (352), (354) gives:
% 245.57/58.03 | (917) all_156_2 = all_154_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_234_2, all_244_7, e2,
% 245.57/58.03 | e3, simplifying with (454), (484) gives:
% 245.57/58.03 | (918) all_244_7 = all_234_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_154_2, all_244_7, e2,
% 245.57/58.03 | e3, simplifying with (352), (484) gives:
% 245.57/58.03 | (919) all_244_7 = all_154_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_244_7, e2, e3,
% 245.57/58.03 | simplifying with (215), (484) gives:
% 245.57/58.03 | (920) all_244_7 = all_56_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_248_11, e2, e3,
% 245.57/58.03 | simplifying with (143), (680) gives:
% 245.57/58.03 | (921) all_248_11 = all_8_2
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_248_11, all_250_7, e2,
% 245.57/58.03 | e3, simplifying with (680), (706) gives:
% 245.57/58.03 | (922) all_250_7 = all_248_11
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_246_7, all_250_7, e2,
% 245.57/58.03 | e3, simplifying with (534), (706) gives:
% 245.57/58.03 | (923) all_250_7 = all_246_7
% 245.57/58.03 |
% 245.57/58.03 | GROUND_INST: instantiating (function-axioms) with all_220_2, all_250_7, e2,
% 245.57/58.03 | e3, simplifying with (437), (706) gives:
% 245.57/58.03 | (924) all_250_7 = all_220_2
% 245.57/58.03 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_156_2, all_250_7, e2,
% 245.57/58.04 | e3, simplifying with (354), (706) gives:
% 245.57/58.04 | (925) all_250_7 = all_156_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_6, all_248_6, e3,
% 245.57/58.04 | e3, simplifying with (535), (681) gives:
% 245.57/58.04 | (926) all_248_6 = all_246_6
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_248_6, all_250_6, e3,
% 245.57/58.04 | e3, simplifying with (681), (707) gives:
% 245.57/58.04 | (927) all_250_6 = all_248_6
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_3, all_250_6, e3,
% 245.57/58.04 | e3, simplifying with (485), (707) gives:
% 245.57/58.04 | (928) all_250_6 = all_244_3
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_146_2, all_208_2, e4,
% 245.57/58.04 | e3, simplifying with (342), (422) gives:
% 245.57/58.04 | (929) all_208_2 = all_146_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_136_2, all_208_2, e4,
% 245.57/58.04 | e3, simplifying with (329), (422) gives:
% 245.57/58.04 | (930) all_208_2 = all_136_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_208_2, all_244_1, e4,
% 245.57/58.04 | e3, simplifying with (422), (486) gives:
% 245.57/58.04 | (931) all_244_1 = all_208_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_168_2, all_244_1, e4,
% 245.57/58.04 | e3, simplifying with (368), (486) gives:
% 245.57/58.04 | (932) all_244_1 = all_168_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_5, all_248_1, e4,
% 245.57/58.04 | e3, simplifying with (536), (682) gives:
% 245.57/58.04 | (933) all_248_1 = all_246_5
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_208_2, all_248_1, e4,
% 245.57/58.04 | e3, simplifying with (422), (682) gives:
% 245.57/58.04 | (934) all_248_1 = all_208_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_176_2, all_248_1, e4,
% 245.57/58.04 | e3, simplifying with (380), (682) gives:
% 245.57/58.04 | (935) all_248_1 = all_176_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_1, all_250_5, e4,
% 245.57/58.04 | e3, simplifying with (486), (708) gives:
% 245.57/58.04 | (936) all_250_5 = all_244_1
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_100_2, all_250_5, e4,
% 245.57/58.04 | e3, simplifying with (278), (708) gives:
% 245.57/58.04 | (937) all_250_5 = all_100_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_128_2, all_132_2, e0,
% 245.57/58.04 | e4, simplifying with (318), (323) gives:
% 245.57/58.04 | (938) all_132_2 = all_128_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_132_2, all_236_2, e0,
% 245.57/58.04 | e4, simplifying with (323), (457) gives:
% 245.57/58.04 | (939) all_236_2 = all_132_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_236_2, all_238_2, e0,
% 245.57/58.04 | e4, simplifying with (457), (459) gives:
% 245.57/58.04 | (940) all_238_2 = all_236_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_17, all_246_4, e0,
% 245.57/58.04 | e4, simplifying with (487), (537) gives:
% 245.57/58.04 | (941) all_246_4 = all_244_17
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_128_2, all_246_4, e0,
% 245.57/58.04 | e4, simplifying with (318), (537) gives:
% 245.57/58.04 | (942) all_246_4 = all_128_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_246_4, e0, e4,
% 245.57/58.04 | simplifying with (212), (537) gives:
% 245.57/58.04 | (943) all_246_4 = all_54_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_238_2, all_248_20, e0,
% 245.57/58.04 | e4, simplifying with (459), (683) gives:
% 245.57/58.04 | (944) all_248_20 = all_238_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_248_20, all_250_4, e0,
% 245.57/58.04 | e4, simplifying with (683), (709) gives:
% 245.57/58.04 | (945) all_250_4 = all_248_20
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_250_4, e0, e4,
% 245.57/58.04 | simplifying with (176), (709) gives:
% 245.57/58.04 | (946) all_250_4 = all_30_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_202_2, e1, e4,
% 245.57/58.04 | simplifying with (170), (414) gives:
% 245.57/58.04 | (947) all_202_2 = all_26_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_202_2, all_222_2, e1,
% 245.57/58.04 | e4, simplifying with (414), (439) gives:
% 245.57/58.04 | (948) all_222_2 = all_202_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_88_2, all_222_2, e1, e4,
% 245.57/58.04 | simplifying with (262), (439) gives:
% 245.57/58.04 | (949) all_222_2 = all_88_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_222_2, e1, e4,
% 245.57/58.04 | simplifying with (197), (439) gives:
% 245.57/58.04 | (950) all_222_2 = all_44_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_10, all_246_3, e1,
% 245.57/58.04 | e4, simplifying with (488), (538) gives:
% 245.57/58.04 | (951) all_246_3 = all_244_10
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_222_2, all_246_3, e1,
% 245.57/58.04 | e4, simplifying with (439), (538) gives:
% 245.57/58.04 | (952) all_246_3 = all_222_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_3, all_248_15, e1,
% 245.57/58.04 | e4, simplifying with (538), (684) gives:
% 245.57/58.04 | (953) all_248_15 = all_246_3
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_248_15, all_250_3, e1,
% 245.57/58.04 | e4, simplifying with (684), (710) gives:
% 245.57/58.04 | (954) all_250_3 = all_248_15
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_216_2, all_250_3, e1,
% 245.57/58.04 | e4, simplifying with (432), (710) gives:
% 245.57/58.04 | (955) all_250_3 = all_216_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_214_2, e2, e4,
% 245.57/58.04 | simplifying with (140), (429) gives:
% 245.57/58.04 | (956) all_214_2 = all_6_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_2, all_248_10, e2,
% 245.57/58.04 | e4, simplifying with (539), (685) gives:
% 245.57/58.04 | (957) all_248_10 = all_246_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_5, all_248_10, e2,
% 245.57/58.04 | e4, simplifying with (489), (685) gives:
% 245.57/58.04 | (958) all_248_10 = all_244_5
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_214_2, all_248_10, e2,
% 245.57/58.04 | e4, simplifying with (429), (685) gives:
% 245.57/58.04 | (959) all_248_10 = all_214_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_196_2, all_248_10, e2,
% 245.57/58.04 | e4, simplifying with (407), (685) gives:
% 245.57/58.04 | (960) all_248_10 = all_196_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_80_2, all_248_10, e2,
% 245.57/58.04 | e4, simplifying with (251), (685) gives:
% 245.57/58.04 | (961) all_248_10 = all_80_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_218_2, all_250_2, e2,
% 245.57/58.04 | e4, simplifying with (435), (711) gives:
% 245.57/58.04 | (962) all_250_2 = all_218_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_214_2, all_250_2, e2,
% 245.57/58.04 | e4, simplifying with (429), (711) gives:
% 245.57/58.04 | (963) all_250_2 = all_214_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_194_2, all_250_2, e2,
% 245.57/58.04 | e4, simplifying with (405), (711) gives:
% 245.57/58.04 | (964) all_250_2 = all_194_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_98_2, all_140_2, e3, e4,
% 245.57/58.04 | simplifying with (276), (335) gives:
% 245.57/58.04 | (965) all_140_2 = all_98_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_140_2, all_182_2, e3,
% 245.57/58.04 | e4, simplifying with (335), (387) gives:
% 245.57/58.04 | (966) all_182_2 = all_140_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_184_2, all_244_2, e3,
% 245.57/58.04 | e4, simplifying with (390), (490) gives:
% 245.57/58.04 | (967) all_244_2 = all_184_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_182_2, all_244_2, e3,
% 245.57/58.04 | e4, simplifying with (387), (490) gives:
% 245.57/58.04 | (968) all_244_2 = all_182_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_182_2, all_246_1, e3,
% 245.57/58.04 | e4, simplifying with (387), (540) gives:
% 245.57/58.04 | (969) all_246_1 = all_182_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_1, all_248_5, e3,
% 245.57/58.04 | e4, simplifying with (540), (686) gives:
% 245.57/58.04 | (970) all_248_5 = all_246_1
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_142_2, all_248_5, e3,
% 245.57/58.04 | e4, simplifying with (338), (686) gives:
% 245.57/58.04 | (971) all_248_5 = all_142_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_2, all_250_1, e3,
% 245.57/58.04 | e4, simplifying with (490), (712) gives:
% 245.57/58.04 | (972) all_250_1 = all_244_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_84_2, all_250_1, e3, e4,
% 245.57/58.04 | simplifying with (257), (712) gives:
% 245.57/58.04 | (973) all_250_1 = all_84_2
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_246_0, all_248_0, e4,
% 245.57/58.04 | e4, simplifying with (541), (687) gives:
% 245.57/58.04 | (974) all_248_0 = all_246_0
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_248_0, all_250_0, e4,
% 245.57/58.04 | e4, simplifying with (687), (713) gives:
% 245.57/58.04 | (975) all_250_0 = all_248_0
% 245.57/58.04 |
% 245.57/58.04 | GROUND_INST: instantiating (function-axioms) with all_244_0, all_250_0, e4,
% 245.57/58.04 | e4, simplifying with (491), (713) gives:
% 245.57/58.04 | (976) all_250_0 = all_244_0
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (975), (976) imply:
% 245.57/58.04 | (977) all_248_0 = all_244_0
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (977) implies:
% 245.57/58.04 | (978) all_248_0 = all_244_0
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (972), (973) imply:
% 245.57/58.04 | (979) all_244_2 = all_84_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (979) implies:
% 245.57/58.04 | (980) all_244_2 = all_84_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (962), (963) imply:
% 245.57/58.04 | (981) all_218_2 = all_214_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (962), (964) imply:
% 245.57/58.04 | (982) all_218_2 = all_194_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (954), (955) imply:
% 245.57/58.04 | (983) all_248_15 = all_216_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (983) implies:
% 245.57/58.04 | (984) all_248_15 = all_216_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (945), (946) imply:
% 245.57/58.04 | (985) all_248_20 = all_30_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (985) implies:
% 245.57/58.04 | (986) all_248_20 = all_30_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (936), (937) imply:
% 245.57/58.04 | (987) all_244_1 = all_100_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (987) implies:
% 245.57/58.04 | (988) all_244_1 = all_100_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (927), (928) imply:
% 245.57/58.04 | (989) all_248_6 = all_244_3
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (989) implies:
% 245.57/58.04 | (990) all_248_6 = all_244_3
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (922), (923) imply:
% 245.57/58.04 | (991) all_248_11 = all_246_7
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (991) implies:
% 245.57/58.04 | (992) all_248_11 = all_246_7
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (923), (925) imply:
% 245.57/58.04 | (993) all_246_7 = all_156_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (923), (924) imply:
% 245.57/58.04 | (994) all_246_7 = all_220_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (915), (916) imply:
% 245.57/58.04 | (995) all_244_12 = all_36_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (995) implies:
% 245.57/58.04 | (996) all_244_12 = all_36_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (905), (907) imply:
% 245.57/58.04 | (997) all_246_9 = all_240_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (905), (906) imply:
% 245.57/58.04 | (998) all_246_9 = all_244_19
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (897), (898) imply:
% 245.57/58.04 | (999) all_246_10 = all_186_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (999) implies:
% 245.57/58.04 | (1000) all_246_10 = all_186_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (888), (889) imply:
% 245.57/58.04 | (1001) all_248_7 = all_246_11
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1001) implies:
% 245.57/58.04 | (1002) all_248_7 = all_246_11
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (879), (880) imply:
% 245.57/58.04 | (1003) all_248_12 = all_244_8
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1003) implies:
% 245.57/58.04 | (1004) all_248_12 = all_244_8
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (876), (877) imply:
% 245.57/58.04 | (1005) all_244_14 = all_106_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1005) implies:
% 245.57/58.04 | (1006) all_244_14 = all_106_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (867), (868) imply:
% 245.57/58.04 | (1007) all_248_22 = all_86_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1007) implies:
% 245.57/58.04 | (1008) all_248_22 = all_86_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (855), (857) imply:
% 245.57/58.04 | (1009) all_244_9 = all_152_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (855), (856) imply:
% 245.57/58.04 | (1010) all_244_9 = all_170_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (855), (858) imply:
% 245.57/58.04 | (1011) all_244_9 = all_144_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (855), (859) imply:
% 245.57/58.04 | (1012) all_244_9 = all_24_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (848), (850) imply:
% 245.57/58.04 | (1013) all_248_8 = all_244_11
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (848), (849) imply:
% 245.57/58.04 | (1014) all_248_8 = all_246_16
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (840), (841) imply:
% 245.57/58.04 | (1015) all_192_2 = all_4_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1015) implies:
% 245.57/58.04 | (1016) all_192_2 = all_4_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (831), (832) imply:
% 245.57/58.04 | (1017) all_248_18 = all_246_18
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1017) implies:
% 245.57/58.04 | (1018) all_248_18 = all_246_18
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (828), (829) imply:
% 245.57/58.04 | (1019) all_248_23 = all_34_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1019) implies:
% 245.57/58.04 | (1020) all_248_23 = all_34_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (819), (820) imply:
% 245.57/58.04 | (1021) all_42_2 = all_18_2
% 245.57/58.04 |
% 245.57/58.04 | SIMP: (1021) implies:
% 245.57/58.04 | (1022) all_42_2 = all_18_2
% 245.57/58.04 |
% 245.57/58.04 | COMBINE_EQS: (818), (820) imply:
% 245.57/58.05 | (1023) all_210_2 = all_18_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1023) implies:
% 245.57/58.05 | (1024) all_210_2 = all_18_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (808), (811) imply:
% 245.57/58.05 | (1025) all_118_2 = all_72_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (808), (810) imply:
% 245.57/58.05 | (1026) all_118_2 = all_90_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (808), (809) imply:
% 245.57/58.05 | (1027) all_118_2 = all_104_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (801), (802) imply:
% 245.57/58.05 | (1028) all_158_2 = all_82_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1028) implies:
% 245.57/58.05 | (1029) all_158_2 = all_82_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (792), (793) imply:
% 245.57/58.05 | (1030) all_246_23 = all_32_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1030) implies:
% 245.57/58.05 | (1031) all_246_23 = all_32_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (782), (784) imply:
% 245.57/58.05 | (1032) all_248_24 = all_244_24
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (782), (783) imply:
% 245.57/58.05 | (1033) all_248_24 = all_246_24
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (974), (978) imply:
% 245.57/58.05 | (1034) all_246_0 = all_244_0
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1034) implies:
% 245.57/58.05 | (1035) all_246_0 = all_244_0
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (933), (934) imply:
% 245.57/58.05 | (1036) all_246_5 = all_208_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (933), (935) imply:
% 245.57/58.05 | (1037) all_246_5 = all_176_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (894), (895) imply:
% 245.57/58.05 | (1038) all_244_4 = all_224_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1038) implies:
% 245.57/58.05 | (1039) all_244_4 = all_224_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (893), (895) imply:
% 245.57/58.05 | (1040) all_246_10 = all_224_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1040) implies:
% 245.57/58.05 | (1041) all_246_10 = all_224_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (895), (896) imply:
% 245.57/58.05 | (1042) all_224_2 = all_148_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (853), (854) imply:
% 245.57/58.05 | (1043) all_246_15 = all_66_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1043) implies:
% 245.57/58.05 | (1044) all_246_15 = all_66_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (816), (817) imply:
% 245.57/58.05 | (1045) all_246_20 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1045) implies:
% 245.57/58.05 | (1046) all_246_20 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (970), (971) imply:
% 245.57/58.05 | (1047) all_246_1 = all_142_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1047) implies:
% 245.57/58.05 | (1048) all_246_1 = all_142_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (926), (990) imply:
% 245.57/58.05 | (1049) all_246_6 = all_244_3
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1049) implies:
% 245.57/58.05 | (1050) all_246_6 = all_244_3
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (887), (1002) imply:
% 245.57/58.05 | (1051) all_246_11 = all_138_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (886), (1002) imply:
% 245.57/58.05 | (1052) all_246_11 = all_172_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1013), (1014) imply:
% 245.57/58.05 | (1053) all_246_16 = all_244_11
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1053) implies:
% 245.57/58.05 | (1054) all_246_16 = all_244_11
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (806), (807) imply:
% 245.57/58.05 | (1055) all_246_21 = all_22_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1055) implies:
% 245.57/58.05 | (1056) all_246_21 = all_22_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (957), (959) imply:
% 245.57/58.05 | (1057) all_246_2 = all_214_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (957), (960) imply:
% 245.57/58.05 | (1058) all_246_2 = all_196_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (957), (961) imply:
% 245.57/58.05 | (1059) all_246_2 = all_80_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (957), (958) imply:
% 245.57/58.05 | (1060) all_246_2 = all_244_5
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (921), (992) imply:
% 245.57/58.05 | (1061) all_246_7 = all_8_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1061) implies:
% 245.57/58.05 | (1062) all_246_7 = all_8_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (878), (1004) imply:
% 245.57/58.05 | (1063) all_246_12 = all_244_8
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1063) implies:
% 245.57/58.05 | (1064) all_246_12 = all_244_8
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (836), (837) imply:
% 245.57/58.05 | (1065) all_246_17 = all_244_13
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1065) implies:
% 245.57/58.05 | (1066) all_246_17 = all_244_13
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (837), (838) imply:
% 245.57/58.05 | (1067) all_244_13 = all_150_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (837), (839) imply:
% 245.57/58.05 | (1068) all_244_13 = all_50_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (798), (799) imply:
% 245.57/58.05 | (1069) all_246_22 = all_244_20
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (798), (800) imply:
% 245.57/58.05 | (1070) all_246_22 = all_28_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (953), (984) imply:
% 245.57/58.05 | (1071) all_246_3 = all_216_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1071) implies:
% 245.57/58.05 | (1072) all_246_3 = all_216_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (913), (914) imply:
% 245.57/58.05 | (1073) all_246_8 = all_46_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1073) implies:
% 245.57/58.05 | (1074) all_246_8 = all_46_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (874), (875) imply:
% 245.57/58.05 | (1075) all_246_13 = all_94_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1075) implies:
% 245.57/58.05 | (1076) all_246_13 = all_94_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (830), (1018) imply:
% 245.57/58.05 | (1077) all_246_18 = all_244_15
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (790), (791) imply:
% 245.57/58.05 | (1078) all_244_22 = all_230_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1078) implies:
% 245.57/58.05 | (1079) all_244_22 = all_230_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (944), (986) imply:
% 245.57/58.05 | (1080) all_238_2 = all_30_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1080) implies:
% 245.57/58.05 | (1081) all_238_2 = all_30_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (903), (904) imply:
% 245.57/58.05 | (1082) all_228_2 = all_48_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1082) implies:
% 245.57/58.05 | (1083) all_228_2 = all_48_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (866), (1008) imply:
% 245.57/58.05 | (1084) all_178_2 = all_86_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1084) implies:
% 245.57/58.05 | (1085) all_178_2 = all_86_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (827), (1020) imply:
% 245.57/58.05 | (1086) all_246_19 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1086) implies:
% 245.57/58.05 | (1087) all_246_19 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1032), (1033) imply:
% 245.57/58.05 | (1088) all_246_24 = all_244_24
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (969), (1048) imply:
% 245.57/58.05 | (1089) all_182_2 = all_142_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1089) implies:
% 245.57/58.05 | (1090) all_182_2 = all_142_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1057), (1060) imply:
% 245.57/58.05 | (1091) all_244_5 = all_214_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1058), (1060) imply:
% 245.57/58.05 | (1092) all_244_5 = all_196_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1059), (1060) imply:
% 245.57/58.05 | (1093) all_244_5 = all_80_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (951), (952) imply:
% 245.57/58.05 | (1094) all_244_10 = all_222_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (951), (1072) imply:
% 245.57/58.05 | (1095) all_244_10 = all_216_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (941), (942) imply:
% 245.57/58.05 | (1096) all_244_17 = all_128_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (941), (943) imply:
% 245.57/58.05 | (1097) all_244_17 = all_54_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1036), (1037) imply:
% 245.57/58.05 | (1098) all_208_2 = all_176_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1098) implies:
% 245.57/58.05 | (1099) all_208_2 = all_176_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (994), (1062) imply:
% 245.57/58.05 | (1100) all_220_2 = all_8_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (993), (994) imply:
% 245.57/58.05 | (1101) all_220_2 = all_156_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (912), (1074) imply:
% 245.57/58.05 | (1102) all_204_2 = all_46_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1102) implies:
% 245.57/58.05 | (1103) all_204_2 = all_46_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (997), (998) imply:
% 245.57/58.05 | (1104) all_244_19 = all_240_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1104) implies:
% 245.57/58.05 | (1105) all_244_19 = all_240_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1000), (1041) imply:
% 245.57/58.05 | (1106) all_224_2 = all_186_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1106) implies:
% 245.57/58.05 | (1107) all_224_2 = all_186_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1051), (1052) imply:
% 245.57/58.05 | (1108) all_172_2 = all_138_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1108) implies:
% 245.57/58.05 | (1109) all_172_2 = all_138_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (873), (1076) imply:
% 245.57/58.05 | (1110) all_244_14 = all_94_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1110) implies:
% 245.57/58.05 | (1111) all_244_14 = all_94_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (864), (865) imply:
% 245.57/58.05 | (1112) all_244_21 = all_40_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1112) implies:
% 245.57/58.05 | (1113) all_244_21 = all_40_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (852), (1044) imply:
% 245.57/58.05 | (1114) all_170_2 = all_66_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1114) implies:
% 245.57/58.05 | (1115) all_170_2 = all_66_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (846), (1054) imply:
% 245.57/58.05 | (1116) all_244_11 = all_166_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (847), (1054) imply:
% 245.57/58.05 | (1117) all_244_11 = all_114_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (835), (1066) imply:
% 245.57/58.05 | (1118) all_244_13 = all_160_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1118) implies:
% 245.57/58.05 | (1119) all_244_13 = all_160_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (826), (1087) imply:
% 245.57/58.05 | (1120) all_244_23 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1120) implies:
% 245.57/58.05 | (1121) all_244_23 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (815), (1046) imply:
% 245.57/58.05 | (1122) all_244_16 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1122) implies:
% 245.57/58.05 | (1123) all_244_16 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (804), (1056) imply:
% 245.57/58.05 | (1124) all_244_18 = all_22_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (804), (805) imply:
% 245.57/58.05 | (1125) all_244_18 = all_104_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1069), (1070) imply:
% 245.57/58.05 | (1126) all_244_20 = all_28_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1126) implies:
% 245.57/58.05 | (1127) all_244_20 = all_28_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (789), (1031) imply:
% 245.57/58.05 | (1128) all_244_22 = all_32_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1128) implies:
% 245.57/58.05 | (1129) all_244_22 = all_32_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (931), (932) imply:
% 245.57/58.05 | (1130) all_208_2 = all_168_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1130) implies:
% 245.57/58.05 | (1131) all_208_2 = all_168_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (932), (988) imply:
% 245.57/58.05 | (1132) all_168_2 = all_100_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (967), (980) imply:
% 245.57/58.05 | (1133) all_184_2 = all_84_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (967), (968) imply:
% 245.57/58.05 | (1134) all_184_2 = all_182_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (892), (1039) imply:
% 245.57/58.05 | (1135) all_224_2 = all_134_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1135) implies:
% 245.57/58.05 | (1136) all_224_2 = all_134_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1092), (1093) imply:
% 245.57/58.05 | (1137) all_196_2 = all_80_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1091), (1092) imply:
% 245.57/58.05 | (1138) all_214_2 = all_196_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1138) implies:
% 245.57/58.05 | (1139) all_214_2 = all_196_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (884), (885) imply:
% 245.57/58.05 | (1140) all_124_2 = all_78_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1140) implies:
% 245.57/58.05 | (1141) all_124_2 = all_78_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (918), (920) imply:
% 245.57/58.05 | (1142) all_234_2 = all_56_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (918), (919) imply:
% 245.57/58.05 | (1143) all_234_2 = all_154_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1011), (1012) imply:
% 245.57/58.05 | (1144) all_144_2 = all_24_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1010), (1011) imply:
% 245.57/58.05 | (1145) all_170_2 = all_144_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1145) implies:
% 245.57/58.05 | (1146) all_170_2 = all_144_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1009), (1011) imply:
% 245.57/58.05 | (1147) all_152_2 = all_144_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1147) implies:
% 245.57/58.05 | (1148) all_152_2 = all_144_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1094), (1095) imply:
% 245.57/58.05 | (1149) all_222_2 = all_216_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1149) implies:
% 245.57/58.05 | (1150) all_222_2 = all_216_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1116), (1117) imply:
% 245.57/58.05 | (1151) all_166_2 = all_114_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1151) implies:
% 245.57/58.05 | (1152) all_166_2 = all_114_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (911), (996) imply:
% 245.57/58.05 | (1153) all_74_2 = all_36_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1153) implies:
% 245.57/58.05 | (1154) all_74_2 = all_36_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1068), (1119) imply:
% 245.57/58.05 | (1155) all_160_2 = all_50_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1067), (1119) imply:
% 245.57/58.05 | (1156) all_160_2 = all_150_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (872), (1006) imply:
% 245.57/58.05 | (1157) all_188_2 = all_106_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1157) implies:
% 245.57/58.05 | (1158) all_188_2 = all_106_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1006), (1111) imply:
% 245.57/58.05 | (1159) all_106_2 = all_94_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (814), (1123) imply:
% 245.57/58.05 | (1160) all_212_2 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1160) implies:
% 245.57/58.05 | (1161) all_212_2 = all_14_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1096), (1097) imply:
% 245.57/58.05 | (1162) all_128_2 = all_54_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1162) implies:
% 245.57/58.05 | (1163) all_128_2 = all_54_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1124), (1125) imply:
% 245.57/58.05 | (1164) all_104_2 = all_22_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1164) implies:
% 245.57/58.05 | (1165) all_104_2 = all_22_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (900), (1105) imply:
% 245.57/58.05 | (1166) all_240_2 = all_226_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (902), (1105) imply:
% 245.57/58.05 | (1167) all_240_2 = all_126_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (901), (1105) imply:
% 245.57/58.05 | (1168) all_240_2 = all_200_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (797), (1127) imply:
% 245.57/58.05 | (1169) all_162_2 = all_28_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1169) implies:
% 245.57/58.05 | (1170) all_162_2 = all_28_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (863), (1113) imply:
% 245.57/58.05 | (1171) all_116_2 = all_40_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1171) implies:
% 245.57/58.05 | (1172) all_116_2 = all_40_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1079), (1129) imply:
% 245.57/58.05 | (1173) all_230_2 = all_32_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (788), (1079) imply:
% 245.57/58.05 | (1174) all_230_2 = all_60_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (787), (1079) imply:
% 245.57/58.05 | (1175) all_230_2 = all_92_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (825), (1121) imply:
% 245.57/58.05 | (1176) all_164_2 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | SIMP: (1176) implies:
% 245.57/58.05 | (1177) all_164_2 = all_34_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (869), (870) imply:
% 245.57/58.05 | (1178) all_190_2 = all_188_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (869), (871) imply:
% 245.57/58.05 | (1179) all_190_2 = all_38_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1167), (1168) imply:
% 245.57/58.05 | (1180) all_200_2 = all_126_2
% 245.57/58.05 |
% 245.57/58.05 | COMBINE_EQS: (1166), (1168) imply:
% 245.57/58.06 | (1181) all_226_2 = all_200_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1181) implies:
% 245.57/58.06 | (1182) all_226_2 = all_200_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (940), (1081) imply:
% 245.57/58.06 | (1183) all_236_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1183) implies:
% 245.57/58.06 | (1184) all_236_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (939), (1184) imply:
% 245.57/58.06 | (1185) all_132_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1185) implies:
% 245.57/58.06 | (1186) all_132_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1142), (1143) imply:
% 245.57/58.06 | (1187) all_154_2 = all_56_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1187) implies:
% 245.57/58.06 | (1188) all_154_2 = all_56_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (823), (824) imply:
% 245.57/58.06 | (1189) all_198_2 = all_110_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1189) implies:
% 245.57/58.06 | (1190) all_198_2 = all_110_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1174), (1175) imply:
% 245.57/58.06 | (1191) all_92_2 = all_60_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1173), (1175) imply:
% 245.57/58.06 | (1192) all_92_2 = all_32_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (899), (1083) imply:
% 245.57/58.06 | (1193) all_226_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1193) implies:
% 245.57/58.06 | (1194) all_226_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1182), (1194) imply:
% 245.57/58.06 | (1195) all_200_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1195) implies:
% 245.57/58.06 | (1196) all_200_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1042), (1107) imply:
% 245.57/58.06 | (1197) all_186_2 = all_148_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1107), (1136) imply:
% 245.57/58.06 | (1198) all_186_2 = all_134_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (950), (1150) imply:
% 245.57/58.06 | (1199) all_216_2 = all_44_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (949), (1150) imply:
% 245.57/58.06 | (1200) all_216_2 = all_88_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (948), (1150) imply:
% 245.57/58.06 | (1201) all_216_2 = all_202_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1100), (1101) imply:
% 245.57/58.06 | (1202) all_156_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1202) implies:
% 245.57/58.06 | (1203) all_156_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (981), (982) imply:
% 245.57/58.06 | (1204) all_214_2 = all_194_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1204) implies:
% 245.57/58.06 | (1205) all_214_2 = all_194_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1199), (1200) imply:
% 245.57/58.06 | (1206) all_88_2 = all_44_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1200), (1201) imply:
% 245.57/58.06 | (1207) all_202_2 = all_88_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1207) implies:
% 245.57/58.06 | (1208) all_202_2 = all_88_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (956), (1205) imply:
% 245.57/58.06 | (1209) all_194_2 = all_6_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1139), (1205) imply:
% 245.57/58.06 | (1210) all_196_2 = all_194_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1210) implies:
% 245.57/58.06 | (1211) all_196_2 = all_194_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (813), (1161) imply:
% 245.57/58.06 | (1212) all_42_2 = all_14_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1212) implies:
% 245.57/58.06 | (1213) all_42_2 = all_14_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (812), (1024) imply:
% 245.57/58.06 | (1214) all_18_2 = all_12_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1214) implies:
% 245.57/58.06 | (1215) all_18_2 = all_12_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (930), (1099) imply:
% 245.57/58.06 | (1216) all_176_2 = all_136_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (929), (1099) imply:
% 245.57/58.06 | (1217) all_176_2 = all_146_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1099), (1131) imply:
% 245.57/58.06 | (1218) all_176_2 = all_168_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (794), (796) imply:
% 245.57/58.06 | (1219) all_162_2 = all_108_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1219) implies:
% 245.57/58.06 | (1220) all_162_2 = all_108_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (795), (796) imply:
% 245.57/58.06 | (1221) all_158_2 = all_108_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1221) implies:
% 245.57/58.06 | (1222) all_158_2 = all_108_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (910), (1103) imply:
% 245.57/58.06 | (1223) all_122_2 = all_46_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1223) implies:
% 245.57/58.06 | (1224) all_122_2 = all_46_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (947), (1208) imply:
% 245.57/58.06 | (1225) all_88_2 = all_26_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1225) implies:
% 245.57/58.06 | (1226) all_88_2 = all_26_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1180), (1196) imply:
% 245.57/58.06 | (1227) all_126_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1227) implies:
% 245.57/58.06 | (1228) all_126_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (822), (1190) imply:
% 245.57/58.06 | (1229) all_110_2 = all_96_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (821), (1190) imply:
% 245.57/58.06 | (1230) all_164_2 = all_110_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1230) implies:
% 245.57/58.06 | (1231) all_164_2 = all_110_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1137), (1211) imply:
% 245.57/58.06 | (1232) all_194_2 = all_80_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1232) implies:
% 245.57/58.06 | (1233) all_194_2 = all_80_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1209), (1233) imply:
% 245.57/58.06 | (1234) all_80_2 = all_6_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1234) implies:
% 245.57/58.06 | (1235) all_80_2 = all_6_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (834), (1016) imply:
% 245.57/58.06 | (1236) all_180_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1236) implies:
% 245.57/58.06 | (1237) all_180_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1178), (1179) imply:
% 245.57/58.06 | (1238) all_188_2 = all_38_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1238) implies:
% 245.57/58.06 | (1239) all_188_2 = all_38_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1158), (1239) imply:
% 245.57/58.06 | (1240) all_106_2 = all_38_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1240) implies:
% 245.57/58.06 | (1241) all_106_2 = all_38_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1197), (1198) imply:
% 245.57/58.06 | (1242) all_148_2 = all_134_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1242) implies:
% 245.57/58.06 | (1243) all_148_2 = all_134_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1133), (1134) imply:
% 245.57/58.06 | (1244) all_182_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1244) implies:
% 245.57/58.06 | (1245) all_182_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (966), (1090) imply:
% 245.57/58.06 | (1246) all_142_2 = all_140_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1090), (1245) imply:
% 245.57/58.06 | (1247) all_142_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (833), (1237) imply:
% 245.57/58.06 | (1248) all_150_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1248) implies:
% 245.57/58.06 | (1249) all_150_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (862), (1085) imply:
% 245.57/58.06 | (1250) all_174_2 = all_86_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1250) implies:
% 245.57/58.06 | (1251) all_174_2 = all_86_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1216), (1217) imply:
% 245.57/58.06 | (1252) all_146_2 = all_136_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1217), (1218) imply:
% 245.57/58.06 | (1253) all_168_2 = all_146_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1253) implies:
% 245.57/58.06 | (1254) all_168_2 = all_146_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (861), (1251) imply:
% 245.57/58.06 | (1255) all_116_2 = all_86_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1255) implies:
% 245.57/58.06 | (1256) all_116_2 = all_86_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (882), (1109) imply:
% 245.57/58.06 | (1257) all_138_2 = all_124_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (883), (1109) imply:
% 245.57/58.06 | (1258) all_138_2 = all_102_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1115), (1146) imply:
% 245.57/58.06 | (1259) all_144_2 = all_66_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1259) implies:
% 245.57/58.06 | (1260) all_144_2 = all_66_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1132), (1254) imply:
% 245.57/58.06 | (1261) all_146_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1261) implies:
% 245.57/58.06 | (1262) all_146_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (845), (1152) imply:
% 245.57/58.06 | (1263) all_130_2 = all_114_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1263) implies:
% 245.57/58.06 | (1264) all_130_2 = all_114_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1177), (1231) imply:
% 245.57/58.06 | (1265) all_110_2 = all_34_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1265) implies:
% 245.57/58.06 | (1266) all_110_2 = all_34_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1170), (1220) imply:
% 245.57/58.06 | (1267) all_108_2 = all_28_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1267) implies:
% 245.57/58.06 | (1268) all_108_2 = all_28_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1155), (1156) imply:
% 245.57/58.06 | (1269) all_150_2 = all_50_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1269) implies:
% 245.57/58.06 | (1270) all_150_2 = all_50_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1029), (1222) imply:
% 245.57/58.06 | (1271) all_108_2 = all_82_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1271) implies:
% 245.57/58.06 | (1272) all_108_2 = all_82_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (917), (1203) imply:
% 245.57/58.06 | (1273) all_154_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1273) implies:
% 245.57/58.06 | (1274) all_154_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1188), (1274) imply:
% 245.57/58.06 | (1275) all_56_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1275) implies:
% 245.57/58.06 | (1276) all_56_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (851), (1148) imply:
% 245.57/58.06 | (1277) all_144_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1277) implies:
% 245.57/58.06 | (1278) all_144_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1249), (1270) imply:
% 245.57/58.06 | (1279) all_50_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1279) implies:
% 245.57/58.06 | (1280) all_50_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (891), (1243) imply:
% 245.57/58.06 | (1281) all_134_2 = all_64_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (890), (1243) imply:
% 245.57/58.06 | (1282) all_134_2 = all_120_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1252), (1262) imply:
% 245.57/58.06 | (1283) all_136_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1283) implies:
% 245.57/58.06 | (1284) all_136_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1144), (1260) imply:
% 245.57/58.06 | (1285) all_66_2 = all_24_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1260), (1278) imply:
% 245.57/58.06 | (1286) all_66_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1246), (1247) imply:
% 245.57/58.06 | (1287) all_140_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1287) implies:
% 245.57/58.06 | (1288) all_140_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (965), (1288) imply:
% 245.57/58.06 | (1289) all_98_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1289) implies:
% 245.57/58.06 | (1290) all_98_2 = all_84_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1257), (1258) imply:
% 245.57/58.06 | (1291) all_124_2 = all_102_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1291) implies:
% 245.57/58.06 | (1292) all_124_2 = all_102_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1281), (1282) imply:
% 245.57/58.06 | (1293) all_120_2 = all_64_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (938), (1186) imply:
% 245.57/58.06 | (1294) all_128_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1294) implies:
% 245.57/58.06 | (1295) all_128_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (843), (1264) imply:
% 245.57/58.06 | (1296) all_114_2 = all_70_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (842), (1264) imply:
% 245.57/58.06 | (1297) all_114_2 = all_112_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (844), (1264) imply:
% 245.57/58.06 | (1298) all_114_2 = all_62_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1163), (1295) imply:
% 245.57/58.06 | (1299) all_54_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1299) implies:
% 245.57/58.06 | (1300) all_54_2 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (881), (1292) imply:
% 245.57/58.06 | (1301) all_102_2 = all_10_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1141), (1292) imply:
% 245.57/58.06 | (1302) all_102_2 = all_78_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (909), (1224) imply:
% 245.57/58.06 | (1303) all_52_2 = all_46_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1303) implies:
% 245.57/58.06 | (1304) all_52_2 = all_46_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1025), (1026) imply:
% 245.57/58.06 | (1305) all_90_2 = all_72_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1026), (1027) imply:
% 245.57/58.06 | (1306) all_104_2 = all_90_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1306) implies:
% 245.57/58.06 | (1307) all_104_2 = all_90_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (860), (1256) imply:
% 245.57/58.06 | (1308) all_86_2 = all_76_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1172), (1256) imply:
% 245.57/58.06 | (1309) all_86_2 = all_40_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1297), (1298) imply:
% 245.57/58.06 | (1310) all_112_2 = all_62_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1296), (1297) imply:
% 245.57/58.06 | (1311) all_112_2 = all_70_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1310), (1311) imply:
% 245.57/58.06 | (1312) all_70_2 = all_62_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1229), (1266) imply:
% 245.57/58.06 | (1313) all_96_2 = all_34_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1313) implies:
% 245.57/58.06 | (1314) all_96_2 = all_34_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1268), (1272) imply:
% 245.57/58.06 | (1315) all_82_2 = all_28_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1315) implies:
% 245.57/58.06 | (1316) all_82_2 = all_28_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1159), (1241) imply:
% 245.57/58.06 | (1317) all_94_2 = all_38_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1165), (1307) imply:
% 245.57/58.06 | (1318) all_90_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1318) implies:
% 245.57/58.06 | (1319) all_90_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1301), (1302) imply:
% 245.57/58.06 | (1320) all_78_2 = all_10_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1191), (1192) imply:
% 245.57/58.06 | (1321) all_60_2 = all_32_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1321) implies:
% 245.57/58.06 | (1322) all_60_2 = all_32_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1305), (1319) imply:
% 245.57/58.06 | (1323) all_72_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1323) implies:
% 245.57/58.06 | (1324) all_72_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1206), (1226) imply:
% 245.57/58.06 | (1325) all_44_2 = all_26_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1308), (1309) imply:
% 245.57/58.06 | (1326) all_76_2 = all_40_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1326) implies:
% 245.57/58.06 | (1327) all_76_2 = all_40_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (908), (1154) imply:
% 245.57/58.06 | (1328) all_52_2 = all_36_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1328) implies:
% 245.57/58.06 | (1329) all_52_2 = all_36_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (803), (1324) imply:
% 245.57/58.06 | (1330) all_68_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1330) implies:
% 245.57/58.06 | (1331) all_68_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1285), (1286) imply:
% 245.57/58.06 | (1332) all_24_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1332) implies:
% 245.57/58.06 | (1333) all_24_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (785), (786) imply:
% 245.57/58.06 | (1334) all_58_2 = all_20_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (785), (1322) imply:
% 245.57/58.06 | (1335) all_58_2 = all_32_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1334), (1335) imply:
% 245.57/58.06 | (1336) all_32_2 = all_20_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1304), (1329) imply:
% 245.57/58.06 | (1337) all_46_2 = all_36_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1022), (1213) imply:
% 245.57/58.06 | (1338) all_18_2 = all_14_2
% 245.57/58.06 |
% 245.57/58.06 | SIMP: (1338) implies:
% 245.57/58.06 | (1339) all_18_2 = all_14_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1215), (1339) imply:
% 245.57/58.06 | (1340) all_14_2 = all_12_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1213), (1340) imply:
% 245.57/58.06 | (1341) all_42_2 = all_12_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1192), (1336) imply:
% 245.57/58.06 | (1342) all_92_2 = all_20_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1026), (1319) imply:
% 245.57/58.06 | (1343) all_118_2 = all_22_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1224), (1337) imply:
% 245.57/58.06 | (1344) all_122_2 = all_36_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1258), (1301) imply:
% 245.57/58.06 | (1345) all_138_2 = all_10_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1155), (1280) imply:
% 245.57/58.06 | (1346) all_160_2 = all_4_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1115), (1286) imply:
% 245.57/58.06 | (1347) all_170_2 = all_16_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1109), (1345) imply:
% 245.57/58.06 | (1348) all_172_2 = all_10_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1251), (1309) imply:
% 245.57/58.06 | (1349) all_174_2 = all_40_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1217), (1262) imply:
% 245.57/58.06 | (1350) all_176_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1085), (1309) imply:
% 245.57/58.06 | (1351) all_178_2 = all_40_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1198), (1281) imply:
% 245.57/58.06 | (1352) all_186_2 = all_64_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1137), (1235) imply:
% 245.57/58.06 | (1353) all_196_2 = all_6_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1190), (1266) imply:
% 245.57/58.06 | (1354) all_198_2 = all_34_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1103), (1337) imply:
% 245.57/58.06 | (1355) all_204_2 = all_36_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1099), (1350) imply:
% 245.57/58.06 | (1356) all_208_2 = all_100_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1200), (1226) imply:
% 245.57/58.06 | (1357) all_216_2 = all_26_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (982), (1209) imply:
% 245.57/58.06 | (1358) all_218_2 = all_6_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1150), (1357) imply:
% 245.57/58.06 | (1359) all_222_2 = all_26_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1107), (1352) imply:
% 245.57/58.06 | (1360) all_224_2 = all_64_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1175), (1342) imply:
% 245.57/58.06 | (1361) all_230_2 = all_20_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1142), (1276) imply:
% 245.57/58.06 | (1362) all_234_2 = all_8_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1168), (1196) imply:
% 245.57/58.06 | (1363) all_240_2 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1079), (1361) imply:
% 245.57/58.06 | (1364) all_244_22 = all_20_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1105), (1363) imply:
% 245.57/58.06 | (1365) all_244_19 = all_48_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1097), (1300) imply:
% 245.57/58.06 | (1366) all_244_17 = all_30_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1123), (1340) imply:
% 245.57/58.06 | (1367) all_244_16 = all_12_2
% 245.57/58.06 |
% 245.57/58.06 | COMBINE_EQS: (1006), (1241) imply:
% 245.57/58.07 | (1368) all_244_14 = all_38_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1119), (1346) imply:
% 245.57/58.07 | (1369) all_244_13 = all_4_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1117), (1298) imply:
% 245.57/58.07 | (1370) all_244_11 = all_62_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1095), (1357) imply:
% 245.57/58.07 | (1371) all_244_10 = all_26_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1011), (1278) imply:
% 245.57/58.07 | (1372) all_244_9 = all_16_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (918), (1362) imply:
% 245.57/58.07 | (1373) all_244_7 = all_8_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (885), (1320) imply:
% 245.57/58.07 | (1374) all_244_6 = all_10_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1092), (1353) imply:
% 245.57/58.07 | (1375) all_244_5 = all_6_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (892), (1281) imply:
% 245.57/58.07 | (1376) all_244_4 = all_64_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1031), (1336) imply:
% 245.57/58.07 | (1377) all_246_23 = all_20_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1046), (1340) imply:
% 245.57/58.07 | (1378) all_246_20 = all_12_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (835), (1346) imply:
% 245.57/58.07 | (1379) all_246_17 = all_4_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1054), (1370) imply:
% 245.57/58.07 | (1380) all_246_16 = all_62_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1044), (1286) imply:
% 245.57/58.07 | (1381) all_246_15 = all_16_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1076), (1317) imply:
% 245.57/58.07 | (1382) all_246_13 = all_38_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1051), (1345) imply:
% 245.57/58.07 | (1383) all_246_11 = all_10_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1000), (1352) imply:
% 245.57/58.07 | (1384) all_246_10 = all_64_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (997), (1363) imply:
% 245.57/58.07 | (1385) all_246_9 = all_48_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1074), (1337) imply:
% 245.57/58.07 | (1386) all_246_8 = all_36_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1037), (1350) imply:
% 245.57/58.07 | (1387) all_246_5 = all_100_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (941), (1366) imply:
% 245.57/58.07 | (1388) all_246_4 = all_30_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (951), (1371) imply:
% 245.57/58.07 | (1389) all_246_3 = all_26_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1060), (1375) imply:
% 245.57/58.07 | (1390) all_246_2 = all_6_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1048), (1247) imply:
% 245.57/58.07 | (1391) all_246_1 = all_84_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1008), (1309) imply:
% 245.57/58.07 | (1392) all_248_22 = all_40_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (791), (1361) imply:
% 245.57/58.07 | (1393) all_248_19 = all_20_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (875), (1317) imply:
% 245.57/58.07 | (1394) all_248_17 = all_38_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (914), (1337) imply:
% 245.57/58.07 | (1395) all_248_16 = all_36_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (984), (1357) imply:
% 245.57/58.07 | (1396) all_248_15 = all_26_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (837), (1369) imply:
% 245.57/58.07 | (1397) all_248_13 = all_4_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (957), (1390) imply:
% 245.57/58.07 | (1398) all_248_10 = all_6_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1013), (1370) imply:
% 245.57/58.07 | (1399) all_248_8 = all_62_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (1002), (1383) imply:
% 245.57/58.07 | (1400) all_248_7 = all_10_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (971), (1247) imply:
% 245.57/58.07 | (1401) all_248_5 = all_84_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (817), (1340) imply:
% 245.57/58.07 | (1402) all_248_4 = all_12_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (854), (1286) imply:
% 245.57/58.07 | (1403) all_248_3 = all_16_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (895), (1360) imply:
% 245.57/58.07 | (1404) all_248_2 = all_64_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (933), (1387) imply:
% 245.57/58.07 | (1405) all_248_1 = all_100_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (793), (1336) imply:
% 245.57/58.07 | (1406) all_250_23 = all_20_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (802), (1316) imply:
% 245.57/58.07 | (1407) all_250_22 = all_28_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (808), (1343) imply:
% 245.57/58.07 | (1408) all_250_21 = all_22_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (820), (1215) imply:
% 245.57/58.07 | (1409) all_250_20 = all_12_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (832), (1077) imply:
% 245.57/58.07 | (1410) all_250_18 = all_244_15
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (848), (1399) imply:
% 245.57/58.07 | (1411) all_250_16 = all_62_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (855), (1372) imply:
% 245.57/58.07 | (1412) all_250_15 = all_16_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (877), (1241) imply:
% 245.57/58.07 | (1413) all_250_13 = all_38_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (889), (1383) imply:
% 245.57/58.07 | (1414) all_250_11 = all_10_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (898), (1352) imply:
% 245.57/58.07 | (1415) all_250_10 = all_64_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (905), (1385) imply:
% 245.57/58.07 | (1416) all_250_9 = all_48_2
% 245.57/58.07 |
% 245.57/58.07 | COMBINE_EQS: (962), (1358) imply:
% 245.57/58.07 | (1417) all_250_2 = all_6_2
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (662), (978), (1405) imply:
% 245.57/58.07 | (1418) ~ (all_244_0 = all_100_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (661), (978), (1404) imply:
% 245.57/58.07 | (1419) ~ (all_244_0 = all_64_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (660), (978), (1403) imply:
% 245.57/58.07 | (1420) ~ (all_244_0 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (659), (978), (1402) imply:
% 245.57/58.07 | (1421) ~ (all_244_0 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (658), (978), (1401) imply:
% 245.57/58.07 | (1422) ~ (all_244_0 = all_84_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (657), (978), (1398) imply:
% 245.57/58.07 | (1423) ~ (all_244_0 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (656), (978), (1396) imply:
% 245.57/58.07 | (1424) ~ (all_244_0 = all_26_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (655), (978), (986) imply:
% 245.57/58.07 | (1425) ~ (all_244_0 = all_30_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (654), (1404), (1405) imply:
% 245.57/58.07 | (1426) ~ (all_100_2 = all_64_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (653), (1403), (1405) imply:
% 245.57/58.07 | (1427) ~ (all_100_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (652), (1402), (1405) imply:
% 245.57/58.07 | (1428) ~ (all_100_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (651), (990), (1405) imply:
% 245.57/58.07 | (1429) ~ (all_244_3 = all_100_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1429) implies:
% 245.57/58.07 | (1430) ~ (all_244_3 = all_100_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (650), (921), (1405) imply:
% 245.57/58.07 | (1431) ~ (all_100_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (649), (1395), (1405) imply:
% 245.57/58.07 | (1432) ~ (all_100_2 = all_36_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (648), (904), (1405) imply:
% 245.57/58.07 | (1433) ~ (all_100_2 = all_48_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (647), (1403), (1404) imply:
% 245.57/58.07 | (1434) ~ (all_64_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (646), (1402), (1404) imply:
% 245.57/58.07 | (1435) ~ (all_64_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (645), (1400), (1404) imply:
% 245.57/58.07 | (1436) ~ (all_64_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (644), (1004), (1404) imply:
% 245.57/58.07 | (1437) ~ (all_244_8 = all_64_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1437) implies:
% 245.57/58.07 | (1438) ~ (all_244_8 = all_64_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (643), (1394), (1404) imply:
% 245.57/58.07 | (1439) ~ (all_64_2 = all_38_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (642), (1392), (1404) imply:
% 245.57/58.07 | (1440) ~ (all_64_2 = all_40_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (641), (1402), (1403) imply:
% 245.57/58.07 | (1441) ~ (all_16_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (640), (1399), (1403) imply:
% 245.57/58.07 | (1442) ~ (all_62_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1442) implies:
% 245.57/58.07 | (1443) ~ (all_62_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (639), (1397), (1403) imply:
% 245.57/58.07 | (1444) ~ (all_16_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (638), (830), (1403) imply:
% 245.57/58.07 | (1445) ~ (all_244_15 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1445) implies:
% 245.57/58.07 | (1446) ~ (all_244_15 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (637), (1020), (1403) imply:
% 245.57/58.07 | (1447) ~ (all_34_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1447) implies:
% 245.57/58.07 | (1448) ~ (all_34_2 = all_16_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (636), (807), (1402) imply:
% 245.57/58.07 | (1449) ~ (all_22_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1449) implies:
% 245.57/58.07 | (1450) ~ (all_22_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (635), (800), (1402) imply:
% 245.57/58.07 | (1451) ~ (all_28_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1451) implies:
% 245.57/58.07 | (1452) ~ (all_28_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (634), (1393), (1402) imply:
% 245.57/58.07 | (1453) ~ (all_20_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1453) implies:
% 245.57/58.07 | (1454) ~ (all_20_2 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (633), (1032), (1402) imply:
% 245.57/58.07 | (1455) ~ (all_244_24 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1455) implies:
% 245.57/58.07 | (1456) ~ (all_244_24 = all_12_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (632), (990), (1401) imply:
% 245.57/58.07 | (1457) ~ (all_244_3 = all_84_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1457) implies:
% 245.57/58.07 | (1458) ~ (all_244_3 = all_84_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (631), (1400), (1401) imply:
% 245.57/58.07 | (1459) ~ (all_84_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (630), (1399), (1401) imply:
% 245.57/58.07 | (1460) ~ (all_84_2 = all_62_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (629), (807), (1401) imply:
% 245.57/58.07 | (1461) ~ (all_84_2 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (628), (1398), (1401) imply:
% 245.57/58.07 | (1462) ~ (all_84_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (627), (1396), (1401) imply:
% 245.57/58.07 | (1463) ~ (all_84_2 = all_26_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (626), (986), (1401) imply:
% 245.57/58.07 | (1464) ~ (all_84_2 = all_30_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (625), (990), (1400) imply:
% 245.57/58.07 | (1465) ~ (all_244_3 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (624), (990), (1399) imply:
% 245.57/58.07 | (1466) ~ (all_244_3 = all_62_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (623), (807), (990) imply:
% 245.57/58.07 | (1467) ~ (all_244_3 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (622), (921), (990) imply:
% 245.57/58.07 | (1468) ~ (all_244_3 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (621), (990), (1395) imply:
% 245.57/58.07 | (1469) ~ (all_244_3 = all_36_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (620), (904), (990) imply:
% 245.57/58.07 | (1470) ~ (all_244_3 = all_48_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (619), (1399), (1400) imply:
% 245.57/58.07 | (1471) ~ (all_62_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1471) implies:
% 245.57/58.07 | (1472) ~ (all_62_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (618), (807), (1400) imply:
% 245.57/58.07 | (1473) ~ (all_22_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1473) implies:
% 245.57/58.07 | (1474) ~ (all_22_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (617), (1004), (1400) imply:
% 245.57/58.07 | (1475) ~ (all_244_8 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1475) implies:
% 245.57/58.07 | (1476) ~ (all_244_8 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (616), (1394), (1400) imply:
% 245.57/58.07 | (1477) ~ (all_38_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1477) implies:
% 245.57/58.07 | (1478) ~ (all_38_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (615), (1392), (1400) imply:
% 245.57/58.07 | (1479) ~ (all_40_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1479) implies:
% 245.57/58.07 | (1480) ~ (all_40_2 = all_10_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (614), (807), (1399) imply:
% 245.57/58.07 | (1481) ~ (all_62_2 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (613), (1397), (1399) imply:
% 245.57/58.07 | (1482) ~ (all_62_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (612), (830), (1399) imply:
% 245.57/58.07 | (1483) ~ (all_244_15 = all_62_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1483) implies:
% 245.57/58.07 | (1484) ~ (all_244_15 = all_62_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (611), (1020), (1399) imply:
% 245.57/58.07 | (1485) ~ (all_62_2 = all_34_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (610), (800), (807) imply:
% 245.57/58.07 | (1486) ~ (all_28_2 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1486) implies:
% 245.57/58.07 | (1487) ~ (all_28_2 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (609), (807), (1393) imply:
% 245.57/58.07 | (1488) ~ (all_22_2 = all_20_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (608), (807), (1032) imply:
% 245.57/58.07 | (1489) ~ (all_244_24 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1489) implies:
% 245.57/58.07 | (1490) ~ (all_244_24 = all_22_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (607), (921), (1398) imply:
% 245.57/58.07 | (1491) ~ (all_8_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1491) implies:
% 245.57/58.07 | (1492) ~ (all_8_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (606), (1004), (1398) imply:
% 245.57/58.07 | (1493) ~ (all_244_8 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1493) implies:
% 245.57/58.07 | (1494) ~ (all_244_8 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (605), (1397), (1398) imply:
% 245.57/58.07 | (1495) ~ (all_6_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (604), (800), (1398) imply:
% 245.57/58.07 | (1496) ~ (all_28_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1496) implies:
% 245.57/58.07 | (1497) ~ (all_28_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (603), (1396), (1398) imply:
% 245.57/58.07 | (1498) ~ (all_26_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1498) implies:
% 245.57/58.07 | (1499) ~ (all_26_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (602), (986), (1398) imply:
% 245.57/58.07 | (1500) ~ (all_30_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1500) implies:
% 245.57/58.07 | (1501) ~ (all_30_2 = all_6_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (601), (921), (1004) imply:
% 245.57/58.07 | (1502) ~ (all_244_8 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1502) implies:
% 245.57/58.07 | (1503) ~ (all_244_8 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (600), (921), (1397) imply:
% 245.57/58.07 | (1504) ~ (all_8_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (599), (800), (921) imply:
% 245.57/58.07 | (1505) ~ (all_28_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1505) implies:
% 245.57/58.07 | (1506) ~ (all_28_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (598), (921), (1395) imply:
% 245.57/58.07 | (1507) ~ (all_36_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1507) implies:
% 245.57/58.07 | (1508) ~ (all_36_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (597), (904), (921) imply:
% 245.57/58.07 | (1509) ~ (all_48_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1509) implies:
% 245.57/58.07 | (1510) ~ (all_48_2 = all_8_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (596), (1004), (1397) imply:
% 245.57/58.07 | (1511) ~ (all_244_8 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (595), (800), (1004) imply:
% 245.57/58.07 | (1512) ~ (all_244_8 = all_28_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (594), (1004), (1394) imply:
% 245.57/58.07 | (1513) ~ (all_244_8 = all_38_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (593), (1004), (1392) imply:
% 245.57/58.07 | (1514) ~ (all_244_8 = all_40_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (592), (800), (1397) imply:
% 245.57/58.07 | (1515) ~ (all_28_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1515) implies:
% 245.57/58.07 | (1516) ~ (all_28_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (591), (830), (1397) imply:
% 245.57/58.07 | (1517) ~ (all_244_15 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1517) implies:
% 245.57/58.07 | (1518) ~ (all_244_15 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (590), (1020), (1397) imply:
% 245.57/58.07 | (1519) ~ (all_34_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | SIMP: (1519) implies:
% 245.57/58.07 | (1520) ~ (all_34_2 = all_4_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (589), (800), (1393) imply:
% 245.57/58.07 | (1521) ~ (all_28_2 = all_20_2)
% 245.57/58.07 |
% 245.57/58.07 | REDUCE: (588), (800), (1032) imply:
% 245.57/58.07 | (1522) ~ (all_244_24 = all_28_2)
% 245.57/58.07 |
% 245.57/58.08 | SIMP: (1522) implies:
% 245.57/58.08 | (1523) ~ (all_244_24 = all_28_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (587), (1395), (1396) imply:
% 245.57/58.08 | (1524) ~ (all_36_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1524) implies:
% 245.57/58.08 | (1525) ~ (all_36_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (586), (1394), (1396) imply:
% 245.57/58.08 | (1526) ~ (all_38_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1526) implies:
% 245.57/58.08 | (1527) ~ (all_38_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (585), (830), (1396) imply:
% 245.57/58.08 | (1528) ~ (all_244_15 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1528) implies:
% 245.57/58.08 | (1529) ~ (all_244_15 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (584), (1393), (1396) imply:
% 245.57/58.08 | (1530) ~ (all_26_2 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (583), (986), (1396) imply:
% 245.57/58.08 | (1531) ~ (all_30_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1531) implies:
% 245.57/58.08 | (1532) ~ (all_30_2 = all_26_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (582), (1394), (1395) imply:
% 245.57/58.08 | (1533) ~ (all_38_2 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1533) implies:
% 245.57/58.08 | (1534) ~ (all_38_2 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (581), (830), (1395) imply:
% 245.57/58.08 | (1535) ~ (all_244_15 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1535) implies:
% 245.57/58.08 | (1536) ~ (all_244_15 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (580), (1393), (1395) imply:
% 245.57/58.08 | (1537) ~ (all_36_2 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (579), (904), (1395) imply:
% 245.57/58.08 | (1538) ~ (all_48_2 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1538) implies:
% 245.57/58.08 | (1539) ~ (all_48_2 = all_36_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (578), (830), (1394) imply:
% 245.57/58.08 | (1540) ~ (all_244_15 = all_38_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1540) implies:
% 245.57/58.08 | (1541) ~ (all_244_15 = all_38_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (577), (1393), (1394) imply:
% 245.57/58.08 | (1542) ~ (all_38_2 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (576), (1392), (1394) imply:
% 245.57/58.08 | (1543) ~ (all_40_2 = all_38_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1543) implies:
% 245.57/58.08 | (1544) ~ (all_40_2 = all_38_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (575), (830), (1393) imply:
% 245.57/58.08 | (1545) ~ (all_244_15 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (574), (830), (1020) imply:
% 245.57/58.08 | (1546) ~ (all_244_15 = all_34_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (573), (1032), (1393) imply:
% 245.57/58.08 | (1547) ~ (all_244_24 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1547) implies:
% 245.57/58.08 | (1548) ~ (all_244_24 = all_20_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (572), (904), (986) imply:
% 245.57/58.08 | (1549) ~ (all_48_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1549) implies:
% 245.57/58.08 | (1550) ~ (all_48_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (571), (986), (1392) imply:
% 245.57/58.08 | (1551) ~ (all_40_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1551) implies:
% 245.57/58.08 | (1552) ~ (all_40_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (570), (986), (1020) imply:
% 245.57/58.08 | (1553) ~ (all_34_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1553) implies:
% 245.57/58.08 | (1554) ~ (all_34_2 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (569), (986), (1032) imply:
% 245.57/58.08 | (1555) ~ (all_244_24 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1555) implies:
% 245.57/58.08 | (1556) ~ (all_244_24 = all_30_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (568), (904), (1392) imply:
% 245.57/58.08 | (1557) ~ (all_48_2 = all_40_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (567), (904), (1020) imply:
% 245.57/58.08 | (1558) ~ (all_48_2 = all_34_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (566), (904), (1032) imply:
% 245.57/58.08 | (1559) ~ (all_244_24 = all_48_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1559) implies:
% 245.57/58.08 | (1560) ~ (all_244_24 = all_48_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (565), (1020), (1392) imply:
% 245.57/58.08 | (1561) ~ (all_40_2 = all_34_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (564), (1032), (1392) imply:
% 245.57/58.08 | (1562) ~ (all_244_24 = all_40_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1562) implies:
% 245.57/58.08 | (1563) ~ (all_244_24 = all_40_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (563), (1020), (1032) imply:
% 245.57/58.08 | (1564) ~ (all_244_24 = all_34_2)
% 245.57/58.08 |
% 245.57/58.08 | SIMP: (1564) implies:
% 245.57/58.08 | (1565) ~ (all_244_24 = all_34_2)
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (561), (1391) imply:
% 245.57/58.08 | (1566) op(all_84_2, e3) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (560), (1390) imply:
% 245.57/58.08 | (1567) op(all_6_2, e2) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (559), (1389) imply:
% 245.57/58.08 | (1568) op(all_26_2, e1) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (558), (1388) imply:
% 245.57/58.08 | (1569) op(all_30_2, e0) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (557), (1387) imply:
% 245.57/58.08 | (1570) op(all_100_2, e4) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (556), (1062) imply:
% 245.57/58.08 | (1571) op(all_8_2, e2) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (555), (1386) imply:
% 245.57/58.08 | (1572) op(all_36_2, e1) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (554), (1385) imply:
% 245.57/58.08 | (1573) op(all_48_2, e0) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (553), (1384) imply:
% 245.57/58.08 | (1574) op(all_64_2, e4) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (552), (1383) imply:
% 245.57/58.08 | (1575) op(all_10_2, e3) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (551), (1382) imply:
% 245.57/58.08 | (1576) op(all_38_2, e1) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (550), (865) imply:
% 245.57/58.08 | (1577) op(all_40_2, e0) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (549), (1381) imply:
% 245.57/58.08 | (1578) op(all_16_2, e4) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (548), (1380) imply:
% 245.57/58.08 | (1579) op(all_62_2, e3) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (547), (1379) imply:
% 245.57/58.08 | (1580) op(all_4_2, e2) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (546), (1087) imply:
% 245.57/58.08 | (1581) op(all_34_2, e0) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (545), (1378) imply:
% 245.57/58.08 | (1582) op(all_12_2, e4) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (544), (1056) imply:
% 245.57/58.08 | (1583) op(all_22_2, e3) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (543), (1070) imply:
% 245.57/58.08 | (1584) op(all_28_2, e2) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (542), (1377) imply:
% 245.57/58.08 | (1585) op(all_20_2, e1) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (515), (980), (988) imply:
% 245.57/58.08 | (1586) op(all_100_2, all_84_2) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (514), (980), (988) imply:
% 245.57/58.08 | (1587) op(all_84_2, all_100_2) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (512), (1375), (1376) imply:
% 245.57/58.08 | (1588) op(all_64_2, all_6_2) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (511), (1375), (1376) imply:
% 245.57/58.08 | (1589) op(all_6_2, all_64_2) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (510), (1373), (1374) imply:
% 245.57/58.08 | (1590) op(all_10_2, all_8_2) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (509), (1373), (1374) imply:
% 245.57/58.08 | (1591) op(all_8_2, all_10_2) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (507), (1371), (1372) imply:
% 245.57/58.08 | (1592) op(all_16_2, all_26_2) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (506), (1371), (1372) imply:
% 245.57/58.08 | (1593) op(all_26_2, all_16_2) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (505), (996), (1370) imply:
% 245.57/58.08 | (1594) op(all_62_2, all_36_2) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (504), (996), (1370) imply:
% 245.57/58.08 | (1595) op(all_36_2, all_62_2) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (503), (1368), (1369) imply:
% 245.57/58.08 | (1596) op(all_4_2, all_38_2) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (502), (1368), (1369) imply:
% 245.57/58.08 | (1597) op(all_38_2, all_4_2) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (500), (1366), (1367) imply:
% 245.57/58.08 | (1598) op(all_12_2, all_30_2) = e4
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (499), (1366), (1367) imply:
% 245.57/58.08 | (1599) op(all_30_2, all_12_2) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (498), (1124), (1365) imply:
% 245.57/58.08 | (1600) op(all_22_2, all_48_2) = e3
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (497), (1124), (1365) imply:
% 245.57/58.08 | (1601) op(all_48_2, all_22_2) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (496), (1113), (1127) imply:
% 245.57/58.08 | (1602) op(all_28_2, all_40_2) = e2
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (495), (1113), (1127) imply:
% 245.57/58.08 | (1603) op(all_40_2, all_28_2) = e0
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (494), (1121), (1364) imply:
% 245.57/58.08 | (1604) op(all_20_2, all_34_2) = e1
% 245.57/58.08 |
% 245.57/58.08 | REDUCE: (493), (1121), (1364) imply:
% 245.57/58.08 | (1605) op(all_34_2, all_20_2) = e0
% 245.57/58.08 |
% 245.57/58.08 | BETA: splitting (138) gives:
% 245.57/58.08 |
% 245.57/58.08 | Case 1:
% 245.57/58.08 | |
% 245.57/58.08 | | (1606) ~ (all_4_2 = e4)
% 245.57/58.08 | |
% 245.57/58.08 | | BETA: splitting (141) gives:
% 245.57/58.08 | |
% 245.96/58.08 | | Case 1:
% 245.96/58.08 | | |
% 245.96/58.08 | | | (1607) ~ (all_6_2 = e1)
% 245.96/58.08 | | |
% 245.96/58.08 | | | BETA: splitting (144) gives:
% 245.96/58.08 | | |
% 245.96/58.08 | | | Case 1:
% 245.96/58.08 | | | |
% 245.96/58.08 | | | | (1608) ~ (all_8_2 = e1)
% 245.96/58.08 | | | |
% 245.96/58.08 | | | | BETA: splitting (147) gives:
% 245.96/58.08 | | | |
% 245.96/58.08 | | | | Case 1:
% 245.96/58.08 | | | | |
% 245.96/58.08 | | | | | (1609) ~ (all_10_2 = e4)
% 245.96/58.08 | | | | |
% 245.96/58.08 | | | | | BETA: splitting (150) gives:
% 245.96/58.08 | | | | |
% 245.96/58.08 | | | | | Case 1:
% 245.96/58.08 | | | | | |
% 245.96/58.08 | | | | | | (1610) ~ (all_12_2 = e2)
% 245.96/58.08 | | | | | |
% 245.96/58.08 | | | | | | BETA: splitting (156) gives:
% 245.96/58.08 | | | | | |
% 245.96/58.08 | | | | | | Case 1:
% 245.96/58.08 | | | | | | |
% 245.96/58.08 | | | | | | | (1611) ~ (all_16_2 = e2)
% 245.96/58.08 | | | | | | |
% 245.96/58.08 | | | | | | | BETA: splitting (159) gives:
% 245.96/58.08 | | | | | | |
% 245.96/58.08 | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | |
% 245.96/58.08 | | | | | | | | (1612) ~ (all_18_2 = e3)
% 245.96/58.08 | | | | | | | |
% 245.96/58.08 | | | | | | | | REDUCE: (1215), (1612) imply:
% 245.96/58.08 | | | | | | | | (1613) ~ (all_12_2 = e3)
% 245.96/58.08 | | | | | | | |
% 245.96/58.08 | | | | | | | | BETA: splitting (162) gives:
% 245.96/58.08 | | | | | | | |
% 245.96/58.08 | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | |
% 245.96/58.08 | | | | | | | | | (1614) ~ (all_20_2 = e4)
% 245.96/58.08 | | | | | | | | |
% 245.96/58.08 | | | | | | | | | BETA: splitting (165) gives:
% 245.96/58.08 | | | | | | | | |
% 245.96/58.08 | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | (1615) ~ (all_22_2 = e1)
% 245.96/58.08 | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | BETA: splitting (168) gives:
% 245.96/58.08 | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | (1616) ~ (all_24_2 = e3)
% 245.96/58.08 | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | REDUCE: (1333), (1616) imply:
% 245.96/58.08 | | | | | | | | | | | (1617) ~ (all_16_2 = e3)
% 245.96/58.08 | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | BETA: splitting (171) gives:
% 245.96/58.08 | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | (1618) ~ (all_26_2 = e3)
% 245.96/58.08 | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | BETA: splitting (174) gives:
% 245.96/58.08 | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | (1619) ~ (all_28_2 = e3)
% 245.96/58.08 | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | BETA: splitting (177) gives:
% 245.96/58.08 | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | (1620) ~ (all_30_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 245.96/58.08 | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | (1621) ~ (all_32_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | REDUCE: (1336), (1621) imply:
% 245.96/58.08 | | | | | | | | | | | | | | | (1622) ~ (all_20_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 245.96/58.08 | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | (1623) ~ (all_34_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | (1624) ~ (all_36_2 = e4)
% 245.96/58.08 | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | (1625) ~ (all_38_2 = e4)
% 245.96/58.08 | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | (1626) ~ (all_40_2 = e4)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | (1627) ~ (all_46_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (1337), (1627) imply:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | (1628) ~ (all_36_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | (1629) ~ (all_44_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1325), (1629) imply:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | (1630) ~ (all_26_2 = e2)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | (1631) ~ (all_48_2 = e1)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | (1632) ~ (all_50_2 = e3)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1280), (1632) imply:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | (1633) ~ (all_4_2 = e3)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | | (1634) ~ (all_58_2 = e3)
% 245.96/58.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (146), (149), (161), (164), (170),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (173), (185), (188), (224), (234), (237), (249),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (257), (265), (271), (287), (313), (467), (473),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (479), (485), (492), (501), (717), (723), (725),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (735), (736), (749), (881), (1241), (1312),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1317), (1319), (1320), (1331), (1334), (1408),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1413), (1414), (1450), (1458), (1465), (1472),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1474), (1478), (1484), (1487), (1488), (1490),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1513), (1573), (1575), (1576), (1579), (1580),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1583), (1596), (1601), (1609), (1613), (1615),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1619), (1622), (1625), (1628), (1630), (1634),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | #960.
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_58_2 = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1334), (1635) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1636) all_20_2 = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1636) implies:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_20_2 = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1545), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1638) ~ (all_244_15 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1548), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1639) ~ (all_244_24 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1542), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1640) ~ (all_38_2 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1537), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1641) ~ (all_36_2 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1642) ~ (all_22_2 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1454), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1643) ~ (all_12_2 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1614), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1644) ~ (e4 = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1585), (1637) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | (1645) op(e3, e1) = e0
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1646) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (1613), (1642), (1646),
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | #958.
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1647) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1647) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_252_22 = e3 & op(e0, e2) = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1648) implies:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) op(e0, e2) = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1619), (1649), (function-axioms) are
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #975.
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) all_252_23 = e3 & op(e0, e1) = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1651) implies:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_252_23 = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e0,
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (1645) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_36_2 = e0
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1154), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_74_2 = e0
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1344), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) all_122_2 = e0
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1469), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) ~ (all_244_3 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1534), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) ~ (all_38_2 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1508), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) ~ (all_8_2 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1658) implies:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) ~ (all_8_2 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1624), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) ~ (e4 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1641), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1661) ~ (e3 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1628), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1662) ~ (e2 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1594), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663) op(all_62_2, e0) = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1595), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1664) op(e0, all_62_2) = e1
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1653) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1665) op(e0, e1) = e3
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1666) ~ (all_122_2 = e0)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1655), (1666) imply:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1667) $false
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1667) is inconsistent.
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1668) ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_122_1) = all_122_0 & $i(all_122_0) &
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_122_1)) | ( ~ (all_122_1 = e2) & op(e1,
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_122_1 & $i(all_122_1))
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1668) gives:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1669) ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, all_122_1) = all_122_0 & $i(all_122_0) &
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_122_1)
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1669) implies:
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670) op(e1, e0) = all_122_1
% 245.96/58.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (149), (155),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (164), (170), (173), (176), (182), (185),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (224), (225), (227), (228),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (237), (243), (249), (252), (255), (257),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260), (265), (274), (278), (336), (362), (383),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (492), (501),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508), (717), (723), (725), (734), (735), (736),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738), (739), (740), (744), (745), (746), (748),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749), (751), (752), (753), (754), (755), (756),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757), (758), (759), (760), (763), (766), (767),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768), (769), (770), (771), (772), (775), (776),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778), (779), (1170), (1235), (1288), (1309),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312), (1314), (1316), (1319), (1320), (1331),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351), (1408), (1413), (1414), (1418), (1419),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434), (1435), (1443), (1450), (1458), (1459),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460), (1461), (1462), (1465), (1466), (1467),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472), (1474), (1476), (1478), (1480), (1481),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482), (1484), (1485), (1487), (1490), (1492),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494), (1495), (1497), (1504), (1506), (1511),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512), (1513), (1514), (1516), (1544), (1554),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561), (1566), (1567), (1573), (1574), (1575),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (1577), (1578), (1581), (1583), (1584),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589), (1592), (1600), (1601), (1606), (1607),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (1614),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615), (1617), (1618), (1619), (1620), (1622),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (1625), (1626), (1628), (1630),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631), (1633), (1638), (1639), (1640), (1642),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645), (1652), (1654), (1656), (1657), (1659),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663), (1664), (1665), (1670), (function-axioms)
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #803.
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1671) ~ (all_122_1 = e2) & op(e1, e0) = all_122_1 &
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_122_1)
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1671) implies:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1672) op(e1, e0) = all_122_1
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (149), (155),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (164), (170), (173), (176), (182), (185),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (224), (225), (227), (228),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (237), (243), (249), (252), (255), (257),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260), (265), (274), (278), (336), (362), (383),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (492), (501),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508), (717), (723), (725), (734), (735), (736),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738), (739), (740), (744), (745), (746), (748),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749), (751), (752), (753), (754), (755), (756),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757), (758), (759), (760), (763), (766), (767),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768), (769), (770), (771), (772), (775), (776),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778), (779), (1170), (1235), (1288), (1309),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312), (1314), (1316), (1319), (1320), (1331),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351), (1408), (1413), (1414), (1418), (1419),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434), (1435), (1443), (1450), (1458), (1459),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460), (1461), (1462), (1465), (1466), (1467),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472), (1474), (1476), (1478), (1480), (1481),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482), (1484), (1485), (1487), (1490), (1492),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494), (1495), (1497), (1504), (1506), (1511),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512), (1513), (1514), (1516), (1544), (1554),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561), (1566), (1567), (1573), (1574), (1575),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (1577), (1578), (1581), (1583), (1584),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589), (1592), (1600), (1601), (1606), (1607),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (1614),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615), (1617), (1618), (1619), (1620), (1622),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (1625), (1626), (1628), (1630),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631), (1633), (1638), (1639), (1640), (1642),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645), (1652), (1654), (1656), (1657), (1659),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663), (1664), (1665), (1672), (function-axioms)
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #803.
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673) all_252_24 = e3 & op(e0, e0) = e3
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1673) implies:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674) op(e0, e0) = e3
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (467), (1639), (1674), (function-axioms) are
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #835.
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | (1675) all_50_2 = e3
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (1280), (1580), (1608), (1675),
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | | #802.
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.10 | | | | | | | | | | | | | | | | | | | | | | (1676) all_48_2 = e1
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1677) ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = all_48_1 & $i(all_48_0) &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e4) & op(e0, e1)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (146), (149), (161), (164), (170), (173),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (182), (185), (188), (219), (224), (234), (237),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (249), (257), (265), (271), (287), (313), (316),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (492), (501), (717),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (723), (725), (735), (736), (749), (881), (1228),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1241), (1312), (1317), (1319), (1320), (1331),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1334), (1408), (1413), (1414), (1450), (1458),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1465), (1470), (1472), (1474), (1478), (1484),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1487), (1488), (1490), (1513), (1573), (1575),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1576), (1579), (1580), (1583), (1596), (1601),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1604), (1609), (1613), (1615), (1619), (1622),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (1623), (1625), (1628), (1630), (1676), (1677),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | | #799.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1678) all_44_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1325), (1678) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1679) all_26_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1568), (1679) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1680) op(e2, e1) = e4
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (1625), (1680), (function-axioms) are
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #935.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1681) all_46_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1682) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = all_46_1 & $i(all_46_0) &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1, e2)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1337), (1681) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1683) all_36_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | SIMP: (1683) implies:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1684) all_36_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (143), (155), (182), (188), (224), (237),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (473), (479), (744), (1312), (1513), (1536),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1572), (1594), (1597), (1608), (1611), (1623),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1682), (1684), (function-axioms) are inconsistent
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | by sub-proof #796.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | (1685) all_40_2 = e4
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1685) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | (1686) op(e4, e0) = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (1620), (1686), (function-axioms) are
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #830.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1687) all_38_2 = e4
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1688) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0
% 245.96/58.11 | | | | | | | | | | | | | | | | | | & op(e1, e4) = all_38_1 & $i(all_38_0) &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1541), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1689) ~ (all_244_15 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1690) ~ (all_64_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1544), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1691) ~ (all_40_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1534), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1692) ~ (all_36_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1527), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1693) ~ (all_26_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | SIMP: (1693) implies:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1694) ~ (all_26_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1542), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1695) ~ (all_20_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1478), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1696) ~ (all_10_2 = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1597), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1697) op(e4, all_4_2) = e1
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | REDUCE: (1576), (1687) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | (1698) op(e4, e1) = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 245.96/58.11 | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | (1699) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (170), (185), (1624), (1698), (1699),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | #795.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | (1700) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (1700) gives:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1701) all_252_11 = e4 & op(e2, e1) = e4
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (1701) implies:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | (1702) all_252_11 = e4
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1688) gives:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1703) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_38_1 & $i(all_38_0) &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1704) op(e1, e4) = all_38_1
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | all_38_1, e4, e1, simplifying with (155), (1704)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1705) all_38_1 = all_16_2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e2,
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (1698) gives:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1706) all_26_2 = e2
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1424), (1706) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1707) ~ (all_244_0 = e2)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1529), (1706) imply:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1708) ~ (all_244_15 = e2)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (14), (137),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (140), (143), (146), (149), (161), (164), (170),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (173), (182), (185), (191), (203), (204), (207),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (219), (224), (225), (227), (228), (234), (237),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (255), (257), (278), (316), (321), (369), (375),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (492), (508),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (715), (717), (736), (742), (743), (744), (745),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (746), (747), (748), (750), (751), (754), (755),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (756), (758), (763), (767), (770), (771), (776),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (778), (844), (1132), (1228), (1280), (1312),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1316), (1331), (1334), (1348), (1406), (1408),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1418), (1419), (1426), (1427), (1434), (1435),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1436), (1443), (1454), (1458), (1460), (1462),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1466), (1470), (1472), (1481), (1482), (1484),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1485), (1488), (1521), (1530), (1537), (1545),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1546), (1561), (1565), (1567), (1573), (1575),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1578), (1579), (1580), (1581), (1583), (1585),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1589), (1592), (1594), (1601), (1604), (1605),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1607), (1608), (1609), (1610), (1611), (1613),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1614), (1615), (1617), (1618), (1619), (1623),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1624), (1690), (1691), (1694), (1697), (1702),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1704), (1705), (1706), (1707), (1708),
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | #740.
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1709) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 &
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1709) implies:
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1710) ~ (all_38_1 = e3)
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | | (1711) op(e1, e4) = all_38_1
% 245.96/58.11 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | all_38_1, e4, e1, simplifying with (155), (1711)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1712) all_38_1 = all_16_2
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e2,
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (1698) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1713) all_26_2 = e2
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1424), (1713) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1714) ~ (all_244_0 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1529), (1713) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1715) ~ (all_244_15 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (14), (137),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (140), (143), (146), (149), (161), (164), (170),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (173), (182), (185), (191), (203), (204), (207),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (219), (224), (225), (227), (228), (234), (237),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (255), (257), (278), (316), (321), (369), (375),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (492), (508),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (715), (717), (736), (742), (743), (744), (745),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (746), (747), (748), (750), (751), (754), (755),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (756), (758), (763), (767), (770), (771), (776),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (778), (844), (1132), (1228), (1280), (1312),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1316), (1331), (1334), (1348), (1406), (1408),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1418), (1419), (1426), (1427), (1434), (1435),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1436), (1443), (1454), (1458), (1460), (1462),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1466), (1470), (1472), (1481), (1482), (1484),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1485), (1488), (1521), (1530), (1537), (1545),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1546), (1561), (1565), (1567), (1573), (1575),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1578), (1579), (1580), (1581), (1583), (1585),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1589), (1592), (1594), (1601), (1604), (1605),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1607), (1608), (1609), (1610), (1611), (1613),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1614), (1615), (1617), (1618), (1619), (1623),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1624), (1690), (1691), (1694), (1697), (1702),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (1711), (1712), (1713), (1714), (1715),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | | #740.
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1716) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (473), (1614), (1689), (1716),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | #750.
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | (1717) all_36_2 = e4
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | REDUCE: (1572), (1717) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | (1718) op(e4, e1) = e3
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1618), (1718), (function-axioms) are
% 245.96/58.12 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #834.
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | (1719) all_34_2 = e2
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1485), (1719) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1720) ~ (all_62_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1448), (1719) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1721) ~ (all_16_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1581), (1719) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1722) op(e2, e0) = e1
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e1,
% 245.96/58.12 | | | | | | | | | | | | | | | | e0, e2, simplifying with (191), (1722) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1723) all_40_2 = e1
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1514), (1723) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1724) ~ (all_244_8 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1440), (1723) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1725) ~ (all_64_2 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1544), (1723) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1726) ~ (all_38_2 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | SIMP: (1726) implies:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1727) ~ (all_38_2 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1480), (1723) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1728) ~ (all_10_2 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | SIMP: (1728) implies:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1729) ~ (all_10_2 = e1)
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | REDUCE: (1577), (1723) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | (1730) op(e1, e0) = e2
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | (1731) ~ (all_38_2 = e4)
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.12 | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | (1732) ~ (all_44_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | REDUCE: (1325), (1732) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | (1733) ~ (all_26_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1734) ~ (all_46_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1337), (1734) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1735) ~ (all_36_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1736) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (1733), (1735), (1736),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | #969.
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1737) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (188), (473), (479), (501), (1580), (1596),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1622), (1724), (1727), (1737), (function-axioms)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #737.
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1738) all_46_2 = e2
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1739) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = all_46_1 & $i(all_46_0) &
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1, e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1337), (1738) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1740) all_36_2 = e2
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | SIMP: (1740) implies:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1741) all_36_2 = e2
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1536), (1741) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1742) ~ (all_244_15 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1534), (1741) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1743) ~ (all_38_2 = e2)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1595), (1741) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1744) op(e2, all_62_2) = e1
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1741) imply:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | (1745) op(e2, e1) = e3
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (1739) gives:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1746) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_46_1 & $i(all_46_0) &
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | $i(all_46_1)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (1746) implies:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1747) op(e1, e2) = all_46_1
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (143), (146), (155), (188), (207), (224),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (473), (744), (745), (1280), (1541), (1580),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1597), (1608), (1611), (1617), (1720), (1729),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1742), (1743), (1744), (1745), (1747),
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | #733.
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1748) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 &
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | $i(all_46_1)
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (1748) implies:
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | | (1749) op(e1, e2) = all_46_1
% 245.96/58.12 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (143), (146), (155), (188), (207), (224),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | (473), (744), (745), (1280), (1541), (1580),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | (1597), (1608), (1611), (1617), (1720), (1729),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | (1742), (1743), (1744), (1745), (1749),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | | #733.
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1750) all_44_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (1325), (1568), (1731), (1750),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.13 | | | | | | | | | | | | | | | | | | #732.
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1751) all_38_2 = e4
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1752) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0
% 245.96/58.13 | | | | | | | | | | | | | | | | | & op(e1, e4) = all_38_1 & $i(all_38_0) &
% 245.96/58.13 | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e4)
% 245.96/58.13 | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | REDUCE: (1541), (1751) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1753) ~ (all_244_15 = e4)
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | REDUCE: (1527), (1751) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1754) ~ (all_26_2 = e4)
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | SIMP: (1754) implies:
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1755) ~ (all_26_2 = e4)
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | REDUCE: (1576), (1751) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | | | (1756) op(e4, e1) = e2
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | BETA: splitting (1752) gives:
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1757) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 245.96/58.13 | | | | | | | | | | | | | | | | | | op(e1, e4) = all_38_1 & $i(all_38_0) &
% 245.96/58.13 | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | ALPHA: (1757) implies:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1758) op(e1, e4) = all_38_1
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 245.96/58.13 | | | | | | | | | | | | | | | | | | all_38_1, e4, e1, simplifying with (155), (1758)
% 245.96/58.13 | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1759) all_38_1 = all_16_2
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e2,
% 245.96/58.13 | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (1756) gives:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1760) all_26_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (137), (143), (146), (164), (207), (224),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (225), (227), (257), (473), (485), (501), (745),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (746), (771), (1280), (1458), (1460), (1466),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1472), (1481), (1579), (1580), (1593), (1606),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1608), (1617), (1618), (1725), (1730), (1753),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1755), (1758), (1759), (1760), (function-axioms)
% 245.96/58.13 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #728.
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1761) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 &
% 245.96/58.13 | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | ALPHA: (1761) implies:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1762) ~ (all_38_1 = e3)
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1763) op(e1, e4) = all_38_1
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 245.96/58.13 | | | | | | | | | | | | | | | | | | all_38_1, e4, e1, simplifying with (155), (1763)
% 245.96/58.13 | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1764) all_38_1 = all_16_2
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e2,
% 245.96/58.13 | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (1756) gives:
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1765) all_26_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (137), (143), (146), (164), (207), (224),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (225), (227), (257), (473), (485), (501), (745),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (746), (771), (1280), (1458), (1460), (1466),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1472), (1481), (1579), (1580), (1593), (1606),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1608), (1617), (1618), (1725), (1730), (1753),
% 245.96/58.13 | | | | | | | | | | | | | | | | | | (1755), (1763), (1764), (1765), (function-axioms)
% 245.96/58.13 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #728.
% 245.96/58.13 | | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | Case 2:
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | (1766) all_32_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (1766) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1767) all_20_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | COMBINE_EQS: (1361), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1768) all_230_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1545), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1769) ~ (all_244_15 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1548), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1770) ~ (all_244_24 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1542), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1771) ~ (all_38_2 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1521), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1772) ~ (all_28_2 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1488), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1773) ~ (all_22_2 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1454), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1774) ~ (all_12_2 = e2)
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1605), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1775) op(all_34_2, e2) = e0
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REDUCE: (1585), (1767) imply:
% 245.96/58.13 | | | | | | | | | | | | | | | (1776) op(e2, e1) = e0
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (14), (137),
% 245.96/58.13 | | | | | | | | | | | | | | | (140), (143), (146), (149), (155), (161), (164),
% 245.96/58.13 | | | | | | | | | | | | | | | (170), (173), (176), (182), (183), (185), (186),
% 245.96/58.13 | | | | | | | | | | | | | | | (188), (191), (192), (207), (224), (225), (227),
% 245.96/58.13 | | | | | | | | | | | | | | | (228), (237), (255), (257), (278), (450), (467),
% 245.96/58.13 | | | | | | | | | | | | | | | (473), (479), (491), (508), (720), (735), (744),
% 245.96/58.13 | | | | | | | | | | | | | | | (747), (751), (754), (755), (756), (758), (778),
% 245.96/58.13 | | | | | | | | | | | | | | | (841), (1280), (1312), (1316), (1418), (1419),
% 245.96/58.13 | | | | | | | | | | | | | | | (1434), (1435), (1460), (1482), (1484), (1485),
% 245.96/58.13 | | | | | | | | | | | | | | | (1512), (1513), (1516), (1527), (1534), (1541),
% 245.96/58.13 | | | | | | | | | | | | | | | (1572), (1574), (1577), (1578), (1579), (1580),
% 245.96/58.13 | | | | | | | | | | | | | | | (1592), (1596), (1597), (1606), (1607), (1608),
% 245.96/58.13 | | | | | | | | | | | | | | | (1609), (1610), (1611), (1614), (1615), (1618),
% 245.96/58.13 | | | | | | | | | | | | | | | (1620), (1768), (1769), (1770), (1771), (1772),
% 245.96/58.13 | | | | | | | | | | | | | | | (1773), (1775), (1776), (function-axioms) are
% 245.96/58.13 | | | | | | | | | | | | | | | inconsistent by sub-proof #708.
% 245.96/58.13 | | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | End of split
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | Case 2:
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | (1777) all_30_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1777) imply:
% 245.96/58.13 | | | | | | | | | | | | | | (1778) all_54_2 = e2
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | REDUCE: (1425), (1777) imply:
% 245.96/58.13 | | | | | | | | | | | | | | (1779) ~ (all_244_0 = e2)
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | REDUCE: (1556), (1777) imply:
% 245.96/58.13 | | | | | | | | | | | | | | (1780) ~ (all_244_24 = e2)
% 245.96/58.13 | | | | | | | | | | | | | |
% 245.96/58.13 | | | | | | | | | | | | | | REDUCE: (1550), (1777) imply:
% 245.96/58.14 | | | | | | | | | | | | | | (1781) ~ (all_48_2 = e2)
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REDUCE: (1552), (1777) imply:
% 245.96/58.14 | | | | | | | | | | | | | | (1782) ~ (all_40_2 = e2)
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REDUCE: (1554), (1777) imply:
% 245.96/58.14 | | | | | | | | | | | | | | (1783) ~ (all_34_2 = e2)
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REDUCE: (1532), (1777) imply:
% 245.96/58.14 | | | | | | | | | | | | | | (1784) ~ (all_26_2 = e2)
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | SIMP: (1784) implies:
% 245.96/58.14 | | | | | | | | | | | | | | (1785) ~ (all_26_2 = e2)
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REDUCE: (1569), (1777) imply:
% 245.96/58.14 | | | | | | | | | | | | | | (1786) op(e2, e0) = e4
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 245.96/58.14 | | | | | | | | | | | | | | (137), (140), (143), (146), (149), (155), (161),
% 245.96/58.14 | | | | | | | | | | | | | | (164), (170), (173), (180), (182), (185), (186),
% 245.96/58.14 | | | | | | | | | | | | | | (188), (191), (192), (201), (203), (204), (207),
% 245.96/58.14 | | | | | | | | | | | | | | (213), (216), (219), (224), (225), (227), (228),
% 245.96/58.14 | | | | | | | | | | | | | | (234), (237), (249), (257), (265), (271), (278),
% 245.96/58.14 | | | | | | | | | | | | | | (287), (313), (316), (369), (400), (450), (467),
% 245.96/58.14 | | | | | | | | | | | | | | (473), (479), (485), (491), (492), (501), (717),
% 245.96/58.14 | | | | | | | | | | | | | | (723), (725), (727), (728), (734), (735), (736),
% 245.96/58.14 | | | | | | | | | | | | | | (737), (739), (741), (744), (746), (747), (749),
% 245.96/58.14 | | | | | | | | | | | | | | (750), (751), (753), (754), (755), (757), (758),
% 245.96/58.14 | | | | | | | | | | | | | | (760), (763), (766), (767), (769), (770), (771),
% 245.96/58.14 | | | | | | | | | | | | | | (772), (775), (776), (778), (779), (881), (916),
% 245.96/58.14 | | | | | | | | | | | | | | (1132), (1179), (1228), (1241), (1276), (1280),
% 245.96/58.14 | | | | | | | | | | | | | | (1312), (1317), (1319), (1320), (1331), (1334),
% 245.96/58.14 | | | | | | | | | | | | | | (1336), (1337), (1361), (1408), (1413), (1414),
% 245.96/58.14 | | | | | | | | | | | | | | (1416), (1419), (1426), (1427), (1434), (1435),
% 245.96/58.14 | | | | | | | | | | | | | | (1436), (1438), (1439), (1440), (1450), (1454),
% 245.96/58.14 | | | | | | | | | | | | | | (1458), (1460), (1465), (1466), (1470), (1472),
% 245.96/58.14 | | | | | | | | | | | | | | (1474), (1476), (1478), (1480), (1481), (1484),
% 245.96/58.14 | | | | | | | | | | | | | | (1487), (1488), (1490), (1512), (1513), (1527),
% 245.96/58.14 | | | | | | | | | | | | | | (1530), (1534), (1536), (1537), (1539), (1541),
% 245.96/58.14 | | | | | | | | | | | | | | (1542), (1544), (1545), (1557), (1561), (1563),
% 245.96/58.14 | | | | | | | | | | | | | | (1567), (1571), (1572), (1573), (1575), (1576),
% 245.96/58.14 | | | | | | | | | | | | | | (1578), (1579), (1580), (1583), (1585), (1589),
% 245.96/58.14 | | | | | | | | | | | | | | (1592), (1594), (1596), (1597), (1600), (1601),
% 245.96/58.14 | | | | | | | | | | | | | | (1604), (1606), (1607), (1608), (1611), (1613),
% 245.96/58.14 | | | | | | | | | | | | | | (1614), (1615), (1618), (1619), (1778), (1779),
% 245.96/58.14 | | | | | | | | | | | | | | (1780), (1781), (1782), (1783), (1785), (1786),
% 245.96/58.14 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.14 | | | | | | | | | | | | | | #651.
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | End of split
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | Case 2:
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | (1787) all_28_2 = e3
% 245.96/58.14 | | | | | | | | | | | | | (1788) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 245.96/58.14 | | | | | | | | | | | | | & op(e2, e3) = all_28_1 & $i(all_28_0) &
% 245.96/58.14 | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3)
% 245.96/58.14 | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1523), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1789) ~ (all_244_24 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1487), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1790) ~ (all_22_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | SIMP: (1790) implies:
% 245.96/58.14 | | | | | | | | | | | | | (1791) ~ (all_22_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1521), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1792) ~ (all_20_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | SIMP: (1792) implies:
% 245.96/58.14 | | | | | | | | | | | | | (1793) ~ (all_20_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1452), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1794) ~ (all_12_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1516), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1795) ~ (all_4_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | SIMP: (1795) implies:
% 245.96/58.14 | | | | | | | | | | | | | (1796) ~ (all_4_2 = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REDUCE: (1584), (1787) imply:
% 245.96/58.14 | | | | | | | | | | | | | (1797) op(e3, e2) = e0
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (11), (12), (13), (14),
% 245.96/58.14 | | | | | | | | | | | | | (137), (140), (143), (146), (149), (155), (161),
% 245.96/58.14 | | | | | | | | | | | | | (164), (170), (173), (180), (182), (183), (185),
% 245.96/58.14 | | | | | | | | | | | | | (188), (189), (201), (224), (234), (237), (249),
% 245.96/58.14 | | | | | | | | | | | | | (265), (271), (287), (304), (313), (467), (473),
% 245.96/58.14 | | | | | | | | | | | | | (479), (492), (501), (717), (720), (723), (725),
% 245.96/58.14 | | | | | | | | | | | | | (735), (736), (744), (758), (759), (761), (841),
% 245.96/58.14 | | | | | | | | | | | | | (881), (1241), (1312), (1317), (1319), (1320),
% 245.96/58.14 | | | | | | | | | | | | | (1331), (1336), (1337), (1343), (1408), (1413),
% 245.96/58.14 | | | | | | | | | | | | | (1414), (1474), (1478), (1490), (1499), (1503),
% 245.96/58.14 | | | | | | | | | | | | | (1504), (1513), (1520), (1527), (1536), (1571),
% 245.96/58.14 | | | | | | | | | | | | | (1572), (1573), (1574), (1575), (1576), (1583),
% 245.96/58.14 | | | | | | | | | | | | | (1585), (1588), (1591), (1594), (1597), (1601),
% 245.96/58.14 | | | | | | | | | | | | | (1606), (1607), (1608), (1609), (1610), (1611),
% 245.96/58.14 | | | | | | | | | | | | | (1613), (1615), (1788), (1789), (1791), (1793),
% 245.96/58.14 | | | | | | | | | | | | | (1796), (1797), (function-axioms) are inconsistent
% 245.96/58.14 | | | | | | | | | | | | | by sub-proof #634.
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | End of split
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | Case 2:
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | (1798) all_26_2 = e3
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1424), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1799) ~ (all_244_0 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1529), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1800) ~ (all_244_15 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1527), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1801) ~ (all_38_2 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1525), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1802) ~ (all_36_2 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1532), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1803) ~ (all_30_2 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1530), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1804) ~ (all_20_2 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | SIMP: (1804) implies:
% 245.96/58.14 | | | | | | | | | | | | (1805) ~ (all_20_2 = e3)
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1593), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1806) op(e3, all_16_2) = e1
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | REDUCE: (1568), (1798) imply:
% 245.96/58.14 | | | | | | | | | | | | (1807) op(e3, e1) = e4
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | BETA: splitting (750) gives:
% 245.96/58.14 | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | Case 1:
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | (1808) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 245.96/58.14 | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | BETA: splitting (1808) gives:
% 245.96/58.14 | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | Case 1:
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | (1809) all_252_9 = e3 & op(e4, e1) = e3
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | ALPHA: (1809) implies:
% 245.96/58.14 | | | | | | | | | | | | | | (1810) all_252_9 = e3
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e4,
% 245.96/58.14 | | | | | | | | | | | | | | e1, e3, simplifying with (185), (1807) gives:
% 245.96/58.14 | | | | | | | | | | | | | | (1811) all_36_2 = e4
% 245.96/58.14 | | | | | | | | | | | | | |
% 245.96/58.14 | | | | | | | | | | | | | | REDUCE: (1536), (1811) imply:
% 245.96/58.15 | | | | | | | | | | | | | | (1812) ~ (all_244_15 = e4)
% 245.96/58.15 | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | REDUCE: (1534), (1811) imply:
% 245.96/58.15 | | | | | | | | | | | | | | (1813) ~ (all_38_2 = e4)
% 245.96/58.15 | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | REDUCE: (1537), (1811) imply:
% 245.96/58.15 | | | | | | | | | | | | | | (1814) ~ (all_20_2 = e4)
% 245.96/58.15 | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | REDUCE: (1594), (1811) imply:
% 245.96/58.15 | | | | | | | | | | | | | | (1815) op(all_62_2, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 245.96/58.15 | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | (1816) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 245.96/58.15 | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 245.96/58.15 | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | BETA: splitting (1816) gives:
% 245.96/58.15 | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | (1817) all_252_9 = e4 & op(e4, e1) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1810), (1817) are inconsistent by sub-proof
% 245.96/58.15 | | | | | | | | | | | | | | | | #633.
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | (1818) all_252_10 = e4 & op(e3, e1) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | ALPHA: (1818) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | (1819) all_252_10 = e4
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | (1820) ~ (all_30_2 = e2)
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | (1821) ~ (all_40_2 = e4)
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | (1822) ~ (all_48_2 = e1)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | (1823) ~ (all_64_2 = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | (1824) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1824) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1825) all_252_0 = e3 & op(e4, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1825) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1826) op(e4, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (491), (1799), (1826), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #813.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1827) all_252_2 = e3 & op(e3, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1827) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1828) op(e3, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (143), (203), (278), (473), (485),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (513), (763), (1608), (1800), (1819), (1822),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1828), (function-axioms) are inconsistent by
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | sub-proof #630.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | (1829) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1829) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1830) all_252_6 = e3 & op(e2, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (1823), (1830), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #940.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1831) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1831) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1832) all_252_12 = e3 & op(e1, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1617), (1832), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #895.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1833) all_252_20 = e3 & op(e0, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1833) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1834) op(e0, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, e3,
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (149), (1834) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1835) all_12_2 = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (1835) imply:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1836) $false
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1836) is inconsistent.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | (1837) all_64_2 = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1434), (1837) imply:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | (1838) ~ (all_16_2 = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1435), (1837) imply:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | (1839) ~ (all_12_2 = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1574), (1837) imply:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | (1840) op(e3, e4) = e2
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | (1841) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1841) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1842) all_252_6 = e4 & op(e2, e4) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1842) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1843) all_252_6 = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1844) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1844) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1845) all_252_0 = e3 & op(e4, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1845) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1846) op(e4, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (491), (1799), (1846), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #813.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_252_2 = e3 & op(e3, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1847) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1848) op(e3, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (143), (203), (278), (473), (485),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (513), (763), (1608), (1800), (1819), (1822),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1848), (function-axioms) are inconsistent by
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #630.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | (1849) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1849) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1850) all_252_6 = e3 & op(e2, e4) = e3
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1843), (1850) are inconsistent by sub-proof
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | #629.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (1851) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (155), (1613), (1617), (1851),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | | #894.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1852) all_252_7 = e4 & op(e2, e3) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1852) implies:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1853) op(e2, e3) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1609), (1853), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | (1854) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1854) gives:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1855) all_252_8 = e4 & op(e2, e2) = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (479), (491), (508), (1418), (1840),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1855), (function-axioms) are inconsistent by
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | sub-proof #808.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (1856) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (191), (1813), (1821), (1856),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | | #933.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | (1857) all_48_2 = e1
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (137), (155), (224), (225), (278), (473),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | (491), (746), (1433), (1573), (1606), (1799),
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | (1806), (1812), (1815), (1857), (function-axioms)
% 245.96/58.15 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #627.
% 245.96/58.15 | | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | (1858) all_40_2 = e4
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1858) imply:
% 245.96/58.15 | | | | | | | | | | | | | | | | | | (1859) op(e4, e0) = e2
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (1820), (1859), (function-axioms) are
% 245.96/58.15 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #830.
% 245.96/58.15 | | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | End of split
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.15 | | | | | | | | | | | | | | | | | (1860) all_30_2 = e2
% 245.96/58.15 | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (137), (146), (149), (155), (176), (182), (188),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (191), (192), (203), (204), (224), (225), (227),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (278), (467), (473), (479), (491), (508), (733),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (738), (739), (740), (746), (756), (776), (778),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1418), (1425), (1433), (1440), (1480), (1544),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1550), (1554), (1556), (1567), (1569), (1573),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1578), (1589), (1606), (1610), (1611), (1613),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1617), (1799), (1803), (1806), (1812), (1815),
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1860), (function-axioms) are inconsistent by
% 245.96/58.16 | | | | | | | | | | | | | | | | | sub-proof #616.
% 245.96/58.16 | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | (1861) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 245.96/58.16 | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 245.96/58.16 | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | REF_CLOSE: (161), (188), (473), (1614), (1812), (1813),
% 245.96/58.16 | | | | | | | | | | | | | | | (1861), (function-axioms) are inconsistent by
% 245.96/58.16 | | | | | | | | | | | | | | | sub-proof #615.
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | (1862) all_252_10 = e3 & op(e3, e1) = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | ALPHA: (1862) implies:
% 245.96/58.16 | | | | | | | | | | | | | | (1863) op(e3, e1) = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REF_CLOSE: (14), (185), (1807), (1863), (function-axioms) are
% 245.96/58.16 | | | | | | | | | | | | | | inconsistent by sub-proof #614.
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | (1864) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 245.96/58.16 | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 245.96/58.16 | | | | | | | | | | | | | op(e0, e1) = e3)
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | BETA: splitting (1864) gives:
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | (1865) all_252_11 = e3 & op(e2, e1) = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REF_CLOSE: (188), (1801), (1865), (function-axioms) are
% 245.96/58.16 | | | | | | | | | | | | | | inconsistent by sub-proof #900.
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | (1866) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 245.96/58.16 | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REF_CLOSE: (161), (473), (1800), (1805), (1866),
% 245.96/58.16 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.16 | | | | | | | | | | | | | | #742.
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | End of split
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | (1867) all_24_2 = e3
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | COMBINE_EQS: (1333), (1867) imply:
% 245.96/58.16 | | | | | | | | | | | (1868) all_16_2 = e3
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1420), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1869) ~ (all_244_0 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1427), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1870) ~ (all_100_2 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1434), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1871) ~ (all_64_2 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1441), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1872) ~ (all_12_2 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1444), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1873) ~ (all_4_2 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | SIMP: (1873) implies:
% 245.96/58.16 | | | | | | | | | | | (1874) ~ (all_4_2 = e3)
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1593), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1875) op(all_26_2, e3) = e1
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | REDUCE: (1578), (1868) imply:
% 245.96/58.16 | | | | | | | | | | | (1876) op(e3, e4) = e1
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | BETA: splitting (778) gives:
% 245.96/58.16 | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | (1877) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 245.96/58.16 | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | REF_CLOSE: (9), (278), (491), (1869), (1876), (1877),
% 245.96/58.16 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.16 | | | | | | | | | | | | #613.
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | (1878) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 245.96/58.16 | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 245.96/58.16 | | | | | | | | | | | | op(e0, e4) = e3)
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | BETA: splitting (1878) gives:
% 245.96/58.16 | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | (1879) all_252_6 = e3 & op(e2, e4) = e3
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | REF_CLOSE: (227), (1871), (1879), (function-axioms) are
% 245.96/58.16 | | | | | | | | | | | | | inconsistent by sub-proof #940.
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | (1880) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 245.96/58.16 | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | BETA: splitting (1880) gives:
% 245.96/58.16 | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | (1881) all_252_12 = e3 & op(e1, e4) = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | ALPHA: (1881) implies:
% 245.96/58.16 | | | | | | | | | | | | | | (1882) all_252_12 = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2,
% 245.96/58.16 | | | | | | | | | | | | | | e1, e4, e3, simplifying with (278), (1876) gives:
% 245.96/58.16 | | | | | | | | | | | | | | (1883) all_100_2 = e1
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | COMBINE_EQS: (1356), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1884) all_208_2 = e1
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1430), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1885) ~ (all_244_3 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1426), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1886) ~ (all_64_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | SIMP: (1886) implies:
% 245.96/58.16 | | | | | | | | | | | | | | (1887) ~ (all_64_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1432), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1888) ~ (all_36_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | SIMP: (1888) implies:
% 245.96/58.16 | | | | | | | | | | | | | | (1889) ~ (all_36_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1428), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1890) ~ (all_12_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | SIMP: (1890) implies:
% 245.96/58.16 | | | | | | | | | | | | | | (1891) ~ (all_12_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1431), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1892) ~ (all_8_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1870), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1893) ~ (e3 = e1)
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1586), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1894) op(e1, all_84_2) = e4
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | REDUCE: (1570), (1883) imply:
% 245.96/58.16 | | | | | | | | | | | | | | (1895) op(e1, e4) = e3
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | BETA: splitting (774) gives:
% 245.96/58.16 | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | (1896) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 245.96/58.16 | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | BETA: splitting (1896) gives:
% 245.96/58.16 | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | (1897) all_252_0 = e1 & op(e4, e4) = e1
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | ALPHA: (1897) implies:
% 245.96/58.16 | | | | | | | | | | | | | | | | (1898) op(e4, e4) = e1
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (491), (1418), (1876), (1898),
% 245.96/58.16 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.16 | | | | | | | | | | | | | | | | #625.
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | (1899) all_252_2 = e1 & op(e3, e4) = e1
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | ALPHA: (1899) implies:
% 245.96/58.16 | | | | | | | | | | | | | | | | (1900) all_252_2 = e1
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | (1901) ~ (all_26_2 = e3)
% 245.96/58.16 | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | (1902) ~ (all_28_2 = e3)
% 245.96/58.16 | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | (1903) ~ (all_30_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | (1904) ~ (all_32_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (1336), (1904) imply:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | (1905) ~ (all_20_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | (1906) ~ (all_34_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | (1907) ~ (all_36_2 = e4)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | (1908) ~ (all_38_2 = e4)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | (1909) ~ (all_40_2 = e4)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | (1910) ~ (all_44_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1325), (1910) imply:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | (1911) ~ (all_26_2 = e2)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) ~ (all_208_2 = e1)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1884), (1912) imply:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) $false
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1913) is inconsistent.
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) ( ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 &
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_208_1) = all_208_0 & $i(all_208_0) &
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_208_1)) | ( ~ (all_208_1 = e2) & op(e4,
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_208_1 & $i(all_208_1))
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1914) gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 &
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, all_208_1) = all_208_0 & $i(all_208_0) &
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_208_1)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1915) implies:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) op(e4, e1) = all_208_1
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2,
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_208_1, e1, e4, simplifying with (170), (1916)
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) all_208_1 = all_26_2
% 245.96/58.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (12), (13), (14), (137), (140),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (149), (155), (161), (164), (173),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (182), (185), (188), (191), (201), (219),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (227), (234), (237), (249), (252), (255),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257), (265), (271), (287), (313), (362), (467),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (473), (479), (485), (492), (501), (717), (718),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (723), (725), (728), (733), (734), (735), (736),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (744), (749), (756), (757), (758), (759), (760),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (771), (772), (776), (777), (780), (881), (916),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170), (1235), (1241), (1312), (1316), (1317),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319), (1320), (1331), (1334), (1337), (1408),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409), (1413), (1414), (1450), (1454), (1458),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461), (1465), (1467), (1472), (1474), (1478),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481), (1484), (1487), (1488), (1490), (1492),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494), (1495), (1497), (1504), (1506), (1508),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511), (1512), (1513), (1516), (1521), (1536),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537), (1567), (1569), (1572), (1573), (1575),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (1579), (1580), (1583), (1584), (1589),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594), (1596), (1597), (1599), (1601), (1607),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (1615),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874), (1876), (1882), (1889), (1891), (1895),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900), (1902), (1903), (1905), (1906), (1907),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908), (1909), (1911), (1916), (1917),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | #601.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) ~ (all_208_1 = e2) & op(e4, e1) = all_208_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_208_1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1918) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) ~ (all_208_1 = e2)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) op(e4, e1) = all_208_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2,
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_208_1, e1, e4, simplifying with (170), (1920)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) all_208_1 = all_26_2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (12), (13), (14), (137), (140),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (146), (149), (155), (161), (164), (173),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (176), (182), (185), (188), (191), (201), (219),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (227), (234), (237), (249), (252), (255),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (257), (265), (271), (287), (313), (362), (467),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (473), (479), (485), (492), (501), (717), (718),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (723), (725), (728), (733), (734), (735), (736),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (744), (749), (756), (757), (758), (759), (760),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (771), (772), (776), (777), (780), (881), (916),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170), (1235), (1241), (1312), (1316), (1317),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319), (1320), (1331), (1334), (1337), (1408),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409), (1413), (1414), (1450), (1454), (1458),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461), (1465), (1467), (1472), (1474), (1478),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481), (1484), (1487), (1488), (1490), (1492),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494), (1495), (1497), (1504), (1506), (1508),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511), (1512), (1513), (1516), (1521), (1536),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537), (1567), (1569), (1572), (1573), (1575),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (1579), (1580), (1583), (1584), (1589),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594), (1596), (1597), (1599), (1601), (1607),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (1615),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874), (1876), (1882), (1889), (1891), (1895),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900), (1902), (1903), (1905), (1906), (1907),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908), (1909), (1911), (1920), (1921),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | #601.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_44_2 = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (1325), (1568), (1908), (1922),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | #732.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1923) all_40_2 = e4
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1923) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1924) op(e4, e0) = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (1903), (1924), (function-axioms) are
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #830.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1925) all_38_2 = e4
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (1925) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1926) all_242_2 = e4
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1439), (1925) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1927) ~ (all_64_2 = e4)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1576), (1925) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1928) op(e4, e1) = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1929) ~ (all_242_2 = e4)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1926), (1929) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1930) $false
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1930) is inconsistent.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1931) ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | all_242_0 & op(e1, e4) = all_242_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e4) = all_242_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_242_1))
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e2,
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (1928) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_26_2 = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1424), (1932) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | (1933) ~ (all_244_0 = e2)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1931) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1934) ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_242_1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1934) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1935) op(e1, e4) = all_242_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (155), (227), (491), (776), (1567),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1589), (1610), (1611), (1900), (1927), (1933),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1935), (function-axioms) are inconsistent by
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #599.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1936) ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_242_1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1936) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1937) op(e1, e4) = all_242_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (155), (227), (491), (776), (1567),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1589), (1610), (1611), (1900), (1927), (1933),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1937), (function-axioms) are inconsistent by
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #599.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | (1938) all_36_2 = e4
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (1938) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | (1939) op(e4, e1) = e3
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1901), (1939), (function-axioms) are
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #834.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1940) all_34_2 = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1581), (1940) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1941) op(e2, e0) = e1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e1,
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (191), (1941) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1942) all_40_2 = e1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (1942) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1943) all_174_2 = e1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1514), (1942) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1944) ~ (all_244_8 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1544), (1942) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1945) ~ (all_38_2 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | SIMP: (1945) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1946) ~ (all_38_2 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1480), (1942) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1947) ~ (all_10_2 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | SIMP: (1947) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1948) ~ (all_10_2 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1942) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | (1949) op(e1, e0) = e2
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | (1950) ~ (all_174_2 = e1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1943), (1950) imply:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | (1951) $false
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1951) is inconsistent.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | (1952) ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | all_174_0 & op(e0, e1) = all_174_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | $i(all_174_0) & $i(all_174_1)) | ( ~ (all_174_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | = e4) & op(e0, e1) = all_174_1 &
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | $i(all_174_1))
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1952) gives:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1953) ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_174_1)
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1953) implies:
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1954) op(e0, e1) = all_174_1
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (137), (146), (161), (164), (170),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (185), (186), (188), (189), (198), (201), (224),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (257), (278), (397), (423), (473),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (479), (485), (491), (501), (746), (749), (768),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1239), (1325), (1337), (1418), (1484), (1541),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1568), (1572), (1580), (1595), (1596), (1606),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1615), (1876), (1884), (1885), (1887), (1894),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1895), (1901), (1905), (1944), (1946), (1948),
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | (1949), (1954), (function-axioms) are inconsistent
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #595.
% 245.96/58.17 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1955) ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 &
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_174_1)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1955) implies:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1956) op(e0, e1) = all_174_1
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (137), (146), (161), (164), (170),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (185), (186), (188), (189), (198), (201), (224),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (257), (278), (397), (423), (473),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (479), (485), (491), (501), (746), (749), (768),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1239), (1325), (1337), (1418), (1484), (1541),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1568), (1572), (1580), (1595), (1596), (1606),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1615), (1876), (1884), (1885), (1887), (1894),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1895), (1901), (1905), (1944), (1946), (1948),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | (1949), (1956), (function-axioms) are inconsistent
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #595.
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1957) all_32_2 = e2
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (1957) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1958) all_20_2 = e2
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1361), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1959) all_230_2 = e2
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1545), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1960) ~ (all_244_15 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1548), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1961) ~ (all_244_24 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1542), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1962) ~ (all_38_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1963) ~ (all_28_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1964) ~ (all_22_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1454), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1965) ~ (all_12_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1605), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1966) op(all_34_2, e2) = e0
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (1585), (1958) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1967) op(e2, e1) = e0
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (11), (12), (14), (137),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (140), (143), (146), (149), (155), (161), (164),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (170), (173), (176), (182), (183), (185), (186),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (188), (191), (192), (207), (224), (225), (227),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (228), (237), (255), (257), (278), (450), (467),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (473), (479), (491), (508), (720), (735), (744),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (747), (751), (754), (755), (756), (758), (778),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (841), (1280), (1312), (1316), (1418), (1419),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1434), (1435), (1460), (1482), (1484), (1485),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1512), (1513), (1516), (1527), (1534), (1541),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1572), (1574), (1577), (1578), (1579), (1580),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1592), (1596), (1597), (1606), (1607), (1608),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1609), (1610), (1611), (1614), (1615), (1901),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1903), (1959), (1960), (1961), (1962), (1963),
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | (1964), (1966), (1967), (function-axioms) are
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #708.
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | End of split
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | Case 2:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1968) all_30_2 = e2
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1969) all_54_2 = e2
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1425), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1970) ~ (all_244_0 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1556), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1971) ~ (all_244_24 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1550), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1972) ~ (all_48_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1552), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1973) ~ (all_40_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1554), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1974) ~ (all_34_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1532), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1975) ~ (all_26_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | SIMP: (1975) implies:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1976) ~ (all_26_2 = e2)
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1569), (1968) imply:
% 245.96/58.18 | | | | | | | | | | | | | | | | | | | (1977) op(e2, e0) = e4
% 245.96/58.18 | | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (137), (140), (143), (146), (149), (155), (161),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (164), (170), (173), (180), (182), (185), (186),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (188), (191), (192), (201), (203), (204), (207),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (213), (216), (219), (224), (225), (227), (228),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (234), (237), (249), (257), (265), (271), (278),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (287), (313), (316), (369), (400), (450), (467),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (473), (479), (485), (491), (492), (501), (717),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (723), (725), (727), (728), (734), (735), (736),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (737), (739), (741), (744), (746), (747), (749),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (750), (751), (753), (754), (755), (757), (758),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (760), (763), (766), (767), (769), (770), (771),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (772), (775), (776), (778), (779), (881), (916),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1132), (1179), (1228), (1241), (1276), (1280),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1312), (1317), (1319), (1320), (1331), (1334),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1336), (1337), (1361), (1408), (1413), (1414),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1416), (1419), (1426), (1427), (1434), (1435),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1436), (1438), (1439), (1440), (1450), (1454),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1458), (1460), (1465), (1466), (1470), (1472),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1474), (1476), (1478), (1480), (1481), (1484),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1487), (1488), (1490), (1512), (1513), (1527),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1530), (1534), (1536), (1537), (1539), (1541),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1542), (1544), (1545), (1557), (1561), (1563),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1567), (1571), (1572), (1573), (1575), (1576),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1578), (1579), (1580), (1583), (1585), (1589),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1592), (1594), (1596), (1597), (1600), (1601),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1604), (1606), (1607), (1608), (1611), (1613),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1614), (1615), (1901), (1902), (1969), (1970),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (1971), (1972), (1973), (1974), (1976), (1977),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.18 | | | | | | | | | | | | | | | | | | | #651.
% 246.37/58.18 | | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1978) all_28_2 = e3
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1979) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 246.37/58.18 | | | | | | | | | | | | | | | | | | & op(e2, e3) = all_28_1 & $i(all_28_0) &
% 246.37/58.18 | | | | | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | REDUCE: (1523), (1978) imply:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1980) ~ (all_244_24 = e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | REDUCE: (1487), (1978) imply:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1981) ~ (all_22_2 = e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | SIMP: (1981) implies:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1982) ~ (all_22_2 = e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | REDUCE: (1521), (1978) imply:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1983) ~ (all_20_2 = e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | SIMP: (1983) implies:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1984) ~ (all_20_2 = e3)
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | REDUCE: (1584), (1978) imply:
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1985) op(e3, e2) = e0
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (11), (12), (13), (14),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (137), (140), (143), (146), (149), (155), (161),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (164), (170), (173), (180), (182), (183), (185),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (188), (189), (201), (224), (234), (237), (249),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (265), (271), (287), (304), (313), (467), (473),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (479), (492), (501), (717), (720), (723), (725),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (735), (736), (744), (758), (759), (761), (841),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (881), (1241), (1312), (1317), (1319), (1320),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1331), (1336), (1337), (1343), (1408), (1413),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1414), (1474), (1478), (1490), (1499), (1503),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1504), (1513), (1520), (1527), (1536), (1571),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1572), (1573), (1574), (1575), (1576), (1583),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1585), (1588), (1591), (1594), (1597), (1601),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1606), (1607), (1608), (1609), (1610), (1611),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1613), (1615), (1874), (1979), (1980), (1982),
% 246.37/58.18 | | | | | | | | | | | | | | | | | | (1984), (1985), (function-axioms) are inconsistent
% 246.37/58.18 | | | | | | | | | | | | | | | | | | by sub-proof #634.
% 246.37/58.18 | | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.18 | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.18 | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | (1986) all_26_2 = e3
% 246.37/58.18 | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | REDUCE: (1875), (1986) imply:
% 246.37/58.18 | | | | | | | | | | | | | | | | | (1987) op(e3, e3) = e1
% 246.37/58.18 | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (485), (1885), (1987), (function-axioms) are
% 246.37/58.18 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #801.
% 246.37/58.18 | | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | | End of split
% 246.37/58.18 | | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | | End of split
% 246.37/58.18 | | | | | | | | | | | | | | |
% 246.37/58.18 | | | | | | | | | | | | | | Case 2:
% 246.37/58.18 | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | (1988) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 246.37/58.19 | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 246.37/58.19 | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 246.37/58.19 | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | BETA: splitting (1988) gives:
% 246.37/58.19 | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | (1989) all_252_6 = e1 & op(e2, e4) = e1
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | ALPHA: (1989) implies:
% 246.37/58.19 | | | | | | | | | | | | | | | | (1990) op(e2, e4) = e1
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | REF_CLOSE: (227), (1887), (1990), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #731.
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | (1991) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 246.37/58.19 | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | BETA: splitting (1991) gives:
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | | (1992) all_252_12 = e1 & op(e1, e4) = e1
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1882), (1992) are inconsistent by sub-proof
% 246.37/58.19 | | | | | | | | | | | | | | | | | #594.
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | | (1993) all_252_20 = e1 & op(e0, e4) = e1
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1891), (1993), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #593.
% 246.37/58.19 | | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | (1994) all_252_20 = e3 & op(e0, e4) = e3
% 246.37/58.19 | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | ALPHA: (1994) implies:
% 246.37/58.19 | | | | | | | | | | | | | | (1995) op(e0, e4) = e3
% 246.37/58.19 | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | | REF_CLOSE: (149), (1613), (1995), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 246.37/58.19 | | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | (1996) all_22_2 = e1
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REDUCE: (1487), (1996) imply:
% 246.37/58.19 | | | | | | | | | | (1997) ~ (all_28_2 = e1)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REDUCE: (1488), (1996) imply:
% 246.37/58.19 | | | | | | | | | | (1998) ~ (all_20_2 = e1)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | SIMP: (1998) implies:
% 246.37/58.19 | | | | | | | | | | (1999) ~ (all_20_2 = e1)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REDUCE: (1583), (1996) imply:
% 246.37/58.19 | | | | | | | | | | (2000) op(e1, e3) = e0
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e0,
% 246.37/58.19 | | | | | | | | | | e3, e1, simplifying with (224), (2000) gives:
% 246.37/58.19 | | | | | | | | | | (2001) all_62_2 = e0
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REDUCE: (1466), (2001) imply:
% 246.37/58.19 | | | | | | | | | | (2002) ~ (all_244_3 = e0)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REDUCE: (1482), (2001) imply:
% 246.37/58.19 | | | | | | | | | | (2003) ~ (all_4_2 = e0)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | SIMP: (2003) implies:
% 246.37/58.19 | | | | | | | | | | (2004) ~ (all_4_2 = e0)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (137), (143), (149), (155),
% 246.37/58.19 | | | | | | | | | | (168), (170), (173), (174), (180), (182), (185),
% 246.37/58.19 | | | | | | | | | | (186), (188), (201), (207), (219), (224), (227),
% 246.37/58.19 | | | | | | | | | | (278), (467), (473), (485), (491), (492), (715),
% 246.37/58.19 | | | | | | | | | | (720), (728), (736), (745), (749), (778), (841),
% 246.37/58.19 | | | | | | | | | | (916), (1280), (1333), (1334), (1336), (1337),
% 246.37/58.19 | | | | | | | | | | (1406), (1420), (1427), (1432), (1434), (1441),
% 246.37/58.19 | | | | | | | | | | (1516), (1521), (1530), (1537), (1545), (1548),
% 246.37/58.19 | | | | | | | | | | (1565), (1576), (1578), (1579), (1580), (1581),
% 246.37/58.19 | | | | | | | | | | (1585), (1594), (1597), (1605), (1606), (1608),
% 246.37/58.19 | | | | | | | | | | (1611), (1613), (1614), (1997), (1999), (2001),
% 246.37/58.19 | | | | | | | | | | (2002), (2004), (function-axioms) are inconsistent
% 246.37/58.19 | | | | | | | | | | by sub-proof #586.
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | (2005) all_20_2 = e4
% 246.37/58.19 | | | | | | | | | (2006) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 246.37/58.19 | | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.19 | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4) =
% 246.37/58.19 | | | | | | | | | all_20_1 & $i(all_20_1))
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | COMBINE_EQS: (786), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2007) all_60_2 = e4
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1548), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2008) ~ (all_244_24 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1542), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2009) ~ (all_38_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1521), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2010) ~ (all_28_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1530), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2011) ~ (all_26_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1488), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2012) ~ (all_22_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1454), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2013) ~ (all_12_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | SIMP: (2013) implies:
% 246.37/58.19 | | | | | | | | | (2014) ~ (all_12_2 = e4)
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1604), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2015) op(e4, all_34_2) = e1
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | REDUCE: (1585), (2005) imply:
% 246.37/58.19 | | | | | | | | | (2016) op(e4, e1) = e0
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | BETA: splitting (737) gives:
% 246.37/58.19 | | | | | | | | |
% 246.37/58.19 | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | (2017) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 246.37/58.19 | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | BETA: splitting (2017) gives:
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | (2018) all_252_20 = e4 & op(e0, e4) = e4
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | REF_CLOSE: (149), (2014), (2018), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | inconsistent by sub-proof #602.
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | (2019) all_252_21 = e4 & op(e0, e3) = e4
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | REF_CLOSE: (164), (2012), (2019), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | inconsistent by sub-proof #805.
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | End of split
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | (2020) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 246.37/58.19 | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 246.37/58.19 | | | | | | | | | | op(e0, e0) = e4)
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | BETA: splitting (2020) gives:
% 246.37/58.19 | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | (2021) all_252_22 = e4 & op(e0, e2) = e4
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | REF_CLOSE: (173), (2010), (2021), (function-axioms) are
% 246.37/58.19 | | | | | | | | | | | inconsistent by sub-proof #585.
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | (2022) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 246.37/58.19 | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | BETA: splitting (2022) gives:
% 246.37/58.19 | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | (2023) all_252_23 = e4 & op(e0, e1) = e4
% 246.37/58.19 | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | ALPHA: (2023) implies:
% 246.37/58.19 | | | | | | | | | | | | (2024) all_252_23 = e4
% 246.37/58.19 | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | BETA: splitting (2006) gives:
% 246.37/58.19 | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | Case 1:
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | (2025) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 246.37/58.19 | | | | | | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.19 | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | ALPHA: (2025) implies:
% 246.37/58.19 | | | | | | | | | | | | | (2026) op(e1, e4) = all_20_1
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 246.37/58.19 | | | | | | | | | | | | | all_20_1, e4, e1, simplifying with (155), (2026)
% 246.37/58.19 | | | | | | | | | | | | | gives:
% 246.37/58.19 | | | | | | | | | | | | | (2027) all_20_1 = all_16_2
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e0,
% 246.37/58.19 | | | | | | | | | | | | | e1, e4, simplifying with (170), (2016) gives:
% 246.37/58.19 | | | | | | | | | | | | | (2028) all_26_2 = e0
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | REDUCE: (1527), (2028) imply:
% 246.37/58.19 | | | | | | | | | | | | | (2029) ~ (all_38_2 = e0)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | REDUCE: (2011), (2028) imply:
% 246.37/58.19 | | | | | | | | | | | | | (2030) ~ (e4 = e0)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (13), (137),
% 246.37/58.19 | | | | | | | | | | | | | (140), (143), (146), (149), (161), (164), (165),
% 246.37/58.19 | | | | | | | | | | | | | (170), (173), (174), (180), (182), (183), (185),
% 246.37/58.19 | | | | | | | | | | | | | (188), (189), (201), (222), (224), (225), (234),
% 246.37/58.19 | | | | | | | | | | | | | (237), (249), (255), (257), (265), (271), (287),
% 246.37/58.19 | | | | | | | | | | | | | (304), (313), (467), (473), (479), (492), (501),
% 246.37/58.19 | | | | | | | | | | | | | (716), (717), (718), (720), (723), (725), (735),
% 246.37/58.19 | | | | | | | | | | | | | (744), (749), (758), (759), (760), (761), (841),
% 246.37/58.19 | | | | | | | | | | | | | (881), (1241), (1312), (1316), (1317), (1319),
% 246.37/58.19 | | | | | | | | | | | | | (1320), (1331), (1336), (1337), (1343), (1407),
% 246.37/58.19 | | | | | | | | | | | | | (1408), (1409), (1413), (1414), (1450), (1452),
% 246.37/58.19 | | | | | | | | | | | | | (1459), (1461), (1472), (1474), (1478), (1481),
% 246.37/58.19 | | | | | | | | | | | | | (1484), (1487), (1490), (1497), (1499), (1503),
% 246.37/58.19 | | | | | | | | | | | | | (1504), (1512), (1513), (1516), (1520), (1527),
% 246.37/58.19 | | | | | | | | | | | | | (1536), (1569), (1571), (1572), (1573), (1574),
% 246.37/58.19 | | | | | | | | | | | | | (1575), (1576), (1577), (1579), (1580), (1583),
% 246.37/58.19 | | | | | | | | | | | | | (1584), (1585), (1588), (1591), (1594), (1596),
% 246.37/58.19 | | | | | | | | | | | | | (1597), (1599), (1601), (1603), (1606), (1607),
% 246.37/58.19 | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (2007),
% 246.37/58.19 | | | | | | | | | | | | | (2009), (2010), (2012), (2014), (2015), (2024),
% 246.37/58.19 | | | | | | | | | | | | | (2026), (2027), (2028), (2029), (function-axioms)
% 246.37/58.19 | | | | | | | | | | | | | are inconsistent by sub-proof #574.
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | Case 2:
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | (2031) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 &
% 246.37/58.19 | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | ALPHA: (2031) implies:
% 246.37/58.19 | | | | | | | | | | | | | (2032) ~ (all_20_1 = e2)
% 246.37/58.19 | | | | | | | | | | | | | (2033) op(e1, e4) = all_20_1
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2,
% 246.37/58.19 | | | | | | | | | | | | | all_20_1, e4, e1, simplifying with (155), (2033)
% 246.37/58.19 | | | | | | | | | | | | | gives:
% 246.37/58.19 | | | | | | | | | | | | | (2034) all_20_1 = all_16_2
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e0,
% 246.37/58.19 | | | | | | | | | | | | | e1, e4, simplifying with (170), (2016) gives:
% 246.37/58.19 | | | | | | | | | | | | | (2035) all_26_2 = e0
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | REDUCE: (1527), (2035) imply:
% 246.37/58.19 | | | | | | | | | | | | | (2036) ~ (all_38_2 = e0)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.19 | | | | | | | | | | | | | REDUCE: (2011), (2035) imply:
% 246.37/58.19 | | | | | | | | | | | | | (2037) ~ (e4 = e0)
% 246.37/58.19 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (13), (137),
% 246.37/58.20 | | | | | | | | | | | | | (140), (143), (146), (149), (161), (164), (165),
% 246.37/58.20 | | | | | | | | | | | | | (170), (173), (174), (180), (182), (183), (185),
% 246.37/58.20 | | | | | | | | | | | | | (188), (189), (201), (222), (224), (225), (234),
% 246.37/58.20 | | | | | | | | | | | | | (237), (249), (255), (257), (265), (271), (287),
% 246.37/58.20 | | | | | | | | | | | | | (304), (313), (467), (473), (479), (492), (501),
% 246.37/58.20 | | | | | | | | | | | | | (716), (717), (718), (720), (723), (725), (735),
% 246.37/58.20 | | | | | | | | | | | | | (744), (749), (758), (759), (760), (761), (841),
% 246.37/58.20 | | | | | | | | | | | | | (881), (1241), (1312), (1316), (1317), (1319),
% 246.37/58.20 | | | | | | | | | | | | | (1320), (1331), (1336), (1337), (1343), (1407),
% 246.37/58.20 | | | | | | | | | | | | | (1408), (1409), (1413), (1414), (1450), (1452),
% 246.37/58.20 | | | | | | | | | | | | | (1459), (1461), (1472), (1474), (1478), (1481),
% 246.37/58.20 | | | | | | | | | | | | | (1484), (1487), (1490), (1497), (1499), (1503),
% 246.37/58.20 | | | | | | | | | | | | | (1504), (1512), (1513), (1516), (1520), (1527),
% 246.37/58.20 | | | | | | | | | | | | | (1536), (1569), (1571), (1572), (1573), (1574),
% 246.37/58.20 | | | | | | | | | | | | | (1575), (1576), (1577), (1579), (1580), (1583),
% 246.37/58.20 | | | | | | | | | | | | | (1584), (1585), (1588), (1591), (1594), (1596),
% 246.37/58.20 | | | | | | | | | | | | | (1597), (1599), (1601), (1603), (1606), (1607),
% 246.37/58.20 | | | | | | | | | | | | | (1608), (1609), (1610), (1611), (1613), (2007),
% 246.37/58.20 | | | | | | | | | | | | | (2009), (2010), (2012), (2014), (2015), (2024),
% 246.37/58.20 | | | | | | | | | | | | | (2033), (2034), (2035), (2036), (function-axioms)
% 246.37/58.20 | | | | | | | | | | | | | are inconsistent by sub-proof #574.
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | End of split
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | (2038) all_252_24 = e4 & op(e0, e0) = e4
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | REF_CLOSE: (467), (2008), (2038), (function-axioms) are
% 246.37/58.20 | | | | | | | | | | | | inconsistent by sub-proof #679.
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | End of split
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | End of split
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | End of split
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | End of split
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | (2039) all_18_2 = e3
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | COMBINE_EQS: (1215), (2039) imply:
% 246.37/58.20 | | | | | | | | (2040) all_12_2 = e3
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | SIMP: (2040) implies:
% 246.37/58.20 | | | | | | | | (2041) all_12_2 = e3
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1421), (2041) imply:
% 246.37/58.20 | | | | | | | | (2042) ~ (all_244_0 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1428), (2041) imply:
% 246.37/58.20 | | | | | | | | (2043) ~ (all_100_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1435), (2041) imply:
% 246.37/58.20 | | | | | | | | (2044) ~ (all_64_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1452), (2041) imply:
% 246.37/58.20 | | | | | | | | (2045) ~ (all_28_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1450), (2041) imply:
% 246.37/58.20 | | | | | | | | (2046) ~ (all_22_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1454), (2041) imply:
% 246.37/58.20 | | | | | | | | (2047) ~ (all_20_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1441), (2041) imply:
% 246.37/58.20 | | | | | | | | (2048) ~ (all_16_2 = e3)
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1599), (2041) imply:
% 246.37/58.20 | | | | | | | | (2049) op(all_30_2, e3) = e0
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1598), (2041) imply:
% 246.37/58.20 | | | | | | | | (2050) op(e3, all_30_2) = e4
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | REDUCE: (1582), (2041) imply:
% 246.37/58.20 | | | | | | | | (2051) op(e3, e4) = e0
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | BETA: splitting (778) gives:
% 246.37/58.20 | | | | | | | |
% 246.37/58.20 | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | (2052) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3
% 246.37/58.20 | | | | | | | | | & op(e3, e4) = e3)
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | BETA: splitting (2052) gives:
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | (2053) all_252_0 = e3 & op(e4, e4) = e3
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | ALPHA: (2053) implies:
% 246.37/58.20 | | | | | | | | | | (2054) op(e4, e4) = e3
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | REF_CLOSE: (491), (2042), (2054), (function-axioms) are
% 246.37/58.20 | | | | | | | | | | inconsistent by sub-proof #813.
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | (2055) all_252_2 = e3 & op(e3, e4) = e3
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | REF_CLOSE: (8), (278), (2051), (2055), (function-axioms) are
% 246.37/58.20 | | | | | | | | | | inconsistent by sub-proof #832.
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | End of split
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | (2056) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 246.37/58.20 | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 246.37/58.20 | | | | | | | | | e4) = e3)
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | BETA: splitting (2056) gives:
% 246.37/58.20 | | | | | | | | |
% 246.37/58.20 | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | (2057) all_252_6 = e3 & op(e2, e4) = e3
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | REF_CLOSE: (227), (2044), (2057), (function-axioms) are
% 246.37/58.20 | | | | | | | | | | inconsistent by sub-proof #940.
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | (2058) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 246.37/58.20 | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | BETA: splitting (2058) gives:
% 246.37/58.20 | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | (2059) all_252_12 = e3 & op(e1, e4) = e3
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REF_CLOSE: (155), (2048), (2059), (function-axioms) are
% 246.37/58.20 | | | | | | | | | | | inconsistent by sub-proof #895.
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | (2060) all_252_20 = e3 & op(e0, e4) = e3
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | ALPHA: (2060) implies:
% 246.37/58.20 | | | | | | | | | | | (2061) all_252_20 = e3
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2,
% 246.37/58.20 | | | | | | | | | | | e0, e4, e3, simplifying with (278), (2051) gives:
% 246.37/58.20 | | | | | | | | | | | (2062) all_100_2 = e0
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | COMBINE_EQS: (1262), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2063) all_146_2 = e0
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1430), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2064) ~ (all_244_3 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1426), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2065) ~ (all_64_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | SIMP: (2065) implies:
% 246.37/58.20 | | | | | | | | | | | (2066) ~ (all_64_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1433), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2067) ~ (all_48_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | SIMP: (2067) implies:
% 246.37/58.20 | | | | | | | | | | | (2068) ~ (all_48_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1432), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2069) ~ (all_36_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | SIMP: (2069) implies:
% 246.37/58.20 | | | | | | | | | | | (2070) ~ (all_36_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1427), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2071) ~ (all_16_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | SIMP: (2071) implies:
% 246.37/58.20 | | | | | | | | | | | (2072) ~ (all_16_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1431), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2073) ~ (all_8_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | SIMP: (2073) implies:
% 246.37/58.20 | | | | | | | | | | | (2074) ~ (all_8_2 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (2043), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2075) ~ (e3 = e0)
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1586), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2076) op(e0, all_84_2) = e4
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | REDUCE: (1587), (2062) imply:
% 246.37/58.20 | | | | | | | | | | | (2077) op(all_84_2, e0) = e3
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | BETA: splitting (772) gives:
% 246.37/58.20 | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | (2078) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 =
% 246.37/58.20 | | | | | | | | | | | | e0 & op(e3, e4) = e0)
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | BETA: splitting (2078) gives:
% 246.37/58.20 | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | (2079) all_252_0 = e0 & op(e4, e4) = e0
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | ALPHA: (2079) implies:
% 246.37/58.20 | | | | | | | | | | | | | (2080) all_252_0 = e0
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 246.37/58.20 | | | | | | | | | | | | | (143), (185), (203), (485), (762), (774), (776),
% 246.37/58.20 | | | | | | | | | | | | | (780), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.20 | | | | | | | | | | | | | (2080), (function-axioms) are inconsistent by
% 246.37/58.20 | | | | | | | | | | | | | sub-proof #559.
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | (2081) all_252_2 = e0 & op(e3, e4) = e0
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | ALPHA: (2081) implies:
% 246.37/58.20 | | | | | | | | | | | | | (2082) all_252_2 = e0
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | BETA: splitting (162) gives:
% 246.37/58.20 | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | (2083) ~ (all_20_2 = e4)
% 246.37/58.20 | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 246.37/58.20 | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | (2084) ~ (all_22_2 = e1)
% 246.37/58.20 | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 246.37/58.20 | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | (2085) ~ (all_26_2 = e3)
% 246.37/58.20 | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 246.37/58.20 | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | (2086) ~ (all_30_2 = e2)
% 246.37/58.20 | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 246.37/58.20 | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | (2087) ~ (all_146_2 = e0)
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | REDUCE: (2063), (2087) imply:
% 246.37/58.20 | | | | | | | | | | | | | | | | | | (2088) $false
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | CLOSE: (2088) is inconsistent.
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | (2089) ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 246.37/58.20 | | | | | | | | | | | | | | | | | | op(e0, all_146_1) = all_146_0 & $i(all_146_0) &
% 246.37/58.20 | | | | | | | | | | | | | | | | | | $i(all_146_1)) | ( ~ (all_146_1 = e2) & op(e4,
% 246.37/58.20 | | | | | | | | | | | | | | | | | | e0) = all_146_1 & $i(all_146_1))
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | BETA: splitting (2089) gives:
% 246.37/58.20 | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2090) ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | op(e0, all_146_1) = all_146_0 & $i(all_146_0) &
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | $i(all_146_1)
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | ALPHA: (2090) implies:
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2091) op(e4, e0) = all_146_1
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (164), (170), (173), (176), (180), (182), (183),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (185), (186), (188), (189), (191), (192), (198),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (201), (203), (204), (207), (224), (225), (227),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (234), (237), (249), (252), (255), (257), (260),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (265), (271), (333), (362), (383), (465), (467),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (473), (479), (485), (491), (513), (715), (717),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (722), (726), (728), (733), (734), (735), (736),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (737), (744), (747), (749), (750), (751), (752),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (755), (756), (757), (758), (759), (760), (761),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (762), (763), (764), (766), (767), (768), (769),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (770), (771), (773), (774), (775), (776), (777),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (778), (779), (780), (781), (871), (916), (1170),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1235), (1280), (1309), (1312), (1316), (1317),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1319), (1320), (1325), (1331), (1336), (1337),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1345), (1351), (1406), (1408), (1412), (1415),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1424), (1434), (1439), (1440), (1443), (1448),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1465), (1474), (1476), (1478), (1480), (1481),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1487), (1488), (1490), (1492), (1494), (1495),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1497), (1501), (1506), (1510), (1513), (1514),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1521), (1525), (1534), (1536), (1537), (1539),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1541), (1546), (1561), (1567), (1568), (1572),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1573), (1575), (1576), (1577), (1579), (1580),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1581), (1583), (1589), (1593), (1594), (1597),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1600), (1601), (1605), (1606), (1607), (1608),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2044), (2045), (2046),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2047), (2048), (2051), (2061), (2064), (2066),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2068), (2070), (2072), (2074), (2076), (2077),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2082), (2083), (2084), (2085), (2086), (2091),
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | #454.
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2092) ~ (all_146_1 = e2) & op(e4, e0) = all_146_1 &
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | $i(all_146_1)
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | ALPHA: (2092) implies:
% 246.37/58.20 | | | | | | | | | | | | | | | | | | | (2093) op(e4, e0) = all_146_1
% 246.37/58.20 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (164), (170), (173), (176), (180), (182), (183),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (185), (186), (188), (189), (191), (192), (198),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (201), (203), (204), (207), (224), (225), (227),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (234), (237), (249), (252), (255), (257), (260),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (265), (271), (333), (362), (383), (465), (467),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (473), (479), (485), (491), (513), (715), (717),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (722), (726), (728), (733), (734), (735), (736),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (737), (744), (747), (749), (750), (751), (752),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (755), (756), (757), (758), (759), (760), (761),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (762), (763), (764), (766), (767), (768), (769),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (770), (771), (773), (774), (775), (776), (777),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (778), (779), (780), (781), (871), (916), (1170),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1235), (1280), (1309), (1312), (1316), (1317),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1319), (1320), (1325), (1331), (1336), (1337),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1345), (1351), (1406), (1408), (1412), (1415),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1424), (1434), (1439), (1440), (1443), (1448),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1465), (1474), (1476), (1478), (1480), (1481),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1487), (1488), (1490), (1492), (1494), (1495),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1497), (1501), (1506), (1510), (1513), (1514),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1521), (1525), (1534), (1536), (1537), (1539),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1541), (1546), (1561), (1567), (1568), (1572),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1573), (1575), (1576), (1577), (1579), (1580),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1581), (1583), (1589), (1593), (1594), (1597),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1600), (1601), (1605), (1606), (1607), (1608),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2044), (2045), (2046),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2047), (2048), (2051), (2061), (2064), (2066),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2068), (2070), (2072), (2074), (2076), (2077),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2082), (2083), (2084), (2085), (2086), (2093),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | #454.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2094) all_30_2 = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1425), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2095) ~ (all_244_0 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1464), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2096) ~ (all_84_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1552), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2097) ~ (all_40_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1532), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2098) ~ (all_26_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | SIMP: (2098) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2099) ~ (all_26_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1501), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2100) ~ (all_6_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | SIMP: (2100) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2101) ~ (all_6_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (2049), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2102) op(e2, e3) = e0
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (1569), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2103) op(e2, e0) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | REDUCE: (2050), (2094) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | (2104) op(e3, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | (2105) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (143), (185), (203), (485), (491), (762),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | (2064), (2068), (2070), (2074), (2095), (2105),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | #459.
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | (2106) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | BETA: splitting (2106) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2107) all_252_6 = e2 & op(e2, e4) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | ALPHA: (2107) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2108) all_252_6 = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | (2109) op(e2, e4) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | (2110) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2110) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | (2111) all_252_0 = e2 & op(e4, e4) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2111) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | (2112) op(e4, e4) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (491), (2095), (2112), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #809.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | (2113) all_252_1 = e2 & op(e4, e3) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (2096), (2113), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #956.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | (2114) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2114) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | (2115) all_252_4 = e2 & op(e4, e2) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (2101), (2115), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #453.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | (2116) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2116) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2117) all_252_9 = e2 & op(e4, e1) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2099), (2117), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #970.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2118) all_252_16 = e2 & op(e4, e0) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2118) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2119) all_252_16 = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e4,
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (191), (2103) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2120) all_40_2 = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (2102) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2121) all_10_2 = e0
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e2,
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (2109) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2122) all_64_2 = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e4,
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2104) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2123) all_8_2 = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1468), (2123) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2124) ~ (all_244_3 = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1476), (2121) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2125) ~ (all_244_8 = e0)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1434), (2122) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2126) ~ (all_16_2 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2044), (2122) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2127) ~ (e3 = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1544), (2120) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2128) ~ (all_38_2 = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2128) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2129) ~ (all_38_2 = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1478), (2121) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2130) ~ (all_38_2 = e0)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1508), (2123) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2131) ~ (all_36_2 = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1575), (2121) imply:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | (2132) op(e0, e3) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | (2133) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (146), (1609), (2108), (2133),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | #724.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | (2134) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2134) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_252_8 = e4 & op(e2, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2135) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | (2136) op(e2, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (479), (491), (508), (2095), (2136),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | #626.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | (2137) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2137) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_252_11 = e4 & op(e2, e1) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2138) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | (2139) op(e2, e1) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2129), (2139), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #935.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_252_18 = e4 & op(e2, e0) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_252_18 = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2142) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_252_20 = e4 & op(e0, e4) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2061), (2143) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) all_252_21 = e4 & op(e0, e3) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2144) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) op(e0, e3) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (164), (2132), (2145), (function-axioms) are
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2146) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_252_22 = e4 & op(e0, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2147) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_252_22 = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) op(e0, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (143), (185), (203), (485), (762), (2064),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068), (2070), (2074), (2124), (2150),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2151) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) all_252_5 = e4 & op(e3, e2) = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2152) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_252_5 = e4
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2154) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (140), (2101), (2153), (2154),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451.
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2155) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2155) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2156) all_252_8 = e2 & op(e2, e2) = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2156) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_252_8 = e2
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 =
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0)
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2158) gives:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2159) all_252_6 = e0 & op(e2, e4) = e0
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2159) implies:
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) all_252_6 = e0
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (143), (155), (185), (203), (485), (762),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (780), (1611), (2048),
% 246.37/58.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2160), (function-axioms) are inconsistent
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #537.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) all_252_7 = e0 & op(e2, e3) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2161) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) all_252_7 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2163) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2164) all_252_6 = e1 & op(e2, e4) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2108), (2164) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2165) all_252_7 = e1 & op(e2, e3) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2165) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2166) all_252_7 = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2162), (2166) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2167) e1 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2167) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2168) e1 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2168) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) $false
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2169) is inconsistent.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2170) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2170) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171) all_252_8 = e1 & op(e2, e2) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2157), (2171) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #665.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2172) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2172) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2173) all_252_11 = e1 & op(e2, e1) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2173) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2174) all_252_11 = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (755) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2175) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2176) all_252_6 = e3 & op(e2, e4) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2176) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2177) all_252_6 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2178) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (11), (12), (13), (14), (143),
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (203), (485), (762), (774), (780), (2051),
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2064), (2068), (2070), (2074), (2177),
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2178), (function-axioms) are inconsistent by
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #535.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2106) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2107), (2177) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #450.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2179) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2179) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2180) all_252_12 = e2 & op(e1, e4) = e2
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1611), (2180), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #926.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2181) all_252_20 = e2 & op(e0, e4) = e2
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2061), (2181) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2182) all_252_7 = e3 & op(e2, e3) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2162), (2182) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #945.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2183) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2183) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2184) all_252_8 = e3 & op(e2, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2184) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2185) all_252_8 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2157), (2185) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #920.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2186) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2186) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2187) all_252_11 = e3 & op(e2, e1) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2174), (2187) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #449.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2188) all_252_18 = e3 & op(e2, e0) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2141), (2188) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #700.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2189) all_252_18 = e1 & op(e2, e0) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2189) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2190) all_252_18 = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2141), (2190) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #448.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2191) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2191) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2192) all_252_8 = e0 & op(e2, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2192) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2193) op(e2, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (479), (2125), (2193), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2194) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2194) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2195) all_252_11 = e0 & op(e2, e1) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2130), (2195), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #904.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2196) all_252_18 = e0 & op(e2, e0) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2196) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2197) all_252_18 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2141), (2197) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2198) e4 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2198) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2199) e4 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (2199) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2200) $false
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2200) is inconsistent.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2201) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) all_252_14 = e2 & op(e1, e2) = e2
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2202) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2203) all_252_14 = e2
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2204) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) all_252_4 = e0 & op(e4, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2205) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_252_4 = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1607), (1608), (2207),
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #928.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2208) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) all_252_8 = e1 & op(e2, e2) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2209) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) all_252_8 = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2211) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_252_4 = e3 & op(e4, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2206), (2212) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #865.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_252_5 = e3 & op(e3, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2213) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) all_252_5 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2153), (2214) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) e4 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (2215) imply:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) $false
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2216) is inconsistent.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2217) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) all_252_8 = e3 & op(e2, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2218) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_252_8 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2210), (2219) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #927.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2220) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_252_14 = e3 & op(e1, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2221) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) all_252_14 = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2203), (2222) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #447.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) all_252_22 = e3 & op(e0, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) op(e0, e2) = e3
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2149), (2224), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2225) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_252_14 = e1 & op(e1, e2) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2203), (2226) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #753.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) all_252_22 = e1 & op(e0, e2) = e1
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2148), (2227) are inconsistent by sub-proof
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #446.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_252_5 = e0 & op(e3, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2228) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) op(e3, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2104), (2229), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #645.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2230) gives:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) all_252_8 = e0 & op(e2, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2231) implies:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) op(e2, e2) = e0
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (479), (2125), (2232), (function-axioms) are
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 246.37/58.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2233) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) all_252_14 = e0 & op(e1, e2) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2234) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_252_14 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1607), (1608), (2236),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #928.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2237) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) all_252_8 = e1 & op(e2, e2) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2238) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_252_8 = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (140), (2101), (2153), (2240),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2155) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_252_8 = e2 & op(e2, e2) = e2
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2239), (2241) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #788.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2201) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2203), (2235) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) e2 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2242) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) e2 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2108), (2243) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) all_252_6 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (143), (155), (185), (203), (485), (762),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (780), (1611), (2048),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2244), (function-axioms) are inconsistent
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #537.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) all_252_22 = e2 & op(e0, e2) = e2
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2148), (2245) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #445.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2246) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) all_252_14 = e1 & op(e1, e2) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2247) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) all_252_14 = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2235), (2248) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) e1 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2249) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) e1 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2250) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) $false
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2251) is inconsistent.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) all_252_22 = e1 & op(e0, e2) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2148), (2252) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #446.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) all_252_22 = e0 & op(e0, e2) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2148), (2253) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #444.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) all_252_22 = e2 & op(e0, e2) = e2
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2148), (2254) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #445.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2255) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2256) all_252_10 = e4 & op(e3, e1) = e4
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2131), (2256), (function-axioms) are
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #914.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_252_17 = e4 & op(e3, e0) = e4
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2257) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258) all_252_17 = e4
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2259) op(e3, e0) = e4
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2260) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2261) all_252_16 = e3 & op(e4, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2119), (2261) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2262) all_252_17 = e3 & op(e3, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2258), (2262) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2263) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2263) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2264) all_252_18 = e3 & op(e2, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2141), (2264) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #663.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2265) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2265) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2266) all_252_19 = e3 & op(e1, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2266) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2267) op(e1, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) all_252_24 = e0 & op(e0, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2268) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2269) all_252_24 = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2270) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (2119), (2259), (2270),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #440.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2271) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2271) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2272) all_252_18 = e1 & op(e2, e0) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2141), (2272) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #624.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2273) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2273) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2274) all_252_19 = e1 & op(e1, e0) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2274) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2275) op(e1, e0) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, e1,
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (182), (2275) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2276) all_34_2 = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, e3,
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (182), (2267) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2277) all_34_2 = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2276), (2277) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2278) e3 = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2278) imply:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2279) $false
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2279) is inconsistent.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2280) all_252_24 = e1 & op(e0, e0) = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2280) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2281) all_252_24 = e1
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2269), (2281) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #623.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2282) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2283) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2283) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2284) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (143), (155), (185), (203), (485), (762),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (780), (1611), (2048),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2108), (2119), (2284), (function-axioms)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #439.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2285) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2285) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2286) all_252_18 = e0 & op(e2, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2141), (2286) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #619.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2287) all_252_19 = e0 & op(e1, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2287) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2288) op(e1, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2267), (2288), (function-axioms) are
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2289) all_252_24 = e3 & op(e0, e0) = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2289) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2290) all_252_24 = e3
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2291) all_252_24 = e0 & op(e0, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2290), (2291) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #533.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2292) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2292) implies:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2293) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2293) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2294) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (143), (155), (185), (203), (485), (762),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (780), (1611), (2048),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2108), (2119), (2294), (function-axioms)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #439.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2295) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2295) gives:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296) all_252_18 = e0 & op(e2, e0) = e0
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2141), (2296) are inconsistent by sub-proof
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #619.
% 246.37/58.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) all_252_19 = e0 & op(e1, e0) = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2297) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2298) all_252_19 = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (2119), (2259), (2299),
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #440.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2300) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 &
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2300) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_252_18 = e1 & op(e2, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2141), (2301) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #624.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2302) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2302) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303) all_252_19 = e1 & op(e1, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2303) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2304) all_252_19 = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2298), (2304) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2305) e1 = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2305) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2306) e1 = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2306) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307) $false
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2307) is inconsistent.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2308) all_252_24 = e1 & op(e0, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2290), (2308) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #526.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2309) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2309) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2310) all_252_23 = e4 & op(e0, e1) = e4
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2083), (2310), (function-axioms) are
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #912.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311) all_252_24 = e4 & op(e0, e0) = e4
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2311) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2312) all_252_24 = e4
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313) op(e0, e0) = e4
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2314) all_252_24 = e0 & op(e0, e0) = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2312), (2314) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2315) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2316) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2316) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (143), (155), (185), (203), (485), (762),
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (780), (1611), (2048),
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051), (2061), (2064), (2068), (2070), (2074),
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2108), (2119), (2317), (function-axioms)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #439.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2318) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) all_252_18 = e0 & op(e2, e0) = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2141), (2319) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #619.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) all_252_19 = e0 & op(e1, e0) = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2320) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) all_252_19 = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) op(e1, e0) = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2323) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2324) all_252_16 = e1 & op(e4, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2119), (2324) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #442.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2325) all_252_17 = e1 & op(e3, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2325) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2326) op(e3, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2327) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2327) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328) all_252_16 = e3 & op(e4, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2119), (2328) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329) all_252_17 = e3 & op(e3, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2326), (2329), (function-axioms) are
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #436.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2330) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2330) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2331) all_252_18 = e3 & op(e2, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2141), (2331) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #700.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2332) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2332) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2333) all_252_19 = e3 & op(e1, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2333) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334) op(e1, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2322), (2334), (function-axioms) are
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2335) all_252_24 = e3 & op(e0, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2335) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2336) op(e0, e0) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (467), (2313), (2336), (function-axioms) are
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2337) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 &
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2337) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2338) all_252_18 = e1 & op(e2, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2141), (2338) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #624.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2339) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2340) all_252_19 = e1 & op(e1, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2340) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2341) all_252_19 = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2321), (2341) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2342) e1 = e0
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (2342) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2343) $false
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2343) is inconsistent.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2344) all_252_24 = e1 & op(e0, e0) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2312), (2344) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #499.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | (2345) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 246.37/58.24 | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (2345) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | (2346) all_252_12 = e2 & op(e1, e4) = e2
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1611), (2346), (function-axioms) are
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #926.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | (2347) all_252_20 = e2 & op(e0, e4) = e2
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2061), (2347) are inconsistent by sub-proof
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | | #560.
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | End of split
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | (2348) all_26_2 = e3
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1529), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2349) ~ (all_244_15 = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1527), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2350) ~ (all_38_2 = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1525), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2351) ~ (all_36_2 = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1530), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2352) ~ (all_20_2 = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1593), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2353) op(e3, all_16_2) = e1
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | REDUCE: (1568), (2348) imply:
% 246.37/58.24 | | | | | | | | | | | | | | | | (2354) op(e3, e1) = e4
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | BETA: splitting (750) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | (2355) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 246.37/58.24 | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 246.37/58.24 | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | BETA: splitting (2355) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.24 | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | (2356) all_252_9 = e3 & op(e4, e1) = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | ALPHA: (2356) implies:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | (2357) all_252_9 = e3
% 246.37/58.24 | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e4,
% 246.37/58.24 | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (2354) gives:
% 246.37/58.24 | | | | | | | | | | | | | | | | | | (2358) all_36_2 = e4
% 246.37/58.24 | | | | | | | | | | | | | | | | | |
% 246.37/58.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1329), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2359) all_52_2 = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1469), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2360) ~ (all_244_3 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1536), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2361) ~ (all_244_15 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1539), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2362) ~ (all_48_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1534), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2363) ~ (all_38_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1537), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2364) ~ (all_20_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1508), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2365) ~ (all_8_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | SIMP: (2365) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2366) ~ (all_8_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (1594), (2358) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2367) op(all_62_2, e4) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | (2368) ~ (all_36_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2354), (2368), (function-axioms) are
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #435.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | (2369) ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | & op(e1, e4) = all_36_1 & $i(all_36_0) &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e1, e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | (2370) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (143), (185), (203), (485), (762), (2064),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | (2068), (2070), (2074), (2360), (2370),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | #452.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | (2371) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2371) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2372) all_252_5 = e4 & op(e3, e2) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2372) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2373) op(e3, e2) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (2366), (2373), (function-axioms) are
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2374) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2374) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2375) all_252_10 = e4 & op(e3, e1) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2375) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2376) all_252_10 = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2377) ~ (all_52_2 = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2359), (2377) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2378) $false
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2378) is inconsistent.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2379) ( ~ (all_52_0 = e2) & op(e4, all_52_1) = all_52_0
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e4) = all_52_1 & $i(all_52_0) &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_52_1)) | ( ~ (all_52_1 = e0) & op(e1, e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | = all_52_1 & $i(all_52_1))
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2369) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2380) ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_36_1 & $i(all_36_0) &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2380) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2381) op(e1, e4) = all_36_1
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (143), (155), (176), (177), (185),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (203), (204), (224), (225), (473),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (485), (491), (513), (733), (739), (740), (741),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (746), (762), (763), (764), (765), (1510), (1573),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (1577), (1606), (1608), (2042), (2050), (2051),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2064), (2068), (2070), (2074), (2082), (2349),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2353), (2354), (2361), (2362), (2366), (2367),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2376), (2379), (2381), (function-axioms) are
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #419.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2382) ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2382) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2383) op(e1, e4) = all_36_1
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (143), (155), (176), (177), (185),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (191), (192), (203), (204), (224), (225), (473),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (485), (491), (513), (733), (739), (740), (741),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (746), (762), (763), (764), (765), (1510), (1573),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (1577), (1606), (1608), (2042), (2050), (2051),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2064), (2068), (2070), (2074), (2082), (2349),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2353), (2354), (2361), (2362), (2366), (2367),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2376), (2379), (2383), (function-axioms) are
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #419.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2384) all_252_17 = e4 & op(e3, e0) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2384) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2385) all_252_17 = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2386) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2386) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2387) all_252_9 = e4 & op(e4, e1) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2357), (2387) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | #633.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2388) all_252_10 = e4 & op(e3, e1) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2388) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2389) all_252_10 = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (143), (185), (203), (485), (762), (763), (764),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (765), (1608), (2064), (2068), (2070), (2074),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2354), (2385), (2389), (function-axioms)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #431.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2390) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (188), (473), (2083), (2361), (2363),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2390), (function-axioms) are inconsistent by
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #615.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2391) all_252_10 = e3 & op(e3, e1) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | ALPHA: (2391) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2392) op(e3, e1) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (185), (2354), (2392), (function-axioms) are
% 246.37/58.25 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #614.
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2393) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 246.37/58.25 | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | op(e0, e1) = e3)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | BETA: splitting (2393) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2394) all_252_11 = e3 & op(e2, e1) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | ALPHA: (2394) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2395) op(e2, e1) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e3,
% 246.37/58.25 | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (188), (2395) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2396) all_38_2 = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REDUCE: (2350), (2396) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2397) $false
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | CLOSE: (2397) is inconsistent.
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2398) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 246.37/58.25 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (473), (2047), (2349), (2398),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | #742.
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | (2399) all_22_2 = e1
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (1481), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2400) ~ (all_62_2 = e1)
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (1487), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2401) ~ (all_28_2 = e1)
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (1488), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2402) ~ (all_20_2 = e1)
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | SIMP: (2402) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | (2403) ~ (all_20_2 = e1)
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (2046), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2404) ~ (e3 = e1)
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (1583), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2405) op(e1, e3) = e0
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | REDUCE: (164), (2399) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | (2406) op(e0, e3) = e1
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | BETA: splitting (734) gives:
% 246.37/58.25 | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | (2407) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 246.37/58.25 | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 246.37/58.25 | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | BETA: splitting (2407) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2408) all_252_20 = e1 & op(e0, e4) = e1
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2061), (2408) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | #565.
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2409) all_252_21 = e1 & op(e0, e3) = e1
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | ALPHA: (2409) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2410) all_252_21 = e1
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e0,
% 246.37/58.25 | | | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (2405) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2411) all_62_2 = e0
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (1298), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2412) all_114_2 = e0
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REDUCE: (1485), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2413) ~ (all_34_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | SIMP: (2413) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2414) ~ (all_34_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REDUCE: (1472), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2415) ~ (all_10_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | SIMP: (2415) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2416) ~ (all_10_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REDUCE: (1482), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2417) ~ (all_4_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | SIMP: (2417) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2418) ~ (all_4_2 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REDUCE: (2400), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2419) ~ (e1 = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | REDUCE: (1594), (2411) imply:
% 246.37/58.25 | | | | | | | | | | | | | | | | | (2420) op(e0, all_36_2) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | BETA: splitting (767) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | (2421) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | BETA: splitting (2421) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | (2422) all_252_1 = e0 & op(e4, e3) = e0
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | ALPHA: (2422) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | (2423) all_252_1 = e0
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | (2424) op(e4, e3) = e0
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | (2425) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2425) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2426) all_252_1 = e4 & op(e4, e3) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2423), (2426) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | #898.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2427) all_252_3 = e4 & op(e3, e3) = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2427) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | (2428) all_252_3 = e4
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2429) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (257), (2424), (2428), (2429),
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | #495.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | (2430) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2430) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2431) all_252_7 = e2 & op(e2, e3) = e2
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2431) implies:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | (2432) all_252_7 = e2
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (770) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | (2433) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2433) gives:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_252_1 = e3 & op(e4, e3) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2423), (2434) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | #840.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_252_3 = e3 & op(e3, e3) = e3
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2428), (2435) are inconsistent by sub-proof
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2436) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2436) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2437) all_252_7 = e3 & op(e2, e3) = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2437) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2438) all_252_7 = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2432), (2438) are inconsistent by sub-proof
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | #939.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | (2439) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2439) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) all_252_13 = e3 & op(e1, e3) = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2440) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) all_252_13 = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) op(e1, e3) = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e3,
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (2405), (2442) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) e3 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2441), (2443) imply:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) all_252_13 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (173), (176), (180), (182), (183), (185),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (298), (343), (378), (450),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (715), (733),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (735), (736), (737), (738), (739), (740), (741),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (743), (744), (745), (746), (747), (751), (752),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (753), (754), (755), (756), (757), (758), (759),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (760), (762), (763), (766), (769), (770), (771),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (779), (780), (781), (1336),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1349), (1361), (1406), (1480), (1512), (1545),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1554), (1558), (1561), (1565), (1577), (1581),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1585), (1597), (1605), (1606), (1607), (1608),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2046), (2047), (2048),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2063), (2064), (2068), (2070), (2074),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2083), (2401), (2403), (2406), (2410),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2412), (2414), (2416), (2418), (2420), (2444),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | #290.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_252_21 = e3 & op(e0, e3) = e3
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2046), (2445), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #959.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | (2446) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2446) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2447) all_252_13 = e2 & op(e1, e3) = e2
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2447) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2448) all_252_13 = e2
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2449) op(e1, e3) = e2
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e3,
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (2405), (2449) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2450) e2 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2448), (2450) imply:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2451) all_252_13 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (164), (173), (176), (180), (182), (183), (185),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (298), (343), (378), (450),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (715), (733),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (735), (736), (737), (738), (739), (740), (741),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (743), (744), (745), (746), (747), (751), (752),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (753), (754), (755), (756), (757), (758), (759),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (760), (762), (763), (766), (769), (770), (771),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (779), (780), (781), (1336),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (1349), (1361), (1406), (1480), (1512), (1545),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (1554), (1558), (1561), (1565), (1577), (1581),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (1585), (1597), (1605), (1606), (1607), (1608),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2046), (2047), (2048),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2061), (2063), (2064), (2068), (2070), (2074),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2082), (2083), (2401), (2403), (2406), (2410),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2412), (2414), (2416), (2418), (2420), (2451),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | #290.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2452) all_252_21 = e2 & op(e0, e3) = e2
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2452) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | (2453) op(e0, e3) = e2
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2406), (2453), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | (2454) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2454) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | (2455) all_252_7 = e4 & op(e2, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2455) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | (2456) op(e2, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1609), (2456), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | (2457) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2457) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2458) all_252_13 = e4 & op(e1, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2458) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2459) all_252_13 = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2460) op(e1, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e4, e3,
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (2405), (2460) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2461) e4 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2459), (2461) imply:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2462) all_252_13 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (164), (173), (176), (180), (182), (183), (185),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (298), (343), (378), (450),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (715), (733),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (735), (736), (737), (738), (739), (740), (741),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (743), (744), (745), (746), (747), (751), (752),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (753), (754), (755), (756), (757), (758), (759),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (760), (762), (763), (766), (769), (770), (771),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (779), (780), (781), (1336),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (1349), (1361), (1406), (1480), (1512), (1545),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (1554), (1558), (1561), (1565), (1577), (1581),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (1585), (1597), (1605), (1606), (1607), (1608),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2046), (2047), (2048),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2061), (2063), (2064), (2068), (2070), (2074),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2082), (2083), (2401), (2403), (2406), (2410),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2412), (2414), (2416), (2418), (2420), (2462),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | #290.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2463) all_252_21 = e4 & op(e0, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2463) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | (2464) op(e0, e3) = e4
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2406), (2464), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #828.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (2465) all_252_3 = e0 & op(e3, e3) = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | ALPHA: (2465) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (2466) all_252_3 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (146), (769), (770), (771), (1609), (2405),
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (2406), (2410), (2466), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #288.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.26 | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | (2467) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 246.37/58.26 | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 246.37/58.26 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0)
% 246.37/58.26 | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | BETA: splitting (2467) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (2468) all_252_7 = e0 & op(e2, e3) = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (2416), (2468), (function-axioms) are
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #816.
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | (2469) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (2469) gives:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | (2470) all_252_13 = e0 & op(e1, e3) = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | ALPHA: (2470) implies:
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | | (2471) all_252_13 = e0
% 246.37/58.26 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (14), (137), (140), (143), (146), (155), (161),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (164), (173), (176), (180), (182), (183), (185),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (188), (191), (203), (298), (343), (378), (450),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (467), (473), (479), (485), (491), (715), (733),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (735), (736), (737), (738), (739), (740), (741),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (743), (744), (745), (746), (747), (751), (752),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (753), (754), (755), (756), (757), (758), (759),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (760), (762), (763), (766), (769), (770), (771),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (774), (776), (778), (779), (780), (781), (1336),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (1349), (1361), (1406), (1480), (1512), (1545),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (1554), (1558), (1561), (1565), (1577), (1581),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (1585), (1597), (1605), (1606), (1607), (1608),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (1609), (1611), (2042), (2046), (2047), (2048),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (2061), (2063), (2064), (2068), (2070), (2074),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (2082), (2083), (2401), (2403), (2406), (2410),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (2412), (2414), (2416), (2418), (2420), (2471),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | #290.
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (2472) all_252_21 = e0 & op(e0, e3) = e0
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (2472) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | (2473) op(e0, e3) = e0
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2406), (2473), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | (2474) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 246.37/58.27 | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 246.37/58.27 | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | BETA: splitting (2474) gives:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2475) all_252_22 = e1 & op(e0, e2) = e1
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | ALPHA: (2475) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2476) op(e0, e2) = e1
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2401), (2476), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2477) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 246.37/58.27 | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | BETA: splitting (2477) gives:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2478) all_252_23 = e1 & op(e0, e1) = e1
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2403), (2478), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #287.
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2479) all_252_24 = e1 & op(e0, e0) = e1
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | ALPHA: (2479) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2480) all_252_24 = e1
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (14), (161), (733), (735), (736), (737), (2061),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2083), (2406), (2480), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #295.
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | (2481) all_20_2 = e4
% 246.37/58.27 | | | | | | | | | | | | | | (2482) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0
% 246.37/58.27 | | | | | | | | | | | | | | & op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.27 | | | | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4)
% 246.37/58.27 | | | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | COMBINE_EQS: (786), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2483) all_60_2 = e4
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1545), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2484) ~ (all_244_15 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1542), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2485) ~ (all_38_2 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1537), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2486) ~ (all_36_2 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1521), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2487) ~ (all_28_2 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1530), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2488) ~ (all_26_2 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1488), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2489) ~ (all_22_2 = e4)
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1604), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2490) op(e4, all_34_2) = e1
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | REDUCE: (1585), (2481) imply:
% 246.37/58.27 | | | | | | | | | | | | | | (2491) op(e4, e1) = e0
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | (2492) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 246.37/58.27 | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | BETA: splitting (2492) gives:
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | (2493) all_252_9 = e4 & op(e4, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | ALPHA: (2493) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | (2494) op(e4, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (170), (2491), (2494), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | inconsistent by sub-proof #286.
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | (2495) all_252_10 = e4 & op(e3, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2486), (2495), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | inconsistent by sub-proof #914.
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | (2496) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 246.37/58.27 | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 246.37/58.27 | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | BETA: splitting (2496) gives:
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | (2497) all_252_11 = e4 & op(e2, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | ALPHA: (2497) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | (2498) op(e2, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2485), (2498), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | inconsistent by sub-proof #935.
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | (2499) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 246.37/58.27 | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | BETA: splitting (2499) gives:
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2500) all_252_15 = e4 & op(e1, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | ALPHA: (2500) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2501) op(e1, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (473), (2484), (2501), (function-axioms) are
% 246.37/58.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #756.
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2502) all_252_23 = e4 & op(e0, e1) = e4
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | ALPHA: (2502) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | (2503) all_252_23 = e4
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives:
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2504) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 246.37/58.27 | | | | | | | | | | | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.27 | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | ALPHA: (2504) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2505) op(e1, e4) = all_20_1
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (137), (140), (143), (146), (155), (161), (164),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (165), (170), (173), (176), (177), (182), (183),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (185), (188), (191), (192), (201), (203), (204),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (207), (222), (224), (225), (227), (237), (240),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (249), (255), (257), (343), (433), (467), (473),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (479), (485), (491), (492), (501), (513), (717),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (722), (728), (729), (733), (734), (735), (736),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (739), (740), (742), (744), (745), (746), (747),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (748), (749), (750), (754), (755), (756), (757),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (758), (759), (762), (763), (764), (765), (766),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (767), (768), (769), (770), (771), (774), (775),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (776), (779), (780), (781), (916), (1280), (1312),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1316), (1320), (1324), (1337), (1357), (1408),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1412), (1417), (1425), (1443), (1472), (1481),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1487), (1492), (1495), (1497), (1499), (1501),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1504), (1506), (1508), (1510), (1511), (1512),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1513), (1516), (1525), (1527), (1529), (1532),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1534), (1536), (1539), (1541), (1568), (1572),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1573), (1575), (1577), (1579), (1580), (1583),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1584), (1588), (1593), (1594), (1597), (1601),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1606), (1607), (1608), (1609), (1611), (2045),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2046), (2047), (2048), (2050), (2051), (2061),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2063), (2064), (2068), (2072), (2074), (2082),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2483), (2484), (2485), (2486), (2487), (2488),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2489), (2490), (2491), (2503), (2505),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.27 | | | | | | | | | | | | | | | | | | #237.
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2506) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 &
% 246.37/58.27 | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | ALPHA: (2506) implies:
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2507) op(e1, e4) = all_20_1
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (137), (140), (143), (146), (155), (161), (164),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (165), (170), (173), (176), (177), (182), (183),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (185), (188), (191), (192), (201), (203), (204),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (207), (222), (224), (225), (227), (237), (240),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (249), (255), (257), (343), (433), (467), (473),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (479), (485), (491), (492), (501), (513), (717),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (722), (728), (729), (733), (734), (735), (736),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (739), (740), (742), (744), (745), (746), (747),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (748), (749), (750), (754), (755), (756), (757),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (758), (759), (762), (763), (764), (765), (766),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (767), (768), (769), (770), (771), (774), (775),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (776), (779), (780), (781), (916), (1280), (1312),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1316), (1320), (1324), (1337), (1357), (1408),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1412), (1417), (1425), (1443), (1472), (1481),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1487), (1492), (1495), (1497), (1499), (1501),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1504), (1506), (1508), (1510), (1511), (1512),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1513), (1516), (1525), (1527), (1529), (1532),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1534), (1536), (1539), (1541), (1568), (1572),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1573), (1575), (1577), (1579), (1580), (1583),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1584), (1588), (1593), (1594), (1597), (1601),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (1606), (1607), (1608), (1609), (1611), (2045),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2046), (2047), (2048), (2050), (2051), (2061),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2063), (2064), (2068), (2072), (2074), (2082),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2483), (2484), (2485), (2486), (2487), (2488),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (2489), (2490), (2491), (2503), (2507),
% 246.37/58.27 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.27 | | | | | | | | | | | | | | | | | | #237.
% 246.37/58.27 | | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | End of split
% 246.37/58.27 | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | Case 2:
% 246.37/58.27 | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | (2508) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 =
% 246.37/58.27 | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 246.37/58.27 | | | | | | | | | | | | op(e0, e4) = e0)
% 246.37/58.27 | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | BETA: splitting (2508) gives:
% 246.37/58.27 | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | Case 1:
% 246.37/58.27 | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | (2509) all_252_6 = e0 & op(e2, e4) = e0
% 246.37/58.27 | | | | | | | | | | | | |
% 246.37/58.27 | | | | | | | | | | | | | ALPHA: (2509) implies:
% 246.37/58.28 | | | | | | | | | | | | | (2510) all_252_6 = e0
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | BETA: splitting (776) gives:
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | (2511) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 246.37/58.28 | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (11), (12), (13), (14), (143),
% 246.37/58.28 | | | | | | | | | | | | | | (185), (203), (485), (762), (774), (780), (2051),
% 246.37/58.28 | | | | | | | | | | | | | | (2061), (2064), (2068), (2070), (2074), (2510),
% 246.37/58.28 | | | | | | | | | | | | | | (2511), (function-axioms) are inconsistent by
% 246.37/58.28 | | | | | | | | | | | | | | sub-proof #549.
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | (2512) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 246.37/58.28 | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 246.37/58.28 | | | | | | | | | | | | | | op(e0, e4) = e2)
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | BETA: splitting (2512) gives:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | (2513) all_252_6 = e2 & op(e2, e4) = e2
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REF_CLOSE: (6), (2510), (2513) are inconsistent by sub-proof
% 246.37/58.28 | | | | | | | | | | | | | | | #892.
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | (2514) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 246.37/58.28 | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | BETA: splitting (2514) gives:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | (2515) all_252_12 = e2 & op(e1, e4) = e2
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1611), (2515), (function-axioms) are
% 246.37/58.28 | | | | | | | | | | | | | | | | inconsistent by sub-proof #926.
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | (2516) all_252_20 = e2 & op(e0, e4) = e2
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2061), (2516) are inconsistent by sub-proof
% 246.37/58.28 | | | | | | | | | | | | | | | | #560.
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | (2517) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20
% 246.37/58.28 | | | | | | | | | | | | | = e0 & op(e0, e4) = e0)
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | BETA: splitting (2517) gives:
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | (2518) all_252_12 = e0 & op(e1, e4) = e0
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | ALPHA: (2518) implies:
% 246.37/58.28 | | | | | | | | | | | | | | (2519) op(e1, e4) = e0
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | REF_CLOSE: (155), (2072), (2519), (function-axioms) are
% 246.37/58.28 | | | | | | | | | | | | | | inconsistent by sub-proof #278.
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | (2520) all_252_20 = e0 & op(e0, e4) = e0
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | REF_CLOSE: (8), (2061), (2520) are inconsistent by sub-proof
% 246.37/58.28 | | | | | | | | | | | | | | #313.
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | End of split
% 246.37/58.28 | | | | | | | |
% 246.37/58.28 | | | | | | | End of split
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | Case 2:
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | (2521) all_16_2 = e2
% 246.37/58.28 | | | | | | | (2522) ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 & op(e2,
% 246.37/58.28 | | | | | | | all_16_1) = all_16_0 & $i(all_16_0) & $i(all_16_1))
% 246.37/58.28 | | | | | | | | ( ~ (all_16_1 = e0) & op(e4, e2) = all_16_1 &
% 246.37/58.28 | | | | | | | $i(all_16_1))
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1420), (2521) imply:
% 246.37/58.28 | | | | | | | (2523) ~ (all_244_0 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1446), (2521) imply:
% 246.37/58.28 | | | | | | | (2524) ~ (all_244_15 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1434), (2521) imply:
% 246.37/58.28 | | | | | | | (2525) ~ (all_64_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1443), (2521) imply:
% 246.37/58.28 | | | | | | | (2526) ~ (all_62_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1448), (2521) imply:
% 246.37/58.28 | | | | | | | (2527) ~ (all_34_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1441), (2521) imply:
% 246.37/58.28 | | | | | | | (2528) ~ (all_12_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1444), (2521) imply:
% 246.37/58.28 | | | | | | | (2529) ~ (all_4_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | SIMP: (2529) implies:
% 246.37/58.28 | | | | | | | (2530) ~ (all_4_2 = e2)
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1593), (2521) imply:
% 246.37/58.28 | | | | | | | (2531) op(all_26_2, e2) = e1
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1592), (2521) imply:
% 246.37/58.28 | | | | | | | (2532) op(e2, all_26_2) = e4
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | REDUCE: (1578), (2521) imply:
% 246.37/58.28 | | | | | | | (2533) op(e2, e4) = e1
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | BETA: splitting (744) gives:
% 246.37/58.28 | | | | | | |
% 246.37/58.28 | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | |
% 246.37/58.28 | | | | | | | | (2534) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2
% 246.37/58.28 | | | | | | | | & op(e1, e3) = e2)
% 246.37/58.28 | | | | | | | |
% 246.37/58.28 | | | | | | | | BETA: splitting (2534) gives:
% 246.37/58.28 | | | | | | | |
% 246.37/58.28 | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | (2535) all_252_12 = e2 & op(e1, e4) = e2
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | ALPHA: (2535) implies:
% 246.37/58.28 | | | | | | | | | (2536) all_252_12 = e2
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e1,
% 246.37/58.28 | | | | | | | | | e4, e2, simplifying with (227), (2533) gives:
% 246.37/58.28 | | | | | | | | | (2537) all_64_2 = e1
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | COMBINE_EQS: (1293), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2538) all_120_2 = e1
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1419), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2539) ~ (all_244_0 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1438), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2540) ~ (all_244_8 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1426), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2541) ~ (all_100_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1440), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2542) ~ (all_40_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | SIMP: (2542) implies:
% 246.37/58.28 | | | | | | | | | (2543) ~ (all_40_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1439), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2544) ~ (all_38_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | SIMP: (2544) implies:
% 246.37/58.28 | | | | | | | | | (2545) ~ (all_38_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1435), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2546) ~ (all_12_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | SIMP: (2546) implies:
% 246.37/58.28 | | | | | | | | | (2547) ~ (all_12_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1436), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2548) ~ (all_10_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | SIMP: (2548) implies:
% 246.37/58.28 | | | | | | | | | (2549) ~ (all_10_2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (2525), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2550) ~ (e2 = e1)
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | REDUCE: (1574), (2537) imply:
% 246.37/58.28 | | | | | | | | | (2551) op(e1, e4) = e2
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | BETA: splitting (753) gives:
% 246.37/58.28 | | | | | | | | |
% 246.37/58.28 | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | (2552) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 246.37/58.28 | | | | | | | | | | e1 & op(e2, e3) = e1)
% 246.37/58.28 | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | BETA: splitting (2552) gives:
% 246.37/58.28 | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | (2553) all_252_6 = e1 & op(e2, e4) = e1
% 246.37/58.28 | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | ALPHA: (2553) implies:
% 246.37/58.28 | | | | | | | | | | | (2554) all_252_6 = e1
% 246.37/58.28 | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | BETA: splitting (159) gives:
% 246.37/58.28 | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | (2555) ~ (all_18_2 = e3)
% 246.37/58.28 | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | REDUCE: (1215), (2555) imply:
% 246.37/58.28 | | | | | | | | | | | | (2556) ~ (all_12_2 = e3)
% 246.37/58.28 | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | BETA: splitting (162) gives:
% 246.37/58.28 | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | (2557) ~ (all_20_2 = e4)
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | BETA: splitting (171) gives:
% 246.37/58.28 | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | (2558) ~ (all_26_2 = e3)
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 246.37/58.28 | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | (2559) ~ (all_30_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (146), (161), (170), (176), (185),
% 246.37/58.28 | | | | | | | | | | | | | | | (188), (189), (191), (192), (473), (479), (491),
% 246.37/58.28 | | | | | | | | | | | | | | | (508), (751), (756), (1534), (1541), (1542),
% 246.37/58.28 | | | | | | | | | | | | | | | (1576), (1577), (1609), (2523), (2532), (2554),
% 246.37/58.28 | | | | | | | | | | | | | | | (2559), (function-axioms) are inconsistent by
% 246.37/58.28 | | | | | | | | | | | | | | | sub-proof #234.
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | (2560) all_30_2 = e2
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2561) all_54_2 = e2
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REDUCE: (1556), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2562) ~ (all_244_24 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REDUCE: (1550), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2563) ~ (all_48_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REDUCE: (1552), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2564) ~ (all_40_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REDUCE: (1532), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2565) ~ (all_26_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | SIMP: (2565) implies:
% 246.37/58.28 | | | | | | | | | | | | | | | (2566) ~ (all_26_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | REDUCE: (1569), (2560) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | (2567) op(e2, e0) = e4
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 246.37/58.28 | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | (2568) ~ (all_54_2 = e2)
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | REDUCE: (2561), (2568) imply:
% 246.37/58.28 | | | | | | | | | | | | | | | | (2569) $false
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | CLOSE: (2569) is inconsistent.
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | (2570) ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0
% 246.37/58.28 | | | | | | | | | | | | | | | | & op(e0, e2) = all_54_1 & $i(all_54_0) &
% 246.37/58.28 | | | | | | | | | | | | | | | | $i(all_54_1)) | ( ~ (all_54_1 = e3) & op(e0, e2)
% 246.37/58.28 | | | | | | | | | | | | | | | | = all_54_1 & $i(all_54_1))
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | BETA: splitting (739) gives:
% 246.37/58.28 | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | (2571) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 246.37/58.28 | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | BETA: splitting (2571) gives:
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | (2572) all_252_16 = e2 & op(e4, e0) = e2
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | ALPHA: (2572) implies:
% 246.37/58.28 | | | | | | | | | | | | | | | | | | (2573) all_252_16 = e2
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | BETA: splitting (2570) gives:
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2574) ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 &
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_54_1 & $i(all_54_0) &
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | $i(all_54_1)
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | ALPHA: (2574) implies:
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2575) op(e0, e2) = all_54_1
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (137), (140), (143),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (146), (149), (161), (164), (170), (173), (180),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (182), (185), (186), (188), (191), (192), (201),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (203), (204), (224), (225), (246), (257), (278),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (307), (400), (450), (467), (473), (479), (485),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (501), (513), (714), (715), (735), (741), (746),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (748), (749), (750), (751), (752), (758), (763),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (764), (784), (1179), (1327), (1336), (1337),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1361), (1406), (1432), (1454), (1460), (1469),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1478), (1484), (1488), (1508), (1510), (1513),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1521), (1525), (1537), (1539), (1541), (1542),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1544), (1548), (1557), (1560), (1561), (1563),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1565), (1572), (1573), (1576), (1578), (1579),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1580), (1585), (1592), (1596), (1597), (1606),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1607), (1608), (2530), (2532), (2536), (2538),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2540), (2541), (2543), (2545), (2554), (2557),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2558), (2562), (2564), (2566), (2567), (2573),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2575), (function-axioms) are inconsistent by
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | sub-proof #219.
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2576) ~ (all_54_1 = e3) & op(e0, e2) = all_54_1 &
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | $i(all_54_1)
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | ALPHA: (2576) implies:
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2577) op(e0, e2) = all_54_1
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (14), (137), (140), (143),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (146), (149), (161), (164), (170), (173), (180),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (182), (185), (186), (188), (191), (192), (201),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (203), (204), (224), (225), (246), (257), (278),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (307), (400), (450), (467), (473), (479), (485),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (501), (513), (714), (715), (735), (741), (746),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (748), (749), (750), (751), (752), (758), (763),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (764), (784), (1179), (1327), (1336), (1337),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1361), (1406), (1432), (1454), (1460), (1469),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1478), (1484), (1488), (1508), (1510), (1513),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1521), (1525), (1537), (1539), (1541), (1542),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1544), (1548), (1557), (1560), (1561), (1563),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1565), (1572), (1573), (1576), (1578), (1579),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1580), (1585), (1592), (1596), (1597), (1606),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (1607), (1608), (2530), (2532), (2536), (2538),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2540), (2541), (2543), (2545), (2554), (2557),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2558), (2562), (2564), (2566), (2567), (2573),
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | (2577), (function-axioms) are inconsistent by
% 246.37/58.28 | | | | | | | | | | | | | | | | | | | sub-proof #219.
% 246.37/58.28 | | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | (2578) all_252_17 = e2 & op(e3, e0) = e2
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (2563), (2578), (function-axioms) are
% 246.37/58.28 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #653.
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | (2579) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 246.37/58.28 | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 246.37/58.28 | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | BETA: splitting (2579) gives:
% 246.37/58.28 | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | (2580) all_252_18 = e2 & op(e2, e0) = e2
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (191), (2567), (2580), (function-axioms) are
% 246.37/58.28 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #702.
% 246.37/58.28 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | (2581) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 246.37/58.29 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (467), (2527), (2562), (2581),
% 246.37/58.29 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.29 | | | | | | | | | | | | | | | | | | #652.
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | (2582) all_26_2 = e3
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | REDUCE: (2532), (2582) imply:
% 246.37/58.29 | | | | | | | | | | | | | | (2583) op(e2, e3) = e4
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | REF_CLOSE: (146), (1609), (2583), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | (2584) all_20_2 = e4
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REDUCE: (1454), (2584) imply:
% 246.37/58.29 | | | | | | | | | | | | | (2585) ~ (all_12_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | SIMP: (2585) implies:
% 246.37/58.29 | | | | | | | | | | | | | (2586) ~ (all_12_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REF_CLOSE: (718), (1409), (1569), (1599), (1610), (2547),
% 246.37/58.29 | | | | | | | | | | | | | (2556), (2586), (function-axioms) are inconsistent
% 246.37/58.29 | | | | | | | | | | | | | by sub-proof #582.
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | (2587) all_18_2 = e3
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | COMBINE_EQS: (1215), (2587) imply:
% 246.37/58.29 | | | | | | | | | | | | (2588) all_12_2 = e3
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | REDUCE: (1421), (2588) imply:
% 246.37/58.29 | | | | | | | | | | | | (2589) ~ (all_244_0 = e3)
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | REDUCE: (1582), (2588) imply:
% 246.37/58.29 | | | | | | | | | | | | (2590) op(e3, e4) = e0
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2,
% 246.37/58.29 | | | | | | | | | | | | e0, e4, e3, simplifying with (278), (2590) gives:
% 246.37/58.29 | | | | | | | | | | | | (2591) all_100_2 = e0
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | REDUCE: (1418), (2591) imply:
% 246.37/58.29 | | | | | | | | | | | | (2592) ~ (all_244_0 = e0)
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | BETA: splitting (731) gives:
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | (2593) all_250_0 = e4
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | COMBINE_EQS: (976), (2593) imply:
% 246.37/58.29 | | | | | | | | | | | | | (2594) all_244_0 = e4
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REDUCE: (1424), (2594) imply:
% 246.37/58.29 | | | | | | | | | | | | | (2595) ~ (all_26_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | SIMP: (2595) implies:
% 246.37/58.29 | | | | | | | | | | | | | (2596) ~ (all_26_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REDUCE: (1423), (2594) imply:
% 246.37/58.29 | | | | | | | | | | | | | (2597) ~ (all_6_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | SIMP: (2597) implies:
% 246.37/58.29 | | | | | | | | | | | | | (2598) ~ (all_6_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REDUCE: (491), (2594) imply:
% 246.37/58.29 | | | | | | | | | | | | | (2599) op(e4, e4) = e4
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | BETA: splitting (162) gives:
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | (2600) ~ (all_20_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | (2601) ~ (all_26_2 = e3)
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | (2602) ~ (all_36_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | (2603) ~ (all_38_2 = e4)
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | (2604) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 246.37/58.29 | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2605) all_252_9 = e4 & op(e4, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | ALPHA: (2605) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2606) op(e4, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e4,
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (2606) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2607) all_26_2 = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | REDUCE: (2596), (2607) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2608) $false
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | CLOSE: (2608) is inconsistent.
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2609) all_252_10 = e4 & op(e3, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2602), (2609), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #914.
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | (2610) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 246.37/58.29 | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 246.37/58.29 | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | BETA: splitting (2610) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2611) all_252_11 = e4 & op(e2, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | ALPHA: (2611) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2612) op(e2, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2603), (2612), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #935.
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | (2613) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (2613) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2614) all_252_15 = e4 & op(e1, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (2614) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2615) op(e1, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_15,
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | e4, e1, e1, simplifying with (473), (2615) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2616) all_244_15 = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (501), (2616) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2617) op(e4, e4) = e1
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, e1, e4,
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | e4, simplifying with (2599), (2617) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2618) e4 = e1
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (2618) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2619) $false
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | CLOSE: (2619) is inconsistent.
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | (2620) all_252_23 = e4 & op(e0, e1) = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2600), (2620), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #912.
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | (2621) all_38_2 = e4
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (161), (170), (185), (473), (479), (491),
% 246.37/58.29 | | | | | | | | | | | | | | | | | (508), (751), (1534), (1541), (1542), (1576),
% 246.37/58.29 | | | | | | | | | | | | | | | | | (2523), (2532), (2621), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 246.37/58.29 | | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | (2622) all_36_2 = e4
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | REDUCE: (1572), (2622) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | | (2623) op(e4, e1) = e3
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2601), (2623), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #834.
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | (2624) all_26_2 = e3
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | REDUCE: (2532), (2624) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | (2625) op(e2, e3) = e4
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | REF_CLOSE: (146), (1609), (2625), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | (2626) all_20_2 = e4
% 246.37/58.29 | | | | | | | | | | | | | | (2627) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0
% 246.37/58.29 | | | | | | | | | | | | | | & op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.29 | | | | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4)
% 246.37/58.29 | | | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | REDUCE: (1585), (2626) imply:
% 246.37/58.29 | | | | | | | | | | | | | | (2628) op(e4, e1) = e0
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | BETA: splitting (2627) gives:
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | (2629) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 246.37/58.29 | | | | | | | | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.37/58.29 | | | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | ALPHA: (2629) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | (2630) ~ (all_20_0 = e3)
% 246.37/58.29 | | | | | | | | | | | | | | | (2631) op(e1, e4) = all_20_1
% 246.37/58.29 | | | | | | | | | | | | | | | (2632) op(e4, all_20_1) = all_20_0
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_20_1,
% 246.37/58.29 | | | | | | | | | | | | | | | e4, e1, simplifying with (2551), (2631) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | (2633) all_20_1 = e2
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e0,
% 246.37/58.29 | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (2628) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | (2634) all_26_2 = e0
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | REDUCE: (2531), (2634) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | (2635) op(e0, e2) = e1
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | REDUCE: (2632), (2633) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | (2636) op(e4, e2) = all_20_0
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | BETA: splitting (2522) gives:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | (2637) ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 &
% 246.37/58.29 | | | | | | | | | | | | | | | | op(e2, all_16_1) = all_16_0 & $i(all_16_0) &
% 246.37/58.29 | | | | | | | | | | | | | | | | $i(all_16_1)
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | ALPHA: (2637) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | | (2638) op(e4, e2) = all_16_1
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (137), (140), (143), (355), (479), (491),
% 246.37/58.29 | | | | | | | | | | | | | | | | (508), (761), (1203), (1571), (1606), (2523),
% 246.37/58.29 | | | | | | | | | | | | | | | | (2598), (2630), (2635), (2636), (2638),
% 246.37/58.29 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.29 | | | | | | | | | | | | | | | | #218.
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | (2639) ~ (all_16_1 = e0) & op(e4, e2) = all_16_1 &
% 246.37/58.29 | | | | | | | | | | | | | | | | $i(all_16_1)
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | ALPHA: (2639) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | | (2640) op(e4, e2) = all_16_1
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (137), (140), (143), (355), (479), (491),
% 246.37/58.29 | | | | | | | | | | | | | | | | (508), (761), (1203), (1571), (1606), (2523),
% 246.37/58.29 | | | | | | | | | | | | | | | | (2598), (2630), (2635), (2636), (2640),
% 246.37/58.29 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.29 | | | | | | | | | | | | | | | | #218.
% 246.37/58.29 | | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | (2641) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 &
% 246.37/58.29 | | | | | | | | | | | | | | | $i(all_20_1)
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | ALPHA: (2641) implies:
% 246.37/58.29 | | | | | | | | | | | | | | | (2642) ~ (all_20_1 = e2)
% 246.37/58.29 | | | | | | | | | | | | | | | (2643) op(e1, e4) = all_20_1
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_20_1,
% 246.37/58.29 | | | | | | | | | | | | | | | e4, e1, simplifying with (2551), (2643) gives:
% 246.37/58.29 | | | | | | | | | | | | | | | (2644) all_20_1 = e2
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | REDUCE: (2642), (2644) imply:
% 246.37/58.29 | | | | | | | | | | | | | | | (2645) $false
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | | CLOSE: (2645) is inconsistent.
% 246.37/58.29 | | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | (2646) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 246.37/58.29 | | | | | | | | | | | | | all_250_0 = e0
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | | REF_CLOSE: (976), (2523), (2539), (2589), (2592), (2646) are
% 246.37/58.29 | | | | | | | | | | | | | inconsistent by sub-proof #217.
% 246.37/58.29 | | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | (2647) all_252_7 = e1 & op(e2, e3) = e1
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | ALPHA: (2647) implies:
% 246.37/58.29 | | | | | | | | | | | (2648) op(e2, e3) = e1
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | REF_CLOSE: (146), (2549), (2648), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | inconsistent by sub-proof #948.
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | (2649) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 246.37/58.29 | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 246.37/58.29 | | | | | | | | | | op(e2, e0) = e1)
% 246.37/58.29 | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | BETA: splitting (2649) gives:
% 246.37/58.29 | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | (2650) all_252_8 = e1 & op(e2, e2) = e1
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | ALPHA: (2650) implies:
% 246.37/58.29 | | | | | | | | | | | (2651) op(e2, e2) = e1
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | REF_CLOSE: (479), (2540), (2651), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | inconsistent by sub-proof #690.
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | (2652) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 246.37/58.29 | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | BETA: splitting (2652) gives:
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | Case 1:
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | (2653) all_252_11 = e1 & op(e2, e1) = e1
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | REF_CLOSE: (188), (2545), (2653), (function-axioms) are
% 246.37/58.29 | | | | | | | | | | | | inconsistent by sub-proof #226.
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | (2654) all_252_18 = e1 & op(e2, e0) = e1
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | ALPHA: (2654) implies:
% 246.37/58.29 | | | | | | | | | | | | (2655) op(e2, e0) = e1
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e1,
% 246.37/58.29 | | | | | | | | | | | | e0, e2, simplifying with (191), (2655) gives:
% 246.37/58.29 | | | | | | | | | | | | (2656) all_40_2 = e1
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | REDUCE: (2543), (2656) imply:
% 246.37/58.29 | | | | | | | | | | | | (2657) $false
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | | CLOSE: (2657) is inconsistent.
% 246.37/58.29 | | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | | |
% 246.37/58.29 | | | | | | | | | End of split
% 246.37/58.29 | | | | | | | | |
% 246.37/58.29 | | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | | |
% 246.37/58.29 | | | | | | | | | (2658) all_252_13 = e2 & op(e1, e3) = e2
% 246.37/58.29 | | | | | | | | |
% 246.37/58.29 | | | | | | | | | ALPHA: (2658) implies:
% 246.37/58.29 | | | | | | | | | (2659) op(e1, e3) = e2
% 246.37/58.29 | | | | | | | | |
% 246.37/58.29 | | | | | | | | | REF_CLOSE: (224), (2526), (2659), (function-axioms) are
% 246.37/58.29 | | | | | | | | | inconsistent by sub-proof #972.
% 246.37/58.29 | | | | | | | | |
% 246.37/58.29 | | | | | | | | End of split
% 246.37/58.29 | | | | | | | |
% 246.37/58.29 | | | | | | | Case 2:
% 246.37/58.29 | | | | | | | |
% 246.37/58.29 | | | | | | | | (2660) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2
% 246.37/58.29 | | | | | | | | & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) =
% 246.37/58.30 | | | | | | | | e2)
% 246.37/58.30 | | | | | | | |
% 246.37/58.30 | | | | | | | | BETA: splitting (2660) gives:
% 246.37/58.30 | | | | | | | |
% 246.37/58.30 | | | | | | | | Case 1:
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | | (2661) all_252_14 = e2 & op(e1, e2) = e2
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | | REF_CLOSE: (137), (2530), (2661), (function-axioms) are
% 246.37/58.30 | | | | | | | | | inconsistent by sub-proof #820.
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | Case 2:
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | | (2662) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 =
% 246.37/58.30 | | | | | | | | | e2 & op(e1, e0) = e2)
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | | REF_CLOSE: (182), (473), (2524), (2527), (2662),
% 246.37/58.30 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.30 | | | | | | | | | #819.
% 246.37/58.30 | | | | | | | | |
% 246.37/58.30 | | | | | | | | End of split
% 246.37/58.30 | | | | | | | |
% 246.37/58.30 | | | | | | | End of split
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | End of split
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | Case 2:
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | (2663) all_12_2 = e2
% 246.37/58.30 | | | | | | (2664) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2,
% 246.37/58.30 | | | | | | all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)) |
% 246.37/58.30 | | | | | | ( ~ (all_12_1 = e1) & op(e4, e2) = all_12_1 &
% 246.37/58.30 | | | | | | $i(all_12_1))
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | COMBINE_EQS: (1340), (2663) imply:
% 246.37/58.30 | | | | | | (2665) all_14_2 = e2
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1421), (2663) imply:
% 246.37/58.30 | | | | | | (2666) ~ (all_244_0 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1456), (2663) imply:
% 246.37/58.30 | | | | | | (2667) ~ (all_244_24 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1428), (2663) imply:
% 246.37/58.30 | | | | | | (2668) ~ (all_100_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1435), (2663) imply:
% 246.37/58.30 | | | | | | (2669) ~ (all_64_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1452), (2663) imply:
% 246.37/58.30 | | | | | | (2670) ~ (all_28_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1450), (2663) imply:
% 246.37/58.30 | | | | | | (2671) ~ (all_22_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1454), (2663) imply:
% 246.37/58.30 | | | | | | (2672) ~ (all_20_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1441), (2663) imply:
% 246.37/58.30 | | | | | | (2673) ~ (all_16_2 = e2)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1598), (2663) imply:
% 246.37/58.30 | | | | | | (2674) op(e2, all_30_2) = e4
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | REDUCE: (1582), (2663) imply:
% 246.37/58.30 | | | | | | (2675) op(e2, e4) = e0
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | BETA: splitting (2664) gives:
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | Case 1:
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | (2676) ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2,
% 246.37/58.30 | | | | | | | all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | ALPHA: (2676) implies:
% 246.37/58.30 | | | | | | | (2677) op(e4, e2) = all_12_1
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 246.37/58.30 | | | | | | | (137), (140), (143), (146), (153), (155), (161), (162),
% 246.37/58.30 | | | | | | | (164), (165), (168), (170), (171), (173), (174), (176),
% 246.37/58.30 | | | | | | | (177), (182), (183), (185), (188), (189), (191), (192),
% 246.37/58.30 | | | | | | | (198), (216), (219), (224), (225), (227), (234), (237),
% 246.37/58.30 | | | | | | | (243), (249), (252), (255), (257), (268), (278), (290),
% 246.37/58.30 | | | | | | | (295), (321), (346), (375), (415), (465), (467), (473),
% 246.37/58.30 | | | | | | | (479), (485), (491), (492), (508), (513), (715), (716),
% 246.37/58.30 | | | | | | | (719), (722), (730), (731), (733), (734), (735), (736),
% 246.37/58.30 | | | | | | | (737), (739), (742), (743), (744), (745), (746), (747),
% 246.37/58.30 | | | | | | | (748), (750), (751), (752), (753), (754), (755), (756),
% 246.37/58.30 | | | | | | | (757), (758), (759), (760), (761), (762), (764), (767),
% 246.37/58.30 | | | | | | | (768), (769), (770), (771), (774), (777), (778), (780),
% 246.37/58.30 | | | | | | | (844), (871), (891), (947), (973), (976), (1154),
% 246.37/58.30 | | | | | | | (1235), (1268), (1276), (1310), (1312), (1316), (1320),
% 246.37/58.30 | | | | | | | (1325), (1331), (1333), (1334), (1342), (1348), (1406),
% 246.37/58.30 | | | | | | | (1407), (1410), (1412), (1418), (1419), (1420), (1422),
% 246.37/58.30 | | | | | | | (1425), (1426), (1427), (1430), (1431), (1432), (1434),
% 246.37/58.30 | | | | | | | (1436), (1438), (1439), (1440), (1443), (1446), (1458),
% 246.37/58.30 | | | | | | | (1459), (1460), (1463), (1466), (1472), (1474), (1478),
% 246.37/58.30 | | | | | | | (1481), (1482), (1484), (1485), (1487), (1488), (1492),
% 246.37/58.30 | | | | | | | (1494), (1497), (1499), (1504), (1506), (1512), (1516),
% 246.37/58.30 | | | | | | | (1520), (1521), (1525), (1527), (1529), (1530), (1532),
% 246.37/58.30 | | | | | | | (1534), (1536), (1541), (1542), (1544), (1545), (1548),
% 246.37/58.30 | | | | | | | (1568), (1570), (1571), (1572), (1576), (1577), (1578),
% 246.37/58.30 | | | | | | | (1579), (1581), (1583), (1584), (1585), (1587), (1589),
% 246.37/58.30 | | | | | | | (1592), (1593), (1597), (1603), (1605), (1606), (1607),
% 246.37/58.30 | | | | | | | (1608), (1609), (2665), (2666), (2667), (2668), (2669),
% 246.37/58.30 | | | | | | | (2670), (2671), (2672), (2673), (2674), (2675), (2677),
% 246.37/58.30 | | | | | | | (function-axioms) are inconsistent by sub-proof #130.
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | Case 2:
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | (2678) ~ (all_12_1 = e1) & op(e4, e2) = all_12_1 &
% 246.37/58.30 | | | | | | | $i(all_12_1)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | ALPHA: (2678) implies:
% 246.37/58.30 | | | | | | | (2679) op(e4, e2) = all_12_1
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 246.37/58.30 | | | | | | | (137), (140), (143), (146), (153), (155), (161), (162),
% 246.37/58.30 | | | | | | | (164), (165), (168), (170), (171), (173), (174), (176),
% 246.37/58.30 | | | | | | | (177), (182), (183), (185), (188), (189), (191), (192),
% 246.37/58.30 | | | | | | | (198), (216), (219), (224), (225), (227), (234), (237),
% 246.37/58.30 | | | | | | | (243), (249), (252), (255), (257), (268), (278), (290),
% 246.37/58.30 | | | | | | | (295), (321), (346), (375), (415), (465), (467), (473),
% 246.37/58.30 | | | | | | | (479), (485), (491), (492), (508), (513), (715), (716),
% 246.37/58.30 | | | | | | | (719), (722), (730), (731), (733), (734), (735), (736),
% 246.37/58.30 | | | | | | | (737), (739), (742), (743), (744), (745), (746), (747),
% 246.37/58.30 | | | | | | | (748), (750), (751), (752), (753), (754), (755), (756),
% 246.37/58.30 | | | | | | | (757), (758), (759), (760), (761), (762), (764), (767),
% 246.37/58.30 | | | | | | | (768), (769), (770), (771), (774), (777), (778), (780),
% 246.37/58.30 | | | | | | | (844), (871), (891), (947), (973), (976), (1154),
% 246.37/58.30 | | | | | | | (1235), (1268), (1276), (1310), (1312), (1316), (1320),
% 246.37/58.30 | | | | | | | (1325), (1331), (1333), (1334), (1342), (1348), (1406),
% 246.37/58.30 | | | | | | | (1407), (1410), (1412), (1418), (1419), (1420), (1422),
% 246.37/58.30 | | | | | | | (1425), (1426), (1427), (1430), (1431), (1432), (1434),
% 246.37/58.30 | | | | | | | (1436), (1438), (1439), (1440), (1443), (1446), (1458),
% 246.37/58.30 | | | | | | | (1459), (1460), (1463), (1466), (1472), (1474), (1478),
% 246.37/58.30 | | | | | | | (1481), (1482), (1484), (1485), (1487), (1488), (1492),
% 246.37/58.30 | | | | | | | (1494), (1497), (1499), (1504), (1506), (1512), (1516),
% 246.37/58.30 | | | | | | | (1520), (1521), (1525), (1527), (1529), (1530), (1532),
% 246.37/58.30 | | | | | | | (1534), (1536), (1541), (1542), (1544), (1545), (1548),
% 246.37/58.30 | | | | | | | (1568), (1570), (1571), (1572), (1576), (1577), (1578),
% 246.37/58.30 | | | | | | | (1579), (1581), (1583), (1584), (1585), (1587), (1589),
% 246.37/58.30 | | | | | | | (1592), (1593), (1597), (1603), (1605), (1606), (1607),
% 246.37/58.30 | | | | | | | (1608), (1609), (2665), (2666), (2667), (2668), (2669),
% 246.37/58.30 | | | | | | | (2670), (2671), (2672), (2673), (2674), (2675), (2679),
% 246.37/58.30 | | | | | | | (function-axioms) are inconsistent by sub-proof #130.
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | End of split
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | End of split
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | Case 2:
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | (2680) all_10_2 = e4
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1476), (2680) imply:
% 246.37/58.30 | | | | | (2681) ~ (all_244_8 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1459), (2680) imply:
% 246.37/58.30 | | | | | (2682) ~ (all_84_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1436), (2680) imply:
% 246.37/58.30 | | | | | (2683) ~ (all_64_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1472), (2680) imply:
% 246.37/58.30 | | | | | (2684) ~ (all_62_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1480), (2680) imply:
% 246.37/58.30 | | | | | (2685) ~ (all_40_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1478), (2680) imply:
% 246.37/58.30 | | | | | (2686) ~ (all_38_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1474), (2680) imply:
% 246.37/58.30 | | | | | (2687) ~ (all_22_2 = e4)
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1575), (2680) imply:
% 246.37/58.30 | | | | | (2688) op(e4, e3) = e2
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | REDUCE: (1591), (2680) imply:
% 246.37/58.30 | | | | | (2689) op(all_8_2, e4) = e2
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | BETA: splitting (756) gives:
% 246.37/58.30 | | | | |
% 246.37/58.30 | | | | | Case 1:
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | (2690) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 246.37/58.30 | | | | | | op(e2, e3) = e4)
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | BETA: splitting (2690) gives:
% 246.37/58.30 | | | | | |
% 246.37/58.30 | | | | | | Case 1:
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | (2691) all_252_6 = e4 & op(e2, e4) = e4
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | ALPHA: (2691) implies:
% 246.37/58.30 | | | | | | | (2692) op(e2, e4) = e4
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REF_CLOSE: (227), (2683), (2692), (function-axioms) are
% 246.37/58.30 | | | | | | | inconsistent by sub-proof #129.
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | Case 2:
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | (2693) all_252_7 = e4 & op(e2, e3) = e4
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | ALPHA: (2693) implies:
% 246.37/58.30 | | | | | | | (2694) all_252_7 = e4
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e2,
% 246.37/58.30 | | | | | | | e3, e4, simplifying with (257), (2688) gives:
% 246.37/58.30 | | | | | | | (2695) all_84_2 = e2
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | COMBINE_EQS: (1245), (2695) imply:
% 246.37/58.30 | | | | | | | (2696) all_182_2 = e2
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | COMBINE_EQS: (1133), (2695) imply:
% 246.37/58.30 | | | | | | | (2697) all_184_2 = e2
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1422), (2695) imply:
% 246.37/58.30 | | | | | | | (2698) ~ (all_244_0 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1458), (2695) imply:
% 246.37/58.30 | | | | | | | (2699) ~ (all_244_3 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1460), (2695) imply:
% 246.37/58.30 | | | | | | | (2700) ~ (all_62_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | SIMP: (2700) implies:
% 246.37/58.30 | | | | | | | (2701) ~ (all_62_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1464), (2695) imply:
% 246.37/58.30 | | | | | | | (2702) ~ (all_30_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | SIMP: (2702) implies:
% 246.37/58.30 | | | | | | | (2703) ~ (all_30_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1463), (2695) imply:
% 246.37/58.30 | | | | | | | (2704) ~ (all_26_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | SIMP: (2704) implies:
% 246.37/58.30 | | | | | | | (2705) ~ (all_26_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1461), (2695) imply:
% 246.37/58.30 | | | | | | | (2706) ~ (all_22_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | SIMP: (2706) implies:
% 246.37/58.30 | | | | | | | (2707) ~ (all_22_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1462), (2695) imply:
% 246.37/58.30 | | | | | | | (2708) ~ (all_6_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | SIMP: (2708) implies:
% 246.37/58.30 | | | | | | | (2709) ~ (all_6_2 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (2682), (2695) imply:
% 246.37/58.30 | | | | | | | (2710) ~ (e4 = e2)
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1586), (2695) imply:
% 246.37/58.30 | | | | | | | (2711) op(all_100_2, e2) = e4
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | REDUCE: (1587), (2695) imply:
% 246.37/58.30 | | | | | | | (2712) op(e2, all_100_2) = e3
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | BETA: splitting (769) gives:
% 246.37/58.30 | | | | | | |
% 246.37/58.30 | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | |
% 246.37/58.31 | | | | | | | | (2713) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 &
% 246.37/58.31 | | | | | | | | op(e3, e3) = e2)
% 246.37/58.31 | | | | | | | |
% 246.37/58.31 | | | | | | | | BETA: splitting (2713) gives:
% 246.37/58.31 | | | | | | | |
% 246.37/58.31 | | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | | |
% 246.37/58.31 | | | | | | | | | (2714) all_252_1 = e2 & op(e4, e3) = e2
% 246.37/58.31 | | | | | | | | |
% 246.37/58.31 | | | | | | | | | ALPHA: (2714) implies:
% 246.37/58.31 | | | | | | | | | (2715) all_252_1 = e2
% 246.37/58.31 | | | | | | | | |
% 246.37/58.31 | | | | | | | | | BETA: splitting (391) gives:
% 246.37/58.31 | | | | | | | | |
% 246.37/58.31 | | | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | (2716) ~ (all_184_2 = e2)
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | REDUCE: (2697), (2716) imply:
% 246.37/58.31 | | | | | | | | | | (2717) $false
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | CLOSE: (2717) is inconsistent.
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | Case 2:
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | (2718) ( ~ (all_184_0 = e0) & op(e3, e2) = all_184_1 &
% 246.37/58.31 | | | | | | | | | | op(e2, all_184_1) = all_184_0 & $i(all_184_0) &
% 246.37/58.31 | | | | | | | | | | $i(all_184_1)) | ( ~ (all_184_1 = e1) & op(e3,
% 246.37/58.31 | | | | | | | | | | e2) = all_184_1 & $i(all_184_1))
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | BETA: splitting (2718) gives:
% 246.37/58.31 | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | (2719) ~ (all_184_0 = e0) & op(e3, e2) = all_184_1 &
% 246.37/58.31 | | | | | | | | | | | op(e2, all_184_1) = all_184_0 & $i(all_184_0) &
% 246.37/58.31 | | | | | | | | | | | $i(all_184_1)
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | ALPHA: (2719) implies:
% 246.37/58.31 | | | | | | | | | | | (2720) op(e3, e2) = all_184_1
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2,
% 246.37/58.31 | | | | | | | | | | | all_184_1, e2, e3, simplifying with (143), (2720)
% 246.37/58.31 | | | | | | | | | | | gives:
% 246.37/58.31 | | | | | | | | | | | (2721) all_184_1 = all_8_2
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | BETA: splitting (150) gives:
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | (2722) ~ (all_12_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.31 | | | | | | | | | | | | (14), (137), (140), (143), (149), (155), (156),
% 246.37/58.31 | | | | | | | | | | | | (159), (161), (162), (164), (165), (168), (170),
% 246.37/58.31 | | | | | | | | | | | | (173), (174), (176), (180), (182), (183), (185),
% 246.37/58.31 | | | | | | | | | | | | (186), (188), (191), (195), (201), (203), (204),
% 246.37/58.31 | | | | | | | | | | | | (207), (216), (219), (222), (224), (227), (228),
% 246.37/58.31 | | | | | | | | | | | | (231), (237), (252), (255), (257), (260), (271),
% 246.37/58.31 | | | | | | | | | | | | (274), (278), (388), (397), (433), (450), (467),
% 246.37/58.31 | | | | | | | | | | | | (473), (479), (485), (491), (492), (501), (513),
% 246.37/58.31 | | | | | | | | | | | | (715), (717), (718), (720), (728), (729), (735),
% 246.37/58.31 | | | | | | | | | | | | (736), (744), (745), (747), (748), (749), (750),
% 246.37/58.31 | | | | | | | | | | | | (751), (755), (757), (758), (759), (762), (763),
% 246.37/58.31 | | | | | | | | | | | | (767), (768), (773), (775), (776), (778), (779),
% 246.37/58.31 | | | | | | | | | | | | (781), (786), (841), (916), (1215), (1235),
% 246.37/58.31 | | | | | | | | | | | | (1239), (1276), (1280), (1286), (1309), (1312),
% 246.37/58.31 | | | | | | | | | | | | (1314), (1316), (1317), (1333), (1334), (1336),
% 246.37/58.31 | | | | | | | | | | | | (1337), (1341), (1357), (1361), (1406), (1408),
% 246.37/58.31 | | | | | | | | | | | | (1409), (1417), (1420), (1426), (1427), (1430),
% 246.37/58.31 | | | | | | | | | | | | (1431), (1432), (1433), (1434), (1438), (1439),
% 246.37/58.31 | | | | | | | | | | | | (1441), (1444), (1452), (1454), (1466), (1470),
% 246.37/58.31 | | | | | | | | | | | | (1482), (1487), (1488), (1494), (1497), (1499),
% 246.37/58.31 | | | | | | | | | | | | (1512), (1513), (1514), (1516), (1521), (1525),
% 246.37/58.31 | | | | | | | | | | | | (1527), (1529), (1530), (1532), (1536), (1537),
% 246.37/58.31 | | | | | | | | | | | | (1539), (1541), (1542), (1544), (1545), (1548),
% 246.37/58.31 | | | | | | | | | | | | (1558), (1565), (1567), (1569), (1571), (1572),
% 246.37/58.31 | | | | | | | | | | | | (1573), (1574), (1576), (1578), (1579), (1580),
% 246.37/58.31 | | | | | | | | | | | | (1581), (1582), (1583), (1585), (1588), (1589),
% 246.37/58.31 | | | | | | | | | | | | (1594), (1595), (1596), (1597), (1599), (1601),
% 246.37/58.31 | | | | | | | | | | | | (1602), (1604), (1605), (1606), (1607), (1608),
% 246.37/58.31 | | | | | | | | | | | | (2682), (2683), (2687), (2688), (2689), (2694),
% 246.37/58.31 | | | | | | | | | | | | (2696), (2698), (2701), (2705), (2707), (2709),
% 246.37/58.31 | | | | | | | | | | | | (2711), (2712), (2715), (2722), (function-axioms)
% 246.37/58.31 | | | | | | | | | | | | are inconsistent by sub-proof #102.
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | Case 2:
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | (2723) all_12_2 = e2
% 246.37/58.31 | | | | | | | | | | | | (2724) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 &
% 246.37/58.31 | | | | | | | | | | | | op(e2, all_12_1) = all_12_0 & $i(all_12_0) &
% 246.37/58.31 | | | | | | | | | | | | $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e4, e2)
% 246.37/58.31 | | | | | | | | | | | | = all_12_1 & $i(all_12_1))
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1456), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2725) ~ (all_244_24 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1435), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2726) ~ (all_64_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1452), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2727) ~ (all_28_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1454), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2728) ~ (all_20_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1441), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2729) ~ (all_16_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1582), (2723) imply:
% 246.37/58.31 | | | | | | | | | | | | (2730) op(e2, e4) = e0
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (12), (13), (14), (137),
% 246.37/58.31 | | | | | | | | | | | | (140), (143), (155), (161), (162), (164), (165),
% 246.37/58.31 | | | | | | | | | | | | (168), (170), (171), (173), (174), (176), (182),
% 246.37/58.31 | | | | | | | | | | | | (183), (185), (186), (188), (191), (201), (207),
% 246.37/58.31 | | | | | | | | | | | | (216), (219), (224), (227), (237), (243), (252),
% 246.37/58.31 | | | | | | | | | | | | (255), (257), (260), (271), (278), (301), (378),
% 246.37/58.31 | | | | | | | | | | | | (388), (397), (467), (473), (479), (485), (491),
% 246.37/58.31 | | | | | | | | | | | | (501), (508), (715), (716), (717), (723), (729),
% 246.37/58.31 | | | | | | | | | | | | (733), (734), (735), (736), (737), (738), (739),
% 246.37/58.31 | | | | | | | | | | | | (742), (744), (745), (746), (747), (749), (751),
% 246.37/58.31 | | | | | | | | | | | | (752), (755), (757), (758), (759), (761), (762),
% 246.37/58.31 | | | | | | | | | | | | (767), (768), (773), (774), (775), (778), (779),
% 246.37/58.31 | | | | | | | | | | | | (780), (1154), (1172), (1235), (1239), (1276),
% 246.37/58.31 | | | | | | | | | | | | (1280), (1309), (1312), (1316), (1317), (1333),
% 246.37/58.31 | | | | | | | | | | | | (1334), (1337), (1349), (1406), (1407), (1408),
% 246.37/58.31 | | | | | | | | | | | | (1413), (1417), (1424), (1434), (1438), (1439),
% 246.37/58.31 | | | | | | | | | | | | (1440), (1448), (1467), (1485), (1487), (1488),
% 246.37/58.31 | | | | | | | | | | | | (1495), (1497), (1499), (1504), (1506), (1508),
% 246.37/58.31 | | | | | | | | | | | | (1511), (1512), (1513), (1514), (1516), (1520),
% 246.37/58.31 | | | | | | | | | | | | (1521), (1525), (1534), (1536), (1537), (1541),
% 246.37/58.31 | | | | | | | | | | | | (1542), (1544), (1545), (1561), (1563), (1565),
% 246.37/58.31 | | | | | | | | | | | | (1568), (1571), (1572), (1573), (1574), (1576),
% 246.37/58.31 | | | | | | | | | | | | (1577), (1578), (1580), (1581), (1583), (1584),
% 246.37/58.31 | | | | | | | | | | | | (1585), (1588), (1589), (1594), (1596), (1597),
% 246.37/58.31 | | | | | | | | | | | | (1601), (1603), (1604), (1605), (1606), (1607),
% 246.37/58.31 | | | | | | | | | | | | (1608), (2683), (2684), (2685), (2686), (2687),
% 246.37/58.31 | | | | | | | | | | | | (2688), (2694), (2696), (2698), (2701), (2703),
% 246.37/58.31 | | | | | | | | | | | | (2705), (2707), (2709), (2711), (2715), (2724),
% 246.37/58.31 | | | | | | | | | | | | (2725), (2726), (2727), (2728), (2729), (2730),
% 246.37/58.31 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.31 | | | | | | | | | | | | #82.
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | End of split
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | Case 2:
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | (2731) ~ (all_184_1 = e1) & op(e3, e2) = all_184_1 &
% 246.37/58.31 | | | | | | | | | | | $i(all_184_1)
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | ALPHA: (2731) implies:
% 246.37/58.31 | | | | | | | | | | | (2732) ~ (all_184_1 = e1)
% 246.37/58.31 | | | | | | | | | | | (2733) op(e3, e2) = all_184_1
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2,
% 246.37/58.31 | | | | | | | | | | | all_184_1, e2, e3, simplifying with (143), (2733)
% 246.37/58.31 | | | | | | | | | | | gives:
% 246.37/58.31 | | | | | | | | | | | (2734) all_184_1 = all_8_2
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | BETA: splitting (150) gives:
% 246.37/58.31 | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | Case 1:
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | (2735) ~ (all_12_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.31 | | | | | | | | | | | | (14), (137), (140), (143), (149), (155), (156),
% 246.37/58.31 | | | | | | | | | | | | (159), (161), (162), (164), (165), (168), (170),
% 246.37/58.31 | | | | | | | | | | | | (173), (174), (176), (180), (182), (183), (185),
% 246.37/58.31 | | | | | | | | | | | | (186), (188), (191), (195), (201), (203), (204),
% 246.37/58.31 | | | | | | | | | | | | (207), (216), (219), (222), (224), (227), (228),
% 246.37/58.31 | | | | | | | | | | | | (231), (237), (252), (255), (257), (260), (271),
% 246.37/58.31 | | | | | | | | | | | | (274), (278), (388), (397), (433), (450), (467),
% 246.37/58.31 | | | | | | | | | | | | (473), (479), (485), (491), (492), (501), (513),
% 246.37/58.31 | | | | | | | | | | | | (715), (717), (718), (720), (728), (729), (735),
% 246.37/58.31 | | | | | | | | | | | | (736), (744), (745), (747), (748), (749), (750),
% 246.37/58.31 | | | | | | | | | | | | (751), (755), (757), (758), (759), (762), (763),
% 246.37/58.31 | | | | | | | | | | | | (767), (768), (773), (775), (776), (778), (779),
% 246.37/58.31 | | | | | | | | | | | | (781), (786), (841), (916), (1215), (1235),
% 246.37/58.31 | | | | | | | | | | | | (1239), (1276), (1280), (1286), (1309), (1312),
% 246.37/58.31 | | | | | | | | | | | | (1314), (1316), (1317), (1333), (1334), (1336),
% 246.37/58.31 | | | | | | | | | | | | (1337), (1341), (1357), (1361), (1406), (1408),
% 246.37/58.31 | | | | | | | | | | | | (1409), (1417), (1420), (1426), (1427), (1430),
% 246.37/58.31 | | | | | | | | | | | | (1431), (1432), (1433), (1434), (1438), (1439),
% 246.37/58.31 | | | | | | | | | | | | (1441), (1444), (1452), (1454), (1466), (1470),
% 246.37/58.31 | | | | | | | | | | | | (1482), (1487), (1488), (1494), (1497), (1499),
% 246.37/58.31 | | | | | | | | | | | | (1512), (1513), (1514), (1516), (1521), (1525),
% 246.37/58.31 | | | | | | | | | | | | (1527), (1529), (1530), (1532), (1536), (1537),
% 246.37/58.31 | | | | | | | | | | | | (1539), (1541), (1542), (1544), (1545), (1548),
% 246.37/58.31 | | | | | | | | | | | | (1558), (1565), (1567), (1569), (1571), (1572),
% 246.37/58.31 | | | | | | | | | | | | (1573), (1574), (1576), (1578), (1579), (1580),
% 246.37/58.31 | | | | | | | | | | | | (1581), (1582), (1583), (1585), (1588), (1589),
% 246.37/58.31 | | | | | | | | | | | | (1594), (1595), (1596), (1597), (1599), (1601),
% 246.37/58.31 | | | | | | | | | | | | (1602), (1604), (1605), (1606), (1607), (1608),
% 246.37/58.31 | | | | | | | | | | | | (2682), (2683), (2687), (2688), (2689), (2694),
% 246.37/58.31 | | | | | | | | | | | | (2696), (2698), (2701), (2705), (2707), (2709),
% 246.37/58.31 | | | | | | | | | | | | (2711), (2712), (2715), (2735), (function-axioms)
% 246.37/58.31 | | | | | | | | | | | | are inconsistent by sub-proof #102.
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | Case 2:
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | (2736) all_12_2 = e2
% 246.37/58.31 | | | | | | | | | | | | (2737) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 &
% 246.37/58.31 | | | | | | | | | | | | op(e2, all_12_1) = all_12_0 & $i(all_12_0) &
% 246.37/58.31 | | | | | | | | | | | | $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e4, e2)
% 246.37/58.31 | | | | | | | | | | | | = all_12_1 & $i(all_12_1))
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1456), (2736) imply:
% 246.37/58.31 | | | | | | | | | | | | (2738) ~ (all_244_24 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.31 | | | | | | | | | | | | REDUCE: (1435), (2736) imply:
% 246.37/58.31 | | | | | | | | | | | | (2739) ~ (all_64_2 = e2)
% 246.37/58.31 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | REDUCE: (1452), (2736) imply:
% 246.37/58.32 | | | | | | | | | | | | (2740) ~ (all_28_2 = e2)
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | REDUCE: (1454), (2736) imply:
% 246.37/58.32 | | | | | | | | | | | | (2741) ~ (all_20_2 = e2)
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | REDUCE: (1441), (2736) imply:
% 246.37/58.32 | | | | | | | | | | | | (2742) ~ (all_16_2 = e2)
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | REDUCE: (1582), (2736) imply:
% 246.37/58.32 | | | | | | | | | | | | (2743) op(e2, e4) = e0
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (12), (13), (14), (137),
% 246.37/58.32 | | | | | | | | | | | | (140), (143), (155), (161), (162), (164), (165),
% 246.37/58.32 | | | | | | | | | | | | (168), (170), (171), (173), (174), (176), (182),
% 246.37/58.32 | | | | | | | | | | | | (183), (185), (186), (188), (191), (201), (207),
% 246.37/58.32 | | | | | | | | | | | | (216), (219), (224), (227), (237), (243), (252),
% 246.37/58.32 | | | | | | | | | | | | (255), (257), (260), (271), (278), (301), (378),
% 246.37/58.32 | | | | | | | | | | | | (388), (397), (467), (473), (479), (485), (491),
% 246.37/58.32 | | | | | | | | | | | | (501), (508), (715), (716), (717), (723), (729),
% 246.37/58.32 | | | | | | | | | | | | (733), (734), (735), (736), (737), (738), (739),
% 246.37/58.32 | | | | | | | | | | | | (742), (744), (745), (746), (747), (749), (751),
% 246.37/58.32 | | | | | | | | | | | | (752), (755), (757), (758), (759), (761), (762),
% 246.37/58.32 | | | | | | | | | | | | (767), (768), (773), (774), (775), (778), (779),
% 246.37/58.32 | | | | | | | | | | | | (780), (1154), (1172), (1235), (1239), (1276),
% 246.37/58.32 | | | | | | | | | | | | (1280), (1309), (1312), (1316), (1317), (1333),
% 246.37/58.32 | | | | | | | | | | | | (1334), (1337), (1349), (1406), (1407), (1408),
% 246.37/58.32 | | | | | | | | | | | | (1413), (1417), (1424), (1434), (1438), (1439),
% 246.37/58.32 | | | | | | | | | | | | (1440), (1448), (1467), (1485), (1487), (1488),
% 246.37/58.32 | | | | | | | | | | | | (1495), (1497), (1499), (1504), (1506), (1508),
% 246.37/58.32 | | | | | | | | | | | | (1511), (1512), (1513), (1514), (1516), (1520),
% 246.37/58.32 | | | | | | | | | | | | (1521), (1525), (1534), (1536), (1537), (1541),
% 246.37/58.32 | | | | | | | | | | | | (1542), (1544), (1545), (1561), (1563), (1565),
% 246.37/58.32 | | | | | | | | | | | | (1568), (1571), (1572), (1573), (1574), (1576),
% 246.37/58.32 | | | | | | | | | | | | (1577), (1578), (1580), (1581), (1583), (1584),
% 246.37/58.32 | | | | | | | | | | | | (1585), (1588), (1589), (1594), (1596), (1597),
% 246.37/58.32 | | | | | | | | | | | | (1601), (1603), (1604), (1605), (1606), (1607),
% 246.37/58.32 | | | | | | | | | | | | (1608), (2683), (2684), (2685), (2686), (2687),
% 246.37/58.32 | | | | | | | | | | | | (2688), (2694), (2696), (2698), (2701), (2703),
% 246.37/58.32 | | | | | | | | | | | | (2705), (2707), (2709), (2711), (2715), (2737),
% 246.37/58.32 | | | | | | | | | | | | (2738), (2739), (2740), (2741), (2742), (2743),
% 246.37/58.32 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.32 | | | | | | | | | | | | #82.
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | End of split
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | End of split
% 246.37/58.32 | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | End of split
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | Case 2:
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | (2744) all_252_3 = e2 & op(e3, e3) = e2
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | ALPHA: (2744) implies:
% 246.37/58.32 | | | | | | | | | (2745) op(e3, e3) = e2
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | REF_CLOSE: (485), (2699), (2745), (function-axioms) are
% 246.37/58.32 | | | | | | | | | inconsistent by sub-proof #694.
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | End of split
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | Case 2:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | (2746) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2
% 246.37/58.32 | | | | | | | | & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 246.37/58.32 | | | | | | | | e2)
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | REF_CLOSE: (13), (164), (224), (2694), (2701), (2707), (2746),
% 246.37/58.32 | | | | | | | | (function-axioms) are inconsistent by sub-proof #81.
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | End of split
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | End of split
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | Case 2:
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | (2747) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 246.37/58.32 | | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REF_CLOSE: (188), (191), (479), (2681), (2685), (2686), (2747),
% 246.37/58.32 | | | | | | (function-axioms) are inconsistent by sub-proof #80.
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | End of split
% 246.37/58.32 | | | | |
% 246.37/58.32 | | | | End of split
% 246.37/58.32 | | | |
% 246.37/58.32 | | | Case 2:
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | (2748) all_8_2 = e1
% 246.37/58.32 | | | | (2749) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) =
% 246.37/58.32 | | | | all_8_0 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) &
% 246.37/58.32 | | | | op(e2, e1) = all_8_1 & $i(all_8_1))
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | COMBINE_EQS: (1362), (2748) imply:
% 246.37/58.32 | | | | (2750) all_234_2 = e1
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1503), (2748) imply:
% 246.37/58.32 | | | | (2751) ~ (all_244_8 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1508), (2748) imply:
% 246.37/58.32 | | | | (2752) ~ (all_36_2 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1506), (2748) imply:
% 246.37/58.32 | | | | (2753) ~ (all_28_2 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1492), (2748) imply:
% 246.37/58.32 | | | | (2754) ~ (all_6_2 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1504), (2748) imply:
% 246.37/58.32 | | | | (2755) ~ (all_4_2 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | SIMP: (2755) implies:
% 246.37/58.32 | | | | (2756) ~ (all_4_2 = e1)
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1590), (2748) imply:
% 246.37/58.32 | | | | (2757) op(all_10_2, e1) = e3
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1591), (2748) imply:
% 246.37/58.32 | | | | (2758) op(e1, all_10_2) = e2
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | REDUCE: (1571), (2748) imply:
% 246.37/58.32 | | | | (2759) op(e1, e2) = e3
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | BETA: splitting (758) gives:
% 246.37/58.32 | | | |
% 246.37/58.32 | | | | Case 1:
% 246.37/58.32 | | | | |
% 246.37/58.32 | | | | | (2760) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 246.37/58.32 | | | | | op(e3, e2) = e1)
% 246.37/58.32 | | | | |
% 246.37/58.32 | | | | | BETA: splitting (2760) gives:
% 246.37/58.32 | | | | |
% 246.37/58.32 | | | | | Case 1:
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | (2761) all_252_4 = e1 & op(e4, e2) = e1
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | ALPHA: (2761) implies:
% 246.37/58.32 | | | | | | (2762) op(e4, e2) = e1
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REF_CLOSE: (140), (1607), (2762), (function-axioms) are inconsistent
% 246.37/58.32 | | | | | | by sub-proof #930.
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | Case 2:
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | (2763) all_252_5 = e1 & op(e3, e2) = e1
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | ALPHA: (2763) implies:
% 246.37/58.32 | | | | | | (2764) all_252_5 = e1
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, e2,
% 246.37/58.32 | | | | | | e1, simplifying with (137), (2759) gives:
% 246.37/58.32 | | | | | | (2765) all_4_2 = e3
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | COMBINE_EQS: (1280), (2765) imply:
% 246.37/58.32 | | | | | | (2766) all_50_2 = e3
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | COMBINE_EQS: (1016), (2765) imply:
% 246.37/58.32 | | | | | | (2767) all_192_2 = e3
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1511), (2765) imply:
% 246.37/58.32 | | | | | | (2768) ~ (all_244_8 = e3)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1516), (2765) imply:
% 246.37/58.32 | | | | | | (2769) ~ (all_28_2 = e3)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1444), (2765) imply:
% 246.37/58.32 | | | | | | (2770) ~ (all_16_2 = e3)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1495), (2765) imply:
% 246.37/58.32 | | | | | | (2771) ~ (all_6_2 = e3)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1606), (2765) imply:
% 246.37/58.32 | | | | | | (2772) ~ (e4 = e3)
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1597), (2765) imply:
% 246.37/58.32 | | | | | | (2773) op(all_38_2, e3) = e1
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | REDUCE: (1596), (2765) imply:
% 246.37/58.32 | | | | | | (2774) op(e3, all_38_2) = e2
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | BETA: splitting (760) gives:
% 246.37/58.32 | | | | | |
% 246.37/58.32 | | | | | | Case 1:
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | (2775) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 &
% 246.37/58.32 | | | | | | | op(e3, e2) = e3)
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | BETA: splitting (2775) gives:
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | (2776) all_252_4 = e3 & op(e4, e2) = e3
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | REF_CLOSE: (140), (2771), (2776), (function-axioms) are
% 246.37/58.32 | | | | | | | | inconsistent by sub-proof #577.
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | Case 2:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | (2777) all_252_5 = e3 & op(e3, e2) = e3
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | ALPHA: (2777) implies:
% 246.37/58.32 | | | | | | | | (2778) all_252_5 = e3
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | COMBINE_EQS: (2764), (2778) imply:
% 246.37/58.32 | | | | | | | | (2779) e3 = e1
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | SIMP: (2779) implies:
% 246.37/58.32 | | | | | | | | (2780) e3 = e1
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | REDUCE: (9), (2780) imply:
% 246.37/58.32 | | | | | | | | (2781) $false
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | CLOSE: (2781) is inconsistent.
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | End of split
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | Case 2:
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | (2782) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 &
% 246.37/58.32 | | | | | | | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | BETA: splitting (2782) gives:
% 246.37/58.32 | | | | | | |
% 246.37/58.32 | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | (2783) all_252_8 = e3 & op(e2, e2) = e3
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | ALPHA: (2783) implies:
% 246.37/58.32 | | | | | | | | (2784) op(e2, e2) = e3
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | REF_CLOSE: (479), (2768), (2784), (function-axioms) are
% 246.37/58.32 | | | | | | | | inconsistent by sub-proof #877.
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | Case 2:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | (2785) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3
% 246.37/58.32 | | | | | | | | & op(e0, e2) = e3)
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | BETA: splitting (2785) gives:
% 246.37/58.32 | | | | | | | |
% 246.37/58.32 | | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | (2786) all_252_14 = e3 & op(e1, e2) = e3
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | ALPHA: (2786) implies:
% 246.37/58.32 | | | | | | | | | (2787) all_252_14 = e3
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | BETA: splitting (147) gives:
% 246.37/58.32 | | | | | | | | |
% 246.37/58.32 | | | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | (2788) ~ (all_10_2 = e4)
% 246.37/58.32 | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | BETA: splitting (207) gives:
% 246.37/58.32 | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | (2789) ~ (all_50_2 = e3)
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | REDUCE: (2766), (2789) imply:
% 246.37/58.32 | | | | | | | | | | | (2790) $false
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | CLOSE: (2790) is inconsistent.
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | Case 2:
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | (2791) ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 246.37/58.32 | | | | | | | | | | | & op(e2, e3) = all_50_1 & $i(all_50_0) &
% 246.37/58.32 | | | | | | | | | | | $i(all_50_1)) | ( ~ (all_50_1 = e4) & op(e2, e3)
% 246.37/58.32 | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | BETA: splitting (2791) gives:
% 246.37/58.32 | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | Case 1:
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | (2792) ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 246.37/58.32 | | | | | | | | | | | | op(e2, e3) = all_50_1 & $i(all_50_0) &
% 246.37/58.32 | | | | | | | | | | | | $i(all_50_1)
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.32 | | | | | | | | | | | | ALPHA: (2792) implies:
% 246.37/58.32 | | | | | | | | | | | | (2793) op(e2, e3) = all_50_1
% 246.37/58.32 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.33 | | | | | | | | | | | | (14), (137), (140), (146), (149), (150), (155),
% 246.37/58.33 | | | | | | | | | | | | (156), (159), (161), (162), (164), (165), (170),
% 246.37/58.33 | | | | | | | | | | | | (171), (173), (176), (177), (180), (182), (183),
% 246.37/58.33 | | | | | | | | | | | | (185), (186), (188), (189), (191), (192), (198),
% 246.37/58.33 | | | | | | | | | | | | (201), (203), (204), (213), (219), (222), (224),
% 246.37/58.33 | | | | | | | | | | | | (225), (227), (228), (234), (237), (246), (249),
% 246.37/58.33 | | | | | | | | | | | | (257), (265), (271), (278), (287), (307), (310),
% 246.37/58.33 | | | | | | | | | | | | (313), (324), (330), (378), (400), (418), (440),
% 246.37/58.33 | | | | | | | | | | | | (443), (450), (455), (465), (467), (473), (479),
% 246.37/58.33 | | | | | | | | | | | | (485), (491), (492), (501), (508), (715), (717),
% 246.37/58.33 | | | | | | | | | | | | (721), (723), (725), (728), (733), (734), (735),
% 246.37/58.33 | | | | | | | | | | | | (736), (738), (739), (740), (744), (746), (748),
% 246.37/58.33 | | | | | | | | | | | | (749), (750), (751), (752), (756), (772), (774),
% 246.37/58.33 | | | | | | | | | | | | (776), (778), (780), (786), (871), (881), (916),
% 246.37/58.33 | | | | | | | | | | | | (1179), (1186), (1215), (1241), (1284), (1293),
% 246.37/58.33 | | | | | | | | | | | | (1300), (1312), (1317), (1319), (1320), (1325),
% 246.37/58.33 | | | | | | | | | | | | (1327), (1331), (1334), (1336), (1337), (1344),
% 246.37/58.33 | | | | | | | | | | | | (1349), (1355), (1359), (1360), (1361), (1406),
% 246.37/58.33 | | | | | | | | | | | | (1408), (1411), (1413), (1414), (1418), (1419),
% 246.37/58.33 | | | | | | | | | | | | (1420), (1421), (1424), (1425), (1426), (1427),
% 246.37/58.33 | | | | | | | | | | | | (1428), (1432), (1433), (1434), (1435), (1436),
% 246.37/58.33 | | | | | | | | | | | | (1438), (1439), (1440), (1441), (1443), (1448),
% 246.37/58.33 | | | | | | | | | | | | (1450), (1454), (1458), (1460), (1465), (1466),
% 246.37/58.33 | | | | | | | | | | | | (1469), (1472), (1474), (1478), (1480), (1481),
% 246.37/58.33 | | | | | | | | | | | | (1484), (1487), (1488), (1490), (1513), (1514),
% 246.37/58.33 | | | | | | | | | | | | (1521), (1525), (1527), (1529), (1530), (1532),
% 246.37/58.33 | | | | | | | | | | | | (1534), (1536), (1537), (1541), (1542), (1544),
% 246.37/58.33 | | | | | | | | | | | | (1545), (1548), (1550), (1552), (1554), (1556),
% 246.37/58.33 | | | | | | | | | | | | (1561), (1563), (1565), (1566), (1567), (1568),
% 246.37/58.33 | | | | | | | | | | | | (1569), (1572), (1573), (1574), (1575), (1576),
% 246.37/58.33 | | | | | | | | | | | | (1577), (1578), (1579), (1580), (1581), (1582),
% 246.37/58.33 | | | | | | | | | | | | (1583), (1585), (1586), (1587), (1589), (1592),
% 246.37/58.33 | | | | | | | | | | | | (1593), (1594), (1595), (1596), (1598), (1601),
% 246.37/58.33 | | | | | | | | | | | | (1602), (1604), (1605), (1606), (1607), (2749),
% 246.37/58.33 | | | | | | | | | | | | (2750), (2751), (2752), (2753), (2758), (2759),
% 246.37/58.33 | | | | | | | | | | | | (2769), (2770), (2773), (2774), (2787), (2788),
% 246.37/58.33 | | | | | | | | | | | | (2793), (function-axioms) are inconsistent by
% 246.37/58.33 | | | | | | | | | | | | sub-proof #41.
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | (2794) ~ (all_50_1 = e4) & op(e2, e3) = all_50_1 &
% 246.37/58.33 | | | | | | | | | | | | $i(all_50_1)
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | ALPHA: (2794) implies:
% 246.37/58.33 | | | | | | | | | | | | (2795) op(e2, e3) = all_50_1
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 246.37/58.33 | | | | | | | | | | | | (14), (137), (140), (146), (149), (150), (155),
% 246.37/58.33 | | | | | | | | | | | | (156), (159), (161), (162), (164), (165), (170),
% 246.37/58.33 | | | | | | | | | | | | (171), (173), (176), (177), (180), (182), (183),
% 246.37/58.33 | | | | | | | | | | | | (185), (186), (188), (189), (191), (192), (198),
% 246.37/58.33 | | | | | | | | | | | | (201), (203), (204), (213), (219), (222), (224),
% 246.37/58.33 | | | | | | | | | | | | (225), (227), (228), (234), (237), (246), (249),
% 246.37/58.33 | | | | | | | | | | | | (257), (265), (271), (278), (287), (307), (310),
% 246.37/58.33 | | | | | | | | | | | | (313), (324), (330), (378), (400), (418), (440),
% 246.37/58.33 | | | | | | | | | | | | (443), (450), (455), (465), (467), (473), (479),
% 246.37/58.33 | | | | | | | | | | | | (485), (491), (492), (501), (508), (715), (717),
% 246.37/58.33 | | | | | | | | | | | | (721), (723), (725), (728), (733), (734), (735),
% 246.37/58.33 | | | | | | | | | | | | (736), (738), (739), (740), (744), (746), (748),
% 246.37/58.33 | | | | | | | | | | | | (749), (750), (751), (752), (756), (772), (774),
% 246.37/58.33 | | | | | | | | | | | | (776), (778), (780), (786), (871), (881), (916),
% 246.37/58.33 | | | | | | | | | | | | (1179), (1186), (1215), (1241), (1284), (1293),
% 246.37/58.33 | | | | | | | | | | | | (1300), (1312), (1317), (1319), (1320), (1325),
% 246.37/58.33 | | | | | | | | | | | | (1327), (1331), (1334), (1336), (1337), (1344),
% 246.37/58.33 | | | | | | | | | | | | (1349), (1355), (1359), (1360), (1361), (1406),
% 246.37/58.33 | | | | | | | | | | | | (1408), (1411), (1413), (1414), (1418), (1419),
% 246.37/58.33 | | | | | | | | | | | | (1420), (1421), (1424), (1425), (1426), (1427),
% 246.37/58.33 | | | | | | | | | | | | (1428), (1432), (1433), (1434), (1435), (1436),
% 246.37/58.33 | | | | | | | | | | | | (1438), (1439), (1440), (1441), (1443), (1448),
% 246.37/58.33 | | | | | | | | | | | | (1450), (1454), (1458), (1460), (1465), (1466),
% 246.37/58.33 | | | | | | | | | | | | (1469), (1472), (1474), (1478), (1480), (1481),
% 246.37/58.33 | | | | | | | | | | | | (1484), (1487), (1488), (1490), (1513), (1514),
% 246.37/58.33 | | | | | | | | | | | | (1521), (1525), (1527), (1529), (1530), (1532),
% 246.37/58.33 | | | | | | | | | | | | (1534), (1536), (1537), (1541), (1542), (1544),
% 246.37/58.33 | | | | | | | | | | | | (1545), (1548), (1550), (1552), (1554), (1556),
% 246.37/58.33 | | | | | | | | | | | | (1561), (1563), (1565), (1566), (1567), (1568),
% 246.37/58.33 | | | | | | | | | | | | (1569), (1572), (1573), (1574), (1575), (1576),
% 246.37/58.33 | | | | | | | | | | | | (1577), (1578), (1579), (1580), (1581), (1582),
% 246.37/58.33 | | | | | | | | | | | | (1583), (1585), (1586), (1587), (1589), (1592),
% 246.37/58.33 | | | | | | | | | | | | (1593), (1594), (1595), (1596), (1598), (1601),
% 246.37/58.33 | | | | | | | | | | | | (1602), (1604), (1605), (1606), (1607), (2749),
% 246.37/58.33 | | | | | | | | | | | | (2750), (2751), (2752), (2753), (2758), (2759),
% 246.37/58.33 | | | | | | | | | | | | (2769), (2770), (2773), (2774), (2787), (2788),
% 246.37/58.33 | | | | | | | | | | | | (2795), (function-axioms) are inconsistent by
% 246.37/58.33 | | | | | | | | | | | | sub-proof #41.
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | End of split
% 246.37/58.33 | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | End of split
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | (2796) all_10_2 = e4
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | COMBINE_EQS: (1301), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2797) all_102_2 = e4
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1476), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2798) ~ (all_244_8 = e4)
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1459), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2799) ~ (all_84_2 = e4)
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1436), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2800) ~ (all_64_2 = e4)
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1480), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2801) ~ (all_40_2 = e4)
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1478), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2802) ~ (all_38_2 = e4)
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (1575), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2803) op(e4, e3) = e2
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (2757), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2804) op(e4, e1) = e3
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | REDUCE: (2758), (2796) imply:
% 246.37/58.33 | | | | | | | | | | (2805) op(e1, e4) = e2
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | BETA: splitting (756) gives:
% 246.37/58.33 | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | (2806) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 246.37/58.33 | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 246.37/58.33 | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | BETA: splitting (2806) gives:
% 246.37/58.33 | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | (2807) all_252_6 = e4 & op(e2, e4) = e4
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | ALPHA: (2807) implies:
% 246.37/58.33 | | | | | | | | | | | | (2808) op(e2, e4) = e4
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | REF_CLOSE: (227), (2800), (2808), (function-axioms) are
% 246.37/58.33 | | | | | | | | | | | | inconsistent by sub-proof #129.
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | (2809) all_252_7 = e4 & op(e2, e3) = e4
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | ALPHA: (2809) implies:
% 246.37/58.33 | | | | | | | | | | | | (2810) all_252_7 = e4
% 246.37/58.33 | | | | | | | | | | | | (2811) op(e2, e3) = e4
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | BETA: splitting (207) gives:
% 246.37/58.33 | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | (2812) ~ (all_50_2 = e3)
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | REDUCE: (2766), (2812) imply:
% 246.37/58.33 | | | | | | | | | | | | | (2813) $false
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | CLOSE: (2813) is inconsistent.
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | (2814) ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 246.37/58.33 | | | | | | | | | | | | | & op(e2, e3) = all_50_1 & $i(all_50_0) &
% 246.37/58.33 | | | | | | | | | | | | | $i(all_50_1)) | ( ~ (all_50_1 = e4) & op(e2, e3)
% 246.37/58.33 | | | | | | | | | | | | | = all_50_1 & $i(all_50_1))
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | BETA: splitting (2814) gives:
% 246.37/58.33 | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | (2815) ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 246.37/58.33 | | | | | | | | | | | | | | op(e2, e3) = all_50_1 & $i(all_50_0) &
% 246.37/58.33 | | | | | | | | | | | | | | $i(all_50_1)
% 246.37/58.33 | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | ALPHA: (2815) implies:
% 246.37/58.33 | | | | | | | | | | | | | | (2816) ~ (all_50_0 = e0)
% 246.37/58.33 | | | | | | | | | | | | | | (2817) op(e2, e3) = all_50_1
% 246.37/58.33 | | | | | | | | | | | | | | (2818) op(e3, all_50_1) = all_50_0
% 246.37/58.33 | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 246.37/58.33 | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | (2819) ~ (all_32_2 = e2)
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | REDUCE: (1336), (2819) imply:
% 246.37/58.33 | | | | | | | | | | | | | | | (2820) ~ (all_20_2 = e2)
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | (2821) ~ (all_102_2 = e4)
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | REDUCE: (2797), (2821) imply:
% 246.37/58.33 | | | | | | | | | | | | | | | | (2822) $false
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | CLOSE: (2822) is inconsistent.
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | (2823) ( ~ (all_102_0 = e0) & op(e4, all_102_1) =
% 246.37/58.33 | | | | | | | | | | | | | | | | all_102_0 & op(e3, e4) = all_102_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | $i(all_102_0) & $i(all_102_1)) | ( ~ (all_102_1
% 246.37/58.33 | | | | | | | | | | | | | | | | = e1) & op(e3, e4) = all_102_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | $i(all_102_1))
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | BETA: splitting (2823) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2824) ~ (all_102_0 = e0) & op(e4, all_102_1) =
% 246.37/58.33 | | | | | | | | | | | | | | | | | all_102_0 & op(e3, e4) = all_102_1 & $i(all_102_0)
% 246.37/58.33 | | | | | | | | | | | | | | | | | & $i(all_102_1)
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | ALPHA: (2824) implies:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2825) op(e3, e4) = all_102_1
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2826) ~ (all_192_2 = e3)
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | REDUCE: (2767), (2826) imply:
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2827) $false
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | CLOSE: (2827) is inconsistent.
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, e2,
% 246.37/58.33 | | | | | | | | | | | | | | | | | | e4, e1, simplifying with (155), (2805) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2828) all_16_2 = e2
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (161), (164), (170), (176), (185), (188),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (195), (224), (227), (257), (278), (473), (479),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (485), (491), (501), (749), (751), (769), (779),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (1341), (1424), (1438), (1439), (1443), (1446),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (1458), (1461), (1499), (1532), (1534), (1536),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (1537), (1568), (1572), (1578), (1580), (1582),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (1596), (2770), (2799), (2803), (2804), (2810),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2811), (2816), (2817), (2818), (2820), (2825),
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2828), (function-axioms) are inconsistent by
% 246.37/58.33 | | | | | | | | | | | | | | | | | | sub-proof #39.
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2829) ~ (all_102_1 = e1) & op(e3, e4) = all_102_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | | $i(all_102_1)
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | ALPHA: (2829) implies:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2830) op(e3, e4) = all_102_1
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, e2,
% 246.37/58.33 | | | | | | | | | | | | | | | | | e4, e1, simplifying with (155), (2805) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2831) all_16_2 = e2
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (161), (164), (170), (176), (185), (188),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (195), (224), (227), (257), (278), (473), (479),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (485), (491), (501), (749), (751), (769), (779),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (1341), (1424), (1438), (1439), (1443), (1446),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (1458), (1461), (1499), (1532), (1534), (1536),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (1537), (1568), (1572), (1578), (1580), (1582),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (1596), (2770), (2799), (2803), (2804), (2810),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2811), (2816), (2817), (2818), (2820), (2830),
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2831), (function-axioms) are inconsistent by
% 246.37/58.33 | | | | | | | | | | | | | | | | | sub-proof #39.
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | End of split
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | End of split
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | (2832) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0
% 246.37/58.33 | | | | | | | | | | | | | | | & op(e1, e2) = all_32_1 & $i(all_32_0) &
% 246.37/58.33 | | | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2)
% 246.37/58.33 | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | BETA: splitting (2832) gives:
% 246.37/58.33 | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | (2833) ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 246.37/58.33 | | | | | | | | | | | | | | | | op(e1, e2) = all_32_1 & $i(all_32_0) &
% 246.37/58.33 | | | | | | | | | | | | | | | | $i(all_32_1)
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | ALPHA: (2833) implies:
% 246.37/58.33 | | | | | | | | | | | | | | | | (2834) ~ (all_32_0 = e4)
% 246.37/58.33 | | | | | | | | | | | | | | | | (2835) op(e1, e2) = all_32_1
% 246.37/58.33 | | | | | | | | | | | | | | | | (2836) op(e2, all_32_1) = all_32_0
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2837) ~ (all_192_2 = e3)
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | REDUCE: (2767), (2837) imply:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2838) $false
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | CLOSE: (2838) is inconsistent.
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2839) ( ~ (all_192_0 = e4) & op(e3, all_192_1) =
% 246.37/58.33 | | | | | | | | | | | | | | | | | all_192_0 & op(e2, e3) = all_192_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | | $i(all_192_0) & $i(all_192_1)) | ( ~ (all_192_1
% 246.37/58.33 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_192_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | | $i(all_192_1))
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 246.37/58.33 | | | | | | | | | | | | | | | | | e2, e1, simplifying with (2759), (2835) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2840) all_32_1 = e3
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_50_1,
% 246.37/58.33 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (2811), (2817) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2841) all_50_1 = e4
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | REDUCE: (2836), (2840) imply:
% 246.37/58.33 | | | | | | | | | | | | | | | | | (2842) op(e2, e3) = all_32_0
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | BETA: splitting (2839) gives:
% 246.37/58.33 | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2843) ~ (all_192_0 = e4) & op(e3, all_192_1) =
% 246.37/58.33 | | | | | | | | | | | | | | | | | | all_192_0 & op(e2, e3) = all_192_1 & $i(all_192_0)
% 246.37/58.33 | | | | | | | | | | | | | | | | | | & $i(all_192_1)
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | ALPHA: (2843) implies:
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2844) op(e2, e3) = all_192_1
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2811), (2834), (2842), (2844), (function-axioms)
% 246.37/58.33 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #38.
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2845) ~ (all_192_1 = e0) & op(e2, e3) = all_192_1 &
% 246.37/58.33 | | | | | | | | | | | | | | | | | | $i(all_192_1)
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | ALPHA: (2845) implies:
% 246.37/58.33 | | | | | | | | | | | | | | | | | | (2846) op(e2, e3) = all_192_1
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2811), (2834), (2842), (2846), (function-axioms)
% 246.37/58.33 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #38.
% 246.37/58.33 | | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | (2847) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 &
% 246.37/58.34 | | | | | | | | | | | | | | | | $i(all_32_1)
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | ALPHA: (2847) implies:
% 246.37/58.34 | | | | | | | | | | | | | | | | (2848) ~ (all_32_1 = e3)
% 246.37/58.34 | | | | | | | | | | | | | | | | (2849) op(e1, e2) = all_32_1
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 246.37/58.34 | | | | | | | | | | | | | | | | e2, e1, simplifying with (2759), (2849) gives:
% 246.37/58.34 | | | | | | | | | | | | | | | | (2850) all_32_1 = e3
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | REDUCE: (2848), (2850) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | | (2851) $false
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | CLOSE: (2851) is inconsistent.
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | (2852) ~ (all_50_1 = e4) & op(e2, e3) = all_50_1 &
% 246.37/58.34 | | | | | | | | | | | | | | $i(all_50_1)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | ALPHA: (2852) implies:
% 246.37/58.34 | | | | | | | | | | | | | | (2853) ~ (all_50_1 = e4)
% 246.37/58.34 | | | | | | | | | | | | | | (2854) op(e2, e3) = all_50_1
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, all_50_1,
% 246.37/58.34 | | | | | | | | | | | | | | e3, e2, simplifying with (2811), (2854) gives:
% 246.37/58.34 | | | | | | | | | | | | | | (2855) all_50_1 = e4
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (2853), (2855) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2856) $false
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | CLOSE: (2856) is inconsistent.
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | (2857) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 246.37/58.34 | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 246.37/58.34 | | | | | | | | | | | op(e2, e0) = e4)
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | REF_CLOSE: (188), (191), (479), (2798), (2801), (2802),
% 246.37/58.34 | | | | | | | | | | | (2857), (function-axioms) are inconsistent by
% 246.37/58.34 | | | | | | | | | | | sub-proof #80.
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | (2858) all_252_22 = e3 & op(e0, e2) = e3
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | ALPHA: (2858) implies:
% 246.37/58.34 | | | | | | | | | (2859) op(e0, e2) = e3
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | REF_CLOSE: (173), (2769), (2859), (function-axioms) are
% 246.37/58.34 | | | | | | | | | inconsistent by sub-proof #975.
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | End of split
% 246.37/58.34 | | | | | | | |
% 246.37/58.34 | | | | | | | End of split
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | End of split
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | End of split
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | Case 2:
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | (2860) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 246.37/58.34 | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | BETA: splitting (2860) gives:
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | Case 1:
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | (2861) all_252_8 = e1 & op(e2, e2) = e1
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | ALPHA: (2861) implies:
% 246.37/58.34 | | | | | | (2862) op(e2, e2) = e1
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | REF_CLOSE: (479), (2751), (2862), (function-axioms) are inconsistent
% 246.37/58.34 | | | | | | by sub-proof #690.
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | Case 2:
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | (2863) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 246.37/58.34 | | | | | | op(e0, e2) = e1)
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | BETA: splitting (2863) gives:
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | Case 1:
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | (2864) all_252_14 = e1 & op(e1, e2) = e1
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | ALPHA: (2864) implies:
% 246.37/58.34 | | | | | | | (2865) op(e1, e2) = e1
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | REF_CLOSE: (9), (2759), (2865), (function-axioms) are inconsistent
% 246.37/58.34 | | | | | | | by sub-proof #56.
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | Case 2:
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | (2866) all_252_22 = e1 & op(e0, e2) = e1
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | ALPHA: (2866) implies:
% 246.37/58.34 | | | | | | | (2867) op(e0, e2) = e1
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | REF_CLOSE: (173), (2753), (2867), (function-axioms) are
% 246.37/58.34 | | | | | | | inconsistent by sub-proof #907.
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | End of split
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | End of split
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | End of split
% 246.37/58.34 | | | |
% 246.37/58.34 | | | End of split
% 246.37/58.34 | | |
% 246.37/58.34 | | Case 2:
% 246.37/58.34 | | |
% 246.37/58.34 | | | (2868) all_6_2 = e1
% 246.37/58.34 | | |
% 246.37/58.34 | | | REDUCE: (1567), (2868) imply:
% 246.37/58.34 | | | (2869) op(e1, e2) = e4
% 246.37/58.34 | | |
% 246.37/58.34 | | | REF_CLOSE: (137), (1606), (2869), (function-axioms) are inconsistent by
% 246.37/58.34 | | | sub-proof #831.
% 246.37/58.34 | | |
% 246.37/58.34 | | End of split
% 246.37/58.34 | |
% 246.37/58.34 | Case 2:
% 246.37/58.34 | |
% 246.37/58.34 | | (2870) all_4_2 = e4
% 246.37/58.34 | | (2871) ( ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2, e4) =
% 246.37/58.34 | | all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) &
% 246.37/58.34 | | op(e2, e4) = all_4_1 & $i(all_4_1))
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1511), (2870) imply:
% 246.37/58.34 | | (2872) ~ (all_244_8 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1518), (2870) imply:
% 246.37/58.34 | | (2873) ~ (all_244_15 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1482), (2870) imply:
% 246.37/58.34 | | (2874) ~ (all_62_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1520), (2870) imply:
% 246.37/58.34 | | (2875) ~ (all_34_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1516), (2870) imply:
% 246.37/58.34 | | (2876) ~ (all_28_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1444), (2870) imply:
% 246.37/58.34 | | (2877) ~ (all_16_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1504), (2870) imply:
% 246.37/58.34 | | (2878) ~ (all_8_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1495), (2870) imply:
% 246.37/58.34 | | (2879) ~ (all_6_2 = e4)
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1597), (2870) imply:
% 246.37/58.34 | | (2880) op(all_38_2, e4) = e1
% 246.37/58.34 | |
% 246.37/58.34 | | REDUCE: (1580), (2870) imply:
% 246.37/58.34 | | (2881) op(e4, e2) = e1
% 246.37/58.34 | |
% 246.37/58.34 | | BETA: splitting (746) gives:
% 246.37/58.34 | |
% 246.37/58.34 | | Case 1:
% 246.37/58.34 | | |
% 246.37/58.34 | | | (2882) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 246.37/58.34 | | | e3) = e4)
% 246.37/58.34 | | |
% 246.37/58.34 | | | BETA: splitting (2882) gives:
% 246.37/58.34 | | |
% 246.37/58.34 | | | Case 1:
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | (2883) all_252_12 = e4 & op(e1, e4) = e4
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REF_CLOSE: (155), (2877), (2883), (function-axioms) are inconsistent by
% 246.37/58.34 | | | | sub-proof #757.
% 246.37/58.34 | | | |
% 246.37/58.34 | | | Case 2:
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | (2884) all_252_13 = e4 & op(e1, e3) = e4
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REF_CLOSE: (224), (2874), (2884), (function-axioms) are inconsistent by
% 246.37/58.34 | | | | sub-proof #952.
% 246.37/58.34 | | | |
% 246.37/58.34 | | | End of split
% 246.37/58.34 | | |
% 246.37/58.34 | | Case 2:
% 246.37/58.34 | | |
% 246.37/58.34 | | | (2885) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 246.37/58.34 | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 246.37/58.34 | | |
% 246.37/58.34 | | | BETA: splitting (2885) gives:
% 246.37/58.34 | | |
% 246.37/58.34 | | | Case 1:
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | (2886) all_252_14 = e4 & op(e1, e2) = e4
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | ALPHA: (2886) implies:
% 246.37/58.34 | | | | (2887) all_252_14 = e4
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, e2, e4,
% 246.37/58.34 | | | | simplifying with (140), (2881) gives:
% 246.37/58.34 | | | | (2888) all_6_2 = e1
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | COMBINE_EQS: (956), (2888) imply:
% 246.37/58.34 | | | | (2889) all_214_2 = e1
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1423), (2888) imply:
% 246.37/58.34 | | | | (2890) ~ (all_244_0 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1494), (2888) imply:
% 246.37/58.34 | | | | (2891) ~ (all_244_8 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1462), (2888) imply:
% 246.37/58.34 | | | | (2892) ~ (all_84_2 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1497), (2888) imply:
% 246.37/58.34 | | | | (2893) ~ (all_28_2 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1499), (2888) imply:
% 246.37/58.34 | | | | (2894) ~ (all_26_2 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1492), (2888) imply:
% 246.37/58.34 | | | | (2895) ~ (all_8_2 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (2879), (2888) imply:
% 246.37/58.34 | | | | (2896) ~ (e4 = e1)
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1588), (2888) imply:
% 246.37/58.34 | | | | (2897) op(all_64_2, e1) = e4
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | REDUCE: (1589), (2888) imply:
% 246.37/58.34 | | | | (2898) op(e1, all_64_2) = e2
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | BETA: splitting (758) gives:
% 246.37/58.34 | | | |
% 246.37/58.34 | | | | Case 1:
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | (2899) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 246.37/58.34 | | | | | op(e3, e2) = e1)
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | BETA: splitting (2899) gives:
% 246.37/58.34 | | | | |
% 246.37/58.34 | | | | | Case 1:
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | (2900) all_252_4 = e1 & op(e4, e2) = e1
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | ALPHA: (2900) implies:
% 246.37/58.34 | | | | | | (2901) all_252_4 = e1
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | BETA: splitting (147) gives:
% 246.37/58.34 | | | | | |
% 246.37/58.34 | | | | | | Case 1:
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | (2902) ~ (all_10_2 = e4)
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | BETA: splitting (150) gives:
% 246.37/58.34 | | | | | | |
% 246.37/58.34 | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | |
% 246.37/58.34 | | | | | | | | (2903) ~ (all_12_2 = e2)
% 246.37/58.34 | | | | | | | |
% 246.37/58.34 | | | | | | | | BETA: splitting (156) gives:
% 246.37/58.34 | | | | | | | |
% 246.37/58.34 | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | (2904) ~ (all_16_2 = e2)
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | BETA: splitting (159) gives:
% 246.37/58.34 | | | | | | | | |
% 246.37/58.34 | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | (2905) ~ (all_18_2 = e3)
% 246.37/58.34 | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | REDUCE: (1215), (2905) imply:
% 246.37/58.34 | | | | | | | | | | (2906) ~ (all_12_2 = e3)
% 246.37/58.34 | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | BETA: splitting (162) gives:
% 246.37/58.34 | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | (2907) ~ (all_20_2 = e4)
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | BETA: splitting (165) gives:
% 246.37/58.34 | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | (2908) ~ (all_22_2 = e1)
% 246.37/58.34 | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | BETA: splitting (168) gives:
% 246.37/58.34 | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | (2909) ~ (all_24_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | REDUCE: (1333), (2909) imply:
% 246.37/58.34 | | | | | | | | | | | | | (2910) ~ (all_16_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | BETA: splitting (174) gives:
% 246.37/58.34 | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | (2911) ~ (all_28_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | (2912) ~ (all_26_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REF_CLOSE: (161), (170), (185), (186), (188), (189), (473),
% 246.37/58.34 | | | | | | | | | | | | | | | (491), (751), (1572), (1578), (1592), (2873),
% 246.37/58.34 | | | | | | | | | | | | | | | (2880), (2890), (2894), (2907), (2912),
% 246.37/58.34 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.34 | | | | | | | | | | | | | | | #36.
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | (2913) all_26_2 = e3
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1424), (2913) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2914) ~ (all_244_0 = e3)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1525), (2913) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2915) ~ (all_36_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1568), (2913) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2916) op(e3, e1) = e4
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e4,
% 246.37/58.34 | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (2916) gives:
% 246.37/58.34 | | | | | | | | | | | | | | | (2917) all_36_2 = e4
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1432), (2917) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2918) ~ (all_100_2 = e4)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1534), (2917) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2919) ~ (all_38_2 = e4)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | REDUCE: (1537), (2917) imply:
% 246.37/58.34 | | | | | | | | | | | | | | | (2920) ~ (all_20_2 = e4)
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | (2921) ~ (all_36_2 = e4)
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | REF_CLOSE: (161), (170), (185), (188), (473), (751), (1578),
% 246.37/58.34 | | | | | | | | | | | | | | | | (1592), (2873), (2894), (2907), (2919), (2921),
% 246.37/58.34 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.37/58.34 | | | | | | | | | | | | | | | | #37.
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | (2922) ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0
% 246.37/58.34 | | | | | | | | | | | | | | | | & op(e1, e4) = all_36_1 & $i(all_36_0) &
% 246.37/58.34 | | | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e1, e4)
% 246.37/58.34 | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | BETA: splitting (2922) gives:
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2923) ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 246.37/58.34 | | | | | | | | | | | | | | | | | op(e1, e4) = all_36_1 & $i(all_36_0) &
% 246.37/58.34 | | | | | | | | | | | | | | | | | $i(all_36_1)
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | ALPHA: (2923) implies:
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2924) op(e1, e4) = all_36_1
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (146), (149), (155), (173), (176),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (177), (188), (191), (192), (213), (227), (228),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (278), (479), (491), (508), (716), (756), (778),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1300), (1407), (1418), (1419), (1434), (1435),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1440), (1566), (1567), (1569), (1574), (1577),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1587), (1589), (1602), (1603), (2876), (2893),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2902), (2906), (2910), (2911), (2914), (2918),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2919), (2924), (function-axioms) are inconsistent
% 246.37/58.34 | | | | | | | | | | | | | | | | | by sub-proof #34.
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2925) ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 &
% 246.37/58.34 | | | | | | | | | | | | | | | | | $i(all_36_1)
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | ALPHA: (2925) implies:
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2926) op(e1, e4) = all_36_1
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (146), (149), (155), (173), (176),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (177), (188), (191), (192), (213), (227), (228),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (278), (479), (491), (508), (716), (756), (778),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1300), (1407), (1418), (1419), (1434), (1435),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1440), (1566), (1567), (1569), (1574), (1577),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (1587), (1589), (1602), (1603), (2876), (2893),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2902), (2906), (2910), (2911), (2914), (2918),
% 246.37/58.34 | | | | | | | | | | | | | | | | | (2919), (2926), (function-axioms) are inconsistent
% 246.37/58.34 | | | | | | | | | | | | | | | | | by sub-proof #34.
% 246.37/58.34 | | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | End of split
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | Case 2:
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | (2927) all_28_2 = e3
% 246.37/58.34 | | | | | | | | | | | | | | (2928) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 246.37/58.34 | | | | | | | | | | | | | | & op(e2, e3) = all_28_1 & $i(all_28_0) &
% 246.37/58.34 | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3)
% 246.37/58.34 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (1512), (2927) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2929) ~ (all_244_8 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (1487), (2927) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2930) ~ (all_22_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | SIMP: (2930) implies:
% 246.37/58.34 | | | | | | | | | | | | | | (2931) ~ (all_22_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (1452), (2927) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2932) ~ (all_12_2 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (2876), (2927) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2933) ~ (e4 = e3)
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | REDUCE: (1584), (2927) imply:
% 246.37/58.34 | | | | | | | | | | | | | | (2934) op(e3, e2) = e0
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | BETA: splitting (2928) gives:
% 246.37/58.34 | | | | | | | | | | | | | |
% 246.37/58.34 | | | | | | | | | | | | | | Case 1:
% 246.37/58.34 | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | (2935) ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 246.37/58.35 | | | | | | | | | | | | | | | op(e2, e3) = all_28_1 & $i(all_28_0) &
% 246.37/58.35 | | | | | | | | | | | | | | | $i(all_28_1)
% 246.37/58.35 | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | ALPHA: (2935) implies:
% 246.37/58.35 | | | | | | | | | | | | | | | (2936) op(e2, e3) = all_28_1
% 246.37/58.35 | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | BETA: splitting (760) gives:
% 246.37/58.35 | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | Case 1:
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | (2937) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 246.37/58.35 | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | BETA: splitting (2937) gives:
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | (2938) all_252_4 = e3 & op(e4, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2901), (2938) are inconsistent by sub-proof
% 246.37/58.35 | | | | | | | | | | | | | | | | | #252.
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | (2939) all_252_5 = e3 & op(e3, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (143), (2934), (2939), (function-axioms) are
% 246.37/58.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #576.
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | End of split
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | Case 2:
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | (2940) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 246.37/58.35 | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 246.37/58.35 | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | BETA: splitting (2940) gives:
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | (2941) all_252_8 = e3 & op(e2, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | ALPHA: (2941) implies:
% 246.37/58.35 | | | | | | | | | | | | | | | | | (2942) op(e2, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (479), (2929), (2942), (function-axioms) are
% 246.37/58.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #877.
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | (2943) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 246.37/58.35 | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | BETA: splitting (2943) gives:
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | Case 1:
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2944) all_252_14 = e3 & op(e1, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2887), (2944) are inconsistent by sub-proof
% 246.37/58.35 | | | | | | | | | | | | | | | | | | #33.
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | Case 2:
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2945) all_252_22 = e3 & op(e0, e2) = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | ALPHA: (2945) implies:
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2946) all_252_22 = e3
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 246.37/58.35 | | | | | | | | | | | | | | | | | | all_28_1, e3, e2, simplifying with (146), (2936)
% 246.37/58.35 | | | | | | | | | | | | | | | | | | gives:
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2947) all_28_1 = all_10_2
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e0,
% 246.37/58.35 | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2934) gives:
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2948) all_8_2 = e0
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | REDUCE: (1503), (2948) imply:
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2949) ~ (all_244_8 = e0)
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (143), (149), (155), (161), (164), (170),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (171), (176), (177), (182), (185), (186), (188),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (189), (191), (192), (201), (224), (227), (228),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (234), (237), (249), (257), (265), (271), (278),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (284), (287), (304), (313), (336), (394), (450),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (467), (473), (479), (491), (492), (501), (508),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (717), (723), (724), (725), (730), (735), (744),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (751), (756), (776), (778), (880), (881), (973),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1165), (1241), (1288), (1312), (1317), (1319),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1320), (1331), (1337), (1343), (1352), (1361),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1408), (1413), (1414), (1418), (1419), (1424),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1425), (1427), (1428), (1432), (1434), (1435),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1438), (1461), (1463), (1464), (1474), (1478),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1480), (1488), (1490), (1513), (1525), (1532),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1534), (1536), (1537), (1544), (1552), (1554),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1566), (1568), (1572), (1573), (1574), (1575),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1576), (1577), (1578), (1583), (1587), (1591),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (1592), (1594), (1597), (1601), (2871), (2872),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2873), (2880), (2890), (2891), (2892), (2894),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2895), (2902), (2903), (2904), (2906), (2907),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2908), (2910), (2929), (2931), (2936), (2946),
% 246.37/58.35 | | | | | | | | | | | | | | | | | | (2947), (2948), (2949), (function-axioms) are
% 246.37/58.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #28.
% 246.37/58.35 | | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | | End of split
% 246.37/58.35 | | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | | End of split
% 246.37/58.35 | | | | | | | | | | | | | | | |
% 246.37/58.35 | | | | | | | | | | | | | | | End of split
% 246.37/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | (2950) ~ (all_28_1 = e4) & op(e2, e3) = all_28_1 &
% 246.62/58.35 | | | | | | | | | | | | | | | $i(all_28_1)
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | ALPHA: (2950) implies:
% 246.62/58.35 | | | | | | | | | | | | | | | (2951) ~ (all_28_1 = e4)
% 246.62/58.35 | | | | | | | | | | | | | | | (2952) op(e2, e3) = all_28_1
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | BETA: splitting (760) gives:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | (2953) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 246.62/58.35 | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | BETA: splitting (2953) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | (2954) all_252_4 = e3 & op(e4, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2901), (2954) are inconsistent by sub-proof
% 246.62/58.35 | | | | | | | | | | | | | | | | | #252.
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | (2955) all_252_5 = e3 & op(e3, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (143), (2934), (2955), (function-axioms) are
% 246.62/58.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #576.
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | (2956) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 246.62/58.35 | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 246.62/58.35 | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | BETA: splitting (2956) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | (2957) all_252_8 = e3 & op(e2, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | ALPHA: (2957) implies:
% 246.62/58.35 | | | | | | | | | | | | | | | | | (2958) op(e2, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (479), (2929), (2958), (function-axioms) are
% 246.62/58.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #877.
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | (2959) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 246.62/58.35 | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | BETA: splitting (2959) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2960) all_252_14 = e3 & op(e1, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2887), (2960) are inconsistent by sub-proof
% 246.62/58.35 | | | | | | | | | | | | | | | | | | #33.
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2961) all_252_22 = e3 & op(e0, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2962) all_252_22 = e3
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 246.62/58.35 | | | | | | | | | | | | | | | | | | all_28_1, e3, e2, simplifying with (146), (2952)
% 246.62/58.35 | | | | | | | | | | | | | | | | | | gives:
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2963) all_28_1 = all_10_2
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e0,
% 246.62/58.35 | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2934) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2964) all_8_2 = e0
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | REDUCE: (1503), (2964) imply:
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2965) ~ (all_244_8 = e0)
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (143), (149), (155), (161), (164), (170),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (171), (176), (177), (182), (185), (186), (188),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (189), (191), (192), (201), (224), (227), (228),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (234), (237), (249), (257), (265), (271), (278),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (284), (287), (304), (313), (336), (394), (450),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (467), (473), (479), (491), (492), (501), (508),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (717), (723), (724), (725), (730), (735), (744),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (751), (756), (776), (778), (880), (881), (973),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1165), (1241), (1288), (1312), (1317), (1319),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1320), (1331), (1337), (1343), (1352), (1361),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1408), (1413), (1414), (1418), (1419), (1424),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1425), (1427), (1428), (1432), (1434), (1435),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1438), (1461), (1463), (1464), (1474), (1478),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1480), (1488), (1490), (1513), (1525), (1532),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1534), (1536), (1537), (1544), (1552), (1554),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1566), (1568), (1572), (1573), (1574), (1575),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1576), (1577), (1578), (1583), (1587), (1591),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (1592), (1594), (1597), (1601), (2871), (2872),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2873), (2880), (2890), (2891), (2892), (2894),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2895), (2902), (2903), (2904), (2906), (2907),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2908), (2910), (2929), (2931), (2952), (2962),
% 246.62/58.35 | | | | | | | | | | | | | | | | | | (2963), (2964), (2965), (function-axioms) are
% 246.62/58.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #28.
% 246.62/58.35 | | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | (2966) all_24_2 = e3
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | COMBINE_EQS: (1333), (2966) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2967) all_16_2 = e3
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (1446), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2968) ~ (all_244_15 = e3)
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (1443), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2969) ~ (all_62_2 = e3)
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (1448), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2970) ~ (all_34_2 = e3)
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (2877), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2971) ~ (e4 = e3)
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (1593), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2972) op(all_26_2, e3) = e1
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | REDUCE: (1578), (2967) imply:
% 246.62/58.35 | | | | | | | | | | | | | (2973) op(e3, e4) = e1
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | BETA: splitting (745) gives:
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | (2974) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 246.62/58.35 | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | BETA: splitting (2974) gives:
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2,
% 246.62/58.35 | | | | | | | | | | | | | | | e1, e4, e3, simplifying with (278), (2973) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | (2975) all_100_2 = e1
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | REDUCE: (1430), (2975) imply:
% 246.62/58.35 | | | | | | | | | | | | | | | (2976) ~ (all_244_3 = e1)
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | REF_CLOSE: (161), (170), (171), (185), (186), (188), (189),
% 246.62/58.35 | | | | | | | | | | | | | | | (473), (485), (491), (751), (1572), (1578),
% 246.62/58.35 | | | | | | | | | | | | | | | (1592), (2873), (2880), (2890), (2894), (2907),
% 246.62/58.35 | | | | | | | | | | | | | | | (2972), (2976), (function-axioms) are inconsistent
% 246.62/58.35 | | | | | | | | | | | | | | | by sub-proof #27.
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | (2977) all_252_13 = e3 & op(e1, e3) = e3
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | ALPHA: (2977) implies:
% 246.62/58.35 | | | | | | | | | | | | | | | (2978) op(e1, e3) = e3
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e3,
% 246.62/58.35 | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (2978) gives:
% 246.62/58.35 | | | | | | | | | | | | | | | (2979) all_62_2 = e3
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | REDUCE: (2969), (2979) imply:
% 246.62/58.35 | | | | | | | | | | | | | | | (2980) $false
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | CLOSE: (2980) is inconsistent.
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | (2981) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 246.62/58.35 | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 246.62/58.35 | | | | | | | | | | | | | | op(e1, e0) = e3)
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | BETA: splitting (2981) gives:
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | Case 1:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | (2982) all_252_14 = e3 & op(e1, e2) = e3
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | REF_CLOSE: (14), (2887), (2982) are inconsistent by sub-proof
% 246.62/58.35 | | | | | | | | | | | | | | | #33.
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | (2983) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 246.62/58.35 | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | | REF_CLOSE: (182), (473), (2968), (2970), (2983),
% 246.62/58.35 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.62/58.35 | | | | | | | | | | | | | | | #821.
% 246.62/58.35 | | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | Case 2:
% 246.62/58.35 | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | (2984) all_22_2 = e1
% 246.62/58.35 | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | | REF_CLOSE: (161), (168), (170), (171), (185), (186), (188),
% 246.62/58.35 | | | | | | | | | | | | (189), (224), (473), (485), (491), (722), (751),
% 246.62/58.35 | | | | | | | | | | | | (1333), (1412), (1443), (1467), (1568), (1572),
% 246.62/58.35 | | | | | | | | | | | | (1578), (1583), (1592), (1593), (2873), (2877),
% 246.62/58.35 | | | | | | | | | | | | (2880), (2890), (2894), (2904), (2907), (2984),
% 246.62/58.35 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.62/58.35 | | | | | | | | | | | | #26.
% 246.62/58.35 | | | | | | | | | | | |
% 246.62/58.35 | | | | | | | | | | | End of split
% 246.62/58.35 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | (2985) all_20_2 = e4
% 246.62/58.36 | | | | | | | | | | | (2986) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0
% 246.62/58.36 | | | | | | | | | | | & op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.62/58.36 | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4)
% 246.62/58.36 | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | COMBINE_EQS: (786), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2987) all_60_2 = e4
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1548), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2988) ~ (all_244_24 = e4)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1542), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2989) ~ (all_38_2 = e4)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1488), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2990) ~ (all_22_2 = e4)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1454), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2991) ~ (all_12_2 = e4)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | SIMP: (2991) implies:
% 246.62/58.36 | | | | | | | | | | | (2992) ~ (all_12_2 = e4)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1605), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2993) op(all_34_2, e4) = e0
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1585), (2985) imply:
% 246.62/58.36 | | | | | | | | | | | (2994) op(e4, e1) = e0
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | BETA: splitting (2986) gives:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | (2995) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 246.62/58.36 | | | | | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) &
% 246.62/58.36 | | | | | | | | | | | | $i(all_20_1)
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | ALPHA: (2995) implies:
% 246.62/58.36 | | | | | | | | | | | | (2996) op(e1, e4) = all_20_1
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (13), (137), (143), (146), (149),
% 246.62/58.36 | | | | | | | | | | | | (155), (161), (164), (165), (170), (173), (174),
% 246.62/58.36 | | | | | | | | | | | | (182), (183), (185), (188), (201), (222), (224),
% 246.62/58.36 | | | | | | | | | | | | (225), (227), (234), (237), (249), (255), (257),
% 246.62/58.36 | | | | | | | | | | | | (265), (271), (287), (304), (313), (410), (430),
% 246.62/58.36 | | | | | | | | | | | | (450), (467), (473), (479), (492), (501), (716),
% 246.62/58.36 | | | | | | | | | | | | (717), (718), (723), (725), (735), (737), (744),
% 246.62/58.36 | | | | | | | | | | | | (749), (760), (881), (1241), (1312), (1316),
% 246.62/58.36 | | | | | | | | | | | | (1317), (1319), (1320), (1331), (1337), (1343),
% 246.62/58.36 | | | | | | | | | | | | (1354), (1361), (1407), (1408), (1409), (1413),
% 246.62/58.36 | | | | | | | | | | | | (1414), (1450), (1452), (1459), (1461), (1472),
% 246.62/58.36 | | | | | | | | | | | | (1474), (1478), (1481), (1484), (1487), (1488),
% 246.62/58.36 | | | | | | | | | | | | (1490), (1503), (1512), (1513), (1527), (1536),
% 246.62/58.36 | | | | | | | | | | | | (1569), (1572), (1573), (1574), (1575), (1576),
% 246.62/58.36 | | | | | | | | | | | | (1577), (1579), (1580), (1583), (1584), (1591),
% 246.62/58.36 | | | | | | | | | | | | (1594), (1596), (1597), (1599), (1601), (1603),
% 246.62/58.36 | | | | | | | | | | | | (2876), (2887), (2889), (2893), (2895), (2901),
% 246.62/58.36 | | | | | | | | | | | | (2902), (2903), (2904), (2906), (2987), (2988),
% 246.62/58.36 | | | | | | | | | | | | (2989), (2990), (2992), (2993), (2994), (2996),
% 246.62/58.36 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.62/58.36 | | | | | | | | | | | | #21.
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | (2997) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 &
% 246.62/58.36 | | | | | | | | | | | | $i(all_20_1)
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | ALPHA: (2997) implies:
% 246.62/58.36 | | | | | | | | | | | | (2998) op(e1, e4) = all_20_1
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (13), (137), (143), (146), (149),
% 246.62/58.36 | | | | | | | | | | | | (155), (161), (164), (165), (170), (173), (174),
% 246.62/58.36 | | | | | | | | | | | | (182), (183), (185), (188), (201), (222), (224),
% 246.62/58.36 | | | | | | | | | | | | (225), (227), (234), (237), (249), (255), (257),
% 246.62/58.36 | | | | | | | | | | | | (265), (271), (287), (304), (313), (410), (430),
% 246.62/58.36 | | | | | | | | | | | | (450), (467), (473), (479), (492), (501), (716),
% 246.62/58.36 | | | | | | | | | | | | (717), (718), (723), (725), (735), (737), (744),
% 246.62/58.36 | | | | | | | | | | | | (749), (760), (881), (1241), (1312), (1316),
% 246.62/58.36 | | | | | | | | | | | | (1317), (1319), (1320), (1331), (1337), (1343),
% 246.62/58.36 | | | | | | | | | | | | (1354), (1361), (1407), (1408), (1409), (1413),
% 246.62/58.36 | | | | | | | | | | | | (1414), (1450), (1452), (1459), (1461), (1472),
% 246.62/58.36 | | | | | | | | | | | | (1474), (1478), (1481), (1484), (1487), (1488),
% 246.62/58.36 | | | | | | | | | | | | (1490), (1503), (1512), (1513), (1527), (1536),
% 246.62/58.36 | | | | | | | | | | | | (1569), (1572), (1573), (1574), (1575), (1576),
% 246.62/58.36 | | | | | | | | | | | | (1577), (1579), (1580), (1583), (1584), (1591),
% 246.62/58.36 | | | | | | | | | | | | (1594), (1596), (1597), (1599), (1601), (1603),
% 246.62/58.36 | | | | | | | | | | | | (2876), (2887), (2889), (2893), (2895), (2901),
% 246.62/58.36 | | | | | | | | | | | | (2902), (2903), (2904), (2906), (2987), (2988),
% 246.62/58.36 | | | | | | | | | | | | (2989), (2990), (2992), (2993), (2994), (2998),
% 246.62/58.36 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 246.62/58.36 | | | | | | | | | | | | #21.
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | End of split
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | End of split
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | (2999) all_18_2 = e3
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | COMBINE_EQS: (1215), (2999) imply:
% 246.62/58.36 | | | | | | | | | | (3000) all_12_2 = e3
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1456), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3001) ~ (all_244_24 = e3)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1452), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3002) ~ (all_28_2 = e3)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1450), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3003) ~ (all_22_2 = e3)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1454), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3004) ~ (all_20_2 = e3)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1441), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3005) ~ (all_16_2 = e3)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1582), (3000) imply:
% 246.62/58.36 | | | | | | | | | | (3006) op(e3, e4) = e0
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | BETA: splitting (736) gives:
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | (3007) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 246.62/58.36 | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | BETA: splitting (3007) gives:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2,
% 246.62/58.36 | | | | | | | | | | | | e0, e4, e3, simplifying with (278), (3006) gives:
% 246.62/58.36 | | | | | | | | | | | | (3008) all_100_2 = e0
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | REDUCE: (1427), (3008) imply:
% 246.62/58.36 | | | | | | | | | | | | (3009) ~ (all_16_2 = e0)
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | SIMP: (3009) implies:
% 246.62/58.36 | | | | | | | | | | | | (3010) ~ (all_16_2 = e0)
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | REF_CLOSE: (722), (1412), (1568), (1593), (2877), (2904),
% 246.62/58.36 | | | | | | | | | | | | (3005), (3010), (function-axioms) are inconsistent
% 246.62/58.36 | | | | | | | | | | | | by sub-proof #466.
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | (3011) all_252_21 = e3 & op(e0, e3) = e3
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | REF_CLOSE: (164), (3003), (3011), (function-axioms) are
% 246.62/58.36 | | | | | | | | | | | | inconsistent by sub-proof #959.
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | End of split
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | (3012) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 246.62/58.36 | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 246.62/58.36 | | | | | | | | | | | op(e0, e0) = e3)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REF_CLOSE: (161), (173), (467), (3001), (3002), (3004),
% 246.62/58.36 | | | | | | | | | | | (3012), (function-axioms) are inconsistent by
% 246.62/58.36 | | | | | | | | | | | sub-proof #743.
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | End of split
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | End of split
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | (3013) all_16_2 = e2
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REF_CLOSE: (227), (372), (473), (479), (501), (1347), (1438),
% 246.62/58.36 | | | | | | | | | (1578), (2898), (3013), (function-axioms) are
% 246.62/58.36 | | | | | | | | | inconsistent by sub-proof #20.
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | End of split
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | (3014) all_12_2 = e2
% 246.62/58.36 | | | | | | | | (3015) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2,
% 246.62/58.36 | | | | | | | | all_12_1) = all_12_0 & $i(all_12_0) &
% 246.62/58.36 | | | | | | | | $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e4, e2) =
% 246.62/58.36 | | | | | | | | all_12_1 & $i(all_12_1))
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | REDUCE: (1421), (3014) imply:
% 246.62/58.36 | | | | | | | | (3016) ~ (all_244_0 = e2)
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | REDUCE: (1435), (3014) imply:
% 246.62/58.36 | | | | | | | | (3017) ~ (all_64_2 = e2)
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | REDUCE: (1454), (3014) imply:
% 246.62/58.36 | | | | | | | | (3018) ~ (all_20_2 = e2)
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | REDUCE: (1582), (3014) imply:
% 246.62/58.36 | | | | | | | | (3019) op(e2, e4) = e0
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | BETA: splitting (3015) gives:
% 246.62/58.36 | | | | | | | |
% 246.62/58.36 | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | (3020) ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2,
% 246.62/58.36 | | | | | | | | | all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | ALPHA: (3020) implies:
% 246.62/58.36 | | | | | | | | | (3021) ~ (all_12_0 = e3)
% 246.62/58.36 | | | | | | | | | (3022) op(e2, all_12_1) = all_12_0
% 246.62/58.36 | | | | | | | | | (3023) op(e4, e2) = all_12_1
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e0,
% 246.62/58.36 | | | | | | | | | e4, e2, simplifying with (227), (3019) gives:
% 246.62/58.36 | | | | | | | | | (3024) all_64_2 = e0
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_12_1,
% 246.62/58.36 | | | | | | | | | e2, e4, simplifying with (2881), (3023) gives:
% 246.62/58.36 | | | | | | | | | (3025) all_12_1 = e1
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (1438), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3026) ~ (all_244_8 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (1440), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3027) ~ (all_40_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | SIMP: (3027) implies:
% 246.62/58.36 | | | | | | | | | (3028) ~ (all_40_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (1439), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3029) ~ (all_38_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | SIMP: (3029) implies:
% 246.62/58.36 | | | | | | | | | (3030) ~ (all_38_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (1436), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3031) ~ (all_10_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | SIMP: (3031) implies:
% 246.62/58.36 | | | | | | | | | (3032) ~ (all_10_2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (3017), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3033) ~ (e2 = e0)
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (2897), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3034) op(e0, e1) = e4
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (3022), (3025) imply:
% 246.62/58.36 | | | | | | | | | (3035) op(e2, e1) = all_12_0
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | REDUCE: (2898), (3024) imply:
% 246.62/58.36 | | | | | | | | | (3036) op(e1, e0) = e2
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | BETA: splitting (201) gives:
% 246.62/58.36 | | | | | | | | |
% 246.62/58.36 | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | (3037) ~ (all_46_2 = e2)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | REDUCE: (1337), (3037) imply:
% 246.62/58.36 | | | | | | | | | | (3038) ~ (all_36_2 = e2)
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | BETA: splitting (430) gives:
% 246.62/58.36 | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | (3039) ~ (all_214_2 = e1)
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (2889), (3039) imply:
% 246.62/58.36 | | | | | | | | | | | (3040) $false
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | CLOSE: (3040) is inconsistent.
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | Case 2:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, e4,
% 246.62/58.36 | | | | | | | | | | | e1, e0, simplifying with (161), (3034) gives:
% 246.62/58.36 | | | | | | | | | | | (3041) all_20_2 = e4
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, e2,
% 246.62/58.36 | | | | | | | | | | | e0, e1, simplifying with (182), (3036) gives:
% 246.62/58.36 | | | | | | | | | | | (3042) all_34_2 = e2
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1581), (3042) imply:
% 246.62/58.36 | | | | | | | | | | | (3043) op(e2, e0) = e1
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | REDUCE: (1585), (3041) imply:
% 246.62/58.36 | | | | | | | | | | | (3044) op(e4, e1) = e0
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | BETA: splitting (756) gives:
% 246.62/58.36 | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | (3045) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 246.62/58.36 | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | BETA: splitting (3045) gives:
% 246.62/58.36 | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | | (3046) all_252_6 = e4 & op(e2, e4) = e4
% 246.62/58.36 | | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | | ALPHA: (3046) implies:
% 246.62/58.36 | | | | | | | | | | | | | (3047) all_252_6 = e4
% 246.62/58.36 | | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | | BETA: splitting (752) gives:
% 246.62/58.36 | | | | | | | | | | | | |
% 246.62/58.36 | | | | | | | | | | | | | Case 1:
% 246.62/58.36 | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | (3048) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 =
% 247.16/58.36 | | | | | | | | | | | | | | e0 & op(e2, e3) = e0)
% 247.16/58.36 | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | BETA: splitting (3048) gives:
% 247.16/58.36 | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | Case 1:
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | (3049) all_252_6 = e0 & op(e2, e4) = e0
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | ALPHA: (3049) implies:
% 247.16/58.36 | | | | | | | | | | | | | | | (3050) all_252_6 = e0
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | COMBINE_EQS: (3047), (3050) imply:
% 247.16/58.36 | | | | | | | | | | | | | | | (3051) e4 = e0
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | REDUCE: (11), (3051) imply:
% 247.16/58.36 | | | | | | | | | | | | | | | (3052) $false
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | CLOSE: (3052) is inconsistent.
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | Case 2:
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | (3053) all_252_7 = e0 & op(e2, e3) = e0
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | | REF_CLOSE: (146), (3032), (3053), (function-axioms) are
% 247.16/58.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #816.
% 247.16/58.36 | | | | | | | | | | | | | | |
% 247.16/58.36 | | | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | (3054) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 =
% 247.16/58.37 | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 &
% 247.16/58.37 | | | | | | | | | | | | | | op(e2, e0) = e0)
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | REF_CLOSE: (188), (191), (479), (3026), (3028), (3030),
% 247.16/58.37 | | | | | | | | | | | | | | (3054), (function-axioms) are inconsistent by
% 247.16/58.37 | | | | | | | | | | | | | | sub-proof #879.
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | (3055) all_252_7 = e4 & op(e2, e3) = e4
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | ALPHA: (3055) implies:
% 247.16/58.37 | | | | | | | | | | | | | (3056) op(e2, e3) = e4
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | REF_CLOSE: (146), (2902), (3056), (function-axioms) are
% 247.16/58.37 | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | (3057) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 247.16/58.37 | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 247.16/58.37 | | | | | | | | | | | | op(e2, e0) = e4)
% 247.16/58.37 | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | BETA: splitting (3057) gives:
% 247.16/58.37 | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | (3058) all_252_8 = e4 & op(e2, e2) = e4
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | ALPHA: (3058) implies:
% 247.16/58.37 | | | | | | | | | | | | | (3059) op(e2, e2) = e4
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | REF_CLOSE: (479), (491), (508), (3016), (3059),
% 247.16/58.37 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 247.16/58.37 | | | | | | | | | | | | | #626.
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | (3060) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 247.16/58.37 | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | BETA: splitting (3060) gives:
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | (3061) all_252_11 = e4 & op(e2, e1) = e4
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | ALPHA: (3061) implies:
% 247.16/58.37 | | | | | | | | | | | | | | (3062) all_252_11 = e4
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | BETA: splitting (749) gives:
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | (3063) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 247.16/58.37 | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | REF_CLOSE: (6), (185), (3038), (3044), (3063),
% 247.16/58.37 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 247.16/58.37 | | | | | | | | | | | | | | | #580.
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | (3064) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 247.16/58.37 | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 247.16/58.37 | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | BETA: splitting (3064) gives:
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | | (3065) all_252_11 = e2 & op(e2, e1) = e2
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3062), (3065) are inconsistent by sub-proof
% 247.16/58.37 | | | | | | | | | | | | | | | | #787.
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | | (3066) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 247.16/58.37 | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | | REF_CLOSE: (161), (473), (479), (501), (2891), (3018),
% 247.16/58.37 | | | | | | | | | | | | | | | | (3066), (function-axioms) are inconsistent by
% 247.16/58.37 | | | | | | | | | | | | | | | | sub-proof #738.
% 247.16/58.37 | | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | (3067) all_252_18 = e4 & op(e2, e0) = e4
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | ALPHA: (3067) implies:
% 247.16/58.37 | | | | | | | | | | | | | | (3068) op(e2, e0) = e4
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | | REF_CLOSE: (12), (3043), (3068), (function-axioms) are
% 247.16/58.37 | | | | | | | | | | | | | | inconsistent by sub-proof #664.
% 247.16/58.37 | | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | (3069) all_46_2 = e2
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | COMBINE_EQS: (1337), (3069) imply:
% 247.16/58.37 | | | | | | | | | | (3070) all_36_2 = e2
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | SIMP: (3070) implies:
% 247.16/58.37 | | | | | | | | | | (3071) all_36_2 = e2
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | REF_CLOSE: (188), (430), (1572), (2889), (3021), (3035),
% 247.16/58.37 | | | | | | | | | | (3071), (function-axioms) are inconsistent by
% 247.16/58.37 | | | | | | | | | | sub-proof #18.
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | End of split
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | (3072) ~ (all_12_1 = e1) & op(e4, e2) = all_12_1 &
% 247.16/58.37 | | | | | | | | | $i(all_12_1)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | ALPHA: (3072) implies:
% 247.16/58.37 | | | | | | | | | (3073) ~ (all_12_1 = e1)
% 247.16/58.37 | | | | | | | | | (3074) op(e4, e2) = all_12_1
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_12_1,
% 247.16/58.37 | | | | | | | | | e2, e4, simplifying with (2881), (3074) gives:
% 247.16/58.37 | | | | | | | | | (3075) all_12_1 = e1
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (3073), (3075) imply:
% 247.16/58.37 | | | | | | | | | (3076) $false
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | CLOSE: (3076) is inconsistent.
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | End of split
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | End of split
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | Case 2:
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | (3077) all_10_2 = e4
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1465), (3077) imply:
% 247.16/58.37 | | | | | | | (3078) ~ (all_244_3 = e4)
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1459), (3077) imply:
% 247.16/58.37 | | | | | | | (3079) ~ (all_84_2 = e4)
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1436), (3077) imply:
% 247.16/58.37 | | | | | | | (3080) ~ (all_64_2 = e4)
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1474), (3077) imply:
% 247.16/58.37 | | | | | | | (3081) ~ (all_22_2 = e4)
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1575), (3077) imply:
% 247.16/58.37 | | | | | | | (3082) op(e4, e3) = e2
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | REDUCE: (1591), (3077) imply:
% 247.16/58.37 | | | | | | | (3083) op(all_8_2, e4) = e2
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | BETA: splitting (771) gives:
% 247.16/58.37 | | | | | | |
% 247.16/58.37 | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | (3084) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 247.16/58.37 | | | | | | | | op(e3, e3) = e4)
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | BETA: splitting (3084) gives:
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | (3085) all_252_1 = e4 & op(e4, e3) = e4
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REF_CLOSE: (257), (3079), (3085), (function-axioms) are
% 247.16/58.37 | | | | | | | | | inconsistent by sub-proof #815.
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | (3086) all_252_3 = e4 & op(e3, e3) = e4
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REF_CLOSE: (485), (3078), (3086), (function-axioms) are
% 247.16/58.37 | | | | | | | | | inconsistent by sub-proof #846.
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | End of split
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | (3087) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4
% 247.16/58.37 | | | | | | | | & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) =
% 247.16/58.37 | | | | | | | | e4)
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | BETA: splitting (3087) gives:
% 247.16/58.37 | | | | | | | |
% 247.16/58.37 | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | (3088) all_252_7 = e4 & op(e2, e3) = e4
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | ALPHA: (3088) implies:
% 247.16/58.37 | | | | | | | | | (3089) all_252_7 = e4
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e2,
% 247.16/58.37 | | | | | | | | | e3, e4, simplifying with (257), (3082) gives:
% 247.16/58.37 | | | | | | | | | (3090) all_84_2 = e2
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | COMBINE_EQS: (1133), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3091) all_184_2 = e2
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (1458), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3092) ~ (all_244_3 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (1460), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3093) ~ (all_62_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | SIMP: (3093) implies:
% 247.16/58.37 | | | | | | | | | (3094) ~ (all_62_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (1463), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3095) ~ (all_26_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | SIMP: (3095) implies:
% 247.16/58.37 | | | | | | | | | (3096) ~ (all_26_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (1461), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3097) ~ (all_22_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | SIMP: (3097) implies:
% 247.16/58.37 | | | | | | | | | (3098) ~ (all_22_2 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | REDUCE: (3079), (3090) imply:
% 247.16/58.37 | | | | | | | | | (3099) ~ (e4 = e2)
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | BETA: splitting (391) gives:
% 247.16/58.37 | | | | | | | | |
% 247.16/58.37 | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | (3100) ~ (all_184_2 = e2)
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | REDUCE: (3091), (3100) imply:
% 247.16/58.37 | | | | | | | | | | (3101) $false
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | CLOSE: (3101) is inconsistent.
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | (3102) ( ~ (all_184_0 = e0) & op(e3, e2) = all_184_1 &
% 247.16/58.37 | | | | | | | | | | op(e2, all_184_1) = all_184_0 & $i(all_184_0) &
% 247.16/58.37 | | | | | | | | | | $i(all_184_1)) | ( ~ (all_184_1 = e1) & op(e3,
% 247.16/58.37 | | | | | | | | | | e2) = all_184_1 & $i(all_184_1))
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | BETA: splitting (3102) gives:
% 247.16/58.37 | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | Case 1:
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | (3103) ~ (all_184_0 = e0) & op(e3, e2) = all_184_1 &
% 247.16/58.37 | | | | | | | | | | | op(e2, all_184_1) = all_184_0 & $i(all_184_0) &
% 247.16/58.37 | | | | | | | | | | | $i(all_184_1)
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | ALPHA: (3103) implies:
% 247.16/58.37 | | | | | | | | | | | (3104) op(e3, e2) = all_184_1
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (12), (13), (14), (143),
% 247.16/58.37 | | | | | | | | | | | (149), (150), (155), (156), (161), (162), (164),
% 247.16/58.37 | | | | | | | | | | | (165), (168), (170), (171), (173), (174), (176),
% 247.16/58.37 | | | | | | | | | | | (180), (182), (183), (185), (186), (188), (189),
% 247.16/58.37 | | | | | | | | | | | (191), (201), (203), (224), (227), (257), (278),
% 247.16/58.37 | | | | | | | | | | | (327), (372), (410), (430), (462), (467), (473),
% 247.16/58.37 | | | | | | | | | | | (479), (485), (491), (501), (716), (717), (722),
% 247.16/58.37 | | | | | | | | | | | (735), (744), (749), (751), (752), (757), (759),
% 247.16/58.37 | | | | | | | | | | | (760), (764), (766), (769), (772), (773), (774),
% 247.16/58.37 | | | | | | | | | | | (778), (779), (780), (781), (1281), (1333),
% 247.16/58.37 | | | | | | | | | | | (1336), (1337), (1347), (1354), (1363), (1407),
% 247.16/58.37 | | | | | | | | | | | (1408), (1412), (1426), (1428), (1433), (1434),
% 247.16/58.37 | | | | | | | | | | | (1435), (1438), (1439), (1440), (1443), (1450),
% 247.16/58.37 | | | | | | | | | | | (1452), (1454), (1456), (1467), (1470), (1487),
% 247.16/58.37 | | | | | | | | | | | (1510), (1521), (1530), (1539), (1544), (1546),
% 247.16/58.37 | | | | | | | | | | | (1558), (1561), (1565), (1566), (1567), (1568),
% 247.16/58.37 | | | | | | | | | | | (1572), (1573), (1574), (1577), (1578), (1580),
% 247.16/58.37 | | | | | | | | | | | (1581), (1582), (1583), (1587), (1589), (1592),
% 247.16/58.37 | | | | | | | | | | | (1593), (1596), (1598), (1601), (1602), (1603),
% 247.16/58.37 | | | | | | | | | | | (1605), (2871), (2873), (2876), (2877), (2878),
% 247.16/58.37 | | | | | | | | | | | (2880), (2881), (2887), (2889), (2890), (2891),
% 247.16/58.37 | | | | | | | | | | | (2893), (2894), (2897), (2898), (2901), (3078),
% 247.16/58.37 | | | | | | | | | | | (3079), (3080), (3081), (3082), (3083), (3089),
% 247.16/58.37 | | | | | | | | | | | (3092), (3094), (3096), (3098), (3104),
% 247.16/58.37 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 247.16/58.37 | | | | | | | | | | | #1.
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | Case 2:
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | (3105) ~ (all_184_1 = e1) & op(e3, e2) = all_184_1 &
% 247.16/58.37 | | | | | | | | | | | $i(all_184_1)
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.37 | | | | | | | | | | | ALPHA: (3105) implies:
% 247.16/58.37 | | | | | | | | | | | (3106) op(e3, e2) = all_184_1
% 247.16/58.37 | | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (12), (13), (14), (143),
% 247.16/58.38 | | | | | | | | | | | (149), (150), (155), (156), (161), (162), (164),
% 247.16/58.38 | | | | | | | | | | | (165), (168), (170), (171), (173), (174), (176),
% 247.16/58.38 | | | | | | | | | | | (180), (182), (183), (185), (186), (188), (189),
% 247.16/58.38 | | | | | | | | | | | (191), (201), (203), (224), (227), (257), (278),
% 247.16/58.38 | | | | | | | | | | | (327), (372), (410), (430), (462), (467), (473),
% 247.16/58.38 | | | | | | | | | | | (479), (485), (491), (501), (716), (717), (722),
% 247.16/58.38 | | | | | | | | | | | (735), (744), (749), (751), (752), (757), (759),
% 247.16/58.38 | | | | | | | | | | | (760), (764), (766), (769), (772), (773), (774),
% 247.16/58.38 | | | | | | | | | | | (778), (779), (780), (781), (1281), (1333),
% 247.16/58.38 | | | | | | | | | | | (1336), (1337), (1347), (1354), (1363), (1407),
% 247.16/58.38 | | | | | | | | | | | (1408), (1412), (1426), (1428), (1433), (1434),
% 247.16/58.38 | | | | | | | | | | | (1435), (1438), (1439), (1440), (1443), (1450),
% 247.16/58.38 | | | | | | | | | | | (1452), (1454), (1456), (1467), (1470), (1487),
% 247.16/58.38 | | | | | | | | | | | (1510), (1521), (1530), (1539), (1544), (1546),
% 247.16/58.38 | | | | | | | | | | | (1558), (1561), (1565), (1566), (1567), (1568),
% 247.16/58.38 | | | | | | | | | | | (1572), (1573), (1574), (1577), (1578), (1580),
% 247.16/58.38 | | | | | | | | | | | (1581), (1582), (1583), (1587), (1589), (1592),
% 247.16/58.38 | | | | | | | | | | | (1593), (1596), (1598), (1601), (1602), (1603),
% 247.16/58.38 | | | | | | | | | | | (1605), (2871), (2873), (2876), (2877), (2878),
% 247.16/58.38 | | | | | | | | | | | (2880), (2881), (2887), (2889), (2890), (2891),
% 247.16/58.38 | | | | | | | | | | | (2893), (2894), (2897), (2898), (2901), (3078),
% 247.16/58.38 | | | | | | | | | | | (3079), (3080), (3081), (3082), (3083), (3089),
% 247.16/58.38 | | | | | | | | | | | (3092), (3094), (3096), (3098), (3106),
% 247.16/58.38 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 247.16/58.38 | | | | | | | | | | | #1.
% 247.16/58.38 | | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | End of split
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | End of split
% 247.16/58.38 | | | | | | | | |
% 247.16/58.38 | | | | | | | | Case 2:
% 247.16/58.38 | | | | | | | | |
% 247.16/58.38 | | | | | | | | | (3107) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 =
% 247.16/58.38 | | | | | | | | | e4 & op(e0, e3) = e4)
% 247.16/58.38 | | | | | | | | |
% 247.16/58.38 | | | | | | | | | BETA: splitting (3107) gives:
% 247.16/58.38 | | | | | | | | |
% 247.16/58.38 | | | | | | | | | Case 1:
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | (3108) all_252_13 = e4 & op(e1, e3) = e4
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | REF_CLOSE: (224), (2874), (3108), (function-axioms) are
% 247.16/58.38 | | | | | | | | | | inconsistent by sub-proof #952.
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | Case 2:
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | (3109) all_252_21 = e4 & op(e0, e3) = e4
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | | REF_CLOSE: (164), (3081), (3109), (function-axioms) are
% 247.16/58.38 | | | | | | | | | | inconsistent by sub-proof #805.
% 247.16/58.38 | | | | | | | | | |
% 247.16/58.38 | | | | | | | | | End of split
% 247.16/58.38 | | | | | | | | |
% 247.16/58.38 | | | | | | | | End of split
% 247.16/58.38 | | | | | | | |
% 247.16/58.38 | | | | | | | End of split
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | End of split
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | Case 2:
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | (3110) all_252_5 = e1 & op(e3, e2) = e1
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | ALPHA: (3110) implies:
% 247.16/58.38 | | | | | | (3111) op(e3, e2) = e1
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | REF_CLOSE: (143), (2895), (3111), (function-axioms) are inconsistent
% 247.16/58.38 | | | | | | by sub-proof #929.
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | End of split
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | Case 2:
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | (3112) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 247.16/58.38 | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | BETA: splitting (3112) gives:
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | Case 1:
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | (3113) all_252_8 = e1 & op(e2, e2) = e1
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | ALPHA: (3113) implies:
% 247.16/58.38 | | | | | | (3114) op(e2, e2) = e1
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | REF_CLOSE: (479), (2891), (3114), (function-axioms) are inconsistent
% 247.16/58.38 | | | | | | by sub-proof #690.
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | Case 2:
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | (3115) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 247.16/58.38 | | | | | | op(e0, e2) = e1)
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | BETA: splitting (3115) gives:
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | | Case 1:
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | (3116) all_252_14 = e1 & op(e1, e2) = e1
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | ALPHA: (3116) implies:
% 247.16/58.38 | | | | | | | (3117) all_252_14 = e1
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | COMBINE_EQS: (2887), (3117) imply:
% 247.16/58.38 | | | | | | | (3118) e4 = e1
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | REDUCE: (12), (3118) imply:
% 247.16/58.38 | | | | | | | (3119) $false
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | CLOSE: (3119) is inconsistent.
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | Case 2:
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | (3120) all_252_22 = e1 & op(e0, e2) = e1
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | ALPHA: (3120) implies:
% 247.16/58.38 | | | | | | | (3121) op(e0, e2) = e1
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | | REF_CLOSE: (173), (2893), (3121), (function-axioms) are
% 247.16/58.38 | | | | | | | inconsistent by sub-proof #907.
% 247.16/58.38 | | | | | | |
% 247.16/58.38 | | | | | | End of split
% 247.16/58.38 | | | | | |
% 247.16/58.38 | | | | | End of split
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | End of split
% 247.16/58.38 | | | |
% 247.16/58.38 | | | Case 2:
% 247.16/58.38 | | | |
% 247.16/58.38 | | | | (3122) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 247.16/58.38 | | | | op(e1, e0) = e4)
% 247.16/58.38 | | | |
% 247.16/58.38 | | | | BETA: splitting (3122) gives:
% 247.16/58.38 | | | |
% 247.16/58.38 | | | | Case 1:
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | (3123) all_252_15 = e4 & op(e1, e1) = e4
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | ALPHA: (3123) implies:
% 247.16/58.38 | | | | | (3124) op(e1, e1) = e4
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | REF_CLOSE: (473), (2873), (3124), (function-axioms) are inconsistent
% 247.16/58.38 | | | | | by sub-proof #756.
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | Case 2:
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | (3125) all_252_19 = e4 & op(e1, e0) = e4
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | | REF_CLOSE: (182), (2875), (3125), (function-axioms) are inconsistent
% 247.16/58.38 | | | | | by sub-proof #677.
% 247.16/58.38 | | | | |
% 247.16/58.38 | | | | End of split
% 247.16/58.38 | | | |
% 247.16/58.38 | | | End of split
% 247.16/58.38 | | |
% 247.16/58.38 | | End of split
% 247.16/58.38 | |
% 247.16/58.38 | End of split
% 247.16/58.38 |
% 247.16/58.38 End of proof
% 247.16/58.38
% 247.16/58.38 Sub-proof #1 shows that the following formulas are inconsistent:
% 247.16/58.38 ----------------------------------------------------------------
% 247.16/58.38 (1) all_240_2 = all_48_2
% 247.16/58.38 (2) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 247.16/58.38 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 247.16/58.38 | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.16/58.38 (3) all_32_2 = all_20_2
% 247.16/58.38 (4) ~ (all_26_2 = e2)
% 247.16/58.38 (5) ~ (all_8_2 = e4)
% 247.16/58.38 (6) ~ (all_100_2 = all_12_2)
% 247.16/58.38 (7) op(all_4_2, e2) = e1
% 247.16/58.38 (8) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 247.16/58.38 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 247.16/58.38 (all_252_16 = e3 & op(e4, e0) = e3)
% 247.16/58.38 (9) all_134_2 = all_64_2
% 247.16/58.38 (10) ~ (all_244_24 = all_34_2)
% 247.16/58.38 (11) ~ (all_40_2 = all_38_2)
% 247.16/58.38 (12) op(all_6_2, e2) = e4
% 247.16/58.38 (13) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 247.16/58.38 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.16/58.38 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 247.16/58.38 (14) op(all_12_2, all_30_2) = e4
% 247.16/58.38 (15) op(e4, e0) = all_30_2
% 247.16/58.38 (16) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 247.16/58.38 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 247.16/58.38 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.38 (17) op(all_28_2, all_40_2) = e2
% 247.16/58.38 (18) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.16/58.38 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.16/58.38 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.16/58.38 (19) ~ (all_22_2 = e2)
% 247.16/58.38 (20) ~ (all_244_3 = e2)
% 247.16/58.38 (21) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 247.16/58.38 all_250_15 = e0
% 247.16/58.38 (22) op(all_64_2, e4) = e2
% 247.16/58.38 (23) ~ (e1 = e0)
% 247.16/58.38 (24) ~ (all_62_2 = e2)
% 247.16/58.38 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.38 (26) ~ (e3 = e2)
% 247.16/58.38 (27) op(e0, e0) = all_244_24
% 247.16/58.38 (28) ~ (all_244_8 = all_64_2)
% 247.16/58.38 (29) op(e2, e2) = all_244_8
% 247.16/58.38 (30) op(all_84_2, all_100_2) = e3
% 247.16/58.38 (31) op(e2, e1) = all_38_2
% 247.16/58.38 (32) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.16/58.38 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.16/58.38 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.16/58.38 (33) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 247.16/58.38 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 247.16/58.38 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 247.16/58.38 (34) ~ (all_64_2 = all_40_2)
% 247.16/58.38 (35) ~ (all_244_3 = all_22_2)
% 247.16/58.38 (36) op(e1, e0) = all_34_2
% 247.16/58.38 (37) ~ (all_240_2 = e4) | ( ~ (all_240_0 = e1) & op(e4, all_240_1) =
% 247.16/58.38 all_240_0 & op(e0, e4) = all_240_1 & $i(all_240_0) & $i(all_240_1)) |
% 247.16/58.38 ( ~ (all_240_1 = e2) & op(e0, e4) = all_240_1 & $i(all_240_1))
% 247.16/58.38 (38) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.16/58.38 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.16/58.38 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.16/58.38 (39) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.16/58.38 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.16/58.38 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.16/58.38 (40) ~ (all_20_2 = all_12_2)
% 247.16/58.38 (41) ~ (all_244_15 = e4)
% 247.16/58.38 (42) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 247.16/58.38 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 247.16/58.38 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 247.16/58.38 (43) ~ (e2 = e1)
% 247.16/58.38 (44) op(all_26_2, e1) = e4
% 247.16/58.38 (45) all_252_7 = e4
% 247.16/58.38 (46) ~ (all_100_2 = all_64_2)
% 247.16/58.38 (47) op(e0, e2) = all_28_2
% 247.16/58.38 (48) ~ (e4 = e1)
% 247.16/58.38 (49) all_252_14 = e4
% 247.16/58.38 (50) op(e4, e2) = e1
% 247.16/58.38 (51) ~ (all_28_2 = e1)
% 247.16/58.38 (52) op(all_6_2, all_64_2) = e2
% 247.16/58.38 (53) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 247.16/58.38 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 247.16/58.38 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 247.16/58.38 (54) ~ (all_16_2 = e4)
% 247.16/58.38 (55) op(all_244_15, all_244_15) = e1
% 247.16/58.38 (56) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 &
% 247.16/58.38 op(e2, all_16_1) = all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 247.16/58.38 (all_16_1 = e0) & op(e4, e2) = all_16_1 & $i(all_16_1))
% 247.16/58.38 (57) all_250_21 = all_22_2
% 247.16/58.38 (58) op(all_34_2, e0) = e1
% 247.16/58.38 (59) ~ (all_244_3 = e4)
% 247.16/58.38 (60) op(e1, e4) = all_16_2
% 247.16/58.38 (61) ~ (all_28_2 = all_20_2)
% 247.16/58.38 (62) ( ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2, e4) = all_4_1 &
% 247.16/58.38 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e2, e4) = all_4_1
% 247.16/58.38 & $i(all_4_1))
% 247.16/58.38 (63) op(e1, e3) = all_62_2
% 247.16/58.38 (64) op(all_16_2, all_26_2) = e4
% 247.16/58.38 (65) ~ (e3 = e0)
% 247.16/58.38 (66) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 247.16/58.38 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 247.16/58.38 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 247.16/58.38 (67) all_198_2 = all_34_2
% 247.16/58.38 (68) ~ (all_48_2 = all_36_2)
% 247.16/58.38 (69) ~ (all_84_2 = e4)
% 247.16/58.38 (70) ~ (all_22_2 = e4)
% 247.16/58.38 (71) ~ (e3 = e1)
% 247.16/58.38 (72) op(e3, e2) = all_184_1
% 247.16/58.38 (73) op(all_48_2, all_22_2) = e0
% 247.16/58.38 (74) op(e3, e1) = all_36_2
% 247.16/58.38 (75) ~ (all_28_2 = all_12_2)
% 247.16/58.38 (76) op(all_40_2, e0) = e2
% 247.16/58.38 (77) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.16/58.38 all_250_22 = e0
% 247.16/58.38 (78) op(e1, all_64_2) = e2
% 247.16/58.38 (79) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.16/58.38 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.16/58.38 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.16/58.39 (80) ~ (all_40_2 = all_34_2)
% 247.16/58.39 (81) ~ (all_48_2 = all_34_2)
% 247.16/58.39 (82) ~ (all_48_2 = all_8_2)
% 247.16/58.39 (83) op(e4, e3) = e2
% 247.16/58.39 (84) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 247.16/58.39 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 247.16/58.39 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 247.16/58.39 (85) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 247.16/58.39 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 247.16/58.39 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 247.16/58.39 (86) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 &
% 247.16/58.39 op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 247.16/58.39 e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 247.16/58.39 (87) ~ (all_244_15 = all_34_2)
% 247.16/58.39 (88) ~ (all_28_2 = e4)
% 247.16/58.39 (89) ~ (all_64_2 = all_12_2)
% 247.16/58.39 (90) op(all_22_2, e3) = e0
% 247.16/58.39 (91) op(e0, e3) = all_22_2
% 247.16/58.39 (92) ~ (all_244_24 = all_12_2)
% 247.16/58.39 (93) ~ (all_28_2 = all_22_2)
% 247.16/58.39 (94) op(all_34_2, all_20_2) = e0
% 247.16/58.39 (95) op(all_84_2, e3) = e4
% 247.16/58.39 (96) op(all_64_2, e1) = e4
% 247.16/58.39 (97) op(e4, e1) = all_26_2
% 247.16/58.39 (98) ~ (all_134_2 = e0) | ( ~ (all_134_0 = e3) & op(e4, e0) = all_134_1 &
% 247.16/58.39 op(e0, all_134_1) = all_134_0 & $i(all_134_0) & $i(all_134_1)) | ( ~
% 247.16/58.39 (all_134_1 = e1) & op(e4, e0) = all_134_1 & $i(all_134_1))
% 247.16/58.39 (99) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.16/58.39 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.16/58.39 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.16/58.39 (100) ~ (all_64_2 = all_38_2)
% 247.16/58.39 (101) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.16/58.39 all_250_21 = e0
% 247.16/58.39 (102) ~ (all_62_2 = all_16_2)
% 247.16/58.39 (103) op(e3, e4) = all_100_2
% 247.16/58.39 (104) ~ (all_244_8 = e1)
% 247.16/58.39 (105) all_250_15 = all_16_2
% 247.16/58.39 (106) op(all_8_2, e4) = e2
% 247.16/58.39 (107) op(e4, e4) = all_244_0
% 247.16/58.39 (108) ~ (all_22_2 = all_12_2)
% 247.16/58.39 (109) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 247.16/58.39 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 247.16/58.39 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.16/58.39 (110) ~ (all_244_0 = e1)
% 247.16/58.39 (111) ~ (e4 = e3)
% 247.16/58.39 (112) op(e1, e1) = all_244_15
% 247.16/58.39 (113) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 247.16/58.39 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 247.16/58.39 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 247.16/58.39 (114) op(e0, e1) = all_20_2
% 247.16/58.39 (115) op(e3, e0) = all_48_2
% 247.16/58.39 (116) op(all_48_2, e0) = e3
% 247.16/58.39 (117) ~ (all_100_2 = all_48_2)
% 247.16/58.39 (118) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 247.16/58.39 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 247.16/58.39 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 247.16/58.39 (119) ~ (all_26_2 = e1)
% 247.16/58.39 (120) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.16/58.39 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.16/58.39 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.16/58.39 (121) op(all_4_2, all_38_2) = e2
% 247.16/58.39 (122) op(e4, e3) = all_84_2
% 247.16/58.39 (123) op(e2, e4) = all_64_2
% 247.16/58.39 (124) all_170_2 = all_16_2
% 247.16/58.39 (125) op(all_40_2, all_28_2) = e0
% 247.16/58.39 (126) ~ (e4 = e2)
% 247.16/58.39 (127) all_252_4 = e1
% 247.16/58.39 (128) ~ (all_12_2 = e2) | ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 &
% 247.16/58.39 op(e2, all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 247.16/58.39 (all_12_1 = e1) & op(e4, e2) = all_12_1 & $i(all_12_1))
% 247.16/58.39 (129) op(e3, e2) = all_8_2
% 247.16/58.39 (130) ~ (all_64_2 = all_16_2)
% 247.16/58.39 (131) op(all_36_2, e1) = e3
% 247.16/58.39 (132) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.39 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.39 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.39 (133) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.39 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.39 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.39 (134) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.16/58.39 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) |
% 247.16/58.39 ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.16/58.39 (135) op(all_16_2, e4) = e1
% 247.16/58.39 (136) op(e2, e0) = all_40_2
% 247.16/58.39 (137) ~ (all_214_2 = e1) | ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 &
% 247.16/58.39 op(e1, all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)) | ( ~
% 247.16/58.39 (all_214_1 = e0) & op(e2, e1) = all_214_1 & $i(all_214_1))
% 247.16/58.39 (138) ~ (all_244_3 = all_48_2)
% 247.16/58.39 (139) all_24_2 = all_16_2
% 247.16/58.39 (140) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.16/58.39 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.16/58.39 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.16/58.39 (141) all_250_22 = all_28_2
% 247.16/58.39 (142) op(e3, e3) = all_244_3
% 247.16/58.39 (143) op(all_38_2, e4) = e1
% 247.16/58.39 (144) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 247.16/58.39 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 247.16/58.39 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 247.16/58.39 (145) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 247.16/58.39 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 247.16/58.39 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 247.16/58.39 (146) ~ (all_26_2 = all_20_2)
% 247.16/58.39 (147) op(all_26_2, all_16_2) = e1
% 247.16/58.39 (148) op(all_12_2, e4) = e0
% 247.16/58.39 (149) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.39 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.39 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.39 (150) all_46_2 = all_36_2
% 247.16/58.39 (151) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 247.16/58.39 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 247.16/58.39 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 247.16/58.39 (152) all_214_2 = e1
% 247.16/58.39 (153) ~ (all_64_2 = e4)
% 247.16/58.39 (154) op(e0, e4) = all_12_2
% 247.16/58.39 (155) ~ (all_170_2 = e2) | ( ~ (all_170_0 = e0) & op(e4, e2) = all_170_1 &
% 247.16/58.39 op(e2, all_170_1) = all_170_0 & $i(all_170_0) & $i(all_170_1)) | ( ~
% 247.16/58.39 (all_170_1 = e3) & op(e4, e2) = all_170_1 & $i(all_170_1))
% 247.16/58.39
% 247.16/58.39 Begin of proof
% 247.16/58.39 |
% 247.16/58.39 | GROUND_INST: instantiating (25) with all_8_2, all_184_1, e2, e3, simplifying
% 247.16/58.39 | with (72), (129) gives:
% 247.16/58.39 | (156) all_184_1 = all_8_2
% 247.16/58.39 |
% 247.16/58.39 | BETA: splitting (128) gives:
% 247.16/58.39 |
% 247.16/58.39 | Case 1:
% 247.16/58.39 | |
% 247.16/58.39 | | (157) ~ (all_12_2 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | BETA: splitting (56) gives:
% 247.16/58.39 | |
% 247.16/58.39 | | Case 1:
% 247.16/58.39 | | |
% 247.16/58.39 | | | (158) ~ (all_16_2 = e2)
% 247.16/58.39 | | |
% 247.16/58.39 | | | BETA: splitting (42) gives:
% 247.16/58.39 | | |
% 247.16/58.39 | | | Case 1:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | (159) ~ (all_20_2 = e4)
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | BETA: splitting (151) gives:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | Case 1:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | (160) ~ (all_22_2 = e1)
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | BETA: splitting (85) gives:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | Case 1:
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | | (161) ~ (all_28_2 = e3)
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | | BETA: splitting (86) gives:
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | | Case 1:
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | (162) ~ (all_26_2 = e3)
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | REF_CLOSE: (18), (25), (31), (32), (38), (41), (64), (74), (97),
% 247.16/58.39 | | | | | | | (107), (110), (112), (114), (119), (131), (135), (143),
% 247.16/58.39 | | | | | | | (159), (162) are inconsistent by sub-proof #36.
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | Case 2:
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | (163) all_26_2 = e3
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | REDUCE: (44), (163) imply:
% 247.16/58.39 | | | | | | | (164) op(e3, e1) = e4
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | GROUND_INST: instantiating (25) with all_36_2, e4, e1, e3,
% 247.16/58.39 | | | | | | | simplifying with (74), (164) gives:
% 247.16/58.39 | | | | | | | (165) all_36_2 = e4
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | BETA: splitting (18) gives:
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | | Case 1:
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | | (166) ~ (all_36_2 = e4)
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | | REF_CLOSE: (25), (74), (164), (166) are inconsistent by
% 247.16/58.39 | | | | | | | | sub-proof #435.
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | Case 2:
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | | (167) ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.16/58.39 | | | | | | | | op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1))
% 247.16/58.39 | | | | | | | | | ( ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 &
% 247.16/58.39 | | | | | | | | $i(all_36_1))
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | | BETA: splitting (167) gives:
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | | Case 1:
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | (168) ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.16/58.39 | | | | | | | | | op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | ALPHA: (168) implies:
% 247.16/58.39 | | | | | | | | | (169) op(e1, e4) = all_36_1
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | GROUND_INST: instantiating (25) with all_16_2, all_36_1, e4,
% 247.16/58.39 | | | | | | | | | e1, simplifying with (60), (169) gives:
% 247.16/58.39 | | | | | | | | | (170) all_36_1 = all_16_2
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | BETA: splitting (66) gives:
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | Case 1:
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | (171) ~ (all_32_2 = e2)
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REDUCE: (3), (171) imply:
% 247.16/58.39 | | | | | | | | | | (172) ~ (all_20_2 = e2)
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REF_CLOSE: (7), (10), (11), (17), (19), (24), (25), (27),
% 247.16/58.39 | | | | | | | | | | (29), (31), (36), (39), (47), (49), (55), (58),
% 247.16/58.39 | | | | | | | | | | (60), (63), (91), (99), (104), (112), (114),
% 247.16/58.39 | | | | | | | | | | (121), (126), (136), (140), (154), (157), (158),
% 247.16/58.39 | | | | | | | | | | (172) are inconsistent by sub-proof #16.
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | Case 2:
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | (173) all_32_2 = e2
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REF_CLOSE: (3), (25), (51), (61), (76), (77), (88), (125),
% 247.16/58.39 | | | | | | | | | | (141), (161), (173) are inconsistent by sub-proof
% 247.16/58.39 | | | | | | | | | | #15.
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | End of split
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | Case 2:
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | (174) ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 &
% 247.16/58.39 | | | | | | | | | $i(all_36_1)
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | ALPHA: (174) implies:
% 247.16/58.39 | | | | | | | | | (175) ~ (all_36_1 = e2)
% 247.16/58.39 | | | | | | | | | (176) op(e1, e4) = all_36_1
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | GROUND_INST: instantiating (25) with all_16_2, all_36_1, e4,
% 247.16/58.39 | | | | | | | | | e1, simplifying with (60), (176) gives:
% 247.16/58.39 | | | | | | | | | (177) all_36_1 = all_16_2
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | BETA: splitting (66) gives:
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | | Case 1:
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | (178) ~ (all_32_2 = e2)
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REDUCE: (3), (178) imply:
% 247.16/58.39 | | | | | | | | | | (179) ~ (all_20_2 = e2)
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REF_CLOSE: (7), (10), (11), (17), (19), (24), (25), (27),
% 247.16/58.39 | | | | | | | | | | (29), (31), (36), (39), (47), (49), (55), (58),
% 247.16/58.39 | | | | | | | | | | (60), (63), (91), (99), (104), (112), (114),
% 247.16/58.39 | | | | | | | | | | (121), (126), (136), (140), (154), (157), (158),
% 247.16/58.39 | | | | | | | | | | (179) are inconsistent by sub-proof #16.
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | Case 2:
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | (180) all_32_2 = e2
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | | REF_CLOSE: (3), (25), (51), (61), (76), (77), (88), (125),
% 247.16/58.39 | | | | | | | | | | (141), (161), (180) are inconsistent by sub-proof
% 247.16/58.39 | | | | | | | | | | #15.
% 247.16/58.39 | | | | | | | | | |
% 247.16/58.39 | | | | | | | | | End of split
% 247.16/58.39 | | | | | | | | |
% 247.16/58.39 | | | | | | | | End of split
% 247.16/58.39 | | | | | | | |
% 247.16/58.39 | | | | | | | End of split
% 247.16/58.39 | | | | | | |
% 247.16/58.39 | | | | | | End of split
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | Case 2:
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | | (181) all_28_2 = e3
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | | REF_CLOSE: (19), (25), (57), (70), (73), (93), (101), (116), (160),
% 247.16/58.39 | | | | | | (181) are inconsistent by sub-proof #115.
% 247.16/58.39 | | | | | |
% 247.16/58.39 | | | | | End of split
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | Case 2:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | (182) all_22_2 = e1
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | REF_CLOSE: (18), (21), (25), (31), (32), (35), (38), (41), (44), (54),
% 247.16/58.39 | | | | | (63), (64), (74), (86), (90), (97), (102), (105), (107),
% 247.16/58.39 | | | | | (110), (112), (114), (118), (119), (131), (135), (139),
% 247.16/58.39 | | | | | (142), (143), (147), (158), (159), (182) are inconsistent
% 247.16/58.39 | | | | | by sub-proof #26.
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | End of split
% 247.16/58.39 | | | |
% 247.16/58.39 | | | Case 2:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | (183) all_20_2 = e4
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | REDUCE: (94), (183) imply:
% 247.16/58.39 | | | | (184) op(all_34_2, e4) = e0
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | BETA: splitting (39) gives:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | Case 1:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | (185) ~ (all_34_2 = e2)
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | REF_CLOSE: (24), (25), (29), (36), (49), (55), (60), (63), (104),
% 247.16/58.39 | | | | | (112), (126), (140), (158), (185) are inconsistent by
% 247.16/58.39 | | | | | sub-proof #17.
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | Case 2:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | (186) all_34_2 = e2
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | REF_CLOSE: (22), (25), (67), (123), (134), (154), (157), (184), (186)
% 247.16/58.39 | | | | | are inconsistent by sub-proof #25.
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | End of split
% 247.16/58.39 | | | |
% 247.16/58.39 | | | End of split
% 247.16/58.39 | | |
% 247.16/58.39 | | Case 2:
% 247.16/58.39 | | |
% 247.16/58.39 | | | (187) all_16_2 = e2
% 247.16/58.39 | | |
% 247.16/58.39 | | | REF_CLOSE: (25), (28), (29), (55), (78), (112), (123), (124), (135),
% 247.16/58.39 | | | (155), (187) are inconsistent by sub-proof #20.
% 247.16/58.39 | | |
% 247.16/58.39 | | End of split
% 247.16/58.39 | |
% 247.16/58.39 | Case 2:
% 247.16/58.39 | |
% 247.16/58.39 | | (188) all_12_2 = e2
% 247.16/58.39 | | (189) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2, all_12_1) =
% 247.16/58.39 | | all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) &
% 247.16/58.39 | | op(e4, e2) = all_12_1 & $i(all_12_1))
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (92), (188) imply:
% 247.16/58.39 | | (190) ~ (all_244_24 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (6), (188) imply:
% 247.16/58.39 | | (191) ~ (all_100_2 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (89), (188) imply:
% 247.16/58.39 | | (192) ~ (all_64_2 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (75), (188) imply:
% 247.16/58.39 | | (193) ~ (all_28_2 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (40), (188) imply:
% 247.16/58.39 | | (194) ~ (all_20_2 = e2)
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (14), (188) imply:
% 247.16/58.39 | | (195) op(e2, all_30_2) = e4
% 247.16/58.39 | |
% 247.16/58.39 | | REDUCE: (148), (188) imply:
% 247.16/58.39 | | (196) op(e2, e4) = e0
% 247.16/58.39 | |
% 247.16/58.39 | | BETA: splitting (99) gives:
% 247.16/58.39 | |
% 247.16/58.39 | | Case 1:
% 247.16/58.39 | | |
% 247.16/58.39 | | | (197) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0,
% 247.16/58.39 | | | e3) = e2)
% 247.16/58.39 | | |
% 247.16/58.39 | | | BETA: splitting (197) gives:
% 247.16/58.39 | | |
% 247.16/58.39 | | | Case 1:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | (198) all_252_20 = e2 & op(e0, e4) = e2
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | ALPHA: (198) implies:
% 247.16/58.39 | | | | (199) all_252_20 = e2
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | BETA: splitting (189) gives:
% 247.16/58.39 | | | |
% 247.16/58.39 | | | | Case 1:
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | (200) ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2, all_12_1)
% 247.16/58.39 | | | | | = all_12_0 & $i(all_12_0) & $i(all_12_1)
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | ALPHA: (200) implies:
% 247.16/58.39 | | | | | (201) ~ (all_12_0 = e3)
% 247.16/58.39 | | | | | (202) op(e2, all_12_1) = all_12_0
% 247.16/58.39 | | | | | (203) op(e4, e2) = all_12_1
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | GROUND_INST: instantiating (25) with all_64_2, e0, e4, e2, simplifying
% 247.16/58.39 | | | | | with (123), (196) gives:
% 247.16/58.39 | | | | | (204) all_64_2 = e0
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | GROUND_INST: instantiating (25) with e1, all_12_1, e2, e4, simplifying
% 247.16/58.39 | | | | | with (50), (203) gives:
% 247.16/58.39 | | | | | (205) all_12_1 = e1
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | COMBINE_EQS: (9), (204) imply:
% 247.16/58.39 | | | | | (206) all_134_2 = e0
% 247.16/58.39 | | | | |
% 247.16/58.39 | | | | | REDUCE: (28), (204) imply:
% 247.16/58.40 | | | | | (207) ~ (all_244_8 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (46), (204) imply:
% 247.16/58.40 | | | | | (208) ~ (all_100_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (34), (204) imply:
% 247.16/58.40 | | | | | (209) ~ (all_40_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | SIMP: (209) implies:
% 247.16/58.40 | | | | | (210) ~ (all_40_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (100), (204) imply:
% 247.16/58.40 | | | | | (211) ~ (all_38_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | SIMP: (211) implies:
% 247.16/58.40 | | | | | (212) ~ (all_38_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (130), (204) imply:
% 247.16/58.40 | | | | | (213) ~ (all_16_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | SIMP: (213) implies:
% 247.16/58.40 | | | | | (214) ~ (all_16_2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (153), (204) imply:
% 247.16/58.40 | | | | | (215) ~ (e4 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | SIMP: (215) implies:
% 247.16/58.40 | | | | | (216) ~ (e4 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (192), (204) imply:
% 247.16/58.40 | | | | | (217) ~ (e2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | SIMP: (217) implies:
% 247.16/58.40 | | | | | (218) ~ (e2 = e0)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (96), (204) imply:
% 247.16/58.40 | | | | | (219) op(e0, e1) = e4
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (202), (205) imply:
% 247.16/58.40 | | | | | (220) op(e2, e1) = all_12_0
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (78), (204) imply:
% 247.16/58.40 | | | | | (221) op(e1, e0) = e2
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | BETA: splitting (79) gives:
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | Case 1:
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | (222) ~ (all_46_2 = e2)
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | REDUCE: (150), (222) imply:
% 247.16/58.40 | | | | | | (223) ~ (all_36_2 = e2)
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | BETA: splitting (98) gives:
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | Case 1:
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | (224) ~ (all_134_2 = e0)
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | REDUCE: (206), (224) imply:
% 247.16/58.40 | | | | | | | (225) $false
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | CLOSE: (225) is inconsistent.
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | Case 2:
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | (226) ( ~ (all_134_0 = e3) & op(e4, e0) = all_134_1 & op(e0,
% 247.16/58.40 | | | | | | | all_134_1) = all_134_0 & $i(all_134_0) &
% 247.16/58.40 | | | | | | | $i(all_134_1)) | ( ~ (all_134_1 = e1) & op(e4, e0) =
% 247.16/58.40 | | | | | | | all_134_1 & $i(all_134_1))
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | BETA: splitting (62) gives:
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | (227) ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2,
% 247.16/58.40 | | | | | | | | e4) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | ALPHA: (227) implies:
% 247.16/58.40 | | | | | | | | (228) op(e2, e4) = all_4_1
% 247.16/58.40 | | | | | | | | (229) op(e4, all_4_1) = all_4_0
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | BETA: splitting (226) gives:
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | (230) ~ (all_134_0 = e3) & op(e4, e0) = all_134_1 & op(e0,
% 247.16/58.40 | | | | | | | | | all_134_1) = all_134_0 & $i(all_134_0) &
% 247.16/58.40 | | | | | | | | | $i(all_134_1)
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | ALPHA: (230) implies:
% 247.16/58.40 | | | | | | | | | (231) op(e4, e0) = all_134_1
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (12), (13), (15),
% 247.16/58.40 | | | | | | | | | (16), (19), (20), (23), (24), (25), (26), (29),
% 247.16/58.40 | | | | | | | | | (30), (31), (33), (36), (37), (43), (45), (47),
% 247.16/58.40 | | | | | | | | | (48), (49), (52), (53), (54), (58), (59), (60),
% 247.16/58.40 | | | | | | | | | (63), (65), (68), (69), (71), (74), (80), (82),
% 247.16/58.40 | | | | | | | | | (83), (84), (87), (91), (95), (97), (103), (106),
% 247.16/58.40 | | | | | | | | | (107), (109), (110), (111), (112), (113), (114),
% 247.16/58.40 | | | | | | | | | (115), (116), (117), (120), (121), (122), (123),
% 247.16/58.40 | | | | | | | | | (126), (127), (129), (132), (133), (136), (138),
% 247.16/58.40 | | | | | | | | | (142), (144), (145), (146), (149), (153), (191),
% 247.16/58.40 | | | | | | | | | (193), (194), (195), (199), (207), (208), (210),
% 247.16/58.40 | | | | | | | | | (212), (214), (216), (218), (219), (221), (223),
% 247.16/58.40 | | | | | | | | | (228), (229), (231) are inconsistent by sub-proof
% 247.16/58.40 | | | | | | | | | #2.
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | (232) ~ (all_134_1 = e1) & op(e4, e0) = all_134_1 &
% 247.16/58.40 | | | | | | | | | $i(all_134_1)
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | ALPHA: (232) implies:
% 247.16/58.40 | | | | | | | | | (233) op(e4, e0) = all_134_1
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (12), (13), (15),
% 247.16/58.40 | | | | | | | | | (16), (19), (20), (23), (24), (25), (26), (29),
% 247.16/58.40 | | | | | | | | | (30), (31), (33), (36), (37), (43), (45), (47),
% 247.16/58.40 | | | | | | | | | (48), (49), (52), (53), (54), (58), (59), (60),
% 247.16/58.40 | | | | | | | | | (63), (65), (68), (69), (71), (74), (80), (82),
% 247.16/58.40 | | | | | | | | | (83), (84), (87), (91), (95), (97), (103), (106),
% 247.16/58.40 | | | | | | | | | (107), (109), (110), (111), (112), (113), (114),
% 247.16/58.40 | | | | | | | | | (115), (116), (117), (120), (121), (122), (123),
% 247.16/58.40 | | | | | | | | | (126), (127), (129), (132), (133), (136), (138),
% 247.16/58.40 | | | | | | | | | (142), (144), (145), (146), (149), (153), (191),
% 247.16/58.40 | | | | | | | | | (193), (194), (195), (199), (207), (208), (210),
% 247.16/58.40 | | | | | | | | | (212), (214), (216), (218), (219), (221), (223),
% 247.16/58.40 | | | | | | | | | (228), (229), (233) are inconsistent by sub-proof
% 247.16/58.40 | | | | | | | | | #2.
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | End of split
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | (234) ~ (all_4_1 = e3) & op(e2, e4) = all_4_1 & $i(all_4_1)
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | ALPHA: (234) implies:
% 247.16/58.40 | | | | | | | | (235) ~ (all_4_1 = e3)
% 247.16/58.40 | | | | | | | | (236) op(e2, e4) = all_4_1
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | BETA: splitting (2) gives:
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | (237) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0
% 247.16/58.40 | | | | | | | | | & op(e3, e4) = e0)
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | BETA: splitting (237) gives:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | (238) all_252_0 = e0 & op(e4, e4) = e0
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | ALPHA: (238) implies:
% 247.16/58.40 | | | | | | | | | | (239) all_252_0 = e0
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | REF_CLOSE: (16), (23), (25), (26), (29), (31), (43), (45),
% 247.16/58.40 | | | | | | | | | | (48), (54), (60), (65), (71), (103), (107), (110),
% 247.16/58.40 | | | | | | | | | | (111), (123), (126), (132), (133), (136), (149),
% 247.16/58.40 | | | | | | | | | | (153), (199), (207), (210), (212), (216), (239)
% 247.16/58.40 | | | | | | | | | | are inconsistent by sub-proof #11.
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | (240) all_252_2 = e0 & op(e3, e4) = e0
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | REF_CLOSE: (25), (103), (208), (240) are inconsistent by
% 247.16/58.40 | | | | | | | | | | sub-proof #43.
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | End of split
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | (241) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0
% 247.16/58.40 | | | | | | | | | & op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4)
% 247.16/58.40 | | | | | | | | | = e0)
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | BETA: splitting (241) gives:
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | (242) all_252_6 = e0 & op(e2, e4) = e0
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | GROUND_INST: instantiating (25) with all_20_2, e4, e1, e0,
% 247.16/58.40 | | | | | | | | | | simplifying with (114), (219) gives:
% 247.16/58.40 | | | | | | | | | | (243) all_20_2 = e4
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | GROUND_INST: instantiating (25) with all_34_2, e2, e0, e1,
% 247.16/58.40 | | | | | | | | | | simplifying with (36), (221) gives:
% 247.16/58.40 | | | | | | | | | | (244) all_34_2 = e2
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | GROUND_INST: instantiating (25) with e0, all_4_1, e4, e2,
% 247.16/58.40 | | | | | | | | | | simplifying with (196), (236) gives:
% 247.16/58.40 | | | | | | | | | | (245) all_4_1 = e0
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | REDUCE: (81), (244) imply:
% 247.16/58.40 | | | | | | | | | | (246) ~ (all_48_2 = e2)
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | REDUCE: (235), (245) imply:
% 247.16/58.40 | | | | | | | | | | (247) ~ (e3 = e0)
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | BETA: splitting (145) gives:
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | (248) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 =
% 247.16/58.40 | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | REF_CLOSE: (20), (25), (103), (142), (191), (248) are
% 247.16/58.40 | | | | | | | | | | | inconsistent by sub-proof #232.
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | (249) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 =
% 247.16/58.40 | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 247.16/58.40 | | | | | | | | | | | op(e3, e0) = e2)
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | BETA: splitting (249) gives:
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | (250) all_252_5 = e2 & op(e3, e2) = e2
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | REF_CLOSE: (12), (23), (25), (26), (29), (43), (47), (49),
% 247.16/58.40 | | | | | | | | | | | | (52), (53), (65), (71), (106), (111), (120),
% 247.16/58.40 | | | | | | | | | | | | (123), (126), (127), (129), (144), (153), (193),
% 247.16/58.40 | | | | | | | | | | | | (207), (216), (218), (250) are inconsistent by
% 247.16/58.40 | | | | | | | | | | | | sub-proof #3.
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | (251) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17
% 247.16/58.40 | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | BETA: splitting (251) gives:
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | Case 1:
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | | (252) all_252_10 = e2 & op(e3, e1) = e2
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | | ALPHA: (252) implies:
% 247.16/58.40 | | | | | | | | | | | | | (253) op(e3, e1) = e2
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | | REF_CLOSE: (25), (74), (223), (253) are inconsistent by
% 247.16/58.40 | | | | | | | | | | | | | sub-proof #984.
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | | (254) all_252_17 = e2 & op(e3, e0) = e2
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | | REF_CLOSE: (25), (115), (246), (254) are inconsistent by
% 247.16/58.40 | | | | | | | | | | | | | sub-proof #653.
% 247.16/58.40 | | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | | End of split
% 247.16/58.40 | | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | | End of split
% 247.16/58.40 | | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | End of split
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | Case 2:
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | (255) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 =
% 247.16/58.40 | | | | | | | | | | e0 & op(e0, e4) = e0)
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | | REF_CLOSE: (25), (60), (199), (214), (218), (255) are
% 247.16/58.40 | | | | | | | | | | inconsistent by sub-proof #42.
% 247.16/58.40 | | | | | | | | | |
% 247.16/58.40 | | | | | | | | | End of split
% 247.16/58.40 | | | | | | | | |
% 247.16/58.40 | | | | | | | | End of split
% 247.16/58.40 | | | | | | | |
% 247.16/58.40 | | | | | | | End of split
% 247.16/58.40 | | | | | | |
% 247.16/58.40 | | | | | | End of split
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | Case 2:
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | (256) all_46_2 = e2
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | COMBINE_EQS: (150), (256) imply:
% 247.16/58.40 | | | | | | (257) all_36_2 = e2
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | | REF_CLOSE: (25), (31), (131), (137), (152), (201), (220), (257) are
% 247.16/58.40 | | | | | | inconsistent by sub-proof #18.
% 247.16/58.40 | | | | | |
% 247.16/58.40 | | | | | End of split
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | Case 2:
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | (258) ~ (all_12_1 = e1) & op(e4, e2) = all_12_1 & $i(all_12_1)
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | ALPHA: (258) implies:
% 247.16/58.40 | | | | | (259) ~ (all_12_1 = e1)
% 247.16/58.40 | | | | | (260) op(e4, e2) = all_12_1
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | GROUND_INST: instantiating (25) with e1, all_12_1, e2, e4, simplifying
% 247.16/58.40 | | | | | with (50), (260) gives:
% 247.16/58.40 | | | | | (261) all_12_1 = e1
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | REDUCE: (259), (261) imply:
% 247.16/58.40 | | | | | (262) $false
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | | CLOSE: (262) is inconsistent.
% 247.16/58.40 | | | | |
% 247.16/58.40 | | | | End of split
% 247.16/58.40 | | | |
% 247.16/58.40 | | | Case 2:
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | (263) all_252_21 = e2 & op(e0, e3) = e2
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | ALPHA: (263) implies:
% 247.16/58.40 | | | | (264) op(e0, e3) = e2
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | REF_CLOSE: (19), (25), (91), (264) are inconsistent by sub-proof #987.
% 247.16/58.40 | | | |
% 247.16/58.40 | | | End of split
% 247.16/58.40 | | |
% 247.16/58.40 | | Case 2:
% 247.16/58.40 | | |
% 247.16/58.40 | | | (265) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.16/58.40 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.16/58.40 | | |
% 247.16/58.40 | | | BETA: splitting (265) gives:
% 247.16/58.40 | | |
% 247.16/58.40 | | | Case 1:
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | (266) all_252_22 = e2 & op(e0, e2) = e2
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | REF_CLOSE: (25), (47), (193), (266) are inconsistent by sub-proof #979.
% 247.16/58.40 | | | |
% 247.16/58.40 | | | Case 2:
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | (267) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 247.16/58.40 | | | | e0) = e2)
% 247.16/58.40 | | | |
% 247.16/58.40 | | | | REF_CLOSE: (25), (27), (114), (190), (194), (267) are inconsistent by
% 247.16/58.40 | | | | sub-proof #977.
% 247.16/58.40 | | | |
% 247.16/58.40 | | | End of split
% 247.16/58.40 | | |
% 247.16/58.40 | | End of split
% 247.16/58.40 | |
% 247.16/58.40 | End of split
% 247.16/58.40 |
% 247.16/58.40 End of proof
% 247.16/58.40
% 247.16/58.40 Sub-proof #2 shows that the following formulas are inconsistent:
% 247.16/58.40 ----------------------------------------------------------------
% 247.16/58.40 (1) all_240_2 = all_48_2
% 247.16/58.40 (2) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 247.16/58.40 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 247.16/58.40 | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.16/58.40 (3) ~ (all_26_2 = e2)
% 247.16/58.40 (4) ~ (all_8_2 = e4)
% 247.16/58.40 (5) op(all_4_2, e2) = e1
% 247.16/58.40 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 247.16/58.40 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 247.16/58.40 (all_252_16 = e3 & op(e4, e0) = e3)
% 247.16/58.40 (7) ~ (all_244_8 = e0)
% 247.16/58.40 (8) op(all_6_2, e2) = e4
% 247.16/58.40 (9) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 247.16/58.40 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 247.16/58.40 | (all_252_21 = e2 & op(e0, e3) = e2)
% 247.16/58.40 (10) op(e4, e0) = all_30_2
% 247.16/58.40 (11) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 247.16/58.40 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 247.16/58.40 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.40 (12) ~ (all_22_2 = e2)
% 247.16/58.40 (13) ~ (all_244_3 = e2)
% 247.16/58.40 (14) ~ (e2 = e0)
% 247.16/58.40 (15) ~ (e1 = e0)
% 247.16/58.40 (16) ~ (all_62_2 = e2)
% 247.16/58.40 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.40 (18) ~ (e3 = e2)
% 247.16/58.40 (19) ~ (e4 = e0)
% 247.16/58.40 (20) op(e2, e2) = all_244_8
% 247.16/58.40 (21) op(all_84_2, all_100_2) = e3
% 247.16/58.40 (22) op(e2, e1) = all_38_2
% 247.16/58.40 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 247.16/58.40 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 247.16/58.40 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 247.16/58.40 (24) op(e1, e0) = all_34_2
% 247.16/58.40 (25) ~ (all_240_2 = e4) | ( ~ (all_240_0 = e1) & op(e4, all_240_1) =
% 247.16/58.40 all_240_0 & op(e0, e4) = all_240_1 & $i(all_240_0) & $i(all_240_1)) |
% 247.16/58.40 ( ~ (all_240_1 = e2) & op(e0, e4) = all_240_1 & $i(all_240_1))
% 247.16/58.40 (26) ~ (all_36_2 = e2)
% 247.16/58.40 (27) op(e4, e0) = all_134_1
% 247.16/58.40 (28) ~ (e2 = e1)
% 247.16/58.40 (29) all_252_7 = e4
% 247.16/58.40 (30) op(e0, e2) = all_28_2
% 247.16/58.40 (31) ~ (e4 = e1)
% 247.16/58.40 (32) all_252_14 = e4
% 247.16/58.40 (33) op(all_6_2, all_64_2) = e2
% 247.16/58.40 (34) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 247.16/58.40 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 247.16/58.40 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 247.16/58.40 (35) ~ (all_16_2 = e4)
% 247.16/58.40 (36) op(all_34_2, e0) = e1
% 247.16/58.40 (37) ~ (all_244_3 = e4)
% 247.16/58.40 (38) op(e1, e4) = all_16_2
% 247.16/58.41 (39) ~ (all_100_2 = e0)
% 247.16/58.41 (40) op(e1, e3) = all_62_2
% 247.16/58.41 (41) ~ (e3 = e0)
% 247.16/58.41 (42) ~ (all_38_2 = e0)
% 247.16/58.41 (43) ~ (all_48_2 = all_36_2)
% 247.16/58.41 (44) ~ (all_84_2 = e4)
% 247.16/58.41 (45) ~ (e3 = e1)
% 247.16/58.41 (46) op(e3, e1) = all_36_2
% 247.16/58.41 (47) op(e1, e0) = e2
% 247.16/58.41 (48) ~ (all_40_2 = all_34_2)
% 247.16/58.41 (49) op(e4, all_4_1) = all_4_0
% 247.16/58.41 (50) ~ (all_48_2 = all_8_2)
% 247.16/58.41 (51) op(e4, e3) = e2
% 247.16/58.41 (52) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 247.16/58.41 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 247.16/58.41 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 247.16/58.41 (53) ~ (all_244_15 = all_34_2)
% 247.16/58.41 (54) ~ (all_28_2 = e2)
% 247.16/58.41 (55) op(e0, e1) = e4
% 247.16/58.41 (56) op(e0, e3) = all_22_2
% 247.16/58.41 (57) ~ (all_40_2 = e0)
% 247.16/58.41 (58) all_252_20 = e2
% 247.16/58.41 (59) op(e2, all_30_2) = e4
% 247.16/58.41 (60) op(all_84_2, e3) = e4
% 247.16/58.41 (61) op(e4, e1) = all_26_2
% 247.16/58.41 (62) op(e3, e4) = all_100_2
% 247.16/58.41 (63) ~ (all_100_2 = e2)
% 247.16/58.41 (64) op(all_8_2, e4) = e2
% 247.16/58.41 (65) op(e4, e4) = all_244_0
% 247.16/58.41 (66) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 247.16/58.41 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 247.16/58.41 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.16/58.41 (67) ~ (all_244_0 = e1)
% 247.16/58.41 (68) ~ (e4 = e3)
% 247.16/58.41 (69) op(e1, e1) = all_244_15
% 247.16/58.41 (70) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 247.16/58.41 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 247.16/58.41 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 247.16/58.41 (71) op(e0, e1) = all_20_2
% 247.16/58.41 (72) op(e3, e0) = all_48_2
% 247.16/58.41 (73) op(all_48_2, e0) = e3
% 247.16/58.41 (74) ~ (all_100_2 = all_48_2)
% 247.16/58.41 (75) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.16/58.41 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.16/58.41 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.16/58.41 (76) op(all_4_2, all_38_2) = e2
% 247.16/58.41 (77) op(e4, e3) = all_84_2
% 247.16/58.41 (78) op(e2, e4) = all_64_2
% 247.16/58.41 (79) ~ (e4 = e2)
% 247.16/58.41 (80) all_252_4 = e1
% 247.16/58.41 (81) op(e3, e2) = all_8_2
% 247.16/58.41 (82) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.41 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.41 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.41 (83) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.41 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.41 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.41 (84) op(e2, e0) = all_40_2
% 247.16/58.41 (85) ~ (all_244_3 = all_48_2)
% 247.16/58.41 (86) op(e2, e4) = all_4_1
% 247.16/58.41 (87) op(e3, e3) = all_244_3
% 247.16/58.41 (88) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 247.16/58.41 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 247.16/58.41 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 247.16/58.41 (89) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 247.16/58.41 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 247.16/58.41 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 247.16/58.41 (90) ~ (all_26_2 = all_20_2)
% 247.16/58.41 (91) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.41 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.41 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.41 (92) ~ (all_64_2 = e4)
% 247.16/58.41 (93) ~ (all_16_2 = e0)
% 247.16/58.41 (94) ~ (all_20_2 = e2)
% 247.16/58.41
% 247.16/58.41 Begin of proof
% 247.16/58.41 |
% 247.16/58.41 | BETA: splitting (25) gives:
% 247.16/58.41 |
% 247.16/58.41 | Case 1:
% 247.16/58.41 | |
% 247.16/58.41 | | (95) ~ (all_240_2 = e4)
% 247.16/58.41 | |
% 247.16/58.41 | | REDUCE: (1), (95) imply:
% 247.16/58.41 | | (96) ~ (all_48_2 = e4)
% 247.16/58.41 | |
% 247.16/58.41 | | BETA: splitting (2) gives:
% 247.16/58.41 | |
% 247.16/58.41 | | Case 1:
% 247.16/58.41 | | |
% 247.16/58.41 | | | (97) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4)
% 247.16/58.41 | | | = e0)
% 247.16/58.41 | | |
% 247.16/58.41 | | | BETA: splitting (97) gives:
% 247.16/58.41 | | |
% 247.16/58.41 | | | Case 1:
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | (98) all_252_0 = e0 & op(e4, e4) = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | ALPHA: (98) implies:
% 247.16/58.41 | | | | (99) all_252_0 = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REF_CLOSE: (7), (11), (15), (17), (18), (19), (20), (22), (28), (29),
% 247.16/58.41 | | | | (31), (35), (38), (41), (42), (45), (57), (58), (62), (65),
% 247.16/58.41 | | | | (67), (68), (78), (79), (82), (83), (84), (91), (92), (99)
% 247.16/58.41 | | | | are inconsistent by sub-proof #11.
% 247.16/58.41 | | | |
% 247.16/58.41 | | | Case 2:
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | (100) all_252_2 = e0 & op(e3, e4) = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REF_CLOSE: (17), (39), (62), (100) are inconsistent by sub-proof #43.
% 247.16/58.41 | | | |
% 247.16/58.41 | | | End of split
% 247.16/58.41 | | |
% 247.16/58.41 | | Case 2:
% 247.16/58.41 | | |
% 247.16/58.41 | | | (101) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1,
% 247.16/58.41 | | | e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.16/58.41 | | |
% 247.16/58.41 | | | BETA: splitting (101) gives:
% 247.16/58.41 | | |
% 247.16/58.41 | | | Case 1:
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | (102) all_252_6 = e0 & op(e2, e4) = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | ALPHA: (102) implies:
% 247.16/58.41 | | | | (103) all_252_6 = e0
% 247.16/58.41 | | | | (104) op(e2, e4) = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | GROUND_INST: instantiating (17) with all_20_2, e4, e1, e0, simplifying
% 247.16/58.41 | | | | with (55), (71) gives:
% 247.16/58.41 | | | | (105) all_20_2 = e4
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | GROUND_INST: instantiating (17) with all_34_2, e2, e0, e1, simplifying
% 247.16/58.41 | | | | with (24), (47) gives:
% 247.16/58.41 | | | | (106) all_34_2 = e2
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | GROUND_INST: instantiating (17) with e0, all_4_1, e4, e2, simplifying
% 247.16/58.41 | | | | with (86), (104) gives:
% 247.16/58.41 | | | | (107) all_4_1 = e0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | GROUND_INST: instantiating (17) with all_30_2, all_134_1, e0, e4,
% 247.16/58.41 | | | | simplifying with (10), (27) gives:
% 247.16/58.41 | | | | (108) all_134_1 = all_30_2
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REDUCE: (53), (106) imply:
% 247.16/58.41 | | | | (109) ~ (all_244_15 = e2)
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REDUCE: (48), (106) imply:
% 247.16/58.41 | | | | (110) ~ (all_40_2 = e2)
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REDUCE: (90), (105) imply:
% 247.16/58.41 | | | | (111) ~ (all_26_2 = e4)
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REDUCE: (36), (106) imply:
% 247.16/58.41 | | | | (112) op(e2, e0) = e1
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REDUCE: (49), (107) imply:
% 247.16/58.41 | | | | (113) op(e4, e0) = all_4_0
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | BETA: splitting (70) gives:
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | Case 1:
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | (114) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3,
% 247.16/58.41 | | | | | e3) = e4)
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | BETA: splitting (114) gives:
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | Case 1:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | (115) all_252_2 = e4 & op(e3, e4) = e4
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | ALPHA: (115) implies:
% 247.16/58.41 | | | | | | (116) all_252_2 = e4
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | BETA: splitting (91) gives:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | Case 1:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | (117) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 247.16/58.41 | | | | | | | op(e3, e4) = e1)
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | REF_CLOSE: (17), (31), (65), (67), (116), (117) are inconsistent
% 247.16/58.41 | | | | | | | by sub-proof #10.
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | Case 2:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | (118) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 247.16/58.41 | | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | BETA: splitting (118) gives:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | (119) all_252_6 = e1 & op(e2, e4) = e1
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | REF_CLOSE: (15), (103), (119) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | #545.
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | (120) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1
% 247.16/58.41 | | | | | | | | & op(e0, e4) = e1)
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | BETA: splitting (120) gives:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (121) all_252_12 = e1 & op(e1, e4) = e1
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | ALPHA: (121) implies:
% 247.16/58.41 | | | | | | | | | (122) all_252_12 = e1
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | BETA: splitting (82) gives:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | (123) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 247.16/58.41 | | | | | | | | | | e3 & op(e3, e4) = e3)
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | BETA: splitting (123) gives:
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | (124) all_252_0 = e3 & op(e4, e4) = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | ALPHA: (124) implies:
% 247.16/58.41 | | | | | | | | | | | (125) all_252_0 = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | BETA: splitting (23) gives:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | (126) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 247.16/58.41 | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | REF_CLOSE: (17), (19), (31), (44), (58), (68), (77), (79),
% 247.16/58.41 | | | | | | | | | | | | (83), (103), (116), (122), (125), (126) are
% 247.16/58.41 | | | | | | | | | | | | inconsistent by sub-proof #8.
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | (127) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 247.16/58.41 | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 247.16/58.41 | | | | | | | | | | | | op(e4, e0) = e4)
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | BETA: splitting (127) gives:
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | (128) all_252_4 = e4 & op(e4, e2) = e4
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | ALPHA: (128) implies:
% 247.16/58.41 | | | | | | | | | | | | | (129) all_252_4 = e4
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | COMBINE_EQS: (80), (129) imply:
% 247.16/58.41 | | | | | | | | | | | | | (130) e4 = e1
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | REF_CLOSE: (19), (31), (58), (68), (79), (83), (103), (116),
% 247.16/58.41 | | | | | | | | | | | | | (122), (125), (130) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | | | | | | #148.
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | (131) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 247.16/58.41 | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | BETA: splitting (131) gives:
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | (132) all_252_9 = e4 & op(e4, e1) = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | REF_CLOSE: (17), (61), (111), (132) are inconsistent by
% 247.16/58.41 | | | | | | | | | | | | | | sub-proof #114.
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | (133) all_252_16 = e4 & op(e4, e0) = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | ALPHA: (133) implies:
% 247.16/58.41 | | | | | | | | | | | | | | (134) op(e4, e0) = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, e4, e0, e4,
% 247.16/58.41 | | | | | | | | | | | | | | simplifying with (10), (134) gives:
% 247.16/58.41 | | | | | | | | | | | | | | (135) all_30_2 = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, all_4_0, e0, e4,
% 247.16/58.41 | | | | | | | | | | | | | | simplifying with (10), (113) gives:
% 247.16/58.41 | | | | | | | | | | | | | | (136) all_30_2 = all_4_0
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | COMBINE_EQS: (135), (136) imply:
% 247.16/58.41 | | | | | | | | | | | | | | (137) all_4_0 = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | REDUCE: (59), (135) imply:
% 247.16/58.41 | | | | | | | | | | | | | | (138) op(e2, e4) = e4
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | | REF_CLOSE: (17), (78), (92), (138) are inconsistent by
% 247.16/58.41 | | | | | | | | | | | | | | sub-proof #129.
% 247.16/58.41 | | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | (139) all_252_2 = e3 & op(e3, e4) = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | ALPHA: (139) implies:
% 247.16/58.41 | | | | | | | | | | | (140) all_252_2 = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | COMBINE_EQS: (116), (140) imply:
% 247.16/58.41 | | | | | | | | | | | (141) e4 = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | REDUCE: (68), (141) imply:
% 247.16/58.41 | | | | | | | | | | | (142) $false
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | (143) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 247.16/58.41 | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 247.16/58.41 | | | | | | | | | | e4) = e3)
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | BETA: splitting (143) gives:
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | (144) all_252_6 = e3 & op(e2, e4) = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | ALPHA: (144) implies:
% 247.16/58.41 | | | | | | | | | | | (145) all_252_6 = e3
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | REF_CLOSE: (41), (103), (145) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | | | | #691.
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | (146) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 247.16/58.41 | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | BETA: splitting (146) gives:
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | (147) all_252_12 = e3 & op(e1, e4) = e3
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (31), (45), (58), (65), (67),
% 247.16/58.41 | | | | | | | | | | | | (91), (103), (116), (147) are inconsistent by
% 247.16/58.41 | | | | | | | | | | | | sub-proof #14.
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | (148) all_252_20 = e3 & op(e0, e4) = e3
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | | REF_CLOSE: (18), (58), (148) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | | | | | #539.
% 247.16/58.41 | | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | | |
% 247.16/58.41 | | | | | | | | | End of split
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (149) all_252_20 = e1 & op(e0, e4) = e1
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REF_CLOSE: (28), (58), (149) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | | #544.
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | End of split
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | End of split
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | End of split
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | Case 2:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | (150) all_252_3 = e4 & op(e3, e3) = e4
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | REF_CLOSE: (17), (37), (87), (150) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | #846.
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | End of split
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | Case 2:
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | (151) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 &
% 247.16/58.41 | | | | | op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | BETA: splitting (151) gives:
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | | Case 1:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | (152) all_252_5 = e4 & op(e3, e2) = e4
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | ALPHA: (152) implies:
% 247.16/58.41 | | | | | | (153) op(e3, e2) = e4
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | REF_CLOSE: (4), (17), (81), (153) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | #502.
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | Case 2:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | (154) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 247.16/58.41 | | | | | | op(e3, e0) = e4)
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | BETA: splitting (154) gives:
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | | Case 1:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | (155) all_252_10 = e4 & op(e3, e1) = e4
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | ALPHA: (155) implies:
% 247.16/58.41 | | | | | | | (156) all_252_10 = e4
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | BETA: splitting (66) gives:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | (157) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 &
% 247.16/58.41 | | | | | | | | op(e3, e1) = e2)
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | BETA: splitting (157) gives:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (158) all_252_9 = e2 & op(e4, e1) = e2
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REF_CLOSE: (3), (17), (61), (158) are inconsistent by
% 247.16/58.41 | | | | | | | | | sub-proof #970.
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (159) all_252_10 = e2 & op(e3, e1) = e2
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REF_CLOSE: (79), (156), (159) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | | | #433.
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | End of split
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | (160) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2
% 247.16/58.41 | | | | | | | | & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) =
% 247.16/58.41 | | | | | | | | e2)
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | BETA: splitting (160) gives:
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 1:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (161) all_252_11 = e2 & op(e2, e1) = e2
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | ALPHA: (161) implies:
% 247.16/58.41 | | | | | | | | | (162) op(e2, e1) = e2
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | GROUND_INST: instantiating (17) with all_40_2, e1, e0, e2,
% 247.16/58.41 | | | | | | | | | simplifying with (84), (112) gives:
% 247.16/58.41 | | | | | | | | | (163) all_40_2 = e1
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | GROUND_INST: instantiating (17) with all_38_2, e2, e1, e2,
% 247.16/58.41 | | | | | | | | | simplifying with (22), (162) gives:
% 247.16/58.41 | | | | | | | | | (164) all_38_2 = e2
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REDUCE: (110), (163) imply:
% 247.16/58.41 | | | | | | | | | (165) ~ (e2 = e1)
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REF_CLOSE: (5), (17), (76), (164), (165) are inconsistent by
% 247.16/58.41 | | | | | | | | | sub-proof #968.
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | Case 2:
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | (166) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 =
% 247.16/58.41 | | | | | | | | | e2 & op(e0, e1) = e2)
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | | REF_CLOSE: (17), (69), (71), (94), (109), (166) are
% 247.16/58.41 | | | | | | | | | inconsistent by sub-proof #965.
% 247.16/58.41 | | | | | | | | |
% 247.16/58.41 | | | | | | | | End of split
% 247.16/58.41 | | | | | | | |
% 247.16/58.41 | | | | | | | End of split
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | Case 2:
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | (167) all_252_17 = e4 & op(e3, e0) = e4
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | | REF_CLOSE: (17), (72), (96), (167) are inconsistent by sub-proof
% 247.16/58.41 | | | | | | | #706.
% 247.16/58.41 | | | | | | |
% 247.16/58.41 | | | | | | End of split
% 247.16/58.41 | | | | | |
% 247.16/58.41 | | | | | End of split
% 247.16/58.41 | | | | |
% 247.16/58.41 | | | | End of split
% 247.16/58.41 | | | |
% 247.16/58.41 | | | Case 2:
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | (168) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 = e0 & op(e0,
% 247.16/58.41 | | | | e4) = e0)
% 247.16/58.41 | | | |
% 247.16/58.41 | | | | REF_CLOSE: (14), (17), (38), (58), (93), (168) are inconsistent by
% 247.16/58.41 | | | | sub-proof #42.
% 247.16/58.41 | | | |
% 247.16/58.41 | | | End of split
% 247.16/58.41 | | |
% 247.16/58.41 | | End of split
% 247.16/58.42 | |
% 247.16/58.42 | Case 2:
% 247.16/58.42 | |
% 247.16/58.42 | | (169) all_240_2 = e4
% 247.16/58.42 | |
% 247.16/58.42 | | COMBINE_EQS: (1), (169) imply:
% 247.16/58.42 | | (170) all_48_2 = e4
% 247.16/58.42 | |
% 247.16/58.42 | | SIMP: (170) implies:
% 247.16/58.42 | | (171) all_48_2 = e4
% 247.16/58.42 | |
% 247.16/58.42 | | REDUCE: (74), (171) imply:
% 247.16/58.42 | | (172) ~ (all_100_2 = e4)
% 247.16/58.42 | |
% 247.16/58.42 | | REDUCE: (43), (171) imply:
% 247.16/58.42 | | (173) ~ (all_36_2 = e4)
% 247.16/58.42 | |
% 247.16/58.42 | | SIMP: (173) implies:
% 247.16/58.42 | | (174) ~ (all_36_2 = e4)
% 247.16/58.42 | |
% 247.16/58.42 | | REDUCE: (50), (171) imply:
% 247.16/58.42 | | (175) ~ (all_8_2 = e4)
% 247.16/58.42 | |
% 247.16/58.42 | | REDUCE: (73), (171) imply:
% 247.16/58.42 | | (176) op(e4, e0) = e3
% 247.16/58.42 | |
% 247.16/58.42 | | BETA: splitting (70) gives:
% 247.16/58.42 | |
% 247.16/58.42 | | Case 1:
% 247.16/58.42 | | |
% 247.16/58.42 | | | (177) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3)
% 247.16/58.42 | | | = e4)
% 247.16/58.42 | | |
% 247.16/58.42 | | | BETA: splitting (177) gives:
% 247.16/58.42 | | |
% 247.16/58.42 | | | Case 1:
% 247.16/58.42 | | | |
% 247.16/58.42 | | | | (178) all_252_2 = e4 & op(e3, e4) = e4
% 247.16/58.42 | | | |
% 247.16/58.42 | | | | ALPHA: (178) implies:
% 247.16/58.42 | | | | (179) all_252_2 = e4
% 247.16/58.42 | | | |
% 247.16/58.42 | | | | BETA: splitting (2) gives:
% 247.16/58.42 | | | |
% 247.16/58.42 | | | | Case 1:
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | | (180) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3,
% 247.16/58.42 | | | | | e4) = e0)
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | | REF_CLOSE: (7), (11), (15), (17), (18), (19), (20), (22), (28), (29),
% 247.16/58.42 | | | | | (31), (39), (41), (42), (45), (57), (58), (62), (65), (67),
% 247.16/58.42 | | | | | (68), (79), (82), (83), (84), (91), (179), (180) are
% 247.16/58.42 | | | | | inconsistent by sub-proof #7.
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | Case 2:
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | | (181) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 &
% 247.16/58.42 | | | | | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | | BETA: splitting (181) gives:
% 247.16/58.42 | | | | |
% 247.16/58.42 | | | | | Case 1:
% 247.16/58.42 | | | | | |
% 247.16/58.42 | | | | | | (182) all_252_6 = e0 & op(e2, e4) = e0
% 247.16/58.42 | | | | | |
% 247.16/58.42 | | | | | | ALPHA: (182) implies:
% 247.16/58.42 | | | | | | (183) all_252_6 = e0
% 247.16/58.42 | | | | | |
% 247.16/58.42 | | | | | | BETA: splitting (91) gives:
% 247.16/58.42 | | | | | |
% 247.16/58.42 | | | | | | Case 1:
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | | (184) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 247.16/58.42 | | | | | | | op(e3, e4) = e1)
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | | REF_CLOSE: (17), (31), (65), (67), (179), (184) are inconsistent
% 247.16/58.42 | | | | | | | by sub-proof #10.
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | Case 2:
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | | (185) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 247.16/58.42 | | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | | BETA: splitting (185) gives:
% 247.16/58.42 | | | | | | |
% 247.16/58.42 | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | | (186) all_252_6 = e1 & op(e2, e4) = e1
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | | REF_CLOSE: (15), (183), (186) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | #545.
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | | (187) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1
% 247.16/58.42 | | | | | | | | & op(e0, e4) = e1)
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | | BETA: splitting (187) gives:
% 247.16/58.42 | | | | | | | |
% 247.16/58.42 | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | |
% 247.16/58.42 | | | | | | | | | (188) all_252_12 = e1 & op(e1, e4) = e1
% 247.16/58.42 | | | | | | | | |
% 247.16/58.42 | | | | | | | | | ALPHA: (188) implies:
% 247.16/58.42 | | | | | | | | | (189) all_252_12 = e1
% 247.16/58.42 | | | | | | | | |
% 247.16/58.42 | | | | | | | | | BETA: splitting (82) gives:
% 247.16/58.42 | | | | | | | | |
% 247.16/58.42 | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | (190) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 247.16/58.42 | | | | | | | | | | e3 & op(e3, e4) = e3)
% 247.16/58.42 | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | BETA: splitting (190) gives:
% 247.16/58.42 | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | (191) all_252_0 = e3 & op(e4, e4) = e3
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | ALPHA: (191) implies:
% 247.16/58.42 | | | | | | | | | | | (192) all_252_0 = e3
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | BETA: splitting (23) gives:
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | (193) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 247.16/58.42 | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | REF_CLOSE: (17), (19), (31), (44), (58), (68), (77), (79),
% 247.16/58.42 | | | | | | | | | | | | (83), (179), (183), (189), (192), (193) are
% 247.16/58.42 | | | | | | | | | | | | inconsistent by sub-proof #8.
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | (194) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 247.16/58.42 | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 247.16/58.42 | | | | | | | | | | | | op(e4, e0) = e4)
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | BETA: splitting (194) gives:
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | (195) all_252_4 = e4 & op(e4, e2) = e4
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | ALPHA: (195) implies:
% 247.16/58.42 | | | | | | | | | | | | | (196) all_252_4 = e4
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | COMBINE_EQS: (80), (196) imply:
% 247.16/58.42 | | | | | | | | | | | | | (197) e4 = e1
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | REF_CLOSE: (19), (31), (58), (68), (79), (83), (179), (183),
% 247.16/58.42 | | | | | | | | | | | | | (189), (192), (197) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | #148.
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | (198) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 247.16/58.42 | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | BETA: splitting (198) gives:
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | (199) all_252_9 = e4 & op(e4, e1) = e4
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | ALPHA: (199) implies:
% 247.16/58.42 | | | | | | | | | | | | | | (200) all_252_9 = e4
% 247.16/58.42 | | | | | | | | | | | | | | (201) op(e4, e1) = e4
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | (202) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 =
% 247.16/58.42 | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (14), (15), (17), (18), (19), (20),
% 247.16/58.42 | | | | | | | | | | | | | | | (22), (28), (29), (31), (41), (42), (45), (51),
% 247.16/58.42 | | | | | | | | | | | | | | | (57), (58), (62), (65), (67), (68), (77), (79),
% 247.16/58.42 | | | | | | | | | | | | | | | (82), (83), (84), (91), (179), (202) are
% 247.16/58.42 | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | (203) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 =
% 247.16/58.42 | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 &
% 247.16/58.42 | | | | | | | | | | | | | | | op(e4, e0) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | (204) all_252_4 = e0 & op(e4, e2) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (80), (204) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | #5.
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | (205) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 =
% 247.16/58.42 | | | | | | | | | | | | | | | | e0 & op(e4, e0) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | (206) all_252_9 = e0 & op(e4, e1) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | (207) op(e4, e1) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (61), (201), (207) are inconsistent by
% 247.16/58.42 | | | | | | | | | | | | | | | | | sub-proof #286.
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | (208) all_252_16 = e0 & op(e4, e0) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | (209) all_252_16 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | (210) op(e4, e0) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | (211) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, e0, e0, e4,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | simplifying with (10), (210) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (212) all_30_2 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, all_134_1, e0,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | e4, simplifying with (10), (27) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (213) all_134_1 = all_30_2
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e3, all_134_1, e0, e4,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | simplifying with (27), (176) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (214) all_134_1 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (214) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (215) all_30_2 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (216) all_30_2 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (216) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (217) e3 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (15), (17), (18), (19), (20), (22),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (28), (29), (31), (41), (42), (45), (57), (58),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (62), (65), (67), (68), (79), (82), (83), (84),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (91), (179), (192), (217) are inconsistent by
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (218) all_252_1 = e3 & op(e4, e3) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (219) all_252_1 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (16), (17), (18), (29), (40),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (56), (79), (87), (219) are inconsistent by
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | sub-proof #40.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | (220) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 247.16/58.42 | | | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (221) all_252_4 = e3 & op(e4, e2) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (80), (221) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | #252.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (222) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (223) all_252_9 = e3 & op(e4, e1) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (224) all_252_9 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (224) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (225) e4 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (31), (58), (68), (79), (83), (179), (183),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (189), (192), (225) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | #9.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (226) all_252_16 = e3 & op(e4, e0) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (227) all_252_16 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (227) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (228) e3 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (15), (17), (18), (19), (20), (22),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (28), (29), (31), (41), (42), (45), (57), (58),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (62), (65), (67), (68), (79), (82), (83), (84),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (91), (179), (192), (228) are inconsistent by
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | sub-proof #4.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | (229) all_252_16 = e4 & op(e4, e0) = e4
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | ALPHA: (229) implies:
% 247.16/58.42 | | | | | | | | | | | | | | (230) all_252_16 = e4
% 247.16/58.42 | | | | | | | | | | | | | | (231) op(e4, e0) = e4
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | (232) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 =
% 247.16/58.42 | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (15), (17), (18), (19), (20), (22),
% 247.16/58.42 | | | | | | | | | | | | | | | (28), (29), (31), (39), (41), (42), (45), (57),
% 247.16/58.42 | | | | | | | | | | | | | | | (58), (62), (65), (67), (68), (79), (82), (83),
% 247.16/58.42 | | | | | | | | | | | | | | | (84), (91), (179), (232) are inconsistent by
% 247.16/58.42 | | | | | | | | | | | | | | | sub-proof #7.
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | (233) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (65), (67), (179), (233) are
% 247.16/58.42 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #10.
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | (234) all_252_6 = e1 & op(e2, e4) = e1
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (183), (234) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | #545.
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | (235) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (14), (15), (17), (18), (19), (20),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | (22), (28), (29), (31), (41), (42), (45), (51),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | (57), (58), (62), (65), (67), (68), (77), (79),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | (82), (83), (84), (91), (179), (235) are
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 &
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_4 = e0 & op(e4, e2) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (80), (237) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | #5.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | (238) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e0) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, e3, e0, e4,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (10), (176) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (239) all_30_2 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_30_2, all_134_1, e0,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | e4, simplifying with (10), (27) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (240) all_134_1 = all_30_2
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e4, all_134_1, e0, e4,
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (27), (231) gives:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (241) all_134_1 = e4
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (240), (241) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (242) all_30_2 = e4
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (243) all_30_2 = e4
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (243) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (244) e4 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (245) e4 = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (31), (58), (68), (79), (83), (179), (183),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (189), (192), (245) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | #9.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (246) all_252_16 = e0 & op(e4, e0) = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (247) all_252_16 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (247) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (248) e4 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (248) imply:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (249) all_252_2 = e0
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (28), (31), (45), (58), (68), (79),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | (83), (91), (183), (192), (249) are inconsistent
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #542.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | (250) all_252_2 = e3 & op(e3, e4) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | (251) op(e3, e4) = e3
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (60), (62), (172), (251) are
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (252) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (18), (28), (31), (41), (45), (58),
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | (65), (67), (91), (179), (183), (252) are
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | (253) all_252_20 = e1 & op(e0, e4) = e1
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (58), (253) are inconsistent by sub-proof
% 247.16/58.42 | | | | | | | | | | | | | | | | | | | #544.
% 247.16/58.42 | | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | (254) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20
% 247.16/58.42 | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0)
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (38), (58), (93), (254) are
% 247.16/58.42 | | | | | | | | | | | | | | | | inconsistent by sub-proof #42.
% 247.16/58.42 | | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | End of split
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | Case 2:
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | (255) all_252_2 = e3 & op(e3, e4) = e3
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | ALPHA: (255) implies:
% 247.16/58.42 | | | | | | | | | | | (256) op(e3, e4) = e3
% 247.16/58.42 | | | | | | | | | | |
% 247.16/58.42 | | | | | | | | | | | REF_CLOSE: (17), (21), (60), (62), (172), (256) are
% 247.16/58.42 | | | | | | | | | | | inconsistent by sub-proof #69.
% 247.16/58.43 | | | | | | | | | | |
% 247.16/58.43 | | | | | | | | | | End of split
% 247.16/58.43 | | | | | | | | | |
% 247.16/58.43 | | | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | | | |
% 247.16/58.43 | | | | | | | | | | (257) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 247.16/58.43 | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 247.16/58.43 | | | | | | | | | | e4) = e3)
% 247.16/58.43 | | | | | | | | | |
% 247.16/58.43 | | | | | | | | | | REF_CLOSE: (15), (17), (18), (28), (31), (41), (45), (58),
% 247.16/58.43 | | | | | | | | | | (65), (67), (91), (179), (183), (257) are
% 247.16/58.43 | | | | | | | | | | inconsistent by sub-proof #13.
% 247.16/58.43 | | | | | | | | | |
% 247.16/58.43 | | | | | | | | | End of split
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | (258) all_252_20 = e1 & op(e0, e4) = e1
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | REF_CLOSE: (28), (58), (258) are inconsistent by sub-proof
% 247.16/58.43 | | | | | | | | | #544.
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | End of split
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | End of split
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | End of split
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | Case 2:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (259) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 247.16/58.43 | | | | | | op(e0, e4) = e0)
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | REF_CLOSE: (14), (17), (38), (58), (93), (259) are inconsistent by
% 247.16/58.43 | | | | | | sub-proof #42.
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | End of split
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | End of split
% 247.16/58.43 | | | |
% 247.16/58.43 | | | Case 2:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | (260) all_252_3 = e4 & op(e3, e3) = e4
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | REF_CLOSE: (17), (37), (87), (260) are inconsistent by sub-proof #846.
% 247.16/58.43 | | | |
% 247.16/58.43 | | | End of split
% 247.16/58.43 | | |
% 247.16/58.43 | | Case 2:
% 247.16/58.43 | | |
% 247.16/58.43 | | | (261) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3,
% 247.16/58.43 | | | e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 247.16/58.43 | | |
% 247.16/58.43 | | | BETA: splitting (261) gives:
% 247.16/58.43 | | |
% 247.16/58.43 | | | Case 1:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | (262) all_252_5 = e4 & op(e3, e2) = e4
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | ALPHA: (262) implies:
% 247.16/58.43 | | | | (263) op(e3, e2) = e4
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | REF_CLOSE: (4), (17), (81), (263) are inconsistent by sub-proof #502.
% 247.16/58.43 | | | |
% 247.16/58.43 | | | Case 2:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | (264) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 & op(e3,
% 247.16/58.43 | | | | e0) = e4)
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | BETA: splitting (264) gives:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | Case 1:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | (265) all_252_10 = e4 & op(e3, e1) = e4
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | REF_CLOSE: (17), (46), (174), (265) are inconsistent by sub-proof
% 247.16/58.43 | | | | | #914.
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | Case 2:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | (266) all_252_17 = e4 & op(e3, e0) = e4
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | ALPHA: (266) implies:
% 247.16/58.43 | | | | | (267) all_252_17 = e4
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | BETA: splitting (89) gives:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | Case 1:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (268) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 &
% 247.16/58.43 | | | | | | op(e3, e3) = e2)
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | REF_CLOSE: (13), (17), (62), (63), (87), (268) are inconsistent by
% 247.16/58.43 | | | | | | sub-proof #232.
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | Case 2:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (269) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 &
% 247.16/58.43 | | | | | | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | BETA: splitting (269) gives:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | Case 1:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (270) all_252_5 = e2 & op(e3, e2) = e2
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | REF_CLOSE: (7), (8), (14), (15), (17), (18), (19), (20), (28),
% 247.16/58.43 | | | | | | | (30), (32), (33), (34), (41), (45), (54), (64), (68),
% 247.16/58.43 | | | | | | | (75), (78), (79), (80), (81), (88), (92), (270) are
% 247.16/58.43 | | | | | | | inconsistent by sub-proof #3.
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | Case 2:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (271) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 247.16/58.43 | | | | | | | op(e3, e0) = e2)
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | BETA: splitting (271) gives:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | Case 1:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | (272) all_252_10 = e2 & op(e3, e1) = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | ALPHA: (272) implies:
% 247.16/58.43 | | | | | | | | (273) op(e3, e1) = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | REF_CLOSE: (17), (26), (46), (273) are inconsistent by sub-proof
% 247.16/58.43 | | | | | | | | #984.
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | (274) all_252_17 = e2 & op(e3, e0) = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | REF_CLOSE: (79), (267), (274) are inconsistent by sub-proof
% 247.16/58.43 | | | | | | | | #432.
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | End of split
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | End of split
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | End of split
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | End of split
% 247.16/58.43 | | | |
% 247.16/58.43 | | | End of split
% 247.16/58.43 | | |
% 247.16/58.43 | | End of split
% 247.16/58.43 | |
% 247.16/58.43 | End of split
% 247.16/58.43 |
% 247.16/58.43 End of proof
% 247.16/58.43
% 247.16/58.43 Sub-proof #3 shows that the following formulas are inconsistent:
% 247.16/58.43 ----------------------------------------------------------------
% 247.16/58.43 (1) ~ (all_244_8 = e0)
% 247.16/58.43 (2) op(all_6_2, e2) = e4
% 247.16/58.43 (3) ~ (e2 = e0)
% 247.16/58.43 (4) ~ (e1 = e0)
% 247.16/58.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.43 (6) ~ (e3 = e2)
% 247.16/58.43 (7) ~ (e4 = e0)
% 247.16/58.43 (8) all_252_5 = e2 & op(e3, e2) = e2
% 247.16/58.43 (9) op(e2, e2) = all_244_8
% 247.16/58.43 (10) ~ (e2 = e1)
% 247.16/58.43 (11) op(e0, e2) = all_28_2
% 247.16/58.43 (12) all_252_14 = e4
% 247.16/58.43 (13) op(all_6_2, all_64_2) = e2
% 247.16/58.43 (14) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 247.16/58.43 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 247.16/58.43 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 247.16/58.43 (15) ~ (e3 = e0)
% 247.16/58.43 (16) ~ (e3 = e1)
% 247.16/58.43 (17) ~ (all_28_2 = e2)
% 247.16/58.43 (18) op(all_8_2, e4) = e2
% 247.16/58.43 (19) ~ (e4 = e3)
% 247.16/58.43 (20) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.16/58.43 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.16/58.43 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.16/58.43 (21) op(e2, e4) = all_64_2
% 247.16/58.43 (22) ~ (e4 = e2)
% 247.16/58.43 (23) all_252_4 = e1
% 247.16/58.43 (24) op(e3, e2) = all_8_2
% 247.16/58.43 (25) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 247.16/58.43 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 247.16/58.43 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 247.16/58.43 (26) ~ (all_64_2 = e4)
% 247.16/58.43
% 247.16/58.43 Begin of proof
% 247.16/58.43 |
% 247.16/58.43 | ALPHA: (8) implies:
% 247.16/58.43 | (27) all_252_5 = e2
% 247.16/58.43 | (28) op(e3, e2) = e2
% 247.16/58.43 |
% 247.16/58.43 | BETA: splitting (14) gives:
% 247.16/58.43 |
% 247.16/58.43 | Case 1:
% 247.16/58.43 | |
% 247.16/58.43 | | (29) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 247.16/58.43 | | e0)
% 247.16/58.43 | |
% 247.16/58.43 | | BETA: splitting (29) gives:
% 247.16/58.43 | |
% 247.16/58.43 | | Case 1:
% 247.16/58.43 | | |
% 247.16/58.43 | | | (30) all_252_4 = e0 & op(e4, e2) = e0
% 247.16/58.43 | | |
% 247.16/58.43 | | | REF_CLOSE: (4), (23), (30) are inconsistent by sub-proof #5.
% 247.16/58.43 | | |
% 247.16/58.43 | | Case 2:
% 247.16/58.43 | | |
% 247.16/58.43 | | | (31) all_252_5 = e0 & op(e3, e2) = e0
% 247.16/58.43 | | |
% 247.16/58.43 | | | ALPHA: (31) implies:
% 247.16/58.43 | | | (32) op(e3, e2) = e0
% 247.16/58.43 | | |
% 247.16/58.43 | | | REF_CLOSE: (3), (5), (28), (32) are inconsistent by sub-proof #643.
% 247.16/58.43 | | |
% 247.16/58.43 | | End of split
% 247.16/58.43 | |
% 247.16/58.43 | Case 2:
% 247.16/58.43 | |
% 247.16/58.43 | | (33) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 247.16/58.43 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 247.16/58.43 | |
% 247.16/58.43 | | BETA: splitting (33) gives:
% 247.16/58.43 | |
% 247.16/58.43 | | Case 1:
% 247.16/58.43 | | |
% 247.16/58.43 | | | (34) all_252_8 = e0 & op(e2, e2) = e0
% 247.16/58.43 | | |
% 247.16/58.43 | | | ALPHA: (34) implies:
% 247.16/58.43 | | | (35) op(e2, e2) = e0
% 247.16/58.43 | | |
% 247.16/58.43 | | | REF_CLOSE: (1), (5), (9), (35) are inconsistent by sub-proof #880.
% 247.16/58.43 | | |
% 247.16/58.43 | | Case 2:
% 247.16/58.43 | | |
% 247.16/58.43 | | | (36) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 247.16/58.43 | | | e2) = e0)
% 247.16/58.43 | | |
% 247.16/58.43 | | | BETA: splitting (36) gives:
% 247.16/58.43 | | |
% 247.16/58.43 | | | Case 1:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | (37) all_252_14 = e0 & op(e1, e2) = e0
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | ALPHA: (37) implies:
% 247.16/58.43 | | | | (38) all_252_14 = e0
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | COMBINE_EQS: (12), (38) imply:
% 247.16/58.43 | | | | (39) e4 = e0
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | REDUCE: (7), (39) imply:
% 247.16/58.43 | | | | (40) $false
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | CLOSE: (40) is inconsistent.
% 247.16/58.43 | | | |
% 247.16/58.43 | | | Case 2:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | (41) all_252_22 = e0 & op(e0, e2) = e0
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | ALPHA: (41) implies:
% 247.16/58.43 | | | | (42) op(e0, e2) = e0
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | BETA: splitting (20) gives:
% 247.16/58.43 | | | |
% 247.16/58.43 | | | | Case 1:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | (43) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3,
% 247.16/58.43 | | | | | e2) = e3)
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | BETA: splitting (43) gives:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | Case 1:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (44) all_252_4 = e3 & op(e4, e2) = e3
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | REF_CLOSE: (16), (23), (44) are inconsistent by sub-proof #252.
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | Case 2:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (45) all_252_5 = e3 & op(e3, e2) = e3
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | ALPHA: (45) implies:
% 247.16/58.43 | | | | | | (46) all_252_5 = e3
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | REF_CLOSE: (6), (27), (46) are inconsistent by sub-proof #507.
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | End of split
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | Case 2:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | (47) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1,
% 247.16/58.43 | | | | | e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | BETA: splitting (47) gives:
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | | Case 1:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (48) all_252_8 = e3 & op(e2, e2) = e3
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | ALPHA: (48) implies:
% 247.16/58.43 | | | | | | (49) all_252_8 = e3
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | BETA: splitting (25) gives:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | Case 1:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (50) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 &
% 247.16/58.43 | | | | | | | op(e3, e2) = e2)
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | BETA: splitting (50) gives:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | Case 1:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | (51) all_252_4 = e2 & op(e4, e2) = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | ALPHA: (51) implies:
% 247.16/58.43 | | | | | | | | (52) all_252_4 = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | COMBINE_EQS: (23), (52) imply:
% 247.16/58.43 | | | | | | | | (53) e2 = e1
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | SIMP: (53) implies:
% 247.16/58.43 | | | | | | | | (54) e2 = e1
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | REDUCE: (10), (54) imply:
% 247.16/58.43 | | | | | | | | (55) $false
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | CLOSE: (55) is inconsistent.
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | REF_CLOSE: (2), (5), (8), (13), (18), (21), (24), (26) are
% 247.16/58.43 | | | | | | | | inconsistent by sub-proof #111.
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | End of split
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | Case 2:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (56) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 &
% 247.16/58.43 | | | | | | | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | BETA: splitting (56) gives:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | Case 1:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | (57) all_252_8 = e2 & op(e2, e2) = e2
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | REF_CLOSE: (6), (49), (57) are inconsistent by sub-proof #703.
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | (58) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 247.16/58.43 | | | | | | | | op(e0, e2) = e2)
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | BETA: splitting (58) gives:
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | | Case 1:
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | (59) all_252_14 = e2 & op(e1, e2) = e2
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | ALPHA: (59) implies:
% 247.16/58.43 | | | | | | | | | (60) all_252_14 = e2
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | COMBINE_EQS: (12), (60) imply:
% 247.16/58.43 | | | | | | | | | (61) e4 = e2
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | SIMP: (61) implies:
% 247.16/58.43 | | | | | | | | | (62) e4 = e2
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | REDUCE: (22), (62) imply:
% 247.16/58.43 | | | | | | | | | (63) $false
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | CLOSE: (63) is inconsistent.
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | Case 2:
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | (64) all_252_22 = e2 & op(e0, e2) = e2
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | | REF_CLOSE: (5), (11), (17), (64) are inconsistent by sub-proof
% 247.16/58.43 | | | | | | | | | #979.
% 247.16/58.43 | | | | | | | | |
% 247.16/58.43 | | | | | | | | End of split
% 247.16/58.43 | | | | | | | |
% 247.16/58.43 | | | | | | | End of split
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | End of split
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | Case 2:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | (65) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 247.16/58.43 | | | | | | op(e0, e2) = e3)
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | BETA: splitting (65) gives:
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | | Case 1:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (66) all_252_14 = e3 & op(e1, e2) = e3
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | REF_CLOSE: (12), (19), (66) are inconsistent by sub-proof #33.
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | Case 2:
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | (67) all_252_22 = e3 & op(e0, e2) = e3
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | ALPHA: (67) implies:
% 247.16/58.43 | | | | | | | (68) op(e0, e2) = e3
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | | REF_CLOSE: (5), (11), (15), (42), (68) are inconsistent by
% 247.16/58.43 | | | | | | | sub-proof #473.
% 247.16/58.43 | | | | | | |
% 247.16/58.43 | | | | | | End of split
% 247.16/58.43 | | | | | |
% 247.16/58.43 | | | | | End of split
% 247.16/58.43 | | | | |
% 247.16/58.43 | | | | End of split
% 247.16/58.43 | | | |
% 247.16/58.43 | | | End of split
% 247.16/58.43 | | |
% 247.16/58.43 | | End of split
% 247.16/58.43 | |
% 247.16/58.43 | End of split
% 247.16/58.43 |
% 247.16/58.43 End of proof
% 247.16/58.43
% 247.16/58.43 Sub-proof #4 shows that the following formulas are inconsistent:
% 247.16/58.43 ----------------------------------------------------------------
% 247.16/58.43 (1) e3 = e0
% 247.16/58.43 (2) ~ (all_244_8 = e0)
% 247.16/58.43 (3) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 247.16/58.43 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 247.16/58.43 | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.43 (4) ~ (e1 = e0)
% 247.16/58.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.43 (6) ~ (e3 = e2)
% 247.16/58.43 (7) ~ (e4 = e0)
% 247.16/58.43 (8) op(e2, e2) = all_244_8
% 247.16/58.43 (9) op(e2, e1) = all_38_2
% 247.16/58.43 (10) ~ (e2 = e1)
% 247.16/58.43 (11) all_252_7 = e4
% 247.16/58.43 (12) ~ (e4 = e1)
% 247.16/58.43 (13) all_252_2 = e4
% 247.16/58.43 (14) ~ (e3 = e0)
% 247.16/58.43 (15) ~ (all_38_2 = e0)
% 247.16/58.43 (16) all_252_0 = e3
% 247.16/58.43 (17) ~ (e3 = e1)
% 247.16/58.43 (18) ~ (all_40_2 = e0)
% 247.16/58.43 (19) all_252_20 = e2
% 247.16/58.43 (20) op(e3, e4) = all_100_2
% 247.16/58.43 (21) op(e4, e4) = all_244_0
% 247.16/58.43 (22) ~ (all_244_0 = e1)
% 247.16/58.43 (23) ~ (e4 = e3)
% 247.16/58.43 (24) ~ (e4 = e2)
% 247.16/58.43 (25) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.43 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.43 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.43 (26) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.43 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.43 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.43 (27) op(e2, e0) = all_40_2
% 247.16/58.43 (28) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.43 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.43 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.43
% 247.16/58.43 Begin of proof
% 247.16/58.43 |
% 247.16/58.43 | SIMP: (1) implies:
% 247.16/58.43 | (29) e3 = e0
% 247.16/58.43 |
% 247.16/58.43 | COMBINE_EQS: (16), (29) imply:
% 247.16/58.43 | (30) all_252_0 = e0
% 247.16/58.43 |
% 247.16/58.43 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 247.16/58.43 | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 247.16/58.43 | (26), (27), (28), (30) are inconsistent by sub-proof #12.
% 247.16/58.43 |
% 247.16/58.43 End of proof
% 247.16/58.43
% 247.16/58.43 Sub-proof #5 shows that the following formulas are inconsistent:
% 247.16/58.43 ----------------------------------------------------------------
% 247.16/58.43 (1) all_252_4 = e0 & op(e4, e2) = e0
% 247.16/58.44 (2) all_252_4 = e1
% 247.16/58.44 (3) ~ (e1 = e0)
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | ALPHA: (1) implies:
% 247.16/58.44 | (4) all_252_4 = e0
% 247.16/58.44 |
% 247.16/58.44 | COMBINE_EQS: (2), (4) imply:
% 247.16/58.44 | (5) e1 = e0
% 247.16/58.44 |
% 247.16/58.44 | REDUCE: (3), (5) imply:
% 247.16/58.44 | (6) $false
% 247.16/58.44 |
% 247.16/58.44 | CLOSE: (6) is inconsistent.
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #6 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) ~ (all_244_8 = e0)
% 247.16/58.44 (2) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 247.16/58.44 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 247.16/58.44 | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.44 (3) ~ (e2 = e0)
% 247.16/58.44 (4) ~ (e1 = e0)
% 247.16/58.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.44 (6) ~ (e3 = e2)
% 247.16/58.44 (7) ~ (e4 = e0)
% 247.16/58.44 (8) op(e2, e2) = all_244_8
% 247.16/58.44 (9) op(e2, e1) = all_38_2
% 247.16/58.44 (10) ~ (e2 = e1)
% 247.16/58.44 (11) all_252_7 = e4
% 247.16/58.44 (12) ~ (e4 = e1)
% 247.16/58.44 (13) all_252_2 = e4
% 247.16/58.44 (14) ~ (e3 = e0)
% 247.16/58.44 (15) ~ (all_38_2 = e0)
% 247.16/58.44 (16) ~ (e3 = e1)
% 247.16/58.44 (17) op(e4, e3) = e2
% 247.16/58.44 (18) ~ (all_40_2 = e0)
% 247.16/58.44 (19) all_252_20 = e2
% 247.16/58.44 (20) op(e3, e4) = all_100_2
% 247.16/58.44 (21) op(e4, e4) = all_244_0
% 247.16/58.44 (22) ~ (all_244_0 = e1)
% 247.16/58.44 (23) ~ (e4 = e3)
% 247.16/58.44 (24) op(e4, e3) = all_84_2
% 247.16/58.44 (25) ~ (e4 = e2)
% 247.16/58.44 (26) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.44 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.44 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.44 (27) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.44 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.44 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.44 (28) op(e2, e0) = all_40_2
% 247.16/58.44 (29) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 247.16/58.44 (30) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.44 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.44 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | BETA: splitting (29) gives:
% 247.16/58.44 |
% 247.16/58.44 | Case 1:
% 247.16/58.44 | |
% 247.16/58.44 | | (31) all_252_0 = e0 & op(e4, e4) = e0
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (31) implies:
% 247.16/58.44 | | (32) all_252_0 = e0
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 247.16/58.44 | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (25), (26),
% 247.16/58.44 | | (27), (28), (30), (32) are inconsistent by sub-proof #12.
% 247.16/58.44 | |
% 247.16/58.44 | Case 2:
% 247.16/58.44 | |
% 247.16/58.44 | | (33) all_252_1 = e0 & op(e4, e3) = e0
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (33) implies:
% 247.16/58.44 | | (34) op(e4, e3) = e0
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (3), (5), (17), (24), (34) are inconsistent by sub-proof #850.
% 247.16/58.44 | |
% 247.16/58.44 | End of split
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #7 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) ~ (all_244_8 = e0)
% 247.16/58.44 (2) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 247.16/58.44 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 247.16/58.44 | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.44 (3) ~ (e1 = e0)
% 247.16/58.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.44 (5) ~ (e3 = e2)
% 247.16/58.44 (6) ~ (e4 = e0)
% 247.16/58.44 (7) op(e2, e2) = all_244_8
% 247.16/58.44 (8) op(e2, e1) = all_38_2
% 247.16/58.44 (9) ~ (e2 = e1)
% 247.16/58.44 (10) all_252_7 = e4
% 247.16/58.44 (11) ~ (e4 = e1)
% 247.16/58.44 (12) ~ (all_100_2 = e0)
% 247.16/58.44 (13) all_252_2 = e4
% 247.16/58.44 (14) ~ (e3 = e0)
% 247.16/58.44 (15) ~ (all_38_2 = e0)
% 247.16/58.44 (16) ~ (e3 = e1)
% 247.16/58.44 (17) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0)
% 247.16/58.44 (18) ~ (all_40_2 = e0)
% 247.16/58.44 (19) all_252_20 = e2
% 247.16/58.44 (20) op(e3, e4) = all_100_2
% 247.16/58.44 (21) op(e4, e4) = all_244_0
% 247.16/58.44 (22) ~ (all_244_0 = e1)
% 247.16/58.44 (23) ~ (e4 = e3)
% 247.16/58.44 (24) ~ (e4 = e2)
% 247.16/58.44 (25) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.44 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.44 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.44 (26) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.44 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.44 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.44 (27) op(e2, e0) = all_40_2
% 247.16/58.44 (28) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.44 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.44 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | BETA: splitting (17) gives:
% 247.16/58.44 |
% 247.16/58.44 | Case 1:
% 247.16/58.44 | |
% 247.16/58.44 | | (29) all_252_0 = e0 & op(e4, e4) = e0
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (29) implies:
% 247.16/58.44 | | (30) all_252_0 = e0
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 247.16/58.44 | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 247.16/58.44 | | (26), (27), (28), (30) are inconsistent by sub-proof #12.
% 247.16/58.44 | |
% 247.16/58.44 | Case 2:
% 247.16/58.44 | |
% 247.16/58.44 | | (31) all_252_2 = e0 & op(e3, e4) = e0
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (4), (12), (20), (31) are inconsistent by sub-proof #43.
% 247.16/58.44 | |
% 247.16/58.44 | End of split
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #8 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) all_252_6 = e0
% 247.16/58.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.44 (3) ~ (e4 = e0)
% 247.16/58.44 (4) ~ (e4 = e1)
% 247.16/58.44 (5) all_252_2 = e4
% 247.16/58.44 (6) all_252_0 = e3
% 247.16/58.44 (7) ~ (all_84_2 = e4)
% 247.16/58.44 (8) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 247.16/58.44 (9) all_252_20 = e2
% 247.16/58.44 (10) ~ (e4 = e3)
% 247.16/58.44 (11) op(e4, e3) = all_84_2
% 247.16/58.44 (12) ~ (e4 = e2)
% 247.16/58.44 (13) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.44 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.44 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.44 (14) all_252_12 = e1
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | BETA: splitting (8) gives:
% 247.16/58.44 |
% 247.16/58.44 | Case 1:
% 247.16/58.44 | |
% 247.16/58.44 | | (15) all_252_0 = e4 & op(e4, e4) = e4
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (15) implies:
% 247.16/58.44 | | (16) all_252_0 = e4
% 247.16/58.44 | |
% 247.16/58.44 | | COMBINE_EQS: (6), (16) imply:
% 247.16/58.44 | | (17) e4 = e3
% 247.16/58.44 | |
% 247.16/58.44 | | SIMP: (17) implies:
% 247.16/58.44 | | (18) e4 = e3
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (12), (13), (14), (18) are
% 247.16/58.44 | | inconsistent by sub-proof #9.
% 247.16/58.44 | |
% 247.16/58.44 | Case 2:
% 247.16/58.44 | |
% 247.16/58.44 | | (19) all_252_1 = e4 & op(e4, e3) = e4
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (2), (7), (11), (19) are inconsistent by sub-proof #815.
% 247.16/58.44 | |
% 247.16/58.44 | End of split
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #9 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) all_252_6 = e0
% 247.16/58.44 (2) ~ (e4 = e0)
% 247.16/58.44 (3) ~ (e4 = e1)
% 247.16/58.44 (4) all_252_2 = e4
% 247.16/58.44 (5) all_252_0 = e3
% 247.16/58.44 (6) all_252_20 = e2
% 247.16/58.44 (7) ~ (e4 = e3)
% 247.16/58.44 (8) e4 = e3
% 247.16/58.44 (9) ~ (e4 = e2)
% 247.16/58.44 (10) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.44 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.44 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.44 (11) all_252_12 = e1
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | COMBINE_EQS: (4), (8) imply:
% 247.16/58.44 | (12) all_252_2 = e3
% 247.16/58.44 |
% 247.16/58.44 | BETA: splitting (10) gives:
% 247.16/58.44 |
% 247.16/58.44 | Case 1:
% 247.16/58.44 | |
% 247.16/58.44 | | (13) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 247.16/58.44 | | e4)
% 247.16/58.44 | |
% 247.16/58.44 | | BETA: splitting (13) gives:
% 247.16/58.44 | |
% 247.16/58.44 | | Case 1:
% 247.16/58.44 | | |
% 247.16/58.44 | | | (14) all_252_0 = e4 & op(e4, e4) = e4
% 247.16/58.44 | | |
% 247.16/58.44 | | | REF_CLOSE: (5), (7), (14) are inconsistent by sub-proof #547.
% 247.16/58.44 | | |
% 247.16/58.44 | | Case 2:
% 247.16/58.44 | | |
% 247.16/58.44 | | | (15) all_252_2 = e4 & op(e3, e4) = e4
% 247.16/58.44 | | |
% 247.16/58.44 | | | REF_CLOSE: (4), (7), (12) are inconsistent by sub-proof #838.
% 247.16/58.44 | | |
% 247.16/58.44 | | End of split
% 247.16/58.44 | |
% 247.16/58.44 | Case 2:
% 247.16/58.44 | |
% 247.16/58.44 | | (16) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.44 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.44 | |
% 247.16/58.44 | | BETA: splitting (16) gives:
% 247.16/58.44 | |
% 247.16/58.44 | | Case 1:
% 247.16/58.44 | | |
% 247.16/58.44 | | | (17) all_252_6 = e4 & op(e2, e4) = e4
% 247.16/58.44 | | |
% 247.16/58.44 | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #387.
% 247.16/58.44 | | |
% 247.16/58.44 | | Case 2:
% 247.16/58.44 | | |
% 247.16/58.44 | | | (18) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 247.16/58.44 | | | e4) = e4)
% 247.16/58.44 | | |
% 247.16/58.44 | | | REF_CLOSE: (3), (6), (9), (11), (18) are inconsistent by sub-proof #190.
% 247.16/58.44 | | |
% 247.16/58.44 | | End of split
% 247.16/58.44 | |
% 247.16/58.44 | End of split
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #10 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.44 (2) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.44 (3) ~ (e4 = e1)
% 247.16/58.44 (4) all_252_2 = e4
% 247.16/58.44 (5) op(e4, e4) = all_244_0
% 247.16/58.44 (6) ~ (all_244_0 = e1)
% 247.16/58.44
% 247.16/58.44 Begin of proof
% 247.16/58.44 |
% 247.16/58.44 | BETA: splitting (2) gives:
% 247.16/58.44 |
% 247.16/58.44 | Case 1:
% 247.16/58.44 | |
% 247.16/58.44 | | (7) all_252_0 = e1 & op(e4, e4) = e1
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (7) implies:
% 247.16/58.44 | | (8) op(e4, e4) = e1
% 247.16/58.44 | |
% 247.16/58.44 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #50.
% 247.16/58.44 | |
% 247.16/58.44 | Case 2:
% 247.16/58.44 | |
% 247.16/58.44 | | (9) all_252_2 = e1 & op(e3, e4) = e1
% 247.16/58.44 | |
% 247.16/58.44 | | ALPHA: (9) implies:
% 247.16/58.44 | | (10) all_252_2 = e1
% 247.16/58.44 | |
% 247.16/58.44 | | COMBINE_EQS: (4), (10) imply:
% 247.16/58.44 | | (11) e4 = e1
% 247.16/58.44 | |
% 247.16/58.44 | | REDUCE: (3), (11) imply:
% 247.16/58.44 | | (12) $false
% 247.16/58.44 | |
% 247.16/58.44 | | CLOSE: (12) is inconsistent.
% 247.16/58.44 | |
% 247.16/58.44 | End of split
% 247.16/58.44 |
% 247.16/58.44 End of proof
% 247.16/58.44
% 247.16/58.44 Sub-proof #11 shows that the following formulas are inconsistent:
% 247.16/58.44 ----------------------------------------------------------------
% 247.16/58.44 (1) all_252_0 = e0
% 247.16/58.44 (2) ~ (all_244_8 = e0)
% 247.16/58.44 (3) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 247.16/58.44 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 247.16/58.44 | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.44 (4) ~ (e1 = e0)
% 247.16/58.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.44 (6) ~ (e3 = e2)
% 247.16/58.44 (7) ~ (e4 = e0)
% 247.16/58.44 (8) op(e2, e2) = all_244_8
% 247.16/58.44 (9) op(e2, e1) = all_38_2
% 247.16/58.44 (10) ~ (e2 = e1)
% 247.16/58.44 (11) all_252_7 = e4
% 247.16/58.44 (12) ~ (e4 = e1)
% 247.16/58.44 (13) ~ (all_16_2 = e4)
% 247.16/58.44 (14) op(e1, e4) = all_16_2
% 247.16/58.44 (15) ~ (e3 = e0)
% 247.16/58.44 (16) ~ (all_38_2 = e0)
% 247.16/58.44 (17) ~ (e3 = e1)
% 247.16/58.44 (18) ~ (all_40_2 = e0)
% 247.16/58.44 (19) all_252_20 = e2
% 247.16/58.44 (20) op(e3, e4) = all_100_2
% 247.16/58.44 (21) op(e4, e4) = all_244_0
% 247.16/58.44 (22) ~ (all_244_0 = e1)
% 247.16/58.44 (23) ~ (e4 = e3)
% 247.16/58.44 (24) op(e2, e4) = all_64_2
% 247.16/58.45 (25) ~ (e4 = e2)
% 247.16/58.45 (26) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.45 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.45 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.45 (27) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.45 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.45 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.45 (28) op(e2, e0) = all_40_2
% 247.16/58.45 (29) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.45 (30) ~ (all_64_2 = e4)
% 247.16/58.45
% 247.16/58.45 Begin of proof
% 247.16/58.45 |
% 247.16/58.45 | BETA: splitting (27) gives:
% 247.16/58.45 |
% 247.16/58.45 | Case 1:
% 247.16/58.45 | |
% 247.16/58.45 | | (31) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 247.16/58.45 | | e4)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (31) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (32) all_252_0 = e4 & op(e4, e4) = e4
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (1), (7), (32) are inconsistent by sub-proof #570.
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (33) all_252_2 = e4 & op(e3, e4) = e4
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (33) implies:
% 247.16/58.45 | | | (34) all_252_2 = e4
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 247.16/58.45 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 247.16/58.45 | | | (26), (27), (28), (29), (34) are inconsistent by sub-proof #12.
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | Case 2:
% 247.16/58.45 | |
% 247.16/58.45 | | (35) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.45 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (35) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (36) all_252_6 = e4 & op(e2, e4) = e4
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (36) implies:
% 247.16/58.45 | | | (37) op(e2, e4) = e4
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (5), (24), (30), (37) are inconsistent by sub-proof #129.
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (38) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 247.16/58.45 | | | e4) = e4)
% 247.16/58.45 | | |
% 247.16/58.45 | | | BETA: splitting (38) gives:
% 247.16/58.45 | | |
% 247.16/58.45 | | | Case 1:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (39) all_252_12 = e4 & op(e1, e4) = e4
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | REF_CLOSE: (5), (13), (14), (39) are inconsistent by sub-proof #757.
% 247.16/58.45 | | | |
% 247.16/58.45 | | | Case 2:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (40) all_252_20 = e4 & op(e0, e4) = e4
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | REF_CLOSE: (19), (25), (40) are inconsistent by sub-proof #534.
% 247.16/58.45 | | | |
% 247.16/58.45 | | | End of split
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | End of split
% 247.16/58.45 |
% 247.16/58.45 End of proof
% 247.16/58.45
% 247.16/58.45 Sub-proof #12 shows that the following formulas are inconsistent:
% 247.16/58.45 ----------------------------------------------------------------
% 247.16/58.45 (1) all_252_0 = e0
% 247.16/58.45 (2) ~ (all_244_8 = e0)
% 247.16/58.45 (3) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 247.16/58.45 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 247.16/58.45 | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.45 (4) ~ (e1 = e0)
% 247.16/58.45 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.45 (6) ~ (e3 = e2)
% 247.16/58.45 (7) ~ (e4 = e0)
% 247.16/58.45 (8) op(e2, e2) = all_244_8
% 247.16/58.45 (9) op(e2, e1) = all_38_2
% 247.16/58.45 (10) ~ (e2 = e1)
% 247.16/58.45 (11) all_252_7 = e4
% 247.16/58.45 (12) ~ (e4 = e1)
% 247.16/58.45 (13) all_252_2 = e4
% 247.16/58.45 (14) ~ (e3 = e0)
% 247.16/58.45 (15) ~ (all_38_2 = e0)
% 247.16/58.45 (16) ~ (e3 = e1)
% 247.16/58.45 (17) ~ (all_40_2 = e0)
% 247.16/58.45 (18) all_252_20 = e2
% 247.16/58.45 (19) op(e3, e4) = all_100_2
% 247.16/58.45 (20) op(e4, e4) = all_244_0
% 247.16/58.45 (21) ~ (all_244_0 = e1)
% 247.16/58.45 (22) ~ (e4 = e3)
% 247.16/58.45 (23) ~ (e4 = e2)
% 247.16/58.45 (24) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.16/58.45 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.16/58.45 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.45 (25) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.16/58.45 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.16/58.45 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.16/58.45 (26) op(e2, e0) = all_40_2
% 247.16/58.45 (27) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.45
% 247.16/58.45 Begin of proof
% 247.16/58.45 |
% 247.16/58.45 | BETA: splitting (3) gives:
% 247.16/58.45 |
% 247.16/58.45 | Case 1:
% 247.16/58.45 | |
% 247.16/58.45 | | (28) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 247.16/58.45 | | e0)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (28) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (29) all_252_6 = e0 & op(e2, e4) = e0
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (29) implies:
% 247.16/58.45 | | | (30) all_252_6 = e0
% 247.16/58.45 | | |
% 247.16/58.45 | | | BETA: splitting (24) gives:
% 247.16/58.45 | | |
% 247.16/58.45 | | | Case 1:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (31) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 247.16/58.45 | | | | e4) = e3)
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | BETA: splitting (31) gives:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | Case 1:
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | | (32) all_252_0 = e3 & op(e4, e4) = e3
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | | REF_CLOSE: (1), (14), (32) are inconsistent by sub-proof #841.
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | Case 2:
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | | (33) all_252_2 = e3 & op(e3, e4) = e3
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | | ALPHA: (33) implies:
% 247.16/58.45 | | | | | (34) all_252_2 = e3
% 247.16/58.45 | | | | | (35) op(e3, e4) = e3
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | | REF_CLOSE: (1), (4), (5), (7), (10), (12), (16), (18), (19), (22),
% 247.16/58.45 | | | | | (23), (25), (27), (30), (34), (35) are inconsistent by
% 247.16/58.45 | | | | | sub-proof #100.
% 247.16/58.45 | | | | |
% 247.16/58.45 | | | | End of split
% 247.16/58.45 | | | |
% 247.16/58.45 | | | Case 2:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (36) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1,
% 247.16/58.45 | | | | e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | REF_CLOSE: (4), (5), (6), (10), (12), (13), (14), (16), (18), (20),
% 247.16/58.45 | | | | (21), (27), (30), (36) are inconsistent by sub-proof #13.
% 247.16/58.45 | | | |
% 247.16/58.45 | | | End of split
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (37) all_252_7 = e0 & op(e2, e3) = e0
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (7), (11), (37) are inconsistent by sub-proof #125.
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | Case 2:
% 247.16/58.45 | |
% 247.16/58.45 | | (38) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 247.16/58.45 | | e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.16/58.45 | |
% 247.16/58.45 | | REF_CLOSE: (2), (5), (8), (9), (15), (17), (26), (38) are inconsistent by
% 247.16/58.45 | | sub-proof #879.
% 247.16/58.45 | |
% 247.16/58.45 | End of split
% 247.16/58.45 |
% 247.16/58.45 End of proof
% 247.16/58.45
% 247.16/58.45 Sub-proof #13 shows that the following formulas are inconsistent:
% 247.16/58.45 ----------------------------------------------------------------
% 247.16/58.45 (1) all_252_6 = e0
% 247.16/58.45 (2) ~ (e1 = e0)
% 247.16/58.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.45 (4) ~ (e3 = e2)
% 247.16/58.45 (5) ~ (e2 = e1)
% 247.16/58.45 (6) ~ (e4 = e1)
% 247.16/58.45 (7) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3)
% 247.16/58.45 | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.16/58.45 (8) all_252_2 = e4
% 247.16/58.45 (9) ~ (e3 = e0)
% 247.16/58.45 (10) ~ (e3 = e1)
% 247.16/58.45 (11) all_252_20 = e2
% 247.16/58.45 (12) op(e4, e4) = all_244_0
% 247.16/58.45 (13) ~ (all_244_0 = e1)
% 247.16/58.45 (14) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.45
% 247.16/58.45 Begin of proof
% 247.16/58.45 |
% 247.16/58.45 | BETA: splitting (7) gives:
% 247.16/58.45 |
% 247.16/58.45 | Case 1:
% 247.16/58.45 | |
% 247.16/58.45 | | (15) all_252_6 = e3 & op(e2, e4) = e3
% 247.16/58.45 | |
% 247.16/58.45 | | ALPHA: (15) implies:
% 247.16/58.45 | | (16) all_252_6 = e3
% 247.16/58.45 | |
% 247.16/58.45 | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #691.
% 247.16/58.45 | |
% 247.16/58.45 | Case 2:
% 247.16/58.45 | |
% 247.16/58.45 | | (17) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4)
% 247.16/58.45 | | = e3)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (17) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (18) all_252_12 = e3 & op(e1, e4) = e3
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (13), (14),
% 247.16/58.45 | | | (18) are inconsistent by sub-proof #14.
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (19) all_252_20 = e3 & op(e0, e4) = e3
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (19) implies:
% 247.16/58.45 | | | (20) all_252_20 = e3
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (4), (11), (20) are inconsistent by sub-proof #520.
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | End of split
% 247.16/58.45 |
% 247.16/58.45 End of proof
% 247.16/58.45
% 247.16/58.45 Sub-proof #14 shows that the following formulas are inconsistent:
% 247.16/58.45 ----------------------------------------------------------------
% 247.16/58.45 (1) all_252_6 = e0
% 247.16/58.45 (2) ~ (e1 = e0)
% 247.16/58.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.45 (4) ~ (e2 = e1)
% 247.16/58.45 (5) ~ (e4 = e1)
% 247.16/58.45 (6) all_252_2 = e4
% 247.16/58.45 (7) all_252_12 = e3 & op(e1, e4) = e3
% 247.16/58.45 (8) ~ (e3 = e1)
% 247.16/58.45 (9) all_252_20 = e2
% 247.16/58.45 (10) op(e4, e4) = all_244_0
% 247.16/58.45 (11) ~ (all_244_0 = e1)
% 247.16/58.45 (12) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.16/58.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.45
% 247.16/58.45 Begin of proof
% 247.16/58.45 |
% 247.16/58.45 | ALPHA: (7) implies:
% 247.16/58.45 | (13) all_252_12 = e3
% 247.16/58.45 |
% 247.16/58.45 | BETA: splitting (12) gives:
% 247.16/58.45 |
% 247.16/58.45 | Case 1:
% 247.16/58.45 | |
% 247.16/58.45 | | (14) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 247.16/58.45 | | e1)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (14) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (15) all_252_0 = e1 & op(e4, e4) = e1
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (15) implies:
% 247.16/58.45 | | | (16) op(e4, e4) = e1
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (3), (10), (11), (16) are inconsistent by sub-proof #50.
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (17) all_252_2 = e1 & op(e3, e4) = e1
% 247.16/58.45 | | |
% 247.16/58.45 | | | ALPHA: (17) implies:
% 247.16/58.45 | | | (18) all_252_2 = e1
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #605.
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | Case 2:
% 247.16/58.45 | |
% 247.16/58.45 | | (19) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.16/58.45 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.16/58.45 | |
% 247.16/58.45 | | BETA: splitting (19) gives:
% 247.16/58.45 | |
% 247.16/58.45 | | Case 1:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (20) all_252_6 = e1 & op(e2, e4) = e1
% 247.16/58.45 | | |
% 247.16/58.45 | | | REF_CLOSE: (1), (2), (20) are inconsistent by sub-proof #545.
% 247.16/58.45 | | |
% 247.16/58.45 | | Case 2:
% 247.16/58.45 | | |
% 247.16/58.45 | | | (21) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 247.16/58.45 | | | e4) = e1)
% 247.16/58.45 | | |
% 247.16/58.45 | | | BETA: splitting (21) gives:
% 247.16/58.45 | | |
% 247.16/58.45 | | | Case 1:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (22) all_252_12 = e1 & op(e1, e4) = e1
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | ALPHA: (22) implies:
% 247.16/58.45 | | | | (23) all_252_12 = e1
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | REF_CLOSE: (8), (13), (23) are inconsistent by sub-proof #385.
% 247.16/58.45 | | | |
% 247.16/58.45 | | | Case 2:
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | (24) all_252_20 = e1 & op(e0, e4) = e1
% 247.16/58.45 | | | |
% 247.16/58.45 | | | | REF_CLOSE: (4), (9), (24) are inconsistent by sub-proof #544.
% 247.16/58.45 | | | |
% 247.16/58.45 | | | End of split
% 247.16/58.45 | | |
% 247.16/58.45 | | End of split
% 247.16/58.45 | |
% 247.16/58.45 | End of split
% 247.16/58.45 |
% 247.16/58.45 End of proof
% 247.16/58.45
% 247.16/58.45 Sub-proof #15 shows that the following formulas are inconsistent:
% 247.16/58.45 ----------------------------------------------------------------
% 247.16/58.45 (1) all_32_2 = all_20_2
% 247.16/58.45 (2) ~ (all_28_2 = e3)
% 247.16/58.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.45 (4) ~ (all_28_2 = e1)
% 247.16/58.45 (5) ~ (all_28_2 = all_20_2)
% 247.16/58.45 (6) op(all_40_2, e0) = e2
% 247.16/58.45 (7) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.16/58.45 all_250_22 = e0
% 247.16/58.45 (8) ~ (all_28_2 = e4)
% 247.16/58.45 (9) all_32_2 = e2
% 247.16/58.45 (10) op(all_40_2, all_28_2) = e0
% 247.16/58.45 (11) all_250_22 = all_28_2
% 247.16/58.45
% 247.16/58.45 Begin of proof
% 247.16/58.45 |
% 247.16/58.45 | COMBINE_EQS: (1), (9) imply:
% 247.16/58.45 | (12) all_20_2 = e2
% 247.16/58.45 |
% 247.16/58.45 | SIMP: (12) implies:
% 247.16/58.45 | (13) all_20_2 = e2
% 247.16/58.45 |
% 247.16/58.45 | REDUCE: (5), (13) imply:
% 247.16/58.45 | (14) ~ (all_28_2 = e2)
% 247.16/58.45 |
% 247.16/58.45 | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (14) are inconsistent by
% 247.16/58.45 | sub-proof #583.
% 247.16/58.45 |
% 247.16/58.45 End of proof
% 247.16/58.45
% 247.16/58.45 Sub-proof #16 shows that the following formulas are inconsistent:
% 247.16/58.45 ----------------------------------------------------------------
% 247.16/58.45 (1) op(all_4_2, e2) = e1
% 247.16/58.45 (2) ~ (all_244_24 = all_34_2)
% 247.16/58.45 (3) ~ (all_40_2 = all_38_2)
% 247.16/58.45 (4) op(all_28_2, all_40_2) = e2
% 247.16/58.45 (5) ~ (all_22_2 = e2)
% 247.16/58.45 (6) ~ (all_62_2 = e2)
% 247.16/58.45 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.45 (8) op(e0, e0) = all_244_24
% 247.16/58.45 (9) op(e2, e2) = all_244_8
% 247.16/58.45 (10) op(e2, e1) = all_38_2
% 247.16/58.46 (11) op(e1, e0) = all_34_2
% 247.16/58.46 (12) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.16/58.46 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.16/58.46 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.16/58.46 (13) op(e0, e2) = all_28_2
% 247.16/58.46 (14) all_252_14 = e4
% 247.16/58.46 (15) op(all_244_15, all_244_15) = e1
% 247.16/58.46 (16) op(all_34_2, e0) = e1
% 247.16/58.46 (17) op(e1, e4) = all_16_2
% 247.16/58.46 (18) op(e1, e3) = all_62_2
% 247.16/58.46 (19) ~ (all_12_2 = e2)
% 247.16/58.46 (20) ~ (all_16_2 = e2)
% 247.16/58.46 (21) op(e0, e3) = all_22_2
% 247.16/58.46 (22) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.16/58.46 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.16/58.46 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.16/58.46 (23) ~ (all_244_8 = e1)
% 247.16/58.46 (24) op(e1, e1) = all_244_15
% 247.16/58.46 (25) op(e0, e1) = all_20_2
% 247.16/58.46 (26) op(all_4_2, all_38_2) = e2
% 247.16/58.46 (27) ~ (e4 = e2)
% 247.16/58.46 (28) op(e2, e0) = all_40_2
% 247.16/58.46 (29) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.16/58.46 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.16/58.46 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.16/58.46 (30) op(e0, e4) = all_12_2
% 247.16/58.46 (31) ~ (all_20_2 = e2)
% 247.16/58.46
% 247.16/58.46 Begin of proof
% 247.16/58.46 |
% 247.16/58.46 | BETA: splitting (12) gives:
% 247.16/58.46 |
% 247.16/58.46 | Case 1:
% 247.16/58.46 | |
% 247.16/58.46 | | (32) ~ (all_34_2 = e2)
% 247.16/58.46 | |
% 247.16/58.46 | | REF_CLOSE: (6), (7), (9), (11), (14), (15), (17), (18), (20), (23), (24),
% 247.16/58.46 | | (27), (29), (32) are inconsistent by sub-proof #17.
% 247.16/58.46 | |
% 247.16/58.46 | Case 2:
% 247.16/58.46 | |
% 247.16/58.46 | | (33) all_34_2 = e2
% 247.16/58.46 | | (34) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) =
% 247.16/58.46 | | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e3) &
% 247.16/58.46 | | op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (2), (33) imply:
% 247.16/58.46 | | (35) ~ (all_244_24 = e2)
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (16), (33) imply:
% 247.16/58.46 | | (36) op(e2, e0) = e1
% 247.16/58.46 | |
% 247.16/58.46 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (13), (19), (21), (22), (25),
% 247.16/58.46 | | (26), (28), (30), (31), (34), (35), (36) are inconsistent by
% 247.16/58.46 | | sub-proof #117.
% 247.16/58.46 | |
% 247.16/58.46 | End of split
% 247.16/58.46 |
% 247.16/58.46 End of proof
% 247.16/58.46
% 247.16/58.46 Sub-proof #17 shows that the following formulas are inconsistent:
% 247.16/58.46 ----------------------------------------------------------------
% 247.16/58.46 (1) ~ (all_62_2 = e2)
% 247.16/58.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.46 (3) op(e2, e2) = all_244_8
% 247.16/58.46 (4) op(e1, e0) = all_34_2
% 247.16/58.46 (5) ~ (all_34_2 = e2)
% 247.16/58.46 (6) all_252_14 = e4
% 247.16/58.46 (7) op(all_244_15, all_244_15) = e1
% 247.16/58.46 (8) op(e1, e4) = all_16_2
% 247.16/58.46 (9) op(e1, e3) = all_62_2
% 247.16/58.46 (10) ~ (all_16_2 = e2)
% 247.16/58.46 (11) ~ (all_244_8 = e1)
% 247.16/58.46 (12) op(e1, e1) = all_244_15
% 247.16/58.46 (13) ~ (e4 = e2)
% 247.16/58.46 (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.16/58.46 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.16/58.46 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.16/58.46
% 247.16/58.46 Begin of proof
% 247.16/58.46 |
% 247.16/58.46 | BETA: splitting (14) gives:
% 247.16/58.46 |
% 247.16/58.46 | Case 1:
% 247.16/58.46 | |
% 247.16/58.46 | | (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 247.16/58.46 | | = e2)
% 247.16/58.46 | |
% 247.16/58.46 | | REF_CLOSE: (1), (2), (8), (9), (10), (15) are inconsistent by sub-proof
% 247.16/58.46 | | #925.
% 247.16/58.46 | |
% 247.16/58.46 | Case 2:
% 247.16/58.46 | |
% 247.16/58.46 | | (16) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 247.16/58.46 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.16/58.46 | |
% 247.16/58.46 | | BETA: splitting (16) gives:
% 247.16/58.46 | |
% 247.16/58.46 | | Case 1:
% 247.16/58.46 | | |
% 247.16/58.46 | | | (17) all_252_14 = e2 & op(e1, e2) = e2
% 247.16/58.46 | | |
% 247.16/58.46 | | | ALPHA: (17) implies:
% 247.16/58.46 | | | (18) all_252_14 = e2
% 247.16/58.46 | | |
% 247.16/58.46 | | | COMBINE_EQS: (6), (18) imply:
% 247.16/58.46 | | | (19) e4 = e2
% 247.16/58.46 | | |
% 247.16/58.46 | | | REDUCE: (13), (19) imply:
% 247.16/58.46 | | | (20) $false
% 247.16/58.46 | | |
% 247.16/58.46 | | | CLOSE: (20) is inconsistent.
% 247.16/58.46 | | |
% 247.16/58.46 | | Case 2:
% 247.16/58.46 | | |
% 247.16/58.46 | | | (21) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 247.16/58.46 | | | e0) = e2)
% 247.16/58.46 | | |
% 247.16/58.46 | | | REF_CLOSE: (2), (3), (4), (5), (7), (11), (12), (21) are inconsistent by
% 247.16/58.46 | | | sub-proof #79.
% 247.16/58.46 | | |
% 247.16/58.46 | | End of split
% 247.16/58.46 | |
% 247.16/58.46 | End of split
% 247.16/58.46 |
% 247.16/58.46 End of proof
% 247.16/58.46
% 247.16/58.46 Sub-proof #18 shows that the following formulas are inconsistent:
% 247.16/58.46 ----------------------------------------------------------------
% 247.16/58.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.46 (2) op(e2, e1) = all_38_2
% 247.16/58.46 (3) all_36_2 = e2
% 247.16/58.46 (4) ~ (all_12_0 = e3)
% 247.16/58.46 (5) op(e2, e1) = all_12_0
% 247.16/58.46 (6) op(all_36_2, e1) = e3
% 247.16/58.46 (7) ~ (all_214_2 = e1) | ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 &
% 247.16/58.46 op(e1, all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)) | ( ~
% 247.16/58.46 (all_214_1 = e0) & op(e2, e1) = all_214_1 & $i(all_214_1))
% 247.16/58.46 (8) all_214_2 = e1
% 247.16/58.46
% 247.16/58.46 Begin of proof
% 247.16/58.46 |
% 247.16/58.46 | REDUCE: (3), (6) imply:
% 247.16/58.46 | (9) op(e2, e1) = e3
% 247.16/58.46 |
% 247.16/58.46 | BETA: splitting (7) gives:
% 247.16/58.46 |
% 247.16/58.46 | Case 1:
% 247.16/58.46 | |
% 247.16/58.46 | | (10) ~ (all_214_2 = e1)
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (8), (10) imply:
% 247.16/58.46 | | (11) $false
% 247.16/58.46 | |
% 247.16/58.46 | | CLOSE: (11) is inconsistent.
% 247.16/58.46 | |
% 247.16/58.46 | Case 2:
% 247.16/58.46 | |
% 247.16/58.46 | | (12) ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 & op(e1, all_214_1) =
% 247.16/58.46 | | all_214_0 & $i(all_214_0) & $i(all_214_1)) | ( ~ (all_214_1 = e0)
% 247.16/58.46 | | & op(e2, e1) = all_214_1 & $i(all_214_1))
% 247.16/58.46 | |
% 247.16/58.46 | | BETA: splitting (12) gives:
% 247.16/58.46 | |
% 247.16/58.46 | | Case 1:
% 247.16/58.46 | | |
% 247.16/58.46 | | | (13) ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 & op(e1, all_214_1) =
% 247.16/58.46 | | | all_214_0 & $i(all_214_0) & $i(all_214_1)
% 247.16/58.46 | | |
% 247.16/58.46 | | | ALPHA: (13) implies:
% 247.16/58.46 | | | (14) op(e2, e1) = all_214_1
% 247.16/58.46 | | |
% 247.16/58.46 | | | REF_CLOSE: (1), (2), (4), (5), (9), (14) are inconsistent by sub-proof
% 247.16/58.46 | | | #19.
% 247.16/58.46 | | |
% 247.16/58.46 | | Case 2:
% 247.16/58.46 | | |
% 247.16/58.46 | | | (15) ~ (all_214_1 = e0) & op(e2, e1) = all_214_1 & $i(all_214_1)
% 247.16/58.46 | | |
% 247.16/58.46 | | | ALPHA: (15) implies:
% 247.16/58.46 | | | (16) op(e2, e1) = all_214_1
% 247.16/58.46 | | |
% 247.16/58.46 | | | REF_CLOSE: (1), (2), (4), (5), (9), (16) are inconsistent by sub-proof
% 247.16/58.46 | | | #19.
% 247.16/58.46 | | |
% 247.16/58.46 | | End of split
% 247.16/58.46 | |
% 247.16/58.46 | End of split
% 247.16/58.46 |
% 247.16/58.46 End of proof
% 247.16/58.46
% 247.16/58.46 Sub-proof #19 shows that the following formulas are inconsistent:
% 247.16/58.46 ----------------------------------------------------------------
% 247.16/58.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.46 (2) op(e2, e1) = all_38_2
% 247.16/58.46 (3) op(e2, e1) = e3
% 247.16/58.46 (4) ~ (all_12_0 = e3)
% 247.16/58.46 (5) op(e2, e1) = all_214_1
% 247.16/58.46 (6) op(e2, e1) = all_12_0
% 247.16/58.46
% 247.16/58.46 Begin of proof
% 247.16/58.46 |
% 247.16/58.46 | GROUND_INST: instantiating (1) with all_38_2, all_12_0, e1, e2, simplifying
% 247.16/58.46 | with (2), (6) gives:
% 247.16/58.46 | (7) all_38_2 = all_12_0
% 247.16/58.46 |
% 247.16/58.46 | GROUND_INST: instantiating (1) with all_38_2, all_214_1, e1, e2, simplifying
% 247.16/58.46 | with (2), (5) gives:
% 247.16/58.46 | (8) all_214_1 = all_38_2
% 247.16/58.46 |
% 247.16/58.46 | GROUND_INST: instantiating (1) with e3, all_214_1, e1, e2, simplifying with
% 247.16/58.46 | (3), (5) gives:
% 247.16/58.46 | (9) all_214_1 = e3
% 247.16/58.46 |
% 247.16/58.46 | COMBINE_EQS: (8), (9) imply:
% 247.16/58.46 | (10) all_38_2 = e3
% 247.16/58.46 |
% 247.16/58.46 | SIMP: (10) implies:
% 247.16/58.46 | (11) all_38_2 = e3
% 247.16/58.46 |
% 247.16/58.46 | COMBINE_EQS: (7), (11) imply:
% 247.16/58.46 | (12) all_12_0 = e3
% 247.16/58.46 |
% 247.16/58.46 | SIMP: (12) implies:
% 247.16/58.46 | (13) all_12_0 = e3
% 247.16/58.46 |
% 247.16/58.46 | REDUCE: (4), (13) imply:
% 247.16/58.46 | (14) $false
% 247.16/58.46 |
% 247.16/58.46 | CLOSE: (14) is inconsistent.
% 247.16/58.46 |
% 247.16/58.46 End of proof
% 247.16/58.46
% 247.16/58.46 Sub-proof #20 shows that the following formulas are inconsistent:
% 247.16/58.46 ----------------------------------------------------------------
% 247.16/58.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.16/58.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.16/58.46 (2) ~ (all_244_8 = all_64_2)
% 247.16/58.46 (3) op(e2, e2) = all_244_8
% 247.16/58.46 (4) op(all_244_15, all_244_15) = e1
% 247.16/58.46 (5) all_16_2 = e2
% 247.16/58.46 (6) op(e1, all_64_2) = e2
% 247.16/58.46 (7) op(e1, e1) = all_244_15
% 247.16/58.46 (8) op(e2, e4) = all_64_2
% 247.16/58.46 (9) all_170_2 = all_16_2
% 247.16/58.46 (10) op(all_16_2, e4) = e1
% 247.16/58.46 (11) ~ (all_170_2 = e2) | ( ~ (all_170_0 = e0) & op(e4, e2) = all_170_1 &
% 247.16/58.46 op(e2, all_170_1) = all_170_0 & $i(all_170_0) & $i(all_170_1)) | ( ~
% 247.16/58.46 (all_170_1 = e3) & op(e4, e2) = all_170_1 & $i(all_170_1))
% 247.16/58.46
% 247.16/58.46 Begin of proof
% 247.16/58.46 |
% 247.16/58.46 | COMBINE_EQS: (5), (9) imply:
% 247.16/58.46 | (12) all_170_2 = e2
% 247.16/58.46 |
% 247.16/58.46 | REDUCE: (5), (10) imply:
% 247.16/58.46 | (13) op(e2, e4) = e1
% 247.16/58.46 |
% 247.16/58.46 | BETA: splitting (11) gives:
% 247.16/58.46 |
% 247.16/58.46 | Case 1:
% 247.16/58.46 | |
% 247.16/58.46 | | (14) ~ (all_170_2 = e2)
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (12), (14) imply:
% 247.16/58.46 | | (15) $false
% 247.16/58.46 | |
% 247.16/58.46 | | CLOSE: (15) is inconsistent.
% 247.16/58.46 | |
% 247.16/58.46 | Case 2:
% 247.16/58.46 | |
% 247.16/58.46 | |
% 247.16/58.46 | | GROUND_INST: instantiating (1) with all_64_2, e1, e4, e2, simplifying with
% 247.16/58.46 | | (8), (13) gives:
% 247.16/58.46 | | (16) all_64_2 = e1
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (2), (16) imply:
% 247.16/58.46 | | (17) ~ (all_244_8 = e1)
% 247.16/58.46 | |
% 247.16/58.46 | | REDUCE: (6), (16) imply:
% 247.16/58.46 | | (18) op(e1, e1) = e2
% 247.16/58.46 | |
% 247.16/58.46 | | REF_CLOSE: (1), (3), (4), (7), (17), (18) are inconsistent by sub-proof
% 247.16/58.46 | | #991.
% 247.16/58.46 | |
% 247.16/58.46 | End of split
% 247.16/58.46 |
% 247.16/58.46 End of proof
% 247.16/58.46
% 247.16/58.46 Sub-proof #21 shows that the following formulas are inconsistent:
% 247.16/58.46 ----------------------------------------------------------------
% 247.16/58.46 (1) ~ (all_10_2 = e4)
% 247.16/58.46 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 247.16/58.46 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 247.16/58.46 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 247.16/58.46 (3) op(all_4_2, e2) = e1
% 247.16/58.46 (4) op(e4, e1) = e0
% 247.16/58.46 (5) ~ (all_84_2 = all_10_2)
% 247.16/58.46 (6) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 247.16/58.46 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 247.16/58.46 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 247.16/58.46 (7) all_94_2 = all_38_2
% 247.16/58.46 (8) op(all_34_2, e4) = e0
% 247.16/58.46 (9) op(all_62_2, all_36_2) = e3
% 247.16/58.46 (10) op(all_38_2, e1) = e2
% 247.65/58.46 (11) all_250_13 = all_38_2
% 247.65/58.46 (12) ~ (e2 = e0)
% 247.65/58.46 (13) op(all_38_2, all_4_2) = e1
% 247.65/58.46 (14) op(all_64_2, e4) = e2
% 247.65/58.47 (15) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 247.65/58.47 all_250_20 = e0
% 247.65/58.47 (16) ~ (all_62_2 = all_22_2)
% 247.65/58.47 (17) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.65/58.47 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.65/58.47 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.65/58.47 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.65/58.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.65/58.47 (19) op(e2, e3) = all_10_2
% 247.65/58.47 (20) ~ (e3 = e2)
% 247.65/58.47 (21) op(e0, e0) = all_244_24
% 247.65/58.47 (22) ~ (all_12_2 = e3)
% 247.65/58.47 (23) op(e2, e2) = all_244_8
% 247.65/58.47 (24) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.65/58.47 all_250_11 = e0
% 247.65/58.47 (25) op(e2, e1) = all_38_2
% 247.65/58.47 (26) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.65/58.47 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.65/58.47 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.65/58.47 (27) op(e1, e0) = all_34_2
% 247.65/58.47 (28) op(all_28_2, e2) = e0
% 247.65/58.47 (29) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.65/58.47 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.65/58.47 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.65/58.47 (30) all_78_2 = all_10_2
% 247.65/58.47 (31) op(e0, e2) = all_28_2
% 247.65/58.47 (32) all_252_14 = e4
% 247.65/58.47 (33) ~ (all_28_2 = e1)
% 247.65/58.47 (34) op(e1, e4) = all_20_1
% 247.65/58.47 (35) all_106_2 = all_38_2
% 247.65/58.47 (36) ~ (all_244_8 = all_38_2)
% 247.65/58.47 (37) op(all_244_15, all_244_15) = e1
% 247.65/58.47 (38) all_250_21 = all_22_2
% 247.65/58.47 (39) op(e1, e4) = all_16_2
% 247.65/58.47 (40) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.65/58.47 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.65/58.47 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.65/58.47 (41) op(e1, e3) = all_62_2
% 247.65/58.47 (42) ~ (e3 = e0)
% 247.65/58.47 (43) all_198_2 = all_34_2
% 247.65/58.47 (44) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.65/58.47 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.65/58.47 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.65/58.47 (45) ~ (all_22_2 = e4)
% 247.65/58.47 (46) all_70_2 = all_62_2
% 247.65/58.47 (47) op(all_48_2, all_22_2) = e0
% 247.65/58.47 (48) ~ (all_12_2 = e2)
% 247.65/58.47 (49) op(e3, e1) = all_36_2
% 247.65/58.47 (50) ~ (all_28_2 = all_12_2)
% 247.65/58.47 (51) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.65/58.47 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.65/58.47 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.65/58.47 (52) ~ (all_16_2 = e2)
% 247.65/58.47 (53) ~ (all_8_2 = e1)
% 247.65/58.47 (54) op(all_40_2, e0) = e2
% 247.65/58.47 (55) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.65/58.47 all_250_22 = e0
% 247.65/58.47 (56) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.65/58.47 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.65/58.47 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.65/58.47 (57) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.65/58.47 all_250_13 = e0
% 247.65/58.47 (58) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.65/58.47 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.65/58.47 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.65/58.47 (59) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 247.65/58.47 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 247.65/58.47 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 247.65/58.47 (60) all_60_2 = e4
% 247.65/58.47 (61) ~ (all_38_2 = e4)
% 247.65/58.47 (62) ~ (all_28_2 = e4)
% 247.65/58.47 (63) op(all_22_2, e3) = e0
% 247.65/58.47 (64) all_68_2 = all_22_2
% 247.65/58.47 (65) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 247.65/58.47 op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 =
% 247.65/58.47 e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 247.65/58.47 (66) op(e0, e3) = all_22_2
% 247.65/58.47 (67) ~ (all_244_24 = e4)
% 247.65/58.47 (68) ~ (all_28_2 = all_22_2)
% 247.65/58.47 (69) op(all_62_2, e3) = e1
% 247.65/58.47 (70) op(e4, e1) = all_26_2
% 247.65/58.47 (71) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.65/58.47 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.65/58.47 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.65/58.47 (72) op(all_10_2, e3) = e2
% 247.65/58.47 (73) op(all_30_2, all_12_2) = e0
% 247.65/58.47 (74) ~ (all_12_2 = e4)
% 247.65/58.47 (75) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.65/58.47 all_250_21 = e0
% 247.65/58.47 (76) ~ (all_244_15 = all_62_2)
% 247.65/58.47 (77) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.65/58.47 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.65/58.47 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.65/58.47 (78) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.65/58.47 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.65/58.47 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.65/58.47 (79) all_250_11 = all_10_2
% 247.65/58.47 (80) ~ (all_22_2 = all_12_2)
% 247.65/58.47 (81) all_230_2 = all_20_2
% 247.65/58.47 (82) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 247.65/58.47 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 247.65/58.47 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.65/58.47 (83) op(e1, e1) = all_244_15
% 247.65/58.47 (84) op(e0, e1) = all_20_2
% 247.65/58.47 (85) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 247.65/58.47 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 247.65/58.47 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 247.65/58.47 (86) op(all_48_2, e0) = e3
% 247.65/58.47 (87) all_82_2 = all_28_2
% 247.65/58.47 (88) ~ (all_84_2 = all_22_2)
% 247.65/58.47 (89) op(e1, e2) = all_4_2
% 247.65/58.47 (90) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.65/58.47 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.65/58.47 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.65/58.47 (91) op(all_4_2, all_38_2) = e2
% 247.65/58.47 (92) op(e4, e3) = all_84_2
% 247.65/58.47 (93) all_118_2 = all_22_2
% 247.65/58.47 (94) ~ (all_62_2 = all_10_2)
% 247.65/58.47 (95) op(e2, e4) = all_64_2
% 247.65/58.47 (96) ~ (all_22_2 = all_10_2)
% 247.65/58.47 (97) ~ (all_38_2 = all_26_2)
% 247.65/58.47 (98) op(all_40_2, all_28_2) = e0
% 247.65/58.47 (99) ~ (e4 = e2)
% 247.65/58.47 (100) all_252_4 = e1
% 247.65/58.47 (101) ~ (all_22_2 = all_20_2)
% 247.65/58.47 (102) ~ (all_244_8 = all_8_2)
% 247.65/58.47 (103) op(e3, e2) = all_8_2
% 247.65/58.47 (104) op(all_36_2, e1) = e3
% 247.65/58.47 (105) ~ (all_38_2 = all_10_2)
% 247.65/58.47 (106) ~ (all_244_15 = all_36_2)
% 247.65/58.47 (107) ~ (all_244_24 = all_22_2)
% 247.65/58.47 (108) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.65/58.47 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) |
% 247.65/58.47 ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.65/58.47 (109) ~ (all_214_2 = e1) | ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 &
% 247.65/58.47 op(e1, all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)) | ( ~
% 247.65/58.47 (all_214_1 = e0) & op(e2, e1) = all_214_1 & $i(all_214_1))
% 247.65/58.47 (110) op(all_8_2, all_10_2) = e2
% 247.65/58.47 (111) ~ (all_244_8 = all_28_2)
% 247.65/58.47 (112) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.65/58.47 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.65/58.47 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.65/58.47 (113) all_250_22 = all_28_2
% 247.65/58.47 (114) all_250_20 = all_12_2
% 247.65/58.47 (115) all_90_2 = all_22_2
% 247.65/58.47 (116) all_46_2 = all_36_2
% 247.65/58.47 (117) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 247.65/58.47 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 247.65/58.47 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 247.65/58.47 (118) all_214_2 = e1
% 247.65/58.47 (119) op(all_30_2, e0) = e4
% 247.65/58.47 (120) op(all_244_24, all_244_24) = e0
% 247.65/58.47 (121) op(e0, e4) = all_12_2
% 247.65/58.47 (122) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.65/58.47 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.65/58.47 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.65/58.47 (123) all_124_2 = all_10_2
% 247.65/58.47
% 247.65/58.47 Begin of proof
% 247.65/58.47 |
% 247.65/58.47 | BETA: splitting (2) gives:
% 247.65/58.47 |
% 247.65/58.47 | Case 1:
% 247.65/58.47 | |
% 247.65/58.47 | | (124) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3)
% 247.65/58.47 | | = e4)
% 247.65/58.47 | |
% 247.65/58.47 | | BETA: splitting (124) gives:
% 247.65/58.47 | |
% 247.65/58.47 | | Case 1:
% 247.65/58.47 | | |
% 247.65/58.47 | | | (125) all_252_20 = e4 & op(e0, e4) = e4
% 247.65/58.47 | | |
% 247.65/58.47 | | | REF_CLOSE: (18), (74), (121), (125) are inconsistent by sub-proof #602.
% 247.65/58.47 | | |
% 247.65/58.47 | | Case 2:
% 247.65/58.47 | | |
% 247.65/58.47 | | | (126) all_252_21 = e4 & op(e0, e3) = e4
% 247.65/58.47 | | |
% 247.65/58.47 | | | REF_CLOSE: (18), (45), (66), (126) are inconsistent by sub-proof #805.
% 247.65/58.47 | | |
% 247.65/58.47 | | End of split
% 247.65/58.47 | |
% 247.65/58.47 | Case 2:
% 247.65/58.47 | |
% 247.65/58.47 | | (127) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1)
% 247.65/58.47 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 247.65/58.47 | |
% 247.65/58.47 | | BETA: splitting (127) gives:
% 247.65/58.47 | |
% 247.65/58.47 | | Case 1:
% 247.65/58.47 | | |
% 247.65/58.47 | | | (128) all_252_22 = e4 & op(e0, e2) = e4
% 247.65/58.47 | | |
% 247.65/58.47 | | | REF_CLOSE: (18), (31), (62), (128) are inconsistent by sub-proof #585.
% 247.65/58.47 | | |
% 247.65/58.47 | | Case 2:
% 247.65/58.47 | | |
% 247.65/58.47 | | | (129) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 247.65/58.47 | | | e0) = e4)
% 247.65/58.47 | | |
% 247.65/58.47 | | | BETA: splitting (129) gives:
% 247.65/58.47 | | |
% 247.65/58.47 | | | Case 1:
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | (130) all_252_23 = e4 & op(e0, e1) = e4
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | ALPHA: (130) implies:
% 247.65/58.47 | | | | (131) all_252_23 = e4
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | GROUND_INST: instantiating (18) with all_16_2, all_20_1, e4, e1,
% 247.65/58.47 | | | | simplifying with (34), (39) gives:
% 247.65/58.47 | | | | (132) all_20_1 = all_16_2
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | GROUND_INST: instantiating (18) with all_26_2, e0, e1, e4, simplifying
% 247.65/58.47 | | | | with (4), (70) gives:
% 247.65/58.47 | | | | (133) all_26_2 = e0
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | REDUCE: (97), (133) imply:
% 247.65/58.47 | | | | (134) ~ (all_38_2 = e0)
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | BETA: splitting (109) gives:
% 247.65/58.47 | | | |
% 247.65/58.47 | | | | Case 1:
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | (135) ~ (all_214_2 = e1)
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | REDUCE: (118), (135) imply:
% 247.65/58.47 | | | | | (136) $false
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | CLOSE: (136) is inconsistent.
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | Case 2:
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | (137) ( ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 & op(e1,
% 247.65/58.47 | | | | | all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)) |
% 247.65/58.47 | | | | | ( ~ (all_214_1 = e0) & op(e2, e1) = all_214_1 &
% 247.65/58.47 | | | | | $i(all_214_1))
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | BETA: splitting (137) gives:
% 247.65/58.47 | | | | |
% 247.65/58.47 | | | | | Case 1:
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | (138) ~ (all_214_0 = e3) & op(e2, e1) = all_214_1 & op(e1,
% 247.65/58.47 | | | | | | all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1)
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | ALPHA: (138) implies:
% 247.65/58.47 | | | | | | (139) op(e2, e1) = all_214_1
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | GROUND_INST: instantiating (18) with all_38_2, all_214_1, e1, e2,
% 247.65/58.47 | | | | | | simplifying with (25), (139) gives:
% 247.65/58.47 | | | | | | (140) all_214_1 = all_38_2
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 247.65/58.47 | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 247.65/58.47 | | | | | | (22), (23), (24), (26), (27), (28), (29), (30), (32),
% 247.65/58.47 | | | | | | (33), (35), (36), (37), (38), (39), (40), (41), (42),
% 247.65/58.47 | | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 247.65/58.47 | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 247.65/58.47 | | | | | | (61), (62), (63), (64), (65), (66), (68), (69), (71),
% 247.65/58.47 | | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 247.65/58.47 | | | | | | (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 247.65/58.47 | | | | | | (90), (91), (92), (93), (94), (95), (96), (98), (99),
% 247.65/58.47 | | | | | | (100), (101), (102), (103), (104), (105), (106), (107),
% 247.65/58.47 | | | | | | (108), (110), (111), (112), (113), (114), (115), (116),
% 247.65/58.47 | | | | | | (117), (119), (120), (121), (122), (123), (131), (134),
% 247.65/58.47 | | | | | | (139), (140) are inconsistent by sub-proof #22.
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | Case 2:
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | (141) ~ (all_214_1 = e0) & op(e2, e1) = all_214_1 &
% 247.65/58.47 | | | | | | $i(all_214_1)
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | ALPHA: (141) implies:
% 247.65/58.47 | | | | | | (142) ~ (all_214_1 = e0)
% 247.65/58.47 | | | | | | (143) op(e2, e1) = all_214_1
% 247.65/58.47 | | | | | |
% 247.65/58.47 | | | | | | GROUND_INST: instantiating (18) with all_38_2, all_214_1, e1, e2,
% 247.65/58.47 | | | | | | simplifying with (25), (143) gives:
% 247.65/58.47 | | | | | | (144) all_214_1 = all_38_2
% 247.65/58.47 | | | | | |
% 247.65/58.48 | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 247.65/58.48 | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 247.65/58.48 | | | | | | (22), (23), (24), (26), (27), (28), (29), (30), (32),
% 247.65/58.48 | | | | | | (33), (35), (36), (37), (38), (39), (40), (41), (42),
% 247.65/58.48 | | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 247.65/58.48 | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 247.65/58.48 | | | | | | (61), (62), (63), (64), (65), (66), (68), (69), (71),
% 247.65/58.48 | | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 247.65/58.48 | | | | | | (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 247.65/58.48 | | | | | | (90), (91), (92), (93), (94), (95), (96), (98), (99),
% 247.65/58.48 | | | | | | (100), (101), (102), (103), (104), (105), (106), (107),
% 247.65/58.48 | | | | | | (108), (110), (111), (112), (113), (114), (115), (116),
% 247.65/58.48 | | | | | | (117), (119), (120), (121), (122), (123), (131), (134),
% 247.65/58.48 | | | | | | (143), (144) are inconsistent by sub-proof #22.
% 247.65/58.48 | | | | | |
% 247.65/58.48 | | | | | End of split
% 247.65/58.48 | | | | |
% 247.65/58.48 | | | | End of split
% 247.65/58.48 | | | |
% 247.65/58.48 | | | Case 2:
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | (145) all_252_24 = e4 & op(e0, e0) = e4
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | REF_CLOSE: (18), (21), (67), (145) are inconsistent by sub-proof #679.
% 247.65/58.48 | | | |
% 247.65/58.48 | | | End of split
% 247.65/58.48 | | |
% 247.65/58.48 | | End of split
% 247.65/58.48 | |
% 247.65/58.48 | End of split
% 247.65/58.48 |
% 247.65/58.48 End of proof
% 247.65/58.48
% 247.65/58.48 Sub-proof #22 shows that the following formulas are inconsistent:
% 247.65/58.48 ----------------------------------------------------------------
% 247.65/58.48 (1) ~ (all_10_2 = e4)
% 247.65/58.48 (2) op(all_4_2, e2) = e1
% 247.65/58.48 (3) op(e4, e1) = e0
% 247.65/58.48 (4) ~ (all_84_2 = all_10_2)
% 247.65/58.48 (5) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 247.65/58.48 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 247.65/58.48 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 247.65/58.48 (6) all_94_2 = all_38_2
% 247.65/58.48 (7) op(all_34_2, e4) = e0
% 247.65/58.48 (8) op(all_62_2, all_36_2) = e3
% 247.65/58.48 (9) op(all_38_2, e1) = e2
% 247.65/58.48 (10) all_250_13 = all_38_2
% 247.65/58.48 (11) ~ (e2 = e0)
% 247.65/58.48 (12) op(all_38_2, all_4_2) = e1
% 247.65/58.48 (13) op(all_64_2, e4) = e2
% 247.65/58.48 (14) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 247.65/58.48 all_250_20 = e0
% 247.65/58.48 (15) ~ (all_62_2 = all_22_2)
% 247.65/58.48 (16) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.65/58.48 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.65/58.48 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.65/58.48 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.65/58.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.65/58.48 (18) op(e2, e3) = all_10_2
% 247.65/58.48 (19) ~ (e3 = e2)
% 247.65/58.48 (20) op(e0, e0) = all_244_24
% 247.65/58.48 (21) ~ (all_12_2 = e3)
% 247.65/58.48 (22) op(e2, e2) = all_244_8
% 247.65/58.48 (23) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.65/58.48 all_250_11 = e0
% 247.65/58.48 (24) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.65/58.48 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.65/58.48 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.65/58.48 (25) op(e1, e0) = all_34_2
% 247.65/58.48 (26) op(all_28_2, e2) = e0
% 247.65/58.48 (27) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.65/58.48 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.65/58.48 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.65/58.48 (28) all_78_2 = all_10_2
% 247.65/58.48 (29) all_252_14 = e4
% 247.65/58.48 (30) ~ (all_28_2 = e1)
% 247.65/58.48 (31) all_106_2 = all_38_2
% 247.65/58.48 (32) ~ (all_244_8 = all_38_2)
% 247.65/58.48 (33) op(all_244_15, all_244_15) = e1
% 247.65/58.48 (34) all_250_21 = all_22_2
% 247.65/58.48 (35) op(e1, e4) = all_16_2
% 247.65/58.48 (36) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.65/58.48 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.65/58.48 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.65/58.48 (37) op(e1, e3) = all_62_2
% 247.65/58.48 (38) ~ (e3 = e0)
% 247.65/58.48 (39) all_198_2 = all_34_2
% 247.65/58.48 (40) ~ (all_38_2 = e0)
% 247.65/58.48 (41) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.65/58.48 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.65/58.48 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.65/58.48 (42) ~ (all_22_2 = e4)
% 247.65/58.48 (43) all_70_2 = all_62_2
% 247.65/58.48 (44) op(all_48_2, all_22_2) = e0
% 247.65/58.48 (45) ~ (all_12_2 = e2)
% 247.65/58.48 (46) op(e3, e1) = all_36_2
% 247.65/58.48 (47) ~ (all_28_2 = all_12_2)
% 247.65/58.48 (48) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.65/58.48 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.65/58.48 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.65/58.48 (49) ~ (all_16_2 = e2)
% 247.65/58.48 (50) ~ (all_8_2 = e1)
% 247.65/58.48 (51) op(all_40_2, e0) = e2
% 247.65/58.48 (52) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.65/58.48 all_250_22 = e0
% 247.65/58.48 (53) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.65/58.48 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.65/58.48 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.65/58.48 (54) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.65/58.48 all_250_13 = e0
% 247.65/58.48 (55) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.65/58.48 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.65/58.48 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.65/58.48 (56) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 247.65/58.48 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 247.65/58.48 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 247.65/58.48 (57) all_60_2 = e4
% 247.65/58.48 (58) ~ (all_38_2 = e4)
% 247.65/58.48 (59) ~ (all_28_2 = e4)
% 247.65/58.48 (60) op(e2, e1) = all_214_1
% 247.65/58.48 (61) op(all_22_2, e3) = e0
% 247.65/58.48 (62) all_68_2 = all_22_2
% 247.65/58.48 (63) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 247.65/58.48 op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 =
% 247.65/58.48 e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 247.65/58.48 (64) op(e0, e3) = all_22_2
% 247.65/58.48 (65) ~ (all_28_2 = all_22_2)
% 247.65/58.48 (66) op(all_62_2, e3) = e1
% 247.65/58.48 (67) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.65/58.48 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.65/58.48 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.65/58.48 (68) op(all_10_2, e3) = e2
% 247.65/58.48 (69) op(all_30_2, all_12_2) = e0
% 247.65/58.48 (70) ~ (all_12_2 = e4)
% 247.65/58.48 (71) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.65/58.48 all_250_21 = e0
% 247.65/58.48 (72) ~ (all_244_15 = all_62_2)
% 247.65/58.48 (73) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.65/58.48 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.65/58.48 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.65/58.48 (74) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.65/58.48 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.65/58.48 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.65/58.48 (75) all_250_11 = all_10_2
% 247.65/58.48 (76) ~ (all_22_2 = all_12_2)
% 247.65/58.48 (77) all_230_2 = all_20_2
% 247.65/58.48 (78) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 247.65/58.48 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 247.65/58.48 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.65/58.48 (79) op(e1, e1) = all_244_15
% 247.65/58.48 (80) op(e0, e1) = all_20_2
% 247.65/58.48 (81) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 247.65/58.48 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 247.65/58.48 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 247.65/58.48 (82) op(all_48_2, e0) = e3
% 247.65/58.48 (83) all_82_2 = all_28_2
% 247.65/58.48 (84) ~ (all_84_2 = all_22_2)
% 247.65/58.48 (85) op(e1, e2) = all_4_2
% 247.65/58.48 (86) all_214_1 = all_38_2
% 247.65/58.48 (87) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.65/58.48 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.65/58.48 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.65/58.48 (88) op(all_4_2, all_38_2) = e2
% 247.65/58.48 (89) op(e4, e3) = all_84_2
% 247.65/58.48 (90) all_118_2 = all_22_2
% 247.65/58.48 (91) ~ (all_62_2 = all_10_2)
% 247.65/58.48 (92) op(e2, e4) = all_64_2
% 247.65/58.48 (93) ~ (all_22_2 = all_10_2)
% 247.65/58.48 (94) op(all_40_2, all_28_2) = e0
% 247.65/58.48 (95) ~ (e4 = e2)
% 247.65/58.48 (96) all_252_4 = e1
% 247.65/58.48 (97) ~ (all_22_2 = all_20_2)
% 247.65/58.48 (98) ~ (all_244_8 = all_8_2)
% 247.65/58.48 (99) op(e3, e2) = all_8_2
% 247.65/58.48 (100) op(all_36_2, e1) = e3
% 247.65/58.48 (101) ~ (all_38_2 = all_10_2)
% 247.65/58.48 (102) ~ (all_244_15 = all_36_2)
% 247.65/58.48 (103) ~ (all_244_24 = all_22_2)
% 247.65/58.48 (104) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.65/58.48 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) |
% 247.65/58.48 ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.65/58.48 (105) op(all_8_2, all_10_2) = e2
% 247.65/58.48 (106) ~ (all_244_8 = all_28_2)
% 247.65/58.48 (107) all_252_23 = e4
% 247.65/58.48 (108) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.65/58.48 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.65/58.48 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.65/58.48 (109) all_250_22 = all_28_2
% 247.65/58.48 (110) all_250_20 = all_12_2
% 247.65/58.48 (111) all_90_2 = all_22_2
% 247.65/58.48 (112) all_46_2 = all_36_2
% 247.65/58.48 (113) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 247.65/58.48 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 247.65/58.48 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 247.65/58.48 (114) op(all_30_2, e0) = e4
% 247.65/58.48 (115) op(all_244_24, all_244_24) = e0
% 247.65/58.48 (116) op(e0, e4) = all_12_2
% 247.65/58.48 (117) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.65/58.48 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.65/58.48 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.65/58.48 (118) all_124_2 = all_10_2
% 247.65/58.48
% 247.65/58.48 Begin of proof
% 247.65/58.48 |
% 247.65/58.48 | REDUCE: (60), (86) imply:
% 247.65/58.48 | (119) op(e2, e1) = all_38_2
% 247.65/58.48 |
% 247.65/58.48 | BETA: splitting (113) gives:
% 247.65/58.48 |
% 247.65/58.48 | Case 1:
% 247.65/58.48 | |
% 247.65/58.48 | | (120) ~ (all_22_2 = e1)
% 247.65/58.48 | |
% 247.65/58.48 | | BETA: splitting (63) gives:
% 247.65/58.48 | |
% 247.65/58.48 | | Case 1:
% 247.65/58.48 | | |
% 247.65/58.48 | | | (121) ~ (all_60_2 = e4)
% 247.65/58.48 | | |
% 247.65/58.48 | | | REDUCE: (57), (121) imply:
% 247.65/58.48 | | | (122) $false
% 247.65/58.48 | | |
% 247.65/58.48 | | | CLOSE: (122) is inconsistent.
% 247.65/58.48 | | |
% 247.65/58.48 | | Case 2:
% 247.65/58.48 | | |
% 247.65/58.48 | | | (123) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 247.65/58.48 | | | all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 = e3) &
% 247.65/58.48 | | | op(e1, e4) = all_60_1 & $i(all_60_1))
% 247.65/58.48 | | |
% 247.65/58.48 | | | BETA: splitting (123) gives:
% 247.65/58.48 | | |
% 247.65/58.48 | | | Case 1:
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | (124) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 247.65/58.48 | | | | all_60_1 & $i(all_60_0) & $i(all_60_1)
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | ALPHA: (124) implies:
% 247.65/58.48 | | | | (125) op(e1, e4) = all_60_1
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 247.65/58.48 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 247.65/58.48 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 247.65/58.48 | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 247.65/58.48 | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 247.65/58.48 | | | | (52), (53), (54), (55), (56), (58), (59), (61), (62), (64),
% 247.65/58.48 | | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 247.65/58.48 | | | | (75), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 247.65/58.48 | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 247.65/58.48 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 247.65/58.48 | | | | (106), (107), (108), (109), (110), (111), (112), (114),
% 247.65/58.48 | | | | (115), (116), (117), (118), (119), (120), (125) are
% 247.65/58.48 | | | | inconsistent by sub-proof #23.
% 247.65/58.48 | | | |
% 247.65/58.48 | | | Case 2:
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | (126) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1)
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | ALPHA: (126) implies:
% 247.65/58.48 | | | | (127) op(e1, e4) = all_60_1
% 247.65/58.48 | | | |
% 247.65/58.48 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 247.65/58.48 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 247.65/58.48 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 247.65/58.48 | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 247.65/58.48 | | | | (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 247.65/58.48 | | | | (52), (53), (54), (55), (56), (58), (59), (61), (62), (64),
% 247.65/58.48 | | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 247.65/58.48 | | | | (75), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 247.65/58.48 | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 247.65/58.48 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 247.65/58.48 | | | | (106), (107), (108), (109), (110), (111), (112), (114),
% 247.65/58.48 | | | | (115), (116), (117), (118), (119), (120), (127) are
% 247.65/58.48 | | | | inconsistent by sub-proof #23.
% 247.65/58.48 | | | |
% 247.65/58.48 | | | End of split
% 247.65/58.48 | | |
% 247.65/58.48 | | End of split
% 247.65/58.48 | |
% 247.65/58.48 | Case 2:
% 247.65/58.48 | |
% 247.65/58.48 | | (128) all_22_2 = e1
% 247.65/58.48 | |
% 247.65/58.48 | | REDUCE: (76), (128) imply:
% 247.65/58.48 | | (129) ~ (all_12_2 = e1)
% 247.65/58.48 | |
% 247.65/58.48 | | SIMP: (129) implies:
% 247.65/58.48 | | (130) ~ (all_12_2 = e1)
% 247.65/58.48 | |
% 247.65/58.48 | | REF_CLOSE: (14), (17), (21), (45), (69), (70), (110), (114), (130) are
% 247.65/58.48 | | inconsistent by sub-proof #582.
% 247.65/58.48 | |
% 247.65/58.48 | End of split
% 247.65/58.48 |
% 247.65/58.49 End of proof
% 247.65/58.49
% 247.65/58.49 Sub-proof #23 shows that the following formulas are inconsistent:
% 247.65/58.49 ----------------------------------------------------------------
% 247.65/58.49 (1) ~ (all_10_2 = e4)
% 247.65/58.49 (2) op(all_4_2, e2) = e1
% 247.65/58.49 (3) op(e4, e1) = e0
% 247.65/58.49 (4) ~ (all_84_2 = all_10_2)
% 247.65/58.49 (5) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 247.65/58.49 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 247.65/58.49 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 247.65/58.49 (6) all_94_2 = all_38_2
% 247.65/58.49 (7) op(all_34_2, e4) = e0
% 247.65/58.49 (8) op(all_62_2, all_36_2) = e3
% 247.65/58.49 (9) op(all_38_2, e1) = e2
% 247.65/58.49 (10) all_250_13 = all_38_2
% 247.65/58.49 (11) ~ (e2 = e0)
% 247.65/58.49 (12) op(all_38_2, all_4_2) = e1
% 247.65/58.49 (13) op(all_64_2, e4) = e2
% 247.65/58.49 (14) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 247.65/58.49 all_250_20 = e0
% 247.65/58.49 (15) ~ (all_62_2 = all_22_2)
% 247.65/58.49 (16) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.65/58.49 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.65/58.49 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.65/58.49 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.65/58.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.65/58.49 (18) op(e2, e3) = all_10_2
% 247.65/58.49 (19) ~ (e3 = e2)
% 247.65/58.49 (20) op(e0, e0) = all_244_24
% 247.65/58.49 (21) ~ (all_12_2 = e3)
% 247.65/58.49 (22) op(e2, e2) = all_244_8
% 247.65/58.49 (23) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.65/58.49 all_250_11 = e0
% 247.65/58.49 (24) op(e2, e1) = all_38_2
% 247.65/58.49 (25) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.65/58.49 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.65/58.49 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.65/58.49 (26) op(e1, e0) = all_34_2
% 247.65/58.49 (27) op(all_28_2, e2) = e0
% 247.65/58.49 (28) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.65/58.49 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.65/58.49 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.65/58.49 (29) all_78_2 = all_10_2
% 247.65/58.49 (30) all_252_14 = e4
% 247.65/58.49 (31) ~ (all_28_2 = e1)
% 247.65/58.49 (32) all_106_2 = all_38_2
% 247.65/58.49 (33) ~ (all_244_8 = all_38_2)
% 247.65/58.49 (34) op(all_244_15, all_244_15) = e1
% 247.65/58.49 (35) all_250_21 = all_22_2
% 247.65/58.49 (36) op(e1, e4) = all_16_2
% 247.65/58.49 (37) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.65/58.49 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.65/58.49 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.65/58.49 (38) op(e1, e3) = all_62_2
% 247.65/58.49 (39) ~ (e3 = e0)
% 247.65/58.49 (40) all_198_2 = all_34_2
% 247.65/58.49 (41) ~ (all_38_2 = e0)
% 247.65/58.49 (42) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.65/58.49 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.65/58.49 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.65/58.49 (43) ~ (all_22_2 = e4)
% 247.65/58.49 (44) all_70_2 = all_62_2
% 247.65/58.49 (45) op(all_48_2, all_22_2) = e0
% 247.65/58.49 (46) ~ (all_12_2 = e2)
% 247.65/58.49 (47) op(e3, e1) = all_36_2
% 247.65/58.49 (48) ~ (all_28_2 = all_12_2)
% 247.65/58.49 (49) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.65/58.49 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.65/58.49 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.65/58.49 (50) ~ (all_16_2 = e2)
% 247.65/58.49 (51) ~ (all_8_2 = e1)
% 247.65/58.49 (52) op(all_40_2, e0) = e2
% 247.65/58.49 (53) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.65/58.49 all_250_22 = e0
% 247.65/58.49 (54) ~ (all_22_2 = e1)
% 247.65/58.49 (55) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.65/58.49 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.65/58.49 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.65/58.49 (56) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.65/58.49 all_250_13 = e0
% 247.65/58.49 (57) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.65/58.49 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.65/58.49 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.65/58.49 (58) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 247.65/58.49 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 247.65/58.49 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 247.65/58.49 (59) ~ (all_38_2 = e4)
% 247.65/58.49 (60) op(e1, e4) = all_60_1
% 247.65/58.49 (61) ~ (all_28_2 = e4)
% 247.65/58.49 (62) op(all_22_2, e3) = e0
% 247.65/58.49 (63) all_68_2 = all_22_2
% 247.65/58.49 (64) op(e0, e3) = all_22_2
% 247.65/58.49 (65) ~ (all_28_2 = all_22_2)
% 247.65/58.49 (66) op(all_62_2, e3) = e1
% 247.65/58.49 (67) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.65/58.49 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.65/58.49 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.65/58.49 (68) op(all_10_2, e3) = e2
% 247.65/58.49 (69) op(all_30_2, all_12_2) = e0
% 247.65/58.49 (70) ~ (all_12_2 = e4)
% 247.65/58.49 (71) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.65/58.49 all_250_21 = e0
% 247.65/58.49 (72) ~ (all_244_15 = all_62_2)
% 247.65/58.49 (73) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.65/58.49 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.65/58.49 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.65/58.49 (74) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.65/58.49 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.65/58.49 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.65/58.49 (75) all_250_11 = all_10_2
% 247.65/58.49 (76) all_230_2 = all_20_2
% 247.65/58.49 (77) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 247.65/58.49 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 247.65/58.49 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.65/58.49 (78) op(e1, e1) = all_244_15
% 247.65/58.49 (79) op(e0, e1) = all_20_2
% 247.65/58.49 (80) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 247.65/58.49 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 247.65/58.49 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 247.65/58.49 (81) op(all_48_2, e0) = e3
% 247.65/58.49 (82) all_82_2 = all_28_2
% 247.65/58.49 (83) ~ (all_84_2 = all_22_2)
% 247.65/58.49 (84) op(e1, e2) = all_4_2
% 247.65/58.49 (85) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.65/58.49 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.65/58.49 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.65/58.49 (86) op(all_4_2, all_38_2) = e2
% 247.65/58.49 (87) op(e4, e3) = all_84_2
% 247.65/58.49 (88) all_118_2 = all_22_2
% 247.65/58.49 (89) ~ (all_62_2 = all_10_2)
% 247.65/58.49 (90) op(e2, e4) = all_64_2
% 247.65/58.49 (91) ~ (all_22_2 = all_10_2)
% 247.65/58.49 (92) op(all_40_2, all_28_2) = e0
% 247.65/58.49 (93) ~ (e4 = e2)
% 247.65/58.49 (94) all_252_4 = e1
% 247.65/58.49 (95) ~ (all_22_2 = all_20_2)
% 247.65/58.49 (96) ~ (all_244_8 = all_8_2)
% 247.65/58.49 (97) op(e3, e2) = all_8_2
% 247.65/58.49 (98) op(all_36_2, e1) = e3
% 247.65/58.49 (99) ~ (all_38_2 = all_10_2)
% 247.65/58.49 (100) ~ (all_244_15 = all_36_2)
% 247.65/58.49 (101) ~ (all_244_24 = all_22_2)
% 247.65/58.49 (102) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.65/58.49 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) |
% 247.65/58.49 ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.65/58.49 (103) op(all_8_2, all_10_2) = e2
% 247.65/58.49 (104) ~ (all_244_8 = all_28_2)
% 247.65/58.49 (105) all_252_23 = e4
% 247.65/58.49 (106) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.65/58.49 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.65/58.49 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.65/58.49 (107) all_250_22 = all_28_2
% 247.65/58.49 (108) all_250_20 = all_12_2
% 247.65/58.49 (109) all_90_2 = all_22_2
% 247.65/58.49 (110) all_46_2 = all_36_2
% 247.65/58.49 (111) op(all_30_2, e0) = e4
% 247.65/58.49 (112) op(all_244_24, all_244_24) = e0
% 247.65/58.49 (113) op(e0, e4) = all_12_2
% 247.65/58.49 (114) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.65/58.49 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.65/58.49 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.65/58.49 (115) all_124_2 = all_10_2
% 247.65/58.49
% 247.65/58.49 Begin of proof
% 247.65/58.49 |
% 247.65/58.49 | GROUND_INST: instantiating (17) with all_16_2, all_60_1, e4, e1, simplifying
% 247.65/58.49 | with (36), (60) gives:
% 247.65/58.49 | (116) all_60_1 = all_16_2
% 247.65/58.49 |
% 247.65/58.49 | BETA: splitting (58) gives:
% 247.65/58.49 |
% 247.65/58.49 | Case 1:
% 247.65/58.49 | |
% 247.65/58.49 | | (117) ~ (all_28_2 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | BETA: splitting (28) gives:
% 247.65/58.49 | |
% 247.65/58.49 | | Case 1:
% 247.65/58.49 | | |
% 247.65/58.49 | | | (118) ~ (all_34_2 = e2)
% 247.65/58.49 | | |
% 247.65/58.49 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 247.65/58.49 | | | (15), (16), (17), (18), (21), (22), (23), (24), (26), (29),
% 247.65/58.49 | | | (33), (34), (35), (36), (37), (38), (41), (43), (44), (45),
% 247.65/58.49 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 247.65/58.49 | | | (56), (57), (59), (61), (64), (65), (66), (68), (69), (70),
% 247.65/58.49 | | | (71), (72), (74), (75), (77), (78), (80), (81), (82), (83),
% 247.65/58.49 | | | (84), (86), (87), (89), (91), (92), (97), (98), (99), (100),
% 247.65/58.49 | | | (105), (106), (107), (108), (109), (110), (111), (115), (117),
% 247.65/58.49 | | | (118) are inconsistent by sub-proof #578.
% 247.65/58.49 | | |
% 247.65/58.49 | | Case 2:
% 247.65/58.49 | | |
% 247.65/58.49 | | | (119) all_34_2 = e2
% 247.65/58.49 | | |
% 247.65/58.49 | | | REF_CLOSE: (7), (13), (17), (40), (46), (90), (102), (113), (119) are
% 247.65/58.49 | | | inconsistent by sub-proof #25.
% 247.65/58.49 | | |
% 247.65/58.49 | | End of split
% 247.65/58.49 | |
% 247.65/58.49 | Case 2:
% 247.65/58.49 | |
% 247.65/58.49 | | (120) all_28_2 = e3
% 247.65/58.49 | | (121) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 247.65/58.49 | | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) &
% 247.65/58.49 | | op(e2, e3) = all_28_1 & $i(all_28_1))
% 247.65/58.49 | |
% 247.65/58.49 | | REDUCE: (104), (120) imply:
% 247.65/58.49 | | (122) ~ (all_244_8 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | REDUCE: (65), (120) imply:
% 247.65/58.49 | | (123) ~ (all_22_2 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | SIMP: (123) implies:
% 247.65/58.49 | | (124) ~ (all_22_2 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | REDUCE: (61), (120) imply:
% 247.65/58.49 | | (125) ~ (e4 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | SIMP: (125) implies:
% 247.65/58.49 | | (126) ~ (e4 = e3)
% 247.65/58.49 | |
% 247.65/58.49 | | REDUCE: (31), (120) imply:
% 247.65/58.49 | | (127) ~ (e3 = e1)
% 247.65/58.49 | |
% 247.65/58.49 | | REDUCE: (27), (120) imply:
% 247.65/58.49 | | (128) op(e3, e2) = e0
% 247.65/58.49 | |
% 247.65/58.49 | | BETA: splitting (121) gives:
% 247.65/58.49 | |
% 247.65/58.49 | | Case 1:
% 247.65/58.49 | | |
% 247.65/58.49 | | | (129) ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 247.65/58.49 | | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 247.65/58.49 | | |
% 247.65/58.49 | | | ALPHA: (129) implies:
% 247.65/58.49 | | | (130) op(e2, e3) = all_28_1
% 247.65/58.49 | | |
% 247.65/58.49 | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (12), (13), (16), (17), (18),
% 247.65/58.49 | | | (19), (20), (22), (23), (24), (25), (26), (28), (29), (30),
% 247.65/58.49 | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (42),
% 247.65/58.49 | | | (43), (44), (45), (46), (47), (49), (50), (51), (54), (55),
% 247.65/58.49 | | | (56), (57), (59), (62), (63), (64), (67), (68), (71), (73),
% 247.65/58.49 | | | (74), (75), (76), (78), (79), (81), (84), (85), (88), (90),
% 247.65/58.49 | | | (91), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 247.65/58.49 | | | (102), (103), (106), (109), (110), (112), (113), (114), (115),
% 247.65/58.49 | | | (122), (124), (126), (127), (128), (130) are inconsistent by
% 247.65/58.49 | | | sub-proof #24.
% 247.65/58.49 | | |
% 247.65/58.49 | | Case 2:
% 247.65/58.49 | | |
% 247.65/58.49 | | | (131) ~ (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1)
% 247.65/58.49 | | |
% 247.65/58.49 | | | ALPHA: (131) implies:
% 247.65/58.49 | | | (132) op(e2, e3) = all_28_1
% 247.65/58.49 | | |
% 247.65/58.49 | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (12), (13), (16), (17), (18),
% 247.65/58.49 | | | (19), (20), (22), (23), (24), (25), (26), (28), (29), (30),
% 247.65/58.49 | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (42),
% 247.65/58.49 | | | (43), (44), (45), (46), (47), (49), (50), (51), (54), (55),
% 247.65/58.49 | | | (56), (57), (59), (62), (63), (64), (67), (68), (71), (73),
% 247.65/58.49 | | | (74), (75), (76), (78), (79), (81), (84), (85), (88), (90),
% 247.65/58.49 | | | (91), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 247.65/58.49 | | | (102), (103), (106), (109), (110), (112), (113), (114), (115),
% 247.65/58.49 | | | (122), (124), (126), (127), (128), (132) are inconsistent by
% 247.65/58.49 | | | sub-proof #24.
% 247.65/58.49 | | |
% 247.65/58.49 | | End of split
% 247.65/58.49 | |
% 247.65/58.49 | End of split
% 247.65/58.49 |
% 247.65/58.50 End of proof
% 247.65/58.50
% 247.65/58.50 Sub-proof #24 shows that the following formulas are inconsistent:
% 247.65/58.50 ----------------------------------------------------------------
% 247.65/58.50 (1) ~ (all_10_2 = e4)
% 247.65/58.50 (2) all_94_2 = all_38_2
% 247.65/58.50 (3) op(all_34_2, e4) = e0
% 247.65/58.50 (4) op(all_62_2, all_36_2) = e3
% 247.65/58.50 (5) op(all_38_2, e1) = e2
% 247.65/58.50 (6) all_250_13 = all_38_2
% 247.65/58.50 (7) op(all_38_2, all_4_2) = e1
% 247.65/58.50 (8) op(all_64_2, e4) = e2
% 247.65/58.50 (9) ~ (all_22_2 = e3)
% 247.65/58.50 (10) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.65/58.50 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.65/58.50 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.65/58.50 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.65/58.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.65/58.50 (12) op(e2, e3) = all_10_2
% 247.65/58.50 (13) ~ (e3 = e2)
% 247.65/58.50 (14) op(e0, e0) = all_244_24
% 247.65/58.50 (15) op(e2, e2) = all_244_8
% 247.65/58.50 (16) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.65/58.50 all_250_11 = e0
% 247.65/58.50 (17) op(e2, e1) = all_38_2
% 247.65/58.50 (18) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.65/58.50 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.65/58.50 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.65/58.50 (19) op(e1, e0) = all_34_2
% 247.65/58.50 (20) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.65/58.50 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.65/58.50 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.65/58.50 (21) all_78_2 = all_10_2
% 247.65/58.50 (22) op(e3, e2) = e0
% 247.65/58.50 (23) all_252_14 = e4
% 247.65/58.50 (24) all_106_2 = all_38_2
% 247.65/58.50 (25) ~ (all_244_8 = all_38_2)
% 247.65/58.50 (26) op(all_244_15, all_244_15) = e1
% 247.65/58.50 (27) all_250_21 = all_22_2
% 247.65/58.50 (28) op(e1, e4) = all_16_2
% 247.65/58.50 (29) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.65/58.50 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.65/58.50 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.65/58.50 (30) op(e1, e3) = all_62_2
% 247.65/58.50 (31) ~ (e3 = e0)
% 247.65/58.50 (32) all_198_2 = all_34_2
% 247.65/58.50 (33) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.65/58.50 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.65/58.50 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.65/58.50 (34) ~ (all_22_2 = e4)
% 247.65/58.50 (35) all_70_2 = all_62_2
% 247.65/58.50 (36) ~ (e3 = e1)
% 247.65/58.50 (37) op(all_48_2, all_22_2) = e0
% 247.65/58.50 (38) ~ (all_12_2 = e2)
% 247.65/58.50 (39) op(e3, e1) = all_36_2
% 247.65/58.50 (40) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.65/58.50 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.65/58.50 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.65/58.50 (41) ~ (all_16_2 = e2)
% 247.65/58.50 (42) ~ (all_8_2 = e1)
% 247.65/58.50 (43) ~ (all_22_2 = e1)
% 247.65/58.50 (44) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.65/58.50 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.65/58.50 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.65/58.50 (45) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.65/58.50 all_250_13 = e0
% 247.65/58.50 (46) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.65/58.50 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.65/58.50 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.65/58.50 (47) ~ (all_38_2 = e4)
% 247.65/58.50 (48) op(all_22_2, e3) = e0
% 247.65/58.50 (49) all_68_2 = all_22_2
% 247.65/58.50 (50) op(e0, e3) = all_22_2
% 247.65/58.50 (51) ~ (all_244_8 = e3)
% 247.65/58.50 (52) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.65/58.50 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.65/58.50 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.65/58.50 (53) op(all_10_2, e3) = e2
% 247.65/58.50 (54) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.65/58.50 all_250_21 = e0
% 247.65/58.50 (55) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.65/58.50 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.65/58.50 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.65/58.50 (56) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.65/58.50 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.65/58.50 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.65/58.50 (57) all_250_11 = all_10_2
% 247.65/58.50 (58) all_230_2 = all_20_2
% 247.65/58.50 (59) ~ (e4 = e3)
% 247.65/58.50 (60) op(e1, e1) = all_244_15
% 247.65/58.50 (61) op(e0, e1) = all_20_2
% 247.65/58.50 (62) op(all_48_2, e0) = e3
% 247.65/58.50 (63) op(e2, e3) = all_28_1
% 247.65/58.50 (64) op(e1, e2) = all_4_2
% 247.65/58.50 (65) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 247.65/58.50 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.65/58.50 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.65/58.50 (66) all_118_2 = all_22_2
% 247.65/58.50 (67) op(e2, e4) = all_64_2
% 247.65/58.50 (68) ~ (all_22_2 = all_10_2)
% 247.65/58.50 (69) ~ (e4 = e2)
% 247.65/58.50 (70) all_252_4 = e1
% 247.65/58.50 (71) ~ (all_22_2 = all_20_2)
% 247.65/58.50 (72) ~ (all_244_8 = all_8_2)
% 247.65/58.50 (73) op(e3, e2) = all_8_2
% 247.65/58.50 (74) op(all_36_2, e1) = e3
% 247.65/58.50 (75) ~ (all_38_2 = all_10_2)
% 247.65/58.50 (76) ~ (all_244_15 = all_36_2)
% 247.65/58.50 (77) ~ (all_244_24 = all_22_2)
% 247.65/58.50 (78) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.65/58.50 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) |
% 247.65/58.50 ( ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.65/58.50 (79) op(all_8_2, all_10_2) = e2
% 247.65/58.50 (80) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.65/58.50 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.65/58.50 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.65/58.50 (81) all_90_2 = all_22_2
% 247.65/58.50 (82) all_46_2 = all_36_2
% 247.65/58.50 (83) op(all_244_24, all_244_24) = e0
% 247.65/58.50 (84) op(e0, e4) = all_12_2
% 247.65/58.50 (85) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.65/58.50 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.65/58.50 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.65/58.50 (86) all_124_2 = all_10_2
% 247.65/58.50
% 247.65/58.50 Begin of proof
% 247.65/58.50 |
% 247.65/58.50 | BETA: splitting (65) gives:
% 247.65/58.50 |
% 247.65/58.50 | Case 1:
% 247.65/58.50 | |
% 247.65/58.50 | | (87) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) =
% 247.65/58.50 | | e3)
% 247.65/58.50 | |
% 247.65/58.50 | | BETA: splitting (87) gives:
% 247.65/58.50 | |
% 247.65/58.50 | | Case 1:
% 247.65/58.50 | | |
% 247.65/58.50 | | | (88) all_252_4 = e3 & op(e4, e2) = e3
% 247.65/58.50 | | |
% 247.65/58.50 | | | REF_CLOSE: (36), (70), (88) are inconsistent by sub-proof #252.
% 247.65/58.50 | | |
% 247.65/58.50 | | Case 2:
% 247.65/58.50 | | |
% 247.65/58.50 | | | (89) all_252_5 = e3 & op(e3, e2) = e3
% 247.65/58.50 | | |
% 247.65/58.50 | | | REF_CLOSE: (11), (22), (31), (73), (89) are inconsistent by sub-proof
% 247.65/58.50 | | | #576.
% 247.65/58.50 | | |
% 247.65/58.50 | | End of split
% 247.65/58.50 | |
% 247.65/58.50 | Case 2:
% 247.65/58.50 | |
% 247.65/58.50 | | (90) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 247.65/58.50 | | e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 247.65/58.50 | |
% 247.65/58.50 | | BETA: splitting (90) gives:
% 247.65/58.50 | |
% 247.65/58.50 | | Case 1:
% 247.65/58.50 | | |
% 247.65/58.50 | | | (91) all_252_8 = e3 & op(e2, e2) = e3
% 247.65/58.50 | | |
% 247.65/58.50 | | | ALPHA: (91) implies:
% 247.65/58.50 | | | (92) op(e2, e2) = e3
% 247.65/58.50 | | |
% 247.65/58.50 | | | REF_CLOSE: (11), (15), (51), (92) are inconsistent by sub-proof #877.
% 247.65/58.50 | | |
% 247.65/58.50 | | Case 2:
% 247.65/58.50 | | |
% 247.65/58.50 | | | (93) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0,
% 247.65/58.50 | | | e2) = e3)
% 247.65/58.50 | | |
% 247.65/58.50 | | | BETA: splitting (93) gives:
% 247.65/58.50 | | |
% 247.65/58.50 | | | Case 1:
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | (94) all_252_14 = e3 & op(e1, e2) = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | ALPHA: (94) implies:
% 247.65/58.50 | | | | (95) all_252_14 = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | COMBINE_EQS: (23), (95) imply:
% 247.65/58.50 | | | | (96) e4 = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | SIMP: (96) implies:
% 247.65/58.50 | | | | (97) e4 = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | REDUCE: (59), (97) imply:
% 247.65/58.50 | | | | (98) $false
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | CLOSE: (98) is inconsistent.
% 247.65/58.50 | | | |
% 247.65/58.50 | | | Case 2:
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | (99) all_252_22 = e3 & op(e0, e2) = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | ALPHA: (99) implies:
% 247.65/58.50 | | | | (100) all_252_22 = e3
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | GROUND_INST: instantiating (11) with all_10_2, all_28_1, e3, e2,
% 247.65/58.50 | | | | simplifying with (12), (63) gives:
% 247.65/58.50 | | | | (101) all_28_1 = all_10_2
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | GROUND_INST: instantiating (11) with all_8_2, e0, e2, e3, simplifying
% 247.65/58.50 | | | | with (22), (73) gives:
% 247.65/58.50 | | | | (102) all_8_2 = e0
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | REDUCE: (72), (102) imply:
% 247.65/58.50 | | | | (103) ~ (all_244_8 = e0)
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | REDUCE: (79), (102) imply:
% 247.65/58.50 | | | | (104) op(e0, all_10_2) = e2
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | BETA: splitting (20) gives:
% 247.65/58.50 | | | |
% 247.65/58.50 | | | | Case 1:
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | | (105) ~ (all_34_2 = e2)
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 247.65/58.50 | | | | | (14), (15), (16), (17), (18), (19), (21), (24), (25), (26),
% 247.65/58.50 | | | | | (27), (28), (29), (30), (33), (34), (35), (37), (38), (39),
% 247.65/58.50 | | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 247.65/58.50 | | | | | (50), (52), (53), (54), (55), (56), (57), (58), (60), (61),
% 247.65/58.50 | | | | | (62), (64), (66), (68), (69), (71), (73), (74), (75), (76),
% 247.65/58.50 | | | | | (77), (80), (81), (82), (83), (84), (85), (86), (100),
% 247.65/58.50 | | | | | (103), (104), (105) are inconsistent by sub-proof #31.
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | Case 2:
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | | (106) all_34_2 = e2
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | | REF_CLOSE: (3), (8), (11), (32), (38), (67), (78), (84), (106) are
% 247.65/58.50 | | | | | inconsistent by sub-proof #25.
% 247.65/58.50 | | | | |
% 247.65/58.50 | | | | End of split
% 247.65/58.50 | | | |
% 247.65/58.50 | | | End of split
% 247.65/58.50 | | |
% 247.65/58.50 | | End of split
% 247.65/58.50 | |
% 247.65/58.50 | End of split
% 247.65/58.50 |
% 247.65/58.50 End of proof
% 247.65/58.50
% 247.65/58.50 Sub-proof #25 shows that the following formulas are inconsistent:
% 247.65/58.50 ----------------------------------------------------------------
% 247.65/58.50 (1) op(all_34_2, e4) = e0
% 247.65/58.50 (2) op(all_64_2, e4) = e2
% 247.65/58.50 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.65/58.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.65/58.50 (4) all_34_2 = e2
% 247.65/58.50 (5) all_198_2 = all_34_2
% 247.65/58.50 (6) ~ (all_12_2 = e2)
% 247.65/58.50 (7) op(e2, e4) = all_64_2
% 247.65/58.50 (8) ~ (all_198_2 = e2) | ( ~ (all_198_0 = e3) & op(e2, all_198_1) =
% 247.65/58.50 all_198_0 & op(e0, e2) = all_198_1 & $i(all_198_0) & $i(all_198_1)) | (
% 247.65/58.50 ~ (all_198_1 = e4) & op(e0, e2) = all_198_1 & $i(all_198_1))
% 247.65/58.50 (9) op(e0, e4) = all_12_2
% 247.65/58.50
% 247.65/58.50 Begin of proof
% 247.65/58.50 |
% 247.65/58.50 | COMBINE_EQS: (4), (5) imply:
% 247.65/58.50 | (10) all_198_2 = e2
% 247.65/58.50 |
% 247.65/58.50 | REDUCE: (1), (4) imply:
% 247.65/58.50 | (11) op(e2, e4) = e0
% 247.65/58.50 |
% 247.65/58.50 | BETA: splitting (8) gives:
% 247.65/58.50 |
% 247.65/58.50 | Case 1:
% 247.65/58.50 | |
% 247.65/58.50 | | (12) ~ (all_198_2 = e2)
% 247.65/58.50 | |
% 247.65/58.50 | | REDUCE: (10), (12) imply:
% 247.65/58.50 | | (13) $false
% 247.65/58.50 | |
% 247.65/58.50 | | CLOSE: (13) is inconsistent.
% 247.65/58.50 | |
% 247.65/58.50 | Case 2:
% 247.65/58.50 | |
% 247.65/58.50 | |
% 247.65/58.50 | | GROUND_INST: instantiating (3) with all_64_2, e0, e4, e2, simplifying with
% 247.65/58.50 | | (7), (11) gives:
% 247.82/58.50 | | (14) all_64_2 = e0
% 247.82/58.50 | |
% 247.82/58.50 | | REDUCE: (2), (14) imply:
% 247.82/58.50 | | (15) op(e0, e4) = e2
% 247.82/58.50 | |
% 247.82/58.50 | | REF_CLOSE: (3), (6), (9), (15) are inconsistent by sub-proof #980.
% 247.82/58.50 | |
% 247.82/58.50 | End of split
% 247.82/58.50 |
% 247.82/58.50 End of proof
% 247.82/58.50
% 247.82/58.50 Sub-proof #26 shows that the following formulas are inconsistent:
% 247.82/58.50 ----------------------------------------------------------------
% 247.82/58.50 (1) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.82/58.50 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.82/58.50 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.82/58.50 (2) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 247.82/58.50 all_250_15 = e0
% 247.82/58.50 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.82/58.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.82/58.50 (4) op(e2, e1) = all_38_2
% 247.82/58.50 (5) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.82/58.50 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.82/58.50 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.82/58.50 (6) ~ (all_244_3 = all_22_2)
% 247.82/58.51 (7) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.82/58.51 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.82/58.51 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.82/58.51 (8) ~ (all_244_15 = e4)
% 247.82/58.51 (9) op(all_26_2, e1) = e4
% 247.82/58.51 (10) ~ (all_16_2 = e4)
% 247.82/58.51 (11) op(e1, e3) = all_62_2
% 247.82/58.51 (12) op(all_16_2, all_26_2) = e4
% 247.82/58.51 (13) op(e3, e1) = all_36_2
% 247.82/58.51 (14) ~ (all_16_2 = e2)
% 247.82/58.51 (15) all_22_2 = e1
% 247.82/58.51 (16) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 &
% 247.82/58.51 op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 247.82/58.51 e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 247.82/58.51 (17) op(all_22_2, e3) = e0
% 247.82/58.51 (18) op(e4, e1) = all_26_2
% 247.82/58.51 (19) ~ (all_62_2 = all_16_2)
% 247.82/58.51 (20) all_250_15 = all_16_2
% 247.82/58.51 (21) op(e4, e4) = all_244_0
% 247.82/58.51 (22) ~ (all_244_0 = e1)
% 247.82/58.51 (23) op(e1, e1) = all_244_15
% 247.82/58.51 (24) op(e0, e1) = all_20_2
% 247.82/58.51 (25) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 247.82/58.51 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 247.82/58.51 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 247.82/58.51 (26) ~ (all_26_2 = e1)
% 247.82/58.51 (27) op(all_36_2, e1) = e3
% 247.82/58.51 (28) ~ (all_20_2 = e4)
% 247.82/58.51 (29) op(all_16_2, e4) = e1
% 247.82/58.51 (30) all_24_2 = all_16_2
% 247.82/58.51 (31) op(e3, e3) = all_244_3
% 247.82/58.51 (32) op(all_38_2, e4) = e1
% 247.82/58.51 (33) op(all_26_2, all_16_2) = e1
% 247.82/58.51
% 247.82/58.51 Begin of proof
% 247.82/58.51 |
% 247.82/58.51 | REDUCE: (6), (15) imply:
% 247.82/58.51 | (34) ~ (all_244_3 = e1)
% 247.82/58.51 |
% 247.82/58.51 | REDUCE: (15), (17) imply:
% 247.82/58.51 | (35) op(e1, e3) = e0
% 247.82/58.51 |
% 247.82/58.51 | GROUND_INST: instantiating (3) with all_62_2, e0, e3, e1, simplifying with
% 247.82/58.51 | (11), (35) gives:
% 247.82/58.51 | (36) all_62_2 = e0
% 247.82/58.51 |
% 247.82/58.51 | REDUCE: (19), (36) imply:
% 247.82/58.51 | (37) ~ (all_16_2 = e0)
% 247.82/58.51 |
% 247.82/58.51 | SIMP: (37) implies:
% 247.82/58.51 | (38) ~ (all_16_2 = e0)
% 247.82/58.51 |
% 247.82/58.51 | BETA: splitting (25) gives:
% 247.82/58.51 |
% 247.82/58.51 | Case 1:
% 247.82/58.51 | |
% 247.82/58.51 | | (39) ~ (all_24_2 = e3)
% 247.82/58.51 | |
% 247.82/58.51 | | REDUCE: (30), (39) imply:
% 247.82/58.51 | | (40) ~ (all_16_2 = e3)
% 247.82/58.51 | |
% 247.82/58.51 | | REF_CLOSE: (2), (3), (9), (10), (14), (20), (33), (38), (40) are
% 247.82/58.51 | | inconsistent by sub-proof #466.
% 247.82/58.51 | |
% 247.82/58.51 | Case 2:
% 247.82/58.51 | |
% 247.82/58.51 | | (41) all_24_2 = e3
% 247.82/58.51 | |
% 247.82/58.51 | | COMBINE_EQS: (30), (41) imply:
% 247.82/58.51 | | (42) all_16_2 = e3
% 247.82/58.51 | |
% 247.82/58.51 | | REDUCE: (33), (42) imply:
% 247.82/58.51 | | (43) op(all_26_2, e3) = e1
% 247.82/58.51 | |
% 247.82/58.51 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (12), (13), (16), (18), (21), (22),
% 247.82/58.51 | | (23), (24), (26), (27), (28), (29), (31), (32), (34), (43) are
% 247.82/58.51 | | inconsistent by sub-proof #27.
% 247.82/58.51 | |
% 247.82/58.51 | End of split
% 247.82/58.51 |
% 247.82/58.51 End of proof
% 247.82/58.51
% 247.82/58.51 Sub-proof #27 shows that the following formulas are inconsistent:
% 247.82/58.51 ----------------------------------------------------------------
% 247.82/58.51 (1) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.82/58.51 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.82/58.51 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.82/58.51 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.82/58.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.82/58.51 (3) ~ (all_244_3 = e1)
% 247.82/58.51 (4) op(e2, e1) = all_38_2
% 247.82/58.51 (5) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.82/58.51 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.82/58.51 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.82/58.51 (6) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.82/58.51 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.82/58.51 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.82/58.51 (7) ~ (all_244_15 = e4)
% 247.82/58.51 (8) op(all_16_2, all_26_2) = e4
% 247.82/58.51 (9) op(e3, e1) = all_36_2
% 247.82/58.51 (10) op(all_26_2, e3) = e1
% 247.82/58.51 (11) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 &
% 247.82/58.51 op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 247.82/58.51 e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 247.82/58.51 (12) op(e4, e1) = all_26_2
% 247.82/58.51 (13) op(e4, e4) = all_244_0
% 247.82/58.51 (14) ~ (all_244_0 = e1)
% 247.82/58.51 (15) op(e1, e1) = all_244_15
% 247.82/58.51 (16) op(e0, e1) = all_20_2
% 247.82/58.51 (17) ~ (all_26_2 = e1)
% 247.82/58.51 (18) op(all_36_2, e1) = e3
% 247.82/58.51 (19) ~ (all_20_2 = e4)
% 247.82/58.51 (20) op(all_16_2, e4) = e1
% 247.82/58.51 (21) op(e3, e3) = all_244_3
% 247.82/58.51 (22) op(all_38_2, e4) = e1
% 247.82/58.51
% 247.82/58.51 Begin of proof
% 247.82/58.51 |
% 247.82/58.51 | BETA: splitting (11) gives:
% 247.82/58.51 |
% 247.82/58.51 | Case 1:
% 247.82/58.51 | |
% 247.82/58.51 | | (23) ~ (all_26_2 = e3)
% 247.82/58.51 | |
% 247.82/58.51 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 247.82/58.51 | | (16), (17), (18), (19), (20), (22), (23) are inconsistent by
% 247.82/58.51 | | sub-proof #36.
% 247.82/58.51 | |
% 247.82/58.51 | Case 2:
% 247.82/58.51 | |
% 247.82/58.51 | | (24) all_26_2 = e3
% 247.82/58.51 | |
% 247.82/58.51 | | REDUCE: (10), (24) imply:
% 247.82/58.51 | | (25) op(e3, e3) = e1
% 247.82/58.51 | |
% 247.82/58.51 | | REF_CLOSE: (2), (3), (21), (25) are inconsistent by sub-proof #801.
% 247.82/58.51 | |
% 247.82/58.51 | End of split
% 247.82/58.51 |
% 247.82/58.51 End of proof
% 247.82/58.51
% 247.82/58.51 Sub-proof #28 shows that the following formulas are inconsistent:
% 247.82/58.51 ----------------------------------------------------------------
% 247.82/58.51 (1) ~ (all_30_2 = all_26_2)
% 247.82/58.51 (2) ~ (all_100_2 = all_12_2)
% 247.82/58.51 (3) ~ (all_84_2 = all_30_2)
% 247.82/58.51 (4) ~ (all_10_2 = e4)
% 247.82/58.51 (5) ~ (all_244_0 = all_30_2)
% 247.82/58.51 (6) all_250_12 = all_244_8
% 247.82/58.51 (7) ~ (all_40_2 = all_38_2)
% 247.82/58.51 (8) all_104_2 = all_22_2
% 247.82/58.51 (9) ~ (all_244_8 = e0)
% 247.82/58.51 (10) op(e4, e0) = all_30_2
% 247.82/58.51 (11) ~ (all_40_2 = all_30_2)
% 247.82/58.51 (12) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.82/58.51 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.82/58.51 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.82/58.51 (13) all_94_2 = all_38_2
% 247.82/58.51 (14) op(all_62_2, all_36_2) = e3
% 247.82/58.51 (15) op(all_38_2, e1) = e2
% 247.82/58.51 (16) all_250_13 = all_38_2
% 247.82/58.51 (17) op(all_38_2, all_4_2) = e1
% 247.82/58.51 (18) op(all_64_2, e4) = e2
% 247.82/58.51 (19) ~ (all_22_2 = e3)
% 247.82/58.51 (20) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.82/58.51 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.82/58.51 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.82/58.51 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.82/58.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.82/58.51 (22) op(e0, e0) = all_244_24
% 247.82/58.51 (23) ~ (all_12_2 = e3)
% 247.82/58.51 (24) ~ (all_244_8 = all_64_2)
% 247.82/58.51 (25) op(all_244_8, all_244_8) = e2
% 247.82/58.51 (26) op(e2, e2) = all_244_8
% 247.82/58.51 (27) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.82/58.51 all_250_11 = e0
% 247.82/58.51 (28) op(all_84_2, all_100_2) = e3
% 247.82/58.51 (29) op(e2, e1) = all_38_2
% 247.82/58.51 (30) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.82/58.51 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.82/58.51 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.82/58.51 (31) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 247.82/58.51 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 247.82/58.51 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.82/58.51 (32) ~ (all_36_2 = all_20_2)
% 247.82/58.51 (33) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.82/58.51 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.82/58.51 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.82/58.51 (34) op(e1, e0) = all_34_2
% 247.82/58.51 (35) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.82/58.51 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.82/58.51 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.82/58.51 (36) all_78_2 = all_10_2
% 247.82/58.51 (37) ~ (all_84_2 = e1)
% 247.82/58.51 (38) ~ (all_244_15 = e4)
% 247.82/58.51 (39) op(all_26_2, e1) = e4
% 247.82/58.51 (40) ~ (all_100_2 = all_36_2)
% 247.82/58.51 (41) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.82/58.51 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 247.82/58.51 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 247.82/58.51 (42) all_106_2 = all_38_2
% 247.82/58.51 (43) ~ (all_244_8 = all_38_2)
% 247.82/58.51 (44) op(all_244_15, all_244_15) = e1
% 247.82/58.51 (45) all_252_22 = e3
% 247.82/58.51 (46) all_250_21 = all_22_2
% 247.82/58.51 (47) op(e1, e4) = all_16_2
% 247.82/58.51 (48) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.82/58.51 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.82/58.51 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.82/58.51 (49) ~ (all_244_0 = all_64_2)
% 247.82/58.51 (50) ~ (all_104_2 = e4) | ( ~ (all_104_0 = e1) & op(e4, all_104_1) =
% 247.82/58.51 all_104_0 & op(e3, e4) = all_104_1 & $i(all_104_0) & $i(all_104_1)) |
% 247.82/58.51 ( ~ (all_104_1 = e2) & op(e3, e4) = all_104_1 & $i(all_104_1))
% 247.82/58.51 (51) ( ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2, e4) = all_4_1 &
% 247.82/58.51 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e2, e4) = all_4_1
% 247.82/58.51 & $i(all_4_1))
% 247.82/58.51 (52) op(e1, e3) = all_62_2
% 247.82/58.51 (53) op(all_16_2, all_26_2) = e4
% 247.82/58.51 (54) ~ (all_244_0 = all_26_2)
% 247.82/58.51 (55) all_140_2 = all_84_2
% 247.82/58.51 (56) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.82/58.51 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.82/58.51 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.82/58.51 (57) ~ (all_40_2 = all_10_2)
% 247.82/58.51 (58) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 247.82/58.51 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 247.82/58.51 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 247.82/58.51 (59) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 247.82/58.51 all_250_1 = e0
% 247.82/58.51 (60) all_70_2 = all_62_2
% 247.82/58.51 (61) op(all_48_2, all_22_2) = e0
% 247.82/58.51 (62) ~ (all_12_2 = e2)
% 247.82/58.51 (63) op(e3, e1) = all_36_2
% 247.82/58.51 (64) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.82/58.51 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.82/58.51 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.82/58.51 (65) ~ (all_16_2 = e2)
% 247.82/58.51 (66) ~ (all_8_2 = e1)
% 247.82/58.51 (67) op(all_40_2, e0) = e2
% 247.82/58.51 (68) ~ (all_22_2 = e1)
% 247.82/58.51 (69) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.82/58.51 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.82/58.51 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.82/58.51 (70) ~ (all_84_2 = all_26_2)
% 247.82/58.51 (71) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.82/58.51 all_250_13 = e0
% 247.82/58.51 (72) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.82/58.51 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.82/58.51 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.82/58.51 (73) ~ (all_36_2 = all_26_2)
% 247.82/58.51 (74) all_8_2 = e0
% 247.82/58.51 (75) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 &
% 247.82/58.51 op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 247.82/58.51 e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 247.82/58.51 (76) ~ (all_64_2 = all_12_2)
% 247.82/58.51 (77) op(all_22_2, e3) = e0
% 247.82/58.51 (78) all_68_2 = all_22_2
% 247.82/58.51 (79) op(e0, e3) = all_22_2
% 247.82/58.51 (80) ~ (all_244_0 = all_100_2)
% 247.82/58.51 (81) op(all_84_2, e3) = e4
% 247.82/58.51 (82) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 247.82/58.51 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 247.82/58.51 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.82/58.51 (83) ~ (all_244_8 = e3)
% 247.82/58.51 (84) op(e4, e1) = all_26_2
% 247.82/58.51 (85) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.82/58.51 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.82/58.51 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.82/58.51 (86) op(all_10_2, e3) = e2
% 247.82/58.51 (87) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.82/58.51 all_250_21 = e0
% 247.82/58.52 (88) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.82/58.52 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.82/58.52 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.82/58.52 (89) all_250_12 = e4 | all_250_12 = e3 | all_250_12 = e2 | all_250_12 = e1 |
% 247.82/58.52 all_250_12 = e0
% 247.82/58.52 (90) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.82/58.52 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.82/58.52 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.82/58.52 (91) op(e3, e4) = all_100_2
% 247.82/58.52 (92) all_250_11 = all_10_2
% 247.82/58.52 (93) ~ (all_244_8 = e1)
% 247.82/58.52 (94) op(e4, e4) = all_244_0
% 247.82/58.52 (95) all_230_2 = all_20_2
% 247.82/58.52 (96) ~ (all_244_0 = e1)
% 247.82/58.52 (97) op(e1, e1) = all_244_15
% 247.82/58.52 (98) ~ (all_186_2 = e3) | ( ~ (all_186_0 = e1) & op(e4, e3) = all_186_1 &
% 247.82/58.52 op(e3, all_186_1) = all_186_0 & $i(all_186_0) & $i(all_186_1)) | ( ~
% 247.82/58.52 (all_186_1 = e0) & op(e4, e3) = all_186_1 & $i(all_186_1))
% 247.82/58.52 (99) ~ (all_34_2 = all_30_2)
% 247.82/58.52 (100) op(e0, e1) = all_20_2
% 247.82/58.52 (101) op(all_48_2, e0) = e3
% 247.82/58.52 (102) ~ (all_38_2 = all_36_2)
% 247.82/58.52 (103) op(e2, e3) = all_28_1
% 247.82/58.52 (104) ~ (all_84_2 = all_22_2)
% 247.82/58.52 (105) op(e1, e2) = all_4_2
% 247.82/58.52 (106) ~ (all_26_2 = e1)
% 247.82/58.52 (107) op(e4, e3) = all_84_2
% 247.82/58.52 (108) all_118_2 = all_22_2
% 247.82/58.52 (109) op(e2, e4) = all_64_2
% 247.82/58.52 (110) ~ (all_22_2 = all_10_2)
% 247.82/58.52 (111) all_28_1 = all_10_2
% 247.82/58.52 (112) ~ (all_22_2 = all_20_2)
% 247.82/58.52 (113) op(e3, e2) = all_8_2
% 247.82/58.52 (114) ~ (all_244_8 = e4)
% 247.82/58.52 (115) ~ (all_64_2 = all_16_2)
% 247.82/58.52 (116) op(all_36_2, e1) = e3
% 247.82/58.52 (117) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.82/58.52 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.82/58.52 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.82/58.52 (118) ~ (all_38_2 = all_10_2)
% 247.82/58.52 (119) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 247.82/58.52 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 247.82/58.52 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 247.82/58.52 (120) ~ (all_244_15 = all_36_2)
% 247.82/58.52 (121) ~ (all_20_2 = e4)
% 247.82/58.52 (122) ~ (all_244_24 = all_22_2)
% 247.82/58.52 (123) all_250_1 = all_84_2
% 247.82/58.52 (124) op(all_16_2, e4) = e1
% 247.82/58.52 (125) ~ (all_100_2 = all_16_2)
% 247.82/58.52 (126) op(e2, e0) = all_40_2
% 247.82/58.52 (127) op(all_8_2, all_10_2) = e2
% 247.82/58.52 (128) ~ (all_16_2 = e3)
% 247.82/58.52 (129) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.82/58.52 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.82/58.52 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.82/58.52 (130) op(all_38_2, e4) = e1
% 247.82/58.52 (131) all_90_2 = all_22_2
% 247.82/58.52 (132) ~ (all_140_2 = e0) | ( ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 &
% 247.82/58.52 op(e0, all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1)) | ( ~
% 247.82/58.52 (all_140_1 = e1) & op(e3, e0) = all_140_1 & $i(all_140_1))
% 247.82/58.52 (133) all_46_2 = all_36_2
% 247.82/58.52 (134) op(all_244_24, all_244_24) = e0
% 247.82/58.52 (135) op(e0, e4) = all_12_2
% 247.82/58.52 (136) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.82/58.52 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.82/58.52 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.82/58.52 (137) all_186_2 = all_64_2
% 247.82/58.52 (138) all_124_2 = all_10_2
% 247.82/58.52
% 247.82/58.52 Begin of proof
% 247.82/58.52 |
% 247.82/58.52 | REDUCE: (74), (127) imply:
% 247.82/58.52 | (139) op(e0, all_10_2) = e2
% 247.82/58.52 |
% 247.82/58.52 | REDUCE: (103), (111) imply:
% 247.82/58.52 | (140) op(e2, e3) = all_10_2
% 247.82/58.52 |
% 247.82/58.52 | BETA: splitting (89) gives:
% 247.82/58.52 |
% 247.82/58.52 | Case 1:
% 247.82/58.52 | |
% 247.82/58.52 | | (141) all_250_12 = e4
% 247.82/58.52 | |
% 247.82/58.52 | | COMBINE_EQS: (6), (141) imply:
% 247.82/58.52 | | (142) all_244_8 = e4
% 247.82/58.52 | |
% 247.82/58.52 | | REDUCE: (114), (142) imply:
% 247.82/58.52 | | (143) $false
% 247.82/58.52 | |
% 247.82/58.52 | | CLOSE: (143) is inconsistent.
% 247.82/58.52 | |
% 247.82/58.52 | Case 2:
% 247.82/58.52 | |
% 247.82/58.52 | | (144) all_250_12 = e3 | all_250_12 = e2 | all_250_12 = e1 | all_250_12 =
% 247.82/58.52 | | e0
% 247.82/58.52 | |
% 247.82/58.52 | | BETA: splitting (144) gives:
% 247.82/58.52 | |
% 247.82/58.52 | | Case 1:
% 247.82/58.52 | | |
% 247.82/58.52 | | | (145) all_250_12 = e3
% 247.82/58.52 | | |
% 247.82/58.52 | | | COMBINE_EQS: (6), (145) imply:
% 247.82/58.52 | | | (146) all_244_8 = e3
% 247.82/58.52 | | |
% 247.82/58.52 | | | REDUCE: (83), (146) imply:
% 247.82/58.52 | | | (147) $false
% 247.82/58.52 | | |
% 247.82/58.52 | | | CLOSE: (147) is inconsistent.
% 247.82/58.52 | | |
% 247.82/58.52 | | Case 2:
% 247.82/58.52 | | |
% 247.82/58.52 | | | (148) ~ (all_250_12 = e3)
% 247.82/58.52 | | | (149) all_250_12 = e2 | all_250_12 = e1 | all_250_12 = e0
% 247.82/58.52 | | |
% 247.82/58.52 | | | BETA: splitting (149) gives:
% 247.82/58.52 | | |
% 247.82/58.52 | | | Case 1:
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | (150) all_250_12 = e2
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | COMBINE_EQS: (6), (150) imply:
% 247.82/58.52 | | | | (151) all_244_8 = e2
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | REDUCE: (24), (151) imply:
% 247.82/58.52 | | | | (152) ~ (all_64_2 = e2)
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | SIMP: (152) implies:
% 247.82/58.52 | | | | (153) ~ (all_64_2 = e2)
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | REDUCE: (83), (151) imply:
% 247.82/58.52 | | | | (154) ~ (e3 = e2)
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | SIMP: (154) implies:
% 247.82/58.52 | | | | (155) ~ (e3 = e2)
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | BETA: splitting (75) gives:
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | Case 1:
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | (156) ~ (all_26_2 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REF_CLOSE: (12), (21), (29), (30), (35), (38), (53), (63), (84), (94),
% 247.82/58.52 | | | | | (96), (97), (100), (106), (116), (121), (124), (130), (156)
% 247.82/58.52 | | | | | are inconsistent by sub-proof #36.
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | Case 2:
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | (157) all_26_2 = e3
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (54), (157) imply:
% 247.82/58.52 | | | | | (158) ~ (all_244_0 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (70), (157) imply:
% 247.82/58.52 | | | | | (159) ~ (all_84_2 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (73), (157) imply:
% 247.82/58.52 | | | | | (160) ~ (all_36_2 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (1), (157) imply:
% 247.82/58.52 | | | | | (161) ~ (all_30_2 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (39), (157) imply:
% 247.82/58.52 | | | | | (162) op(e3, e1) = e4
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | GROUND_INST: instantiating (21) with all_36_2, e4, e1, e3, simplifying
% 247.82/58.52 | | | | | with (63), (162) gives:
% 247.82/58.52 | | | | | (163) all_36_2 = e4
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (40), (163) imply:
% 247.82/58.52 | | | | | (164) ~ (all_100_2 = e4)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (102), (163) imply:
% 247.82/58.52 | | | | | (165) ~ (all_38_2 = e4)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (32), (163) imply:
% 247.82/58.52 | | | | | (166) ~ (all_20_2 = e4)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (160), (163) imply:
% 247.82/58.52 | | | | | (167) ~ (e4 = e3)
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | BETA: splitting (12) gives:
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | Case 1:
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | | (168) ~ (all_36_2 = e4)
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | | REF_CLOSE: (21), (29), (35), (38), (53), (63), (84), (97), (100),
% 247.82/58.52 | | | | | | (106), (121), (124), (165), (168) are inconsistent by
% 247.82/58.52 | | | | | | sub-proof #37.
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | Case 2:
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | | (169) ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 & op(e1,
% 247.82/58.52 | | | | | | e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 247.82/58.52 | | | | | | (all_36_1 = e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | | BETA: splitting (169) gives:
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | | Case 1:
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | (170) ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 & op(e1,
% 247.82/58.52 | | | | | | | e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | ALPHA: (170) implies:
% 247.82/58.52 | | | | | | | (171) op(e1, e4) = all_36_1
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 247.82/58.52 | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 247.82/58.52 | | | | | | | (23), (25), (26), (27), (28), (29), (31), (33), (34),
% 247.82/58.52 | | | | | | | (36), (37), (41), (42), (43), (44), (45), (46), (47),
% 247.82/58.52 | | | | | | | (48), (49), (50), (51), (52), (55), (56), (57), (58),
% 247.82/58.52 | | | | | | | (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 247.82/58.52 | | | | | | | (68), (69), (71), (72), (76), (77), (78), (79), (80),
% 247.82/58.52 | | | | | | | (81), (82), (85), (86), (87), (88), (90), (91), (92),
% 247.82/58.52 | | | | | | | (94), (95), (97), (98), (99), (100), (101), (104),
% 247.82/58.52 | | | | | | | (105), (107), (108), (109), (110), (112), (113), (115),
% 247.82/58.52 | | | | | | | (116), (117), (118), (119), (120), (122), (123), (125),
% 247.82/58.52 | | | | | | | (126), (128), (129), (131), (132), (133), (134), (135),
% 247.82/58.52 | | | | | | | (136), (137), (138), (139), (140), (153), (155), (158),
% 247.82/58.52 | | | | | | | (159), (161), (164), (165), (167), (171) are
% 247.82/58.52 | | | | | | | inconsistent by sub-proof #29.
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | Case 2:
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | (172) ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 & $i(all_36_1)
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | ALPHA: (172) implies:
% 247.82/58.52 | | | | | | | (173) op(e1, e4) = all_36_1
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (13),
% 247.82/58.52 | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 247.82/58.52 | | | | | | | (23), (25), (26), (27), (28), (29), (31), (33), (34),
% 247.82/58.52 | | | | | | | (36), (37), (41), (42), (43), (44), (45), (46), (47),
% 247.82/58.52 | | | | | | | (48), (49), (50), (51), (52), (55), (56), (57), (58),
% 247.82/58.52 | | | | | | | (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 247.82/58.52 | | | | | | | (68), (69), (71), (72), (76), (77), (78), (79), (80),
% 247.82/58.52 | | | | | | | (81), (82), (85), (86), (87), (88), (90), (91), (92),
% 247.82/58.52 | | | | | | | (94), (95), (97), (98), (99), (100), (101), (104),
% 247.82/58.52 | | | | | | | (105), (107), (108), (109), (110), (112), (113), (115),
% 247.82/58.52 | | | | | | | (116), (117), (118), (119), (120), (122), (123), (125),
% 247.82/58.52 | | | | | | | (126), (128), (129), (131), (132), (133), (134), (135),
% 247.82/58.52 | | | | | | | (136), (137), (138), (139), (140), (153), (155), (158),
% 247.82/58.52 | | | | | | | (159), (161), (164), (165), (167), (173) are
% 247.82/58.52 | | | | | | | inconsistent by sub-proof #29.
% 247.82/58.52 | | | | | | |
% 247.82/58.52 | | | | | | End of split
% 247.82/58.52 | | | | | |
% 247.82/58.52 | | | | | End of split
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | End of split
% 247.82/58.52 | | | |
% 247.82/58.52 | | | Case 2:
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | (174) all_250_12 = e1 | all_250_12 = e0
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | BETA: splitting (174) gives:
% 247.82/58.52 | | | |
% 247.82/58.52 | | | | Case 1:
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | (175) all_250_12 = e1
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | COMBINE_EQS: (6), (175) imply:
% 247.82/58.52 | | | | | (176) all_244_8 = e1
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | SIMP: (176) implies:
% 247.82/58.52 | | | | | (177) all_244_8 = e1
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (93), (177) imply:
% 247.82/58.52 | | | | | (178) $false
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | CLOSE: (178) is inconsistent.
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | Case 2:
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | (179) all_250_12 = e0
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | COMBINE_EQS: (6), (179) imply:
% 247.82/58.52 | | | | | (180) all_244_8 = e0
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | SIMP: (180) implies:
% 247.82/58.52 | | | | | (181) all_244_8 = e0
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | REDUCE: (9), (181) imply:
% 247.82/58.52 | | | | | (182) $false
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | | CLOSE: (182) is inconsistent.
% 247.82/58.52 | | | | |
% 247.82/58.52 | | | | End of split
% 247.82/58.52 | | | |
% 247.82/58.52 | | | End of split
% 247.82/58.52 | | |
% 247.82/58.52 | | End of split
% 247.82/58.52 | |
% 247.82/58.52 | End of split
% 247.82/58.52 |
% 247.82/58.52 End of proof
% 247.82/58.52
% 247.82/58.52 Sub-proof #29 shows that the following formulas are inconsistent:
% 247.82/58.52 ----------------------------------------------------------------
% 247.82/58.52 (1) ~ (all_100_2 = all_12_2)
% 247.82/58.52 (2) ~ (all_84_2 = all_30_2)
% 247.82/58.52 (3) ~ (all_10_2 = e4)
% 247.82/58.52 (4) ~ (all_244_0 = all_30_2)
% 247.82/58.52 (5) ~ (all_40_2 = all_38_2)
% 247.82/58.52 (6) all_104_2 = all_22_2
% 247.82/58.52 (7) ~ (all_244_8 = e0)
% 247.82/58.52 (8) op(e4, e0) = all_30_2
% 247.82/58.52 (9) ~ (all_40_2 = all_30_2)
% 247.82/58.52 (10) all_94_2 = all_38_2
% 247.82/58.52 (11) op(all_62_2, all_36_2) = e3
% 247.82/58.52 (12) op(all_38_2, e1) = e2
% 247.82/58.52 (13) all_250_13 = all_38_2
% 247.82/58.52 (14) ~ (all_30_2 = e3)
% 247.82/58.52 (15) op(all_38_2, all_4_2) = e1
% 247.82/58.52 (16) op(all_64_2, e4) = e2
% 247.82/58.52 (17) ~ (all_22_2 = e3)
% 247.82/58.52 (18) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.82/58.52 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.82/58.52 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.82/58.52 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.82/58.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.82/58.52 (20) op(e2, e3) = all_10_2
% 247.82/58.52 (21) ~ (e3 = e2)
% 247.82/58.52 (22) op(e0, e0) = all_244_24
% 247.82/58.52 (23) ~ (all_84_2 = e3)
% 247.82/58.52 (24) ~ (all_12_2 = e3)
% 247.82/58.52 (25) op(all_244_8, all_244_8) = e2
% 247.82/58.52 (26) op(e2, e2) = all_244_8
% 247.82/58.52 (27) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.82/58.52 all_250_11 = e0
% 247.82/58.52 (28) ~ (all_64_2 = e2)
% 247.82/58.52 (29) op(all_84_2, all_100_2) = e3
% 247.82/58.52 (30) op(e2, e1) = all_38_2
% 247.82/58.52 (31) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 247.82/58.52 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 247.82/58.52 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.82/58.52 (32) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.82/58.52 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.82/58.52 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.82/58.52 (33) op(e1, e0) = all_34_2
% 247.82/58.52 (34) all_78_2 = all_10_2
% 247.82/58.52 (35) ~ (all_84_2 = e1)
% 247.82/58.52 (36) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.82/58.52 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 247.82/58.52 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 247.82/58.52 (37) all_106_2 = all_38_2
% 247.82/58.52 (38) ~ (all_244_8 = all_38_2)
% 247.82/58.52 (39) op(all_244_15, all_244_15) = e1
% 247.82/58.52 (40) all_252_22 = e3
% 247.82/58.52 (41) all_250_21 = all_22_2
% 247.82/58.52 (42) op(e1, e4) = all_16_2
% 247.82/58.52 (43) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.82/58.52 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.82/58.52 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.82/58.52 (44) ~ (all_244_0 = all_64_2)
% 247.82/58.52 (45) ~ (all_104_2 = e4) | ( ~ (all_104_0 = e1) & op(e4, all_104_1) =
% 247.82/58.52 all_104_0 & op(e3, e4) = all_104_1 & $i(all_104_0) & $i(all_104_1)) |
% 247.82/58.52 ( ~ (all_104_1 = e2) & op(e3, e4) = all_104_1 & $i(all_104_1))
% 247.82/58.53 (46) ( ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 & op(e2, e4) = all_4_1 &
% 247.82/58.53 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e2, e4) = all_4_1
% 247.82/58.53 & $i(all_4_1))
% 247.82/58.53 (47) op(e1, e3) = all_62_2
% 247.82/58.53 (48) all_140_2 = all_84_2
% 247.82/58.53 (49) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.82/58.53 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.82/58.53 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.82/58.53 (50) ~ (all_40_2 = all_10_2)
% 247.82/58.53 (51) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 247.82/58.53 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 247.82/58.53 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 247.82/58.53 (52) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 247.82/58.53 all_250_1 = e0
% 247.82/58.53 (53) all_70_2 = all_62_2
% 247.82/58.53 (54) op(e0, all_10_2) = e2
% 247.82/58.53 (55) op(all_48_2, all_22_2) = e0
% 247.82/58.53 (56) ~ (all_12_2 = e2)
% 247.82/58.53 (57) op(e3, e1) = all_36_2
% 247.82/58.53 (58) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.82/58.53 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.82/58.53 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.82/58.53 (59) ~ (all_16_2 = e2)
% 247.82/58.53 (60) ~ (all_8_2 = e1)
% 247.82/58.53 (61) op(all_40_2, e0) = e2
% 247.82/58.53 (62) ~ (all_22_2 = e1)
% 247.82/58.53 (63) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.82/58.53 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.82/58.53 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.82/58.53 (64) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.82/58.53 all_250_13 = e0
% 247.82/58.53 (65) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.82/58.53 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.82/58.53 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.82/58.53 (66) ~ (all_100_2 = e4)
% 247.82/58.53 (67) ~ (all_38_2 = e4)
% 247.82/58.53 (68) ~ (all_64_2 = all_12_2)
% 247.82/58.53 (69) op(all_22_2, e3) = e0
% 247.82/58.53 (70) all_68_2 = all_22_2
% 247.82/58.53 (71) op(e0, e3) = all_22_2
% 247.82/58.53 (72) ~ (all_244_0 = all_100_2)
% 247.82/58.53 (73) op(all_84_2, e3) = e4
% 247.82/58.53 (74) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 247.82/58.53 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 247.82/58.53 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.82/58.53 (75) op(e1, e4) = all_36_1
% 247.82/58.53 (76) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.82/58.53 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.82/58.53 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.82/58.53 (77) op(all_10_2, e3) = e2
% 247.82/58.53 (78) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.82/58.53 all_250_21 = e0
% 247.82/58.53 (79) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.82/58.53 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.82/58.53 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.82/58.53 (80) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.82/58.53 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.82/58.53 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.82/58.53 (81) op(e3, e4) = all_100_2
% 247.82/58.53 (82) all_250_11 = all_10_2
% 247.82/58.53 (83) op(e4, e4) = all_244_0
% 247.82/58.53 (84) all_230_2 = all_20_2
% 247.82/58.53 (85) ~ (e4 = e3)
% 247.82/58.53 (86) op(e1, e1) = all_244_15
% 247.82/58.53 (87) ~ (all_186_2 = e3) | ( ~ (all_186_0 = e1) & op(e4, e3) = all_186_1 &
% 247.82/58.53 op(e3, all_186_1) = all_186_0 & $i(all_186_0) & $i(all_186_1)) | ( ~
% 247.82/58.53 (all_186_1 = e0) & op(e4, e3) = all_186_1 & $i(all_186_1))
% 247.82/58.53 (88) ~ (all_34_2 = all_30_2)
% 247.82/58.53 (89) op(e0, e1) = all_20_2
% 247.82/58.53 (90) op(all_48_2, e0) = e3
% 247.82/58.53 (91) ~ (all_84_2 = all_22_2)
% 247.82/58.53 (92) op(e1, e2) = all_4_2
% 247.82/58.53 (93) op(e4, e3) = all_84_2
% 247.82/58.53 (94) all_118_2 = all_22_2
% 247.82/58.53 (95) op(e2, e4) = all_64_2
% 247.82/58.53 (96) ~ (all_22_2 = all_10_2)
% 247.82/58.53 (97) ~ (all_22_2 = all_20_2)
% 247.82/58.53 (98) op(e3, e2) = all_8_2
% 247.82/58.53 (99) ~ (all_64_2 = all_16_2)
% 247.82/58.53 (100) op(all_36_2, e1) = e3
% 247.82/58.53 (101) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.82/58.53 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.82/58.53 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.82/58.53 (102) ~ (all_38_2 = all_10_2)
% 247.82/58.53 (103) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 247.82/58.53 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 247.82/58.53 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 247.82/58.53 (104) ~ (all_244_15 = all_36_2)
% 247.82/58.53 (105) ~ (all_244_24 = all_22_2)
% 247.82/58.53 (106) all_250_1 = all_84_2
% 247.82/58.53 (107) ~ (all_100_2 = all_16_2)
% 247.82/58.53 (108) op(e2, e0) = all_40_2
% 247.82/58.53 (109) ~ (all_16_2 = e3)
% 247.82/58.53 (110) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.82/58.53 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.82/58.53 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.82/58.53 (111) ~ (all_244_0 = e3)
% 247.82/58.53 (112) all_90_2 = all_22_2
% 247.82/58.53 (113) ~ (all_140_2 = e0) | ( ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 &
% 247.82/58.53 op(e0, all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1)) | ( ~
% 247.82/58.53 (all_140_1 = e1) & op(e3, e0) = all_140_1 & $i(all_140_1))
% 247.82/58.53 (114) all_46_2 = all_36_2
% 247.82/58.53 (115) op(all_244_24, all_244_24) = e0
% 247.82/58.53 (116) op(e0, e4) = all_12_2
% 247.82/58.53 (117) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.82/58.53 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.82/58.53 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.82/58.53 (118) all_186_2 = all_64_2
% 247.82/58.53 (119) all_124_2 = all_10_2
% 247.82/58.53
% 247.82/58.53 Begin of proof
% 247.82/58.53 |
% 247.82/58.53 | GROUND_INST: instantiating (19) with all_16_2, all_36_1, e4, e1, simplifying
% 247.82/58.53 | with (42), (75) gives:
% 247.82/58.53 | (120) all_36_1 = all_16_2
% 247.82/58.53 |
% 247.82/58.53 | BETA: splitting (31) gives:
% 247.82/58.53 |
% 247.82/58.53 | Case 1:
% 247.82/58.53 | |
% 247.82/58.53 | | (121) ~ (all_30_2 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | REF_CLOSE: (3), (8), (16), (19), (20), (21), (24), (25), (26), (29), (30),
% 247.82/58.53 | | (36), (42), (44), (51), (61), (66), (67), (68), (72), (73), (74),
% 247.82/58.53 | | (81), (83), (85), (95), (99), (101), (108), (109), (111), (116),
% 247.82/58.53 | | (121) are inconsistent by sub-proof #67.
% 247.82/58.53 | |
% 247.82/58.53 | Case 2:
% 247.82/58.53 | |
% 247.82/58.53 | | (122) all_30_2 = e2
% 247.82/58.53 | |
% 247.82/58.53 | | REDUCE: (4), (122) imply:
% 247.82/58.53 | | (123) ~ (all_244_0 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | REDUCE: (2), (122) imply:
% 247.82/58.53 | | (124) ~ (all_84_2 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | REDUCE: (9), (122) imply:
% 247.82/58.53 | | (125) ~ (all_40_2 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | REDUCE: (88), (122) imply:
% 247.82/58.53 | | (126) ~ (all_34_2 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | REDUCE: (14), (122) imply:
% 247.82/58.53 | | (127) ~ (e3 = e2)
% 247.82/58.53 | |
% 247.82/58.53 | | BETA: splitting (103) gives:
% 247.82/58.53 | |
% 247.82/58.53 | | Case 1:
% 247.82/58.53 | | |
% 247.82/58.53 | | | (128) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4)
% 247.82/58.53 | | | = e2)
% 247.82/58.53 | | |
% 247.82/58.53 | | | BETA: splitting (128) gives:
% 247.82/58.53 | | |
% 247.82/58.53 | | | Case 1:
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | (129) all_252_0 = e2 & op(e4, e4) = e2
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | ALPHA: (129) implies:
% 247.82/58.53 | | | | (130) op(e4, e4) = e2
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | REF_CLOSE: (19), (83), (123), (130) are inconsistent by sub-proof #809.
% 247.82/58.53 | | | |
% 247.82/58.53 | | | Case 2:
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | (131) all_252_2 = e2 & op(e3, e4) = e2
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | ALPHA: (131) implies:
% 247.82/58.53 | | | | (132) op(e3, e4) = e2
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | BETA: splitting (101) gives:
% 247.82/58.53 | | | |
% 247.82/58.53 | | | | Case 1:
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | | (133) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 247.82/58.53 | | | | | e4) = e3)
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | | REF_CLOSE: (19), (29), (66), (73), (81), (83), (111), (133) are
% 247.82/58.53 | | | | | inconsistent by sub-proof #32.
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | Case 2:
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | | (134) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 247.82/58.53 | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | | BETA: splitting (134) gives:
% 247.82/58.53 | | | | |
% 247.82/58.53 | | | | | Case 1:
% 247.82/58.53 | | | | | |
% 247.82/58.53 | | | | | | (135) all_252_6 = e3 & op(e2, e4) = e3
% 247.82/58.53 | | | | | |
% 247.82/58.53 | | | | | | ALPHA: (135) implies:
% 247.82/58.53 | | | | | | (136) all_252_6 = e3
% 247.82/58.53 | | | | | | (137) op(e2, e4) = e3
% 247.82/58.53 | | | | | |
% 247.82/58.53 | | | | | | BETA: splitting (74) gives:
% 247.82/58.53 | | | | | |
% 247.82/58.53 | | | | | | Case 1:
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | | (138) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 247.82/58.53 | | | | | | | op(e2, e3) = e4)
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | | REF_CLOSE: (3), (19), (20), (85), (136), (138) are inconsistent by
% 247.82/58.53 | | | | | | | sub-proof #810.
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | Case 2:
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | | (139) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 247.82/58.53 | | | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | | BETA: splitting (139) gives:
% 247.82/58.53 | | | | | | |
% 247.82/58.53 | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | (140) all_252_8 = e4 & op(e2, e2) = e4
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | ALPHA: (140) implies:
% 247.82/58.53 | | | | | | | | (141) op(e2, e2) = e4
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | REF_CLOSE: (19), (25), (26), (83), (123), (141) are inconsistent
% 247.82/58.53 | | | | | | | | by sub-proof #626.
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | (142) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4
% 247.82/58.53 | | | | | | | | & op(e2, e0) = e4)
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | BETA: splitting (142) gives:
% 247.82/58.53 | | | | | | | |
% 247.82/58.53 | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | (143) all_252_11 = e4 & op(e2, e1) = e4
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | ALPHA: (143) implies:
% 247.82/58.53 | | | | | | | | | (144) op(e2, e1) = e4
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REF_CLOSE: (19), (30), (67), (144) are inconsistent by
% 247.82/58.53 | | | | | | | | | sub-proof #935.
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | (145) all_252_18 = e4 & op(e2, e0) = e4
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | ALPHA: (145) implies:
% 247.82/58.53 | | | | | | | | | (146) op(e2, e0) = e4
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | GROUND_INST: instantiating (19) with all_40_2, e4, e0, e2,
% 247.82/58.53 | | | | | | | | | simplifying with (108), (146) gives:
% 247.82/58.53 | | | | | | | | | (147) all_40_2 = e4
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | GROUND_INST: instantiating (19) with all_64_2, e3, e4, e2,
% 247.82/58.53 | | | | | | | | | simplifying with (95), (137) gives:
% 247.82/58.53 | | | | | | | | | (148) all_64_2 = e3
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | GROUND_INST: instantiating (19) with all_100_2, e2, e4, e3,
% 247.82/58.53 | | | | | | | | | simplifying with (81), (132) gives:
% 247.82/58.53 | | | | | | | | | (149) all_100_2 = e2
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | COMBINE_EQS: (118), (148) imply:
% 247.82/58.53 | | | | | | | | | (150) all_186_2 = e3
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (107), (149) imply:
% 247.82/58.53 | | | | | | | | | (151) ~ (all_16_2 = e2)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (1), (149) imply:
% 247.82/58.53 | | | | | | | | | (152) ~ (all_12_2 = e2)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (99), (148) imply:
% 247.82/58.53 | | | | | | | | | (153) ~ (all_16_2 = e3)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (68), (148) imply:
% 247.82/58.53 | | | | | | | | | (154) ~ (all_12_2 = e3)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (5), (147) imply:
% 247.82/58.53 | | | | | | | | | (155) ~ (all_38_2 = e4)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (50), (147) imply:
% 247.82/58.53 | | | | | | | | | (156) ~ (all_10_2 = e4)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | REDUCE: (125), (147) imply:
% 247.82/58.53 | | | | | | | | | (157) ~ (e4 = e2)
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | BETA: splitting (45) gives:
% 247.82/58.53 | | | | | | | | |
% 247.82/58.53 | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | (158) ~ (all_104_2 = e4)
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | REDUCE: (6), (158) imply:
% 247.82/58.53 | | | | | | | | | | (159) ~ (all_22_2 = e4)
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | REF_CLOSE: (3), (7), (10), (11), (12), (13), (15), (17),
% 247.82/58.53 | | | | | | | | | | (18), (19), (20), (21), (22), (26), (27), (30),
% 247.82/58.53 | | | | | | | | | | (32), (33), (34), (37), (38), (39), (40), (41),
% 247.82/58.53 | | | | | | | | | | (42), (43), (47), (49), (53), (54), (55), (56),
% 247.82/58.53 | | | | | | | | | | (57), (58), (59), (60), (62), (63), (64), (65),
% 247.82/58.53 | | | | | | | | | | (67), (69), (70), (71), (76), (77), (78), (79),
% 247.82/58.53 | | | | | | | | | | (80), (82), (84), (86), (89), (90), (92), (94),
% 247.82/58.53 | | | | | | | | | | (96), (97), (98), (100), (102), (104), (105),
% 247.82/58.53 | | | | | | | | | | (110), (112), (114), (115), (116), (117), (119),
% 247.82/58.53 | | | | | | | | | | (126), (157), (159) are inconsistent by sub-proof
% 247.82/58.53 | | | | | | | | | | #31.
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | (160) all_104_2 = e4
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | COMBINE_EQS: (6), (160) imply:
% 247.82/58.53 | | | | | | | | | | (161) all_22_2 = e4
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | REDUCE: (91), (161) imply:
% 247.82/58.53 | | | | | | | | | | (162) ~ (all_84_2 = e4)
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | BETA: splitting (46) gives:
% 247.82/58.53 | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | (163) ~ (all_4_0 = e0) & op(e4, all_4_1) = all_4_0 &
% 247.82/58.53 | | | | | | | | | | | op(e2, e4) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 247.82/58.53 | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | ALPHA: (163) implies:
% 247.82/58.53 | | | | | | | | | | | (164) ~ (all_4_0 = e0)
% 247.82/58.53 | | | | | | | | | | | (165) op(e2, e4) = all_4_1
% 247.82/58.53 | | | | | | | | | | | (166) op(e4, all_4_1) = all_4_0
% 247.82/58.53 | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | BETA: splitting (52) gives:
% 247.82/58.53 | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | (167) all_250_1 = e4
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | COMBINE_EQS: (106), (167) imply:
% 247.82/58.53 | | | | | | | | | | | | (168) all_84_2 = e4
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | SIMP: (168) implies:
% 247.82/58.53 | | | | | | | | | | | | (169) all_84_2 = e4
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | REDUCE: (162), (169) imply:
% 247.82/58.53 | | | | | | | | | | | | (170) $false
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | (171) all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 247.82/58.53 | | | | | | | | | | | | all_250_1 = e0
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | BETA: splitting (171) gives:
% 247.82/58.53 | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | (172) all_250_1 = e3
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | COMBINE_EQS: (106), (172) imply:
% 247.82/58.53 | | | | | | | | | | | | | (173) all_84_2 = e3
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | REDUCE: (23), (173) imply:
% 247.82/58.53 | | | | | | | | | | | | | (174) $false
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | (175) all_250_1 = e2 | all_250_1 = e1 | all_250_1 = e0
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | BETA: splitting (175) gives:
% 247.82/58.53 | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | (176) all_250_1 = e2
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | COMBINE_EQS: (106), (176) imply:
% 247.82/58.53 | | | | | | | | | | | | | | (177) all_84_2 = e2
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | REDUCE: (124), (177) imply:
% 247.82/58.53 | | | | | | | | | | | | | | (178) $false
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | CLOSE: (178) is inconsistent.
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | (179) all_250_1 = e1 | all_250_1 = e0
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 247.82/58.53 | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | (180) all_250_1 = e1
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | COMBINE_EQS: (106), (180) imply:
% 247.82/58.53 | | | | | | | | | | | | | | | (181) all_84_2 = e1
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | REDUCE: (35), (181) imply:
% 247.82/58.53 | | | | | | | | | | | | | | | (182) $false
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | (183) all_250_1 = e0
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | COMBINE_EQS: (106), (183) imply:
% 247.82/58.53 | | | | | | | | | | | | | | | (184) all_84_2 = e0
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | COMBINE_EQS: (48), (184) imply:
% 247.82/58.53 | | | | | | | | | | | | | | | (185) all_140_2 = e0
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | REDUCE: (93), (184) imply:
% 247.82/58.53 | | | | | | | | | | | | | | | (186) op(e4, e3) = e0
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 247.82/58.53 | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | Case 1:
% 247.82/58.53 | | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | | (187) ~ (all_64_2 = e3)
% 247.82/58.53 | | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | | REF_CLOSE: (19), (24), (29), (42), (66), (73), (81), (83),
% 247.82/58.53 | | | | | | | | | | | | | | | | (95), (101), (109), (111), (116), (187) are
% 247.82/58.53 | | | | | | | | | | | | | | | | inconsistent by sub-proof #68.
% 247.82/58.53 | | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | Case 2:
% 247.82/58.53 | | | | | | | | | | | | | | | |
% 247.82/58.53 | | | | | | | | | | | | | | | | (188) ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.82/58.53 | | | | | | | | | | | | | | | | op(e3, all_64_1) = all_64_0 & $i(all_64_0) &
% 247.82/58.54 | | | | | | | | | | | | | | | | $i(all_64_1)) | ( ~ (all_64_1 = e1) & op(e4, e3)
% 247.82/58.54 | | | | | | | | | | | | | | | | = all_64_1 & $i(all_64_1))
% 247.82/58.54 | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | Case 1:
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | (189) ~ (all_186_2 = e3)
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | REDUCE: (150), (189) imply:
% 247.82/58.54 | | | | | | | | | | | | | | | | | (190) $false
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | Case 2:
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | (191) ( ~ (all_186_0 = e1) & op(e4, e3) = all_186_1 &
% 247.82/58.54 | | | | | | | | | | | | | | | | | op(e3, all_186_1) = all_186_0 & $i(all_186_0) &
% 247.82/58.54 | | | | | | | | | | | | | | | | | $i(all_186_1)) | ( ~ (all_186_1 = e0) & op(e4,
% 247.82/58.54 | | | | | | | | | | | | | | | | | e3) = all_186_1 & $i(all_186_1))
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | Case 1:
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (192) ~ (all_186_0 = e1) & op(e4, e3) = all_186_1 &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | op(e3, all_186_1) = all_186_0 & $i(all_186_0) &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | $i(all_186_1)
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (193) op(e4, e3) = all_186_1
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | Case 1:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | (194) ~ (all_140_2 = e0)
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | REDUCE: (185), (194) imply:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | (195) $false
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | Case 2:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e3, all_4_1, e4, e2,
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | simplifying with (137), (165) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | (196) all_4_1 = e3
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e0, all_186_1, e3, e4,
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | simplifying with (186), (193) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | (197) all_186_1 = e0
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | REDUCE: (166), (196) imply:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | (198) op(e4, e3) = all_4_0
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | (199) ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | op(e3, all_64_1) = all_64_0 & $i(all_64_0) &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | $i(all_64_1)
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | (200) op(e4, e3) = all_64_1
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (164), (186), (198), (200) are inconsistent
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | by sub-proof #30.
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | (201) ~ (all_64_1 = e1) & op(e4, e3) = all_64_1 &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | $i(all_64_1)
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | (202) op(e4, e3) = all_64_1
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (164), (186), (198), (202) are inconsistent
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | | by sub-proof #30.
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | Case 2:
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (203) ~ (all_186_1 = e0) & op(e4, e3) = all_186_1 &
% 247.82/58.54 | | | | | | | | | | | | | | | | | | $i(all_186_1)
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (204) ~ (all_186_1 = e0)
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (205) op(e4, e3) = all_186_1
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e0, all_186_1, e3, e4,
% 247.82/58.54 | | | | | | | | | | | | | | | | | | simplifying with (186), (205) gives:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (206) all_186_1 = e0
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | REDUCE: (204), (206) imply:
% 247.82/58.54 | | | | | | | | | | | | | | | | | | (207) $false
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 247.82/58.54 | | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | End of split
% 247.82/58.54 | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | Case 2:
% 247.82/58.54 | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | (208) ~ (all_4_1 = e3) & op(e2, e4) = all_4_1 &
% 247.82/58.54 | | | | | | | | | | | $i(all_4_1)
% 247.82/58.54 | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | ALPHA: (208) implies:
% 247.82/58.54 | | | | | | | | | | | (209) ~ (all_4_1 = e3)
% 247.82/58.54 | | | | | | | | | | | (210) op(e2, e4) = all_4_1
% 247.82/58.54 | | | | | | | | | | |
% 247.82/58.54 | | | | | | | | | | | GROUND_INST: instantiating (19) with e3, all_4_1, e4, e2,
% 247.82/58.54 | | | | | | | | | | | simplifying with (137), (210) gives:
% 247.82/58.54 | | | | | | | | | | | (211) all_4_1 = e3
% 247.82/58.54 | | | | | | | | | | |
% 247.99/58.54 | | | | | | | | | | | REDUCE: (209), (211) imply:
% 247.99/58.54 | | | | | | | | | | | (212) $false
% 247.99/58.54 | | | | | | | | | | |
% 247.99/58.54 | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 247.99/58.54 | | | | | | | | | | |
% 247.99/58.54 | | | | | | | | | | End of split
% 247.99/58.54 | | | | | | | | | |
% 247.99/58.54 | | | | | | | | | End of split
% 247.99/58.54 | | | | | | | | |
% 247.99/58.54 | | | | | | | | End of split
% 247.99/58.54 | | | | | | | |
% 247.99/58.54 | | | | | | | End of split
% 247.99/58.54 | | | | | | |
% 247.99/58.54 | | | | | | End of split
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | Case 2:
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | (213) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 247.99/58.54 | | | | | | op(e0, e4) = e3)
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | REF_CLOSE: (19), (24), (42), (109), (116), (213) are inconsistent by
% 247.99/58.54 | | | | | | sub-proof #894.
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | End of split
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | End of split
% 247.99/58.54 | | | |
% 247.99/58.54 | | | End of split
% 247.99/58.54 | | |
% 247.99/58.54 | | Case 2:
% 247.99/58.54 | | |
% 247.99/58.54 | | | (214) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 247.99/58.54 | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 247.99/58.54 | | |
% 247.99/58.54 | | | BETA: splitting (214) gives:
% 247.99/58.54 | | |
% 247.99/58.54 | | | Case 1:
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | (215) all_252_6 = e2 & op(e2, e4) = e2
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | ALPHA: (215) implies:
% 247.99/58.54 | | | | (216) all_252_6 = e2
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | BETA: splitting (101) gives:
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | Case 1:
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | | (217) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 247.99/58.54 | | | | | e4) = e3)
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | | REF_CLOSE: (19), (29), (66), (73), (81), (83), (111), (217) are
% 247.99/58.54 | | | | | inconsistent by sub-proof #32.
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | Case 2:
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | | (218) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 247.99/58.54 | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | | BETA: splitting (218) gives:
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | | Case 1:
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | (219) all_252_6 = e3 & op(e2, e4) = e3
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | ALPHA: (219) implies:
% 247.99/58.54 | | | | | | (220) all_252_6 = e3
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | COMBINE_EQS: (216), (220) imply:
% 247.99/58.54 | | | | | | (221) e3 = e2
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | REDUCE: (21), (221) imply:
% 247.99/58.54 | | | | | | (222) $false
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | CLOSE: (222) is inconsistent.
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | Case 2:
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | (223) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 247.99/58.54 | | | | | | op(e0, e4) = e3)
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | | REF_CLOSE: (19), (24), (42), (109), (116), (223) are inconsistent by
% 247.99/58.54 | | | | | | sub-proof #894.
% 247.99/58.54 | | | | | |
% 247.99/58.54 | | | | | End of split
% 247.99/58.54 | | | | |
% 247.99/58.54 | | | | End of split
% 247.99/58.54 | | | |
% 247.99/58.54 | | | Case 2:
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | (224) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 247.99/58.54 | | | | e4) = e2)
% 247.99/58.54 | | | |
% 247.99/58.54 | | | | REF_CLOSE: (19), (42), (56), (59), (116), (224) are inconsistent by
% 247.99/58.54 | | | | sub-proof #891.
% 247.99/58.54 | | | |
% 247.99/58.54 | | | End of split
% 247.99/58.54 | | |
% 247.99/58.54 | | End of split
% 247.99/58.54 | |
% 247.99/58.54 | End of split
% 247.99/58.54 |
% 247.99/58.54 End of proof
% 247.99/58.54
% 247.99/58.54 Sub-proof #30 shows that the following formulas are inconsistent:
% 247.99/58.54 ----------------------------------------------------------------
% 247.99/58.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.54 (2) ~ (all_4_0 = e0)
% 247.99/58.54 (3) op(e4, e3) = all_64_1
% 247.99/58.54 (4) op(e4, e3) = e0
% 247.99/58.54 (5) op(e4, e3) = all_4_0
% 247.99/58.54
% 247.99/58.54 Begin of proof
% 247.99/58.54 |
% 247.99/58.54 | GROUND_INST: instantiating (1) with e0, all_64_1, e3, e4, simplifying with
% 247.99/58.54 | (3), (4) gives:
% 247.99/58.54 | (6) all_64_1 = e0
% 247.99/58.54 |
% 247.99/58.54 | GROUND_INST: instantiating (1) with all_4_0, all_64_1, e3, e4, simplifying
% 247.99/58.54 | with (3), (5) gives:
% 247.99/58.54 | (7) all_64_1 = all_4_0
% 247.99/58.54 |
% 247.99/58.54 | COMBINE_EQS: (6), (7) imply:
% 247.99/58.54 | (8) all_4_0 = e0
% 247.99/58.54 |
% 247.99/58.54 | REDUCE: (2), (8) imply:
% 247.99/58.54 | (9) $false
% 247.99/58.54 |
% 247.99/58.54 | CLOSE: (9) is inconsistent.
% 247.99/58.54 |
% 247.99/58.54 End of proof
% 247.99/58.54
% 247.99/58.54 Sub-proof #31 shows that the following formulas are inconsistent:
% 247.99/58.54 ----------------------------------------------------------------
% 247.99/58.54 (1) ~ (all_10_2 = e4)
% 247.99/58.54 (2) ~ (all_244_8 = e0)
% 247.99/58.54 (3) all_94_2 = all_38_2
% 247.99/58.54 (4) op(all_62_2, all_36_2) = e3
% 247.99/58.54 (5) op(all_38_2, e1) = e2
% 247.99/58.54 (6) all_250_13 = all_38_2
% 247.99/58.54 (7) op(all_38_2, all_4_2) = e1
% 247.99/58.54 (8) ~ (all_22_2 = e3)
% 247.99/58.54 (9) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.99/58.54 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.99/58.54 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.99/58.54 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.54 (11) op(e2, e3) = all_10_2
% 247.99/58.54 (12) ~ (e3 = e2)
% 247.99/58.54 (13) op(e0, e0) = all_244_24
% 247.99/58.54 (14) op(e2, e2) = all_244_8
% 247.99/58.54 (15) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.99/58.54 all_250_11 = e0
% 247.99/58.54 (16) op(e2, e1) = all_38_2
% 247.99/58.54 (17) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.99/58.54 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.99/58.54 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.99/58.54 (18) op(e1, e0) = all_34_2
% 247.99/58.54 (19) all_78_2 = all_10_2
% 247.99/58.54 (20) ~ (all_34_2 = e2)
% 247.99/58.54 (21) all_106_2 = all_38_2
% 247.99/58.54 (22) ~ (all_244_8 = all_38_2)
% 247.99/58.54 (23) op(all_244_15, all_244_15) = e1
% 247.99/58.54 (24) all_252_22 = e3
% 247.99/58.54 (25) all_250_21 = all_22_2
% 247.99/58.54 (26) op(e1, e4) = all_16_2
% 247.99/58.54 (27) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.99/58.54 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.99/58.54 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.99/58.54 (28) op(e1, e3) = all_62_2
% 247.99/58.54 (29) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.99/58.54 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.99/58.54 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.99/58.54 (30) ~ (all_22_2 = e4)
% 247.99/58.54 (31) all_70_2 = all_62_2
% 247.99/58.54 (32) op(e0, all_10_2) = e2
% 247.99/58.54 (33) op(all_48_2, all_22_2) = e0
% 247.99/58.54 (34) ~ (all_12_2 = e2)
% 247.99/58.54 (35) op(e3, e1) = all_36_2
% 247.99/58.54 (36) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.99/58.54 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.99/58.54 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.99/58.54 (37) ~ (all_16_2 = e2)
% 247.99/58.54 (38) ~ (all_8_2 = e1)
% 247.99/58.54 (39) ~ (all_22_2 = e1)
% 247.99/58.54 (40) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 247.99/58.54 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 247.99/58.54 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.99/58.54 (41) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.99/58.54 all_250_13 = e0
% 247.99/58.54 (42) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.99/58.54 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.99/58.54 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.99/58.54 (43) ~ (all_38_2 = e4)
% 247.99/58.54 (44) op(all_22_2, e3) = e0
% 247.99/58.54 (45) all_68_2 = all_22_2
% 247.99/58.54 (46) op(e0, e3) = all_22_2
% 247.99/58.54 (47) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.99/58.54 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.99/58.54 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.99/58.54 (48) op(all_10_2, e3) = e2
% 247.99/58.54 (49) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.99/58.54 all_250_21 = e0
% 247.99/58.54 (50) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 247.99/58.54 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 247.99/58.54 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 247.99/58.54 (51) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.99/58.54 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.99/58.54 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.99/58.54 (52) all_250_11 = all_10_2
% 247.99/58.54 (53) all_230_2 = all_20_2
% 247.99/58.54 (54) op(e1, e1) = all_244_15
% 247.99/58.54 (55) op(e0, e1) = all_20_2
% 247.99/58.54 (56) op(all_48_2, e0) = e3
% 247.99/58.54 (57) op(e1, e2) = all_4_2
% 247.99/58.54 (58) all_118_2 = all_22_2
% 247.99/58.54 (59) ~ (all_22_2 = all_10_2)
% 247.99/58.54 (60) ~ (e4 = e2)
% 247.99/58.54 (61) ~ (all_22_2 = all_20_2)
% 247.99/58.54 (62) op(e3, e2) = all_8_2
% 247.99/58.54 (63) op(all_36_2, e1) = e3
% 247.99/58.54 (64) ~ (all_38_2 = all_10_2)
% 247.99/58.54 (65) ~ (all_244_15 = all_36_2)
% 247.99/58.54 (66) ~ (all_244_24 = all_22_2)
% 247.99/58.54 (67) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.99/58.54 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.99/58.54 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.99/58.54 (68) all_90_2 = all_22_2
% 247.99/58.54 (69) all_46_2 = all_36_2
% 247.99/58.54 (70) op(all_244_24, all_244_24) = e0
% 247.99/58.54 (71) op(e0, e4) = all_12_2
% 247.99/58.54 (72) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.99/58.54 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.99/58.54 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.99/58.54 (73) all_124_2 = all_10_2
% 247.99/58.54
% 247.99/58.54 Begin of proof
% 247.99/58.54 |
% 247.99/58.54 | BETA: splitting (29) gives:
% 247.99/58.54 |
% 247.99/58.54 | Case 1:
% 247.99/58.54 | |
% 247.99/58.54 | | (74) ~ (all_230_2 = e2)
% 247.99/58.54 | |
% 247.99/58.54 | | REDUCE: (53), (74) imply:
% 247.99/58.54 | | (75) ~ (all_20_2 = e2)
% 247.99/58.54 | |
% 247.99/58.54 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 247.99/58.54 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 247.99/58.54 | | (25), (26), (27), (28), (31), (32), (33), (34), (35), (36), (37),
% 247.99/58.54 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 247.99/58.54 | | (49), (50), (51), (52), (54), (55), (56), (57), (58), (59), (60),
% 247.99/58.54 | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 247.99/58.54 | | (73), (75) are inconsistent by sub-proof #647.
% 247.99/58.54 | |
% 247.99/58.54 | Case 2:
% 247.99/58.54 | |
% 247.99/58.54 | | (76) all_230_2 = e2
% 247.99/58.54 | |
% 247.99/58.54 | | COMBINE_EQS: (53), (76) imply:
% 247.99/58.54 | | (77) all_20_2 = e2
% 247.99/58.54 | |
% 247.99/58.54 | | REDUCE: (61), (77) imply:
% 247.99/58.54 | | (78) ~ (all_22_2 = e2)
% 247.99/58.54 | |
% 247.99/58.54 | | REF_CLOSE: (8), (10), (25), (30), (33), (39), (49), (56), (78) are
% 247.99/58.54 | | inconsistent by sub-proof #957.
% 247.99/58.54 | |
% 247.99/58.54 | End of split
% 247.99/58.54 |
% 247.99/58.55 End of proof
% 247.99/58.55
% 247.99/58.55 Sub-proof #32 shows that the following formulas are inconsistent:
% 247.99/58.55 ----------------------------------------------------------------
% 247.99/58.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.55 (2) op(all_84_2, all_100_2) = e3
% 247.99/58.55 (3) ~ (all_100_2 = e4)
% 247.99/58.55 (4) op(all_84_2, e3) = e4
% 247.99/58.55 (5) op(e3, e4) = all_100_2
% 247.99/58.55 (6) op(e4, e4) = all_244_0
% 247.99/58.55 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.99/58.55 (8) ~ (all_244_0 = e3)
% 247.99/58.55
% 247.99/58.55 Begin of proof
% 247.99/58.55 |
% 247.99/58.55 | BETA: splitting (7) gives:
% 247.99/58.55 |
% 247.99/58.55 | Case 1:
% 247.99/58.55 | |
% 247.99/58.55 | | (9) all_252_0 = e3 & op(e4, e4) = e3
% 247.99/58.55 | |
% 247.99/58.55 | | ALPHA: (9) implies:
% 247.99/58.55 | | (10) op(e4, e4) = e3
% 247.99/58.55 | |
% 247.99/58.55 | | REF_CLOSE: (1), (6), (8), (10) are inconsistent by sub-proof #813.
% 247.99/58.55 | |
% 247.99/58.55 | Case 2:
% 247.99/58.55 | |
% 247.99/58.55 | | (11) all_252_2 = e3 & op(e3, e4) = e3
% 247.99/58.55 | |
% 247.99/58.55 | | ALPHA: (11) implies:
% 247.99/58.55 | | (12) op(e3, e4) = e3
% 247.99/58.55 | |
% 247.99/58.55 | | REF_CLOSE: (1), (2), (3), (4), (5), (12) are inconsistent by sub-proof #69.
% 247.99/58.55 | |
% 247.99/58.55 | End of split
% 247.99/58.55 |
% 247.99/58.55 End of proof
% 247.99/58.55
% 247.99/58.55 Sub-proof #33 shows that the following formulas are inconsistent:
% 247.99/58.55 ----------------------------------------------------------------
% 247.99/58.55 (1) all_252_14 = e3 & op(e1, e2) = e3
% 247.99/58.55 (2) all_252_14 = e4
% 247.99/58.55 (3) ~ (e4 = e3)
% 247.99/58.55
% 247.99/58.55 Begin of proof
% 247.99/58.55 |
% 247.99/58.55 | ALPHA: (1) implies:
% 247.99/58.55 | (4) all_252_14 = e3
% 247.99/58.55 |
% 247.99/58.55 | COMBINE_EQS: (2), (4) imply:
% 247.99/58.55 | (5) e4 = e3
% 247.99/58.55 |
% 247.99/58.55 | REDUCE: (3), (5) imply:
% 247.99/58.55 | (6) $false
% 247.99/58.55 |
% 247.99/58.55 | CLOSE: (6) is inconsistent.
% 247.99/58.55 |
% 247.99/58.55 End of proof
% 247.99/58.55
% 247.99/58.55 Sub-proof #34 shows that the following formulas are inconsistent:
% 247.99/58.55 ----------------------------------------------------------------
% 247.99/58.55 (1) ~ (all_10_2 = e4)
% 247.99/58.55 (2) op(all_6_2, e2) = e4
% 247.99/58.55 (3) op(e4, e0) = all_30_2
% 247.99/58.55 (4) op(all_28_2, all_40_2) = e2
% 247.99/58.55 (5) op(all_64_2, e4) = e2
% 247.99/58.55 (6) ~ (all_28_2 = e3)
% 247.99/58.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.55 (8) op(e2, e3) = all_10_2
% 247.99/58.55 (9) ~ (e3 = e2)
% 247.99/58.55 (10) ~ (all_12_2 = e3)
% 247.99/58.55 (11) op(all_244_8, all_244_8) = e2
% 247.99/58.55 (12) op(e2, e2) = all_244_8
% 247.99/58.55 (13) op(all_84_2, all_100_2) = e3
% 247.99/58.55 (14) op(e2, e1) = all_38_2
% 247.99/58.55 (15) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 247.99/58.55 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 247.99/58.55 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.99/58.55 (16) ~ (all_64_2 = all_40_2)
% 247.99/58.55 (17) op(e0, e2) = all_28_2
% 247.99/58.55 (18) ~ (all_28_2 = e1)
% 247.99/58.55 (19) op(all_6_2, all_64_2) = e2
% 247.99/58.55 (20) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.99/58.55 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 247.99/58.55 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 247.99/58.55 (21) op(e1, e4) = all_16_2
% 247.99/58.55 (22) ~ (all_244_0 = all_64_2)
% 247.99/58.55 (23) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 247.99/58.55 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 247.99/58.55 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 247.99/58.55 (24) ~ (all_54_2 = e2) | ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 &
% 247.99/58.55 op(e0, e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 =
% 247.99/58.55 e3) & op(e0, e2) = all_54_1 & $i(all_54_1))
% 247.99/58.55 (25) op(all_40_2, e0) = e2
% 247.99/58.55 (26) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.99/58.55 all_250_22 = e0
% 247.99/58.55 (27) ~ (all_100_2 = e4)
% 247.99/58.55 (28) ~ (all_38_2 = e4)
% 247.99/58.55 (29) ~ (all_28_2 = e4)
% 247.99/58.55 (30) ~ (all_64_2 = all_12_2)
% 247.99/58.55 (31) ~ (all_244_0 = all_100_2)
% 247.99/58.55 (32) op(all_84_2, e3) = e4
% 247.99/58.55 (33) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 247.99/58.55 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 247.99/58.55 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.99/58.55 (34) op(e1, e4) = all_36_1
% 247.99/58.55 (35) op(e3, e4) = all_100_2
% 247.99/58.55 (36) op(e4, e4) = all_244_0
% 247.99/58.55 (37) all_54_2 = all_30_2
% 247.99/58.55 (38) ~ (e4 = e3)
% 247.99/58.55 (39) op(e2, e4) = all_64_2
% 247.99/58.55 (40) op(all_40_2, all_28_2) = e0
% 247.99/58.55 (41) ~ (all_64_2 = all_16_2)
% 247.99/58.55 (42) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.99/58.55 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.99/58.55 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.99/58.55 (43) op(e2, e0) = all_40_2
% 247.99/58.55 (44) ~ (all_16_2 = e3)
% 247.99/58.55 (45) all_250_22 = all_28_2
% 247.99/58.55 (46) ~ (all_244_0 = e3)
% 247.99/58.55 (47) op(all_30_2, e0) = e4
% 247.99/58.55 (48) op(e0, e4) = all_12_2
% 247.99/58.55
% 247.99/58.55 Begin of proof
% 247.99/58.55 |
% 247.99/58.55 | GROUND_INST: instantiating (7) with all_16_2, all_36_1, e4, e1, simplifying
% 247.99/58.55 | with (21), (34) gives:
% 247.99/58.55 | (49) all_36_1 = all_16_2
% 247.99/58.55 |
% 247.99/58.55 | BETA: splitting (15) gives:
% 247.99/58.55 |
% 247.99/58.55 | Case 1:
% 247.99/58.55 | |
% 247.99/58.55 | | (50) ~ (all_30_2 = e2)
% 247.99/58.55 | |
% 247.99/58.55 | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14), (20),
% 247.99/58.55 | | (21), (22), (23), (25), (27), (28), (30), (31), (32), (33), (35),
% 247.99/58.55 | | (36), (38), (39), (41), (42), (43), (44), (46), (48), (50) are
% 247.99/58.55 | | inconsistent by sub-proof #67.
% 247.99/58.55 | |
% 247.99/58.55 | Case 2:
% 247.99/58.55 | |
% 247.99/58.55 | | (51) all_30_2 = e2
% 247.99/58.55 | | (52) ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 & op(e0, e2) =
% 247.99/58.55 | | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e1) &
% 247.99/58.55 | | op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.99/58.55 | |
% 247.99/58.55 | | COMBINE_EQS: (37), (51) imply:
% 247.99/58.55 | | (53) all_54_2 = e2
% 247.99/58.55 | |
% 247.99/58.55 | | REDUCE: (47), (51) imply:
% 247.99/58.55 | | (54) op(e2, e0) = e4
% 247.99/58.55 | |
% 247.99/58.55 | | BETA: splitting (52) gives:
% 247.99/58.55 | |
% 247.99/58.55 | | Case 1:
% 247.99/58.55 | | |
% 247.99/58.55 | | |
% 247.99/58.55 | | | GROUND_INST: instantiating (7) with all_40_2, e4, e0, e2, simplifying with
% 247.99/58.55 | | | (43), (54) gives:
% 247.99/58.55 | | | (55) all_40_2 = e4
% 247.99/58.55 | | |
% 247.99/58.55 | | | REDUCE: (16), (55) imply:
% 247.99/58.55 | | | (56) ~ (all_64_2 = e4)
% 247.99/58.55 | | |
% 247.99/58.55 | | | REF_CLOSE: (2), (4), (6), (7), (18), (19), (25), (26), (29), (39), (40),
% 247.99/58.55 | | | (45), (55), (56) are inconsistent by sub-proof #35.
% 247.99/58.55 | | |
% 247.99/58.55 | | Case 2:
% 247.99/58.55 | | |
% 247.99/58.55 | | | (57) ~ (all_30_1 = e1) & op(e0, e2) = all_30_1 & $i(all_30_1)
% 247.99/58.55 | | |
% 247.99/58.55 | | | ALPHA: (57) implies:
% 247.99/58.55 | | | (58) ~ (all_30_1 = e1)
% 247.99/58.55 | | | (59) op(e0, e2) = all_30_1
% 247.99/58.55 | | |
% 247.99/58.55 | | | BETA: splitting (24) gives:
% 247.99/58.55 | | |
% 247.99/58.55 | | | Case 1:
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | (60) ~ (all_54_2 = e2)
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REDUCE: (53), (60) imply:
% 247.99/58.55 | | | | (61) $false
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | CLOSE: (61) is inconsistent.
% 247.99/58.55 | | | |
% 247.99/58.55 | | | Case 2:
% 247.99/58.55 | | | |
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | GROUND_INST: instantiating (7) with all_28_2, all_30_1, e2, e0,
% 247.99/58.55 | | | | simplifying with (17), (59) gives:
% 247.99/58.55 | | | | (62) all_30_1 = all_28_2
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | GROUND_INST: instantiating (7) with all_40_2, e4, e0, e2, simplifying
% 247.99/58.55 | | | | with (43), (54) gives:
% 247.99/58.55 | | | | (63) all_40_2 = e4
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REDUCE: (16), (63) imply:
% 247.99/58.55 | | | | (64) ~ (all_64_2 = e4)
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REF_CLOSE: (2), (4), (6), (7), (18), (19), (25), (26), (29), (39), (40),
% 247.99/58.55 | | | | (45), (63), (64) are inconsistent by sub-proof #35.
% 247.99/58.55 | | | |
% 247.99/58.55 | | | End of split
% 247.99/58.55 | | |
% 247.99/58.55 | | End of split
% 247.99/58.55 | |
% 247.99/58.55 | End of split
% 247.99/58.55 |
% 247.99/58.55 End of proof
% 247.99/58.55
% 247.99/58.55 Sub-proof #35 shows that the following formulas are inconsistent:
% 247.99/58.55 ----------------------------------------------------------------
% 247.99/58.55 (1) op(all_6_2, e2) = e4
% 247.99/58.55 (2) op(all_28_2, all_40_2) = e2
% 247.99/58.55 (3) ~ (all_28_2 = e3)
% 247.99/58.55 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.55 (5) all_40_2 = e4
% 247.99/58.55 (6) ~ (all_28_2 = e1)
% 247.99/58.55 (7) op(all_6_2, all_64_2) = e2
% 247.99/58.55 (8) op(all_40_2, e0) = e2
% 247.99/58.55 (9) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 247.99/58.55 all_250_22 = e0
% 247.99/58.55 (10) ~ (all_28_2 = e4)
% 247.99/58.55 (11) op(e2, e4) = all_64_2
% 247.99/58.55 (12) op(all_40_2, all_28_2) = e0
% 247.99/58.55 (13) all_250_22 = all_28_2
% 247.99/58.55 (14) ~ (all_64_2 = e4)
% 247.99/58.55
% 247.99/58.55 Begin of proof
% 247.99/58.55 |
% 247.99/58.55 | REDUCE: (2), (5) imply:
% 247.99/58.55 | (15) op(all_28_2, e4) = e2
% 247.99/58.55 |
% 247.99/58.55 | BETA: splitting (9) gives:
% 247.99/58.55 |
% 247.99/58.55 | Case 1:
% 247.99/58.55 | |
% 247.99/58.55 | | (16) all_250_22 = e4
% 247.99/58.55 | |
% 247.99/58.55 | | COMBINE_EQS: (13), (16) imply:
% 247.99/58.55 | | (17) all_28_2 = e4
% 247.99/58.55 | |
% 247.99/58.55 | | REDUCE: (10), (17) imply:
% 247.99/58.55 | | (18) $false
% 247.99/58.55 | |
% 247.99/58.55 | | CLOSE: (18) is inconsistent.
% 247.99/58.55 | |
% 247.99/58.55 | Case 2:
% 247.99/58.55 | |
% 247.99/58.55 | | (19) all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 | all_250_22 =
% 247.99/58.55 | | e0
% 247.99/58.55 | |
% 247.99/58.55 | | BETA: splitting (19) gives:
% 247.99/58.55 | |
% 247.99/58.55 | | Case 1:
% 247.99/58.55 | | |
% 247.99/58.55 | | | (20) all_250_22 = e3
% 247.99/58.55 | | |
% 247.99/58.55 | | | COMBINE_EQS: (13), (20) imply:
% 247.99/58.55 | | | (21) all_28_2 = e3
% 247.99/58.55 | | |
% 247.99/58.55 | | | REDUCE: (3), (21) imply:
% 247.99/58.55 | | | (22) $false
% 247.99/58.55 | | |
% 247.99/58.55 | | | CLOSE: (22) is inconsistent.
% 247.99/58.55 | | |
% 247.99/58.55 | | Case 2:
% 247.99/58.55 | | |
% 247.99/58.55 | | | (23) all_250_22 = e2 | all_250_22 = e1 | all_250_22 = e0
% 247.99/58.55 | | |
% 247.99/58.55 | | | BETA: splitting (23) gives:
% 247.99/58.55 | | |
% 247.99/58.55 | | | Case 1:
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | (24) all_250_22 = e2
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | COMBINE_EQS: (13), (24) imply:
% 247.99/58.55 | | | | (25) all_28_2 = e2
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REDUCE: (15), (25) imply:
% 247.99/58.55 | | | | (26) op(e2, e4) = e2
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REF_CLOSE: (1), (4), (7), (11), (14), (26) are inconsistent by sub-proof
% 247.99/58.55 | | | | #790.
% 247.99/58.55 | | | |
% 247.99/58.55 | | | Case 2:
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | (27) ~ (all_250_22 = e2)
% 247.99/58.55 | | | | (28) all_250_22 = e1 | all_250_22 = e0
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REDUCE: (13), (27) imply:
% 247.99/58.55 | | | | (29) ~ (all_28_2 = e2)
% 247.99/58.55 | | | |
% 247.99/58.55 | | | | REF_CLOSE: (4), (6), (8), (12), (13), (28), (29) are inconsistent by
% 247.99/58.55 | | | | sub-proof #584.
% 247.99/58.55 | | | |
% 247.99/58.55 | | | End of split
% 247.99/58.55 | | |
% 247.99/58.55 | | End of split
% 247.99/58.55 | |
% 247.99/58.55 | End of split
% 247.99/58.55 |
% 247.99/58.55 End of proof
% 247.99/58.55
% 247.99/58.55 Sub-proof #36 shows that the following formulas are inconsistent:
% 247.99/58.55 ----------------------------------------------------------------
% 247.99/58.55 (1) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.99/58.55 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.99/58.55 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.99/58.55 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.55 (3) op(e2, e1) = all_38_2
% 247.99/58.55 (4) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.99/58.55 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.99/58.55 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.99/58.55 (5) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.99/58.55 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.99/58.55 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.99/58.55 (6) ~ (all_244_15 = e4)
% 247.99/58.55 (7) op(all_16_2, all_26_2) = e4
% 247.99/58.55 (8) op(e3, e1) = all_36_2
% 247.99/58.55 (9) op(e4, e1) = all_26_2
% 247.99/58.55 (10) op(e4, e4) = all_244_0
% 247.99/58.55 (11) ~ (all_244_0 = e1)
% 247.99/58.55 (12) op(e1, e1) = all_244_15
% 247.99/58.55 (13) op(e0, e1) = all_20_2
% 247.99/58.55 (14) ~ (all_26_2 = e3)
% 247.99/58.55 (15) ~ (all_26_2 = e1)
% 247.99/58.55 (16) op(all_36_2, e1) = e3
% 247.99/58.55 (17) ~ (all_20_2 = e4)
% 247.99/58.55 (18) op(all_16_2, e4) = e1
% 247.99/58.55 (19) op(all_38_2, e4) = e1
% 247.99/58.55
% 247.99/58.55 Begin of proof
% 247.99/58.55 |
% 247.99/58.55 | BETA: splitting (1) gives:
% 247.99/58.55 |
% 247.99/58.55 | Case 1:
% 247.99/58.55 | |
% 247.99/58.55 | | (20) ~ (all_36_2 = e4)
% 247.99/58.55 | |
% 247.99/58.55 | | BETA: splitting (4) gives:
% 247.99/58.55 | |
% 247.99/58.55 | | Case 1:
% 247.99/58.55 | | |
% 247.99/58.55 | | | (21) ~ (all_38_2 = e4)
% 247.99/58.55 | | |
% 247.99/58.55 | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13), (15), (17),
% 247.99/58.55 | | | (18), (20), (21) are inconsistent by sub-proof #37.
% 247.99/58.56 | | |
% 247.99/58.56 | | Case 2:
% 247.99/58.56 | | |
% 247.99/58.56 | | | (22) all_38_2 = e4
% 247.99/58.56 | | |
% 247.99/58.56 | | | REDUCE: (19), (22) imply:
% 247.99/58.56 | | | (23) op(e4, e4) = e1
% 247.99/58.56 | | |
% 247.99/58.56 | | | REF_CLOSE: (2), (10), (11), (23) are inconsistent by sub-proof #50.
% 247.99/58.56 | | |
% 247.99/58.56 | | End of split
% 247.99/58.56 | |
% 247.99/58.56 | Case 2:
% 247.99/58.56 | |
% 247.99/58.56 | | (24) all_36_2 = e4
% 247.99/58.56 | |
% 247.99/58.56 | | REDUCE: (16), (24) imply:
% 247.99/58.56 | | (25) op(e4, e1) = e3
% 247.99/58.56 | |
% 247.99/58.56 | | REF_CLOSE: (2), (9), (14), (25) are inconsistent by sub-proof #834.
% 247.99/58.56 | |
% 247.99/58.56 | End of split
% 247.99/58.56 |
% 247.99/58.56 End of proof
% 247.99/58.56
% 247.99/58.56 Sub-proof #37 shows that the following formulas are inconsistent:
% 247.99/58.56 ----------------------------------------------------------------
% 247.99/58.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.56 (2) op(e2, e1) = all_38_2
% 247.99/58.56 (3) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.99/58.56 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.99/58.56 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.99/58.56 (4) ~ (all_244_15 = e4)
% 247.99/58.56 (5) op(all_16_2, all_26_2) = e4
% 247.99/58.56 (6) ~ (all_36_2 = e4)
% 247.99/58.56 (7) op(e3, e1) = all_36_2
% 247.99/58.56 (8) ~ (all_38_2 = e4)
% 247.99/58.56 (9) op(e4, e1) = all_26_2
% 247.99/58.56 (10) op(e1, e1) = all_244_15
% 247.99/58.56 (11) op(e0, e1) = all_20_2
% 247.99/58.56 (12) ~ (all_26_2 = e1)
% 247.99/58.56 (13) ~ (all_20_2 = e4)
% 247.99/58.56 (14) op(all_16_2, e4) = e1
% 247.99/58.56
% 247.99/58.56 Begin of proof
% 247.99/58.56 |
% 247.99/58.56 | BETA: splitting (3) gives:
% 247.99/58.56 |
% 247.99/58.56 | Case 1:
% 247.99/58.56 | |
% 247.99/58.56 | | (15) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 247.99/58.56 | | e4)
% 247.99/58.56 | |
% 247.99/58.56 | | BETA: splitting (15) gives:
% 247.99/58.56 | |
% 247.99/58.56 | | Case 1:
% 247.99/58.56 | | |
% 247.99/58.56 | | | (16) all_252_9 = e4 & op(e4, e1) = e4
% 247.99/58.56 | | |
% 247.99/58.56 | | | ALPHA: (16) implies:
% 247.99/58.56 | | | (17) op(e4, e1) = e4
% 247.99/58.56 | | |
% 247.99/58.56 | | | GROUND_INST: instantiating (1) with all_26_2, e4, e1, e4, simplifying with
% 247.99/58.56 | | | (9), (17) gives:
% 247.99/58.56 | | | (18) all_26_2 = e4
% 247.99/58.56 | | |
% 247.99/58.56 | | | REDUCE: (12), (18) imply:
% 247.99/58.56 | | | (19) ~ (e4 = e1)
% 247.99/58.56 | | |
% 247.99/58.56 | | | REF_CLOSE: (1), (5), (14), (18), (19) are inconsistent by sub-proof #918.
% 247.99/58.56 | | |
% 247.99/58.56 | | Case 2:
% 247.99/58.56 | | |
% 247.99/58.56 | | | (20) all_252_10 = e4 & op(e3, e1) = e4
% 247.99/58.56 | | |
% 247.99/58.56 | | | REF_CLOSE: (1), (6), (7), (20) are inconsistent by sub-proof #914.
% 247.99/58.56 | | |
% 247.99/58.56 | | End of split
% 247.99/58.56 | |
% 247.99/58.56 | Case 2:
% 247.99/58.56 | |
% 247.99/58.56 | | (21) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 247.99/58.56 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.99/58.56 | |
% 247.99/58.56 | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (13), (21) are inconsistent by
% 247.99/58.56 | | sub-proof #615.
% 247.99/58.56 | |
% 247.99/58.56 | End of split
% 247.99/58.56 |
% 247.99/58.56 End of proof
% 247.99/58.56
% 247.99/58.56 Sub-proof #38 shows that the following formulas are inconsistent:
% 247.99/58.56 ----------------------------------------------------------------
% 247.99/58.56 (1) op(e2, e3) = all_32_0
% 247.99/58.56 (2) op(e2, e3) = all_192_1
% 247.99/58.56 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.56 (4) ~ (all_32_0 = e4)
% 247.99/58.56 (5) op(e2, e3) = e4
% 247.99/58.56
% 247.99/58.56 Begin of proof
% 247.99/58.56 |
% 247.99/58.56 | GROUND_INST: instantiating (3) with e4, all_192_1, e3, e2, simplifying with
% 247.99/58.56 | (2), (5) gives:
% 247.99/58.56 | (6) all_192_1 = e4
% 247.99/58.56 |
% 247.99/58.56 | GROUND_INST: instantiating (3) with all_32_0, all_192_1, e3, e2, simplifying
% 247.99/58.56 | with (1), (2) gives:
% 247.99/58.56 | (7) all_192_1 = all_32_0
% 247.99/58.56 |
% 247.99/58.56 | COMBINE_EQS: (6), (7) imply:
% 247.99/58.56 | (8) all_32_0 = e4
% 247.99/58.56 |
% 247.99/58.56 | REDUCE: (4), (8) imply:
% 247.99/58.56 | (9) $false
% 247.99/58.56 |
% 247.99/58.56 | CLOSE: (9) is inconsistent.
% 247.99/58.56 |
% 247.99/58.56 End of proof
% 247.99/58.56
% 247.99/58.56 Sub-proof #39 shows that the following formulas are inconsistent:
% 247.99/58.56 ----------------------------------------------------------------
% 247.99/58.56 (1) ~ (all_30_2 = all_26_2)
% 247.99/58.56 (2) op(all_4_2, e2) = e1
% 247.99/58.56 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 247.99/58.56 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 247.99/58.56 (all_252_16 = e3 & op(e4, e0) = e3)
% 247.99/58.56 (4) op(e2, e3) = all_50_1
% 247.99/58.56 (5) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 247.99/58.56 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 247.99/58.56 | (all_252_21 = e2 & op(e0, e3) = e2)
% 247.99/58.56 (6) op(e4, e0) = all_30_2
% 247.99/58.56 (7) op(e3, e4) = all_102_1
% 247.99/58.56 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.56 (9) op(e3, all_50_1) = all_50_0
% 247.99/58.56 (10) ~ (all_244_8 = all_64_2)
% 247.99/58.56 (11) op(e2, e2) = all_244_8
% 247.99/58.56 (12) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(e4, e3) = all_42_1 &
% 247.99/58.56 op(e3, all_42_1) = all_42_0 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 247.99/58.56 (all_42_1 = e2) & op(e4, e3) = all_42_1 & $i(all_42_1))
% 247.99/58.56 (13) op(e2, e1) = all_38_2
% 247.99/58.58 (14) ~ (all_36_2 = all_20_2)
% 247.99/58.58 (15) ~ (all_244_15 = all_16_2)
% 247.99/58.58 (16) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.99/58.58 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.99/58.58 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.99/58.58 (17) op(e4, e2) = all_6_2
% 247.99/58.58 (18) op(all_26_2, e1) = e4
% 247.99/58.58 (19) all_252_7 = e4
% 247.99/58.58 (20) op(all_244_15, all_244_15) = e1
% 247.99/58.58 (21) ~ (all_244_3 = all_84_2)
% 247.99/58.58 (22) op(e1, e3) = all_62_2
% 247.99/58.58 (23) ~ (all_244_0 = all_26_2)
% 247.99/58.58 (24) ~ (all_84_2 = e4)
% 247.99/58.58 (25) ~ (all_50_0 = e0)
% 247.99/58.58 (26) op(e3, e1) = all_36_2
% 247.99/58.58 (27) all_16_2 = e2
% 247.99/58.58 (28) op(e4, e3) = e2
% 247.99/58.58 (29) op(e4, e1) = e3
% 247.99/58.58 (30) ~ (all_26_2 = all_6_2)
% 247.99/58.58 (31) op(e0, e3) = all_22_2
% 247.99/58.58 (32) op(e4, e1) = all_26_2
% 247.99/58.58 (33) ~ (all_64_2 = all_38_2)
% 247.99/58.58 (34) ~ (all_62_2 = all_16_2)
% 247.99/58.58 (35) op(e3, e4) = all_100_2
% 247.99/58.58 (36) op(e4, e4) = all_244_0
% 247.99/58.58 (37) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 247.99/58.58 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 247.99/58.58 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.99/58.58 (38) op(e2, e3) = e4
% 247.99/58.58 (39) op(e1, e1) = all_244_15
% 247.99/58.58 (40) op(e0, e1) = all_20_2
% 247.99/58.58 (41) ~ (all_38_2 = all_36_2)
% 247.99/58.58 (42) ~ (all_84_2 = all_22_2)
% 247.99/58.58 (43) op(all_4_2, all_38_2) = e2
% 247.99/58.58 (44) op(e4, e3) = all_84_2
% 247.99/58.58 (45) op(e2, e4) = all_64_2
% 247.99/58.58 (46) op(all_36_2, e1) = e3
% 247.99/58.58 (47) ~ (all_244_15 = all_36_2)
% 247.99/58.58 (48) all_42_2 = all_12_2
% 247.99/58.58 (49) op(all_16_2, e4) = e1
% 247.99/58.58 (50) ~ (all_16_2 = e3)
% 247.99/58.58 (51) op(e3, e3) = all_244_3
% 247.99/58.58 (52) op(all_12_2, e4) = e0
% 247.99/58.58 (53) ~ (all_20_2 = e2)
% 247.99/58.58
% 247.99/58.58 Begin of proof
% 247.99/58.58 |
% 247.99/58.58 | GROUND_INST: instantiating (8) with e4, all_50_1, e3, e2, simplifying with
% 247.99/58.58 | (4), (38) gives:
% 247.99/58.59 | (54) all_50_1 = e4
% 247.99/58.59 |
% 247.99/58.59 | GROUND_INST: instantiating (8) with all_100_2, all_102_1, e4, e3, simplifying
% 247.99/58.59 | with (7), (35) gives:
% 247.99/58.59 | (55) all_102_1 = all_100_2
% 247.99/58.59 |
% 247.99/58.59 | GROUND_INST: instantiating (8) with all_26_2, e3, e1, e4, simplifying with
% 247.99/58.59 | (29), (32) gives:
% 247.99/58.59 | (56) all_26_2 = e3
% 247.99/58.59 |
% 247.99/58.59 | GROUND_INST: instantiating (8) with all_84_2, e2, e3, e4, simplifying with
% 247.99/58.59 | (28), (44) gives:
% 247.99/58.59 | (57) all_84_2 = e2
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (23), (56) imply:
% 247.99/58.59 | (58) ~ (all_244_0 = e3)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (21), (57) imply:
% 247.99/58.59 | (59) ~ (all_244_3 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (15), (27) imply:
% 247.99/58.59 | (60) ~ (all_244_15 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (42), (57) imply:
% 247.99/58.59 | (61) ~ (all_22_2 = e2)
% 247.99/58.59 |
% 247.99/58.59 | SIMP: (61) implies:
% 247.99/58.59 | (62) ~ (all_22_2 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (24), (57) imply:
% 247.99/58.59 | (63) ~ (e4 = e2)
% 247.99/58.59 |
% 247.99/58.59 | SIMP: (63) implies:
% 247.99/58.59 | (64) ~ (e4 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (27), (34) imply:
% 247.99/58.59 | (65) ~ (all_62_2 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (1), (56) imply:
% 247.99/58.59 | (66) ~ (all_30_2 = e3)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (30), (56) imply:
% 247.99/58.59 | (67) ~ (all_6_2 = e3)
% 247.99/58.59 |
% 247.99/58.59 | SIMP: (67) implies:
% 247.99/58.59 | (68) ~ (all_6_2 = e3)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (27), (50) imply:
% 247.99/58.59 | (69) ~ (e3 = e2)
% 247.99/58.59 |
% 247.99/58.59 | SIMP: (69) implies:
% 247.99/58.59 | (70) ~ (e3 = e2)
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (18), (56) imply:
% 247.99/58.59 | (71) op(e3, e1) = e4
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (27), (49) imply:
% 247.99/58.59 | (72) op(e2, e4) = e1
% 247.99/58.59 |
% 247.99/58.59 | REDUCE: (9), (54) imply:
% 247.99/58.59 | (73) op(e3, e4) = all_50_0
% 247.99/58.59 |
% 247.99/58.59 | BETA: splitting (3) gives:
% 247.99/58.59 |
% 247.99/58.59 | Case 1:
% 247.99/58.59 | |
% 247.99/58.59 | | (74) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) =
% 247.99/58.59 | | e3)
% 247.99/58.59 | |
% 247.99/58.59 | | BETA: splitting (74) gives:
% 247.99/58.59 | |
% 247.99/58.59 | | Case 1:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (75) all_252_0 = e3 & op(e4, e4) = e3
% 247.99/58.59 | | |
% 247.99/58.59 | | | ALPHA: (75) implies:
% 247.99/58.59 | | | (76) op(e4, e4) = e3
% 247.99/58.59 | | |
% 247.99/58.59 | | | REF_CLOSE: (8), (36), (58), (76) are inconsistent by sub-proof #813.
% 247.99/58.59 | | |
% 247.99/58.59 | | Case 2:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (77) all_252_1 = e3 & op(e4, e3) = e3
% 247.99/58.59 | | |
% 247.99/58.59 | | | ALPHA: (77) implies:
% 247.99/58.59 | | | (78) all_252_1 = e3
% 247.99/58.59 | | |
% 247.99/58.59 | | | REF_CLOSE: (5), (8), (19), (22), (31), (51), (59), (62), (64), (65), (70),
% 247.99/58.59 | | | (78) are inconsistent by sub-proof #40.
% 247.99/58.59 | | |
% 247.99/58.59 | | End of split
% 247.99/58.59 | |
% 247.99/58.59 | Case 2:
% 247.99/58.59 | |
% 247.99/58.59 | | (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) =
% 247.99/58.59 | | e3) | (all_252_16 = e3 & op(e4, e0) = e3)
% 247.99/58.59 | |
% 247.99/58.59 | | BETA: splitting (79) gives:
% 247.99/58.59 | |
% 247.99/58.59 | | Case 1:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (80) all_252_4 = e3 & op(e4, e2) = e3
% 247.99/58.59 | | |
% 247.99/58.59 | | | REF_CLOSE: (8), (17), (68), (80) are inconsistent by sub-proof #577.
% 247.99/58.59 | | |
% 247.99/58.59 | | Case 2:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (81) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = e3 & op(e4, e0)
% 247.99/58.59 | | | = e3)
% 247.99/58.59 | | |
% 247.99/58.59 | | | BETA: splitting (81) gives:
% 247.99/58.59 | | |
% 247.99/58.59 | | | Case 1:
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | (82) all_252_9 = e3 & op(e4, e1) = e3
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | ALPHA: (82) implies:
% 247.99/58.59 | | | | (83) all_252_9 = e3
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | BETA: splitting (12) gives:
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | Case 1:
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | GROUND_INST: instantiating (8) with all_64_2, e1, e4, e2, simplifying
% 247.99/58.59 | | | | | with (45), (72) gives:
% 247.99/58.59 | | | | | (84) all_64_2 = e1
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | GROUND_INST: instantiating (8) with all_36_2, e4, e1, e3, simplifying
% 247.99/58.59 | | | | | with (26), (71) gives:
% 247.99/58.59 | | | | | (85) all_36_2 = e4
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (10), (84) imply:
% 247.99/58.59 | | | | | (86) ~ (all_244_8 = e1)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (47), (85) imply:
% 247.99/58.59 | | | | | (87) ~ (all_244_15 = e4)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (33), (84) imply:
% 247.99/58.59 | | | | | (88) ~ (all_38_2 = e1)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | SIMP: (88) implies:
% 247.99/58.59 | | | | | (89) ~ (all_38_2 = e1)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (41), (85) imply:
% 247.99/58.59 | | | | | (90) ~ (all_38_2 = e4)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (14), (85) imply:
% 247.99/58.59 | | | | | (91) ~ (all_20_2 = e4)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | SIMP: (91) implies:
% 247.99/58.59 | | | | | (92) ~ (all_20_2 = e4)
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | BETA: splitting (37) gives:
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | Case 1:
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | | (93) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 &
% 247.99/58.59 | | | | | | op(e3, e1) = e2)
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | | BETA: splitting (93) gives:
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | | Case 1:
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | (94) all_252_9 = e2 & op(e4, e1) = e2
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | ALPHA: (94) implies:
% 247.99/58.59 | | | | | | | (95) all_252_9 = e2
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | REF_CLOSE: (70), (83), (95) are inconsistent by sub-proof #186.
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | Case 2:
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | (96) all_252_10 = e2 & op(e3, e1) = e2
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | ALPHA: (96) implies:
% 247.99/58.59 | | | | | | | (97) op(e3, e1) = e2
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | BETA: splitting (16) gives:
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | | Case 1:
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | | (98) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 &
% 247.99/58.59 | | | | | | | | op(e3, e1) = e4)
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | | BETA: splitting (98) gives:
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | | Case 1:
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | (99) all_252_9 = e4 & op(e4, e1) = e4
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | ALPHA: (99) implies:
% 247.99/58.59 | | | | | | | | | (100) op(e4, e1) = e4
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | GROUND_INST: instantiating (8) with e2, e4, e1, e3, simplifying
% 247.99/58.59 | | | | | | | | | with (71), (97) gives:
% 247.99/58.59 | | | | | | | | | (101) e4 = e2
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | GROUND_INST: instantiating (8) with all_26_2, e4, e1, e4,
% 247.99/58.59 | | | | | | | | | simplifying with (32), (100) gives:
% 247.99/58.59 | | | | | | | | | (102) all_26_2 = e4
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | COMBINE_EQS: (56), (102) imply:
% 247.99/58.59 | | | | | | | | | (103) e4 = e3
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | SIMP: (103) implies:
% 247.99/58.59 | | | | | | | | | (104) e4 = e3
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | COMBINE_EQS: (101), (104) imply:
% 247.99/58.59 | | | | | | | | | (105) e3 = e2
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | REDUCE: (70), (105) imply:
% 247.99/58.59 | | | | | | | | | (106) $false
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | CLOSE: (106) is inconsistent.
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | Case 2:
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | (107) all_252_10 = e4 & op(e3, e1) = e4
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | ALPHA: (107) implies:
% 247.99/58.59 | | | | | | | | | (108) all_252_10 = e4
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | BETA: splitting (37) gives:
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | | Case 1:
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | BETA: splitting (93) gives:
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | Case 1:
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | (109) all_252_9 = e2 & op(e4, e1) = e2
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | ALPHA: (109) implies:
% 247.99/58.59 | | | | | | | | | | | (110) all_252_9 = e2
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | COMBINE_EQS: (83), (110) imply:
% 247.99/58.59 | | | | | | | | | | | (111) e3 = e2
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | REDUCE: (70), (111) imply:
% 247.99/58.59 | | | | | | | | | | | (112) $false
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | Case 2:
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | REF_CLOSE: (64), (96), (108) are inconsistent by sub-proof
% 247.99/58.59 | | | | | | | | | | | #433.
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | End of split
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | Case 2:
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | (113) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 =
% 247.99/58.59 | | | | | | | | | | e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0,
% 247.99/58.59 | | | | | | | | | | e1) = e2)
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | BETA: splitting (113) gives:
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | Case 1:
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | (114) all_252_11 = e2 & op(e2, e1) = e2
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | ALPHA: (114) implies:
% 247.99/58.59 | | | | | | | | | | | (115) op(e2, e1) = e2
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (43), (89), (115) are inconsistent
% 247.99/58.59 | | | | | | | | | | | by sub-proof #739.
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | Case 2:
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | (116) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 247.99/58.59 | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | | REF_CLOSE: (8), (39), (40), (53), (60), (116) are
% 247.99/58.59 | | | | | | | | | | | inconsistent by sub-proof #965.
% 247.99/58.59 | | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | | End of split
% 247.99/58.59 | | | | | | | | | |
% 247.99/58.59 | | | | | | | | | End of split
% 247.99/58.59 | | | | | | | | |
% 247.99/58.59 | | | | | | | | End of split
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | Case 2:
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | | (117) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4
% 247.99/58.59 | | | | | | | | & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 247.99/58.59 | | | | | | | | e4)
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | | REF_CLOSE: (8), (13), (39), (40), (87), (90), (92), (117) are
% 247.99/58.59 | | | | | | | | inconsistent by sub-proof #615.
% 247.99/58.59 | | | | | | | |
% 247.99/58.59 | | | | | | | End of split
% 247.99/58.59 | | | | | | |
% 247.99/58.59 | | | | | | End of split
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | Case 2:
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | | (118) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 &
% 247.99/58.59 | | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | | REF_CLOSE: (2), (8), (11), (13), (20), (39), (40), (43), (53), (86),
% 247.99/58.59 | | | | | | (89), (118) are inconsistent by sub-proof #737.
% 247.99/58.59 | | | | | |
% 247.99/58.59 | | | | | End of split
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | Case 2:
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | (119) all_42_2 = e3
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | COMBINE_EQS: (48), (119) imply:
% 247.99/58.59 | | | | | (120) all_12_2 = e3
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | SIMP: (120) implies:
% 247.99/58.59 | | | | | (121) all_12_2 = e3
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (52), (121) imply:
% 247.99/58.59 | | | | | (122) op(e3, e4) = e0
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | GROUND_INST: instantiating (8) with all_100_2, e0, e4, e3, simplifying
% 247.99/58.59 | | | | | with (35), (122) gives:
% 247.99/58.59 | | | | | (123) all_100_2 = e0
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | GROUND_INST: instantiating (8) with all_100_2, all_50_0, e4, e3,
% 247.99/58.59 | | | | | simplifying with (35), (73) gives:
% 247.99/58.59 | | | | | (124) all_100_2 = all_50_0
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | COMBINE_EQS: (123), (124) imply:
% 247.99/58.59 | | | | | (125) all_50_0 = e0
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | REDUCE: (25), (125) imply:
% 247.99/58.59 | | | | | (126) $false
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | | CLOSE: (126) is inconsistent.
% 247.99/58.59 | | | | |
% 247.99/58.59 | | | | End of split
% 247.99/58.59 | | | |
% 247.99/58.59 | | | Case 2:
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | (127) all_252_16 = e3 & op(e4, e0) = e3
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | ALPHA: (127) implies:
% 247.99/58.59 | | | | (128) op(e4, e0) = e3
% 247.99/58.59 | | | |
% 247.99/58.59 | | | | REF_CLOSE: (6), (8), (66), (128) are inconsistent by sub-proof #622.
% 247.99/58.59 | | | |
% 247.99/58.59 | | | End of split
% 247.99/58.59 | | |
% 247.99/58.59 | | End of split
% 247.99/58.59 | |
% 247.99/58.59 | End of split
% 247.99/58.59 |
% 247.99/58.59 End of proof
% 247.99/58.59
% 247.99/58.59 Sub-proof #40 shows that the following formulas are inconsistent:
% 247.99/58.59 ----------------------------------------------------------------
% 247.99/58.59 (1) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 247.99/58.59 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 247.99/58.59 | (all_252_21 = e2 & op(e0, e3) = e2)
% 247.99/58.59 (2) ~ (all_22_2 = e2)
% 247.99/58.59 (3) ~ (all_244_3 = e2)
% 247.99/58.59 (4) ~ (all_62_2 = e2)
% 247.99/58.59 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.59 (6) ~ (e3 = e2)
% 247.99/58.59 (7) all_252_7 = e4
% 247.99/58.59 (8) op(e1, e3) = all_62_2
% 247.99/58.59 (9) op(e0, e3) = all_22_2
% 247.99/58.59 (10) all_252_1 = e3
% 247.99/58.59 (11) ~ (e4 = e2)
% 247.99/58.59 (12) op(e3, e3) = all_244_3
% 247.99/58.59
% 247.99/58.59 Begin of proof
% 247.99/58.59 |
% 247.99/58.59 | BETA: splitting (1) gives:
% 247.99/58.59 |
% 247.99/58.59 | Case 1:
% 247.99/58.59 | |
% 247.99/58.59 | | (13) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 247.99/58.59 | | e2)
% 247.99/58.59 | |
% 247.99/58.59 | | BETA: splitting (13) gives:
% 247.99/58.59 | |
% 247.99/58.59 | | Case 1:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (14) all_252_1 = e2 & op(e4, e3) = e2
% 247.99/58.59 | | |
% 247.99/58.59 | | | REF_CLOSE: (6), (10), (14) are inconsistent by sub-proof #372.
% 247.99/58.59 | | |
% 247.99/58.59 | | Case 2:
% 247.99/58.59 | | |
% 247.99/58.59 | | | (15) all_252_3 = e2 & op(e3, e3) = e2
% 247.99/58.59 | | |
% 247.99/58.59 | | | ALPHA: (15) implies:
% 247.99/58.59 | | | (16) op(e3, e3) = e2
% 247.99/58.59 | | |
% 247.99/58.59 | | | REF_CLOSE: (3), (5), (12), (16) are inconsistent by sub-proof #694.
% 247.99/58.59 | | |
% 247.99/58.59 | | End of split
% 247.99/58.59 | |
% 247.99/58.59 | Case 2:
% 247.99/58.59 | |
% 247.99/58.59 | | (17) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.99/58.59 | | e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 247.99/58.59 | |
% 247.99/58.59 | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (11), (17) are inconsistent by
% 247.99/58.59 | | sub-proof #81.
% 247.99/58.59 | |
% 247.99/58.59 | End of split
% 247.99/58.59 |
% 247.99/58.59 End of proof
% 247.99/58.59
% 247.99/58.59 Sub-proof #41 shows that the following formulas are inconsistent:
% 247.99/58.59 ----------------------------------------------------------------
% 247.99/58.59 (1) ~ (all_224_2 = e1) | ( ~ (all_224_0 = e0) & op(e4, e1) = all_224_1 &
% 247.99/58.59 op(e1, all_224_1) = all_224_0 & $i(all_224_0) & $i(all_224_1)) | ( ~
% 247.99/58.59 (all_224_1 = e3) & op(e4, e1) = all_224_1 & $i(all_224_1))
% 247.99/58.59 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 247.99/58.59 all_250_23 = e0
% 247.99/58.59 (3) ~ (all_30_2 = all_26_2)
% 247.99/58.59 (4) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 247.99/58.59 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 247.99/58.59 | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.99/58.59 (5) all_252_14 = e3
% 247.99/58.59 (6) all_32_2 = all_20_2
% 247.99/58.59 (7) all_18_2 = all_12_2
% 247.99/58.59 (8) ~ (all_100_2 = all_12_2)
% 247.99/58.59 (9) ~ (all_4_2 = e4)
% 247.99/58.59 (10) ~ (all_10_2 = e4)
% 247.99/58.59 (11) ~ (all_244_0 = all_30_2)
% 247.99/58.59 (12) all_250_16 = all_62_2
% 247.99/58.59 (13) op(all_4_2, e2) = e1
% 247.99/58.59 (14) ~ (all_244_24 = all_34_2)
% 247.99/58.59 (15) ~ (all_76_2 = e4) | ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 &
% 247.99/58.59 op(e0, e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 =
% 247.99/58.59 e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 247.99/58.59 (16) ~ (all_244_24 = all_40_2)
% 247.99/58.59 (17) op(all_36_2, all_62_2) = e1
% 247.99/58.59 (18) ~ (all_40_2 = all_38_2)
% 247.99/58.59 (19) op(all_6_2, e2) = e4
% 247.99/58.59 (20) op(e2, e3) = all_50_1
% 247.99/58.59 (21) op(all_12_2, all_30_2) = e4
% 247.99/58.59 (22) op(e4, e0) = all_30_2
% 247.99/58.59 (23) all_250_8 = all_36_2
% 247.99/58.59 (24) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 247.99/58.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 247.99/58.59 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.99/58.59 (25) op(all_28_2, all_40_2) = e2
% 247.99/58.59 (26) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 247.99/58.59 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 247.99/58.59 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 247.99/58.60 (27) ~ (all_136_2 = e0) | ( ~ (all_136_0 = e2) & op(e4, e0) = all_136_1 &
% 247.99/58.60 op(e0, all_136_1) = all_136_0 & $i(all_136_0) & $i(all_136_1)) | ( ~
% 247.99/58.60 (all_136_1 = e1) & op(e4, e0) = all_136_1 & $i(all_136_1))
% 247.99/58.60 (28) all_174_2 = all_40_2
% 247.99/58.60 (29) ~ (all_40_2 = all_30_2)
% 247.99/58.60 (30) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.99/58.60 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.99/58.60 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 247.99/58.60 (31) op(all_100_2, all_84_2) = e4
% 247.99/58.60 (32) all_94_2 = all_38_2
% 247.99/58.60 (33) op(all_62_2, all_36_2) = e3
% 247.99/58.60 (34) op(all_38_2, e1) = e2
% 247.99/58.60 (35) all_250_13 = all_38_2
% 247.99/58.60 (36) ~ (e2 = e0)
% 247.99/58.60 (37) op(all_64_2, e4) = e2
% 247.99/58.60 (38) ~ (e1 = e0)
% 247.99/58.60 (39) ~ (all_244_24 = all_20_2)
% 247.99/58.60 (40) ~ (all_28_2 = e3)
% 247.99/58.60 (41) ~ (all_62_2 = all_22_2)
% 247.99/58.60 (42) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 247.99/58.60 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 247.99/58.60 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 247.99/58.60 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.60 (44) op(e2, e3) = all_10_2
% 247.99/58.60 (45) ~ (e3 = e2)
% 247.99/58.60 (46) op(e0, e0) = all_244_24
% 247.99/58.60 (47) ~ (e4 = e0)
% 247.99/58.60 (48) all_234_2 = e1
% 247.99/58.60 (49) ~ (all_244_8 = all_64_2)
% 247.99/58.60 (50) op(all_244_8, all_244_8) = e2
% 247.99/58.60 (51) op(e2, e2) = all_244_8
% 247.99/58.60 (52) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 247.99/58.60 all_250_11 = e0
% 247.99/58.60 (53) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 247.99/58.60 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 247.99/58.60 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 247.99/58.60 (54) op(all_84_2, all_100_2) = e3
% 247.99/58.60 (55) ~ (all_244_0 = all_12_2)
% 247.99/58.60 (56) op(e2, e1) = all_38_2
% 247.99/58.60 (57) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.99/58.60 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.99/58.60 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.99/58.60 (58) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 247.99/58.60 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 247.99/58.60 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.99/58.60 (59) ~ (all_36_2 = all_20_2)
% 247.99/58.60 (60) ~ (all_64_2 = all_40_2)
% 247.99/58.60 (61) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 247.99/58.60 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 247.99/58.60 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 247.99/58.60 (62) ~ (all_84_2 = all_62_2)
% 247.99/58.60 (63) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 247.99/58.60 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 247.99/58.60 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.99/58.60 (64) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 247.99/58.60 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 247.99/58.60 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 247.99/58.60 (65) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 247.99/58.60 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 247.99/58.60 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 247.99/58.60 (66) ~ (all_244_15 = all_26_2)
% 247.99/58.60 (67) op(e1, e0) = all_34_2
% 247.99/58.60 (68) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 247.99/58.60 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 247.99/58.60 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 247.99/58.60 (69) op(e4, e2) = all_6_2
% 247.99/58.60 (70) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.99/58.60 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 247.99/58.60 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 247.99/58.60 (71) op(e3, all_38_2) = e2
% 247.99/58.60 (72) op(e1, all_10_2) = e2
% 247.99/58.60 (73) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 247.99/58.60 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 247.99/58.60 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 247.99/58.60 (74) ~ (all_244_0 = all_16_2)
% 247.99/58.60 (75) all_78_2 = all_10_2
% 247.99/58.60 (76) all_224_2 = all_64_2
% 247.99/58.60 (77) ~ (all_20_2 = all_12_2)
% 247.99/58.60 (78) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 247.99/58.60 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 247.99/58.60 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 247.99/58.60 (79) ~ (all_18_2 = e3) | ( ~ (all_18_0 = e2) & op(e4, e3) = all_18_1 &
% 247.99/58.60 op(e3, all_18_1) = all_18_0 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 247.99/58.60 (all_18_1 = e1) & op(e4, e3) = all_18_1 & $i(all_18_1))
% 247.99/58.60 (80) ~ (e2 = e1)
% 247.99/58.60 (81) op(all_26_2, e1) = e4
% 247.99/58.60 (82) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 247.99/58.60 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 247.99/58.60 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 247.99/58.60 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 247.99/58.60 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 247.99/58.60 op(e0, e1) = e0)))
% 247.99/58.60 (83) ~ (all_100_2 = all_36_2)
% 247.99/58.60 (84) ~ (all_100_2 = all_64_2)
% 247.99/58.60 (85) ~ (all_222_2 = e0) | ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 &
% 247.99/58.60 op(e0, all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | ( ~
% 247.99/58.60 (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 247.99/58.60 (86) op(e0, e2) = all_28_2
% 247.99/58.60 (87) ~ (e4 = e1)
% 247.99/58.60 (88) ~ (all_28_2 = e1)
% 247.99/58.60 (89) op(all_6_2, all_64_2) = e2
% 247.99/58.60 (90) ~ (all_64_2 = all_10_2)
% 247.99/58.60 (91) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 247.99/58.60 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 247.99/58.60 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 247.99/58.60 (92) ~ (all_6_2 = e1)
% 247.99/58.60 (93) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 247.99/58.60 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 247.99/58.60 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 247.99/58.60 (94) all_106_2 = all_38_2
% 247.99/58.60 (95) ~ (all_244_8 = all_38_2)
% 247.99/58.60 (96) op(all_244_15, all_244_15) = e1
% 247.99/58.60 (97) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 &
% 247.99/58.60 op(e2, all_16_1) = all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 247.99/58.60 (all_16_1 = e0) & op(e4, e2) = all_16_1 & $i(all_16_1))
% 247.99/58.60 (98) all_250_21 = all_22_2
% 247.99/58.60 (99) op(all_34_2, e0) = e1
% 247.99/58.60 (100) ~ (all_244_3 = all_84_2)
% 247.99/58.60 (101) op(e1, e4) = all_16_2
% 247.99/58.60 (102) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 247.99/58.60 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 247.99/58.60 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 247.99/58.60 (103) ~ (all_48_2 = all_30_2)
% 247.99/58.60 (104) ~ (all_244_0 = all_64_2)
% 247.99/58.60 (105) ~ (all_244_3 = all_36_2)
% 247.99/58.60 (106) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 247.99/58.60 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 247.99/58.60 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 247.99/58.60 (107) all_132_2 = all_30_2
% 247.99/58.60 (108) ~ (all_28_2 = all_20_2)
% 247.99/58.60 (109) op(e1, e3) = all_62_2
% 247.99/58.60 (110) op(all_16_2, all_26_2) = e4
% 247.99/58.60 (111) ~ (all_244_0 = all_26_2)
% 247.99/58.60 (112) ~ (e3 = e0)
% 247.99/58.60 (113) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0
% 247.99/58.60 & op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 247.99/58.60 (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 247.99/58.60 (114) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 247.99/58.60 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 247.99/58.60 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 247.99/58.60 (115) ~ (all_40_2 = all_10_2)
% 247.99/58.60 (116) all_204_2 = all_36_2
% 247.99/58.60 (117) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0
% 247.99/58.60 & op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~
% 247.99/58.60 (all_58_1 = e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 247.99/58.60 (118) op(all_20_2, e1) = e0
% 247.99/58.60 (119) all_136_2 = all_100_2
% 247.99/58.60 (120) ~ (all_244_3 = all_10_2)
% 247.99/58.60 (121) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0
% 247.99/58.60 & op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 247.99/58.60 (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 247.99/58.60 (122) all_70_2 = all_62_2
% 247.99/58.60 (123) ~ (e3 = e1)
% 247.99/58.60 (124) op(all_48_2, all_22_2) = e0
% 247.99/58.60 (125) op(e3, e1) = all_36_2
% 247.99/58.60 (126) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 247.99/58.60 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 247.99/58.60 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 247.99/58.60 (127) ~ (all_54_2 = e2) | ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0
% 247.99/58.60 & op(e0, e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~
% 247.99/58.60 (all_54_1 = e3) & op(e0, e2) = all_54_1 & $i(all_54_1))
% 247.99/58.60 (128) ~ (all_244_3 = all_62_2)
% 247.99/58.60 (129) op(all_40_2, e0) = e2
% 247.99/58.60 (130) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 247.99/58.60 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 247.99/58.60 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 247.99/58.60 (131) ~ (all_244_8 = all_40_2)
% 247.99/58.60 (132) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 247.99/58.60 all_250_8 = e0
% 247.99/58.60 (133) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 247.99/58.60 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 247.99/58.60 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 247.99/58.60 (134) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 247.99/58.60 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 247.99/58.60 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 247.99/58.60 (135) ~ (all_40_2 = all_34_2)
% 247.99/58.60 (136) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 247.99/58.60 all_250_13 = e0
% 247.99/58.60 (137) ~ (all_244_15 = all_38_2)
% 247.99/58.60 (138) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 247.99/58.60 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 247.99/58.60 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 247.99/58.60 (139) ~ (all_36_2 = all_26_2)
% 247.99/58.60 (140) all_44_2 = all_26_2
% 247.99/58.60 (141) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 247.99/58.60 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 247.99/58.60 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 247.99/58.60 (142) all_190_2 = all_38_2
% 247.99/58.60 (143) all_222_2 = all_26_2
% 247.99/58.60 (144) op(all_38_2, e3) = e1
% 247.99/58.60 (145) ~ (all_64_2 = all_12_2)
% 247.99/58.60 (146) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 247.99/58.60 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 247.99/58.60 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 247.99/58.60 (147) op(all_22_2, e3) = e0
% 247.99/58.60 (148) all_68_2 = all_22_2
% 247.99/58.60 (149) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0
% 247.99/58.60 & op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~
% 247.99/58.60 (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 247.99/58.60 (150) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 247.99/58.60 all_250_16 = e0
% 247.99/58.60 (151) op(all_20_2, all_34_2) = e1
% 247.99/58.60 (152) op(e0, e3) = all_22_2
% 247.99/58.60 (153) ~ (all_244_0 = all_100_2)
% 247.99/58.60 (154) ~ (all_28_2 = all_22_2)
% 247.99/58.60 (155) all_242_2 = all_38_2
% 247.99/58.60 (156) op(all_34_2, all_20_2) = e0
% 247.99/58.60 (157) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 247.99/58.60 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 247.99/58.60 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 247.99/58.60 (158) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 247.99/58.60 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 247.99/58.60 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 247.99/58.60 (159) op(all_84_2, e3) = e4
% 247.99/58.60 (160) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 247.99/58.60 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 247.99/58.60 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.99/58.60 (161) all_58_2 = all_20_2
% 247.99/58.60 (162) op(all_62_2, e3) = e1
% 247.99/58.60 (163) op(e4, e1) = all_26_2
% 247.99/58.60 (164) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 247.99/58.60 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 247.99/58.60 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 247.99/58.60 (165) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 247.99/58.60 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 247.99/58.60 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 247.99/58.60 (166) ~ (all_64_2 = all_38_2)
% 247.99/58.60 (167) op(all_10_2, e3) = e2
% 247.99/58.60 (168) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 247.99/58.60 all_250_21 = e0
% 247.99/58.60 (169) ~ (all_244_15 = all_62_2)
% 247.99/58.60 (170) ~ (all_62_2 = all_16_2)
% 247.99/58.60 (171) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 247.99/58.60 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 247.99/58.60 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 247.99/58.60 (172) op(e3, e4) = all_100_2
% 247.99/58.60 (173) all_250_11 = all_10_2
% 247.99/58.60 (174) ~ (all_244_8 = e1)
% 247.99/58.60 (175) op(e4, e4) = all_244_0
% 247.99/58.60 (176) ~ (all_22_2 = all_12_2)
% 247.99/58.60 (177) all_230_2 = all_20_2
% 247.99/58.60 (178) all_54_2 = all_30_2
% 247.99/58.60 (179) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 247.99/58.60 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 247.99/58.60 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 247.99/58.60 (180) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 247.99/58.60 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 247.99/58.60 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 247.99/58.60 (181) ~ (e4 = e3)
% 247.99/58.60 (182) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 247.99/58.60 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 247.99/58.60 all_8_1 & $i(all_8_1))
% 247.99/58.60 (183) op(e1, e1) = all_244_15
% 247.99/58.60 (184) op(e1, e2) = e3
% 247.99/58.60 (185) ~ (all_34_2 = all_30_2)
% 247.99/58.60 (186) op(e0, e1) = all_20_2
% 247.99/58.60 (187) ~ (all_244_15 = all_20_2)
% 247.99/58.60 (188) op(e3, e0) = all_48_2
% 247.99/58.61 (189) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 247.99/58.61 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 247.99/58.61 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 247.99/58.61 (190) op(all_48_2, e0) = e3
% 247.99/58.61 (191) ~ (all_38_2 = all_36_2)
% 247.99/58.61 (192) op(e1, e2) = all_4_2
% 247.99/58.61 (193) ~ (all_100_2 = all_48_2)
% 247.99/58.61 (194) op(all_4_2, all_38_2) = e2
% 247.99/58.61 (195) op(e4, e3) = all_84_2
% 247.99/58.61 (196) ~ (all_62_2 = all_10_2)
% 247.99/58.61 (197) op(e2, e4) = all_64_2
% 247.99/58.61 (198) ~ (all_22_2 = all_10_2)
% 247.99/58.61 (199) ~ (all_36_2 = e1)
% 247.99/58.61 (200) all_60_2 = all_20_2
% 247.99/58.61 (201) ~ (all_38_2 = all_26_2)
% 247.99/58.61 (202) ~ (e4 = e2)
% 247.99/58.61 (203) ~ (all_244_24 = all_30_2)
% 247.99/58.61 (204) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 247.99/58.61 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 247.99/58.61 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 247.99/58.61 (205) ~ (all_22_2 = all_20_2)
% 247.99/58.61 (206) ~ (all_12_2 = e2) | ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 &
% 247.99/58.61 op(e2, all_12_1) = all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 247.99/58.61 (all_12_1 = e1) & op(e4, e2) = all_12_1 & $i(all_12_1))
% 247.99/58.61 (207) all_122_2 = all_36_2
% 247.99/58.61 (208) ~ (all_34_2 = all_16_2)
% 247.99/58.61 (209) ~ (all_64_2 = all_16_2)
% 247.99/58.61 (210) op(all_36_2, e1) = e3
% 247.99/58.61 (211) ~ (all_38_2 = all_20_2)
% 247.99/58.61 (212) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 247.99/58.61 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 247.99/58.61 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.99/58.61 (213) ~ (all_38_2 = all_10_2)
% 247.99/58.61 (214) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 247.99/58.61 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 247.99/58.61 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 247.99/58.61 (215) ~ (all_244_15 = all_36_2)
% 247.99/58.61 (216) ~ (all_244_24 = all_22_2)
% 247.99/58.61 (217) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 247.99/58.61 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 247.99/58.61 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 247.99/58.61 (218) op(all_16_2, e4) = e1
% 247.99/58.61 (219) ~ (all_100_2 = all_16_2)
% 247.99/58.61 (220) op(e2, e0) = all_40_2
% 247.99/58.61 (221) ~ (all_16_2 = e3)
% 247.99/58.61 (222) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 247.99/58.61 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.99/58.61 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.99/58.61 (223) op(e3, e3) = all_244_3
% 247.99/58.61 (224) ~ (all_16_2 = all_12_2)
% 247.99/58.61 (225) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 247.99/58.61 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 247.99/58.61 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 247.99/58.61 (226) ~ (all_26_2 = all_20_2)
% 247.99/58.61 (227) all_90_2 = all_22_2
% 247.99/58.61 (228) op(all_26_2, all_16_2) = e1
% 247.99/58.61 (229) op(all_12_2, e4) = e0
% 247.99/58.61 (230) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 247.99/58.61 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 247.99/58.61 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.99/58.61 (231) all_46_2 = all_36_2
% 247.99/58.61 (232) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 247.99/58.61 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 247.99/58.61 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 247.99/58.61 (233) op(all_30_2, e0) = e4
% 247.99/58.61 (234) op(all_244_24, all_244_24) = e0
% 247.99/58.61 (235) op(e0, e4) = all_12_2
% 247.99/58.61 (236) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 247.99/58.61 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 247.99/58.61 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 247.99/58.61 (237) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 247.99/58.61 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 247.99/58.61 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 247.99/58.61 (238) all_250_23 = all_20_2
% 247.99/58.61 (239) all_76_2 = all_40_2
% 247.99/58.61 (240) all_124_2 = all_10_2
% 247.99/58.61 (241) all_120_2 = all_64_2
% 247.99/58.61
% 247.99/58.61 Begin of proof
% 247.99/58.61 |
% 247.99/58.61 | GROUND_INST: instantiating (43) with all_10_2, all_50_1, e3, e2, simplifying
% 247.99/58.61 | with (20), (44) gives:
% 247.99/58.61 | (242) all_50_1 = all_10_2
% 247.99/58.61 |
% 247.99/58.61 | BETA: splitting (206) gives:
% 247.99/58.61 |
% 247.99/58.61 | Case 1:
% 247.99/58.61 | |
% 247.99/58.61 | | (243) ~ (all_12_2 = e2)
% 247.99/58.61 | |
% 247.99/58.61 | | BETA: splitting (97) gives:
% 247.99/58.61 | |
% 247.99/58.61 | | Case 1:
% 247.99/58.61 | | |
% 247.99/58.61 | | | (244) ~ (all_16_2 = e2)
% 247.99/58.61 | | |
% 247.99/58.61 | | | BETA: splitting (79) gives:
% 247.99/58.61 | | |
% 247.99/58.61 | | | Case 1:
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | (245) ~ (all_18_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (7), (245) imply:
% 247.99/58.61 | | | | (246) ~ (all_12_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | BETA: splitting (78) gives:
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | Case 1:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | (247) ~ (all_20_2 = e4)
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | BETA: splitting (232) gives:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | Case 1:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (248) ~ (all_22_2 = e1)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (3), (5), (6), (9), (10), (11), (12), (13), (14), (16),
% 247.99/58.61 | | | | | | (17), (18), (19), (22), (23), (25), (26), (29), (30),
% 247.99/58.61 | | | | | | (32), (33), (34), (35), (36), (37), (38), (40), (42),
% 247.99/58.61 | | | | | | (43), (44), (45), (46), (47), (48), (50), (51), (52),
% 247.99/58.61 | | | | | | (53), (54), (56), (57), (58), (59), (60), (63), (64),
% 247.99/58.61 | | | | | | (67), (70), (71), (72), (73), (75), (80), (81), (82),
% 247.99/58.61 | | | | | | (83), (86), (88), (89), (93), (94), (95), (96), (98),
% 247.99/58.61 | | | | | | (99), (100), (101), (102), (103), (104), (105), (106),
% 247.99/58.61 | | | | | | (107), (109), (111), (112), (113), (114), (115), (116),
% 247.99/58.61 | | | | | | (117), (118), (120), (121), (122), (123), (124), (125),
% 247.99/58.61 | | | | | | (126), (129), (130), (131), (132), (133), (134), (136),
% 247.99/58.61 | | | | | | (137), (138), (139), (140), (141), (144), (145), (146),
% 247.99/58.61 | | | | | | (147), (148), (150), (152), (153), (154), (155), (157),
% 247.99/58.61 | | | | | | (158), (159), (160), (161), (162), (163), (164), (165),
% 247.99/58.61 | | | | | | (167), (168), (169), (171), (172), (173), (174), (175),
% 247.99/58.61 | | | | | | (176), (177), (179), (180), (181), (182), (183), (185),
% 247.99/58.61 | | | | | | (186), (188), (189), (190), (191), (192), (193), (194),
% 247.99/58.61 | | | | | | (195), (196), (197), (198), (199), (201), (202), (203),
% 247.99/58.61 | | | | | | (205), (207), (209), (210), (212), (213), (214), (215),
% 247.99/58.61 | | | | | | (216), (218), (219), (220), (221), (222), (223), (227),
% 247.99/58.61 | | | | | | (228), (229), (231), (233), (234), (235), (236), (237),
% 247.99/58.61 | | | | | | (240), (243), (244), (246), (248) are inconsistent by
% 247.99/58.61 | | | | | | sub-proof #65.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | Case 2:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (249) all_22_2 = e1
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (205), (249) imply:
% 247.99/58.61 | | | | | | (250) ~ (all_20_2 = e1)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | SIMP: (250) implies:
% 247.99/58.61 | | | | | | (251) ~ (all_20_2 = e1)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (147), (249) imply:
% 247.99/58.61 | | | | | | (252) op(e1, e3) = e0
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | GROUND_INST: instantiating (43) with all_62_2, e0, e3, e1,
% 247.99/58.61 | | | | | | simplifying with (109), (252) gives:
% 247.99/58.61 | | | | | | (253) all_62_2 = e0
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (128), (253) imply:
% 247.99/58.61 | | | | | | (254) ~ (all_244_3 = e0)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (33), (253) imply:
% 247.99/58.61 | | | | | | (255) op(e0, all_36_2) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (162), (253) imply:
% 247.99/58.61 | | | | | | (256) op(e0, e3) = e1
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (2), (6), (23), (30), (36), (39), (40), (43), (45), (46),
% 247.99/58.61 | | | | | | (56), (59), (86), (99), (106), (113), (117), (118),
% 247.99/58.61 | | | | | | (123), (125), (132), (134), (156), (161), (163), (180),
% 247.99/58.61 | | | | | | (183), (187), (199), (223), (226), (231), (234), (235),
% 247.99/58.61 | | | | | | (238), (246), (247), (251), (254), (255), (256) are
% 247.99/58.61 | | | | | | inconsistent by sub-proof #587.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | End of split
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | Case 2:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | (257) all_20_2 = e4
% 247.99/58.61 | | | | | (258) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1,
% 247.99/58.61 | | | | | e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 247.99/58.61 | | | | | (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | COMBINE_EQS: (200), (257) imply:
% 247.99/58.61 | | | | | (259) all_60_2 = e4
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | REDUCE: (226), (257) imply:
% 247.99/58.61 | | | | | (260) ~ (all_26_2 = e4)
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | REDUCE: (151), (257) imply:
% 247.99/58.61 | | | | | (261) op(e4, all_34_2) = e1
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | REDUCE: (118), (257) imply:
% 247.99/58.61 | | | | | (262) op(e4, e1) = e0
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | BETA: splitting (258) gives:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | Case 1:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (263) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1,
% 247.99/58.61 | | | | | | e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | ALPHA: (263) implies:
% 247.99/58.61 | | | | | | (264) op(e1, e4) = all_20_1
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (3), (5), (6), (9), (10), (11), (12), (13), (14), (16),
% 247.99/58.61 | | | | | | (17), (18), (19), (22), (23), (25), (26), (29), (30),
% 247.99/58.61 | | | | | | (32), (33), (34), (35), (36), (37), (38), (40), (42),
% 247.99/58.61 | | | | | | (43), (44), (45), (46), (48), (50), (51), (52), (53),
% 247.99/58.61 | | | | | | (54), (56), (57), (58), (59), (60), (63), (64), (67),
% 247.99/58.61 | | | | | | (69), (70), (71), (72), (73), (75), (80), (81), (82),
% 247.99/58.61 | | | | | | (83), (85), (86), (88), (89), (92), (93), (94), (95),
% 247.99/58.61 | | | | | | (96), (98), (99), (100), (101), (102), (103), (104),
% 247.99/58.61 | | | | | | (105), (106), (107), (109), (111), (112), (113), (114),
% 247.99/58.61 | | | | | | (115), (116), (117), (118), (120), (121), (122), (123),
% 247.99/58.61 | | | | | | (124), (125), (126), (129), (130), (131), (132), (133),
% 247.99/58.61 | | | | | | (134), (136), (137), (138), (139), (140), (141), (143),
% 247.99/58.61 | | | | | | (144), (145), (146), (147), (148), (149), (150), (152),
% 247.99/58.61 | | | | | | (153), (154), (155), (157), (158), (159), (160), (161),
% 247.99/58.61 | | | | | | (162), (163), (164), (165), (167), (168), (169), (171),
% 247.99/58.61 | | | | | | (172), (173), (174), (175), (176), (177), (179), (180),
% 247.99/58.61 | | | | | | (181), (182), (183), (185), (186), (188), (189), (190),
% 247.99/58.61 | | | | | | (191), (192), (193), (194), (195), (196), (197), (198),
% 247.99/58.61 | | | | | | (199), (201), (202), (203), (205), (207), (209), (210),
% 247.99/58.61 | | | | | | (212), (213), (214), (215), (216), (218), (219), (220),
% 247.99/58.61 | | | | | | (221), (222), (223), (227), (228), (229), (231), (232),
% 247.99/58.61 | | | | | | (233), (234), (235), (236), (237), (240), (243), (244),
% 247.99/58.61 | | | | | | (246), (259), (260), (261), (262), (264) are inconsistent
% 247.99/58.61 | | | | | | by sub-proof #57.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | Case 2:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (265) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | ALPHA: (265) implies:
% 247.99/58.61 | | | | | | (266) op(e1, e4) = all_20_1
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (3), (5), (6), (9), (10), (11), (12), (13), (14), (16),
% 247.99/58.61 | | | | | | (17), (18), (19), (22), (23), (25), (26), (29), (30),
% 247.99/58.61 | | | | | | (32), (33), (34), (35), (36), (37), (38), (40), (42),
% 247.99/58.61 | | | | | | (43), (44), (45), (46), (48), (50), (51), (52), (53),
% 247.99/58.61 | | | | | | (54), (56), (57), (58), (59), (60), (63), (64), (67),
% 247.99/58.61 | | | | | | (69), (70), (71), (72), (73), (75), (80), (81), (82),
% 247.99/58.61 | | | | | | (83), (85), (86), (88), (89), (92), (93), (94), (95),
% 247.99/58.61 | | | | | | (96), (98), (99), (100), (101), (102), (103), (104),
% 247.99/58.61 | | | | | | (105), (106), (107), (109), (111), (112), (113), (114),
% 247.99/58.61 | | | | | | (115), (116), (117), (118), (120), (121), (122), (123),
% 247.99/58.61 | | | | | | (124), (125), (126), (129), (130), (131), (132), (133),
% 247.99/58.61 | | | | | | (134), (136), (137), (138), (139), (140), (141), (143),
% 247.99/58.61 | | | | | | (144), (145), (146), (147), (148), (149), (150), (152),
% 247.99/58.61 | | | | | | (153), (154), (155), (157), (158), (159), (160), (161),
% 247.99/58.61 | | | | | | (162), (163), (164), (165), (167), (168), (169), (171),
% 247.99/58.61 | | | | | | (172), (173), (174), (175), (176), (177), (179), (180),
% 247.99/58.61 | | | | | | (181), (182), (183), (185), (186), (188), (189), (190),
% 247.99/58.61 | | | | | | (191), (192), (193), (194), (195), (196), (197), (198),
% 247.99/58.61 | | | | | | (199), (201), (202), (203), (205), (207), (209), (210),
% 247.99/58.61 | | | | | | (212), (213), (214), (215), (216), (218), (219), (220),
% 247.99/58.61 | | | | | | (221), (222), (223), (227), (228), (229), (231), (232),
% 247.99/58.61 | | | | | | (233), (234), (235), (236), (237), (240), (243), (244),
% 247.99/58.61 | | | | | | (246), (259), (260), (261), (262), (266) are inconsistent
% 247.99/58.61 | | | | | | by sub-proof #57.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | End of split
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | End of split
% 247.99/58.61 | | | |
% 247.99/58.61 | | | Case 2:
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | (267) all_18_2 = e3
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | COMBINE_EQS: (7), (267) imply:
% 247.99/58.61 | | | | (268) all_12_2 = e3
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (55), (268) imply:
% 247.99/58.61 | | | | (269) ~ (all_244_0 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (8), (268) imply:
% 247.99/58.61 | | | | (270) ~ (all_100_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (145), (268) imply:
% 247.99/58.61 | | | | (271) ~ (all_64_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (176), (268) imply:
% 247.99/58.61 | | | | (272) ~ (all_22_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (77), (268) imply:
% 247.99/58.61 | | | | (273) ~ (all_20_2 = e3)
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | REDUCE: (229), (268) imply:
% 247.99/58.61 | | | | (274) op(e3, e4) = e0
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | BETA: splitting (212) gives:
% 247.99/58.61 | | | |
% 247.99/58.61 | | | | Case 1:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | (275) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 247.99/58.61 | | | | | e4) = e3)
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | BETA: splitting (275) gives:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | Case 1:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (276) all_252_0 = e3 & op(e4, e4) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | ALPHA: (276) implies:
% 247.99/58.61 | | | | | | (277) op(e4, e4) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (43), (175), (269), (277) are inconsistent by sub-proof
% 247.99/58.61 | | | | | | #813.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | Case 2:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (278) all_252_2 = e3 & op(e3, e4) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | ALPHA: (278) implies:
% 247.99/58.61 | | | | | | (279) op(e3, e4) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | GROUND_INST: instantiating (43) with all_100_2, e3, e4, e3,
% 247.99/58.61 | | | | | | simplifying with (172), (279) gives:
% 247.99/58.61 | | | | | | (280) all_100_2 = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REDUCE: (270), (280) imply:
% 247.99/58.61 | | | | | | (281) $false
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | CLOSE: (281) is inconsistent.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | End of split
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | Case 2:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | (282) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 247.99/58.61 | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | BETA: splitting (282) gives:
% 247.99/58.61 | | | | |
% 247.99/58.61 | | | | | Case 1:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (283) all_252_6 = e3 & op(e2, e4) = e3
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | REF_CLOSE: (43), (197), (271), (283) are inconsistent by sub-proof
% 247.99/58.61 | | | | | | #940.
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | Case 2:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | (284) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 247.99/58.61 | | | | | | op(e0, e4) = e3)
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | BETA: splitting (284) gives:
% 247.99/58.61 | | | | | |
% 247.99/58.61 | | | | | | Case 1:
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | (285) all_252_12 = e3 & op(e1, e4) = e3
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | REF_CLOSE: (43), (101), (221), (285) are inconsistent by sub-proof
% 247.99/58.61 | | | | | | | #895.
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | Case 2:
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | (286) all_252_20 = e3 & op(e0, e4) = e3
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | ALPHA: (286) implies:
% 247.99/58.61 | | | | | | | (287) all_252_20 = e3
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | GROUND_INST: instantiating (43) with all_100_2, e0, e4, e3,
% 247.99/58.61 | | | | | | | simplifying with (172), (274) gives:
% 247.99/58.61 | | | | | | | (288) all_100_2 = e0
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | COMBINE_EQS: (119), (288) imply:
% 247.99/58.61 | | | | | | | (289) all_136_2 = e0
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | REDUCE: (31), (288) imply:
% 247.99/58.61 | | | | | | | (290) op(e0, all_84_2) = e4
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | REDUCE: (54), (288) imply:
% 247.99/58.61 | | | | | | | (291) op(all_84_2, e0) = e3
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | BETA: splitting (78) gives:
% 247.99/58.61 | | | | | | |
% 247.99/58.61 | | | | | | | Case 1:
% 247.99/58.61 | | | | | | | |
% 247.99/58.61 | | | | | | | | (292) ~ (all_20_2 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | BETA: splitting (232) gives:
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | (293) ~ (all_22_2 = e1)
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | BETA: splitting (70) gives:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (294) ~ (all_34_2 = e2)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | BETA: splitting (171) gives:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (295) ~ (all_90_2 = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REDUCE: (227), (295) imply:
% 247.99/58.62 | | | | | | | | | | | (296) ~ (all_22_2 = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (43), (46), (64), (98), (124), (147), (148),
% 247.99/58.62 | | | | | | | | | | | (168), (190), (195), (272), (290), (291), (293),
% 247.99/58.62 | | | | | | | | | | | (296) are inconsistent by sub-proof #455.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (297) all_90_2 = e2
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | COMBINE_EQS: (227), (297) imply:
% 247.99/58.62 | | | | | | | | | | | (298) all_22_2 = e2
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | SIMP: (298) implies:
% 247.99/58.62 | | | | | | | | | | | (299) all_22_2 = e2
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REDUCE: (41), (299) imply:
% 247.99/58.62 | | | | | | | | | | | (300) ~ (all_62_2 = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REDUCE: (272), (299) imply:
% 247.99/58.62 | | | | | | | | | | | (301) ~ (e3 = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (5), (43), (45), (51), (67), (96), (101), (109),
% 247.99/58.62 | | | | | | | | | | | (174), (183), (222), (244), (294), (300) are
% 247.99/58.62 | | | | | | | | | | | inconsistent by sub-proof #78.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (302) all_34_2 = e2
% 247.99/58.62 | | | | | | | | | | (303) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.99/58.62 | | | | | | | | | | op(e0, e2) = all_34_1 & $i(all_34_0) &
% 247.99/58.62 | | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e3) & op(e0, e2)
% 247.99/58.62 | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (99), (302) imply:
% 247.99/58.62 | | | | | | | | | | (304) op(e2, e0) = e1
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (151), (302) imply:
% 247.99/58.62 | | | | | | | | | | (305) op(all_20_2, e2) = e1
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | BETA: splitting (303) gives:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (306) ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 247.99/58.62 | | | | | | | | | | | op(e0, e2) = all_34_1 & $i(all_34_0) &
% 247.99/58.62 | | | | | | | | | | | $i(all_34_1)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | ALPHA: (306) implies:
% 247.99/58.62 | | | | | | | | | | | (307) op(e0, e2) = all_34_1
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (16), (27), (28), (43), (46), (86), (88), (123),
% 247.99/58.62 | | | | | | | | | | | (130), (152), (184), (186), (220), (225), (273),
% 247.99/58.62 | | | | | | | | | | | (287), (289), (293), (304), (305), (307) are
% 247.99/58.62 | | | | | | | | | | | inconsistent by sub-proof #54.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (308) ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 &
% 247.99/58.62 | | | | | | | | | | | $i(all_34_1)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | ALPHA: (308) implies:
% 247.99/58.62 | | | | | | | | | | | (309) op(e0, e2) = all_34_1
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (16), (27), (28), (43), (46), (86), (88), (123),
% 247.99/58.62 | | | | | | | | | | | (130), (152), (184), (186), (220), (225), (273),
% 247.99/58.62 | | | | | | | | | | | (287), (289), (293), (304), (305), (309) are
% 247.99/58.62 | | | | | | | | | | | inconsistent by sub-proof #54.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | (310) all_22_2 = e1
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | REDUCE: (205), (310) imply:
% 247.99/58.62 | | | | | | | | | (311) ~ (all_20_2 = e1)
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | SIMP: (311) implies:
% 247.99/58.62 | | | | | | | | | (312) ~ (all_20_2 = e1)
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | REDUCE: (147), (310) imply:
% 247.99/58.62 | | | | | | | | | (313) op(e1, e3) = e0
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | BETA: splitting (113) gives:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (314) ~ (all_32_2 = e2)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (6), (314) imply:
% 247.99/58.62 | | | | | | | | | | (315) ~ (all_20_2 = e2)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REF_CLOSE: (2), (43), (99), (156), (238), (273), (292),
% 247.99/58.62 | | | | | | | | | | (312), (315) are inconsistent by sub-proof #780.
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (316) all_32_2 = e2
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | COMBINE_EQS: (6), (316) imply:
% 247.99/58.62 | | | | | | | | | | (317) all_20_2 = e2
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | SIMP: (317) implies:
% 247.99/58.62 | | | | | | | | | | (318) all_20_2 = e2
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (273), (318) imply:
% 247.99/58.62 | | | | | | | | | | (319) ~ (e3 = e2)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (151), (318) imply:
% 247.99/58.62 | | | | | | | | | | (320) op(e2, all_34_2) = e1
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | BETA: splitting (222) gives:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (321) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 247.99/58.62 | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (36), (43), (101), (244), (313), (321) are
% 247.99/58.62 | | | | | | | | | | | inconsistent by sub-proof #64.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (322) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 247.99/58.62 | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 247.99/58.62 | | | | | | | | | | | op(e1, e0) = e2)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | BETA: splitting (322) gives:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | (323) all_252_14 = e2 & op(e1, e2) = e2
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | REF_CLOSE: (5), (45), (323) are inconsistent by sub-proof
% 247.99/58.62 | | | | | | | | | | | | #76.
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | (324) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 247.99/58.62 | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | BETA: splitting (324) gives:
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | (325) all_252_15 = e2 & op(e1, e1) = e2
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | ALPHA: (325) implies:
% 247.99/58.62 | | | | | | | | | | | | | (326) op(e1, e1) = e2
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | REF_CLOSE: (43), (51), (96), (174), (183), (326) are
% 247.99/58.62 | | | | | | | | | | | | | inconsistent by sub-proof #991.
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | (327) all_252_19 = e2 & op(e1, e0) = e2
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | ALPHA: (327) implies:
% 247.99/58.62 | | | | | | | | | | | | | (328) op(e1, e0) = e2
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_34_2, e2, e0, e1,
% 247.99/58.62 | | | | | | | | | | | | | simplifying with (67), (328) gives:
% 247.99/58.62 | | | | | | | | | | | | | (329) all_34_2 = e2
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | REDUCE: (320), (329) imply:
% 247.99/58.62 | | | | | | | | | | | | | (330) op(e2, e2) = e1
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | | REF_CLOSE: (43), (51), (174), (330) are inconsistent by
% 247.99/58.62 | | | | | | | | | | | | | sub-proof #690.
% 247.99/58.62 | | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | End of split
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | (331) all_20_2 = e4
% 247.99/58.62 | | | | | | | | (332) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 247.99/58.62 | | | | | | | | op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1))
% 247.99/58.62 | | | | | | | | | ( ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 &
% 247.99/58.62 | | | | | | | | $i(all_20_1))
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | COMBINE_EQS: (200), (331) imply:
% 247.99/58.62 | | | | | | | | (333) all_60_2 = e4
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (187), (331) imply:
% 247.99/58.62 | | | | | | | | (334) ~ (all_244_15 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (211), (331) imply:
% 247.99/58.62 | | | | | | | | (335) ~ (all_38_2 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (59), (331) imply:
% 247.99/58.62 | | | | | | | | (336) ~ (all_36_2 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (226), (331) imply:
% 247.99/58.62 | | | | | | | | (337) ~ (all_26_2 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (151), (331) imply:
% 247.99/58.62 | | | | | | | | (338) op(e4, all_34_2) = e1
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | REDUCE: (118), (331) imply:
% 247.99/58.62 | | | | | | | | (339) op(e4, e1) = e0
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | BETA: splitting (149) gives:
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | (340) ~ (all_60_2 = e4)
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | REDUCE: (333), (340) imply:
% 247.99/58.62 | | | | | | | | | (341) $false
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | CLOSE: (341) is inconsistent.
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | (342) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 247.99/58.62 | | | | | | | | | op(e1, e4) = all_60_1 & $i(all_60_0) &
% 247.99/58.62 | | | | | | | | | $i(all_60_1)) | ( ~ (all_60_1 = e3) & op(e1, e4) =
% 247.99/58.62 | | | | | | | | | all_60_1 & $i(all_60_1))
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | BETA: splitting (342) gives:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (343) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 247.99/58.62 | | | | | | | | | | op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | ALPHA: (343) implies:
% 247.99/58.62 | | | | | | | | | | (344) op(e1, e4) = all_60_1
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REF_CLOSE: (5), (36), (43), (45), (46), (51), (56), (66),
% 247.99/58.62 | | | | | | | | | | (67), (68), (69), (70), (85), (86), (87), (88),
% 247.99/58.62 | | | | | | | | | | (92), (96), (101), (123), (125), (130), (143),
% 247.99/58.62 | | | | | | | | | | (147), (152), (163), (174), (183), (222), (232),
% 247.99/58.62 | | | | | | | | | | (234), (244), (287), (332), (334), (335), (336),
% 247.99/58.62 | | | | | | | | | | (337), (338), (339), (344) are inconsistent by
% 247.99/58.62 | | | | | | | | | | sub-proof #51.
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (345) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 &
% 247.99/58.62 | | | | | | | | | | $i(all_60_1)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | ALPHA: (345) implies:
% 247.99/58.62 | | | | | | | | | | (346) op(e1, e4) = all_60_1
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REF_CLOSE: (5), (36), (43), (45), (46), (51), (56), (66),
% 247.99/58.62 | | | | | | | | | | (67), (68), (69), (70), (85), (86), (87), (88),
% 247.99/58.62 | | | | | | | | | | (92), (96), (101), (123), (125), (130), (143),
% 247.99/58.62 | | | | | | | | | | (147), (152), (163), (174), (183), (222), (232),
% 247.99/58.62 | | | | | | | | | | (234), (244), (287), (332), (334), (335), (336),
% 247.99/58.62 | | | | | | | | | | (337), (338), (339), (346) are inconsistent by
% 247.99/58.62 | | | | | | | | | | sub-proof #51.
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | End of split
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | End of split
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | End of split
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | End of split
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | End of split
% 247.99/58.62 | | | |
% 247.99/58.62 | | | End of split
% 247.99/58.62 | | |
% 247.99/58.62 | | Case 2:
% 247.99/58.62 | | |
% 247.99/58.62 | | | (347) all_16_2 = e2
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (74), (347) imply:
% 247.99/58.62 | | | (348) ~ (all_244_0 = e2)
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (209), (347) imply:
% 247.99/58.62 | | | (349) ~ (all_64_2 = e2)
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (170), (347) imply:
% 247.99/58.62 | | | (350) ~ (all_62_2 = e2)
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (208), (347) imply:
% 247.99/58.62 | | | (351) ~ (all_34_2 = e2)
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (221), (347) imply:
% 247.99/58.62 | | | (352) ~ (e3 = e2)
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (228), (347) imply:
% 247.99/58.62 | | | (353) op(all_26_2, e2) = e1
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (110), (347) imply:
% 247.99/58.62 | | | (354) op(e2, all_26_2) = e4
% 247.99/58.62 | | |
% 247.99/58.62 | | | REDUCE: (218), (347) imply:
% 247.99/58.62 | | | (355) op(e2, e4) = e1
% 247.99/58.62 | | |
% 247.99/58.62 | | | BETA: splitting (222) gives:
% 247.99/58.62 | | |
% 247.99/58.62 | | | Case 1:
% 247.99/58.62 | | | |
% 247.99/58.62 | | | | (356) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 247.99/58.62 | | | | e3) = e2)
% 247.99/58.62 | | | |
% 247.99/58.62 | | | | BETA: splitting (356) gives:
% 247.99/58.62 | | | |
% 247.99/58.62 | | | | Case 1:
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | (357) all_252_12 = e2 & op(e1, e4) = e2
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | ALPHA: (357) implies:
% 247.99/58.62 | | | | | (358) all_252_12 = e2
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | GROUND_INST: instantiating (43) with all_64_2, e1, e4, e2, simplifying
% 247.99/58.62 | | | | | with (197), (355) gives:
% 247.99/58.62 | | | | | (359) all_64_2 = e1
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | COMBINE_EQS: (241), (359) imply:
% 247.99/58.62 | | | | | (360) all_120_2 = e1
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | COMBINE_EQS: (76), (359) imply:
% 247.99/58.62 | | | | | (361) all_224_2 = e1
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (104), (359) imply:
% 247.99/58.62 | | | | | (362) ~ (all_244_0 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (84), (359) imply:
% 247.99/58.62 | | | | | (363) ~ (all_100_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (60), (359) imply:
% 247.99/58.62 | | | | | (364) ~ (all_40_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | SIMP: (364) implies:
% 247.99/58.62 | | | | | (365) ~ (all_40_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (166), (359) imply:
% 247.99/58.62 | | | | | (366) ~ (all_38_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | SIMP: (366) implies:
% 247.99/58.62 | | | | | (367) ~ (all_38_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (145), (359) imply:
% 247.99/58.62 | | | | | (368) ~ (all_12_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | SIMP: (368) implies:
% 247.99/58.62 | | | | | (369) ~ (all_12_2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | REDUCE: (349), (359) imply:
% 247.99/58.62 | | | | | (370) ~ (e2 = e1)
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | BETA: splitting (230) gives:
% 247.99/58.62 | | | | |
% 247.99/58.62 | | | | | Case 1:
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | (371) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 247.99/58.62 | | | | | | op(e3, e4) = e1)
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | BETA: splitting (371) gives:
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | Case 1:
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | (372) all_252_0 = e1 & op(e4, e4) = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | ALPHA: (372) implies:
% 247.99/58.62 | | | | | | | (373) op(e4, e4) = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | REF_CLOSE: (43), (175), (362), (373) are inconsistent by sub-proof
% 247.99/58.62 | | | | | | | #50.
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | Case 2:
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | (374) all_252_2 = e1 & op(e3, e4) = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | ALPHA: (374) implies:
% 247.99/58.62 | | | | | | | (375) op(e3, e4) = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | REF_CLOSE: (43), (172), (363), (375) are inconsistent by sub-proof
% 247.99/58.62 | | | | | | | #628.
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | End of split
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | Case 2:
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | (376) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 247.99/58.62 | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | BETA: splitting (376) gives:
% 247.99/58.62 | | | | | |
% 247.99/58.62 | | | | | | Case 1:
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | (377) all_252_6 = e1 & op(e2, e4) = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | ALPHA: (377) implies:
% 247.99/58.62 | | | | | | | (378) all_252_6 = e1
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | BETA: splitting (78) gives:
% 247.99/58.62 | | | | | | |
% 247.99/58.62 | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | (379) ~ (all_20_2 = e4)
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | BETA: splitting (141) gives:
% 247.99/58.62 | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | (380) ~ (all_26_2 = e3)
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | BETA: splitting (1) gives:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (381) ~ (all_224_2 = e1)
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | REDUCE: (361), (381) imply:
% 247.99/58.62 | | | | | | | | | | (382) $false
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | CLOSE: (382) is inconsistent.
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | (383) ( ~ (all_224_0 = e0) & op(e4, e1) = all_224_1 &
% 247.99/58.62 | | | | | | | | | | op(e1, all_224_1) = all_224_0 & $i(all_224_0) &
% 247.99/58.62 | | | | | | | | | | $i(all_224_1)) | ( ~ (all_224_1 = e3) & op(e4,
% 247.99/58.62 | | | | | | | | | | e1) = all_224_1 & $i(all_224_1))
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | BETA: splitting (383) gives:
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 1:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (384) ~ (all_224_0 = e0) & op(e4, e1) = all_224_1 &
% 247.99/58.62 | | | | | | | | | | | op(e1, all_224_1) = all_224_0 & $i(all_224_0) &
% 247.99/58.62 | | | | | | | | | | | $i(all_224_1)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | ALPHA: (384) implies:
% 247.99/58.62 | | | | | | | | | | | (385) op(e4, e1) = all_224_1
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (10), (11), (13), (15), (18), (22),
% 247.99/58.62 | | | | | | | | | | | (24), (30), (34), (39), (43), (44), (45), (46),
% 247.99/58.62 | | | | | | | | | | | (50), (51), (56), (57), (58), (61), (62), (65),
% 247.99/58.62 | | | | | | | | | | | (67), (68), (71), (77), (80), (86), (87), (91),
% 247.99/58.62 | | | | | | | | | | | (95), (96), (105), (108), (109), (110), (112),
% 247.99/58.62 | | | | | | | | | | | (113), (114), (115), (116), (118), (121), (123),
% 247.99/58.62 | | | | | | | | | | | (125), (127), (129), (134), (135), (137), (142),
% 247.99/58.62 | | | | | | | | | | | (152), (158), (160), (162), (163), (164), (169),
% 247.99/58.62 | | | | | | | | | | | (174), (175), (177), (178), (179), (180), (181),
% 247.99/58.62 | | | | | | | | | | | (183), (186), (189), (191), (192), (194), (195),
% 247.99/58.62 | | | | | | | | | | | (202), (204), (205), (210), (211), (213), (218),
% 247.99/58.62 | | | | | | | | | | | (220), (223), (231), (233), (235), (239), (348),
% 247.99/58.62 | | | | | | | | | | | (354), (358), (360), (365), (367), (378), (379),
% 247.99/58.62 | | | | | | | | | | | (380), (385) are inconsistent by sub-proof #45.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | (386) ~ (all_224_1 = e3) & op(e4, e1) = all_224_1 &
% 247.99/58.62 | | | | | | | | | | | $i(all_224_1)
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | ALPHA: (386) implies:
% 247.99/58.62 | | | | | | | | | | | (387) op(e4, e1) = all_224_1
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (10), (11), (13), (15), (18), (22),
% 247.99/58.62 | | | | | | | | | | | (24), (30), (34), (39), (43), (44), (45), (46),
% 247.99/58.62 | | | | | | | | | | | (50), (51), (56), (57), (58), (61), (62), (65),
% 247.99/58.62 | | | | | | | | | | | (67), (68), (71), (77), (80), (86), (87), (91),
% 247.99/58.62 | | | | | | | | | | | (95), (96), (105), (108), (109), (110), (112),
% 247.99/58.62 | | | | | | | | | | | (113), (114), (115), (116), (118), (121), (123),
% 247.99/58.62 | | | | | | | | | | | (125), (127), (129), (134), (135), (137), (142),
% 247.99/58.62 | | | | | | | | | | | (152), (158), (160), (162), (163), (164), (169),
% 247.99/58.62 | | | | | | | | | | | (174), (175), (177), (178), (179), (180), (181),
% 247.99/58.62 | | | | | | | | | | | (183), (186), (189), (191), (192), (194), (195),
% 247.99/58.62 | | | | | | | | | | | (202), (204), (205), (210), (211), (213), (218),
% 247.99/58.62 | | | | | | | | | | | (220), (223), (231), (233), (235), (239), (348),
% 247.99/58.62 | | | | | | | | | | | (354), (358), (360), (365), (367), (378), (379),
% 247.99/58.62 | | | | | | | | | | | (380), (387) are inconsistent by sub-proof #45.
% 247.99/58.62 | | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | | |
% 247.99/58.62 | | | | | | | | | End of split
% 247.99/58.62 | | | | | | | | |
% 247.99/58.62 | | | | | | | | Case 2:
% 247.99/58.62 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | (388) all_26_2 = e3
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | REDUCE: (354), (388) imply:
% 247.99/58.63 | | | | | | | | | (389) op(e2, e3) = e4
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | REF_CLOSE: (10), (43), (44), (389) are inconsistent by
% 247.99/58.63 | | | | | | | | | sub-proof #953.
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | End of split
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | Case 2:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | (390) all_20_2 = e4
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REDUCE: (118), (390) imply:
% 247.99/58.63 | | | | | | | | (391) op(e4, e1) = e0
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | GROUND_INST: instantiating (43) with all_26_2, e0, e1, e4,
% 247.99/58.63 | | | | | | | | simplifying with (163), (391) gives:
% 247.99/58.63 | | | | | | | | (392) all_26_2 = e0
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REDUCE: (353), (392) imply:
% 247.99/58.63 | | | | | | | | (393) op(e0, e2) = e1
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REF_CLOSE: (43), (86), (88), (393) are inconsistent by sub-proof
% 247.99/58.63 | | | | | | | | #907.
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | End of split
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | Case 2:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | (394) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 247.99/58.63 | | | | | | | op(e0, e4) = e1)
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | BETA: splitting (394) gives:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | Case 1:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | (395) all_252_12 = e1 & op(e1, e4) = e1
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REF_CLOSE: (80), (358), (395) are inconsistent by sub-proof
% 247.99/58.63 | | | | | | | | #562.
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | Case 2:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | (396) all_252_20 = e1 & op(e0, e4) = e1
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REF_CLOSE: (43), (235), (369), (396) are inconsistent by
% 247.99/58.63 | | | | | | | | sub-proof #593.
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | End of split
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | End of split
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | End of split
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | Case 2:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | (397) all_252_13 = e2 & op(e1, e3) = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | ALPHA: (397) implies:
% 247.99/58.63 | | | | | (398) op(e1, e3) = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REF_CLOSE: (43), (109), (350), (398) are inconsistent by sub-proof
% 247.99/58.63 | | | | | #972.
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | End of split
% 247.99/58.63 | | | |
% 247.99/58.63 | | | Case 2:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | (399) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 247.99/58.63 | | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | BETA: splitting (399) gives:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | Case 1:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | (400) all_252_14 = e2 & op(e1, e2) = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REF_CLOSE: (5), (45), (400) are inconsistent by sub-proof #76.
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | Case 2:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | (401) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 247.99/58.63 | | | | | op(e1, e0) = e2)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REF_CLOSE: (43), (51), (67), (96), (174), (183), (351), (401) are
% 247.99/58.63 | | | | | inconsistent by sub-proof #79.
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | End of split
% 247.99/58.63 | | | |
% 247.99/58.63 | | | End of split
% 247.99/58.63 | | |
% 247.99/58.63 | | End of split
% 247.99/58.63 | |
% 247.99/58.63 | Case 2:
% 247.99/58.63 | |
% 247.99/58.63 | | (402) all_12_2 = e2
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (55), (402) imply:
% 247.99/58.63 | | (403) ~ (all_244_0 = e2)
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (8), (402) imply:
% 247.99/58.63 | | (404) ~ (all_100_2 = e2)
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (145), (402) imply:
% 247.99/58.63 | | (405) ~ (all_64_2 = e2)
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (224), (402) imply:
% 247.99/58.63 | | (406) ~ (all_16_2 = e2)
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (21), (402) imply:
% 247.99/58.63 | | (407) op(e2, all_30_2) = e4
% 247.99/58.63 | |
% 247.99/58.63 | | REDUCE: (229), (402) imply:
% 247.99/58.63 | | (408) op(e2, e4) = e0
% 247.99/58.63 | |
% 247.99/58.63 | | BETA: splitting (214) gives:
% 247.99/58.63 | |
% 247.99/58.63 | | Case 1:
% 247.99/58.63 | | |
% 247.99/58.63 | | | (409) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4)
% 247.99/58.63 | | | = e2)
% 247.99/58.63 | | |
% 247.99/58.63 | | | BETA: splitting (409) gives:
% 247.99/58.63 | | |
% 247.99/58.63 | | | Case 1:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | (410) all_252_0 = e2 & op(e4, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | ALPHA: (410) implies:
% 247.99/58.63 | | | | (411) op(e4, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | REF_CLOSE: (43), (175), (403), (411) are inconsistent by sub-proof #809.
% 247.99/58.63 | | | |
% 247.99/58.63 | | | Case 2:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | (412) all_252_2 = e2 & op(e3, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | ALPHA: (412) implies:
% 247.99/58.63 | | | | (413) op(e3, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | REF_CLOSE: (43), (172), (404), (413) are inconsistent by sub-proof #233.
% 247.99/58.63 | | | |
% 247.99/58.63 | | | End of split
% 247.99/58.63 | | |
% 247.99/58.63 | | Case 2:
% 247.99/58.63 | | |
% 247.99/58.63 | | | (414) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 247.99/58.63 | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 247.99/58.63 | | |
% 247.99/58.63 | | | BETA: splitting (414) gives:
% 247.99/58.63 | | |
% 247.99/58.63 | | | Case 1:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | (415) all_252_6 = e2 & op(e2, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | ALPHA: (415) implies:
% 247.99/58.63 | | | | (416) all_252_6 = e2
% 247.99/58.63 | | | | (417) op(e2, e4) = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | GROUND_INST: instantiating (43) with all_64_2, e0, e4, e2, simplifying
% 247.99/58.63 | | | | with (197), (408) gives:
% 247.99/58.63 | | | | (418) all_64_2 = e0
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | GROUND_INST: instantiating (43) with all_64_2, e2, e4, e2, simplifying
% 247.99/58.63 | | | | with (197), (417) gives:
% 247.99/58.63 | | | | (419) all_64_2 = e2
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | COMBINE_EQS: (418), (419) imply:
% 247.99/58.63 | | | | (420) e2 = e0
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | COMBINE_EQS: (416), (420) imply:
% 247.99/58.63 | | | | (421) all_252_6 = e0
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | REF_CLOSE: (10), (11), (22), (43), (44), (47), (50), (51), (56), (57),
% 247.99/58.63 | | | | (58), (71), (121), (129), (160), (172), (175), (220), (403),
% 247.99/58.63 | | | | (404), (407), (421) are inconsistent by sub-proof #44.
% 247.99/58.63 | | | |
% 247.99/58.63 | | | Case 2:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | (422) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 247.99/58.63 | | | | e4) = e2)
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | BETA: splitting (422) gives:
% 247.99/58.63 | | | |
% 247.99/58.63 | | | | Case 1:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | (423) all_252_12 = e2 & op(e1, e4) = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REF_CLOSE: (43), (101), (406), (423) are inconsistent by sub-proof
% 247.99/58.63 | | | | | #926.
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | Case 2:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | (424) all_252_20 = e2 & op(e0, e4) = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | ALPHA: (424) implies:
% 247.99/58.63 | | | | | (425) all_252_20 = e2
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | GROUND_INST: instantiating (43) with all_64_2, e0, e4, e2, simplifying
% 247.99/58.63 | | | | | with (197), (408) gives:
% 247.99/58.63 | | | | | (426) all_64_2 = e0
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (49), (426) imply:
% 247.99/58.63 | | | | | (427) ~ (all_244_8 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (84), (426) imply:
% 247.99/58.63 | | | | | (428) ~ (all_100_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (60), (426) imply:
% 247.99/58.63 | | | | | (429) ~ (all_40_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | SIMP: (429) implies:
% 247.99/58.63 | | | | | (430) ~ (all_40_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (166), (426) imply:
% 247.99/58.63 | | | | | (431) ~ (all_38_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | SIMP: (431) implies:
% 247.99/58.63 | | | | | (432) ~ (all_38_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (209), (426) imply:
% 247.99/58.63 | | | | | (433) ~ (all_16_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | SIMP: (433) implies:
% 247.99/58.63 | | | | | (434) ~ (all_16_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (90), (426) imply:
% 247.99/58.63 | | | | | (435) ~ (all_10_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | SIMP: (435) implies:
% 247.99/58.63 | | | | | (436) ~ (all_10_2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | REDUCE: (405), (426) imply:
% 247.99/58.63 | | | | | (437) ~ (e2 = e0)
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | BETA: splitting (4) gives:
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | | Case 1:
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | (438) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 &
% 247.99/58.63 | | | | | | op(e3, e4) = e0)
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | BETA: splitting (438) gives:
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | Case 1:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | (439) all_252_0 = e0 & op(e4, e4) = e0
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | ALPHA: (439) implies:
% 247.99/58.63 | | | | | | | (440) all_252_0 = e0
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | BETA: splitting (24) gives:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | Case 1:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | (441) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 &
% 247.99/58.63 | | | | | | | | op(e2, e3) = e0)
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | BETA: splitting (441) gives:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | Case 1:
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | (442) all_252_6 = e0 & op(e2, e4) = e0
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | ALPHA: (442) implies:
% 247.99/58.63 | | | | | | | | | (443) all_252_6 = e0
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | REF_CLOSE: (38), (43), (45), (47), (80), (87), (101), (112),
% 247.99/58.63 | | | | | | | | | (123), (172), (181), (202), (212), (217), (221),
% 247.99/58.63 | | | | | | | | | (230), (425), (440), (443) are inconsistent by
% 247.99/58.63 | | | | | | | | | sub-proof #99.
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | Case 2:
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | (444) all_252_7 = e0 & op(e2, e3) = e0
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | | REF_CLOSE: (43), (44), (436), (444) are inconsistent by
% 247.99/58.63 | | | | | | | | | sub-proof #816.
% 247.99/58.63 | | | | | | | | |
% 247.99/58.63 | | | | | | | | End of split
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | Case 2:
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | (445) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 247.99/58.63 | | | | | | | | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) =
% 247.99/58.63 | | | | | | | | e0)
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | | REF_CLOSE: (43), (51), (56), (220), (427), (430), (432), (445)
% 247.99/58.63 | | | | | | | | are inconsistent by sub-proof #879.
% 247.99/58.63 | | | | | | | |
% 247.99/58.63 | | | | | | | End of split
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | Case 2:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | (446) all_252_2 = e0 & op(e3, e4) = e0
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | REF_CLOSE: (43), (172), (428), (446) are inconsistent by sub-proof
% 247.99/58.63 | | | | | | | #43.
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | End of split
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | Case 2:
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | (447) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 &
% 247.99/58.63 | | | | | | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | BETA: splitting (447) gives:
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | | Case 1:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | (448) all_252_6 = e0 & op(e2, e4) = e0
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | ALPHA: (448) implies:
% 247.99/58.63 | | | | | | | (449) all_252_6 = e0
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | REF_CLOSE: (10), (11), (22), (43), (44), (47), (50), (51), (56),
% 247.99/58.63 | | | | | | | (57), (58), (71), (121), (129), (160), (172), (175),
% 247.99/58.63 | | | | | | | (220), (403), (404), (407), (449) are inconsistent by
% 247.99/58.63 | | | | | | | sub-proof #44.
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | Case 2:
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | (450) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 247.99/58.63 | | | | | | | op(e0, e4) = e0)
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | | REF_CLOSE: (36), (43), (101), (425), (434), (450) are inconsistent
% 247.99/58.63 | | | | | | | by sub-proof #42.
% 247.99/58.63 | | | | | | |
% 247.99/58.63 | | | | | | End of split
% 247.99/58.63 | | | | | |
% 247.99/58.63 | | | | | End of split
% 247.99/58.63 | | | | |
% 247.99/58.63 | | | | End of split
% 247.99/58.63 | | | |
% 247.99/58.63 | | | End of split
% 247.99/58.63 | | |
% 247.99/58.63 | | End of split
% 247.99/58.63 | |
% 247.99/58.63 | End of split
% 247.99/58.63 |
% 247.99/58.63 End of proof
% 247.99/58.63
% 247.99/58.63 Sub-proof #42 shows that the following formulas are inconsistent:
% 247.99/58.63 ----------------------------------------------------------------
% 247.99/58.63 (1) ~ (e2 = e0)
% 247.99/58.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.63 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)
% 247.99/58.63 (4) op(e1, e4) = all_16_2
% 247.99/58.63 (5) all_252_20 = e2
% 247.99/58.63 (6) ~ (all_16_2 = e0)
% 247.99/58.63
% 247.99/58.63 Begin of proof
% 247.99/58.63 |
% 247.99/58.63 | BETA: splitting (3) gives:
% 247.99/58.63 |
% 247.99/58.63 | Case 1:
% 247.99/58.63 | |
% 247.99/58.63 | | (7) all_252_12 = e0 & op(e1, e4) = e0
% 247.99/58.63 | |
% 247.99/58.63 | | ALPHA: (7) implies:
% 247.99/58.63 | | (8) op(e1, e4) = e0
% 247.99/58.63 | |
% 247.99/58.63 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #278.
% 247.99/58.63 | |
% 247.99/58.63 | Case 2:
% 247.99/58.63 | |
% 247.99/58.63 | | (9) all_252_20 = e0 & op(e0, e4) = e0
% 247.99/58.63 | |
% 247.99/58.63 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #185.
% 247.99/58.63 | |
% 247.99/58.63 | End of split
% 247.99/58.63 |
% 247.99/58.63 End of proof
% 247.99/58.63
% 247.99/58.63 Sub-proof #43 shows that the following formulas are inconsistent:
% 247.99/58.63 ----------------------------------------------------------------
% 247.99/58.63 (1) all_252_2 = e0 & op(e3, e4) = e0
% 247.99/58.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.63 (3) op(e3, e4) = all_100_2
% 247.99/58.63 (4) ~ (all_100_2 = e0)
% 247.99/58.63
% 247.99/58.63 Begin of proof
% 247.99/58.63 |
% 247.99/58.63 | ALPHA: (1) implies:
% 247.99/58.63 | (5) op(e3, e4) = e0
% 247.99/58.63 |
% 247.99/58.63 | GROUND_INST: instantiating (2) with all_100_2, e0, e4, e3, simplifying with
% 247.99/58.63 | (3), (5) gives:
% 247.99/58.63 | (6) all_100_2 = e0
% 247.99/58.63 |
% 247.99/58.63 | REDUCE: (4), (6) imply:
% 247.99/58.63 | (7) $false
% 247.99/58.63 |
% 247.99/58.63 | CLOSE: (7) is inconsistent.
% 247.99/58.63 |
% 247.99/58.63 End of proof
% 247.99/58.63
% 247.99/58.63 Sub-proof #44 shows that the following formulas are inconsistent:
% 247.99/58.63 ----------------------------------------------------------------
% 247.99/58.63 (1) ~ (all_10_2 = e4)
% 247.99/58.63 (2) ~ (all_244_0 = all_30_2)
% 247.99/58.63 (3) op(e4, e0) = all_30_2
% 247.99/58.63 (4) all_252_6 = e0
% 247.99/58.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 247.99/58.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 247.99/58.63 (6) op(e2, e3) = all_10_2
% 247.99/58.63 (7) ~ (e4 = e0)
% 247.99/58.63 (8) op(all_244_8, all_244_8) = e2
% 247.99/58.63 (9) op(e2, e2) = all_244_8
% 247.99/58.63 (10) op(e2, e1) = all_38_2
% 247.99/58.63 (11) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 247.99/58.63 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 247.99/58.63 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 247.99/58.63 (12) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 247.99/58.63 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 247.99/58.63 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 247.99/58.63 (13) op(e3, all_38_2) = e2
% 247.99/58.63 (14) ~ (all_244_0 = e2)
% 247.99/58.63 (15) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 247.99/58.63 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 247.99/58.63 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 247.99/58.63 (16) op(all_40_2, e0) = e2
% 247.99/58.63 (17) op(e2, all_30_2) = e4
% 247.99/58.63 (18) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 247.99/58.63 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 247.99/58.63 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 247.99/58.63 (19) op(e3, e4) = all_100_2
% 247.99/58.63 (20) ~ (all_100_2 = e2)
% 247.99/58.63 (21) op(e4, e4) = all_244_0
% 247.99/58.63 (22) op(e2, e0) = all_40_2
% 247.99/58.63
% 247.99/58.63 Begin of proof
% 247.99/58.63 |
% 247.99/58.63 | BETA: splitting (12) gives:
% 247.99/58.63 |
% 247.99/58.63 | Case 1:
% 247.99/58.63 | |
% 247.99/58.63 | | (23) ~ (all_30_2 = e2)
% 247.99/58.63 | |
% 247.99/58.63 | | BETA: splitting (11) gives:
% 247.99/58.63 | |
% 247.99/58.63 | | Case 1:
% 247.99/58.63 | | |
% 247.99/58.63 | | | (24) ~ (all_38_2 = e4)
% 247.99/58.63 | | |
% 247.99/58.63 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (14), (15), (16),
% 247.99/58.63 | | | (18), (21), (22), (23), (24) are inconsistent by sub-proof
% 247.99/58.63 | | | #216.
% 247.99/58.63 | | |
% 247.99/58.63 | | Case 2:
% 247.99/58.63 | | |
% 247.99/58.63 | | | (25) all_38_2 = e4
% 247.99/58.63 | | |
% 247.99/58.63 | | | REDUCE: (13), (25) imply:
% 247.99/58.63 | | | (26) op(e3, e4) = e2
% 247.99/58.63 | | |
% 247.99/58.63 | | | REF_CLOSE: (5), (19), (20), (26) are inconsistent by sub-proof #233.
% 247.99/58.63 | | |
% 247.99/58.63 | | End of split
% 247.99/58.63 | |
% 247.99/58.63 | Case 2:
% 247.99/58.63 | |
% 247.99/58.63 | | (27) all_30_2 = e2
% 247.99/58.63 | |
% 247.99/58.63 | | REF_CLOSE: (2), (5), (8), (9), (17), (21), (27) are inconsistent by
% 247.99/58.63 | | sub-proof #162.
% 247.99/58.63 | |
% 247.99/58.63 | End of split
% 247.99/58.63 |
% 247.99/58.64 End of proof
% 247.99/58.64
% 247.99/58.64 Sub-proof #45 shows that the following formulas are inconsistent:
% 247.99/58.64 ----------------------------------------------------------------
% 247.99/58.64 (1) ~ (all_30_2 = all_26_2)
% 247.99/58.64 (2) all_32_2 = all_20_2
% 247.99/58.64 (3) ~ (all_4_2 = e4)
% 247.99/58.64 (4) ~ (all_10_2 = e4)
% 247.99/58.64 (5) ~ (all_244_0 = all_30_2)
% 247.99/58.64 (6) all_120_2 = e1
% 247.99/58.64 (7) op(all_4_2, e2) = e1
% 247.99/58.64 (8) ~ (all_76_2 = e4) | ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 &
% 247.99/58.64 op(e0, e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 =
% 247.99/58.64 e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 247.99/58.64 (9) ~ (all_38_2 = e1)
% 247.99/58.64 (10) ~ (all_40_2 = all_38_2)
% 247.99/58.64 (11) op(e4, e0) = all_30_2
% 247.99/58.64 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 247.99/58.64 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 247.99/58.64 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 247.99/58.64 (13) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 247.99/58.64 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 247.99/58.64 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.64 (14) op(e2, all_26_2) = e4
% 248.43/58.64 (15) op(all_38_2, e1) = e2
% 248.43/58.64 (16) all_252_12 = e2
% 248.43/58.64 (17) ~ (all_244_24 = all_20_2)
% 248.43/58.64 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.64 (19) op(e2, e3) = all_10_2
% 248.43/58.64 (20) ~ (e3 = e2)
% 248.43/58.64 (21) op(e0, e0) = all_244_24
% 248.43/58.64 (22) op(all_244_8, all_244_8) = e2
% 248.43/58.64 (23) op(e2, e2) = all_244_8
% 248.43/58.64 (24) all_252_6 = e1
% 248.43/58.64 (25) op(e2, e1) = all_38_2
% 248.43/58.64 (26) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.43/58.64 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.43/58.64 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.43/58.64 (27) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.43/58.64 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.43/58.64 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.43/58.64 (28) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 248.43/58.64 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 248.43/58.64 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 248.43/58.64 (29) ~ (all_84_2 = all_62_2)
% 248.43/58.64 (30) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 248.43/58.64 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 248.43/58.64 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 248.43/58.64 (31) op(e1, e0) = all_34_2
% 248.43/58.64 (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.64 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.64 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.64 (33) op(e3, all_38_2) = e2
% 248.43/58.64 (34) ~ (all_20_2 = all_12_2)
% 248.43/58.64 (35) ~ (e2 = e1)
% 248.43/58.64 (36) op(e0, e2) = all_28_2
% 248.43/58.64 (37) ~ (e4 = e1)
% 248.43/58.64 (38) ~ (all_244_0 = e2)
% 248.43/58.64 (39) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 248.43/58.64 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.43/58.64 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 248.43/58.64 (40) ~ (all_244_8 = all_38_2)
% 248.43/58.64 (41) op(all_244_15, all_244_15) = e1
% 248.43/58.64 (42) ~ (all_244_3 = all_36_2)
% 248.43/58.64 (43) ~ (all_28_2 = all_20_2)
% 248.43/58.64 (44) op(e1, e3) = all_62_2
% 248.43/58.64 (45) op(all_16_2, all_26_2) = e4
% 248.43/58.64 (46) ~ (e3 = e0)
% 248.43/58.64 (47) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.64 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.64 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.64 (48) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.64 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.64 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.64 (49) ~ (all_40_2 = all_10_2)
% 248.43/58.64 (50) all_204_2 = all_36_2
% 248.43/58.64 (51) op(all_20_2, e1) = e0
% 248.43/58.64 (52) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.43/58.64 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.43/58.64 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.43/58.64 (53) ~ (e3 = e1)
% 248.43/58.64 (54) op(e3, e1) = all_36_2
% 248.43/58.64 (55) ~ (all_54_2 = e2) | ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 &
% 248.43/58.64 op(e0, e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 =
% 248.43/58.64 e3) & op(e0, e2) = all_54_1 & $i(all_54_1))
% 248.43/58.64 (56) op(all_40_2, e0) = e2
% 248.43/58.64 (57) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.43/58.64 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.43/58.64 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.64 (58) ~ (all_40_2 = all_34_2)
% 248.43/58.64 (59) ~ (all_244_15 = all_38_2)
% 248.43/58.64 (60) all_190_2 = all_38_2
% 248.43/58.64 (61) op(e0, e3) = all_22_2
% 248.43/58.64 (62) ~ (all_40_2 = e1)
% 248.43/58.64 (63) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.64 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.64 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.64 (64) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.43/58.64 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.43/58.64 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.43/58.64 (65) op(all_62_2, e3) = e1
% 248.43/58.64 (66) op(e4, e1) = all_26_2
% 248.43/58.64 (67) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.64 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.64 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.64 (68) ~ (all_244_15 = all_62_2)
% 248.43/58.64 (69) ~ (all_244_8 = e1)
% 248.43/58.64 (70) op(e4, e4) = all_244_0
% 248.43/58.64 (71) all_230_2 = all_20_2
% 248.43/58.64 (72) all_54_2 = all_30_2
% 248.43/58.64 (73) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.64 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.64 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.64 (74) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.43/58.64 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.43/58.64 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.64 (75) ~ (e4 = e3)
% 248.43/58.64 (76) op(e1, e1) = all_244_15
% 248.43/58.64 (77) op(e0, e1) = all_20_2
% 248.43/58.64 (78) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.43/58.64 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.43/58.64 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.64 (79) ~ (all_38_2 = all_36_2)
% 248.43/58.64 (80) ~ (all_26_2 = e3)
% 248.43/58.64 (81) op(e1, e2) = all_4_2
% 248.43/58.64 (82) op(all_4_2, all_38_2) = e2
% 248.43/58.64 (83) op(e4, e3) = all_84_2
% 248.43/58.64 (84) ~ (e4 = e2)
% 248.43/58.64 (85) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 248.43/58.64 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 248.43/58.64 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 248.43/58.64 (86) ~ (all_22_2 = all_20_2)
% 248.43/58.64 (87) op(all_36_2, e1) = e3
% 248.43/58.64 (88) ~ (all_38_2 = all_20_2)
% 248.43/58.64 (89) ~ (all_38_2 = all_10_2)
% 248.43/58.64 (90) ~ (all_20_2 = e4)
% 248.43/58.64 (91) op(all_16_2, e4) = e1
% 248.43/58.64 (92) op(e2, e0) = all_40_2
% 248.43/58.64 (93) op(e3, e3) = all_244_3
% 248.43/58.64 (94) all_46_2 = all_36_2
% 248.43/58.64 (95) op(all_30_2, e0) = e4
% 248.43/58.64 (96) op(e0, e4) = all_12_2
% 248.43/58.64 (97) op(e4, e1) = all_224_1
% 248.43/58.64 (98) all_76_2 = all_40_2
% 248.43/58.64
% 248.43/58.64 Begin of proof
% 248.43/58.64 |
% 248.43/58.64 | GROUND_INST: instantiating (18) with all_26_2, all_224_1, e1, e4, simplifying
% 248.43/58.64 | with (66), (97) gives:
% 248.43/58.64 | (99) all_224_1 = all_26_2
% 248.43/58.64 |
% 248.43/58.64 | BETA: splitting (27) gives:
% 248.43/58.64 |
% 248.43/58.64 | Case 1:
% 248.43/58.64 | |
% 248.43/58.64 | | (100) ~ (all_30_2 = e2)
% 248.43/58.64 | |
% 248.43/58.64 | | REF_CLOSE: (4), (11), (14), (15), (18), (19), (22), (23), (24), (25), (26),
% 248.43/58.64 | | (32), (37), (38), (52), (54), (56), (59), (64), (66), (70), (76),
% 248.43/58.64 | | (77), (79), (84), (88), (92), (100) are inconsistent by sub-proof
% 248.43/58.64 | | #234.
% 248.43/58.64 | |
% 248.43/58.64 | Case 2:
% 248.43/58.64 | |
% 248.43/58.64 | | (101) all_30_2 = e2
% 248.43/58.64 | | (102) ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 & op(e0, e2) =
% 248.43/58.64 | | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e1) &
% 248.43/58.64 | | op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.43/58.64 | |
% 248.43/58.64 | | COMBINE_EQS: (72), (101) imply:
% 248.43/58.64 | | (103) all_54_2 = e2
% 248.43/58.64 | |
% 248.43/58.64 | | REDUCE: (1), (101) imply:
% 248.43/58.64 | | (104) ~ (all_26_2 = e2)
% 248.43/58.64 | |
% 248.43/58.64 | | SIMP: (104) implies:
% 248.43/58.64 | | (105) ~ (all_26_2 = e2)
% 248.43/58.64 | |
% 248.43/58.64 | | REDUCE: (95), (101) imply:
% 248.43/58.64 | | (106) op(e2, e0) = e4
% 248.43/58.64 | |
% 248.43/58.64 | | BETA: splitting (55) gives:
% 248.43/58.64 | |
% 248.43/58.64 | | Case 1:
% 248.43/58.64 | | |
% 248.43/58.64 | | | (107) ~ (all_54_2 = e2)
% 248.43/58.64 | | |
% 248.43/58.64 | | | REDUCE: (103), (107) imply:
% 248.43/58.64 | | | (108) $false
% 248.43/58.64 | | |
% 248.43/58.64 | | | CLOSE: (108) is inconsistent.
% 248.43/58.64 | | |
% 248.43/58.64 | | Case 2:
% 248.43/58.64 | | |
% 248.43/58.64 | | | (109) ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0, e2) =
% 248.43/58.64 | | | all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 = e3) &
% 248.43/58.64 | | | op(e0, e2) = all_54_1 & $i(all_54_1))
% 248.43/58.64 | | |
% 248.43/58.64 | | | BETA: splitting (102) gives:
% 248.43/58.64 | | |
% 248.43/58.64 | | | Case 1:
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | (110) ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 & op(e0, e2) =
% 248.43/58.64 | | | | all_30_1 & $i(all_30_0) & $i(all_30_1)
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | ALPHA: (110) implies:
% 248.43/58.64 | | | | (111) op(e0, e2) = all_30_1
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (12), (13), (14), (16),
% 248.43/58.64 | | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (28),
% 248.43/58.64 | | | | (29), (30), (31), (32), (33), (34), (35), (36), (38), (39),
% 248.43/58.64 | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 248.43/58.64 | | | | (50), (51), (52), (53), (54), (57), (58), (60), (61), (62),
% 248.43/58.64 | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (73),
% 248.43/58.64 | | | | (74), (75), (76), (77), (78), (80), (81), (82), (83), (85),
% 248.43/58.64 | | | | (86), (87), (89), (90), (91), (92), (93), (94), (96), (98),
% 248.43/58.64 | | | | (105), (106), (109), (111) are inconsistent by sub-proof #46.
% 248.43/58.64 | | | |
% 248.43/58.64 | | | Case 2:
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | (112) ~ (all_30_1 = e1) & op(e0, e2) = all_30_1 & $i(all_30_1)
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | ALPHA: (112) implies:
% 248.43/58.64 | | | | (113) op(e0, e2) = all_30_1
% 248.43/58.64 | | | |
% 248.43/58.64 | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (12), (13), (14), (16),
% 248.43/58.64 | | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (28),
% 248.43/58.64 | | | | (29), (30), (31), (32), (33), (34), (35), (36), (38), (39),
% 248.43/58.64 | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 248.43/58.64 | | | | (50), (51), (52), (53), (54), (57), (58), (60), (61), (62),
% 248.43/58.64 | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (73),
% 248.43/58.64 | | | | (74), (75), (76), (77), (78), (80), (81), (82), (83), (85),
% 248.43/58.64 | | | | (86), (87), (89), (90), (91), (92), (93), (94), (96), (98),
% 248.43/58.64 | | | | (105), (106), (109), (113) are inconsistent by sub-proof #46.
% 248.43/58.64 | | | |
% 248.43/58.64 | | | End of split
% 248.43/58.64 | | |
% 248.43/58.64 | | End of split
% 248.43/58.64 | |
% 248.43/58.64 | End of split
% 248.43/58.64 |
% 248.43/58.64 End of proof
% 248.43/58.64
% 248.43/58.64 Sub-proof #46 shows that the following formulas are inconsistent:
% 248.43/58.64 ----------------------------------------------------------------
% 248.43/58.64 (1) all_32_2 = all_20_2
% 248.43/58.64 (2) ~ (all_26_2 = e2)
% 248.43/58.64 (3) ~ (all_4_2 = e4)
% 248.43/58.64 (4) all_120_2 = e1
% 248.43/58.64 (5) op(all_4_2, e2) = e1
% 248.43/58.64 (6) ~ (all_76_2 = e4) | ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 &
% 248.43/58.64 op(e0, e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 =
% 248.43/58.64 e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 248.43/58.64 (7) ~ (all_38_2 = e1)
% 248.43/58.64 (8) ~ (all_40_2 = all_38_2)
% 248.43/58.64 (9) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 248.43/58.64 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 248.43/58.64 | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.43/58.64 (10) ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0, e2) =
% 248.43/58.64 all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 = e3) & op(e0,
% 248.43/58.64 e2) = all_54_1 & $i(all_54_1))
% 248.43/58.64 (11) op(e0, e2) = all_30_1
% 248.43/58.64 (12) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.43/58.64 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.43/58.64 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.64 (13) op(e2, e0) = e4
% 248.43/58.64 (14) op(e2, all_26_2) = e4
% 248.43/58.64 (15) all_252_12 = e2
% 248.43/58.64 (16) ~ (all_244_24 = all_20_2)
% 248.43/58.64 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.64 (18) op(e2, e3) = all_10_2
% 248.43/58.64 (19) ~ (e3 = e2)
% 248.43/58.64 (20) op(e0, e0) = all_244_24
% 248.43/58.64 (21) op(all_244_8, all_244_8) = e2
% 248.43/58.64 (22) op(e2, e2) = all_244_8
% 248.43/58.64 (23) all_252_6 = e1
% 248.43/58.64 (24) op(e2, e1) = all_38_2
% 248.43/58.64 (25) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 248.43/58.64 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 248.43/58.64 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 248.43/58.64 (26) ~ (all_84_2 = all_62_2)
% 248.43/58.64 (27) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 248.43/58.64 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 248.43/58.64 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 248.43/58.64 (28) op(e1, e0) = all_34_2
% 248.43/58.64 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.64 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.64 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.64 (30) op(e3, all_38_2) = e2
% 248.43/58.64 (31) ~ (all_20_2 = all_12_2)
% 248.43/58.64 (32) ~ (e2 = e1)
% 248.43/58.64 (33) op(e0, e2) = all_28_2
% 248.43/58.64 (34) ~ (all_244_0 = e2)
% 248.43/58.65 (35) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 248.43/58.65 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.43/58.65 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 248.43/58.65 (36) ~ (all_244_8 = all_38_2)
% 248.43/58.65 (37) op(all_244_15, all_244_15) = e1
% 248.43/58.65 (38) ~ (all_244_3 = all_36_2)
% 248.43/58.65 (39) ~ (all_28_2 = all_20_2)
% 248.43/58.65 (40) op(e1, e3) = all_62_2
% 248.43/58.65 (41) op(all_16_2, all_26_2) = e4
% 248.43/58.65 (42) ~ (e3 = e0)
% 248.43/58.65 (43) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.65 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.65 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.65 (44) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.65 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.65 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.65 (45) ~ (all_40_2 = all_10_2)
% 248.43/58.65 (46) all_204_2 = all_36_2
% 248.43/58.65 (47) op(all_20_2, e1) = e0
% 248.43/58.65 (48) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.43/58.65 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.43/58.65 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.43/58.65 (49) ~ (e3 = e1)
% 248.43/58.65 (50) op(e3, e1) = all_36_2
% 248.43/58.65 (51) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.43/58.65 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.43/58.65 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.65 (52) ~ (all_40_2 = all_34_2)
% 248.43/58.65 (53) all_190_2 = all_38_2
% 248.43/58.65 (54) op(e0, e3) = all_22_2
% 248.43/58.65 (55) ~ (all_40_2 = e1)
% 248.43/58.65 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.65 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.65 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.65 (57) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.43/58.65 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.43/58.65 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.43/58.65 (58) op(all_62_2, e3) = e1
% 248.43/58.65 (59) op(e4, e1) = all_26_2
% 248.43/58.65 (60) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.65 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.65 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.65 (61) ~ (all_244_15 = all_62_2)
% 248.43/58.65 (62) ~ (all_244_8 = e1)
% 248.43/58.65 (63) op(e4, e4) = all_244_0
% 248.43/58.65 (64) all_230_2 = all_20_2
% 248.43/58.65 (65) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.65 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.65 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.65 (66) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.43/58.65 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.43/58.65 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.65 (67) ~ (e4 = e3)
% 248.43/58.65 (68) op(e1, e1) = all_244_15
% 248.43/58.65 (69) op(e0, e1) = all_20_2
% 248.43/58.65 (70) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.43/58.65 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.43/58.65 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.65 (71) ~ (all_26_2 = e3)
% 248.43/58.65 (72) op(e1, e2) = all_4_2
% 248.43/58.65 (73) op(all_4_2, all_38_2) = e2
% 248.43/58.65 (74) op(e4, e3) = all_84_2
% 248.43/58.65 (75) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 248.43/58.65 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 248.43/58.65 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 248.43/58.65 (76) ~ (all_22_2 = all_20_2)
% 248.43/58.65 (77) op(all_36_2, e1) = e3
% 248.43/58.65 (78) ~ (all_38_2 = all_10_2)
% 248.43/58.65 (79) ~ (all_20_2 = e4)
% 248.43/58.65 (80) op(all_16_2, e4) = e1
% 248.43/58.65 (81) op(e2, e0) = all_40_2
% 248.43/58.65 (82) op(e3, e3) = all_244_3
% 248.43/58.65 (83) all_46_2 = all_36_2
% 248.43/58.65 (84) op(e0, e4) = all_12_2
% 248.43/58.65 (85) all_76_2 = all_40_2
% 248.43/58.65
% 248.43/58.65 Begin of proof
% 248.43/58.65 |
% 248.43/58.65 | GROUND_INST: instantiating (17) with all_28_2, all_30_1, e2, e0, simplifying
% 248.43/58.65 | with (11), (33) gives:
% 248.43/58.65 | (86) all_30_1 = all_28_2
% 248.43/58.65 |
% 248.43/58.65 | GROUND_INST: instantiating (17) with all_40_2, e4, e0, e2, simplifying with
% 248.43/58.65 | (13), (81) gives:
% 248.43/58.65 | (87) all_40_2 = e4
% 248.43/58.65 |
% 248.43/58.65 | COMBINE_EQS: (85), (87) imply:
% 248.43/58.65 | (88) all_76_2 = e4
% 248.43/58.65 |
% 248.43/58.65 | REDUCE: (8), (87) imply:
% 248.43/58.65 | (89) ~ (all_38_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | SIMP: (89) implies:
% 248.43/58.65 | (90) ~ (all_38_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | REDUCE: (52), (87) imply:
% 248.43/58.65 | (91) ~ (all_34_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | SIMP: (91) implies:
% 248.43/58.65 | (92) ~ (all_34_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | REDUCE: (45), (87) imply:
% 248.43/58.65 | (93) ~ (all_10_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | SIMP: (93) implies:
% 248.43/58.65 | (94) ~ (all_10_2 = e4)
% 248.43/58.65 |
% 248.43/58.65 | REDUCE: (55), (87) imply:
% 248.43/58.65 | (95) ~ (e4 = e1)
% 248.43/58.65 |
% 248.43/58.65 | BETA: splitting (6) gives:
% 248.43/58.65 |
% 248.43/58.65 | Case 1:
% 248.43/58.65 | |
% 248.43/58.65 | | (96) ~ (all_76_2 = e4)
% 248.43/58.65 | |
% 248.43/58.65 | | REDUCE: (88), (96) imply:
% 248.43/58.65 | | (97) $false
% 248.43/58.65 | |
% 248.43/58.65 | | CLOSE: (97) is inconsistent.
% 248.43/58.65 | |
% 248.43/58.65 | Case 2:
% 248.43/58.65 | |
% 248.43/58.65 | | (98) ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0, e4) =
% 248.43/58.65 | | all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 = e1) &
% 248.43/58.65 | | op(e0, e4) = all_76_1 & $i(all_76_1))
% 248.43/58.65 | |
% 248.43/58.65 | | BETA: splitting (48) gives:
% 248.43/58.65 | |
% 248.43/58.65 | | Case 1:
% 248.43/58.65 | | |
% 248.43/58.65 | | | (99) ~ (all_40_2 = e4)
% 248.43/58.65 | | |
% 248.43/58.65 | | | REF_CLOSE: (13), (17), (81), (99) are inconsistent by sub-proof #707.
% 248.43/58.65 | | |
% 248.43/58.65 | | Case 2:
% 248.43/58.65 | | |
% 248.43/58.65 | | | (100) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 248.43/58.65 | | | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 248.43/58.65 | | | op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.43/58.65 | | |
% 248.43/58.65 | | | BETA: splitting (57) gives:
% 248.43/58.65 | | |
% 248.43/58.65 | | | Case 1:
% 248.43/58.65 | | | |
% 248.43/58.65 | | | | (101) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 248.43/58.65 | | | | e3) = e4)
% 248.43/58.65 | | | |
% 248.43/58.65 | | | | REF_CLOSE: (17), (18), (23), (94), (95), (101) are inconsistent by
% 248.43/58.65 | | | | sub-proof #236.
% 248.43/58.65 | | | |
% 248.43/58.65 | | | Case 2:
% 248.43/58.65 | | | |
% 248.43/58.65 | | | | (102) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2,
% 248.43/58.65 | | | | e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.43/58.65 | | | |
% 248.43/58.65 | | | | BETA: splitting (102) gives:
% 248.43/58.65 | | | |
% 248.43/58.65 | | | | Case 1:
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | (103) all_252_8 = e4 & op(e2, e2) = e4
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | ALPHA: (103) implies:
% 248.43/58.65 | | | | | (104) op(e2, e2) = e4
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | REF_CLOSE: (17), (21), (22), (34), (63), (104) are inconsistent by
% 248.43/58.65 | | | | | sub-proof #626.
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | Case 2:
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | (105) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 248.43/58.65 | | | | | op(e2, e0) = e4)
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | BETA: splitting (105) gives:
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | | Case 1:
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | (106) all_252_11 = e4 & op(e2, e1) = e4
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | ALPHA: (106) implies:
% 248.43/58.65 | | | | | | (107) op(e2, e1) = e4
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | REF_CLOSE: (17), (24), (90), (107) are inconsistent by sub-proof
% 248.43/58.65 | | | | | | #935.
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | Case 2:
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | (108) all_252_18 = e4 & op(e2, e0) = e4
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | ALPHA: (108) implies:
% 248.43/58.65 | | | | | | (109) all_252_18 = e4
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | BETA: splitting (10) gives:
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | | Case 1:
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | (110) ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0,
% 248.43/58.65 | | | | | | | e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | ALPHA: (110) implies:
% 248.43/58.65 | | | | | | | (111) op(e0, e2) = all_54_1
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (12), (14), (15),
% 248.43/58.65 | | | | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 248.43/58.65 | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 248.43/58.65 | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 248.43/58.65 | | | | | | | (46), (47), (49), (50), (51), (53), (54), (56), (58),
% 248.43/58.65 | | | | | | | (59), (60), (61), (62), (64), (65), (66), (67), (68),
% 248.43/58.65 | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 248.43/58.65 | | | | | | | (78), (79), (80), (82), (83), (84), (90), (92), (95),
% 248.43/58.65 | | | | | | | (98), (100), (109), (111) are inconsistent by sub-proof
% 248.43/58.65 | | | | | | | #47.
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | Case 2:
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | (112) ~ (all_54_1 = e3) & op(e0, e2) = all_54_1 & $i(all_54_1)
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | ALPHA: (112) implies:
% 248.43/58.65 | | | | | | | (113) op(e0, e2) = all_54_1
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (12), (14), (15),
% 248.43/58.65 | | | | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 248.43/58.65 | | | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 248.43/58.65 | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 248.43/58.65 | | | | | | | (46), (47), (49), (50), (51), (53), (54), (56), (58),
% 248.43/58.65 | | | | | | | (59), (60), (61), (62), (64), (65), (66), (67), (68),
% 248.43/58.65 | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 248.43/58.65 | | | | | | | (78), (79), (80), (82), (83), (84), (90), (92), (95),
% 248.43/58.65 | | | | | | | (98), (100), (109), (113) are inconsistent by sub-proof
% 248.43/58.65 | | | | | | | #47.
% 248.43/58.65 | | | | | | |
% 248.43/58.65 | | | | | | End of split
% 248.43/58.65 | | | | | |
% 248.43/58.65 | | | | | End of split
% 248.43/58.65 | | | | |
% 248.43/58.65 | | | | End of split
% 248.43/58.65 | | | |
% 248.43/58.65 | | | End of split
% 248.43/58.65 | | |
% 248.43/58.65 | | End of split
% 248.43/58.65 | |
% 248.43/58.65 | End of split
% 248.43/58.65 |
% 248.43/58.65 End of proof
% 248.43/58.65
% 248.43/58.65 Sub-proof #47 shows that the following formulas are inconsistent:
% 248.43/58.65 ----------------------------------------------------------------
% 248.43/58.65 (1) all_32_2 = all_20_2
% 248.43/58.65 (2) ~ (all_26_2 = e2)
% 248.43/58.65 (3) ~ (all_4_2 = e4)
% 248.43/58.65 (4) all_120_2 = e1
% 248.43/58.65 (5) op(all_4_2, e2) = e1
% 248.43/58.65 (6) ~ (all_38_2 = e1)
% 248.43/58.65 (7) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 248.43/58.65 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 248.43/58.65 | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.43/58.65 (8) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.43/58.65 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.43/58.65 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.65 (9) op(e2, all_26_2) = e4
% 248.43/58.65 (10) all_252_12 = e2
% 248.43/58.65 (11) ~ (all_244_24 = all_20_2)
% 248.43/58.65 (12) all_252_18 = e4
% 248.43/58.65 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.65 (14) op(e2, e3) = all_10_2
% 248.43/58.65 (15) ~ (e3 = e2)
% 248.43/58.65 (16) op(e0, e0) = all_244_24
% 248.43/58.65 (17) op(e2, e2) = all_244_8
% 248.43/58.65 (18) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 248.43/58.65 all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0,
% 248.43/58.65 e4) = all_40_1 & $i(all_40_1))
% 248.43/58.65 (19) all_252_6 = e1
% 248.43/58.65 (20) op(e2, e1) = all_38_2
% 248.43/58.65 (21) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 248.43/58.65 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 248.43/58.65 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 248.43/58.65 (22) ~ (all_84_2 = all_62_2)
% 248.43/58.65 (23) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 248.43/58.65 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 248.43/58.65 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 248.43/58.65 (24) op(e1, e0) = all_34_2
% 248.43/58.65 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.65 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.65 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.65 (26) op(e3, all_38_2) = e2
% 248.43/58.65 (27) ~ (all_20_2 = all_12_2)
% 248.43/58.65 (28) ~ (e2 = e1)
% 248.43/58.65 (29) ~ (all_34_2 = e4)
% 248.43/58.65 (30) op(e0, e2) = all_28_2
% 248.43/58.65 (31) ~ (e4 = e1)
% 248.43/58.65 (32) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 248.43/58.65 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.43/58.65 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 248.43/58.65 (33) ~ (all_244_8 = all_38_2)
% 248.43/58.65 (34) op(all_244_15, all_244_15) = e1
% 248.43/58.65 (35) ~ (all_244_3 = all_36_2)
% 248.43/58.65 (36) ~ (all_28_2 = all_20_2)
% 248.43/58.65 (37) op(e1, e3) = all_62_2
% 248.43/58.65 (38) op(all_16_2, all_26_2) = e4
% 248.43/58.65 (39) ~ (e3 = e0)
% 248.43/58.65 (40) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.65 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.65 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.65 (41) op(e0, e2) = all_54_1
% 248.43/58.65 (42) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.65 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.65 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.65 (43) all_204_2 = all_36_2
% 248.43/58.65 (44) op(all_20_2, e1) = e0
% 248.43/58.65 (45) ~ (e3 = e1)
% 248.43/58.65 (46) op(e3, e1) = all_36_2
% 248.43/58.65 (47) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.43/58.65 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.43/58.65 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.65 (48) ~ (all_38_2 = e4)
% 248.43/58.65 (49) all_190_2 = all_38_2
% 248.43/58.65 (50) op(e0, e3) = all_22_2
% 248.43/58.65 (51) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.65 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.65 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.65 (52) op(all_62_2, e3) = e1
% 248.43/58.65 (53) op(e4, e1) = all_26_2
% 248.43/58.65 (54) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.65 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.65 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.65 (55) ~ (all_244_15 = all_62_2)
% 248.43/58.65 (56) ~ (all_244_8 = e1)
% 248.43/58.66 (57) all_230_2 = all_20_2
% 248.43/58.66 (58) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.66 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.66 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.66 (59) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.43/58.66 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.43/58.66 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.66 (60) ~ (e4 = e3)
% 248.43/58.66 (61) op(e1, e1) = all_244_15
% 248.43/58.66 (62) op(e0, e1) = all_20_2
% 248.43/58.66 (63) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.43/58.66 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.43/58.66 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.66 (64) ~ (all_26_2 = e3)
% 248.43/58.66 (65) op(e1, e2) = all_4_2
% 248.43/58.66 (66) op(all_4_2, all_38_2) = e2
% 248.43/58.66 (67) op(e4, e3) = all_84_2
% 248.43/58.66 (68) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 248.43/58.66 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 248.43/58.66 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 248.43/58.66 (69) ~ (all_22_2 = all_20_2)
% 248.43/58.66 (70) op(all_36_2, e1) = e3
% 248.43/58.66 (71) ~ (all_38_2 = all_10_2)
% 248.43/58.66 (72) ~ (all_20_2 = e4)
% 248.43/58.66 (73) op(all_16_2, e4) = e1
% 248.43/58.66 (74) ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0, e4) =
% 248.43/58.66 all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 = e1) & op(e0,
% 248.43/58.66 e4) = all_76_1 & $i(all_76_1))
% 248.43/58.66 (75) op(e3, e3) = all_244_3
% 248.43/58.66 (76) all_46_2 = all_36_2
% 248.43/58.66 (77) op(e0, e4) = all_12_2
% 248.43/58.66
% 248.43/58.66 Begin of proof
% 248.43/58.66 |
% 248.43/58.66 | BETA: splitting (18) gives:
% 248.43/58.66 |
% 248.43/58.66 | Case 1:
% 248.43/58.66 | |
% 248.43/58.66 | | (78) ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 248.43/58.66 | | all_40_1 & $i(all_40_0) & $i(all_40_1)
% 248.43/58.66 | |
% 248.43/58.66 | | ALPHA: (78) implies:
% 248.43/58.66 | | (79) op(e0, e4) = all_40_1
% 248.43/58.66 | |
% 248.43/58.66 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.43/58.66 | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 248.43/58.66 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 248.43/58.66 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 248.43/58.66 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 248.43/58.66 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.43/58.66 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (79) are
% 248.43/58.66 | | inconsistent by sub-proof #48.
% 248.43/58.66 | |
% 248.43/58.66 | Case 2:
% 248.43/58.66 | |
% 248.43/58.66 | | (80) ~ (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1)
% 248.43/58.66 | |
% 248.43/58.66 | | ALPHA: (80) implies:
% 248.43/58.66 | | (81) op(e0, e4) = all_40_1
% 248.43/58.66 | |
% 248.43/58.66 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.43/58.66 | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 248.43/58.66 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 248.43/58.66 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 248.43/58.66 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 248.43/58.66 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.43/58.66 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (81) are
% 248.43/58.66 | | inconsistent by sub-proof #48.
% 248.43/58.66 | |
% 248.43/58.66 | End of split
% 248.43/58.66 |
% 248.43/58.66 End of proof
% 248.43/58.66
% 248.43/58.66 Sub-proof #48 shows that the following formulas are inconsistent:
% 248.43/58.66 ----------------------------------------------------------------
% 248.43/58.66 (1) all_32_2 = all_20_2
% 248.43/58.66 (2) ~ (all_26_2 = e2)
% 248.43/58.66 (3) ~ (all_4_2 = e4)
% 248.43/58.66 (4) all_120_2 = e1
% 248.43/58.66 (5) op(all_4_2, e2) = e1
% 248.43/58.66 (6) ~ (all_38_2 = e1)
% 248.43/58.66 (7) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 248.43/58.66 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 248.43/58.66 | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.43/58.66 (8) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.43/58.66 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.43/58.66 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.66 (9) op(e2, all_26_2) = e4
% 248.43/58.66 (10) all_252_12 = e2
% 248.43/58.66 (11) ~ (all_244_24 = all_20_2)
% 248.43/58.66 (12) all_252_18 = e4
% 248.43/58.66 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.66 (14) op(e2, e3) = all_10_2
% 248.43/58.66 (15) ~ (e3 = e2)
% 248.43/58.66 (16) op(e0, e0) = all_244_24
% 248.43/58.66 (17) op(e2, e2) = all_244_8
% 248.43/58.66 (18) all_252_6 = e1
% 248.43/58.66 (19) op(e2, e1) = all_38_2
% 248.43/58.66 (20) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 248.43/58.66 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 248.43/58.66 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 248.43/58.66 (21) ~ (all_84_2 = all_62_2)
% 248.43/58.66 (22) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 248.43/58.66 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 248.43/58.66 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 248.43/58.66 (23) op(e1, e0) = all_34_2
% 248.43/58.66 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.66 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.66 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.66 (25) op(e3, all_38_2) = e2
% 248.43/58.66 (26) ~ (all_20_2 = all_12_2)
% 248.43/58.66 (27) ~ (e2 = e1)
% 248.43/58.66 (28) ~ (all_34_2 = e4)
% 248.43/58.66 (29) op(e0, e2) = all_28_2
% 248.43/58.66 (30) ~ (e4 = e1)
% 248.43/58.66 (31) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 248.43/58.66 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.43/58.66 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 248.43/58.66 (32) ~ (all_244_8 = all_38_2)
% 248.43/58.66 (33) op(all_244_15, all_244_15) = e1
% 248.43/58.66 (34) ~ (all_244_3 = all_36_2)
% 248.43/58.66 (35) ~ (all_28_2 = all_20_2)
% 248.43/58.66 (36) op(e1, e3) = all_62_2
% 248.43/58.66 (37) op(all_16_2, all_26_2) = e4
% 248.43/58.66 (38) ~ (e3 = e0)
% 248.43/58.66 (39) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.66 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.66 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.66 (40) op(e0, e2) = all_54_1
% 248.43/58.66 (41) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.66 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.66 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.66 (42) all_204_2 = all_36_2
% 248.43/58.66 (43) op(all_20_2, e1) = e0
% 248.43/58.66 (44) ~ (e3 = e1)
% 248.43/58.66 (45) op(e3, e1) = all_36_2
% 248.43/58.66 (46) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.43/58.66 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.43/58.66 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.66 (47) ~ (all_38_2 = e4)
% 248.43/58.66 (48) all_190_2 = all_38_2
% 248.43/58.66 (49) op(e0, e3) = all_22_2
% 248.43/58.66 (50) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.66 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.66 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.66 (51) op(all_62_2, e3) = e1
% 248.43/58.66 (52) op(e4, e1) = all_26_2
% 248.43/58.66 (53) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.66 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.66 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.66 (54) ~ (all_244_15 = all_62_2)
% 248.43/58.66 (55) ~ (all_244_8 = e1)
% 248.43/58.66 (56) all_230_2 = all_20_2
% 248.43/58.66 (57) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.66 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.66 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.66 (58) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.43/58.66 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.43/58.66 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.66 (59) ~ (e4 = e3)
% 248.43/58.66 (60) op(e1, e1) = all_244_15
% 248.43/58.66 (61) op(e0, e1) = all_20_2
% 248.43/58.66 (62) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.43/58.66 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.43/58.66 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.66 (63) ~ (all_26_2 = e3)
% 248.43/58.66 (64) op(e1, e2) = all_4_2
% 248.43/58.66 (65) op(all_4_2, all_38_2) = e2
% 248.43/58.66 (66) op(e4, e3) = all_84_2
% 248.43/58.66 (67) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 248.43/58.66 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 248.43/58.66 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 248.43/58.66 (68) ~ (all_22_2 = all_20_2)
% 248.43/58.66 (69) op(all_36_2, e1) = e3
% 248.43/58.66 (70) ~ (all_38_2 = all_10_2)
% 248.43/58.66 (71) ~ (all_20_2 = e4)
% 248.43/58.66 (72) op(all_16_2, e4) = e1
% 248.43/58.66 (73) ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0, e4) =
% 248.43/58.66 all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 = e1) & op(e0,
% 248.43/58.66 e4) = all_76_1 & $i(all_76_1))
% 248.43/58.66 (74) op(e0, e4) = all_40_1
% 248.43/58.66 (75) op(e3, e3) = all_244_3
% 248.43/58.66 (76) all_46_2 = all_36_2
% 248.43/58.66 (77) op(e0, e4) = all_12_2
% 248.43/58.66
% 248.43/58.66 Begin of proof
% 248.43/58.66 |
% 248.43/58.66 | GROUND_INST: instantiating (13) with all_28_2, all_54_1, e2, e0, simplifying
% 248.43/58.66 | with (29), (40) gives:
% 248.43/58.66 | (78) all_54_1 = all_28_2
% 248.43/58.66 |
% 248.43/58.66 | GROUND_INST: instantiating (13) with all_12_2, all_40_1, e4, e0, simplifying
% 248.43/58.66 | with (74), (77) gives:
% 248.43/58.66 | (79) all_40_1 = all_12_2
% 248.43/58.66 |
% 248.43/58.66 | BETA: splitting (73) gives:
% 248.43/58.66 |
% 248.43/58.66 | Case 1:
% 248.43/58.66 | |
% 248.43/58.66 | | (80) ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0, e4) =
% 248.43/58.66 | | all_76_1 & $i(all_76_0) & $i(all_76_1)
% 248.43/58.66 | |
% 248.43/58.66 | | ALPHA: (80) implies:
% 248.43/58.66 | | (81) op(e0, e4) = all_76_1
% 248.43/58.66 | |
% 248.43/58.66 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.43/58.66 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 248.43/58.66 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 248.43/58.66 | | (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 248.43/58.66 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 248.43/58.66 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.43/58.66 | | (69), (70), (71), (72), (74), (75), (76), (77), (81) are
% 248.43/58.66 | | inconsistent by sub-proof #49.
% 248.43/58.66 | |
% 248.43/58.66 | Case 2:
% 248.43/58.66 | |
% 248.43/58.66 | | (82) ~ (all_76_1 = e1) & op(e0, e4) = all_76_1 & $i(all_76_1)
% 248.43/58.66 | |
% 248.43/58.66 | | ALPHA: (82) implies:
% 248.43/58.66 | | (83) op(e0, e4) = all_76_1
% 248.43/58.66 | |
% 248.43/58.66 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.43/58.66 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 248.43/58.66 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 248.43/58.66 | | (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 248.43/58.66 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 248.43/58.66 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.43/58.66 | | (69), (70), (71), (72), (74), (75), (76), (77), (83) are
% 248.43/58.66 | | inconsistent by sub-proof #49.
% 248.43/58.66 | |
% 248.43/58.66 | End of split
% 248.43/58.66 |
% 248.43/58.66 End of proof
% 248.43/58.66
% 248.43/58.66 Sub-proof #49 shows that the following formulas are inconsistent:
% 248.43/58.66 ----------------------------------------------------------------
% 248.43/58.66 (1) all_32_2 = all_20_2
% 248.43/58.66 (2) ~ (all_26_2 = e2)
% 248.43/58.66 (3) ~ (all_4_2 = e4)
% 248.43/58.66 (4) all_120_2 = e1
% 248.43/58.66 (5) op(all_4_2, e2) = e1
% 248.43/58.66 (6) ~ (all_38_2 = e1)
% 248.43/58.66 (7) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 248.43/58.66 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 248.43/58.66 | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.43/58.66 (8) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.43/58.66 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.43/58.66 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.66 (9) op(e2, all_26_2) = e4
% 248.43/58.66 (10) all_252_12 = e2
% 248.43/58.66 (11) ~ (all_244_24 = all_20_2)
% 248.43/58.66 (12) all_252_18 = e4
% 248.43/58.66 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.66 (14) op(e2, e3) = all_10_2
% 248.43/58.66 (15) ~ (e3 = e2)
% 248.43/58.66 (16) op(e0, e0) = all_244_24
% 248.43/58.66 (17) op(e2, e2) = all_244_8
% 248.43/58.66 (18) all_252_6 = e1
% 248.43/58.66 (19) op(e2, e1) = all_38_2
% 248.43/58.66 (20) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 248.43/58.66 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 248.43/58.66 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 248.43/58.66 (21) ~ (all_84_2 = all_62_2)
% 248.43/58.66 (22) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 248.43/58.66 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 248.43/58.66 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 248.43/58.66 (23) op(e1, e0) = all_34_2
% 248.43/58.66 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.66 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.66 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.66 (25) op(e3, all_38_2) = e2
% 248.43/58.66 (26) ~ (all_20_2 = all_12_2)
% 248.43/58.66 (27) ~ (e2 = e1)
% 248.43/58.66 (28) ~ (all_34_2 = e4)
% 248.43/58.66 (29) op(e0, e2) = all_28_2
% 248.43/58.66 (30) ~ (e4 = e1)
% 248.43/58.67 (31) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 248.43/58.67 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.43/58.67 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 248.43/58.67 (32) ~ (all_244_8 = all_38_2)
% 248.43/58.67 (33) op(all_244_15, all_244_15) = e1
% 248.43/58.67 (34) ~ (all_244_3 = all_36_2)
% 248.43/58.67 (35) ~ (all_28_2 = all_20_2)
% 248.43/58.67 (36) op(e1, e3) = all_62_2
% 248.43/58.67 (37) op(all_16_2, all_26_2) = e4
% 248.43/58.67 (38) ~ (e3 = e0)
% 248.43/58.67 (39) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.67 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.67 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.67 (40) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.67 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.67 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.67 (41) all_204_2 = all_36_2
% 248.43/58.67 (42) op(all_20_2, e1) = e0
% 248.43/58.67 (43) ~ (e3 = e1)
% 248.43/58.67 (44) op(e3, e1) = all_36_2
% 248.43/58.67 (45) op(e0, e4) = all_76_1
% 248.43/58.67 (46) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.43/58.67 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.43/58.67 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.67 (47) ~ (all_38_2 = e4)
% 248.43/58.67 (48) all_190_2 = all_38_2
% 248.43/58.67 (49) op(e0, e3) = all_22_2
% 248.43/58.67 (50) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.67 (51) op(all_62_2, e3) = e1
% 248.43/58.67 (52) op(e4, e1) = all_26_2
% 248.43/58.67 (53) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.67 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.67 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.67 (54) ~ (all_244_15 = all_62_2)
% 248.43/58.67 (55) ~ (all_244_8 = e1)
% 248.43/58.67 (56) all_230_2 = all_20_2
% 248.43/58.67 (57) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.67 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.67 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.67 (58) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.43/58.67 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.43/58.67 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.67 (59) ~ (e4 = e3)
% 248.43/58.67 (60) op(e1, e1) = all_244_15
% 248.43/58.67 (61) op(e0, e1) = all_20_2
% 248.43/58.67 (62) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.43/58.67 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.43/58.67 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.67 (63) ~ (all_26_2 = e3)
% 248.43/58.67 (64) op(e1, e2) = all_4_2
% 248.43/58.67 (65) op(all_4_2, all_38_2) = e2
% 248.43/58.67 (66) op(e4, e3) = all_84_2
% 248.43/58.67 (67) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 248.43/58.67 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 248.43/58.67 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 248.43/58.67 (68) ~ (all_22_2 = all_20_2)
% 248.43/58.67 (69) op(all_36_2, e1) = e3
% 248.43/58.67 (70) ~ (all_38_2 = all_10_2)
% 248.43/58.67 (71) ~ (all_20_2 = e4)
% 248.43/58.67 (72) op(all_16_2, e4) = e1
% 248.43/58.67 (73) op(e0, e4) = all_40_1
% 248.43/58.67 (74) op(e3, e3) = all_244_3
% 248.43/58.67 (75) all_46_2 = all_36_2
% 248.43/58.67 (76) op(e0, e4) = all_12_2
% 248.43/58.67
% 248.43/58.67 Begin of proof
% 248.43/58.67 |
% 248.43/58.67 | GROUND_INST: instantiating (13) with all_12_2, all_76_1, e4, e0, simplifying
% 248.43/58.67 | with (45), (76) gives:
% 248.43/58.67 | (77) all_76_1 = all_12_2
% 248.43/58.67 |
% 248.43/58.67 | BETA: splitting (39) gives:
% 248.43/58.67 |
% 248.43/58.67 | Case 1:
% 248.43/58.67 | |
% 248.43/58.67 | | (78) ~ (all_32_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (1), (78) imply:
% 248.43/58.67 | | (79) ~ (all_20_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REF_CLOSE: (2), (5), (6), (13), (17), (19), (25), (33), (34), (41), (44),
% 248.43/58.67 | | (46), (52), (55), (57), (58), (60), (61), (65), (69), (74), (75),
% 248.43/58.67 | | (79) are inconsistent by sub-proof #74.
% 248.43/58.67 | |
% 248.43/58.67 | Case 2:
% 248.43/58.67 | |
% 248.43/58.67 | | (80) all_32_2 = e2
% 248.43/58.67 | |
% 248.43/58.67 | | COMBINE_EQS: (1), (80) imply:
% 248.43/58.67 | | (81) all_20_2 = e2
% 248.43/58.67 | |
% 248.43/58.67 | | COMBINE_EQS: (56), (81) imply:
% 248.43/58.67 | | (82) all_230_2 = e2
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (11), (81) imply:
% 248.43/58.67 | | (83) ~ (all_244_24 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (35), (81) imply:
% 248.43/58.67 | | (84) ~ (all_28_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (68), (81) imply:
% 248.43/58.67 | | (85) ~ (all_22_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (26), (81) imply:
% 248.43/58.67 | | (86) ~ (all_12_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | SIMP: (86) implies:
% 248.43/58.67 | | (87) ~ (all_12_2 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (71), (81) imply:
% 248.43/58.67 | | (88) ~ (e4 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | SIMP: (88) implies:
% 248.43/58.67 | | (89) ~ (e4 = e2)
% 248.43/58.67 | |
% 248.43/58.67 | | REDUCE: (42), (81) imply:
% 248.43/58.67 | | (90) op(e2, e1) = e0
% 248.43/58.67 | |
% 248.43/58.67 | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15), (16),
% 248.43/58.67 | | (17), (18), (19), (20), (21), (22), (23), (24), (27), (28), (29),
% 248.43/58.67 | | (30), (31), (32), (36), (37), (38), (40), (43), (44), (47), (48),
% 248.43/58.67 | | (49), (50), (51), (52), (53), (54), (59), (60), (61), (62), (63),
% 248.43/58.67 | | (64), (66), (67), (69), (70), (71), (72), (73), (76), (82), (83),
% 248.43/58.67 | | (84), (85), (87), (89), (90) are inconsistent by sub-proof #222.
% 248.43/58.67 | |
% 248.43/58.67 | End of split
% 248.43/58.67 |
% 248.43/58.67 End of proof
% 248.43/58.67
% 248.43/58.67 Sub-proof #50 shows that the following formulas are inconsistent:
% 248.43/58.67 ----------------------------------------------------------------
% 248.43/58.67 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.67 (2) op(e4, e4) = all_244_0
% 248.43/58.67 (3) op(e4, e4) = e1
% 248.43/58.67 (4) ~ (all_244_0 = e1)
% 248.43/58.67
% 248.43/58.67 Begin of proof
% 248.43/58.67 |
% 248.43/58.67 | GROUND_INST: instantiating (1) with all_244_0, e1, e4, e4, simplifying with
% 248.43/58.67 | (2), (3) gives:
% 248.43/58.67 | (5) all_244_0 = e1
% 248.43/58.67 |
% 248.43/58.67 | REDUCE: (4), (5) imply:
% 248.43/58.67 | (6) $false
% 248.43/58.67 |
% 248.43/58.67 | CLOSE: (6) is inconsistent.
% 248.43/58.67 |
% 248.43/58.67 End of proof
% 248.43/58.67
% 248.43/58.67 Sub-proof #51 shows that the following formulas are inconsistent:
% 248.43/58.67 ----------------------------------------------------------------
% 248.43/58.67 (1) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4) = all_20_1
% 248.43/58.67 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4) =
% 248.43/58.67 all_20_1 & $i(all_20_1))
% 248.43/58.67 (2) all_252_14 = e3
% 248.43/58.67 (3) op(e4, e1) = e0
% 248.43/58.67 (4) ~ (e2 = e0)
% 248.43/58.67 (5) op(e4, all_34_2) = e1
% 248.43/58.67 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.67 (7) ~ (e3 = e2)
% 248.43/58.67 (8) op(e0, e0) = all_244_24
% 248.43/58.67 (9) op(e2, e2) = all_244_8
% 248.43/58.67 (10) op(e2, e1) = all_38_2
% 248.43/58.67 (11) ~ (all_244_15 = all_26_2)
% 248.43/58.67 (12) op(e1, e0) = all_34_2
% 248.43/58.67 (13) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.43/58.67 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.43/58.67 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.67 (14) op(e4, e2) = all_6_2
% 248.43/58.67 (15) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.43/58.67 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.43/58.67 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.43/58.67 (16) ~ (all_244_15 = e4)
% 248.43/58.67 (17) ~ (all_222_2 = e0) | ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 &
% 248.43/58.67 op(e0, all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | ( ~
% 248.43/58.67 (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 248.43/58.67 (18) op(e0, e2) = all_28_2
% 248.43/58.67 (19) ~ (e4 = e1)
% 248.43/58.67 (20) ~ (all_28_2 = e1)
% 248.43/58.67 (21) ~ (all_6_2 = e1)
% 248.43/58.67 (22) op(all_244_15, all_244_15) = e1
% 248.43/58.67 (23) op(e1, e4) = all_16_2
% 248.43/58.67 (24) ~ (all_36_2 = e4)
% 248.43/58.67 (25) ~ (e3 = e1)
% 248.43/58.67 (26) op(e3, e1) = all_36_2
% 248.43/58.67 (27) ~ (all_16_2 = e2)
% 248.43/58.67 (28) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.43/58.67 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.67 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.67 (29) ~ (all_38_2 = e4)
% 248.43/58.67 (30) op(e1, e4) = all_60_1
% 248.43/58.67 (31) all_222_2 = all_26_2
% 248.43/58.67 (32) op(all_22_2, e3) = e0
% 248.43/58.67 (33) op(e0, e3) = all_22_2
% 248.43/58.67 (34) ~ (all_26_2 = e4)
% 248.43/58.67 (35) op(e4, e1) = all_26_2
% 248.43/58.67 (36) ~ (all_244_8 = e1)
% 248.43/58.67 (37) op(e1, e1) = all_244_15
% 248.43/58.67 (38) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.43/58.67 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.43/58.67 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.43/58.67 (39) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.43/58.67 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.43/58.67 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.43/58.67 (40) op(all_244_24, all_244_24) = e0
% 248.43/58.67 (41) all_252_20 = e3
% 248.43/58.67
% 248.43/58.67 Begin of proof
% 248.43/58.67 |
% 248.43/58.67 | BETA: splitting (13) gives:
% 248.43/58.67 |
% 248.43/58.67 | Case 1:
% 248.43/58.67 | |
% 248.43/58.67 | | (42) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 248.43/58.67 | | e4)
% 248.43/58.67 | |
% 248.43/58.67 | | BETA: splitting (42) gives:
% 248.43/58.67 | |
% 248.43/58.67 | | Case 1:
% 248.43/58.67 | | |
% 248.43/58.67 | | | (43) all_252_9 = e4 & op(e4, e1) = e4
% 248.43/58.67 | | |
% 248.43/58.67 | | | REF_CLOSE: (6), (34), (35), (43) are inconsistent by sub-proof #114.
% 248.43/58.67 | | |
% 248.43/58.67 | | Case 2:
% 248.43/58.67 | | |
% 248.43/58.67 | | | (44) all_252_10 = e4 & op(e3, e1) = e4
% 248.43/58.67 | | |
% 248.43/58.67 | | | REF_CLOSE: (6), (24), (26), (44) are inconsistent by sub-proof #914.
% 248.43/58.67 | | |
% 248.43/58.67 | | End of split
% 248.43/58.67 | |
% 248.43/58.67 | Case 2:
% 248.43/58.67 | |
% 248.43/58.67 | | (45) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 248.43/58.67 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.43/58.67 | |
% 248.43/58.67 | | BETA: splitting (45) gives:
% 248.43/58.67 | |
% 248.43/58.67 | | Case 1:
% 248.43/58.67 | | |
% 248.43/58.67 | | | (46) all_252_11 = e4 & op(e2, e1) = e4
% 248.43/58.67 | | |
% 248.43/58.67 | | | ALPHA: (46) implies:
% 248.43/58.67 | | | (47) op(e2, e1) = e4
% 248.43/58.67 | | |
% 248.43/58.67 | | | REF_CLOSE: (6), (10), (29), (47) are inconsistent by sub-proof #935.
% 248.43/58.67 | | |
% 248.43/58.67 | | Case 2:
% 248.43/58.67 | | |
% 248.43/58.67 | | | (48) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0,
% 248.43/58.67 | | | e1) = e4)
% 248.43/58.67 | | |
% 248.43/58.67 | | | BETA: splitting (48) gives:
% 248.43/58.67 | | |
% 248.43/58.67 | | | Case 1:
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | (49) all_252_15 = e4 & op(e1, e1) = e4
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | ALPHA: (49) implies:
% 248.43/58.67 | | | | (50) op(e1, e1) = e4
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | REF_CLOSE: (6), (16), (37), (50) are inconsistent by sub-proof #756.
% 248.43/58.67 | | | |
% 248.43/58.67 | | | Case 2:
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | (51) all_252_23 = e4 & op(e0, e1) = e4
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | ALPHA: (51) implies:
% 248.43/58.67 | | | | (52) all_252_23 = e4
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | GROUND_INST: instantiating (6) with all_16_2, all_60_1, e4, e1,
% 248.43/58.67 | | | | simplifying with (23), (30) gives:
% 248.43/58.67 | | | | (53) all_60_1 = all_16_2
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | GROUND_INST: instantiating (6) with all_26_2, e0, e1, e4, simplifying
% 248.43/58.67 | | | | with (3), (35) gives:
% 248.43/58.67 | | | | (54) all_26_2 = e0
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | COMBINE_EQS: (31), (54) imply:
% 248.43/58.67 | | | | (55) all_222_2 = e0
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | REDUCE: (11), (54) imply:
% 248.43/58.67 | | | | (56) ~ (all_244_15 = e0)
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | BETA: splitting (17) gives:
% 248.43/58.67 | | | |
% 248.43/58.67 | | | | Case 1:
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | (57) ~ (all_222_2 = e0)
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | REDUCE: (55), (57) imply:
% 248.43/58.67 | | | | | (58) $false
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | CLOSE: (58) is inconsistent.
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | Case 2:
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | (59) ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.67 | | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) |
% 248.43/58.67 | | | | | ( ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | BETA: splitting (59) gives:
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | | Case 1:
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | (60) ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.67 | | | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | ALPHA: (60) implies:
% 248.43/58.67 | | | | | | (61) op(e1, e0) = all_222_1
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (14), (15),
% 248.43/58.67 | | | | | | (18), (19), (20), (21), (22), (23), (25), (27), (28),
% 248.43/58.67 | | | | | | (32), (33), (36), (37), (38), (39), (40), (41), (52),
% 248.43/58.67 | | | | | | (56), (61) are inconsistent by sub-proof #52.
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | Case 2:
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | (62) ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1)
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | ALPHA: (62) implies:
% 248.43/58.67 | | | | | | (63) op(e1, e0) = all_222_1
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (14), (15),
% 248.43/58.67 | | | | | | (18), (19), (20), (21), (22), (23), (25), (27), (28),
% 248.43/58.67 | | | | | | (32), (33), (36), (37), (38), (39), (40), (41), (52),
% 248.43/58.67 | | | | | | (56), (63) are inconsistent by sub-proof #52.
% 248.43/58.67 | | | | | |
% 248.43/58.67 | | | | | End of split
% 248.43/58.67 | | | | |
% 248.43/58.67 | | | | End of split
% 248.43/58.67 | | | |
% 248.43/58.67 | | | End of split
% 248.43/58.67 | | |
% 248.43/58.67 | | End of split
% 248.43/58.67 | |
% 248.43/58.67 | End of split
% 248.43/58.67 |
% 248.43/58.67 End of proof
% 248.43/58.67
% 248.43/58.67 Sub-proof #52 shows that the following formulas are inconsistent:
% 248.43/58.67 ----------------------------------------------------------------
% 248.43/58.67 (1) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4) = all_20_1
% 248.43/58.67 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e2) & op(e1, e4) =
% 248.43/58.67 all_20_1 & $i(all_20_1))
% 248.43/58.67 (2) all_252_14 = e3
% 248.43/58.67 (3) ~ (e2 = e0)
% 248.43/58.67 (4) op(e4, all_34_2) = e1
% 248.43/58.67 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.67 (6) ~ (e3 = e2)
% 248.43/58.67 (7) op(e0, e0) = all_244_24
% 248.43/58.67 (8) op(e2, e2) = all_244_8
% 248.43/58.67 (9) op(e1, e0) = all_34_2
% 248.43/58.67 (10) op(e4, e2) = all_6_2
% 248.43/58.67 (11) ~ (all_244_15 = e0)
% 248.43/58.67 (12) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.43/58.67 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.43/58.67 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.43/58.67 (13) op(e0, e2) = all_28_2
% 248.43/58.67 (14) ~ (e4 = e1)
% 248.43/58.67 (15) ~ (all_28_2 = e1)
% 248.43/58.67 (16) ~ (all_6_2 = e1)
% 248.43/58.67 (17) op(all_244_15, all_244_15) = e1
% 248.43/58.67 (18) op(e1, e4) = all_16_2
% 248.43/58.67 (19) op(e1, e0) = all_222_1
% 248.43/58.67 (20) ~ (e3 = e1)
% 248.43/58.67 (21) ~ (all_16_2 = e2)
% 248.43/58.67 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.43/58.67 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.67 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.67 (23) op(all_22_2, e3) = e0
% 248.43/58.68 (24) op(e0, e3) = all_22_2
% 248.43/58.68 (25) ~ (all_244_8 = e1)
% 248.43/58.68 (26) op(e1, e1) = all_244_15
% 248.43/58.68 (27) all_252_23 = e4
% 248.43/58.68 (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.43/58.68 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.43/58.68 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.43/58.68 (29) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.43/58.68 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.43/58.68 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.43/58.68 (30) op(all_244_24, all_244_24) = e0
% 248.43/58.68 (31) all_252_20 = e3
% 248.43/58.68
% 248.43/58.68 Begin of proof
% 248.43/58.68 |
% 248.43/58.68 | BETA: splitting (1) gives:
% 248.43/58.68 |
% 248.43/58.68 | Case 1:
% 248.43/58.68 | |
% 248.43/58.68 | | (32) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4) =
% 248.43/58.68 | | all_20_1 & $i(all_20_0) & $i(all_20_1)
% 248.43/58.68 | |
% 248.43/58.68 | | ALPHA: (32) implies:
% 248.43/58.68 | | (33) op(e1, e4) = all_20_1
% 248.43/58.68 | |
% 248.43/58.68 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 248.43/58.68 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 248.43/58.68 | | (25), (26), (27), (28), (29), (30), (31), (33) are inconsistent
% 248.43/58.68 | | by sub-proof #53.
% 248.43/58.68 | |
% 248.43/58.68 | Case 2:
% 248.43/58.68 | |
% 248.43/58.68 | | (34) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1)
% 248.43/58.68 | |
% 248.43/58.68 | | ALPHA: (34) implies:
% 248.43/58.68 | | (35) op(e1, e4) = all_20_1
% 248.43/58.68 | |
% 248.43/58.68 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 248.43/58.68 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 248.43/58.68 | | (25), (26), (27), (28), (29), (30), (31), (35) are inconsistent
% 248.43/58.68 | | by sub-proof #53.
% 248.43/58.68 | |
% 248.43/58.68 | End of split
% 248.43/58.68 |
% 248.43/58.68 End of proof
% 248.43/58.68
% 248.43/58.68 Sub-proof #53 shows that the following formulas are inconsistent:
% 248.43/58.68 ----------------------------------------------------------------
% 248.43/58.68 (1) all_252_14 = e3
% 248.43/58.68 (2) ~ (e2 = e0)
% 248.43/58.68 (3) op(e4, all_34_2) = e1
% 248.43/58.68 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.68 (5) ~ (e3 = e2)
% 248.43/58.68 (6) op(e0, e0) = all_244_24
% 248.43/58.68 (7) op(e2, e2) = all_244_8
% 248.43/58.68 (8) op(e1, e0) = all_34_2
% 248.43/58.68 (9) op(e4, e2) = all_6_2
% 248.43/58.68 (10) ~ (all_244_15 = e0)
% 248.43/58.68 (11) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.43/58.68 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.43/58.68 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.43/58.68 (12) op(e0, e2) = all_28_2
% 248.43/58.68 (13) ~ (e4 = e1)
% 248.43/58.68 (14) ~ (all_28_2 = e1)
% 248.43/58.68 (15) ~ (all_6_2 = e1)
% 248.43/58.68 (16) op(e1, e4) = all_20_1
% 248.43/58.68 (17) op(all_244_15, all_244_15) = e1
% 248.43/58.68 (18) op(e1, e4) = all_16_2
% 248.43/58.68 (19) op(e1, e0) = all_222_1
% 248.43/58.68 (20) ~ (e3 = e1)
% 248.43/58.68 (21) ~ (all_16_2 = e2)
% 248.43/58.68 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.43/58.68 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.68 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.68 (23) op(all_22_2, e3) = e0
% 248.43/58.68 (24) op(e0, e3) = all_22_2
% 248.43/58.68 (25) ~ (all_244_8 = e1)
% 248.43/58.68 (26) op(e1, e1) = all_244_15
% 248.43/58.68 (27) all_252_23 = e4
% 248.43/58.68 (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.43/58.68 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.43/58.68 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.43/58.68 (29) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.43/58.68 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.43/58.68 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.43/58.68 (30) op(all_244_24, all_244_24) = e0
% 248.43/58.68 (31) all_252_20 = e3
% 248.43/58.68
% 248.43/58.68 Begin of proof
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (4) with all_34_2, all_222_1, e0, e1, simplifying
% 248.43/58.68 | with (8), (19) gives:
% 248.43/58.68 | (32) all_222_1 = all_34_2
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (4) with all_16_2, all_20_1, e4, e1, simplifying
% 248.43/58.68 | with (16), (18) gives:
% 248.43/58.68 | (33) all_20_1 = all_16_2
% 248.43/58.68 |
% 248.43/58.68 | BETA: splitting (29) gives:
% 248.43/58.68 |
% 248.43/58.68 | Case 1:
% 248.43/58.68 | |
% 248.43/58.68 | | (34) ~ (all_22_2 = e1)
% 248.43/58.68 | |
% 248.43/58.68 | | REF_CLOSE: (4), (6), (10), (12), (13), (14), (20), (22), (24), (26), (27),
% 248.43/58.68 | | (30), (31), (34) are inconsistent by sub-proof #283.
% 248.43/58.68 | |
% 248.43/58.68 | Case 2:
% 248.43/58.68 | |
% 248.43/58.68 | | (35) all_22_2 = e1
% 248.43/58.68 | |
% 248.43/58.68 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (15), (17), (18),
% 248.43/58.68 | | (21), (23), (25), (26), (28), (35) are inconsistent by sub-proof
% 248.43/58.68 | | #63.
% 248.43/58.68 | |
% 248.43/58.68 | End of split
% 248.43/58.68 |
% 248.43/58.68 End of proof
% 248.43/58.68
% 248.43/58.68 Sub-proof #54 shows that the following formulas are inconsistent:
% 248.43/58.68 ----------------------------------------------------------------
% 248.43/58.68 (1) all_136_2 = e0
% 248.43/58.68 (2) ~ (all_244_24 = all_40_2)
% 248.43/58.68 (3) ~ (all_136_2 = e0) | ( ~ (all_136_0 = e2) & op(e4, e0) = all_136_1 &
% 248.43/58.68 op(e0, all_136_1) = all_136_0 & $i(all_136_0) & $i(all_136_1)) | ( ~
% 248.43/58.68 (all_136_1 = e1) & op(e4, e0) = all_136_1 & $i(all_136_1))
% 248.43/58.68 (4) all_174_2 = all_40_2
% 248.43/58.68 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.68 (6) op(e0, e0) = all_244_24
% 248.43/58.68 (7) op(e2, e0) = e1
% 248.43/58.68 (8) op(e0, e2) = all_28_2
% 248.43/58.68 (9) ~ (all_28_2 = e1)
% 248.43/58.68 (10) ~ (e3 = e1)
% 248.43/58.68 (11) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.43/58.68 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.68 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.68 (12) ~ (all_22_2 = e1)
% 248.43/58.68 (13) op(e0, e2) = all_34_1
% 248.43/58.68 (14) op(e0, e3) = all_22_2
% 248.43/58.68 (15) op(all_20_2, e2) = e1
% 248.43/58.68 (16) op(e1, e2) = e3
% 248.43/58.68 (17) op(e0, e1) = all_20_2
% 248.43/58.68 (18) op(e2, e0) = all_40_2
% 248.43/58.68 (19) ~ (all_20_2 = e3)
% 248.43/58.68 (20) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 248.43/58.68 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 248.43/58.68 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.43/58.68 (21) all_252_20 = e3
% 248.43/58.68
% 248.43/58.68 Begin of proof
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (5) with all_28_2, all_34_1, e2, e0, simplifying
% 248.43/58.68 | with (8), (13) gives:
% 248.43/58.68 | (22) all_34_1 = all_28_2
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (5) with all_40_2, e1, e0, e2, simplifying with
% 248.43/58.68 | (7), (18) gives:
% 248.43/58.68 | (23) all_40_2 = e1
% 248.43/58.68 |
% 248.43/58.68 | COMBINE_EQS: (4), (23) imply:
% 248.43/58.68 | (24) all_174_2 = e1
% 248.43/58.68 |
% 248.43/58.68 | REDUCE: (2), (23) imply:
% 248.43/58.68 | (25) ~ (all_244_24 = e1)
% 248.43/58.68 |
% 248.43/58.68 | BETA: splitting (20) gives:
% 248.43/58.68 |
% 248.43/58.68 | Case 1:
% 248.43/58.68 | |
% 248.43/58.68 | | (26) ~ (all_174_2 = e1)
% 248.43/58.68 | |
% 248.43/58.68 | | REDUCE: (24), (26) imply:
% 248.43/58.68 | | (27) $false
% 248.43/58.68 | |
% 248.43/58.68 | | CLOSE: (27) is inconsistent.
% 248.43/58.68 | |
% 248.43/58.68 | Case 2:
% 248.43/58.68 | |
% 248.43/58.68 | | (28) ( ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0, e1) =
% 248.43/58.68 | | all_174_1 & $i(all_174_0) & $i(all_174_1)) | ( ~ (all_174_1 = e4)
% 248.43/58.68 | | & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.43/58.68 | |
% 248.43/58.68 | | BETA: splitting (11) gives:
% 248.43/58.68 | |
% 248.43/58.68 | | Case 1:
% 248.43/58.68 | | |
% 248.43/58.68 | | | (29) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0,
% 248.43/58.68 | | | e3) = e1)
% 248.43/58.68 | | |
% 248.43/58.68 | | | REF_CLOSE: (5), (10), (12), (14), (21), (29) are inconsistent by sub-proof
% 248.43/58.68 | | | #285.
% 248.43/58.68 | | |
% 248.43/58.68 | | Case 2:
% 248.43/58.68 | | |
% 248.43/58.68 | | | (30) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.68 | | | e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.68 | | |
% 248.43/58.68 | | | BETA: splitting (30) gives:
% 248.43/58.68 | | |
% 248.43/58.68 | | | Case 1:
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | (31) all_252_22 = e1 & op(e0, e2) = e1
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | ALPHA: (31) implies:
% 248.43/58.68 | | | | (32) op(e0, e2) = e1
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | REF_CLOSE: (5), (8), (9), (32) are inconsistent by sub-proof #907.
% 248.43/58.68 | | | |
% 248.43/58.68 | | | Case 2:
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | (33) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 248.43/58.68 | | | | e0) = e1)
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | BETA: splitting (33) gives:
% 248.43/58.68 | | | |
% 248.43/58.68 | | | | Case 1:
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | (34) all_252_23 = e1 & op(e0, e1) = e1
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | ALPHA: (34) implies:
% 248.43/58.68 | | | | | (35) op(e0, e1) = e1
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | BETA: splitting (28) gives:
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | Case 1:
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | (36) ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0,
% 248.43/58.68 | | | | | | e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | ALPHA: (36) implies:
% 248.43/58.68 | | | | | | (37) op(e0, e1) = all_174_1
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | GROUND_INST: instantiating (5) with all_20_2, all_174_1, e1, e0,
% 248.43/58.68 | | | | | | simplifying with (17), (37) gives:
% 248.43/58.68 | | | | | | (38) all_174_1 = all_20_2
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | REF_CLOSE: (5), (15), (16), (19), (35), (37), (38) are inconsistent
% 248.43/58.68 | | | | | | by sub-proof #55.
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | Case 2:
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | (39) ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1)
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | ALPHA: (39) implies:
% 248.43/58.68 | | | | | | (40) op(e0, e1) = all_174_1
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | BETA: splitting (3) gives:
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | | Case 1:
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | | (41) ~ (all_136_2 = e0)
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | | REDUCE: (1), (41) imply:
% 248.43/58.68 | | | | | | | (42) $false
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | | CLOSE: (42) is inconsistent.
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | Case 2:
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | | GROUND_INST: instantiating (5) with all_20_2, all_174_1, e1, e0,
% 248.43/58.68 | | | | | | | simplifying with (17), (40) gives:
% 248.43/58.68 | | | | | | | (43) all_174_1 = all_20_2
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | | REF_CLOSE: (5), (15), (16), (19), (35), (40), (43) are
% 248.43/58.68 | | | | | | | inconsistent by sub-proof #55.
% 248.43/58.68 | | | | | | |
% 248.43/58.68 | | | | | | End of split
% 248.43/58.68 | | | | | |
% 248.43/58.68 | | | | | End of split
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | Case 2:
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | (44) all_252_24 = e1 & op(e0, e0) = e1
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | | REF_CLOSE: (5), (6), (25), (44) are inconsistent by sub-proof #71.
% 248.43/58.68 | | | | |
% 248.43/58.68 | | | | End of split
% 248.43/58.68 | | | |
% 248.43/58.68 | | | End of split
% 248.43/58.68 | | |
% 248.43/58.68 | | End of split
% 248.43/58.68 | |
% 248.43/58.68 | End of split
% 248.43/58.68 |
% 248.43/58.68 End of proof
% 248.43/58.68
% 248.43/58.68 Sub-proof #55 shows that the following formulas are inconsistent:
% 248.43/58.68 ----------------------------------------------------------------
% 248.43/58.68 (1) all_174_1 = all_20_2
% 248.43/58.68 (2) op(e0, e1) = all_174_1
% 248.43/58.68 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.68 (4) op(e0, e1) = e1
% 248.43/58.68 (5) op(all_20_2, e2) = e1
% 248.43/58.68 (6) op(e1, e2) = e3
% 248.43/58.68 (7) ~ (all_20_2 = e3)
% 248.43/58.68
% 248.43/58.68 Begin of proof
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (3) with e1, all_174_1, e1, e0, simplifying with
% 248.43/58.68 | (2), (4) gives:
% 248.43/58.68 | (8) all_174_1 = e1
% 248.43/58.68 |
% 248.43/58.68 | COMBINE_EQS: (1), (8) imply:
% 248.43/58.68 | (9) all_20_2 = e1
% 248.43/58.68 |
% 248.43/58.68 | SIMP: (9) implies:
% 248.43/58.68 | (10) all_20_2 = e1
% 248.43/58.68 |
% 248.43/58.68 | REDUCE: (7), (10) imply:
% 248.43/58.68 | (11) ~ (e3 = e1)
% 248.43/58.68 |
% 248.43/58.68 | SIMP: (11) implies:
% 248.43/58.68 | (12) ~ (e3 = e1)
% 248.43/58.68 |
% 248.43/58.68 | REDUCE: (5), (10) imply:
% 248.43/58.68 | (13) op(e1, e2) = e1
% 248.43/58.68 |
% 248.43/58.68 | REF_CLOSE: (3), (6), (12), (13) are inconsistent by sub-proof #56.
% 248.43/58.68 |
% 248.43/58.68 End of proof
% 248.43/58.68
% 248.43/58.68 Sub-proof #56 shows that the following formulas are inconsistent:
% 248.43/58.68 ----------------------------------------------------------------
% 248.43/58.68 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.68 (2) op(e1, e2) = e3
% 248.43/58.68 (3) op(e1, e2) = e1
% 248.43/58.68 (4) ~ (e3 = e1)
% 248.43/58.68
% 248.43/58.68 Begin of proof
% 248.43/58.68 |
% 248.43/58.68 | GROUND_INST: instantiating (1) with e3, e1, e2, e1, simplifying with (2), (3)
% 248.43/58.68 | gives:
% 248.43/58.68 | (5) e3 = e1
% 248.43/58.68 |
% 248.43/58.68 | REDUCE: (4), (5) imply:
% 248.43/58.68 | (6) $false
% 248.43/58.68 |
% 248.43/58.68 | CLOSE: (6) is inconsistent.
% 248.43/58.68 |
% 248.43/58.68 End of proof
% 248.43/58.68
% 248.43/58.68 Sub-proof #57 shows that the following formulas are inconsistent:
% 248.43/58.68 ----------------------------------------------------------------
% 248.43/58.68 (1) ~ (all_30_2 = all_26_2)
% 248.43/58.68 (2) all_252_14 = e3
% 248.43/58.68 (3) all_32_2 = all_20_2
% 248.43/58.68 (4) ~ (all_4_2 = e4)
% 248.43/58.68 (5) ~ (all_10_2 = e4)
% 248.43/58.68 (6) ~ (all_244_0 = all_30_2)
% 248.43/58.68 (7) all_250_16 = all_62_2
% 248.43/58.68 (8) op(all_4_2, e2) = e1
% 248.43/58.68 (9) ~ (all_244_24 = all_34_2)
% 248.43/58.68 (10) ~ (all_244_24 = all_40_2)
% 248.43/58.68 (11) op(all_36_2, all_62_2) = e1
% 248.43/58.68 (12) ~ (all_40_2 = all_38_2)
% 248.43/58.68 (13) op(all_6_2, e2) = e4
% 248.43/58.68 (14) op(e4, e1) = e0
% 248.43/58.68 (15) op(e4, e0) = all_30_2
% 248.43/58.68 (16) all_250_8 = all_36_2
% 248.43/58.68 (17) op(all_28_2, all_40_2) = e2
% 248.43/58.68 (18) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.43/58.68 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.43/58.68 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.43/58.68 (19) ~ (all_40_2 = all_30_2)
% 248.43/58.68 (20) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.43/58.68 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.43/58.68 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.43/58.68 (21) all_94_2 = all_38_2
% 248.43/58.68 (22) op(all_62_2, all_36_2) = e3
% 248.43/58.68 (23) op(all_38_2, e1) = e2
% 248.43/58.68 (24) all_250_13 = all_38_2
% 248.43/58.68 (25) ~ (e2 = e0)
% 248.43/58.68 (26) op(all_64_2, e4) = e2
% 248.43/58.68 (27) ~ (e1 = e0)
% 248.43/58.68 (28) ~ (all_28_2 = e3)
% 248.43/58.68 (29) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.43/58.68 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.43/58.68 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.43/58.68 (30) op(e4, all_34_2) = e1
% 248.43/58.68 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.43/58.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.43/58.68 (32) op(e2, e3) = all_10_2
% 248.43/58.68 (33) ~ (e3 = e2)
% 248.43/58.68 (34) op(e0, e0) = all_244_24
% 248.43/58.68 (35) all_234_2 = e1
% 248.43/58.68 (36) ~ (all_12_2 = e3)
% 248.43/58.68 (37) op(all_244_8, all_244_8) = e2
% 248.43/58.68 (38) op(e2, e2) = all_244_8
% 248.43/58.68 (39) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.43/58.68 all_250_11 = e0
% 248.43/58.68 (40) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.43/58.68 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.43/58.68 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.43/58.68 (41) op(all_84_2, all_100_2) = e3
% 248.43/58.68 (42) op(e2, e1) = all_38_2
% 248.43/58.68 (43) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.43/58.68 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.43/58.68 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.43/58.68 (44) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.43/58.68 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.43/58.68 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.43/58.68 (45) ~ (all_36_2 = all_20_2)
% 248.43/58.68 (46) ~ (all_64_2 = all_40_2)
% 248.43/58.68 (47) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.43/58.68 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.43/58.68 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.68 (48) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.43/58.68 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.43/58.68 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.43/58.68 (49) op(e1, e0) = all_34_2
% 248.43/58.68 (50) op(e4, e2) = all_6_2
% 248.43/58.68 (51) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.43/58.68 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.43/58.68 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.43/58.68 (52) op(e3, all_38_2) = e2
% 248.43/58.69 (53) op(e1, all_10_2) = e2
% 248.43/58.69 (54) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.43/58.69 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.43/58.69 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.43/58.69 (55) all_78_2 = all_10_2
% 248.43/58.69 (56) ~ (e2 = e1)
% 248.43/58.69 (57) op(all_26_2, e1) = e4
% 248.43/58.69 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.43/58.69 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.43/58.69 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.43/58.69 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.43/58.69 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.43/58.69 op(e0, e1) = e0)))
% 248.43/58.69 (59) ~ (all_100_2 = all_36_2)
% 248.43/58.69 (60) ~ (all_222_2 = e0) | ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 &
% 248.43/58.69 op(e0, all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | ( ~
% 248.43/58.69 (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 248.43/58.69 (61) op(e0, e2) = all_28_2
% 248.43/58.69 (62) ~ (all_28_2 = e1)
% 248.43/58.69 (63) op(all_6_2, all_64_2) = e2
% 248.43/58.69 (64) ~ (all_6_2 = e1)
% 248.43/58.69 (65) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.43/58.69 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.43/58.69 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.43/58.69 (66) op(e1, e4) = all_20_1
% 248.43/58.69 (67) all_106_2 = all_38_2
% 248.43/58.69 (68) ~ (all_244_8 = all_38_2)
% 248.43/58.69 (69) op(all_244_15, all_244_15) = e1
% 248.43/58.69 (70) all_250_21 = all_22_2
% 248.43/58.69 (71) op(all_34_2, e0) = e1
% 248.43/58.69 (72) ~ (all_244_3 = all_84_2)
% 248.43/58.69 (73) op(e1, e4) = all_16_2
% 248.43/58.69 (74) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.43/58.69 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.43/58.69 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.43/58.69 (75) ~ (all_48_2 = all_30_2)
% 248.43/58.69 (76) ~ (all_244_0 = all_64_2)
% 248.43/58.69 (77) ~ (all_244_3 = all_36_2)
% 248.43/58.69 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.43/58.69 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.43/58.69 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.43/58.69 (79) all_132_2 = all_30_2
% 248.43/58.69 (80) op(e1, e3) = all_62_2
% 248.43/58.69 (81) ~ (all_244_0 = all_26_2)
% 248.43/58.69 (82) ~ (e3 = e0)
% 248.43/58.69 (83) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.43/58.69 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.43/58.69 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.43/58.69 (84) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.43/58.69 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.43/58.69 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.43/58.69 (85) ~ (all_40_2 = all_10_2)
% 248.43/58.69 (86) all_204_2 = all_36_2
% 248.43/58.69 (87) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.43/58.69 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.43/58.69 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.43/58.69 (88) op(all_20_2, e1) = e0
% 248.43/58.69 (89) ~ (all_244_3 = all_10_2)
% 248.43/58.69 (90) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.43/58.69 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.43/58.69 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.43/58.69 (91) all_70_2 = all_62_2
% 248.43/58.69 (92) ~ (e3 = e1)
% 248.43/58.69 (93) op(all_48_2, all_22_2) = e0
% 248.43/58.69 (94) ~ (all_12_2 = e2)
% 248.43/58.69 (95) op(e3, e1) = all_36_2
% 248.43/58.69 (96) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.43/58.69 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.43/58.69 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.43/58.69 (97) ~ (all_16_2 = e2)
% 248.43/58.69 (98) op(all_40_2, e0) = e2
% 248.43/58.69 (99) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.43/58.69 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.43/58.69 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.69 (100) ~ (all_244_8 = all_40_2)
% 248.43/58.69 (101) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.43/58.69 all_250_8 = e0
% 248.43/58.69 (102) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.43/58.69 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.43/58.69 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.43/58.69 (103) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.43/58.69 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.43/58.69 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.43/58.69 (104) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.43/58.69 all_250_13 = e0
% 248.43/58.69 (105) ~ (all_244_15 = all_38_2)
% 248.43/58.69 (106) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.43/58.69 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.43/58.69 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.43/58.69 (107) ~ (all_36_2 = all_26_2)
% 248.43/58.69 (108) all_44_2 = all_26_2
% 248.43/58.69 (109) all_60_2 = e4
% 248.43/58.69 (110) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.43/58.69 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.43/58.69 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.43/58.69 (111) all_222_2 = all_26_2
% 248.43/58.69 (112) op(all_38_2, e3) = e1
% 248.43/58.69 (113) ~ (all_64_2 = all_12_2)
% 248.43/58.69 (114) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.43/58.69 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.43/58.69 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.43/58.69 (115) op(all_22_2, e3) = e0
% 248.43/58.69 (116) all_68_2 = all_22_2
% 248.43/58.69 (117) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0
% 248.43/58.69 & op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~
% 248.43/58.69 (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 248.43/58.69 (118) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.43/58.69 all_250_16 = e0
% 248.43/58.69 (119) op(e0, e3) = all_22_2
% 248.43/58.69 (120) ~ (all_26_2 = e4)
% 248.43/58.69 (121) ~ (all_244_0 = all_100_2)
% 248.43/58.69 (122) ~ (all_28_2 = all_22_2)
% 248.43/58.69 (123) all_242_2 = all_38_2
% 248.43/58.69 (124) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.43/58.69 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.43/58.69 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.43/58.69 (125) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.43/58.69 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.43/58.69 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.43/58.69 (126) op(all_84_2, e3) = e4
% 248.43/58.69 (127) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.43/58.69 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.43/58.69 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.43/58.69 (128) all_58_2 = all_20_2
% 248.43/58.69 (129) op(all_62_2, e3) = e1
% 248.43/58.69 (130) op(e4, e1) = all_26_2
% 248.43/58.69 (131) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.43/58.69 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.43/58.69 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.43/58.69 (132) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.43/58.69 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.43/58.69 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.43/58.69 (133) op(all_10_2, e3) = e2
% 248.43/58.69 (134) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.43/58.69 all_250_21 = e0
% 248.43/58.69 (135) ~ (all_244_15 = all_62_2)
% 248.43/58.69 (136) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.43/58.69 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.43/58.69 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.43/58.69 (137) op(e3, e4) = all_100_2
% 248.43/58.69 (138) all_250_11 = all_10_2
% 248.43/58.69 (139) ~ (all_244_8 = e1)
% 248.43/58.69 (140) op(e4, e4) = all_244_0
% 248.43/58.69 (141) ~ (all_22_2 = all_12_2)
% 248.43/58.69 (142) all_230_2 = all_20_2
% 248.43/58.69 (143) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.43/58.69 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.43/58.69 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.43/58.69 (144) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.43/58.69 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.43/58.69 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.43/58.69 (145) ~ (e4 = e3)
% 248.43/58.69 (146) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.43/58.69 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.43/58.69 all_8_1 & $i(all_8_1))
% 248.43/58.69 (147) op(e1, e1) = all_244_15
% 248.43/58.69 (148) ~ (all_34_2 = all_30_2)
% 248.43/58.69 (149) op(e0, e1) = all_20_2
% 248.43/58.69 (150) op(e3, e0) = all_48_2
% 248.43/58.69 (151) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.43/58.69 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.43/58.69 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.43/58.69 (152) op(all_48_2, e0) = e3
% 248.43/58.69 (153) ~ (all_38_2 = all_36_2)
% 248.43/58.69 (154) op(e1, e2) = all_4_2
% 248.43/58.69 (155) ~ (all_100_2 = all_48_2)
% 248.43/58.69 (156) op(all_4_2, all_38_2) = e2
% 248.43/58.69 (157) op(e4, e3) = all_84_2
% 248.43/58.69 (158) ~ (all_62_2 = all_10_2)
% 248.43/58.69 (159) op(e2, e4) = all_64_2
% 248.43/58.69 (160) ~ (all_22_2 = all_10_2)
% 248.43/58.69 (161) ~ (all_36_2 = e1)
% 248.43/58.69 (162) ~ (all_38_2 = all_26_2)
% 248.43/58.69 (163) ~ (e4 = e2)
% 248.43/58.69 (164) ~ (all_244_24 = all_30_2)
% 248.43/58.69 (165) ~ (all_22_2 = all_20_2)
% 248.43/58.69 (166) all_122_2 = all_36_2
% 248.43/58.69 (167) ~ (all_64_2 = all_16_2)
% 248.43/58.69 (168) op(all_36_2, e1) = e3
% 248.43/58.69 (169) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.43/58.69 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.43/58.69 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.43/58.69 (170) ~ (all_38_2 = all_10_2)
% 248.43/58.69 (171) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.43/58.69 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.43/58.69 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.43/58.69 (172) ~ (all_244_15 = all_36_2)
% 248.43/58.69 (173) ~ (all_244_24 = all_22_2)
% 248.43/58.69 (174) op(all_16_2, e4) = e1
% 248.43/58.69 (175) ~ (all_100_2 = all_16_2)
% 248.43/58.69 (176) op(e2, e0) = all_40_2
% 248.43/58.69 (177) ~ (all_16_2 = e3)
% 248.43/58.69 (178) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.43/58.69 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.43/58.69 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.43/58.69 (179) op(e3, e3) = all_244_3
% 248.43/58.69 (180) all_90_2 = all_22_2
% 248.43/58.69 (181) op(all_26_2, all_16_2) = e1
% 248.43/58.69 (182) op(all_12_2, e4) = e0
% 248.43/58.69 (183) all_46_2 = all_36_2
% 248.43/58.69 (184) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.43/58.69 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.43/58.69 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.43/58.69 (185) op(all_30_2, e0) = e4
% 248.43/58.69 (186) op(all_244_24, all_244_24) = e0
% 248.43/58.69 (187) op(e0, e4) = all_12_2
% 248.43/58.69 (188) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.43/58.69 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.43/58.69 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.43/58.69 (189) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.43/58.69 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.43/58.69 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.43/58.69 (190) all_124_2 = all_10_2
% 248.43/58.69
% 248.43/58.69 Begin of proof
% 248.43/58.69 |
% 248.43/58.69 | BETA: splitting (117) gives:
% 248.43/58.69 |
% 248.43/58.69 | Case 1:
% 248.43/58.69 | |
% 248.43/58.69 | | (191) ~ (all_60_2 = e4)
% 248.43/58.69 | |
% 248.43/58.69 | | REDUCE: (109), (191) imply:
% 248.43/58.69 | | (192) $false
% 248.43/58.69 | |
% 248.43/58.69 | | CLOSE: (192) is inconsistent.
% 248.43/58.69 | |
% 248.43/58.69 | Case 2:
% 248.43/58.69 | |
% 248.43/58.69 | | (193) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 248.43/58.69 | | all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 = e3) &
% 248.43/58.69 | | op(e1, e4) = all_60_1 & $i(all_60_1))
% 248.43/58.69 | |
% 248.43/58.69 | | GROUND_INST: instantiating (31) with all_16_2, all_20_1, e4, e1, simplifying
% 248.43/58.69 | | with (66), (73) gives:
% 248.43/58.69 | | (194) all_20_1 = all_16_2
% 248.43/58.69 | |
% 248.43/58.69 | | GROUND_INST: instantiating (31) with all_26_2, e0, e1, e4, simplifying with
% 248.43/58.69 | | (14), (130) gives:
% 248.43/58.69 | | (195) all_26_2 = e0
% 248.43/58.69 | |
% 248.43/58.69 | | COMBINE_EQS: (111), (195) imply:
% 248.43/58.69 | | (196) all_222_2 = e0
% 248.43/58.69 | |
% 248.43/58.69 | | REDUCE: (120), (195) imply:
% 248.43/58.69 | | (197) ~ (e4 = e0)
% 248.43/58.69 | |
% 248.43/58.69 | | SIMP: (197) implies:
% 248.43/58.69 | | (198) ~ (e4 = e0)
% 248.43/58.69 | |
% 248.43/58.69 | | BETA: splitting (193) gives:
% 248.43/58.69 | |
% 248.43/58.69 | | Case 1:
% 248.43/58.69 | | |
% 248.43/58.69 | | | (199) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 248.43/58.69 | | | all_60_1 & $i(all_60_0) & $i(all_60_1)
% 248.43/58.69 | | |
% 248.43/58.69 | | | ALPHA: (199) implies:
% 248.43/58.69 | | | (200) op(e1, e4) = all_60_1
% 248.43/58.69 | | |
% 248.43/58.69 | | | BETA: splitting (60) gives:
% 248.43/58.69 | | |
% 248.43/58.69 | | | Case 1:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | (201) ~ (all_222_2 = e0)
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | REDUCE: (196), (201) imply:
% 248.43/58.69 | | | | (202) $false
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | CLOSE: (202) is inconsistent.
% 248.43/58.69 | | | |
% 248.43/58.69 | | | Case 2:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | (203) ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.69 | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | (
% 248.43/58.69 | | | | ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | BETA: splitting (203) gives:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | Case 1:
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | (204) ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.69 | | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | ALPHA: (204) implies:
% 248.43/58.69 | | | | | (205) op(e1, e0) = all_222_1
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.43/58.69 | | | | | (12), (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.43/58.69 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.43/58.69 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.43/58.69 | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.43/58.69 | | | | | (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 248.43/58.69 | | | | | (64), (65), (67), (68), (69), (70), (71), (72), (73), (74),
% 248.43/58.69 | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 248.43/58.69 | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 248.43/58.69 | | | | | (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 248.43/58.69 | | | | | (104), (105), (106), (107), (108), (110), (112), (113),
% 248.43/58.69 | | | | | (114), (115), (116), (118), (119), (121), (122), (123),
% 248.43/58.69 | | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 248.43/58.69 | | | | | (132), (133), (134), (135), (136), (137), (138), (139),
% 248.43/58.69 | | | | | (140), (141), (142), (143), (144), (145), (146), (147),
% 248.43/58.69 | | | | | (148), (149), (150), (151), (152), (153), (154), (155),
% 248.43/58.69 | | | | | (156), (157), (158), (159), (160), (161), (162), (163),
% 248.43/58.69 | | | | | (164), (165), (166), (167), (168), (169), (170), (171),
% 248.43/58.69 | | | | | (172), (173), (174), (175), (176), (177), (178), (179),
% 248.43/58.69 | | | | | (180), (181), (182), (183), (184), (185), (186), (187),
% 248.43/58.69 | | | | | (188), (189), (190), (198), (200), (205) are inconsistent
% 248.43/58.69 | | | | | by sub-proof #60.
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | Case 2:
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | (206) ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1)
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | ALPHA: (206) implies:
% 248.43/58.69 | | | | | (207) op(e1, e0) = all_222_1
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.43/58.69 | | | | | (12), (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.43/58.69 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.43/58.69 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.43/58.69 | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.43/58.69 | | | | | (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 248.43/58.69 | | | | | (64), (65), (67), (68), (69), (70), (71), (72), (73), (74),
% 248.43/58.69 | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 248.43/58.69 | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 248.43/58.69 | | | | | (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 248.43/58.69 | | | | | (104), (105), (106), (107), (108), (110), (112), (113),
% 248.43/58.69 | | | | | (114), (115), (116), (118), (119), (121), (122), (123),
% 248.43/58.69 | | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 248.43/58.69 | | | | | (132), (133), (134), (135), (136), (137), (138), (139),
% 248.43/58.69 | | | | | (140), (141), (142), (143), (144), (145), (146), (147),
% 248.43/58.69 | | | | | (148), (149), (150), (151), (152), (153), (154), (155),
% 248.43/58.69 | | | | | (156), (157), (158), (159), (160), (161), (162), (163),
% 248.43/58.69 | | | | | (164), (165), (166), (167), (168), (169), (170), (171),
% 248.43/58.69 | | | | | (172), (173), (174), (175), (176), (177), (178), (179),
% 248.43/58.69 | | | | | (180), (181), (182), (183), (184), (185), (186), (187),
% 248.43/58.69 | | | | | (188), (189), (190), (198), (200), (207) are inconsistent
% 248.43/58.69 | | | | | by sub-proof #60.
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | End of split
% 248.43/58.69 | | | |
% 248.43/58.69 | | | End of split
% 248.43/58.69 | | |
% 248.43/58.69 | | Case 2:
% 248.43/58.69 | | |
% 248.43/58.69 | | | (208) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1)
% 248.43/58.69 | | |
% 248.43/58.69 | | | ALPHA: (208) implies:
% 248.43/58.69 | | | (209) ~ (all_60_1 = e3)
% 248.43/58.69 | | | (210) op(e1, e4) = all_60_1
% 248.43/58.69 | | |
% 248.43/58.69 | | | BETA: splitting (60) gives:
% 248.43/58.69 | | |
% 248.43/58.69 | | | Case 1:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | (211) ~ (all_222_2 = e0)
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | REDUCE: (196), (211) imply:
% 248.43/58.69 | | | | (212) $false
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | CLOSE: (212) is inconsistent.
% 248.43/58.69 | | | |
% 248.43/58.69 | | | Case 2:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | (213) ( ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.69 | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)) | (
% 248.43/58.69 | | | | ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1))
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | BETA: splitting (213) gives:
% 248.43/58.69 | | | |
% 248.43/58.69 | | | | Case 1:
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | (214) ~ (all_222_0 = e2) & op(e1, e0) = all_222_1 & op(e0,
% 248.43/58.69 | | | | | all_222_1) = all_222_0 & $i(all_222_0) & $i(all_222_1)
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | ALPHA: (214) implies:
% 248.43/58.69 | | | | | (215) op(e1, e0) = all_222_1
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.43/58.69 | | | | | (12), (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.43/58.69 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.43/58.69 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.43/58.69 | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.43/58.69 | | | | | (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 248.43/58.69 | | | | | (64), (65), (67), (68), (69), (70), (71), (72), (73), (74),
% 248.43/58.69 | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 248.43/58.69 | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 248.43/58.69 | | | | | (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 248.43/58.69 | | | | | (104), (105), (106), (107), (108), (110), (112), (113),
% 248.43/58.69 | | | | | (114), (115), (116), (118), (119), (121), (122), (123),
% 248.43/58.69 | | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 248.43/58.69 | | | | | (132), (133), (134), (135), (136), (137), (138), (139),
% 248.43/58.69 | | | | | (140), (141), (142), (143), (144), (145), (146), (147),
% 248.43/58.69 | | | | | (148), (149), (150), (151), (152), (153), (154), (155),
% 248.43/58.69 | | | | | (156), (157), (158), (159), (160), (161), (162), (163),
% 248.43/58.69 | | | | | (164), (165), (166), (167), (168), (169), (170), (171),
% 248.43/58.69 | | | | | (172), (173), (174), (175), (176), (178), (179), (180),
% 248.43/58.69 | | | | | (181), (182), (183), (184), (185), (186), (187), (188),
% 248.43/58.69 | | | | | (189), (190), (198), (209), (210), (215) are inconsistent
% 248.43/58.69 | | | | | by sub-proof #58.
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | Case 2:
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | (216) ~ (all_222_1 = e3) & op(e1, e0) = all_222_1 & $i(all_222_1)
% 248.43/58.69 | | | | |
% 248.43/58.69 | | | | | ALPHA: (216) implies:
% 248.43/58.69 | | | | | (217) op(e1, e0) = all_222_1
% 248.43/58.69 | | | | |
% 248.43/58.70 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.43/58.70 | | | | | (12), (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.43/58.70 | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.43/58.70 | | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.43/58.70 | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.43/58.70 | | | | | (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 248.43/58.70 | | | | | (64), (65), (67), (68), (69), (70), (71), (72), (73), (74),
% 248.43/58.70 | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 248.43/58.70 | | | | | (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 248.43/58.70 | | | | | (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 248.43/58.70 | | | | | (104), (105), (106), (107), (108), (110), (112), (113),
% 248.43/58.70 | | | | | (114), (115), (116), (118), (119), (121), (122), (123),
% 248.43/58.70 | | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 248.43/58.70 | | | | | (132), (133), (134), (135), (136), (137), (138), (139),
% 248.43/58.70 | | | | | (140), (141), (142), (143), (144), (145), (146), (147),
% 248.43/58.70 | | | | | (148), (149), (150), (151), (152), (153), (154), (155),
% 248.43/58.70 | | | | | (156), (157), (158), (159), (160), (161), (162), (163),
% 248.43/58.70 | | | | | (164), (165), (166), (167), (168), (169), (170), (171),
% 248.43/58.70 | | | | | (172), (173), (174), (175), (176), (178), (179), (180),
% 248.43/58.70 | | | | | (181), (182), (183), (184), (185), (186), (187), (188),
% 248.43/58.70 | | | | | (189), (190), (198), (209), (210), (217) are inconsistent
% 248.43/58.70 | | | | | by sub-proof #58.
% 248.43/58.70 | | | | |
% 248.43/58.70 | | | | End of split
% 248.43/58.70 | | | |
% 248.43/58.70 | | | End of split
% 248.43/58.70 | | |
% 248.43/58.70 | | End of split
% 248.43/58.70 | |
% 248.43/58.70 | End of split
% 248.43/58.70 |
% 248.43/58.70 End of proof
% 248.43/58.70
% 248.43/58.70 Sub-proof #58 shows that the following formulas are inconsistent:
% 248.43/58.70 ----------------------------------------------------------------
% 248.43/58.70 (1) ~ (all_30_2 = all_26_2)
% 248.43/58.70 (2) all_252_14 = e3
% 248.43/58.70 (3) all_32_2 = all_20_2
% 248.43/58.70 (4) ~ (all_4_2 = e4)
% 248.43/58.70 (5) ~ (all_10_2 = e4)
% 248.43/58.70 (6) ~ (all_244_0 = all_30_2)
% 248.43/58.70 (7) all_250_16 = all_62_2
% 248.43/58.70 (8) op(all_4_2, e2) = e1
% 248.43/58.70 (9) ~ (all_244_24 = all_34_2)
% 248.43/58.70 (10) ~ (all_244_24 = all_40_2)
% 248.43/58.70 (11) op(all_36_2, all_62_2) = e1
% 248.43/58.70 (12) ~ (all_40_2 = all_38_2)
% 248.43/58.70 (13) op(all_6_2, e2) = e4
% 248.43/58.70 (14) op(e4, e0) = all_30_2
% 248.43/58.70 (15) all_250_8 = all_36_2
% 248.43/58.70 (16) op(all_28_2, all_40_2) = e2
% 248.64/58.70 (17) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.70 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.70 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.70 (18) ~ (all_40_2 = all_30_2)
% 248.64/58.70 (19) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.70 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.70 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.70 (20) all_94_2 = all_38_2
% 248.64/58.70 (21) op(all_62_2, all_36_2) = e3
% 248.64/58.70 (22) op(all_38_2, e1) = e2
% 248.64/58.70 (23) all_250_13 = all_38_2
% 248.64/58.70 (24) ~ (e2 = e0)
% 248.64/58.70 (25) op(all_64_2, e4) = e2
% 248.64/58.70 (26) ~ (e1 = e0)
% 248.64/58.70 (27) ~ (all_28_2 = e3)
% 248.64/58.70 (28) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.70 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.70 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.70 (29) op(e4, all_34_2) = e1
% 248.64/58.70 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.70 (31) op(e2, e3) = all_10_2
% 248.64/58.70 (32) ~ (e3 = e2)
% 248.64/58.70 (33) op(e0, e0) = all_244_24
% 248.64/58.70 (34) ~ (e4 = e0)
% 248.64/58.70 (35) all_234_2 = e1
% 248.64/58.70 (36) ~ (all_12_2 = e3)
% 248.64/58.70 (37) op(all_244_8, all_244_8) = e2
% 248.64/58.70 (38) op(e2, e2) = all_244_8
% 248.64/58.70 (39) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.70 all_250_11 = e0
% 248.64/58.70 (40) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.70 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.70 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.70 (41) op(all_84_2, all_100_2) = e3
% 248.64/58.70 (42) op(e2, e1) = all_38_2
% 248.64/58.70 (43) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.70 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.70 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.70 (44) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.70 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.70 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.70 (45) ~ (all_36_2 = all_20_2)
% 248.64/58.70 (46) ~ (all_64_2 = all_40_2)
% 248.64/58.70 (47) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.70 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.70 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.70 (48) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.70 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.70 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.70 (49) op(e1, e0) = all_34_2
% 248.64/58.70 (50) op(e4, e2) = all_6_2
% 248.64/58.70 (51) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.70 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.70 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.70 (52) op(e3, all_38_2) = e2
% 248.64/58.70 (53) op(e1, all_10_2) = e2
% 248.64/58.70 (54) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.70 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.70 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.70 (55) all_78_2 = all_10_2
% 248.64/58.70 (56) ~ (e2 = e1)
% 248.64/58.70 (57) op(all_26_2, e1) = e4
% 248.64/58.70 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.70 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.70 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.70 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.70 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.70 op(e0, e1) = e0)))
% 248.64/58.70 (59) ~ (all_100_2 = all_36_2)
% 248.64/58.70 (60) op(e0, e2) = all_28_2
% 248.64/58.70 (61) ~ (all_28_2 = e1)
% 248.64/58.70 (62) op(all_6_2, all_64_2) = e2
% 248.64/58.70 (63) ~ (all_6_2 = e1)
% 248.64/58.70 (64) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.70 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.70 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.70 (65) all_106_2 = all_38_2
% 248.64/58.70 (66) ~ (all_244_8 = all_38_2)
% 248.64/58.70 (67) op(all_244_15, all_244_15) = e1
% 248.64/58.70 (68) all_250_21 = all_22_2
% 248.64/58.70 (69) op(all_34_2, e0) = e1
% 248.64/58.70 (70) ~ (all_244_3 = all_84_2)
% 248.64/58.70 (71) op(e1, e4) = all_16_2
% 248.64/58.70 (72) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.70 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.70 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.70 (73) ~ (all_48_2 = all_30_2)
% 248.64/58.70 (74) ~ (all_244_0 = all_64_2)
% 248.64/58.70 (75) ~ (all_244_3 = all_36_2)
% 248.64/58.70 (76) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.70 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.70 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.70 (77) all_132_2 = all_30_2
% 248.64/58.70 (78) op(e1, e3) = all_62_2
% 248.64/58.70 (79) ~ (all_244_0 = all_26_2)
% 248.64/58.70 (80) op(e1, e0) = all_222_1
% 248.64/58.70 (81) ~ (e3 = e0)
% 248.64/58.70 (82) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.70 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.70 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.70 (83) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.70 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.70 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.70 (84) ~ (all_40_2 = all_10_2)
% 248.64/58.70 (85) all_204_2 = all_36_2
% 248.64/58.70 (86) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.70 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.70 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.70 (87) op(all_20_2, e1) = e0
% 248.64/58.70 (88) ~ (all_244_3 = all_10_2)
% 248.64/58.70 (89) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.70 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.70 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.70 (90) all_70_2 = all_62_2
% 248.64/58.70 (91) ~ (e3 = e1)
% 248.64/58.70 (92) op(all_48_2, all_22_2) = e0
% 248.64/58.70 (93) ~ (all_12_2 = e2)
% 248.64/58.70 (94) op(e3, e1) = all_36_2
% 248.64/58.70 (95) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.70 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.70 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.70 (96) ~ (all_16_2 = e2)
% 248.64/58.70 (97) op(all_40_2, e0) = e2
% 248.64/58.70 (98) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.70 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.70 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.70 (99) ~ (all_244_8 = all_40_2)
% 248.64/58.70 (100) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.70 all_250_8 = e0
% 248.64/58.70 (101) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.70 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.70 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.70 (102) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.64/58.70 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.64/58.70 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.70 (103) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.70 all_250_13 = e0
% 248.64/58.70 (104) ~ (all_244_15 = all_38_2)
% 248.64/58.70 (105) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.70 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.70 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.70 (106) ~ (all_36_2 = all_26_2)
% 248.64/58.70 (107) all_44_2 = all_26_2
% 248.64/58.70 (108) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.70 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.70 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.70 (109) op(e1, e4) = all_60_1
% 248.64/58.70 (110) op(all_38_2, e3) = e1
% 248.64/58.70 (111) ~ (all_64_2 = all_12_2)
% 248.64/58.70 (112) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.70 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.70 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.70 (113) op(all_22_2, e3) = e0
% 248.64/58.70 (114) all_68_2 = all_22_2
% 248.64/58.70 (115) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.70 all_250_16 = e0
% 248.64/58.70 (116) op(e0, e3) = all_22_2
% 248.64/58.70 (117) ~ (all_244_0 = all_100_2)
% 248.64/58.70 (118) ~ (all_28_2 = all_22_2)
% 248.64/58.70 (119) all_242_2 = all_38_2
% 248.64/58.70 (120) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.70 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.70 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.70 (121) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.70 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.70 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.70 (122) op(all_84_2, e3) = e4
% 248.64/58.70 (123) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.70 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.70 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.70 (124) all_58_2 = all_20_2
% 248.64/58.70 (125) op(all_62_2, e3) = e1
% 248.64/58.70 (126) op(e4, e1) = all_26_2
% 248.64/58.70 (127) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.70 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.70 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.70 (128) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.70 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.70 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.70 (129) op(all_10_2, e3) = e2
% 248.64/58.70 (130) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.70 all_250_21 = e0
% 248.64/58.70 (131) ~ (all_244_15 = all_62_2)
% 248.64/58.70 (132) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.70 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.70 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.70 (133) op(e3, e4) = all_100_2
% 248.64/58.70 (134) all_250_11 = all_10_2
% 248.64/58.70 (135) ~ (all_244_8 = e1)
% 248.64/58.70 (136) op(e4, e4) = all_244_0
% 248.64/58.70 (137) ~ (all_22_2 = all_12_2)
% 248.64/58.70 (138) all_230_2 = all_20_2
% 248.64/58.70 (139) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.70 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.70 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.70 (140) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.70 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.70 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.70 (141) ~ (e4 = e3)
% 248.64/58.70 (142) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.70 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.70 all_8_1 & $i(all_8_1))
% 248.64/58.70 (143) op(e1, e1) = all_244_15
% 248.64/58.70 (144) ~ (all_34_2 = all_30_2)
% 248.64/58.70 (145) op(e0, e1) = all_20_2
% 248.64/58.70 (146) op(e3, e0) = all_48_2
% 248.64/58.70 (147) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.70 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.70 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.70 (148) op(all_48_2, e0) = e3
% 248.64/58.70 (149) ~ (all_38_2 = all_36_2)
% 248.64/58.70 (150) op(e1, e2) = all_4_2
% 248.64/58.70 (151) ~ (all_100_2 = all_48_2)
% 248.64/58.70 (152) op(all_4_2, all_38_2) = e2
% 248.64/58.70 (153) op(e4, e3) = all_84_2
% 248.64/58.70 (154) ~ (all_62_2 = all_10_2)
% 248.64/58.70 (155) op(e2, e4) = all_64_2
% 248.64/58.70 (156) ~ (all_22_2 = all_10_2)
% 248.64/58.70 (157) ~ (all_36_2 = e1)
% 248.64/58.70 (158) ~ (all_60_1 = e3)
% 248.64/58.70 (159) ~ (all_38_2 = all_26_2)
% 248.64/58.70 (160) ~ (e4 = e2)
% 248.64/58.70 (161) ~ (all_244_24 = all_30_2)
% 248.64/58.70 (162) ~ (all_22_2 = all_20_2)
% 248.64/58.70 (163) all_122_2 = all_36_2
% 248.64/58.70 (164) ~ (all_64_2 = all_16_2)
% 248.64/58.70 (165) op(all_36_2, e1) = e3
% 248.64/58.70 (166) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.70 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.70 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.70 (167) ~ (all_38_2 = all_10_2)
% 248.64/58.70 (168) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.70 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.70 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.70 (169) ~ (all_244_15 = all_36_2)
% 248.64/58.70 (170) ~ (all_244_24 = all_22_2)
% 248.64/58.70 (171) op(all_16_2, e4) = e1
% 248.64/58.70 (172) ~ (all_100_2 = all_16_2)
% 248.64/58.70 (173) op(e2, e0) = all_40_2
% 248.64/58.70 (174) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.70 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.70 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.70 (175) op(e3, e3) = all_244_3
% 248.64/58.70 (176) all_90_2 = all_22_2
% 248.64/58.70 (177) op(all_26_2, all_16_2) = e1
% 248.64/58.70 (178) op(all_12_2, e4) = e0
% 248.64/58.70 (179) all_46_2 = all_36_2
% 248.64/58.70 (180) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.64/58.70 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.64/58.70 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.64/58.70 (181) op(all_30_2, e0) = e4
% 248.64/58.70 (182) op(all_244_24, all_244_24) = e0
% 248.64/58.70 (183) op(e0, e4) = all_12_2
% 248.64/58.70 (184) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.70 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.70 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.70 (185) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.70 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.70 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.70 (186) all_124_2 = all_10_2
% 248.64/58.70
% 248.64/58.70 Begin of proof
% 248.64/58.70 |
% 248.64/58.70 | BETA: splitting (184) gives:
% 248.64/58.70 |
% 248.64/58.70 | Case 1:
% 248.64/58.70 | |
% 248.64/58.70 | | (187) ~ (all_234_2 = e1)
% 248.64/58.70 | |
% 248.64/58.70 | | REDUCE: (35), (187) imply:
% 248.64/58.70 | | (188) $false
% 248.64/58.70 | |
% 248.64/58.70 | | CLOSE: (188) is inconsistent.
% 248.64/58.70 | |
% 248.64/58.70 | Case 2:
% 248.64/58.70 | |
% 248.64/58.70 | | (189) ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 & op(e1, all_234_1) =
% 248.64/58.70 | | all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~ (all_234_1 = e0)
% 248.64/58.70 | | & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.70 | |
% 248.64/58.70 | | BETA: splitting (189) gives:
% 248.64/58.70 | |
% 248.64/58.70 | | Case 1:
% 248.64/58.70 | | |
% 248.64/58.70 | | | (190) ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 & op(e1, all_234_1)
% 248.64/58.70 | | | = all_234_0 & $i(all_234_0) & $i(all_234_1)
% 248.64/58.70 | | |
% 248.64/58.70 | | | ALPHA: (190) implies:
% 248.64/58.70 | | | (191) op(e2, e1) = all_234_1
% 248.64/58.70 | | |
% 248.64/58.70 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.70 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.64/58.70 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.64/58.70 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.64/58.70 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.64/58.70 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 248.64/58.70 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 248.64/58.70 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 248.64/58.70 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.70 | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.70 | | | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.70 | | | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.70 | | | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.70 | | | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.70 | | | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.70 | | | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.70 | | | (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 248.64/58.70 | | | (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 248.64/58.70 | | | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 248.64/58.70 | | | (184), (185), (186), (191) are inconsistent by sub-proof #59.
% 248.64/58.70 | | |
% 248.64/58.71 | | Case 2:
% 248.64/58.71 | | |
% 248.64/58.71 | | | (192) ~ (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1)
% 248.64/58.71 | | |
% 248.64/58.71 | | | ALPHA: (192) implies:
% 248.64/58.71 | | | (193) op(e2, e1) = all_234_1
% 248.64/58.71 | | |
% 248.64/58.71 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.71 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.64/58.71 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.64/58.71 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.64/58.71 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.64/58.71 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 248.64/58.71 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 248.64/58.71 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 248.64/58.71 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.71 | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.71 | | | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.71 | | | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.71 | | | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.71 | | | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.71 | | | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.71 | | | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.71 | | | (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 248.64/58.71 | | | (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 248.64/58.71 | | | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 248.64/58.71 | | | (184), (185), (186), (193) are inconsistent by sub-proof #59.
% 248.64/58.71 | | |
% 248.64/58.71 | | End of split
% 248.64/58.71 | |
% 248.64/58.71 | End of split
% 248.64/58.71 |
% 248.64/58.71 End of proof
% 248.64/58.71
% 248.64/58.71 Sub-proof #59 shows that the following formulas are inconsistent:
% 248.64/58.71 ----------------------------------------------------------------
% 248.64/58.71 (1) ~ (all_30_2 = all_26_2)
% 248.64/58.71 (2) all_252_14 = e3
% 248.64/58.71 (3) all_32_2 = all_20_2
% 248.64/58.71 (4) ~ (all_4_2 = e4)
% 248.64/58.71 (5) ~ (all_10_2 = e4)
% 248.64/58.71 (6) ~ (all_244_0 = all_30_2)
% 248.64/58.71 (7) all_250_16 = all_62_2
% 248.64/58.71 (8) op(all_4_2, e2) = e1
% 248.64/58.71 (9) ~ (all_244_24 = all_34_2)
% 248.64/58.71 (10) ~ (all_244_24 = all_40_2)
% 248.64/58.71 (11) op(all_36_2, all_62_2) = e1
% 248.64/58.71 (12) ~ (all_40_2 = all_38_2)
% 248.64/58.71 (13) op(all_6_2, e2) = e4
% 248.64/58.71 (14) op(e2, e1) = all_234_1
% 248.64/58.71 (15) op(e4, e0) = all_30_2
% 248.64/58.71 (16) all_250_8 = all_36_2
% 248.64/58.71 (17) op(all_28_2, all_40_2) = e2
% 248.64/58.71 (18) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.71 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.71 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.71 (19) ~ (all_40_2 = all_30_2)
% 248.64/58.71 (20) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.71 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.71 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.71 (21) all_94_2 = all_38_2
% 248.64/58.71 (22) op(all_62_2, all_36_2) = e3
% 248.64/58.71 (23) op(all_38_2, e1) = e2
% 248.64/58.71 (24) all_250_13 = all_38_2
% 248.64/58.71 (25) ~ (e2 = e0)
% 248.64/58.71 (26) op(all_64_2, e4) = e2
% 248.64/58.71 (27) ~ (e1 = e0)
% 248.64/58.71 (28) ~ (all_28_2 = e3)
% 248.64/58.71 (29) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.71 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.71 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.71 (30) op(e4, all_34_2) = e1
% 248.64/58.71 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.71 (32) op(e2, e3) = all_10_2
% 248.64/58.71 (33) ~ (e3 = e2)
% 248.64/58.71 (34) op(e0, e0) = all_244_24
% 248.64/58.71 (35) ~ (e4 = e0)
% 248.64/58.71 (36) all_234_2 = e1
% 248.64/58.71 (37) ~ (all_12_2 = e3)
% 248.64/58.71 (38) op(all_244_8, all_244_8) = e2
% 248.64/58.71 (39) op(e2, e2) = all_244_8
% 248.64/58.71 (40) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.71 all_250_11 = e0
% 248.64/58.71 (41) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.71 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.71 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.71 (42) op(all_84_2, all_100_2) = e3
% 248.64/58.71 (43) op(e2, e1) = all_38_2
% 248.64/58.71 (44) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.71 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.71 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.71 (45) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.71 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.71 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.71 (46) ~ (all_36_2 = all_20_2)
% 248.64/58.71 (47) ~ (all_64_2 = all_40_2)
% 248.64/58.71 (48) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.71 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.71 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.71 (49) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.71 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.71 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.71 (50) op(e1, e0) = all_34_2
% 248.64/58.71 (51) op(e4, e2) = all_6_2
% 248.64/58.71 (52) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.71 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.71 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.71 (53) op(e3, all_38_2) = e2
% 248.64/58.71 (54) op(e1, all_10_2) = e2
% 248.64/58.71 (55) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.71 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.71 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.71 (56) all_78_2 = all_10_2
% 248.64/58.71 (57) ~ (e2 = e1)
% 248.64/58.71 (58) op(all_26_2, e1) = e4
% 248.64/58.71 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.71 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.71 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.71 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.71 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.71 op(e0, e1) = e0)))
% 248.64/58.71 (60) ~ (all_100_2 = all_36_2)
% 248.64/58.71 (61) op(e0, e2) = all_28_2
% 248.64/58.71 (62) ~ (all_28_2 = e1)
% 248.64/58.71 (63) op(all_6_2, all_64_2) = e2
% 248.64/58.71 (64) ~ (all_6_2 = e1)
% 248.64/58.71 (65) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.71 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.71 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.71 (66) all_106_2 = all_38_2
% 248.64/58.71 (67) ~ (all_244_8 = all_38_2)
% 248.64/58.71 (68) op(all_244_15, all_244_15) = e1
% 248.64/58.71 (69) all_250_21 = all_22_2
% 248.64/58.71 (70) op(all_34_2, e0) = e1
% 248.64/58.71 (71) ~ (all_244_3 = all_84_2)
% 248.64/58.71 (72) op(e1, e4) = all_16_2
% 248.64/58.71 (73) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.71 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.71 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.71 (74) ~ (all_48_2 = all_30_2)
% 248.64/58.71 (75) ~ (all_244_0 = all_64_2)
% 248.64/58.71 (76) ~ (all_244_3 = all_36_2)
% 248.64/58.71 (77) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.71 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.71 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.71 (78) all_132_2 = all_30_2
% 248.64/58.71 (79) op(e1, e3) = all_62_2
% 248.64/58.71 (80) ~ (all_244_0 = all_26_2)
% 248.64/58.71 (81) op(e1, e0) = all_222_1
% 248.64/58.71 (82) ~ (e3 = e0)
% 248.64/58.71 (83) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.71 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.71 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.71 (84) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.71 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.71 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.71 (85) ~ (all_40_2 = all_10_2)
% 248.64/58.71 (86) all_204_2 = all_36_2
% 248.64/58.71 (87) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.71 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.71 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.71 (88) op(all_20_2, e1) = e0
% 248.64/58.71 (89) ~ (all_244_3 = all_10_2)
% 248.64/58.71 (90) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.71 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.71 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.71 (91) all_70_2 = all_62_2
% 248.64/58.71 (92) ~ (e3 = e1)
% 248.64/58.71 (93) op(all_48_2, all_22_2) = e0
% 248.64/58.71 (94) ~ (all_12_2 = e2)
% 248.64/58.71 (95) op(e3, e1) = all_36_2
% 248.64/58.71 (96) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.71 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.71 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.71 (97) ~ (all_16_2 = e2)
% 248.64/58.71 (98) op(all_40_2, e0) = e2
% 248.64/58.71 (99) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.71 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.71 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.71 (100) ~ (all_244_8 = all_40_2)
% 248.64/58.71 (101) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.71 all_250_8 = e0
% 248.64/58.71 (102) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.71 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.71 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.71 (103) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.64/58.71 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.64/58.71 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.71 (104) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.71 all_250_13 = e0
% 248.64/58.71 (105) ~ (all_244_15 = all_38_2)
% 248.64/58.71 (106) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.71 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.71 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.71 (107) ~ (all_36_2 = all_26_2)
% 248.64/58.71 (108) all_44_2 = all_26_2
% 248.64/58.71 (109) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.71 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.71 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.71 (110) op(e1, e4) = all_60_1
% 248.64/58.71 (111) op(all_38_2, e3) = e1
% 248.64/58.71 (112) ~ (all_64_2 = all_12_2)
% 248.64/58.71 (113) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.71 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.71 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.71 (114) op(all_22_2, e3) = e0
% 248.64/58.71 (115) all_68_2 = all_22_2
% 248.64/58.71 (116) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.71 all_250_16 = e0
% 248.64/58.71 (117) op(e0, e3) = all_22_2
% 248.64/58.71 (118) ~ (all_244_0 = all_100_2)
% 248.64/58.71 (119) ~ (all_28_2 = all_22_2)
% 248.64/58.71 (120) all_242_2 = all_38_2
% 248.64/58.71 (121) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.71 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.71 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.71 (122) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.71 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.71 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.71 (123) op(all_84_2, e3) = e4
% 248.64/58.71 (124) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.71 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.71 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.71 (125) all_58_2 = all_20_2
% 248.64/58.71 (126) op(all_62_2, e3) = e1
% 248.64/58.71 (127) op(e4, e1) = all_26_2
% 248.64/58.71 (128) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.71 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.71 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.71 (129) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.71 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.71 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.71 (130) op(all_10_2, e3) = e2
% 248.64/58.71 (131) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.71 all_250_21 = e0
% 248.64/58.71 (132) ~ (all_244_15 = all_62_2)
% 248.64/58.71 (133) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.71 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.71 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.71 (134) op(e3, e4) = all_100_2
% 248.64/58.71 (135) all_250_11 = all_10_2
% 248.64/58.71 (136) ~ (all_244_8 = e1)
% 248.64/58.71 (137) op(e4, e4) = all_244_0
% 248.64/58.71 (138) ~ (all_22_2 = all_12_2)
% 248.64/58.71 (139) all_230_2 = all_20_2
% 248.64/58.71 (140) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.71 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.71 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.71 (141) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.71 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.71 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.71 (142) ~ (e4 = e3)
% 248.64/58.71 (143) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.71 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.71 all_8_1 & $i(all_8_1))
% 248.64/58.71 (144) op(e1, e1) = all_244_15
% 248.64/58.71 (145) ~ (all_34_2 = all_30_2)
% 248.64/58.71 (146) op(e0, e1) = all_20_2
% 248.64/58.71 (147) op(e3, e0) = all_48_2
% 248.64/58.71 (148) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.71 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.71 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.71 (149) op(all_48_2, e0) = e3
% 248.64/58.71 (150) ~ (all_38_2 = all_36_2)
% 248.64/58.71 (151) op(e1, e2) = all_4_2
% 248.64/58.71 (152) ~ (all_100_2 = all_48_2)
% 248.64/58.71 (153) op(all_4_2, all_38_2) = e2
% 248.64/58.71 (154) op(e4, e3) = all_84_2
% 248.64/58.71 (155) ~ (all_62_2 = all_10_2)
% 248.64/58.71 (156) op(e2, e4) = all_64_2
% 248.64/58.71 (157) ~ (all_22_2 = all_10_2)
% 248.64/58.71 (158) ~ (all_36_2 = e1)
% 248.64/58.71 (159) ~ (all_60_1 = e3)
% 248.64/58.71 (160) ~ (all_38_2 = all_26_2)
% 248.64/58.71 (161) ~ (e4 = e2)
% 248.64/58.71 (162) ~ (all_244_24 = all_30_2)
% 248.64/58.71 (163) ~ (all_22_2 = all_20_2)
% 248.64/58.71 (164) all_122_2 = all_36_2
% 248.64/58.71 (165) ~ (all_64_2 = all_16_2)
% 248.64/58.71 (166) op(all_36_2, e1) = e3
% 248.64/58.71 (167) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.71 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.71 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.71 (168) ~ (all_38_2 = all_10_2)
% 248.64/58.71 (169) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.71 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.71 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.71 (170) ~ (all_244_15 = all_36_2)
% 248.64/58.71 (171) ~ (all_244_24 = all_22_2)
% 248.64/58.71 (172) op(all_16_2, e4) = e1
% 248.64/58.71 (173) ~ (all_100_2 = all_16_2)
% 248.64/58.71 (174) op(e2, e0) = all_40_2
% 248.64/58.71 (175) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.71 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.71 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.71 (176) op(e3, e3) = all_244_3
% 248.64/58.71 (177) all_90_2 = all_22_2
% 248.64/58.71 (178) op(all_26_2, all_16_2) = e1
% 248.64/58.71 (179) op(all_12_2, e4) = e0
% 248.64/58.71 (180) all_46_2 = all_36_2
% 248.64/58.71 (181) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.64/58.71 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.64/58.71 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.64/58.71 (182) op(all_30_2, e0) = e4
% 248.64/58.71 (183) op(all_244_24, all_244_24) = e0
% 248.64/58.71 (184) op(e0, e4) = all_12_2
% 248.64/58.71 (185) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.71 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.71 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.71 (186) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.71 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.71 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.71 (187) all_124_2 = all_10_2
% 248.64/58.71
% 248.64/58.71 Begin of proof
% 248.64/58.71 |
% 248.64/58.71 | GROUND_INST: instantiating (31) with all_34_2, all_222_1, e0, e1, simplifying
% 248.64/58.71 | with (50), (81) gives:
% 248.64/58.71 | (188) all_222_1 = all_34_2
% 248.64/58.71 |
% 248.64/58.71 | GROUND_INST: instantiating (31) with all_16_2, all_60_1, e4, e1, simplifying
% 248.64/58.71 | with (72), (110) gives:
% 248.64/58.71 | (189) all_60_1 = all_16_2
% 248.64/58.71 |
% 248.64/58.71 | GROUND_INST: instantiating (31) with all_38_2, all_234_1, e1, e2, simplifying
% 248.64/58.71 | with (14), (43) gives:
% 248.64/58.71 | (190) all_234_1 = all_38_2
% 248.64/58.71 |
% 248.64/58.71 | REDUCE: (159), (189) imply:
% 248.64/58.71 | (191) ~ (all_16_2 = e3)
% 248.64/58.71 |
% 248.64/58.71 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.71 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 248.64/58.71 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 248.64/58.71 | (35), (36), (37), (38), (39), (40), (41), (42), (44), (45), (46),
% 248.64/58.71 | (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 248.64/58.71 | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 248.64/58.71 | (70), (71), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 248.64/58.71 | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.71 | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.71 | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.71 | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.71 | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.71 | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.71 | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.71 | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.71 | (157), (158), (160), (161), (162), (163), (164), (165), (166),
% 248.64/58.71 | (167), (168), (169), (170), (171), (172), (173), (174), (175),
% 248.64/58.71 | (176), (177), (178), (179), (180), (181), (182), (183), (184),
% 248.64/58.71 | (185), (186), (187), (188), (189), (190), (191) are inconsistent by
% 248.64/58.71 | sub-proof #62.
% 248.64/58.71 |
% 248.64/58.71 End of proof
% 248.64/58.71
% 248.64/58.71 Sub-proof #60 shows that the following formulas are inconsistent:
% 248.64/58.71 ----------------------------------------------------------------
% 248.64/58.71 (1) ~ (all_30_2 = all_26_2)
% 248.64/58.71 (2) all_252_14 = e3
% 248.64/58.71 (3) all_32_2 = all_20_2
% 248.64/58.71 (4) ~ (all_4_2 = e4)
% 248.64/58.71 (5) ~ (all_10_2 = e4)
% 248.64/58.71 (6) ~ (all_244_0 = all_30_2)
% 248.64/58.71 (7) all_250_16 = all_62_2
% 248.64/58.71 (8) op(all_4_2, e2) = e1
% 248.64/58.71 (9) ~ (all_244_24 = all_34_2)
% 248.64/58.71 (10) ~ (all_244_24 = all_40_2)
% 248.64/58.71 (11) op(all_36_2, all_62_2) = e1
% 248.64/58.71 (12) ~ (all_40_2 = all_38_2)
% 248.64/58.71 (13) op(all_6_2, e2) = e4
% 248.64/58.71 (14) op(e4, e0) = all_30_2
% 248.64/58.71 (15) all_250_8 = all_36_2
% 248.64/58.71 (16) op(all_28_2, all_40_2) = e2
% 248.64/58.71 (17) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.71 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.71 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.71 (18) ~ (all_40_2 = all_30_2)
% 248.64/58.72 (19) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.72 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.72 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.72 (20) all_94_2 = all_38_2
% 248.64/58.72 (21) op(all_62_2, all_36_2) = e3
% 248.64/58.72 (22) op(all_38_2, e1) = e2
% 248.64/58.72 (23) all_250_13 = all_38_2
% 248.64/58.72 (24) ~ (e2 = e0)
% 248.64/58.72 (25) op(all_64_2, e4) = e2
% 248.64/58.72 (26) ~ (e1 = e0)
% 248.64/58.72 (27) ~ (all_28_2 = e3)
% 248.64/58.72 (28) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.72 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.72 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.72 (29) op(e4, all_34_2) = e1
% 248.64/58.72 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.72 (31) op(e2, e3) = all_10_2
% 248.64/58.72 (32) ~ (e3 = e2)
% 248.64/58.72 (33) op(e0, e0) = all_244_24
% 248.64/58.72 (34) ~ (e4 = e0)
% 248.64/58.72 (35) all_234_2 = e1
% 248.64/58.72 (36) ~ (all_12_2 = e3)
% 248.64/58.72 (37) op(all_244_8, all_244_8) = e2
% 248.64/58.72 (38) op(e2, e2) = all_244_8
% 248.64/58.72 (39) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.72 all_250_11 = e0
% 248.64/58.72 (40) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.72 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.72 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.72 (41) op(all_84_2, all_100_2) = e3
% 248.64/58.72 (42) op(e2, e1) = all_38_2
% 248.64/58.72 (43) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.72 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.72 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.72 (44) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.72 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.72 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.72 (45) ~ (all_36_2 = all_20_2)
% 248.64/58.72 (46) ~ (all_64_2 = all_40_2)
% 248.64/58.72 (47) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.72 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.72 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.72 (48) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.72 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.72 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.72 (49) op(e1, e0) = all_34_2
% 248.64/58.72 (50) op(e4, e2) = all_6_2
% 248.64/58.72 (51) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.72 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.72 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.72 (52) op(e3, all_38_2) = e2
% 248.64/58.72 (53) op(e1, all_10_2) = e2
% 248.64/58.72 (54) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.72 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.72 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.72 (55) all_78_2 = all_10_2
% 248.64/58.72 (56) ~ (e2 = e1)
% 248.64/58.72 (57) op(all_26_2, e1) = e4
% 248.64/58.72 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.72 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.72 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.72 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.72 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.72 op(e0, e1) = e0)))
% 248.64/58.72 (59) ~ (all_100_2 = all_36_2)
% 248.64/58.72 (60) op(e0, e2) = all_28_2
% 248.64/58.72 (61) ~ (all_28_2 = e1)
% 248.64/58.72 (62) op(all_6_2, all_64_2) = e2
% 248.64/58.72 (63) ~ (all_6_2 = e1)
% 248.64/58.72 (64) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.72 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.72 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.72 (65) all_106_2 = all_38_2
% 248.64/58.72 (66) ~ (all_244_8 = all_38_2)
% 248.64/58.72 (67) op(all_244_15, all_244_15) = e1
% 248.64/58.72 (68) all_250_21 = all_22_2
% 248.64/58.72 (69) op(all_34_2, e0) = e1
% 248.64/58.72 (70) ~ (all_244_3 = all_84_2)
% 248.64/58.72 (71) op(e1, e4) = all_16_2
% 248.64/58.72 (72) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.72 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.72 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.72 (73) ~ (all_48_2 = all_30_2)
% 248.64/58.72 (74) ~ (all_244_0 = all_64_2)
% 248.64/58.72 (75) ~ (all_244_3 = all_36_2)
% 248.64/58.72 (76) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.72 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.72 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.72 (77) all_132_2 = all_30_2
% 248.64/58.72 (78) op(e1, e3) = all_62_2
% 248.64/58.72 (79) ~ (all_244_0 = all_26_2)
% 248.64/58.72 (80) op(e1, e0) = all_222_1
% 248.64/58.72 (81) ~ (e3 = e0)
% 248.64/58.72 (82) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.72 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.72 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.72 (83) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.72 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.72 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.72 (84) ~ (all_40_2 = all_10_2)
% 248.64/58.72 (85) all_204_2 = all_36_2
% 248.64/58.72 (86) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.72 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.72 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.72 (87) op(all_20_2, e1) = e0
% 248.64/58.72 (88) ~ (all_244_3 = all_10_2)
% 248.64/58.72 (89) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.72 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.72 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.72 (90) all_70_2 = all_62_2
% 248.64/58.72 (91) ~ (e3 = e1)
% 248.64/58.72 (92) op(all_48_2, all_22_2) = e0
% 248.64/58.72 (93) ~ (all_12_2 = e2)
% 248.64/58.72 (94) op(e3, e1) = all_36_2
% 248.64/58.72 (95) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.72 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.72 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.72 (96) ~ (all_16_2 = e2)
% 248.64/58.72 (97) op(all_40_2, e0) = e2
% 248.64/58.72 (98) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.72 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.72 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.72 (99) ~ (all_244_8 = all_40_2)
% 248.64/58.72 (100) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.72 all_250_8 = e0
% 248.64/58.72 (101) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.72 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.72 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.72 (102) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.64/58.72 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.64/58.72 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.72 (103) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.72 all_250_13 = e0
% 248.64/58.72 (104) ~ (all_244_15 = all_38_2)
% 248.64/58.72 (105) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.72 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.72 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.72 (106) ~ (all_36_2 = all_26_2)
% 248.64/58.72 (107) all_44_2 = all_26_2
% 248.64/58.72 (108) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.72 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.72 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.72 (109) op(e1, e4) = all_60_1
% 248.64/58.72 (110) op(all_38_2, e3) = e1
% 248.64/58.72 (111) ~ (all_64_2 = all_12_2)
% 248.64/58.72 (112) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.72 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.72 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.72 (113) op(all_22_2, e3) = e0
% 248.64/58.72 (114) all_68_2 = all_22_2
% 248.64/58.72 (115) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.72 all_250_16 = e0
% 248.64/58.72 (116) op(e0, e3) = all_22_2
% 248.64/58.72 (117) ~ (all_244_0 = all_100_2)
% 248.64/58.72 (118) ~ (all_28_2 = all_22_2)
% 248.64/58.72 (119) all_242_2 = all_38_2
% 248.64/58.72 (120) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.72 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.72 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.72 (121) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.72 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.72 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.72 (122) op(all_84_2, e3) = e4
% 248.64/58.72 (123) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.72 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.72 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.72 (124) all_58_2 = all_20_2
% 248.64/58.72 (125) op(all_62_2, e3) = e1
% 248.64/58.72 (126) op(e4, e1) = all_26_2
% 248.64/58.72 (127) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.72 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.72 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.72 (128) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.72 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.72 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.72 (129) op(all_10_2, e3) = e2
% 248.64/58.72 (130) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.72 all_250_21 = e0
% 248.64/58.72 (131) ~ (all_244_15 = all_62_2)
% 248.64/58.72 (132) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.72 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.72 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.72 (133) op(e3, e4) = all_100_2
% 248.64/58.72 (134) all_250_11 = all_10_2
% 248.64/58.72 (135) ~ (all_244_8 = e1)
% 248.64/58.72 (136) op(e4, e4) = all_244_0
% 248.64/58.72 (137) ~ (all_22_2 = all_12_2)
% 248.64/58.72 (138) all_230_2 = all_20_2
% 248.64/58.72 (139) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.72 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.72 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.72 (140) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.72 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.72 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.72 (141) ~ (e4 = e3)
% 248.64/58.72 (142) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.72 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.72 all_8_1 & $i(all_8_1))
% 248.64/58.72 (143) op(e1, e1) = all_244_15
% 248.64/58.72 (144) ~ (all_34_2 = all_30_2)
% 248.64/58.72 (145) op(e0, e1) = all_20_2
% 248.64/58.72 (146) op(e3, e0) = all_48_2
% 248.64/58.72 (147) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.72 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.72 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.72 (148) op(all_48_2, e0) = e3
% 248.64/58.72 (149) ~ (all_38_2 = all_36_2)
% 248.64/58.72 (150) op(e1, e2) = all_4_2
% 248.64/58.72 (151) ~ (all_100_2 = all_48_2)
% 248.64/58.72 (152) op(all_4_2, all_38_2) = e2
% 248.64/58.72 (153) op(e4, e3) = all_84_2
% 248.64/58.72 (154) ~ (all_62_2 = all_10_2)
% 248.64/58.72 (155) op(e2, e4) = all_64_2
% 248.64/58.72 (156) ~ (all_22_2 = all_10_2)
% 248.64/58.72 (157) ~ (all_36_2 = e1)
% 248.64/58.72 (158) ~ (all_38_2 = all_26_2)
% 248.64/58.72 (159) ~ (e4 = e2)
% 248.64/58.72 (160) ~ (all_244_24 = all_30_2)
% 248.64/58.72 (161) ~ (all_22_2 = all_20_2)
% 248.64/58.72 (162) all_122_2 = all_36_2
% 248.64/58.72 (163) ~ (all_64_2 = all_16_2)
% 248.64/58.72 (164) op(all_36_2, e1) = e3
% 248.64/58.72 (165) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.72 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.72 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.72 (166) ~ (all_38_2 = all_10_2)
% 248.64/58.72 (167) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.72 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.72 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.72 (168) ~ (all_244_15 = all_36_2)
% 248.64/58.72 (169) ~ (all_244_24 = all_22_2)
% 248.64/58.72 (170) op(all_16_2, e4) = e1
% 248.64/58.72 (171) ~ (all_100_2 = all_16_2)
% 248.64/58.72 (172) op(e2, e0) = all_40_2
% 248.64/58.72 (173) ~ (all_16_2 = e3)
% 248.64/58.72 (174) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.72 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.72 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.72 (175) op(e3, e3) = all_244_3
% 248.64/58.72 (176) all_90_2 = all_22_2
% 248.64/58.72 (177) op(all_26_2, all_16_2) = e1
% 248.64/58.72 (178) op(all_12_2, e4) = e0
% 248.64/58.72 (179) all_46_2 = all_36_2
% 248.64/58.72 (180) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.64/58.72 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.64/58.72 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.64/58.72 (181) op(all_30_2, e0) = e4
% 248.64/58.72 (182) op(all_244_24, all_244_24) = e0
% 248.64/58.72 (183) op(e0, e4) = all_12_2
% 248.64/58.72 (184) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.72 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.72 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.72 (185) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.72 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.72 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.72 (186) all_124_2 = all_10_2
% 248.64/58.72
% 248.64/58.72 Begin of proof
% 248.64/58.72 |
% 248.64/58.72 | BETA: splitting (184) gives:
% 248.64/58.72 |
% 248.64/58.72 | Case 1:
% 248.64/58.72 | |
% 248.64/58.72 | | (187) ~ (all_234_2 = e1)
% 248.64/58.72 | |
% 248.64/58.72 | | REDUCE: (35), (187) imply:
% 248.64/58.72 | | (188) $false
% 248.64/58.72 | |
% 248.64/58.72 | | CLOSE: (188) is inconsistent.
% 248.64/58.72 | |
% 248.64/58.72 | Case 2:
% 248.64/58.72 | |
% 248.64/58.72 | | (189) ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 & op(e1, all_234_1) =
% 248.64/58.72 | | all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~ (all_234_1 = e0)
% 248.64/58.72 | | & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.72 | |
% 248.64/58.72 | | BETA: splitting (189) gives:
% 248.64/58.72 | |
% 248.64/58.72 | | Case 1:
% 248.64/58.72 | | |
% 248.64/58.72 | | | (190) ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 & op(e1, all_234_1)
% 248.64/58.72 | | | = all_234_0 & $i(all_234_0) & $i(all_234_1)
% 248.64/58.72 | | |
% 248.64/58.72 | | | ALPHA: (190) implies:
% 248.64/58.72 | | | (191) op(e2, e1) = all_234_1
% 248.64/58.72 | | |
% 248.64/58.72 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.72 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.64/58.72 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.64/58.72 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.64/58.72 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.64/58.72 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 248.64/58.72 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 248.64/58.72 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 248.64/58.72 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.72 | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.72 | | | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.72 | | | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.72 | | | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.72 | | | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.72 | | | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.72 | | | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.72 | | | (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 248.64/58.72 | | | (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 248.64/58.72 | | | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 248.64/58.72 | | | (184), (185), (186), (191) are inconsistent by sub-proof #61.
% 248.64/58.72 | | |
% 248.64/58.72 | | Case 2:
% 248.64/58.72 | | |
% 248.64/58.72 | | | (192) ~ (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1)
% 248.64/58.72 | | |
% 248.64/58.72 | | | ALPHA: (192) implies:
% 248.64/58.72 | | | (193) op(e2, e1) = all_234_1
% 248.64/58.72 | | |
% 248.64/58.72 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.72 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 248.64/58.72 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 248.64/58.72 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 248.64/58.72 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 248.64/58.72 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 248.64/58.72 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 248.64/58.72 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 248.64/58.72 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.72 | | | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.72 | | | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.72 | | | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.72 | | | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.72 | | | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.72 | | | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.72 | | | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.72 | | | (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 248.64/58.72 | | | (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 248.64/58.72 | | | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 248.64/58.72 | | | (184), (185), (186), (193) are inconsistent by sub-proof #61.
% 248.64/58.72 | | |
% 248.64/58.72 | | End of split
% 248.64/58.72 | |
% 248.64/58.72 | End of split
% 248.64/58.72 |
% 248.64/58.72 End of proof
% 248.64/58.72
% 248.64/58.72 Sub-proof #61 shows that the following formulas are inconsistent:
% 248.64/58.72 ----------------------------------------------------------------
% 248.64/58.72 (1) ~ (all_30_2 = all_26_2)
% 248.64/58.72 (2) all_252_14 = e3
% 248.64/58.72 (3) all_32_2 = all_20_2
% 248.64/58.72 (4) ~ (all_4_2 = e4)
% 248.64/58.72 (5) ~ (all_10_2 = e4)
% 248.64/58.72 (6) ~ (all_244_0 = all_30_2)
% 248.64/58.72 (7) all_250_16 = all_62_2
% 248.64/58.72 (8) op(all_4_2, e2) = e1
% 248.64/58.72 (9) ~ (all_244_24 = all_34_2)
% 248.64/58.72 (10) ~ (all_244_24 = all_40_2)
% 248.64/58.72 (11) op(all_36_2, all_62_2) = e1
% 248.64/58.72 (12) ~ (all_40_2 = all_38_2)
% 248.64/58.72 (13) op(all_6_2, e2) = e4
% 248.64/58.72 (14) op(e2, e1) = all_234_1
% 248.64/58.72 (15) op(e4, e0) = all_30_2
% 248.64/58.72 (16) all_250_8 = all_36_2
% 248.64/58.72 (17) op(all_28_2, all_40_2) = e2
% 248.64/58.72 (18) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.72 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.72 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.72 (19) ~ (all_40_2 = all_30_2)
% 248.64/58.72 (20) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.72 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.72 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.72 (21) all_94_2 = all_38_2
% 248.64/58.72 (22) op(all_62_2, all_36_2) = e3
% 248.64/58.72 (23) op(all_38_2, e1) = e2
% 248.64/58.72 (24) all_250_13 = all_38_2
% 248.64/58.72 (25) ~ (e2 = e0)
% 248.64/58.72 (26) op(all_64_2, e4) = e2
% 248.64/58.72 (27) ~ (e1 = e0)
% 248.64/58.72 (28) ~ (all_28_2 = e3)
% 248.64/58.72 (29) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.72 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.72 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.72 (30) op(e4, all_34_2) = e1
% 248.64/58.72 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.72 (32) op(e2, e3) = all_10_2
% 248.64/58.72 (33) ~ (e3 = e2)
% 248.64/58.72 (34) op(e0, e0) = all_244_24
% 248.64/58.72 (35) ~ (e4 = e0)
% 248.64/58.72 (36) all_234_2 = e1
% 248.64/58.72 (37) ~ (all_12_2 = e3)
% 248.64/58.72 (38) op(all_244_8, all_244_8) = e2
% 248.64/58.72 (39) op(e2, e2) = all_244_8
% 248.64/58.73 (40) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.73 all_250_11 = e0
% 248.64/58.73 (41) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.73 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.73 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.73 (42) op(all_84_2, all_100_2) = e3
% 248.64/58.73 (43) op(e2, e1) = all_38_2
% 248.64/58.73 (44) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.73 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.73 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.73 (45) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.73 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.73 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.73 (46) ~ (all_36_2 = all_20_2)
% 248.64/58.73 (47) ~ (all_64_2 = all_40_2)
% 248.64/58.73 (48) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.73 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.73 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.73 (49) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.73 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.73 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.73 (50) op(e1, e0) = all_34_2
% 248.64/58.73 (51) op(e4, e2) = all_6_2
% 248.64/58.73 (52) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.73 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.73 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.73 (53) op(e3, all_38_2) = e2
% 248.64/58.73 (54) op(e1, all_10_2) = e2
% 248.64/58.73 (55) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.73 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.73 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.73 (56) all_78_2 = all_10_2
% 248.64/58.73 (57) ~ (e2 = e1)
% 248.64/58.73 (58) op(all_26_2, e1) = e4
% 248.64/58.73 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.73 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.73 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.73 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.73 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.73 op(e0, e1) = e0)))
% 248.64/58.73 (60) ~ (all_100_2 = all_36_2)
% 248.64/58.73 (61) op(e0, e2) = all_28_2
% 248.64/58.73 (62) ~ (all_28_2 = e1)
% 248.64/58.73 (63) op(all_6_2, all_64_2) = e2
% 248.64/58.73 (64) ~ (all_6_2 = e1)
% 248.64/58.73 (65) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.73 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.73 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.73 (66) all_106_2 = all_38_2
% 248.64/58.73 (67) ~ (all_244_8 = all_38_2)
% 248.64/58.73 (68) op(all_244_15, all_244_15) = e1
% 248.64/58.73 (69) all_250_21 = all_22_2
% 248.64/58.73 (70) op(all_34_2, e0) = e1
% 248.64/58.73 (71) ~ (all_244_3 = all_84_2)
% 248.64/58.73 (72) op(e1, e4) = all_16_2
% 248.64/58.73 (73) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.73 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.73 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.73 (74) ~ (all_48_2 = all_30_2)
% 248.64/58.73 (75) ~ (all_244_0 = all_64_2)
% 248.64/58.73 (76) ~ (all_244_3 = all_36_2)
% 248.64/58.73 (77) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.73 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.73 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.73 (78) all_132_2 = all_30_2
% 248.64/58.73 (79) op(e1, e3) = all_62_2
% 248.64/58.73 (80) ~ (all_244_0 = all_26_2)
% 248.64/58.73 (81) op(e1, e0) = all_222_1
% 248.64/58.73 (82) ~ (e3 = e0)
% 248.64/58.73 (83) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.73 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.73 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.73 (84) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.73 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.73 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.73 (85) ~ (all_40_2 = all_10_2)
% 248.64/58.73 (86) all_204_2 = all_36_2
% 248.64/58.73 (87) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.73 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.73 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.73 (88) op(all_20_2, e1) = e0
% 248.64/58.73 (89) ~ (all_244_3 = all_10_2)
% 248.64/58.73 (90) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.73 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.73 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.73 (91) all_70_2 = all_62_2
% 248.64/58.73 (92) ~ (e3 = e1)
% 248.64/58.73 (93) op(all_48_2, all_22_2) = e0
% 248.64/58.73 (94) ~ (all_12_2 = e2)
% 248.64/58.73 (95) op(e3, e1) = all_36_2
% 248.64/58.73 (96) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.73 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.73 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.73 (97) ~ (all_16_2 = e2)
% 248.64/58.73 (98) op(all_40_2, e0) = e2
% 248.64/58.73 (99) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.73 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.73 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.73 (100) ~ (all_244_8 = all_40_2)
% 248.64/58.73 (101) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.73 all_250_8 = e0
% 248.64/58.73 (102) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.73 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.73 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.73 (103) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.64/58.73 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.64/58.73 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.73 (104) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.73 all_250_13 = e0
% 248.64/58.73 (105) ~ (all_244_15 = all_38_2)
% 248.64/58.73 (106) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.73 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.73 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.73 (107) ~ (all_36_2 = all_26_2)
% 248.64/58.73 (108) all_44_2 = all_26_2
% 248.64/58.73 (109) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.73 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.73 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.73 (110) op(e1, e4) = all_60_1
% 248.64/58.73 (111) op(all_38_2, e3) = e1
% 248.64/58.73 (112) ~ (all_64_2 = all_12_2)
% 248.64/58.73 (113) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.73 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.73 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.73 (114) op(all_22_2, e3) = e0
% 248.64/58.73 (115) all_68_2 = all_22_2
% 248.64/58.73 (116) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.73 all_250_16 = e0
% 248.64/58.73 (117) op(e0, e3) = all_22_2
% 248.64/58.73 (118) ~ (all_244_0 = all_100_2)
% 248.64/58.73 (119) ~ (all_28_2 = all_22_2)
% 248.64/58.73 (120) all_242_2 = all_38_2
% 248.64/58.73 (121) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.73 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.73 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.73 (122) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.73 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.73 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.73 (123) op(all_84_2, e3) = e4
% 248.64/58.73 (124) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.73 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.73 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.73 (125) all_58_2 = all_20_2
% 248.64/58.73 (126) op(all_62_2, e3) = e1
% 248.64/58.73 (127) op(e4, e1) = all_26_2
% 248.64/58.73 (128) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.73 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.73 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.73 (129) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.73 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.73 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.73 (130) op(all_10_2, e3) = e2
% 248.64/58.73 (131) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.73 all_250_21 = e0
% 248.64/58.73 (132) ~ (all_244_15 = all_62_2)
% 248.64/58.73 (133) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.73 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.73 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.73 (134) op(e3, e4) = all_100_2
% 248.64/58.73 (135) all_250_11 = all_10_2
% 248.64/58.73 (136) ~ (all_244_8 = e1)
% 248.64/58.73 (137) op(e4, e4) = all_244_0
% 248.64/58.73 (138) ~ (all_22_2 = all_12_2)
% 248.64/58.73 (139) all_230_2 = all_20_2
% 248.64/58.73 (140) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.73 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.73 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.73 (141) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.73 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.73 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.73 (142) ~ (e4 = e3)
% 248.64/58.73 (143) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.73 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.73 all_8_1 & $i(all_8_1))
% 248.64/58.73 (144) op(e1, e1) = all_244_15
% 248.64/58.73 (145) ~ (all_34_2 = all_30_2)
% 248.64/58.73 (146) op(e0, e1) = all_20_2
% 248.64/58.73 (147) op(e3, e0) = all_48_2
% 248.64/58.73 (148) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.73 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.73 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.73 (149) op(all_48_2, e0) = e3
% 248.64/58.73 (150) ~ (all_38_2 = all_36_2)
% 248.64/58.73 (151) op(e1, e2) = all_4_2
% 248.64/58.73 (152) ~ (all_100_2 = all_48_2)
% 248.64/58.73 (153) op(all_4_2, all_38_2) = e2
% 248.64/58.73 (154) op(e4, e3) = all_84_2
% 248.64/58.73 (155) ~ (all_62_2 = all_10_2)
% 248.64/58.73 (156) op(e2, e4) = all_64_2
% 248.64/58.73 (157) ~ (all_22_2 = all_10_2)
% 248.64/58.73 (158) ~ (all_36_2 = e1)
% 248.64/58.73 (159) ~ (all_38_2 = all_26_2)
% 248.64/58.73 (160) ~ (e4 = e2)
% 248.64/58.73 (161) ~ (all_244_24 = all_30_2)
% 248.64/58.73 (162) ~ (all_22_2 = all_20_2)
% 248.64/58.73 (163) all_122_2 = all_36_2
% 248.64/58.73 (164) ~ (all_64_2 = all_16_2)
% 248.64/58.73 (165) op(all_36_2, e1) = e3
% 248.64/58.73 (166) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.73 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.73 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.73 (167) ~ (all_38_2 = all_10_2)
% 248.64/58.73 (168) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.73 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.73 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.73 (169) ~ (all_244_15 = all_36_2)
% 248.64/58.73 (170) ~ (all_244_24 = all_22_2)
% 248.64/58.73 (171) op(all_16_2, e4) = e1
% 248.64/58.73 (172) ~ (all_100_2 = all_16_2)
% 248.64/58.73 (173) op(e2, e0) = all_40_2
% 248.64/58.73 (174) ~ (all_16_2 = e3)
% 248.64/58.73 (175) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.73 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.73 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.73 (176) op(e3, e3) = all_244_3
% 248.64/58.73 (177) all_90_2 = all_22_2
% 248.64/58.73 (178) op(all_26_2, all_16_2) = e1
% 248.64/58.73 (179) op(all_12_2, e4) = e0
% 248.64/58.73 (180) all_46_2 = all_36_2
% 248.64/58.73 (181) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.64/58.73 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.64/58.73 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.64/58.73 (182) op(all_30_2, e0) = e4
% 248.64/58.73 (183) op(all_244_24, all_244_24) = e0
% 248.64/58.73 (184) op(e0, e4) = all_12_2
% 248.64/58.73 (185) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.73 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.73 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.73 (186) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.73 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.73 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.73 (187) all_124_2 = all_10_2
% 248.64/58.73
% 248.64/58.73 Begin of proof
% 248.64/58.73 |
% 248.64/58.73 | GROUND_INST: instantiating (31) with all_34_2, all_222_1, e0, e1, simplifying
% 248.64/58.73 | with (50), (81) gives:
% 248.64/58.73 | (188) all_222_1 = all_34_2
% 248.64/58.73 |
% 248.64/58.73 | GROUND_INST: instantiating (31) with all_16_2, all_60_1, e4, e1, simplifying
% 248.64/58.73 | with (72), (110) gives:
% 248.64/58.73 | (189) all_60_1 = all_16_2
% 248.64/58.73 |
% 248.64/58.73 | GROUND_INST: instantiating (31) with all_38_2, all_234_1, e1, e2, simplifying
% 248.64/58.73 | with (14), (43) gives:
% 248.64/58.73 | (190) all_234_1 = all_38_2
% 248.64/58.73 |
% 248.64/58.73 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.64/58.73 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 248.64/58.73 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 248.64/58.73 | (35), (36), (37), (38), (39), (40), (41), (42), (44), (45), (46),
% 248.64/58.73 | (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 248.64/58.73 | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 248.64/58.73 | (70), (71), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 248.64/58.73 | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 248.64/58.73 | (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 248.64/58.73 | (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 248.64/58.73 | (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 248.64/58.73 | (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 248.64/58.73 | (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 248.64/58.73 | (139), (140), (141), (142), (143), (144), (145), (146), (147),
% 248.64/58.73 | (148), (149), (150), (151), (152), (153), (154), (155), (156),
% 248.64/58.73 | (157), (158), (159), (160), (161), (162), (163), (164), (165),
% 248.64/58.73 | (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 248.64/58.73 | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 248.64/58.73 | (184), (185), (186), (187), (188), (189), (190) are inconsistent by
% 248.64/58.73 | sub-proof #62.
% 248.64/58.73 |
% 248.64/58.73 End of proof
% 248.64/58.73
% 248.64/58.73 Sub-proof #62 shows that the following formulas are inconsistent:
% 248.64/58.73 ----------------------------------------------------------------
% 248.64/58.73 (1) ~ (all_30_2 = all_26_2)
% 248.64/58.73 (2) all_252_14 = e3
% 248.64/58.73 (3) all_234_1 = all_38_2
% 248.64/58.73 (4) all_32_2 = all_20_2
% 248.64/58.73 (5) ~ (all_4_2 = e4)
% 248.64/58.73 (6) ~ (all_10_2 = e4)
% 248.64/58.73 (7) ~ (all_244_0 = all_30_2)
% 248.64/58.73 (8) all_250_16 = all_62_2
% 248.64/58.73 (9) op(all_4_2, e2) = e1
% 248.64/58.73 (10) ~ (all_244_24 = all_34_2)
% 248.64/58.73 (11) ~ (all_244_24 = all_40_2)
% 248.64/58.73 (12) op(all_36_2, all_62_2) = e1
% 248.64/58.73 (13) ~ (all_40_2 = all_38_2)
% 248.64/58.73 (14) op(all_6_2, e2) = e4
% 248.64/58.73 (15) op(e2, e1) = all_234_1
% 248.64/58.73 (16) op(e4, e0) = all_30_2
% 248.64/58.73 (17) all_250_8 = all_36_2
% 248.64/58.73 (18) op(all_28_2, all_40_2) = e2
% 248.64/58.73 (19) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.73 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.73 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.73 (20) ~ (all_40_2 = all_30_2)
% 248.64/58.73 (21) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.73 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.73 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.73 (22) all_94_2 = all_38_2
% 248.64/58.73 (23) op(all_62_2, all_36_2) = e3
% 248.64/58.73 (24) op(all_38_2, e1) = e2
% 248.64/58.73 (25) all_250_13 = all_38_2
% 248.64/58.73 (26) ~ (e2 = e0)
% 248.64/58.73 (27) op(all_64_2, e4) = e2
% 248.64/58.73 (28) ~ (e1 = e0)
% 248.64/58.73 (29) ~ (all_28_2 = e3)
% 248.64/58.73 (30) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.73 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.73 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.73 (31) op(e4, all_34_2) = e1
% 248.64/58.73 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.73 (33) op(e2, e3) = all_10_2
% 248.64/58.73 (34) ~ (e3 = e2)
% 248.64/58.73 (35) op(e0, e0) = all_244_24
% 248.64/58.73 (36) ~ (e4 = e0)
% 248.64/58.73 (37) all_234_2 = e1
% 248.64/58.73 (38) ~ (all_12_2 = e3)
% 248.64/58.73 (39) op(all_244_8, all_244_8) = e2
% 248.64/58.73 (40) op(e2, e2) = all_244_8
% 248.64/58.73 (41) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.73 all_250_11 = e0
% 248.64/58.73 (42) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.73 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.73 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.73 (43) op(all_84_2, all_100_2) = e3
% 248.64/58.74 (44) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.74 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.74 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.74 (45) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.74 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.74 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.74 (46) ~ (all_36_2 = all_20_2)
% 248.64/58.74 (47) ~ (all_64_2 = all_40_2)
% 248.64/58.74 (48) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.74 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.74 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.74 (49) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.74 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.74 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.74 (50) op(e4, e2) = all_6_2
% 248.64/58.74 (51) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.74 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.74 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.74 (52) op(e3, all_38_2) = e2
% 248.64/58.74 (53) op(e1, all_10_2) = e2
% 248.64/58.74 (54) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.74 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.74 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.74 (55) all_78_2 = all_10_2
% 248.64/58.74 (56) ~ (e2 = e1)
% 248.64/58.74 (57) all_222_1 = all_34_2
% 248.64/58.74 (58) op(all_26_2, e1) = e4
% 248.64/58.74 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.74 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.74 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.74 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.74 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.74 op(e0, e1) = e0)))
% 248.64/58.74 (60) ~ (all_100_2 = all_36_2)
% 248.64/58.74 (61) op(e0, e2) = all_28_2
% 248.64/58.74 (62) ~ (all_28_2 = e1)
% 248.64/58.74 (63) op(all_6_2, all_64_2) = e2
% 248.64/58.74 (64) ~ (all_6_2 = e1)
% 248.64/58.74 (65) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.74 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.74 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.74 (66) all_106_2 = all_38_2
% 248.64/58.74 (67) ~ (all_244_8 = all_38_2)
% 248.64/58.74 (68) op(all_244_15, all_244_15) = e1
% 248.64/58.74 (69) all_250_21 = all_22_2
% 248.64/58.74 (70) op(all_34_2, e0) = e1
% 248.64/58.74 (71) ~ (all_244_3 = all_84_2)
% 248.64/58.74 (72) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.74 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.74 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.74 (73) ~ (all_48_2 = all_30_2)
% 248.64/58.74 (74) ~ (all_244_0 = all_64_2)
% 248.64/58.74 (75) ~ (all_244_3 = all_36_2)
% 248.64/58.74 (76) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.74 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.74 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.74 (77) all_132_2 = all_30_2
% 248.64/58.74 (78) op(e1, e3) = all_62_2
% 248.64/58.74 (79) ~ (all_244_0 = all_26_2)
% 248.64/58.74 (80) op(e1, e0) = all_222_1
% 248.64/58.74 (81) ~ (e3 = e0)
% 248.64/58.74 (82) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.74 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.74 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.74 (83) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.74 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.74 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.74 (84) ~ (all_40_2 = all_10_2)
% 248.64/58.74 (85) all_204_2 = all_36_2
% 248.64/58.74 (86) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.74 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.74 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.74 (87) op(all_20_2, e1) = e0
% 248.64/58.74 (88) ~ (all_244_3 = all_10_2)
% 248.64/58.74 (89) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.74 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.74 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.74 (90) all_60_1 = all_16_2
% 248.64/58.74 (91) all_70_2 = all_62_2
% 248.64/58.74 (92) ~ (e3 = e1)
% 248.64/58.74 (93) op(all_48_2, all_22_2) = e0
% 248.64/58.74 (94) ~ (all_12_2 = e2)
% 248.64/58.74 (95) op(e3, e1) = all_36_2
% 248.64/58.74 (96) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.74 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.74 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.74 (97) ~ (all_16_2 = e2)
% 248.64/58.74 (98) op(all_40_2, e0) = e2
% 248.64/58.74 (99) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.74 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.74 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.74 (100) ~ (all_244_8 = all_40_2)
% 248.64/58.74 (101) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.74 all_250_8 = e0
% 248.64/58.74 (102) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.74 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.74 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.74 (103) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.64/58.74 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.64/58.74 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.74 (104) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.74 all_250_13 = e0
% 248.64/58.74 (105) ~ (all_244_15 = all_38_2)
% 248.64/58.74 (106) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.74 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.74 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.74 (107) ~ (all_36_2 = all_26_2)
% 248.64/58.74 (108) all_44_2 = all_26_2
% 248.64/58.74 (109) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.74 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.74 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.74 (110) op(e1, e4) = all_60_1
% 248.64/58.74 (111) op(all_38_2, e3) = e1
% 248.64/58.74 (112) ~ (all_64_2 = all_12_2)
% 248.64/58.74 (113) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.74 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.74 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.74 (114) op(all_22_2, e3) = e0
% 248.64/58.74 (115) all_68_2 = all_22_2
% 248.64/58.74 (116) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.74 all_250_16 = e0
% 248.64/58.74 (117) op(e0, e3) = all_22_2
% 248.64/58.74 (118) ~ (all_244_0 = all_100_2)
% 248.64/58.74 (119) ~ (all_28_2 = all_22_2)
% 248.64/58.74 (120) all_242_2 = all_38_2
% 248.64/58.74 (121) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.74 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.74 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.74 (122) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.74 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.74 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.74 (123) op(all_84_2, e3) = e4
% 248.64/58.74 (124) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.74 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.74 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.74 (125) all_58_2 = all_20_2
% 248.64/58.74 (126) op(all_62_2, e3) = e1
% 248.64/58.74 (127) op(e4, e1) = all_26_2
% 248.64/58.74 (128) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.74 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.74 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.74 (129) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.74 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.74 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.74 (130) op(all_10_2, e3) = e2
% 248.64/58.74 (131) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.74 all_250_21 = e0
% 248.64/58.74 (132) ~ (all_244_15 = all_62_2)
% 248.64/58.74 (133) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.74 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.74 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.74 (134) op(e3, e4) = all_100_2
% 248.64/58.74 (135) all_250_11 = all_10_2
% 248.64/58.74 (136) ~ (all_244_8 = e1)
% 248.64/58.74 (137) op(e4, e4) = all_244_0
% 248.64/58.74 (138) ~ (all_22_2 = all_12_2)
% 248.64/58.74 (139) all_230_2 = all_20_2
% 248.64/58.74 (140) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.74 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.74 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.74 (141) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.74 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.74 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.74 (142) ~ (e4 = e3)
% 248.64/58.74 (143) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.74 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.74 all_8_1 & $i(all_8_1))
% 248.64/58.74 (144) op(e1, e1) = all_244_15
% 248.64/58.74 (145) ~ (all_34_2 = all_30_2)
% 248.64/58.74 (146) op(e0, e1) = all_20_2
% 248.64/58.74 (147) op(e3, e0) = all_48_2
% 248.64/58.74 (148) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.74 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.74 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.74 (149) op(all_48_2, e0) = e3
% 248.64/58.74 (150) ~ (all_38_2 = all_36_2)
% 248.64/58.74 (151) op(e1, e2) = all_4_2
% 248.64/58.74 (152) ~ (all_100_2 = all_48_2)
% 248.64/58.74 (153) op(all_4_2, all_38_2) = e2
% 248.64/58.74 (154) op(e4, e3) = all_84_2
% 248.64/58.74 (155) ~ (all_62_2 = all_10_2)
% 248.64/58.74 (156) op(e2, e4) = all_64_2
% 248.64/58.74 (157) ~ (all_22_2 = all_10_2)
% 248.64/58.74 (158) ~ (all_36_2 = e1)
% 248.64/58.74 (159) ~ (all_38_2 = all_26_2)
% 248.64/58.74 (160) ~ (e4 = e2)
% 248.64/58.74 (161) ~ (all_244_24 = all_30_2)
% 248.64/58.74 (162) ~ (all_22_2 = all_20_2)
% 248.64/58.74 (163) all_122_2 = all_36_2
% 248.64/58.74 (164) ~ (all_64_2 = all_16_2)
% 248.64/58.74 (165) op(all_36_2, e1) = e3
% 248.64/58.74 (166) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.74 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.74 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.74 (167) ~ (all_38_2 = all_10_2)
% 248.64/58.74 (168) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.74 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.74 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.74 (169) ~ (all_244_15 = all_36_2)
% 248.64/58.74 (170) ~ (all_244_24 = all_22_2)
% 248.64/58.74 (171) op(all_16_2, e4) = e1
% 248.64/58.74 (172) ~ (all_100_2 = all_16_2)
% 248.64/58.74 (173) op(e2, e0) = all_40_2
% 248.64/58.74 (174) ~ (all_16_2 = e3)
% 248.64/58.74 (175) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.74 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.74 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.74 (176) op(e3, e3) = all_244_3
% 248.64/58.74 (177) all_90_2 = all_22_2
% 248.64/58.74 (178) op(all_26_2, all_16_2) = e1
% 248.64/58.74 (179) op(all_12_2, e4) = e0
% 248.64/58.74 (180) all_46_2 = all_36_2
% 248.64/58.74 (181) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.64/58.74 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.64/58.74 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.64/58.74 (182) op(all_30_2, e0) = e4
% 248.64/58.74 (183) op(all_244_24, all_244_24) = e0
% 248.64/58.74 (184) op(e0, e4) = all_12_2
% 248.64/58.74 (185) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.74 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.74 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.74 (186) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.74 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.74 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.74 (187) all_124_2 = all_10_2
% 248.64/58.74
% 248.64/58.74 Begin of proof
% 248.64/58.74 |
% 248.64/58.74 | REDUCE: (3), (15) imply:
% 248.64/58.74 | (188) op(e2, e1) = all_38_2
% 248.64/58.74 |
% 248.64/58.74 | REDUCE: (90), (110) imply:
% 248.64/58.74 | (189) op(e1, e4) = all_16_2
% 248.64/58.74 |
% 248.64/58.74 | REDUCE: (57), (80) imply:
% 248.64/58.74 | (190) op(e1, e0) = all_34_2
% 248.64/58.74 |
% 248.64/58.74 | BETA: splitting (181) gives:
% 248.64/58.74 |
% 248.64/58.74 | Case 1:
% 248.64/58.74 | |
% 248.64/58.74 | | (191) ~ (all_22_2 = e1)
% 248.64/58.74 | |
% 248.64/58.74 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 248.64/58.74 | | (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 248.64/58.74 | | (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 248.64/58.74 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 248.64/58.74 | | (49), (51), (52), (53), (54), (55), (56), (58), (59), (60), (61),
% 248.64/58.74 | | (62), (63), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 248.64/58.74 | | (74), (75), (76), (77), (78), (79), (81), (82), (83), (84), (85),
% 248.64/58.74 | | (86), (87), (88), (89), (91), (92), (93), (94), (95), (96), (97),
% 248.64/58.74 | | (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 248.64/58.74 | | (107), (108), (109), (111), (112), (113), (114), (115), (116),
% 248.64/58.74 | | (117), (118), (119), (120), (121), (122), (123), (124), (125),
% 248.64/58.74 | | (126), (127), (128), (129), (130), (131), (132), (133), (134),
% 248.64/58.74 | | (135), (136), (137), (138), (139), (140), (141), (142), (143),
% 248.64/58.74 | | (144), (145), (146), (147), (148), (149), (150), (151), (152),
% 248.64/58.74 | | (153), (154), (155), (156), (157), (158), (159), (160), (161),
% 248.64/58.74 | | (162), (163), (164), (165), (166), (167), (168), (169), (170),
% 248.64/58.74 | | (171), (172), (173), (174), (175), (176), (177), (178), (179),
% 248.64/58.74 | | (180), (182), (183), (184), (185), (186), (187), (188), (189),
% 248.64/58.74 | | (190), (191) are inconsistent by sub-proof #65.
% 248.64/58.74 | |
% 248.64/58.74 | Case 2:
% 248.64/58.74 | |
% 248.64/58.74 | | (192) all_22_2 = e1
% 248.64/58.74 | |
% 248.64/58.74 | | REF_CLOSE: (2), (26), (31), (32), (34), (40), (50), (51), (64), (68), (97),
% 248.64/58.74 | | (114), (136), (144), (175), (189), (190), (192) are inconsistent
% 248.64/58.74 | | by sub-proof #63.
% 248.64/58.74 | |
% 248.64/58.74 | End of split
% 248.64/58.74 |
% 248.64/58.74 End of proof
% 248.64/58.74
% 248.64/58.74 Sub-proof #63 shows that the following formulas are inconsistent:
% 248.64/58.74 ----------------------------------------------------------------
% 248.64/58.74 (1) all_252_14 = e3
% 248.64/58.74 (2) ~ (e2 = e0)
% 248.64/58.74 (3) op(e4, all_34_2) = e1
% 248.64/58.74 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.74 (5) ~ (e3 = e2)
% 248.64/58.74 (6) op(e2, e2) = all_244_8
% 248.64/58.74 (7) op(e1, e0) = all_34_2
% 248.64/58.74 (8) op(e4, e2) = all_6_2
% 248.64/58.74 (9) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.74 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.74 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.74 (10) ~ (all_6_2 = e1)
% 248.64/58.74 (11) op(all_244_15, all_244_15) = e1
% 248.64/58.74 (12) op(e1, e4) = all_16_2
% 248.64/58.74 (13) ~ (all_16_2 = e2)
% 248.64/58.74 (14) all_22_2 = e1
% 248.64/58.74 (15) op(all_22_2, e3) = e0
% 248.64/58.74 (16) ~ (all_244_8 = e1)
% 248.64/58.74 (17) op(e1, e1) = all_244_15
% 248.64/58.74 (18) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.74 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.74 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.74
% 248.64/58.74 Begin of proof
% 248.64/58.74 |
% 248.64/58.74 | REDUCE: (14), (15) imply:
% 248.64/58.74 | (19) op(e1, e3) = e0
% 248.64/58.74 |
% 248.64/58.74 | BETA: splitting (9) gives:
% 248.64/58.74 |
% 248.64/58.74 | Case 1:
% 248.64/58.74 | |
% 248.64/58.74 | | (20) ~ (all_34_2 = e2)
% 248.64/58.74 | |
% 248.64/58.74 | | BETA: splitting (18) gives:
% 248.64/58.74 | |
% 248.64/58.74 | | Case 1:
% 248.64/58.74 | | |
% 248.64/58.74 | | | (21) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 248.64/58.74 | | | e3) = e2)
% 248.64/58.74 | | |
% 248.64/58.74 | | | REF_CLOSE: (2), (4), (12), (13), (19), (21) are inconsistent by sub-proof
% 248.64/58.74 | | | #64.
% 248.64/58.74 | | |
% 248.64/58.74 | | Case 2:
% 248.64/58.74 | | |
% 248.64/58.74 | | | (22) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.74 | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.74 | | |
% 248.64/58.74 | | | BETA: splitting (22) gives:
% 248.64/58.74 | | |
% 248.64/58.74 | | | Case 1:
% 248.64/58.74 | | | |
% 248.64/58.74 | | | | (23) all_252_14 = e2 & op(e1, e2) = e2
% 248.64/58.74 | | | |
% 248.64/58.74 | | | | REF_CLOSE: (1), (5), (23) are inconsistent by sub-proof #76.
% 248.64/58.74 | | | |
% 248.64/58.74 | | | Case 2:
% 248.64/58.74 | | | |
% 248.64/58.74 | | | | (24) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.74 | | | | e0) = e2)
% 248.64/58.74 | | | |
% 248.64/58.74 | | | | REF_CLOSE: (4), (6), (7), (11), (16), (17), (20), (24) are inconsistent
% 248.64/58.74 | | | | by sub-proof #79.
% 248.64/58.74 | | | |
% 248.64/58.74 | | | End of split
% 248.64/58.74 | | |
% 248.64/58.74 | | End of split
% 248.64/58.74 | |
% 248.64/58.74 | Case 2:
% 248.64/58.74 | |
% 248.64/58.74 | | (25) all_34_2 = e2
% 248.64/58.74 | |
% 248.64/58.74 | | REDUCE: (3), (25) imply:
% 248.64/58.74 | | (26) op(e4, e2) = e1
% 248.64/58.74 | |
% 248.64/58.74 | | REF_CLOSE: (4), (8), (10), (26) are inconsistent by sub-proof #930.
% 248.64/58.74 | |
% 248.64/58.74 | End of split
% 248.64/58.74 |
% 248.64/58.74 End of proof
% 248.64/58.74
% 248.64/58.74 Sub-proof #64 shows that the following formulas are inconsistent:
% 248.64/58.74 ----------------------------------------------------------------
% 248.64/58.74 (1) op(e1, e3) = e0
% 248.64/58.74 (2) ~ (e2 = e0)
% 248.64/58.74 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.74 (4) op(e1, e4) = all_16_2
% 248.64/58.74 (5) ~ (all_16_2 = e2)
% 248.64/58.74 (6) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 248.64/58.74
% 248.64/58.74 Begin of proof
% 248.64/58.74 |
% 248.64/58.74 | BETA: splitting (6) gives:
% 248.64/58.74 |
% 248.64/58.74 | Case 1:
% 248.64/58.74 | |
% 248.64/58.74 | | (7) all_252_12 = e2 & op(e1, e4) = e2
% 248.64/58.74 | |
% 248.64/58.74 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #926.
% 248.64/58.74 | |
% 248.64/58.74 | Case 2:
% 248.64/58.74 | |
% 248.64/58.74 | | (8) all_252_13 = e2 & op(e1, e3) = e2
% 248.64/58.74 | |
% 248.64/58.74 | | ALPHA: (8) implies:
% 248.64/58.74 | | (9) op(e1, e3) = e2
% 248.64/58.74 | |
% 248.64/58.74 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #776.
% 248.64/58.74 | |
% 248.64/58.74 | End of split
% 248.64/58.74 |
% 248.64/58.74 End of proof
% 248.64/58.74
% 248.64/58.74 Sub-proof #65 shows that the following formulas are inconsistent:
% 248.64/58.74 ----------------------------------------------------------------
% 248.64/58.74 (1) ~ (all_30_2 = all_26_2)
% 248.64/58.74 (2) all_252_14 = e3
% 248.64/58.74 (3) all_32_2 = all_20_2
% 248.64/58.74 (4) ~ (all_4_2 = e4)
% 248.64/58.74 (5) ~ (all_10_2 = e4)
% 248.64/58.74 (6) ~ (all_244_0 = all_30_2)
% 248.64/58.74 (7) all_250_16 = all_62_2
% 248.64/58.74 (8) op(all_4_2, e2) = e1
% 248.64/58.74 (9) ~ (all_244_24 = all_34_2)
% 248.64/58.74 (10) ~ (all_244_24 = all_40_2)
% 248.64/58.74 (11) op(all_36_2, all_62_2) = e1
% 248.64/58.74 (12) ~ (all_40_2 = all_38_2)
% 248.64/58.74 (13) op(all_6_2, e2) = e4
% 248.64/58.74 (14) op(e4, e0) = all_30_2
% 248.64/58.74 (15) all_250_8 = all_36_2
% 248.64/58.74 (16) op(all_28_2, all_40_2) = e2
% 248.64/58.74 (17) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.64/58.74 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.64/58.74 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.64/58.74 (18) ~ (all_40_2 = all_30_2)
% 248.64/58.75 (19) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.64/58.75 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.64/58.75 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.64/58.75 (20) all_94_2 = all_38_2
% 248.64/58.75 (21) op(all_62_2, all_36_2) = e3
% 248.64/58.75 (22) op(all_38_2, e1) = e2
% 248.64/58.75 (23) all_250_13 = all_38_2
% 248.64/58.75 (24) ~ (e2 = e0)
% 248.64/58.75 (25) op(all_64_2, e4) = e2
% 248.64/58.75 (26) ~ (e1 = e0)
% 248.64/58.75 (27) ~ (all_28_2 = e3)
% 248.64/58.75 (28) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.64/58.75 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.64/58.75 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.64/58.75 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.64/58.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.64/58.75 (30) op(e2, e3) = all_10_2
% 248.64/58.75 (31) ~ (e3 = e2)
% 248.64/58.75 (32) op(e0, e0) = all_244_24
% 248.64/58.75 (33) ~ (e4 = e0)
% 248.64/58.75 (34) all_234_2 = e1
% 248.64/58.75 (35) ~ (all_12_2 = e3)
% 248.64/58.75 (36) op(all_244_8, all_244_8) = e2
% 248.64/58.75 (37) op(e2, e2) = all_244_8
% 248.64/58.75 (38) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 248.64/58.75 all_250_11 = e0
% 248.64/58.75 (39) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.64/58.75 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.64/58.75 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.64/58.75 (40) op(all_84_2, all_100_2) = e3
% 248.64/58.75 (41) op(e2, e1) = all_38_2
% 248.64/58.75 (42) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.64/58.75 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.64/58.75 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.75 (43) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.64/58.75 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.64/58.75 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.64/58.75 (44) ~ (all_36_2 = all_20_2)
% 248.64/58.75 (45) ~ (all_64_2 = all_40_2)
% 248.64/58.75 (46) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.64/58.75 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.64/58.75 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.75 (47) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 248.64/58.75 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 248.64/58.75 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 248.64/58.75 (48) op(e1, e0) = all_34_2
% 248.64/58.75 (49) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.64/58.75 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.75 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.75 (50) op(e3, all_38_2) = e2
% 248.64/58.75 (51) op(e1, all_10_2) = e2
% 248.64/58.75 (52) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.64/58.75 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.64/58.75 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.75 (53) all_78_2 = all_10_2
% 248.64/58.75 (54) ~ (e2 = e1)
% 248.64/58.75 (55) op(all_26_2, e1) = e4
% 248.64/58.75 (56) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.64/58.75 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.64/58.75 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.64/58.75 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.64/58.75 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.64/58.75 op(e0, e1) = e0)))
% 248.64/58.75 (57) ~ (all_100_2 = all_36_2)
% 248.64/58.75 (58) op(e0, e2) = all_28_2
% 248.64/58.75 (59) ~ (all_28_2 = e1)
% 248.64/58.75 (60) op(all_6_2, all_64_2) = e2
% 248.64/58.75 (61) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.64/58.75 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.64/58.75 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.64/58.75 (62) all_106_2 = all_38_2
% 248.64/58.75 (63) ~ (all_244_8 = all_38_2)
% 248.64/58.75 (64) op(all_244_15, all_244_15) = e1
% 248.64/58.75 (65) all_250_21 = all_22_2
% 248.64/58.75 (66) op(all_34_2, e0) = e1
% 248.64/58.75 (67) ~ (all_244_3 = all_84_2)
% 248.64/58.75 (68) op(e1, e4) = all_16_2
% 248.64/58.75 (69) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 248.64/58.75 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 248.64/58.75 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 248.64/58.75 (70) ~ (all_48_2 = all_30_2)
% 248.64/58.75 (71) ~ (all_244_0 = all_64_2)
% 248.64/58.75 (72) ~ (all_244_3 = all_36_2)
% 248.64/58.75 (73) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.64/58.75 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.64/58.75 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.64/58.75 (74) all_132_2 = all_30_2
% 248.64/58.75 (75) op(e1, e3) = all_62_2
% 248.64/58.75 (76) ~ (all_244_0 = all_26_2)
% 248.64/58.75 (77) ~ (e3 = e0)
% 248.64/58.75 (78) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 248.64/58.75 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 248.64/58.75 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 248.64/58.75 (79) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 248.64/58.75 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 248.64/58.75 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 248.64/58.75 (80) ~ (all_40_2 = all_10_2)
% 248.64/58.75 (81) all_204_2 = all_36_2
% 248.64/58.75 (82) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.64/58.75 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.64/58.75 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.64/58.75 (83) op(all_20_2, e1) = e0
% 248.64/58.75 (84) ~ (all_244_3 = all_10_2)
% 248.64/58.75 (85) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.64/58.75 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.64/58.75 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.64/58.75 (86) all_70_2 = all_62_2
% 248.64/58.75 (87) ~ (e3 = e1)
% 248.64/58.75 (88) op(all_48_2, all_22_2) = e0
% 248.64/58.75 (89) ~ (all_12_2 = e2)
% 248.64/58.75 (90) op(e3, e1) = all_36_2
% 248.64/58.75 (91) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 248.64/58.75 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 248.64/58.75 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 248.64/58.75 (92) ~ (all_16_2 = e2)
% 248.64/58.75 (93) op(all_40_2, e0) = e2
% 248.64/58.75 (94) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.64/58.75 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.64/58.75 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.75 (95) ~ (all_22_2 = e1)
% 248.64/58.75 (96) ~ (all_244_8 = all_40_2)
% 248.64/58.75 (97) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.75 all_250_8 = e0
% 248.64/58.75 (98) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.64/58.75 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.64/58.75 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.64/58.75 (99) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.64/58.75 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.64/58.75 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.64/58.75 (100) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.64/58.75 all_250_13 = e0
% 248.64/58.75 (101) ~ (all_244_15 = all_38_2)
% 248.64/58.75 (102) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.64/58.75 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.64/58.75 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.64/58.75 (103) ~ (all_36_2 = all_26_2)
% 248.64/58.75 (104) all_44_2 = all_26_2
% 248.64/58.75 (105) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.64/58.75 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.64/58.75 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.64/58.75 (106) op(all_38_2, e3) = e1
% 248.64/58.75 (107) ~ (all_64_2 = all_12_2)
% 248.64/58.75 (108) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 248.64/58.75 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 248.64/58.75 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.64/58.75 (109) op(all_22_2, e3) = e0
% 248.64/58.75 (110) all_68_2 = all_22_2
% 248.64/58.75 (111) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.64/58.75 all_250_16 = e0
% 248.64/58.75 (112) op(e0, e3) = all_22_2
% 248.64/58.75 (113) ~ (all_244_0 = all_100_2)
% 248.64/58.75 (114) ~ (all_28_2 = all_22_2)
% 248.64/58.75 (115) all_242_2 = all_38_2
% 248.64/58.75 (116) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.64/58.75 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.64/58.75 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.64/58.75 (117) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.64/58.75 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.64/58.75 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.64/58.75 (118) op(all_84_2, e3) = e4
% 248.64/58.75 (119) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.64/58.75 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.64/58.75 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.64/58.75 (120) all_58_2 = all_20_2
% 248.64/58.75 (121) op(all_62_2, e3) = e1
% 248.64/58.75 (122) op(e4, e1) = all_26_2
% 248.64/58.75 (123) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.64/58.75 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.64/58.75 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.64/58.75 (124) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.64/58.75 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.64/58.75 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.64/58.75 (125) op(all_10_2, e3) = e2
% 248.64/58.75 (126) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.64/58.75 all_250_21 = e0
% 248.64/58.75 (127) ~ (all_244_15 = all_62_2)
% 248.64/58.75 (128) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.64/58.75 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.64/58.75 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.64/58.75 (129) op(e3, e4) = all_100_2
% 248.64/58.75 (130) all_250_11 = all_10_2
% 248.64/58.75 (131) ~ (all_244_8 = e1)
% 248.64/58.75 (132) op(e4, e4) = all_244_0
% 248.64/58.75 (133) ~ (all_22_2 = all_12_2)
% 248.64/58.75 (134) all_230_2 = all_20_2
% 248.64/58.75 (135) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.64/58.75 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.64/58.75 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.64/58.75 (136) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.64/58.75 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.75 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.64/58.75 (137) ~ (e4 = e3)
% 248.64/58.75 (138) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.64/58.75 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) =
% 248.64/58.75 all_8_1 & $i(all_8_1))
% 248.64/58.75 (139) op(e1, e1) = all_244_15
% 248.64/58.75 (140) ~ (all_34_2 = all_30_2)
% 248.64/58.75 (141) op(e0, e1) = all_20_2
% 248.64/58.75 (142) op(e3, e0) = all_48_2
% 248.64/58.75 (143) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 248.64/58.75 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 248.64/58.75 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.64/58.75 (144) op(all_48_2, e0) = e3
% 248.64/58.75 (145) ~ (all_38_2 = all_36_2)
% 248.64/58.75 (146) op(e1, e2) = all_4_2
% 248.64/58.75 (147) ~ (all_100_2 = all_48_2)
% 248.64/58.75 (148) op(all_4_2, all_38_2) = e2
% 248.64/58.75 (149) op(e4, e3) = all_84_2
% 248.64/58.75 (150) ~ (all_62_2 = all_10_2)
% 248.64/58.75 (151) op(e2, e4) = all_64_2
% 248.64/58.75 (152) ~ (all_22_2 = all_10_2)
% 248.64/58.75 (153) ~ (all_36_2 = e1)
% 248.64/58.75 (154) ~ (all_38_2 = all_26_2)
% 248.64/58.75 (155) ~ (e4 = e2)
% 248.64/58.75 (156) ~ (all_244_24 = all_30_2)
% 248.64/58.75 (157) ~ (all_22_2 = all_20_2)
% 248.64/58.75 (158) all_122_2 = all_36_2
% 248.64/58.75 (159) ~ (all_64_2 = all_16_2)
% 248.64/58.75 (160) op(all_36_2, e1) = e3
% 248.64/58.75 (161) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.64/58.75 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.64/58.75 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.64/58.75 (162) ~ (all_38_2 = all_10_2)
% 248.64/58.75 (163) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.64/58.75 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.64/58.75 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.64/58.75 (164) ~ (all_244_15 = all_36_2)
% 248.64/58.75 (165) ~ (all_244_24 = all_22_2)
% 248.64/58.75 (166) op(all_16_2, e4) = e1
% 248.64/58.75 (167) ~ (all_100_2 = all_16_2)
% 248.64/58.75 (168) op(e2, e0) = all_40_2
% 248.64/58.75 (169) ~ (all_16_2 = e3)
% 248.64/58.75 (170) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.64/58.75 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.64/58.75 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.64/58.75 (171) op(e3, e3) = all_244_3
% 248.64/58.75 (172) all_90_2 = all_22_2
% 248.64/58.75 (173) op(all_26_2, all_16_2) = e1
% 248.64/58.75 (174) op(all_12_2, e4) = e0
% 248.64/58.75 (175) all_46_2 = all_36_2
% 248.64/58.75 (176) op(all_30_2, e0) = e4
% 248.64/58.75 (177) op(all_244_24, all_244_24) = e0
% 248.64/58.75 (178) op(e0, e4) = all_12_2
% 248.64/58.75 (179) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.64/58.75 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.64/58.75 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.64/58.75 (180) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 248.64/58.75 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 248.64/58.75 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 248.64/58.75 (181) all_124_2 = all_10_2
% 248.64/58.75
% 248.64/58.75 Begin of proof
% 248.64/58.75 |
% 248.64/58.75 | BETA: splitting (105) gives:
% 248.64/58.75 |
% 248.64/58.75 | Case 1:
% 248.64/58.75 | |
% 248.64/58.75 | | (182) ~ (all_26_2 = e3)
% 248.64/58.75 | |
% 248.64/58.75 | | BETA: splitting (78) gives:
% 248.64/58.75 | |
% 248.64/58.75 | | Case 1:
% 248.64/58.75 | | |
% 248.64/58.75 | | | (183) ~ (all_32_2 = e2)
% 248.64/58.75 | | |
% 248.64/58.75 | | | REDUCE: (3), (183) imply:
% 248.64/58.75 | | | (184) ~ (all_20_2 = e2)
% 248.64/58.75 | | |
% 248.64/58.75 | | | BETA: splitting (49) gives:
% 248.64/58.75 | | |
% 248.64/58.75 | | | Case 1:
% 248.64/58.75 | | | |
% 248.64/58.75 | | | | (185) ~ (all_34_2 = e2)
% 248.64/58.75 | | | |
% 248.64/58.75 | | | | BETA: splitting (19) gives:
% 248.64/58.75 | | | |
% 248.64/58.75 | | | | Case 1:
% 248.64/58.75 | | | | |
% 248.64/58.75 | | | | | (186) ~ (all_36_2 = e4)
% 248.64/58.75 | | | | |
% 248.64/58.75 | | | | | BETA: splitting (42) gives:
% 248.64/58.75 | | | | |
% 248.64/58.75 | | | | | Case 1:
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | (187) ~ (all_38_2 = e4)
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | BETA: splitting (17) gives:
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | Case 1:
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | (188) ~ (all_44_2 = e2)
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | REDUCE: (104), (188) imply:
% 248.64/58.75 | | | | | | | (189) ~ (all_26_2 = e2)
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | BETA: splitting (99) gives:
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | (190) ~ (all_46_2 = e2)
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | REDUCE: (175), (190) imply:
% 248.64/58.75 | | | | | | | | (191) ~ (all_36_2 = e2)
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | BETA: splitting (82) gives:
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | (192) ~ (all_58_2 = e3)
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | REF_CLOSE: (5), (8), (20), (22), (23), (27), (28), (29), (30),
% 248.64/58.75 | | | | | | | | | (31), (32), (35), (37), (38), (41), (47), (53),
% 248.64/58.75 | | | | | | | | | (58), (62), (63), (64), (65), (67), (69), (73),
% 248.64/58.75 | | | | | | | | | (75), (84), (86), (88), (90), (91), (95), (100),
% 248.64/58.75 | | | | | | | | | (102), (109), (110), (112), (114), (120), (121),
% 248.64/58.75 | | | | | | | | | (122), (123), (125), (126), (127), (128), (130),
% 248.64/58.75 | | | | | | | | | (133), (136), (137), (139), (141), (144), (148),
% 248.64/58.75 | | | | | | | | | (149), (150), (152), (157), (162), (165), (171),
% 248.64/58.75 | | | | | | | | | (172), (177), (178), (180), (181), (184), (187),
% 248.64/58.75 | | | | | | | | | (189), (191), (192) are inconsistent by sub-proof
% 248.64/58.75 | | | | | | | | | #960.
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | (193) all_58_2 = e3
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | COMBINE_EQS: (120), (193) imply:
% 248.64/58.75 | | | | | | | | | (194) all_20_2 = e3
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | SIMP: (194) implies:
% 248.64/58.75 | | | | | | | | | (195) all_20_2 = e3
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | REDUCE: (44), (195) imply:
% 248.64/58.75 | | | | | | | | | (196) ~ (all_36_2 = e3)
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | BETA: splitting (97) gives:
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | (197) all_250_8 = e4
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | COMBINE_EQS: (15), (197) imply:
% 248.64/58.75 | | | | | | | | | | (198) all_36_2 = e4
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | REDUCE: (186), (198) imply:
% 248.64/58.75 | | | | | | | | | | (199) $false
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | CLOSE: (199) is inconsistent.
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | (200) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.64/58.75 | | | | | | | | | | all_250_8 = e0
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | BETA: splitting (200) gives:
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | (201) all_250_8 = e3
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | COMBINE_EQS: (15), (201) imply:
% 248.64/58.75 | | | | | | | | | | | (202) all_36_2 = e3
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | REDUCE: (196), (202) imply:
% 248.64/58.75 | | | | | | | | | | | (203) $false
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | (204) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | BETA: splitting (204) gives:
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | (205) all_250_8 = e2
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | COMBINE_EQS: (15), (205) imply:
% 248.64/58.75 | | | | | | | | | | | | (206) all_36_2 = e2
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | REDUCE: (191), (206) imply:
% 248.64/58.75 | | | | | | | | | | | | (207) $false
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | (208) all_250_8 = e1 | all_250_8 = e0
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | BETA: splitting (208) gives:
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | (209) all_250_8 = e1
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | COMBINE_EQS: (15), (209) imply:
% 248.64/58.75 | | | | | | | | | | | | | (210) all_36_2 = e1
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | REDUCE: (153), (210) imply:
% 248.64/58.75 | | | | | | | | | | | | | (211) $false
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | (212) all_250_8 = e0
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | COMBINE_EQS: (15), (212) imply:
% 248.64/58.75 | | | | | | | | | | | | | (213) all_36_2 = e0
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | REDUCE: (11), (213) imply:
% 248.64/58.75 | | | | | | | | | | | | | (214) op(e0, all_62_2) = e1
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | BETA: splitting (102) gives:
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | Case 1:
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | (215) ~ (all_70_2 = e2)
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | REDUCE: (86), (215) imply:
% 248.64/58.75 | | | | | | | | | | | | | | (216) ~ (all_62_2 = e2)
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | REF_CLOSE: (2), (29), (31), (37), (48), (64), (68), (75),
% 248.64/58.75 | | | | | | | | | | | | | | (92), (131), (139), (170), (185), (216) are
% 248.64/58.75 | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | (217) all_70_2 = e2
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | COMBINE_EQS: (86), (217) imply:
% 248.64/58.75 | | | | | | | | | | | | | | (218) all_62_2 = e2
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | SIMP: (218) implies:
% 248.64/58.75 | | | | | | | | | | | | | | (219) all_62_2 = e2
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | REDUCE: (214), (219) imply:
% 248.64/58.75 | | | | | | | | | | | | | | (220) op(e0, e2) = e1
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | | REF_CLOSE: (29), (58), (59), (220) are inconsistent by
% 248.64/58.75 | | | | | | | | | | | | | | sub-proof #907.
% 248.64/58.75 | | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | | End of split
% 248.64/58.75 | | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | | End of split
% 248.64/58.75 | | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | | End of split
% 248.64/58.75 | | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | | End of split
% 248.64/58.75 | | | | | | | | | |
% 248.64/58.75 | | | | | | | | | End of split
% 248.64/58.75 | | | | | | | | |
% 248.64/58.75 | | | | | | | | End of split
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | Case 2:
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | (221) all_46_2 = e2
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | | REF_CLOSE: (29), (41), (50), (72), (81), (135), (160), (171),
% 248.64/58.75 | | | | | | | | (175), (221) are inconsistent by sub-proof #77.
% 248.64/58.75 | | | | | | | |
% 248.64/58.75 | | | | | | | End of split
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | Case 2:
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | (222) all_44_2 = e2
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | | REF_CLOSE: (29), (41), (55), (104), (187), (222) are inconsistent
% 248.64/58.75 | | | | | | | by sub-proof #732.
% 248.64/58.75 | | | | | | |
% 248.64/58.75 | | | | | | End of split
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | Case 2:
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | (223) all_38_2 = e4
% 248.64/58.75 | | | | | | (224) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1,
% 248.64/58.75 | | | | | | e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 248.64/58.75 | | | | | | (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | REDUCE: (154), (223) imply:
% 248.64/58.75 | | | | | | (225) ~ (all_26_2 = e4)
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | SIMP: (225) implies:
% 248.64/58.75 | | | | | | (226) ~ (all_26_2 = e4)
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | REDUCE: (106), (223) imply:
% 248.64/58.75 | | | | | | (227) op(e4, e3) = e1
% 248.64/58.75 | | | | | |
% 248.64/58.75 | | | | | | REDUCE: (22), (223) imply:
% 248.64/58.75 | | | | | | (228) op(e4, e1) = e2
% 248.64/58.75 | | | | | |
% 248.64/58.76 | | | | | | REDUCE: (50), (223) imply:
% 248.64/58.76 | | | | | | (229) op(e3, e4) = e2
% 248.64/58.76 | | | | | |
% 248.64/58.76 | | | | | | BETA: splitting (224) gives:
% 248.64/58.76 | | | | | |
% 248.64/58.76 | | | | | | Case 1:
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | (230) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1,
% 248.64/58.76 | | | | | | | e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | ALPHA: (230) implies:
% 248.64/58.76 | | | | | | | (231) op(e1, e4) = all_38_1
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | REF_CLOSE: (2), (29), (34), (37), (48), (64), (68), (75), (118),
% 248.64/58.76 | | | | | | | (122), (129), (131), (139), (149), (167), (170), (179),
% 248.64/58.76 | | | | | | | (182), (185), (226), (227), (228), (229), (231) are
% 248.64/58.76 | | | | | | | inconsistent by sub-proof #75.
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | Case 2:
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | (232) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1)
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | ALPHA: (232) implies:
% 248.64/58.76 | | | | | | | (233) op(e1, e4) = all_38_1
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | | REF_CLOSE: (2), (29), (34), (37), (48), (64), (68), (75), (118),
% 248.64/58.76 | | | | | | | (122), (129), (131), (139), (149), (167), (170), (179),
% 248.64/58.76 | | | | | | | (182), (185), (226), (227), (228), (229), (233) are
% 248.64/58.76 | | | | | | | inconsistent by sub-proof #75.
% 248.64/58.76 | | | | | | |
% 248.64/58.76 | | | | | | End of split
% 248.64/58.76 | | | | | |
% 248.64/58.76 | | | | | End of split
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | Case 2:
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | (234) all_36_2 = e4
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | REDUCE: (160), (234) imply:
% 248.64/58.76 | | | | | (235) op(e4, e1) = e3
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | REF_CLOSE: (29), (122), (182), (235) are inconsistent by sub-proof
% 248.64/58.76 | | | | | #834.
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | End of split
% 248.64/58.76 | | | |
% 248.64/58.76 | | | Case 2:
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | (236) all_34_2 = e2
% 248.64/58.76 | | | | (237) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2)
% 248.64/58.76 | | | | = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.64/58.76 | | | | e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | REDUCE: (9), (236) imply:
% 248.64/58.76 | | | | (238) ~ (all_244_24 = e2)
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | REDUCE: (140), (236) imply:
% 248.64/58.76 | | | | (239) ~ (all_30_2 = e2)
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | SIMP: (239) implies:
% 248.64/58.76 | | | | (240) ~ (all_30_2 = e2)
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | REDUCE: (66), (236) imply:
% 248.64/58.76 | | | | (241) op(e2, e0) = e1
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | BETA: splitting (237) gives:
% 248.64/58.76 | | | |
% 248.64/58.76 | | | | Case 1:
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | (242) ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2)
% 248.64/58.76 | | | | | = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | ALPHA: (242) implies:
% 248.64/58.76 | | | | | (243) op(e0, e2) = all_34_1
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | GROUND_INST: instantiating (29) with all_28_2, all_34_1, e2, e0,
% 248.64/58.76 | | | | | simplifying with (58), (243) gives:
% 248.64/58.76 | | | | | (244) all_34_1 = all_28_2
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | GROUND_INST: instantiating (29) with all_40_2, e1, e0, e2, simplifying
% 248.64/58.76 | | | | | with (168), (241) gives:
% 248.64/58.76 | | | | | (245) all_40_2 = e1
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | REDUCE: (10), (245) imply:
% 248.64/58.76 | | | | | (246) ~ (all_244_24 = e1)
% 248.64/58.76 | | | | |
% 248.64/58.76 | | | | | REDUCE: (45), (245) imply:
% 248.64/58.76 | | | | | (247) ~ (all_64_2 = e1)
% 248.64/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (12), (245) imply:
% 248.79/58.76 | | | | | (248) ~ (all_38_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | SIMP: (248) implies:
% 248.79/58.76 | | | | | (249) ~ (all_38_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (18), (245) imply:
% 248.79/58.76 | | | | | (250) ~ (all_30_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | SIMP: (250) implies:
% 248.79/58.76 | | | | | (251) ~ (all_30_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REF_CLOSE: (4), (7), (8), (12), (14), (15), (16), (17), (21), (22),
% 248.79/58.76 | | | | | (27), (29), (30), (32), (35), (37), (39), (41), (42), (50),
% 248.79/58.76 | | | | | (51), (55), (59), (64), (68), (72), (73), (74), (75), (81),
% 248.79/58.76 | | | | | (89), (90), (94), (95), (97), (98), (99), (101), (103),
% 248.79/58.76 | | | | | (104), (109), (111), (112), (114), (115), (117), (121),
% 248.79/58.76 | | | | | (122), (123), (124), (128), (131), (133), (135), (136),
% 248.79/58.76 | | | | | (138), (139), (141), (145), (146), (148), (151), (153),
% 248.79/58.76 | | | | | (154), (156), (157), (158), (160), (165), (168), (171),
% 248.79/58.76 | | | | | (172), (173), (174), (175), (178), (184), (237), (238),
% 248.79/58.76 | | | | | (240), (243), (244), (245), (246), (247), (249), (251) are
% 248.79/58.76 | | | | | inconsistent by sub-proof #70.
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | Case 2:
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | (252) ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 & $i(all_34_1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | ALPHA: (252) implies:
% 248.79/58.76 | | | | | (253) ~ (all_34_1 = e3)
% 248.79/58.76 | | | | | (254) op(e0, e2) = all_34_1
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | GROUND_INST: instantiating (29) with all_28_2, all_34_1, e2, e0,
% 248.79/58.76 | | | | | simplifying with (58), (254) gives:
% 248.79/58.76 | | | | | (255) all_34_1 = all_28_2
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | GROUND_INST: instantiating (29) with all_40_2, e1, e0, e2, simplifying
% 248.79/58.76 | | | | | with (168), (241) gives:
% 248.79/58.76 | | | | | (256) all_40_2 = e1
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (10), (256) imply:
% 248.79/58.76 | | | | | (257) ~ (all_244_24 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (45), (256) imply:
% 248.79/58.76 | | | | | (258) ~ (all_64_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (12), (256) imply:
% 248.79/58.76 | | | | | (259) ~ (all_38_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | SIMP: (259) implies:
% 248.79/58.76 | | | | | (260) ~ (all_38_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REDUCE: (18), (256) imply:
% 248.79/58.76 | | | | | (261) ~ (all_30_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | SIMP: (261) implies:
% 248.79/58.76 | | | | | (262) ~ (all_30_2 = e1)
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | | REF_CLOSE: (4), (7), (8), (12), (14), (15), (16), (17), (21), (22),
% 248.79/58.76 | | | | | (27), (29), (30), (32), (35), (37), (39), (41), (42), (50),
% 248.79/58.76 | | | | | (51), (55), (59), (64), (68), (72), (73), (74), (75), (81),
% 248.79/58.76 | | | | | (89), (90), (94), (95), (97), (98), (99), (101), (103),
% 248.79/58.76 | | | | | (104), (109), (111), (112), (114), (115), (117), (121),
% 248.79/58.76 | | | | | (122), (123), (124), (128), (131), (133), (135), (136),
% 248.79/58.76 | | | | | (138), (139), (141), (145), (146), (148), (151), (153),
% 248.79/58.76 | | | | | (154), (156), (157), (158), (160), (165), (168), (171),
% 248.79/58.76 | | | | | (172), (173), (174), (175), (178), (184), (237), (238),
% 248.79/58.76 | | | | | (240), (254), (255), (256), (257), (258), (260), (262) are
% 248.79/58.76 | | | | | inconsistent by sub-proof #70.
% 248.79/58.76 | | | | |
% 248.79/58.76 | | | | End of split
% 248.79/58.76 | | | |
% 248.79/58.76 | | | End of split
% 248.79/58.76 | | |
% 248.79/58.76 | | Case 2:
% 248.79/58.76 | | |
% 248.79/58.76 | | | (263) all_32_2 = e2
% 248.79/58.76 | | |
% 248.79/58.76 | | | COMBINE_EQS: (3), (263) imply:
% 248.79/58.76 | | | (264) all_20_2 = e2
% 248.79/58.76 | | |
% 248.79/58.76 | | | SIMP: (264) implies:
% 248.79/58.76 | | | (265) all_20_2 = e2
% 248.79/58.76 | | |
% 248.79/58.76 | | | COMBINE_EQS: (134), (265) imply:
% 248.79/58.76 | | | (266) all_230_2 = e2
% 248.79/58.76 | | |
% 248.79/58.76 | | | REDUCE: (83), (265) imply:
% 248.79/58.76 | | | (267) op(e2, e1) = e0
% 248.79/58.76 | | |
% 248.79/58.76 | | | BETA: splitting (79) gives:
% 248.79/58.76 | | |
% 248.79/58.76 | | | Case 1:
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | (268) ~ (all_230_2 = e2)
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | REDUCE: (266), (268) imply:
% 248.79/58.76 | | | | (269) $false
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | CLOSE: (269) is inconsistent.
% 248.79/58.76 | | | |
% 248.79/58.76 | | | Case 2:
% 248.79/58.76 | | | |
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | GROUND_INST: instantiating (29) with all_38_2, e0, e1, e2, simplifying
% 248.79/58.76 | | | | with (41), (267) gives:
% 248.79/58.76 | | | | (270) all_38_2 = e0
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | REDUCE: (106), (270) imply:
% 248.79/58.76 | | | | (271) op(e0, e3) = e1
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | REF_CLOSE: (29), (95), (112), (271) are inconsistent by sub-proof #714.
% 248.79/58.76 | | | |
% 248.79/58.76 | | | End of split
% 248.79/58.76 | | |
% 248.79/58.76 | | End of split
% 248.79/58.76 | |
% 248.79/58.76 | Case 2:
% 248.79/58.76 | |
% 248.79/58.76 | | (272) all_26_2 = e3
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (76), (272) imply:
% 248.79/58.76 | | (273) ~ (all_244_0 = e3)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (103), (272) imply:
% 248.79/58.76 | | (274) ~ (all_36_2 = e3)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (1), (272) imply:
% 248.79/58.76 | | (275) ~ (all_30_2 = e3)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (173), (272) imply:
% 248.79/58.76 | | (276) op(e3, all_16_2) = e1
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (55), (272) imply:
% 248.79/58.76 | | (277) op(e3, e1) = e4
% 248.79/58.76 | |
% 248.79/58.76 | | GROUND_INST: instantiating (29) with all_36_2, e4, e1, e3, simplifying with
% 248.79/58.76 | | (90), (277) gives:
% 248.79/58.76 | | (278) all_36_2 = e4
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (164), (278) imply:
% 248.79/58.76 | | (279) ~ (all_244_15 = e4)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (57), (278) imply:
% 248.79/58.76 | | (280) ~ (all_100_2 = e4)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (145), (278) imply:
% 248.79/58.76 | | (281) ~ (all_38_2 = e4)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (153), (278) imply:
% 248.79/58.76 | | (282) ~ (e4 = e1)
% 248.79/58.76 | |
% 248.79/58.76 | | REDUCE: (21), (278) imply:
% 248.79/58.76 | | (283) op(all_62_2, e4) = e3
% 248.79/58.76 | |
% 248.79/58.76 | | BETA: splitting (19) gives:
% 248.79/58.76 | |
% 248.79/58.76 | | Case 1:
% 248.79/58.76 | | |
% 248.79/58.76 | | | (284) ~ (all_36_2 = e4)
% 248.79/58.76 | | |
% 248.79/58.76 | | | REF_CLOSE: (29), (90), (277), (284) are inconsistent by sub-proof #435.
% 248.79/58.76 | | |
% 248.79/58.76 | | Case 2:
% 248.79/58.76 | | |
% 248.79/58.76 | | | (285) ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 & op(e1, e4) =
% 248.79/58.76 | | | all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) &
% 248.79/58.76 | | | op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.79/58.76 | | |
% 248.79/58.76 | | | BETA: splitting (285) gives:
% 248.79/58.76 | | |
% 248.79/58.76 | | | Case 1:
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | (286) ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 & op(e1, e4) =
% 248.79/58.76 | | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | ALPHA: (286) implies:
% 248.79/58.76 | | | | (287) op(e1, e4) = all_36_1
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | GROUND_INST: instantiating (29) with all_16_2, all_36_1, e4, e1,
% 248.79/58.76 | | | | simplifying with (68), (287) gives:
% 248.79/58.76 | | | | (288) all_36_1 = all_16_2
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | REF_CLOSE: (4), (5), (6), (12), (13), (14), (24), (25), (26), (29),
% 248.79/58.76 | | | | (30), (31), (32), (33), (35), (36), (37), (40), (41), (43),
% 248.79/58.76 | | | | (45), (46), (48), (52), (54), (56), (60), (61), (70), (71),
% 248.79/58.76 | | | | (75), (77), (80), (85), (87), (89), (92), (93), (107), (108),
% 248.79/58.76 | | | | (113), (116), (117), (118), (119), (129), (132), (137),
% 248.79/58.76 | | | | (139), (140), (142), (143), (144), (146), (147), (151),
% 248.79/58.76 | | | | (155), (156), (159), (161), (163), (166), (168), (169),
% 248.79/58.76 | | | | (176), (178), (273), (275), (276), (279), (280), (281),
% 248.79/58.76 | | | | (282), (283), (287), (288) are inconsistent by sub-proof #66.
% 248.79/58.76 | | | |
% 248.79/58.76 | | | Case 2:
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | (289) ~ (all_36_1 = e2) & op(e1, e4) = all_36_1 & $i(all_36_1)
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | ALPHA: (289) implies:
% 248.79/58.76 | | | | (290) ~ (all_36_1 = e2)
% 248.79/58.76 | | | | (291) op(e1, e4) = all_36_1
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | GROUND_INST: instantiating (29) with all_16_2, all_36_1, e4, e1,
% 248.79/58.76 | | | | simplifying with (68), (291) gives:
% 248.79/58.76 | | | | (292) all_36_1 = all_16_2
% 248.79/58.76 | | | |
% 248.79/58.76 | | | | REF_CLOSE: (4), (5), (6), (12), (13), (14), (24), (25), (26), (29),
% 248.79/58.76 | | | | (30), (31), (32), (33), (35), (36), (37), (40), (41), (43),
% 248.79/58.76 | | | | (45), (46), (48), (52), (54), (56), (60), (61), (70), (71),
% 248.79/58.76 | | | | (75), (77), (80), (85), (87), (89), (92), (93), (107), (108),
% 248.79/58.76 | | | | (113), (116), (117), (118), (119), (129), (132), (137),
% 248.79/58.76 | | | | (139), (140), (142), (143), (144), (146), (147), (151),
% 248.79/58.76 | | | | (155), (156), (159), (161), (163), (166), (168), (169),
% 248.79/58.76 | | | | (176), (178), (273), (275), (276), (279), (280), (281),
% 248.79/58.76 | | | | (282), (283), (291), (292) are inconsistent by sub-proof #66.
% 248.79/58.76 | | | |
% 248.79/58.76 | | | End of split
% 248.79/58.76 | | |
% 248.79/58.76 | | End of split
% 248.79/58.76 | |
% 248.79/58.76 | End of split
% 248.79/58.76 |
% 248.79/58.76 End of proof
% 248.79/58.76
% 248.79/58.76 Sub-proof #66 shows that the following formulas are inconsistent:
% 248.79/58.76 ----------------------------------------------------------------
% 248.79/58.76 (1) op(all_62_2, e4) = e3
% 248.79/58.76 (2) ~ (all_4_2 = e4)
% 248.79/58.76 (3) ~ (all_10_2 = e4)
% 248.79/58.76 (4) ~ (all_244_0 = all_30_2)
% 248.79/58.76 (5) op(e3, all_16_2) = e1
% 248.79/58.76 (6) ~ (all_40_2 = all_38_2)
% 248.79/58.76 (7) op(all_6_2, e2) = e4
% 248.79/58.76 (8) op(e4, e0) = all_30_2
% 248.79/58.76 (9) ~ (all_30_2 = e3)
% 248.79/58.76 (10) ~ (e2 = e0)
% 248.79/58.76 (11) op(all_64_2, e4) = e2
% 248.79/58.76 (12) ~ (e1 = e0)
% 248.79/58.76 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.76 (14) op(e2, e3) = all_10_2
% 248.79/58.76 (15) ~ (e3 = e2)
% 248.79/58.76 (16) op(e0, e0) = all_244_24
% 248.79/58.76 (17) ~ (e4 = e0)
% 248.79/58.76 (18) ~ (all_12_2 = e3)
% 248.79/58.76 (19) op(all_244_8, all_244_8) = e2
% 248.79/58.76 (20) op(e2, e2) = all_244_8
% 248.79/58.76 (21) op(all_84_2, all_100_2) = e3
% 248.79/58.76 (22) op(e2, e1) = all_38_2
% 248.79/58.76 (23) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 248.79/58.76 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 248.79/58.76 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 248.79/58.76 (24) ~ (all_64_2 = all_40_2)
% 248.79/58.76 (25) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.79/58.76 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.79/58.76 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.76 (26) op(e1, e0) = all_34_2
% 248.79/58.76 (27) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 248.79/58.76 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 248.79/58.76 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.76 (28) ~ (all_244_15 = e4)
% 248.79/58.76 (29) ~ (e2 = e1)
% 248.79/58.76 (30) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.76 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.76 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.76 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.76 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.76 op(e0, e1) = e0)))
% 248.79/58.76 (31) ~ (e4 = e1)
% 248.79/58.76 (32) op(all_6_2, all_64_2) = e2
% 248.79/58.76 (33) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.79/58.76 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.79/58.76 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.79/58.76 (34) ~ (all_48_2 = all_30_2)
% 248.79/58.76 (35) ~ (all_244_0 = all_64_2)
% 248.79/58.76 (36) op(e1, e3) = all_62_2
% 248.79/58.76 (37) ~ (e3 = e0)
% 248.79/58.76 (38) ~ (all_40_2 = all_10_2)
% 248.79/58.76 (39) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.79/58.76 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.79/58.76 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.79/58.76 (40) ~ (e3 = e1)
% 248.79/58.76 (41) ~ (all_12_2 = e2)
% 248.79/58.76 (42) ~ (all_16_2 = e2)
% 248.79/58.76 (43) op(all_40_2, e0) = e2
% 248.79/58.76 (44) ~ (all_100_2 = e4)
% 248.79/58.76 (45) ~ (all_38_2 = e4)
% 248.79/58.76 (46) ~ (all_64_2 = all_12_2)
% 248.79/58.76 (47) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 248.79/58.76 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 248.79/58.76 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 248.79/58.76 (48) ~ (all_244_0 = all_100_2)
% 248.79/58.76 (49) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.79/58.76 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.79/58.76 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.76 (50) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.79/58.76 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.79/58.76 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.79/58.76 (51) op(all_84_2, e3) = e4
% 248.79/58.76 (52) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.79/58.76 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.79/58.76 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.79/58.76 (53) op(e1, e4) = all_36_1
% 248.79/58.76 (54) op(e3, e4) = all_100_2
% 248.79/58.76 (55) op(e4, e4) = all_244_0
% 248.79/58.76 (56) ~ (e4 = e3)
% 248.79/58.76 (57) op(e1, e1) = all_244_15
% 248.79/58.76 (58) ~ (all_34_2 = all_30_2)
% 248.79/58.76 (59) op(e3, e0) = all_48_2
% 248.79/58.76 (60) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 248.79/58.76 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 248.79/58.76 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 248.79/58.76 (61) op(all_48_2, e0) = e3
% 248.79/58.76 (62) op(e1, e2) = all_4_2
% 248.79/58.76 (63) ~ (all_100_2 = all_48_2)
% 248.79/58.76 (64) op(e2, e4) = all_64_2
% 248.79/58.76 (65) ~ (e4 = e2)
% 248.79/58.76 (66) ~ (all_244_24 = all_30_2)
% 248.79/58.76 (67) ~ (all_64_2 = all_16_2)
% 248.79/58.76 (68) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.79/58.76 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.76 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.76 (69) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 248.79/58.76 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 248.79/58.76 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 248.79/58.76 (70) all_36_1 = all_16_2
% 248.79/58.76 (71) op(all_16_2, e4) = e1
% 248.79/58.76 (72) op(e2, e0) = all_40_2
% 248.79/58.76 (73) ~ (all_16_2 = e3)
% 248.79/58.76 (74) ~ (all_244_0 = e3)
% 248.79/58.76 (75) op(all_30_2, e0) = e4
% 248.79/58.76 (76) op(e0, e4) = all_12_2
% 248.79/58.76
% 248.79/58.76 Begin of proof
% 248.79/58.76 |
% 248.79/58.76 | REDUCE: (53), (70) imply:
% 248.79/58.76 | (77) op(e1, e4) = all_16_2
% 248.79/58.76 |
% 248.79/58.76 | BETA: splitting (23) gives:
% 248.79/58.76 |
% 248.79/58.76 | Case 1:
% 248.79/58.76 | |
% 248.79/58.76 | | (78) ~ (all_30_2 = e2)
% 248.79/58.76 | |
% 248.79/58.77 | | REF_CLOSE: (3), (8), (11), (13), (14), (15), (18), (19), (20), (21), (22),
% 248.79/58.77 | | (33), (35), (39), (43), (44), (45), (46), (48), (51), (52), (54),
% 248.79/58.77 | | (55), (56), (64), (67), (68), (72), (73), (74), (76), (77), (78)
% 248.79/58.77 | | are inconsistent by sub-proof #67.
% 248.79/58.77 | |
% 248.79/58.77 | Case 2:
% 248.79/58.77 | |
% 248.79/58.77 | | (79) all_30_2 = e2
% 248.79/58.77 | |
% 248.79/58.77 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 248.79/58.77 | | (16), (17), (18), (19), (20), (22), (24), (25), (26), (27), (28),
% 248.79/58.77 | | (29), (30), (31), (32), (34), (36), (37), (38), (39), (40), (41),
% 248.79/58.77 | | (42), (47), (48), (49), (50), (52), (54), (55), (56), (57), (58),
% 248.79/58.77 | | (59), (60), (61), (62), (63), (64), (65), (66), (68), (69), (71),
% 248.79/58.77 | | (72), (73), (74), (75), (76), (77), (79) are inconsistent by
% 248.79/58.77 | | sub-proof #616.
% 248.79/58.77 | |
% 248.79/58.77 | End of split
% 248.79/58.77 |
% 248.79/58.77 End of proof
% 248.79/58.77
% 248.79/58.77 Sub-proof #67 shows that the following formulas are inconsistent:
% 248.79/58.77 ----------------------------------------------------------------
% 248.79/58.77 (1) ~ (all_10_2 = e4)
% 248.79/58.77 (2) op(e4, e0) = all_30_2
% 248.79/58.77 (3) op(all_64_2, e4) = e2
% 248.79/58.77 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.77 (5) op(e2, e3) = all_10_2
% 248.79/58.77 (6) ~ (e3 = e2)
% 248.79/58.77 (7) ~ (all_12_2 = e3)
% 248.79/58.77 (8) op(all_244_8, all_244_8) = e2
% 248.79/58.77 (9) op(e2, e2) = all_244_8
% 248.79/58.77 (10) op(all_84_2, all_100_2) = e3
% 248.79/58.77 (11) op(e2, e1) = all_38_2
% 248.79/58.77 (12) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 248.79/58.77 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 248.79/58.77 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 248.79/58.77 (13) op(e1, e4) = all_16_2
% 248.79/58.77 (14) ~ (all_244_0 = all_64_2)
% 248.79/58.77 (15) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 248.79/58.77 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 248.79/58.77 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 248.79/58.77 (16) ~ (all_30_2 = e2)
% 248.79/58.77 (17) op(all_40_2, e0) = e2
% 248.79/58.77 (18) ~ (all_100_2 = e4)
% 248.79/58.77 (19) ~ (all_38_2 = e4)
% 248.79/58.77 (20) ~ (all_64_2 = all_12_2)
% 248.79/58.77 (21) ~ (all_244_0 = all_100_2)
% 248.79/58.77 (22) op(all_84_2, e3) = e4
% 248.79/58.77 (23) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 248.79/58.77 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 248.79/58.77 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.79/58.77 (24) op(e3, e4) = all_100_2
% 248.79/58.77 (25) op(e4, e4) = all_244_0
% 248.79/58.77 (26) ~ (e4 = e3)
% 248.79/58.77 (27) op(e2, e4) = all_64_2
% 248.79/58.77 (28) ~ (all_64_2 = all_16_2)
% 248.79/58.77 (29) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.79/58.77 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.77 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.77 (30) op(e2, e0) = all_40_2
% 248.79/58.77 (31) ~ (all_16_2 = e3)
% 248.79/58.77 (32) ~ (all_244_0 = e3)
% 248.79/58.77 (33) op(e0, e4) = all_12_2
% 248.79/58.77
% 248.79/58.77 Begin of proof
% 248.79/58.77 |
% 248.79/58.77 | BETA: splitting (15) gives:
% 248.79/58.77 |
% 248.79/58.77 | Case 1:
% 248.79/58.77 | |
% 248.79/58.77 | | (34) ~ (all_40_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | BETA: splitting (12) gives:
% 248.79/58.77 | |
% 248.79/58.77 | | Case 1:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (35) ~ (all_64_2 = e3)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (4), (7), (10), (13), (18), (22), (24), (25), (27), (29), (31),
% 248.79/58.77 | | | (32), (33), (35) are inconsistent by sub-proof #68.
% 248.79/58.77 | | |
% 248.79/58.77 | | Case 2:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (36) all_64_2 = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | REDUCE: (28), (36) imply:
% 248.79/58.77 | | | (37) ~ (all_16_2 = e3)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REDUCE: (20), (36) imply:
% 248.79/58.77 | | | (38) ~ (all_12_2 = e3)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REDUCE: (3), (36) imply:
% 248.79/58.77 | | | (39) op(e3, e4) = e2
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (13), (19), (21),
% 248.79/58.77 | | | (23), (24), (25), (26), (29), (30), (31), (32), (33), (34),
% 248.79/58.77 | | | (39) are inconsistent by sub-proof #807.
% 248.79/58.77 | | |
% 248.79/58.77 | | End of split
% 248.79/58.77 | |
% 248.79/58.77 | Case 2:
% 248.79/58.77 | |
% 248.79/58.77 | | (40) all_40_2 = e4
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (17), (40) imply:
% 248.79/58.77 | | (41) op(e4, e0) = e2
% 248.79/58.77 | |
% 248.79/58.77 | | REF_CLOSE: (2), (4), (16), (41) are inconsistent by sub-proof #830.
% 248.79/58.77 | |
% 248.79/58.77 | End of split
% 248.79/58.77 |
% 248.79/58.77 End of proof
% 248.79/58.77
% 248.79/58.77 Sub-proof #68 shows that the following formulas are inconsistent:
% 248.79/58.77 ----------------------------------------------------------------
% 248.79/58.77 (1) ~ (all_64_2 = e3)
% 248.79/58.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.77 (3) ~ (all_12_2 = e3)
% 248.79/58.77 (4) op(all_84_2, all_100_2) = e3
% 248.79/58.77 (5) op(e1, e4) = all_16_2
% 248.79/58.77 (6) ~ (all_100_2 = e4)
% 248.79/58.77 (7) op(all_84_2, e3) = e4
% 248.79/58.77 (8) op(e3, e4) = all_100_2
% 248.79/58.77 (9) op(e4, e4) = all_244_0
% 248.79/58.77 (10) op(e2, e4) = all_64_2
% 248.79/58.77 (11) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.79/58.77 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.77 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.77 (12) ~ (all_16_2 = e3)
% 248.79/58.77 (13) ~ (all_244_0 = e3)
% 248.79/58.77 (14) op(e0, e4) = all_12_2
% 248.79/58.77
% 248.79/58.77 Begin of proof
% 248.79/58.77 |
% 248.79/58.77 | BETA: splitting (11) gives:
% 248.79/58.77 |
% 248.79/58.77 | Case 1:
% 248.79/58.77 | |
% 248.79/58.77 | | (15) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 248.79/58.77 | | e3)
% 248.79/58.77 | |
% 248.79/58.77 | | BETA: splitting (15) gives:
% 248.79/58.77 | |
% 248.79/58.77 | | Case 1:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (16) all_252_0 = e3 & op(e4, e4) = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | ALPHA: (16) implies:
% 248.79/58.77 | | | (17) op(e4, e4) = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (2), (9), (13), (17) are inconsistent by sub-proof #813.
% 248.79/58.77 | | |
% 248.79/58.77 | | Case 2:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (18) all_252_2 = e3 & op(e3, e4) = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | ALPHA: (18) implies:
% 248.79/58.77 | | | (19) op(e3, e4) = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (2), (4), (6), (7), (8), (19) are inconsistent by sub-proof
% 248.79/58.77 | | | #69.
% 248.79/58.77 | | |
% 248.79/58.77 | | End of split
% 248.79/58.77 | |
% 248.79/58.77 | Case 2:
% 248.79/58.77 | |
% 248.79/58.77 | | (20) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.77 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.77 | |
% 248.79/58.77 | | BETA: splitting (20) gives:
% 248.79/58.77 | |
% 248.79/58.77 | | Case 1:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (21) all_252_6 = e3 & op(e2, e4) = e3
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (1), (2), (10), (21) are inconsistent by sub-proof #940.
% 248.79/58.77 | | |
% 248.79/58.77 | | Case 2:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (22) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 248.79/58.77 | | | e4) = e3)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (2), (3), (5), (12), (14), (22) are inconsistent by sub-proof
% 248.79/58.77 | | | #894.
% 248.79/58.77 | | |
% 248.79/58.77 | | End of split
% 248.79/58.77 | |
% 248.79/58.77 | End of split
% 248.79/58.77 |
% 248.79/58.77 End of proof
% 248.79/58.77
% 248.79/58.77 Sub-proof #69 shows that the following formulas are inconsistent:
% 248.79/58.77 ----------------------------------------------------------------
% 248.79/58.77 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.77 (2) op(all_84_2, all_100_2) = e3
% 248.79/58.77 (3) op(e3, e4) = e3
% 248.79/58.77 (4) ~ (all_100_2 = e4)
% 248.79/58.77 (5) op(all_84_2, e3) = e4
% 248.79/58.77 (6) op(e3, e4) = all_100_2
% 248.79/58.77
% 248.79/58.77 Begin of proof
% 248.79/58.77 |
% 248.79/58.77 | GROUND_INST: instantiating (1) with all_100_2, e3, e4, e3, simplifying with
% 248.79/58.77 | (3), (6) gives:
% 248.79/58.77 | (7) all_100_2 = e3
% 248.79/58.77 |
% 248.79/58.77 | REDUCE: (4), (7) imply:
% 248.79/58.77 | (8) ~ (e4 = e3)
% 248.79/58.77 |
% 248.79/58.77 | SIMP: (8) implies:
% 248.79/58.77 | (9) ~ (e4 = e3)
% 248.79/58.77 |
% 248.79/58.77 | REDUCE: (2), (7) imply:
% 248.79/58.77 | (10) op(all_84_2, e3) = e3
% 248.79/58.77 |
% 248.79/58.77 | GROUND_INST: instantiating (1) with e4, e3, e3, all_84_2, simplifying with
% 248.79/58.77 | (5), (10) gives:
% 248.79/58.77 | (11) e4 = e3
% 248.79/58.77 |
% 248.79/58.77 | REDUCE: (9), (11) imply:
% 248.79/58.77 | (12) $false
% 248.79/58.77 |
% 248.79/58.77 | CLOSE: (12) is inconsistent.
% 248.79/58.77 |
% 248.79/58.77 End of proof
% 248.79/58.77
% 248.79/58.77 Sub-proof #70 shows that the following formulas are inconsistent:
% 248.79/58.77 ----------------------------------------------------------------
% 248.79/58.77 (1) ~ (all_4_2 = e4)
% 248.79/58.77 (2) all_250_16 = all_62_2
% 248.79/58.77 (3) op(all_4_2, e2) = e1
% 248.79/58.77 (4) ~ (all_38_2 = e1)
% 248.79/58.77 (5) ~ (all_40_2 = all_38_2)
% 248.79/58.77 (6) op(e4, e0) = all_30_2
% 248.79/58.77 (7) all_250_8 = all_36_2
% 248.79/58.77 (8) op(all_28_2, all_40_2) = e2
% 248.79/58.77 (9) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 248.79/58.77 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 248.79/58.77 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 248.79/58.77 (10) op(all_62_2, all_36_2) = e3
% 248.79/58.77 (11) op(all_38_2, e1) = e2
% 248.79/58.77 (12) ~ (all_30_2 = e1)
% 248.79/58.77 (13) ~ (all_28_2 = e3)
% 248.79/58.77 (14) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) =
% 248.79/58.77 all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e3) & op(e0,
% 248.79/58.77 e2) = all_34_1 & $i(all_34_1))
% 248.79/58.77 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.77 (16) op(e2, e3) = all_10_2
% 248.79/58.77 (17) op(e0, e0) = all_244_24
% 248.79/58.77 (18) ~ (all_12_2 = e3)
% 248.79/58.77 (19) op(e2, e2) = all_244_8
% 248.79/58.77 (20) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.79/58.77 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.79/58.77 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.79/58.77 (21) op(e2, e1) = all_38_2
% 248.79/58.77 (22) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 248.79/58.77 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 248.79/58.77 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.79/58.77 (23) all_34_1 = all_28_2
% 248.79/58.77 (24) op(e3, all_38_2) = e2
% 248.79/58.77 (25) op(e1, all_10_2) = e2
% 248.79/58.77 (26) op(all_26_2, e1) = e4
% 248.79/58.77 (27) ~ (all_28_2 = e1)
% 248.79/58.77 (28) op(all_244_15, all_244_15) = e1
% 248.79/58.77 (29) op(e1, e4) = all_16_2
% 248.79/58.77 (30) ~ (all_244_3 = all_36_2)
% 248.79/58.77 (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.77 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.77 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.77 (32) all_132_2 = all_30_2
% 248.79/58.77 (33) op(e1, e3) = all_62_2
% 248.79/58.77 (34) all_204_2 = all_36_2
% 248.79/58.77 (35) ~ (all_30_2 = e2)
% 248.79/58.77 (36) ~ (all_12_2 = e2)
% 248.79/58.77 (37) op(e3, e1) = all_36_2
% 248.79/58.77 (38) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.79/58.77 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.79/58.77 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.77 (39) ~ (all_22_2 = e1)
% 248.79/58.77 (40) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.79/58.77 all_250_8 = e0
% 248.79/58.77 (41) ~ (all_64_2 = e1)
% 248.79/58.77 (42) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.79/58.77 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 248.79/58.77 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 248.79/58.77 (43) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.79/58.77 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.79/58.77 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.77 (44) ~ (all_244_15 = all_38_2)
% 248.79/58.77 (45) ~ (all_36_2 = all_26_2)
% 248.79/58.77 (46) all_44_2 = all_26_2
% 248.79/58.77 (47) op(all_22_2, e3) = e0
% 248.79/58.77 (48) op(e0, e2) = all_34_1
% 248.79/58.77 (49) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.79/58.77 all_250_16 = e0
% 248.79/58.77 (50) op(e0, e3) = all_22_2
% 248.79/58.77 (51) ~ (all_28_2 = all_22_2)
% 248.79/58.77 (52) all_242_2 = all_38_2
% 248.79/58.77 (53) all_40_2 = e1
% 248.79/58.77 (54) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.79/58.77 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.79/58.77 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.79/58.77 (55) ~ (all_244_24 = e1)
% 248.79/58.77 (56) op(all_62_2, e3) = e1
% 248.79/58.77 (57) op(e4, e1) = all_26_2
% 248.79/58.77 (58) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.79/58.77 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.79/58.77 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.77 (59) ~ (all_132_2 = e3) | ( ~ (all_132_0 = e1) & op(e3, all_132_1) =
% 248.79/58.77 all_132_0 & op(e0, e3) = all_132_1 & $i(all_132_0) & $i(all_132_1)) |
% 248.79/58.77 ( ~ (all_132_1 = e2) & op(e0, e3) = all_132_1 & $i(all_132_1))
% 248.79/58.77 (60) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 248.79/58.77 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 248.79/58.77 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 248.79/58.77 (61) ~ (all_244_8 = e1)
% 248.79/58.77 (62) ~ (all_22_2 = all_12_2)
% 248.79/58.77 (63) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.79/58.77 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.79/58.77 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.79/58.77 (64) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.77 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.77 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.77 (65) ( ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) = all_8_0 &
% 248.79/58.77 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e4) & op(e2, e1) = all_8_1
% 248.79/58.77 & $i(all_8_1))
% 248.79/58.77 (66) op(e1, e1) = all_244_15
% 248.79/58.77 (67) op(e0, e1) = all_20_2
% 248.79/58.77 (68) ~ (all_38_2 = all_36_2)
% 248.79/58.77 (69) ~ (all_244_24 = e2)
% 248.79/58.77 (70) op(e1, e2) = all_4_2
% 248.79/58.77 (71) op(all_4_2, all_38_2) = e2
% 248.79/58.77 (72) op(e2, e4) = all_64_2
% 248.79/58.77 (73) ~ (all_36_2 = e1)
% 248.79/58.77 (74) ~ (all_38_2 = all_26_2)
% 248.79/58.77 (75) ~ (all_244_24 = all_30_2)
% 248.79/58.77 (76) ~ (all_22_2 = all_20_2)
% 248.79/58.77 (77) all_122_2 = all_36_2
% 248.79/58.77 (78) op(all_36_2, e1) = e3
% 248.79/58.77 (79) ~ (all_244_24 = all_22_2)
% 248.79/58.77 (80) op(e2, e0) = all_40_2
% 248.79/58.77 (81) op(e3, e3) = all_244_3
% 248.79/58.77 (82) all_90_2 = all_22_2
% 248.79/58.77 (83) op(all_26_2, all_16_2) = e1
% 248.79/58.77 (84) op(all_12_2, e4) = e0
% 248.79/58.77 (85) all_46_2 = all_36_2
% 248.79/58.77 (86) op(e0, e4) = all_12_2
% 248.79/58.77 (87) ~ (all_20_2 = e2)
% 248.79/58.77
% 248.79/58.77 Begin of proof
% 248.79/58.77 |
% 248.79/58.77 | REDUCE: (53), (80) imply:
% 248.79/58.77 | (88) op(e2, e0) = e1
% 248.79/58.77 |
% 248.79/58.77 | REDUCE: (23), (48) imply:
% 248.79/58.77 | (89) op(e0, e2) = all_28_2
% 248.79/58.77 |
% 248.79/58.77 | BETA: splitting (22) gives:
% 248.79/58.77 |
% 248.79/58.77 | Case 1:
% 248.79/58.77 | |
% 248.79/58.77 | | (90) ~ (all_38_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | BETA: splitting (9) gives:
% 248.79/58.77 | |
% 248.79/58.77 | | Case 1:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (91) ~ (all_44_2 = e2)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REDUCE: (46), (91) imply:
% 248.79/58.77 | | | (92) ~ (all_26_2 = e2)
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (3), (4), (15), (19), (21), (24), (28), (30), (34), (37), (43),
% 248.79/58.77 | | | (57), (61), (63), (64), (66), (67), (71), (78), (81), (85),
% 248.79/58.77 | | | (87), (92) are inconsistent by sub-proof #74.
% 248.79/58.77 | | |
% 248.79/58.77 | | Case 2:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (93) all_44_2 = e2
% 248.79/58.77 | | |
% 248.79/58.77 | | | REF_CLOSE: (15), (21), (26), (46), (90), (93) are inconsistent by
% 248.79/58.77 | | | sub-proof #732.
% 248.79/58.77 | | |
% 248.79/58.77 | | End of split
% 248.79/58.77 | |
% 248.79/58.77 | Case 2:
% 248.79/58.77 | |
% 248.79/58.77 | | (94) all_38_2 = e4
% 248.79/58.77 | | (95) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1, e4) =
% 248.79/58.77 | | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 248.79/58.77 | | op(e1, e4) = all_38_1 & $i(all_38_1))
% 248.79/58.77 | |
% 248.79/58.77 | | COMBINE_EQS: (52), (94) imply:
% 248.79/58.77 | | (96) all_242_2 = e4
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (44), (94) imply:
% 248.79/58.77 | | (97) ~ (all_244_15 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (68), (94) imply:
% 248.79/58.77 | | (98) ~ (all_36_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | SIMP: (98) implies:
% 248.79/58.77 | | (99) ~ (all_36_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (74), (94) imply:
% 248.79/58.77 | | (100) ~ (all_26_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | SIMP: (100) implies:
% 248.79/58.77 | | (101) ~ (all_26_2 = e4)
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (11), (94) imply:
% 248.79/58.77 | | (102) op(e4, e1) = e2
% 248.79/58.77 | |
% 248.79/58.77 | | REDUCE: (21), (94) imply:
% 248.79/58.77 | | (103) op(e2, e1) = e4
% 248.79/58.77 | |
% 248.79/58.77 | | BETA: splitting (65) gives:
% 248.79/58.77 | |
% 248.79/58.77 | | Case 1:
% 248.79/58.77 | | |
% 248.79/58.77 | | | (104) ~ (all_8_0 = e0) & op(e2, e1) = all_8_1 & op(e1, all_8_1) =
% 248.79/58.77 | | | all_8_0 & $i(all_8_0) & $i(all_8_1)
% 248.79/58.77 | | |
% 248.79/58.77 | | | ALPHA: (104) implies:
% 248.79/58.77 | | | (105) ~ (all_8_0 = e0)
% 248.79/58.77 | | | (106) op(e1, all_8_1) = all_8_0
% 248.79/58.77 | | | (107) op(e2, e1) = all_8_1
% 248.79/58.77 | | |
% 248.79/58.77 | | | BETA: splitting (60) gives:
% 248.79/58.77 | | |
% 248.79/58.77 | | | Case 1:
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | (108) ~ (all_90_2 = e2)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (82), (108) imply:
% 248.79/58.77 | | | | (109) ~ (all_22_2 = e2)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REF_CLOSE: (3), (5), (8), (14), (15), (17), (21), (36), (50), (58),
% 248.79/58.77 | | | | (67), (69), (71), (80), (86), (87), (88), (89), (109) are
% 248.79/58.77 | | | | inconsistent by sub-proof #117.
% 248.79/58.77 | | | |
% 248.79/58.77 | | | Case 2:
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | (110) all_90_2 = e2
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | COMBINE_EQS: (82), (110) imply:
% 248.79/58.77 | | | | (111) all_22_2 = e2
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (51), (111) imply:
% 248.79/58.77 | | | | (112) ~ (all_28_2 = e2)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (76), (111) imply:
% 248.79/58.77 | | | | (113) ~ (all_20_2 = e2)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (62), (111) imply:
% 248.79/58.77 | | | | (114) ~ (all_12_2 = e2)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (39), (111) imply:
% 248.79/58.77 | | | | (115) ~ (e2 = e1)
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (47), (111) imply:
% 248.79/58.77 | | | | (116) op(e2, e3) = e0
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | REDUCE: (50), (111) imply:
% 248.79/58.77 | | | | (117) op(e0, e3) = e2
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | BETA: splitting (59) gives:
% 248.79/58.77 | | | |
% 248.79/58.77 | | | | Case 1:
% 248.79/58.77 | | | | |
% 248.79/58.77 | | | | | (118) ~ (all_132_2 = e3)
% 248.79/58.77 | | | | |
% 248.79/58.77 | | | | | REDUCE: (32), (118) imply:
% 248.79/58.77 | | | | | (119) ~ (all_30_2 = e3)
% 248.79/58.77 | | | | |
% 248.79/58.77 | | | | | BETA: splitting (95) gives:
% 248.79/58.77 | | | | |
% 248.79/58.77 | | | | | Case 1:
% 248.79/58.77 | | | | | |
% 248.79/58.77 | | | | | | (120) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1,
% 248.79/58.77 | | | | | | e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 248.79/58.77 | | | | | |
% 248.79/58.77 | | | | | | ALPHA: (120) implies:
% 248.79/58.77 | | | | | | (121) op(e1, e4) = all_38_1
% 248.79/58.77 | | | | | |
% 248.79/58.78 | | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (15), (16), (20), (25), (29),
% 248.79/58.78 | | | | | | (33), (40), (41), (45), (49), (54), (56), (57), (66),
% 248.79/58.78 | | | | | | (70), (72), (73), (77), (83), (97), (99), (101), (102),
% 248.79/58.78 | | | | | | (116), (119), (121) are inconsistent by sub-proof #73.
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | Case 2:
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | (122) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1)
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | ALPHA: (122) implies:
% 248.79/58.78 | | | | | | (123) op(e1, e4) = all_38_1
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (15), (16), (20), (25), (29),
% 248.79/58.78 | | | | | | (33), (40), (41), (45), (49), (54), (56), (57), (66),
% 248.79/58.78 | | | | | | (70), (72), (73), (77), (83), (97), (99), (101), (102),
% 248.79/58.78 | | | | | | (116), (119), (123) are inconsistent by sub-proof #73.
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | End of split
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | Case 2:
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | (124) all_132_2 = e3
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | COMBINE_EQS: (32), (124) imply:
% 248.79/58.78 | | | | | (125) all_30_2 = e3
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | SIMP: (125) implies:
% 248.79/58.78 | | | | | (126) all_30_2 = e3
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | REDUCE: (75), (126) imply:
% 248.79/58.78 | | | | | (127) ~ (all_244_24 = e3)
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | REDUCE: (35), (126) imply:
% 248.79/58.78 | | | | | (128) ~ (e3 = e2)
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | REDUCE: (12), (126) imply:
% 248.79/58.78 | | | | | (129) ~ (e3 = e1)
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | BETA: splitting (31) gives:
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | | Case 1:
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | (130) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 248.79/58.78 | | | | | | op(e0, e3) = e3)
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | REF_CLOSE: (15), (17), (18), (36), (58), (67), (69), (86), (87),
% 248.79/58.78 | | | | | | (89), (112), (128), (130) are inconsistent by sub-proof
% 248.79/58.78 | | | | | | #976.
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | Case 2:
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | (131) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 248.79/58.78 | | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | BETA: splitting (131) gives:
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | | Case 1:
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | (132) all_252_22 = e3 & op(e0, e2) = e3
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | ALPHA: (132) implies:
% 248.79/58.78 | | | | | | | (133) op(e0, e2) = e3
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | REF_CLOSE: (13), (15), (89), (133) are inconsistent by sub-proof
% 248.79/58.78 | | | | | | | #975.
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | Case 2:
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | (134) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 248.79/58.78 | | | | | | | op(e0, e0) = e3)
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | BETA: splitting (134) gives:
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | (135) all_252_23 = e3 & op(e0, e1) = e3
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | ALPHA: (135) implies:
% 248.79/58.78 | | | | | | | | (136) op(e0, e1) = e3
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | BETA: splitting (38) gives:
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | (137) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 =
% 248.79/58.78 | | | | | | | | | e1 & op(e0, e3) = e1)
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | BETA: splitting (137) gives:
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | (138) all_252_20 = e1 & op(e0, e4) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | ALPHA: (138) implies:
% 248.79/58.78 | | | | | | | | | | (139) op(e0, e4) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | BETA: splitting (42) gives:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | (140) ~ (all_242_2 = e4)
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | REDUCE: (96), (140) imply:
% 248.79/58.78 | | | | | | | | | | | (141) $false
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | (142) ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.79/58.78 | | | | | | | | | | | all_242_0 & op(e1, e4) = all_242_1 &
% 248.79/58.78 | | | | | | | | | | | $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1
% 248.79/58.78 | | | | | | | | | | | = e0) & op(e1, e4) = all_242_1 &
% 248.79/58.78 | | | | | | | | | | | $i(all_242_1))
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_12_2, e1, e4, e0,
% 248.79/58.78 | | | | | | | | | | | simplifying with (86), (139) gives:
% 248.79/58.78 | | | | | | | | | | | (143) all_12_2 = e1
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | GROUND_INST: instantiating (15) with e4, all_8_1, e1, e2,
% 248.79/58.78 | | | | | | | | | | | simplifying with (103), (107) gives:
% 248.79/58.78 | | | | | | | | | | | (144) all_8_1 = e4
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | REDUCE: (84), (143) imply:
% 248.79/58.78 | | | | | | | | | | | (145) op(e1, e4) = e0
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | REDUCE: (106), (144) imply:
% 248.79/58.78 | | | | | | | | | | | (146) op(e1, e4) = all_8_0
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | BETA: splitting (142) gives:
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | (147) ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 248.79/58.78 | | | | | | | | | | | | all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0)
% 248.79/58.78 | | | | | | | | | | | | & $i(all_242_1)
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | ALPHA: (147) implies:
% 248.79/58.78 | | | | | | | | | | | | (148) op(e1, e4) = all_242_1
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | REF_CLOSE: (15), (105), (145), (146), (148) are inconsistent
% 248.79/58.78 | | | | | | | | | | | | by sub-proof #72.
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | (149) ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 &
% 248.79/58.78 | | | | | | | | | | | | $i(all_242_1)
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | ALPHA: (149) implies:
% 248.79/58.78 | | | | | | | | | | | | (150) op(e1, e4) = all_242_1
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | | REF_CLOSE: (15), (105), (145), (146), (150) are inconsistent
% 248.79/58.78 | | | | | | | | | | | | by sub-proof #72.
% 248.79/58.78 | | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | End of split
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | End of split
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | (151) all_252_21 = e1 & op(e0, e3) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | ALPHA: (151) implies:
% 248.79/58.78 | | | | | | | | | | (152) op(e0, e3) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | REF_CLOSE: (15), (115), (117), (152) are inconsistent by
% 248.79/58.78 | | | | | | | | | | sub-proof #941.
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | End of split
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | (153) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 =
% 248.79/58.78 | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 248.79/58.78 | | | | | | | | | e0) = e1)
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | BETA: splitting (153) gives:
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | (154) all_252_22 = e1 & op(e0, e2) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | ALPHA: (154) implies:
% 248.79/58.78 | | | | | | | | | | (155) op(e0, e2) = e1
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | REF_CLOSE: (15), (27), (89), (155) are inconsistent by
% 248.79/58.78 | | | | | | | | | | sub-proof #907.
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | (156) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 =
% 248.79/58.78 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | BETA: splitting (156) gives:
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | Case 1:
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | (157) all_252_23 = e1 & op(e0, e1) = e1
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | ALPHA: (157) implies:
% 248.79/58.78 | | | | | | | | | | | (158) op(e0, e1) = e1
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | REF_CLOSE: (15), (129), (136), (158) are inconsistent by
% 248.79/58.78 | | | | | | | | | | | sub-proof #915.
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | (159) all_252_24 = e1 & op(e0, e0) = e1
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | | REF_CLOSE: (15), (17), (55), (159) are inconsistent by
% 248.79/58.78 | | | | | | | | | | | sub-proof #71.
% 248.79/58.78 | | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | | End of split
% 248.79/58.78 | | | | | | | | | |
% 248.79/58.78 | | | | | | | | | End of split
% 248.79/58.78 | | | | | | | | |
% 248.79/58.78 | | | | | | | | End of split
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | Case 2:
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | (160) all_252_24 = e3 & op(e0, e0) = e3
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | ALPHA: (160) implies:
% 248.79/58.78 | | | | | | | | (161) op(e0, e0) = e3
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | | REF_CLOSE: (15), (17), (127), (161) are inconsistent by
% 248.79/58.78 | | | | | | | | sub-proof #835.
% 248.79/58.78 | | | | | | | |
% 248.79/58.78 | | | | | | | End of split
% 248.79/58.78 | | | | | | |
% 248.79/58.78 | | | | | | End of split
% 248.79/58.78 | | | | | |
% 248.79/58.78 | | | | | End of split
% 248.79/58.78 | | | | |
% 248.79/58.78 | | | | End of split
% 248.79/58.78 | | | |
% 248.79/58.78 | | | End of split
% 248.79/58.78 | | |
% 248.79/58.78 | | Case 2:
% 248.79/58.78 | | |
% 248.79/58.78 | | | (162) ~ (all_8_1 = e4) & op(e2, e1) = all_8_1 & $i(all_8_1)
% 248.79/58.78 | | |
% 248.79/58.78 | | | ALPHA: (162) implies:
% 248.79/58.78 | | | (163) ~ (all_8_1 = e4)
% 248.79/58.78 | | | (164) op(e2, e1) = all_8_1
% 248.79/58.78 | | |
% 248.79/58.78 | | | GROUND_INST: instantiating (15) with e4, all_8_1, e1, e2, simplifying with
% 248.79/58.78 | | | (103), (164) gives:
% 248.79/58.78 | | | (165) all_8_1 = e4
% 248.79/58.78 | | |
% 248.79/58.78 | | | REDUCE: (163), (165) imply:
% 248.79/58.78 | | | (166) $false
% 248.79/58.78 | | |
% 248.79/58.78 | | | CLOSE: (166) is inconsistent.
% 248.79/58.78 | | |
% 248.79/58.78 | | End of split
% 248.79/58.78 | |
% 248.79/58.78 | End of split
% 248.79/58.78 |
% 248.79/58.78 End of proof
% 248.79/58.78
% 248.79/58.78 Sub-proof #71 shows that the following formulas are inconsistent:
% 248.79/58.78 ----------------------------------------------------------------
% 248.79/58.78 (1) all_252_24 = e1 & op(e0, e0) = e1
% 248.79/58.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.78 (3) op(e0, e0) = all_244_24
% 248.79/58.78 (4) ~ (all_244_24 = e1)
% 248.79/58.78
% 248.79/58.78 Begin of proof
% 248.79/58.78 |
% 248.79/58.78 | ALPHA: (1) implies:
% 248.79/58.78 | (5) op(e0, e0) = e1
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (2) with all_244_24, e1, e0, e0, simplifying with
% 248.79/58.78 | (3), (5) gives:
% 248.79/58.78 | (6) all_244_24 = e1
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (4), (6) imply:
% 248.79/58.78 | (7) $false
% 248.79/58.78 |
% 248.79/58.78 | CLOSE: (7) is inconsistent.
% 248.79/58.78 |
% 248.79/58.78 End of proof
% 248.79/58.78
% 248.79/58.78 Sub-proof #72 shows that the following formulas are inconsistent:
% 248.79/58.78 ----------------------------------------------------------------
% 248.79/58.78 (1) ~ (all_8_0 = e0)
% 248.79/58.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.78 (3) op(e1, e4) = e0
% 248.79/58.78 (4) op(e1, e4) = all_242_1
% 248.79/58.78 (5) op(e1, e4) = all_8_0
% 248.79/58.78
% 248.79/58.78 Begin of proof
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (2) with e0, all_242_1, e4, e1, simplifying with
% 248.79/58.78 | (3), (4) gives:
% 248.79/58.78 | (6) all_242_1 = e0
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (2) with all_8_0, all_242_1, e4, e1, simplifying
% 248.79/58.78 | with (4), (5) gives:
% 248.79/58.78 | (7) all_242_1 = all_8_0
% 248.79/58.78 |
% 248.79/58.78 | COMBINE_EQS: (6), (7) imply:
% 248.79/58.78 | (8) all_8_0 = e0
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (1), (8) imply:
% 248.79/58.78 | (9) $false
% 248.79/58.78 |
% 248.79/58.78 | CLOSE: (9) is inconsistent.
% 248.79/58.78 |
% 248.79/58.78 End of proof
% 248.79/58.78
% 248.79/58.78 Sub-proof #73 shows that the following formulas are inconsistent:
% 248.79/58.78 ----------------------------------------------------------------
% 248.79/58.78 (1) ~ (all_4_2 = e4)
% 248.79/58.78 (2) all_250_16 = all_62_2
% 248.79/58.78 (3) op(e4, e0) = all_30_2
% 248.79/58.78 (4) all_250_8 = all_36_2
% 248.79/58.78 (5) op(all_62_2, all_36_2) = e3
% 248.79/58.78 (6) ~ (all_30_2 = e3)
% 248.79/58.78 (7) op(e4, e1) = e2
% 248.79/58.78 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.78 (9) op(e2, e3) = all_10_2
% 248.79/58.78 (10) ~ (all_122_2 = e0) | ( ~ (all_122_0 = e4) & op(e1, e0) = all_122_1 &
% 248.79/58.78 op(e0, all_122_1) = all_122_0 & $i(all_122_0) & $i(all_122_1)) | ( ~
% 248.79/58.78 (all_122_1 = e2) & op(e1, e0) = all_122_1 & $i(all_122_1))
% 248.79/58.78 (11) op(e1, all_10_2) = e2
% 248.79/58.78 (12) ~ (all_244_15 = e4)
% 248.79/58.78 (13) op(e1, e4) = all_16_2
% 248.79/58.78 (14) op(e1, e3) = all_62_2
% 248.79/58.78 (15) ~ (all_36_2 = e4)
% 248.79/58.78 (16) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 248.79/58.78 all_250_8 = e0
% 248.79/58.78 (17) ~ (all_64_2 = e1)
% 248.79/58.78 (18) op(e2, e3) = e0
% 248.79/58.78 (19) ~ (all_36_2 = all_26_2)
% 248.79/58.78 (20) op(e1, e4) = all_38_1
% 248.79/58.78 (21) all_250_16 = e4 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 |
% 248.79/58.78 all_250_16 = e0
% 248.79/58.78 (22) ~ (all_26_2 = e4)
% 248.79/58.78 (23) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.79/58.78 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.79/58.78 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.79/58.78 (24) op(all_62_2, e3) = e1
% 248.79/58.78 (25) op(e4, e1) = all_26_2
% 248.79/58.78 (26) op(e1, e1) = all_244_15
% 248.79/58.78 (27) op(e1, e2) = all_4_2
% 248.79/58.78 (28) op(e2, e4) = all_64_2
% 248.79/58.78 (29) ~ (all_36_2 = e1)
% 248.79/58.78 (30) all_122_2 = all_36_2
% 248.79/58.78 (31) op(all_26_2, all_16_2) = e1
% 248.79/58.78
% 248.79/58.78 Begin of proof
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (8) with all_16_2, all_38_1, e4, e1, simplifying
% 248.79/58.78 | with (13), (20) gives:
% 248.79/58.78 | (32) all_38_1 = all_16_2
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (8) with all_10_2, e0, e3, e2, simplifying with
% 248.79/58.78 | (9), (18) gives:
% 248.79/58.78 | (33) all_10_2 = e0
% 248.79/58.78 |
% 248.79/58.78 | GROUND_INST: instantiating (8) with all_26_2, e2, e1, e4, simplifying with
% 248.79/58.78 | (7), (25) gives:
% 248.79/58.78 | (34) all_26_2 = e2
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (19), (34) imply:
% 248.79/58.78 | (35) ~ (all_36_2 = e2)
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (22), (34) imply:
% 248.79/58.78 | (36) ~ (e4 = e2)
% 248.79/58.78 |
% 248.79/58.78 | SIMP: (36) implies:
% 248.79/58.78 | (37) ~ (e4 = e2)
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (31), (34) imply:
% 248.79/58.78 | (38) op(e2, all_16_2) = e1
% 248.79/58.78 |
% 248.79/58.78 | REDUCE: (11), (33) imply:
% 248.79/58.78 | (39) op(e1, e0) = e2
% 248.79/58.78 |
% 248.79/58.78 | BETA: splitting (10) gives:
% 248.79/58.78 |
% 248.79/58.78 | Case 1:
% 248.79/58.78 | |
% 248.79/58.78 | | (40) ~ (all_122_2 = e0)
% 248.79/58.78 | |
% 248.79/58.78 | | REDUCE: (30), (40) imply:
% 248.79/58.78 | | (41) ~ (all_36_2 = e0)
% 248.79/58.78 | |
% 248.79/58.78 | | REF_CLOSE: (4), (5), (8), (15), (16), (24), (29), (35), (41) are
% 248.79/58.78 | | inconsistent by sub-proof #658.
% 248.79/58.78 | |
% 248.79/58.78 | Case 2:
% 248.79/58.78 | |
% 248.79/58.78 | | (42) all_122_2 = e0
% 248.79/58.78 | |
% 248.79/58.78 | | COMBINE_EQS: (30), (42) imply:
% 248.79/58.78 | | (43) all_36_2 = e0
% 248.79/58.78 | |
% 248.79/58.78 | | REDUCE: (5), (43) imply:
% 248.79/58.78 | | (44) op(all_62_2, e0) = e3
% 248.79/58.78 | |
% 248.79/58.78 | | BETA: splitting (21) gives:
% 248.79/58.78 | |
% 248.79/58.78 | | Case 1:
% 248.79/58.78 | | |
% 248.79/58.78 | | | (45) all_250_16 = e4
% 248.79/58.78 | | |
% 248.79/58.78 | | | COMBINE_EQS: (2), (45) imply:
% 248.79/58.78 | | | (46) all_62_2 = e4
% 248.79/58.78 | | |
% 248.79/58.78 | | | SIMP: (46) implies:
% 248.79/58.78 | | | (47) all_62_2 = e4
% 248.79/58.78 | | |
% 248.79/58.78 | | | REDUCE: (44), (47) imply:
% 248.79/58.78 | | | (48) op(e4, e0) = e3
% 248.79/58.78 | | |
% 248.79/58.78 | | | REF_CLOSE: (3), (6), (8), (48) are inconsistent by sub-proof #622.
% 248.79/58.78 | | |
% 248.79/58.78 | | Case 2:
% 248.79/58.78 | | |
% 248.79/58.78 | | | (49) ~ (all_250_16 = e4)
% 248.79/58.78 | | |
% 248.79/58.78 | | | REDUCE: (2), (49) imply:
% 248.79/58.78 | | | (50) ~ (all_62_2 = e4)
% 248.79/58.78 | | |
% 248.79/58.78 | | | REF_CLOSE: (1), (8), (12), (13), (14), (17), (23), (26), (27), (28), (37),
% 248.79/58.78 | | | (38), (39), (50) are inconsistent by sub-proof #729.
% 248.79/58.78 | | |
% 248.79/58.78 | | End of split
% 248.79/58.78 | |
% 248.79/58.78 | End of split
% 248.79/58.78 |
% 248.79/58.78 End of proof
% 248.79/58.78
% 248.79/58.78 Sub-proof #74 shows that the following formulas are inconsistent:
% 248.79/58.78 ----------------------------------------------------------------
% 248.79/58.78 (1) ~ (all_26_2 = e2)
% 248.79/58.78 (2) op(all_4_2, e2) = e1
% 248.79/58.78 (3) ~ (all_38_2 = e1)
% 248.79/58.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.78 (5) op(e2, e2) = all_244_8
% 248.79/58.78 (6) op(e2, e1) = all_38_2
% 248.79/58.78 (7) op(e3, all_38_2) = e2
% 248.79/58.78 (8) op(all_244_15, all_244_15) = e1
% 248.79/58.78 (9) ~ (all_244_3 = all_36_2)
% 248.79/58.78 (10) all_204_2 = all_36_2
% 248.79/58.78 (11) op(e3, e1) = all_36_2
% 248.79/58.78 (12) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.79/58.78 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.79/58.78 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.78 (13) op(e4, e1) = all_26_2
% 248.79/58.78 (14) ~ (all_244_8 = e1)
% 248.79/58.78 (15) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.79/58.78 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) |
% 248.79/58.78 ( ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.79/58.78 (16) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.78 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.78 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.78 (17) op(e1, e1) = all_244_15
% 248.79/58.78 (18) op(e0, e1) = all_20_2
% 248.79/58.78 (19) op(all_4_2, all_38_2) = e2
% 248.79/58.78 (20) op(all_36_2, e1) = e3
% 248.79/58.78 (21) op(e3, e3) = all_244_3
% 248.79/58.78 (22) all_46_2 = all_36_2
% 248.79/58.78 (23) ~ (all_20_2 = e2)
% 248.79/58.78
% 248.79/58.78 Begin of proof
% 248.79/58.78 |
% 248.79/58.78 | BETA: splitting (12) gives:
% 248.79/58.78 |
% 248.79/58.78 | Case 1:
% 248.79/58.78 | |
% 248.79/58.78 | | (24) ~ (all_46_2 = e2)
% 248.79/58.78 | |
% 248.79/58.78 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (13), (14), (16), (17),
% 248.79/58.78 | | (18), (19), (22), (23), (24) are inconsistent by sub-proof #598.
% 248.79/58.78 | |
% 248.79/58.78 | Case 2:
% 248.79/58.78 | |
% 248.79/58.78 | | (25) all_46_2 = e2
% 248.79/58.78 | |
% 248.79/58.78 | | REF_CLOSE: (4), (6), (7), (9), (10), (15), (20), (21), (22), (25) are
% 248.79/58.78 | | inconsistent by sub-proof #77.
% 248.79/58.78 | |
% 248.79/58.78 | End of split
% 248.79/58.78 |
% 248.79/58.78 End of proof
% 248.79/58.78
% 248.79/58.78 Sub-proof #75 shows that the following formulas are inconsistent:
% 248.79/58.78 ----------------------------------------------------------------
% 248.79/58.78 (1) all_252_14 = e3
% 248.79/58.78 (2) op(e3, e4) = e2
% 248.79/58.78 (3) op(e4, e1) = e2
% 248.79/58.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.78 (5) all_234_2 = e1
% 248.79/58.78 (6) op(e2, e2) = all_244_8
% 248.79/58.78 (7) op(e1, e0) = all_34_2
% 248.79/58.78 (8) ~ (all_34_2 = e2)
% 248.79/58.78 (9) op(all_244_15, all_244_15) = e1
% 248.79/58.78 (10) op(e1, e4) = all_16_2
% 248.79/58.78 (11) op(e1, e3) = all_62_2
% 248.79/58.78 (12) op(e1, e4) = all_38_1
% 248.79/58.78 (13) ~ (all_26_2 = e4)
% 248.79/58.78 (14) op(all_84_2, e3) = e4
% 248.79/58.78 (15) op(e4, e1) = all_26_2
% 248.79/58.78 (16) op(e3, e4) = all_100_2
% 248.79/58.78 (17) ~ (all_244_8 = e1)
% 248.79/58.78 (18) op(e1, e1) = all_244_15
% 248.79/58.78 (19) ~ (all_26_2 = e3)
% 248.79/58.78 (20) op(e4, e3) = all_84_2
% 248.79/58.78 (21) ~ (all_100_2 = all_16_2)
% 248.79/58.78 (22) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.78 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.78 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.78 (23) ~ (all_234_2 = e1) | ( ~ (all_234_0 = e4) & op(e2, e1) = all_234_1 &
% 248.79/58.78 op(e1, all_234_1) = all_234_0 & $i(all_234_0) & $i(all_234_1)) | ( ~
% 248.79/58.78 (all_234_1 = e0) & op(e2, e1) = all_234_1 & $i(all_234_1))
% 248.79/58.78 (24) op(e4, e3) = e1
% 248.79/58.78
% 248.79/58.78 Begin of proof
% 248.79/58.78 |
% 248.79/58.78 | BETA: splitting (23) gives:
% 248.79/58.78 |
% 248.79/58.78 | Case 1:
% 248.79/58.78 | |
% 248.79/58.78 | | (25) ~ (all_234_2 = e1)
% 248.79/58.78 | |
% 248.79/58.78 | | REDUCE: (5), (25) imply:
% 248.79/58.78 | | (26) $false
% 248.79/58.78 | |
% 248.79/58.78 | | CLOSE: (26) is inconsistent.
% 248.79/58.78 | |
% 248.79/58.78 | Case 2:
% 248.79/58.78 | |
% 248.79/58.78 | |
% 248.79/58.78 | | GROUND_INST: instantiating (4) with all_16_2, all_38_1, e4, e1, simplifying
% 248.79/58.78 | | with (10), (12) gives:
% 248.79/58.78 | | (27) all_38_1 = all_16_2
% 248.79/58.78 | |
% 248.79/58.78 | | GROUND_INST: instantiating (4) with all_100_2, e2, e4, e3, simplifying with
% 248.79/58.78 | | (2), (16) gives:
% 248.79/58.78 | | (28) all_100_2 = e2
% 248.79/58.78 | |
% 248.79/58.78 | | GROUND_INST: instantiating (4) with all_26_2, e2, e1, e4, simplifying with
% 248.79/58.78 | | (3), (15) gives:
% 248.79/58.78 | | (29) all_26_2 = e2
% 248.79/58.78 | |
% 248.79/58.78 | | GROUND_INST: instantiating (4) with all_84_2, e1, e3, e4, simplifying with
% 248.79/58.78 | | (20), (24) gives:
% 248.79/58.79 | | (30) all_84_2 = e1
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (21), (28) imply:
% 248.79/58.79 | | (31) ~ (all_16_2 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | SIMP: (31) implies:
% 248.79/58.79 | | (32) ~ (all_16_2 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (13), (29) imply:
% 248.79/58.79 | | (33) ~ (e4 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | SIMP: (33) implies:
% 248.79/58.79 | | (34) ~ (e4 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (19), (29) imply:
% 248.79/58.79 | | (35) ~ (e3 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | SIMP: (35) implies:
% 248.79/58.79 | | (36) ~ (e3 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (14), (30) imply:
% 248.79/58.79 | | (37) op(e1, e3) = e4
% 248.79/58.79 | |
% 248.79/58.79 | | BETA: splitting (22) gives:
% 248.79/58.79 | |
% 248.79/58.79 | | Case 1:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (38) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 248.79/58.79 | | | e3) = e2)
% 248.79/58.79 | | |
% 248.79/58.79 | | | BETA: splitting (38) gives:
% 248.79/58.79 | | |
% 248.79/58.79 | | | Case 1:
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | (39) all_252_12 = e2 & op(e1, e4) = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | REF_CLOSE: (4), (10), (32), (39) are inconsistent by sub-proof #926.
% 248.79/58.79 | | | |
% 248.79/58.79 | | | Case 2:
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | (40) all_252_13 = e2 & op(e1, e3) = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | ALPHA: (40) implies:
% 248.79/58.79 | | | | (41) op(e1, e3) = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | GROUND_INST: instantiating (4) with all_62_2, e2, e3, e1, simplifying
% 248.79/58.79 | | | | with (11), (41) gives:
% 248.79/58.79 | | | | (42) all_62_2 = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | GROUND_INST: instantiating (4) with all_62_2, e4, e3, e1, simplifying
% 248.79/58.79 | | | | with (11), (37) gives:
% 248.79/58.79 | | | | (43) all_62_2 = e4
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | COMBINE_EQS: (42), (43) imply:
% 248.79/58.79 | | | | (44) e4 = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | REDUCE: (34), (44) imply:
% 248.79/58.79 | | | | (45) $false
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | CLOSE: (45) is inconsistent.
% 248.79/58.79 | | | |
% 248.79/58.79 | | | End of split
% 248.79/58.79 | | |
% 248.79/58.79 | | Case 2:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (46) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.79 | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.79 | | |
% 248.79/58.79 | | | BETA: splitting (46) gives:
% 248.79/58.79 | | |
% 248.79/58.79 | | | Case 1:
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | (47) all_252_14 = e2 & op(e1, e2) = e2
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | REF_CLOSE: (1), (36), (47) are inconsistent by sub-proof #76.
% 248.79/58.79 | | | |
% 248.79/58.79 | | | Case 2:
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | (48) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 248.79/58.79 | | | | e0) = e2)
% 248.79/58.79 | | | |
% 248.79/58.79 | | | | REF_CLOSE: (4), (6), (7), (8), (9), (17), (18), (48) are inconsistent by
% 248.79/58.79 | | | | sub-proof #79.
% 248.79/58.79 | | | |
% 248.79/58.79 | | | End of split
% 248.79/58.79 | | |
% 248.79/58.79 | | End of split
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #76 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) all_252_14 = e2 & op(e1, e2) = e2
% 248.79/58.79 (2) all_252_14 = e3
% 248.79/58.79 (3) ~ (e3 = e2)
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | ALPHA: (1) implies:
% 248.79/58.79 | (4) all_252_14 = e2
% 248.79/58.79 |
% 248.79/58.79 | COMBINE_EQS: (2), (4) imply:
% 248.79/58.79 | (5) e3 = e2
% 248.79/58.79 |
% 248.79/58.79 | REDUCE: (3), (5) imply:
% 248.79/58.79 | (6) $false
% 248.79/58.79 |
% 248.79/58.79 | CLOSE: (6) is inconsistent.
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #77 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (2) op(e2, e1) = all_38_2
% 248.79/58.79 (3) op(e3, all_38_2) = e2
% 248.79/58.79 (4) ~ (all_244_3 = all_36_2)
% 248.79/58.79 (5) all_204_2 = all_36_2
% 248.79/58.79 (6) all_46_2 = e2
% 248.79/58.79 (7) ~ (all_204_2 = e2) | ( ~ (all_204_0 = e4) & op(e2, all_204_1) =
% 248.79/58.79 all_204_0 & op(e1, e2) = all_204_1 & $i(all_204_0) & $i(all_204_1)) | (
% 248.79/58.79 ~ (all_204_1 = e0) & op(e1, e2) = all_204_1 & $i(all_204_1))
% 248.79/58.79 (8) op(all_36_2, e1) = e3
% 248.79/58.79 (9) op(e3, e3) = all_244_3
% 248.79/58.79 (10) all_46_2 = all_36_2
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | COMBINE_EQS: (6), (10) imply:
% 248.79/58.79 | (11) all_36_2 = e2
% 248.79/58.79 |
% 248.79/58.79 | SIMP: (11) implies:
% 248.79/58.79 | (12) all_36_2 = e2
% 248.79/58.79 |
% 248.79/58.79 | COMBINE_EQS: (5), (12) imply:
% 248.79/58.79 | (13) all_204_2 = e2
% 248.79/58.79 |
% 248.79/58.79 | REDUCE: (4), (12) imply:
% 248.79/58.79 | (14) ~ (all_244_3 = e2)
% 248.79/58.79 |
% 248.79/58.79 | REDUCE: (8), (12) imply:
% 248.79/58.79 | (15) op(e2, e1) = e3
% 248.79/58.79 |
% 248.79/58.79 | BETA: splitting (7) gives:
% 248.79/58.79 |
% 248.79/58.79 | Case 1:
% 248.79/58.79 | |
% 248.79/58.79 | | (16) ~ (all_204_2 = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (13), (16) imply:
% 248.79/58.79 | | (17) $false
% 248.79/58.79 | |
% 248.79/58.79 | | CLOSE: (17) is inconsistent.
% 248.79/58.79 | |
% 248.79/58.79 | Case 2:
% 248.79/58.79 | |
% 248.79/58.79 | |
% 248.79/58.79 | | GROUND_INST: instantiating (1) with all_38_2, e3, e1, e2, simplifying with
% 248.79/58.79 | | (2), (15) gives:
% 248.79/58.79 | | (18) all_38_2 = e3
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (3), (18) imply:
% 248.79/58.79 | | (19) op(e3, e3) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (1), (9), (14), (19) are inconsistent by sub-proof #694.
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #78 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) all_252_14 = e3
% 248.79/58.79 (2) ~ (all_62_2 = e2)
% 248.79/58.79 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (4) ~ (e3 = e2)
% 248.79/58.79 (5) op(e2, e2) = all_244_8
% 248.79/58.79 (6) op(e1, e0) = all_34_2
% 248.79/58.79 (7) ~ (all_34_2 = e2)
% 248.79/58.79 (8) op(all_244_15, all_244_15) = e1
% 248.79/58.79 (9) op(e1, e4) = all_16_2
% 248.79/58.79 (10) op(e1, e3) = all_62_2
% 248.79/58.79 (11) ~ (all_16_2 = e2)
% 248.79/58.79 (12) ~ (all_244_8 = e1)
% 248.79/58.79 (13) op(e1, e1) = all_244_15
% 248.79/58.79 (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.79 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.79 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | BETA: splitting (14) gives:
% 248.79/58.79 |
% 248.79/58.79 | Case 1:
% 248.79/58.79 | |
% 248.79/58.79 | | (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 248.79/58.79 | | = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (2), (3), (9), (10), (11), (15) are inconsistent by sub-proof
% 248.79/58.79 | | #925.
% 248.79/58.79 | |
% 248.79/58.79 | Case 2:
% 248.79/58.79 | |
% 248.79/58.79 | | (16) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 248.79/58.79 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | BETA: splitting (16) gives:
% 248.79/58.79 | |
% 248.79/58.79 | | Case 1:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (17) all_252_14 = e2 & op(e1, e2) = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | ALPHA: (17) implies:
% 248.79/58.79 | | | (18) all_252_14 = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | REF_CLOSE: (1), (4), (18) are inconsistent by sub-proof #447.
% 248.79/58.79 | | |
% 248.79/58.79 | | Case 2:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (19) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 248.79/58.79 | | | e0) = e2)
% 248.79/58.79 | | |
% 248.79/58.79 | | | REF_CLOSE: (3), (5), (6), (7), (8), (12), (13), (19) are inconsistent by
% 248.79/58.79 | | | sub-proof #79.
% 248.79/58.79 | | |
% 248.79/58.79 | | End of split
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #79 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.79 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (3) op(e2, e2) = all_244_8
% 248.79/58.79 (4) op(e1, e0) = all_34_2
% 248.79/58.79 (5) ~ (all_34_2 = e2)
% 248.79/58.79 (6) op(all_244_15, all_244_15) = e1
% 248.79/58.79 (7) ~ (all_244_8 = e1)
% 248.79/58.79 (8) op(e1, e1) = all_244_15
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | BETA: splitting (1) gives:
% 248.79/58.79 |
% 248.79/58.79 | Case 1:
% 248.79/58.79 | |
% 248.79/58.79 | | (9) all_252_15 = e2 & op(e1, e1) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | ALPHA: (9) implies:
% 248.79/58.79 | | (10) op(e1, e1) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (2), (3), (6), (7), (8), (10) are inconsistent by sub-proof #991.
% 248.79/58.79 | |
% 248.79/58.79 | Case 2:
% 248.79/58.79 | |
% 248.79/58.79 | | (11) all_252_19 = e2 & op(e1, e0) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | ALPHA: (11) implies:
% 248.79/58.79 | | (12) op(e1, e0) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #909.
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #80 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (2) op(e2, e2) = all_244_8
% 248.79/58.79 (3) op(e2, e1) = all_38_2
% 248.79/58.79 (4) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = e4)
% 248.79/58.79 | (all_252_18 = e4 & op(e2, e0) = e4)
% 248.79/58.79 (5) ~ (all_40_2 = e4)
% 248.79/58.79 (6) ~ (all_38_2 = e4)
% 248.79/58.79 (7) ~ (all_244_8 = e4)
% 248.79/58.79 (8) op(e2, e0) = all_40_2
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | BETA: splitting (4) gives:
% 248.79/58.79 |
% 248.79/58.79 | Case 1:
% 248.79/58.79 | |
% 248.79/58.79 | | (9) all_252_8 = e4 & op(e2, e2) = e4
% 248.79/58.79 | |
% 248.79/58.79 | | ALPHA: (9) implies:
% 248.79/58.79 | | (10) op(e2, e2) = e4
% 248.79/58.79 | |
% 248.79/58.79 | | GROUND_INST: instantiating (1) with all_244_8, e4, e2, e2, simplifying with
% 248.79/58.79 | | (2), (10) gives:
% 248.79/58.79 | | (11) all_244_8 = e4
% 248.79/58.79 | |
% 248.79/58.79 | | REDUCE: (7), (11) imply:
% 248.79/58.79 | | (12) $false
% 248.79/58.79 | |
% 248.79/58.79 | | CLOSE: (12) is inconsistent.
% 248.79/58.79 | |
% 248.79/58.79 | Case 2:
% 248.79/58.79 | |
% 248.79/58.79 | | (13) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0)
% 248.79/58.79 | | = e4)
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (1), (3), (5), (6), (8), (13) are inconsistent by sub-proof #933.
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #81 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 248.79/58.79 | (all_252_21 = e2 & op(e0, e3) = e2)
% 248.79/58.79 (2) ~ (all_22_2 = e2)
% 248.79/58.79 (3) ~ (all_62_2 = e2)
% 248.79/58.79 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (5) all_252_7 = e4
% 248.79/58.79 (6) op(e1, e3) = all_62_2
% 248.79/58.79 (7) op(e0, e3) = all_22_2
% 248.79/58.79 (8) ~ (e4 = e2)
% 248.79/58.79
% 248.79/58.79 Begin of proof
% 248.79/58.79 |
% 248.79/58.79 | BETA: splitting (1) gives:
% 248.79/58.79 |
% 248.79/58.79 | Case 1:
% 248.79/58.79 | |
% 248.79/58.79 | | (9) all_252_7 = e2 & op(e2, e3) = e2
% 248.79/58.79 | |
% 248.79/58.79 | | REF_CLOSE: (5), (8), (9) are inconsistent by sub-proof #371.
% 248.79/58.79 | |
% 248.79/58.79 | Case 2:
% 248.79/58.79 | |
% 248.79/58.79 | | (10) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3)
% 248.79/58.79 | | = e2)
% 248.79/58.79 | |
% 248.79/58.79 | | BETA: splitting (10) gives:
% 248.79/58.79 | |
% 248.79/58.79 | | Case 1:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (11) all_252_13 = e2 & op(e1, e3) = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | ALPHA: (11) implies:
% 248.79/58.79 | | | (12) op(e1, e3) = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | REF_CLOSE: (3), (4), (6), (12) are inconsistent by sub-proof #972.
% 248.79/58.79 | | |
% 248.79/58.79 | | Case 2:
% 248.79/58.79 | | |
% 248.79/58.79 | | | (13) all_252_21 = e2 & op(e0, e3) = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | ALPHA: (13) implies:
% 248.79/58.79 | | | (14) op(e0, e3) = e2
% 248.79/58.79 | | |
% 248.79/58.79 | | | REF_CLOSE: (2), (4), (7), (14) are inconsistent by sub-proof #987.
% 248.79/58.79 | | |
% 248.79/58.79 | | End of split
% 248.79/58.79 | |
% 248.79/58.79 | End of split
% 248.79/58.79 |
% 248.79/58.79 End of proof
% 248.79/58.79
% 248.79/58.79 Sub-proof #82 shows that the following formulas are inconsistent:
% 248.79/58.79 ----------------------------------------------------------------
% 248.79/58.79 (1) ~ (all_244_8 = all_4_2)
% 248.79/58.79 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 248.79/58.79 all_250_23 = e0
% 248.79/58.79 (3) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 248.79/58.79 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 248.79/58.79 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 248.79/58.79 (4) ~ (all_26_2 = e2)
% 248.79/58.79 (5) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 248.79/58.79 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 248.79/58.79 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 248.79/58.79 (6) ~ (all_4_2 = e4)
% 248.79/58.79 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.79 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.79 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.79 (8) op(all_4_2, e2) = e1
% 248.79/58.79 (9) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 248.79/58.79 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 248.79/58.79 (all_252_16 = e3 & op(e4, e0) = e3)
% 248.79/58.79 (10) ~ (all_244_24 = all_34_2)
% 248.79/58.79 (11) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.79 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 248.79/58.79 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 248.79/58.79 (12) ~ (all_244_24 = all_40_2)
% 248.79/58.79 (13) ~ (all_40_2 = all_38_2)
% 248.79/58.79 (14) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 248.79/58.79 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 248.79/58.79 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 248.79/58.79 (15) op(e4, e0) = all_30_2
% 248.79/58.79 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 248.79/58.79 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 248.79/58.79 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.79 (17) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 248.79/58.79 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 248.79/58.79 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.79/58.79 (18) all_174_2 = all_40_2
% 248.79/58.79 (19) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 248.79/58.79 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 248.79/58.79 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 248.79/58.79 (20) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.79/58.79 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.79/58.79 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.79/58.79 (21) ~ (all_22_2 = e2)
% 248.79/58.79 (22) all_94_2 = all_38_2
% 248.79/58.79 (23) op(all_62_2, all_36_2) = e3
% 248.79/58.79 (24) op(all_38_2, e1) = e2
% 248.79/58.79 (25) all_250_13 = all_38_2
% 248.79/58.79 (26) ~ (all_28_2 = all_6_2)
% 248.79/58.79 (27) op(all_38_2, all_4_2) = e1
% 248.79/58.79 (28) op(all_64_2, e4) = e2
% 248.79/58.79 (29) ~ (e1 = e0)
% 248.79/58.79 (30) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.79/58.79 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.79/58.79 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.79/58.79 (31) ~ (all_62_2 = e2)
% 248.79/58.79 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.79 (33) ~ (e3 = e2)
% 248.79/58.79 (34) op(e0, e0) = all_244_24
% 248.79/58.79 (35) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 248.79/58.79 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 248.79/58.79 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 248.79/58.79 (36) ~ (all_244_8 = all_64_2)
% 248.79/58.79 (37) op(all_244_8, all_244_8) = e2
% 248.79/58.79 (38) op(e2, e2) = all_244_8
% 248.79/58.79 (39) ~ (all_64_2 = e2)
% 248.79/58.79 (40) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 248.79/58.79 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 248.79/58.79 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 248.79/58.79 (41) op(e2, e1) = all_38_2
% 248.79/58.79 (42) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.79 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.79 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.79 (43) ~ (all_36_2 = all_20_2)
% 248.79/58.79 (44) ~ (all_64_2 = all_40_2)
% 248.79/58.79 (45) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.79/58.79 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.79/58.79 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.79 (46) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 248.79/58.79 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 248.79/58.79 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 248.79/58.79 (47) ~ (all_244_3 = all_22_2)
% 248.79/58.79 (48) op(e1, e0) = all_34_2
% 248.79/58.79 (49) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 248.79/58.79 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 248.79/58.79 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 248.79/58.79 (50) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.79/58.79 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.79/58.79 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.79/58.79 (51) ~ (all_40_2 = e4)
% 248.79/58.79 (52) op(all_28_2, e2) = e0
% 248.79/58.79 (53) op(e4, e2) = all_6_2
% 248.79/58.79 (54) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.79/58.79 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.79/58.79 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.79/58.79 (55) ~ (all_8_2 = all_4_2)
% 248.79/58.79 (56) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 248.79/58.79 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 248.79/58.79 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 248.79/58.79 (57) ~ (e2 = e1)
% 248.79/58.79 (58) op(all_26_2, e1) = e4
% 248.79/58.79 (59) all_252_7 = e4
% 248.79/58.79 (60) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.79 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.79 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.79 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.79 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.79 op(e0, e1) = e0)))
% 248.79/58.79 (61) all_56_2 = all_8_2
% 248.79/58.79 (62) op(e0, e2) = all_28_2
% 248.79/58.79 (63) ~ (e4 = e1)
% 248.79/58.79 (64) ~ (all_244_0 = e2)
% 248.79/58.79 (65) op(all_6_2, all_64_2) = e2
% 248.79/58.79 (66) ~ (all_6_2 = e1)
% 248.79/58.79 (67) ~ (all_62_2 = all_34_2)
% 248.79/58.79 (68) ~ (all_244_8 = all_38_2)
% 248.79/58.79 (69) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 248.79/58.79 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 248.79/58.79 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 248.79/58.79 (70) op(all_244_15, all_244_15) = e1
% 248.79/58.79 (71) all_80_2 = all_6_2
% 248.79/58.79 (72) all_250_21 = all_22_2
% 248.79/58.79 (73) all_50_2 = all_4_2
% 248.79/58.79 (74) op(all_34_2, e0) = e1
% 248.79/58.79 (75) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 248.79/58.79 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 248.79/58.79 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 248.79/58.79 (76) op(e1, e4) = all_16_2
% 248.79/58.79 (77) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 248.79/58.79 all_250_2 = e0
% 248.79/58.79 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.79 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.79 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.79 (79) ~ (all_28_2 = all_20_2)
% 248.79/58.80 (80) op(e1, e3) = all_62_2
% 248.79/58.80 (81) op(all_100_2, e2) = e4
% 248.79/58.80 (82) ~ (all_244_0 = all_26_2)
% 248.79/58.80 (83) ~ (e3 = e0)
% 248.79/58.80 (84) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 248.79/58.80 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 248.79/58.80 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 248.79/58.80 (85) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.79/58.80 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.79/58.80 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.79/58.80 (86) op(all_20_2, e1) = e0
% 248.79/58.80 (87) ~ (all_30_2 = e2)
% 248.79/58.80 (88) all_252_1 = e2
% 248.79/58.80 (89) ~ (all_6_2 = e2)
% 248.79/58.80 (90) ~ (all_22_2 = e4)
% 248.79/58.80 (91) all_70_2 = all_62_2
% 248.79/58.80 (92) ~ (all_36_2 = all_8_2)
% 248.79/58.80 (93) ~ (e3 = e1)
% 248.79/58.80 (94) op(all_48_2, all_22_2) = e0
% 248.79/58.80 (95) op(e3, e1) = all_36_2
% 248.79/58.80 (96) ~ (all_16_2 = e2)
% 248.79/58.80 (97) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 248.79/58.80 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 248.79/58.80 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 248.79/58.80 (98) ~ (all_8_2 = e1)
% 248.79/58.80 (99) op(all_40_2, e0) = e2
% 248.79/58.80 (100) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.79/58.80 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.79/58.80 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.80 (101) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 248.79/58.80 all_250_22 = e0
% 248.79/58.80 (102) ~ (all_244_8 = all_40_2)
% 248.79/58.80 (103) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 248.79/58.80 all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) |
% 248.79/58.80 ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.80 (104) ~ (all_28_2 = all_4_2)
% 248.79/58.80 (105) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.80 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.80 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.80 (106) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.79/58.80 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.79/58.80 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.80 (107) ~ (all_40_2 = all_34_2)
% 248.79/58.80 (108) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.79/58.80 all_250_13 = e0
% 248.79/58.80 (109) ~ (all_244_15 = all_38_2)
% 248.79/58.80 (110) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.79/58.80 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.79/58.80 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.79/58.80 (111) ~ (all_36_2 = all_26_2)
% 248.79/58.80 (112) op(e4, e3) = e2
% 248.79/58.80 (113) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 248.79/58.80 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 248.79/58.80 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 248.79/58.80 (114) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 248.79/58.80 & op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 248.79/58.80 (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 248.79/58.80 (115) all_74_2 = all_36_2
% 248.79/58.80 (116) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.79/58.80 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.79/58.80 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.79/58.80 (117) ~ (all_38_2 = e4)
% 248.79/58.80 (118) all_182_2 = e2
% 248.79/58.80 (119) ~ (all_26_2 = all_6_2)
% 248.79/58.80 (120) ( ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2, all_12_1) =
% 248.79/58.80 all_12_0 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) &
% 248.79/58.80 op(e4, e2) = all_12_1 & $i(all_12_1))
% 248.79/58.80 (121) ~ (all_28_2 = e2)
% 248.79/58.80 (122) op(all_22_2, e3) = e0
% 248.79/58.80 (123) op(all_20_2, all_34_2) = e1
% 248.79/58.80 (124) op(e0, e3) = all_22_2
% 248.79/58.80 (125) ~ (all_28_2 = all_22_2)
% 248.79/58.80 (126) op(all_34_2, all_20_2) = e0
% 248.79/58.80 (127) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.79/58.80 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.79/58.80 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.80 (128) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.79/58.80 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.79/58.80 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.79/58.80 (129) all_58_2 = all_20_2
% 248.79/58.80 (130) op(e4, e1) = all_26_2
% 248.79/58.80 (131) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.79/58.80 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.79/58.80 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.80 (132) ~ (all_64_2 = all_38_2)
% 248.79/58.80 (133) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.79/58.80 all_250_21 = e0
% 248.79/58.80 (134) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 248.79/58.80 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.80 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 248.79/58.80 (135) op(e3, e4) = all_100_2
% 248.79/58.80 (136) op(e4, e4) = all_244_0
% 248.79/58.80 (137) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.79/58.80 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.80 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.80 (138) ~ (e4 = e3)
% 248.79/58.80 (139) op(e1, e1) = all_244_15
% 248.79/58.80 (140) op(e0, e1) = all_20_2
% 248.79/58.80 (141) ~ (all_244_15 = all_20_2)
% 248.79/58.80 (142) op(all_48_2, e0) = e3
% 248.79/58.80 (143) ~ (all_38_2 = all_36_2)
% 248.79/58.80 (144) op(e2, e4) = e0
% 248.79/58.80 (145) all_82_2 = all_28_2
% 248.79/58.80 (146) ~ (all_244_24 = e2)
% 248.79/58.80 (147) op(e1, e2) = all_4_2
% 248.79/58.80 (148) ~ (all_28_2 = all_8_2)
% 248.79/58.80 (149) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 248.79/58.80 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 248.79/58.80 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 248.79/58.80 (150) op(all_4_2, all_38_2) = e2
% 248.79/58.80 (151) op(e4, e3) = all_84_2
% 248.79/58.80 (152) all_86_2 = all_40_2
% 248.79/58.80 (153) all_116_2 = all_40_2
% 248.79/58.80 (154) op(e2, e4) = all_64_2
% 248.79/58.80 (155) ~ (all_6_2 = all_4_2)
% 248.79/58.80 (156) op(all_40_2, all_28_2) = e0
% 248.79/58.80 (157) ~ (e4 = e2)
% 248.79/58.80 (158) ~ (all_22_2 = all_20_2)
% 248.79/58.80 (159) op(e3, e2) = all_8_2
% 248.79/58.80 (160) ~ (all_34_2 = all_16_2)
% 248.79/58.80 (161) ~ (all_64_2 = all_16_2)
% 248.79/58.80 (162) op(all_36_2, e1) = e3
% 248.79/58.80 (163) ~ (all_38_2 = all_20_2)
% 248.79/58.80 (164) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.79/58.80 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.80 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.80 (165) ~ (all_244_15 = all_36_2)
% 248.79/58.80 (166) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 248.79/58.80 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 248.79/58.80 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 248.79/58.80 (167) op(all_16_2, e4) = e1
% 248.79/58.80 (168) op(e2, e0) = all_40_2
% 248.79/58.80 (169) op(all_8_2, e2) = e3
% 248.79/58.80 (170) ~ (all_244_8 = all_28_2)
% 248.79/58.80 (171) all_24_2 = all_16_2
% 248.79/58.80 (172) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.80 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.80 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.80 (173) all_250_22 = all_28_2
% 248.79/58.80 (174) op(e3, e3) = all_244_3
% 248.79/58.80 (175) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 248.79/58.80 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 248.79/58.80 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 248.79/58.80 (176) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 248.79/58.80 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 248.79/58.80 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.79/58.80 (177) all_188_2 = all_38_2
% 248.79/58.80 (178) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.80 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.80 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.80 (179) ~ (all_62_2 = e4)
% 248.79/58.80 (180) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 248.79/58.80 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 248.79/58.80 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 248.79/58.80 (181) all_250_2 = all_6_2
% 248.79/58.80 (182) all_46_2 = all_36_2
% 248.79/58.80 (183) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.79/58.80 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.79/58.80 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.79/58.80 (184) ~ (all_64_2 = e4)
% 248.79/58.80 (185) ~ (all_34_2 = all_4_2)
% 248.79/58.80 (186) ~ (all_20_2 = e2)
% 248.79/58.80 (187) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 248.79/58.80 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 248.79/58.80 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.80 (188) op(all_64_2, all_6_2) = e4
% 248.79/58.80 (189) all_250_23 = all_20_2
% 248.79/58.80
% 248.79/58.80 Begin of proof
% 248.79/58.80 |
% 248.79/58.80 | BETA: splitting (131) gives:
% 248.79/58.80 |
% 248.79/58.80 | Case 1:
% 248.79/58.80 | |
% 248.79/58.80 | | (190) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 248.79/58.80 | | = e2)
% 248.79/58.80 | |
% 248.79/58.80 | | BETA: splitting (190) gives:
% 248.79/58.80 | |
% 248.79/58.80 | | Case 1:
% 248.79/58.80 | | |
% 248.79/58.80 | | | (191) all_252_20 = e2 & op(e0, e4) = e2
% 248.79/58.80 | | |
% 248.79/58.80 | | | ALPHA: (191) implies:
% 248.79/58.80 | | | (192) all_252_20 = e2
% 248.79/58.80 | | |
% 248.79/58.80 | | | BETA: splitting (120) gives:
% 248.79/58.80 | | |
% 248.79/58.80 | | | Case 1:
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | (193) ~ (all_12_0 = e3) & op(e4, e2) = all_12_1 & op(e2, all_12_1) =
% 248.79/58.80 | | | | all_12_0 & $i(all_12_0) & $i(all_12_1)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | ALPHA: (193) implies:
% 248.79/58.80 | | | | (194) op(e4, e2) = all_12_1
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | GROUND_INST: instantiating (32) with all_64_2, e0, e4, e2, simplifying
% 248.79/58.80 | | | | with (144), (154) gives:
% 248.79/58.80 | | | | (195) all_64_2 = e0
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | GROUND_INST: instantiating (32) with all_6_2, all_12_1, e2, e4,
% 248.79/58.80 | | | | simplifying with (53), (194) gives:
% 248.79/58.80 | | | | (196) all_12_1 = all_6_2
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (36), (195) imply:
% 248.79/58.80 | | | | (197) ~ (all_244_8 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (44), (195) imply:
% 248.79/58.80 | | | | (198) ~ (all_40_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (198) implies:
% 248.79/58.80 | | | | (199) ~ (all_40_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (132), (195) imply:
% 248.79/58.80 | | | | (200) ~ (all_38_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (200) implies:
% 248.79/58.80 | | | | (201) ~ (all_38_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (161), (195) imply:
% 248.79/58.80 | | | | (202) ~ (all_16_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (202) implies:
% 248.79/58.80 | | | | (203) ~ (all_16_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (184), (195) imply:
% 248.79/58.80 | | | | (204) ~ (e4 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (204) implies:
% 248.79/58.80 | | | | (205) ~ (e4 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (39), (195) imply:
% 248.79/58.80 | | | | (206) ~ (e2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (206) implies:
% 248.79/58.80 | | | | (207) ~ (e2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.79/58.80 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 248.79/58.80 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 248.79/58.80 | | | | (32), (33), (34), (35), (37), (38), (40), (41), (42), (43),
% 248.79/58.80 | | | | (45), (46), (47), (48), (49), (50), (51), (52), (54), (55),
% 248.79/58.80 | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 248.79/58.80 | | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 248.79/58.80 | | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 248.79/58.80 | | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 248.79/58.80 | | | | (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 248.79/58.80 | | | | (105), (106), (107), (108), (109), (110), (111), (112),
% 248.79/58.80 | | | | (113), (114), (115), (116), (117), (118), (119), (121),
% 248.79/58.80 | | | | (122), (123), (124), (125), (126), (127), (128), (129),
% 248.79/58.80 | | | | (130), (131), (133), (134), (135), (136), (137), (138),
% 248.79/58.80 | | | | (139), (140), (141), (142), (143), (145), (146), (147),
% 248.79/58.80 | | | | (148), (149), (150), (151), (152), (153), (155), (156),
% 248.79/58.80 | | | | (157), (158), (159), (160), (162), (163), (164), (165),
% 248.79/58.80 | | | | (166), (167), (168), (169), (170), (171), (172), (173),
% 248.79/58.80 | | | | (174), (175), (176), (177), (178), (179), (180), (181),
% 248.79/58.80 | | | | (182), (183), (185), (186), (187), (188), (189), (192),
% 248.79/58.80 | | | | (194), (195), (196), (197), (199), (201), (203), (205), (207)
% 248.79/58.80 | | | | are inconsistent by sub-proof #83.
% 248.79/58.80 | | | |
% 248.79/58.80 | | | Case 2:
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | (208) ~ (all_12_1 = e1) & op(e4, e2) = all_12_1 & $i(all_12_1)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | ALPHA: (208) implies:
% 248.79/58.80 | | | | (209) ~ (all_12_1 = e1)
% 248.79/58.80 | | | | (210) op(e4, e2) = all_12_1
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | GROUND_INST: instantiating (32) with all_64_2, e0, e4, e2, simplifying
% 248.79/58.80 | | | | with (144), (154) gives:
% 248.79/58.80 | | | | (211) all_64_2 = e0
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | GROUND_INST: instantiating (32) with all_6_2, all_12_1, e2, e4,
% 248.79/58.80 | | | | simplifying with (53), (210) gives:
% 248.79/58.80 | | | | (212) all_12_1 = all_6_2
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (36), (211) imply:
% 248.79/58.80 | | | | (213) ~ (all_244_8 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (44), (211) imply:
% 248.79/58.80 | | | | (214) ~ (all_40_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (214) implies:
% 248.79/58.80 | | | | (215) ~ (all_40_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (132), (211) imply:
% 248.79/58.80 | | | | (216) ~ (all_38_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (216) implies:
% 248.79/58.80 | | | | (217) ~ (all_38_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (161), (211) imply:
% 248.79/58.80 | | | | (218) ~ (all_16_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (218) implies:
% 248.79/58.80 | | | | (219) ~ (all_16_2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (184), (211) imply:
% 248.79/58.80 | | | | (220) ~ (e4 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (220) implies:
% 248.79/58.80 | | | | (221) ~ (e4 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REDUCE: (39), (211) imply:
% 248.79/58.80 | | | | (222) ~ (e2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | SIMP: (222) implies:
% 248.79/58.80 | | | | (223) ~ (e2 = e0)
% 248.79/58.80 | | | |
% 248.79/58.80 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 248.79/58.80 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 248.79/58.80 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 248.79/58.80 | | | | (32), (33), (34), (35), (37), (38), (40), (41), (42), (43),
% 248.79/58.80 | | | | (45), (46), (47), (48), (49), (50), (51), (52), (54), (55),
% 248.79/58.80 | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 248.79/58.80 | | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 248.79/58.80 | | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 248.79/58.80 | | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 248.79/58.80 | | | | (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 248.79/58.80 | | | | (105), (106), (107), (108), (109), (110), (111), (112),
% 248.79/58.80 | | | | (113), (114), (115), (116), (117), (118), (119), (121),
% 248.79/58.80 | | | | (122), (123), (124), (125), (126), (127), (128), (129),
% 248.79/58.80 | | | | (130), (131), (133), (134), (135), (136), (137), (138),
% 248.79/58.80 | | | | (139), (140), (141), (142), (143), (145), (146), (147),
% 248.79/58.80 | | | | (148), (149), (150), (151), (152), (153), (155), (156),
% 248.79/58.80 | | | | (157), (158), (159), (160), (162), (163), (164), (165),
% 248.79/58.80 | | | | (166), (167), (168), (169), (170), (171), (172), (173),
% 248.79/58.80 | | | | (174), (175), (176), (177), (178), (179), (180), (181),
% 248.79/58.80 | | | | (182), (183), (185), (186), (187), (188), (189), (192),
% 248.79/58.80 | | | | (210), (211), (212), (213), (215), (217), (219), (221), (223)
% 248.79/58.80 | | | | are inconsistent by sub-proof #83.
% 248.79/58.80 | | | |
% 248.79/58.80 | | | End of split
% 248.79/58.80 | | |
% 248.79/58.80 | | Case 2:
% 248.79/58.80 | | |
% 248.79/58.80 | | | (224) all_252_21 = e2 & op(e0, e3) = e2
% 248.79/58.80 | | |
% 248.79/58.80 | | | ALPHA: (224) implies:
% 248.79/58.80 | | | (225) op(e0, e3) = e2
% 248.79/58.80 | | |
% 248.79/58.80 | | | REF_CLOSE: (21), (32), (124), (225) are inconsistent by sub-proof #987.
% 248.79/58.80 | | |
% 248.79/58.80 | | End of split
% 248.79/58.80 | |
% 248.79/58.80 | Case 2:
% 248.79/58.80 | |
% 248.79/58.80 | | (226) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1)
% 248.79/58.80 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.80 | |
% 248.79/58.80 | | BETA: splitting (226) gives:
% 248.79/58.80 | |
% 248.79/58.80 | | Case 1:
% 248.79/58.80 | | |
% 248.79/58.80 | | | (227) all_252_22 = e2 & op(e0, e2) = e2
% 248.79/58.80 | | |
% 248.79/58.80 | | | REF_CLOSE: (32), (62), (121), (227) are inconsistent by sub-proof #979.
% 248.79/58.80 | | |
% 248.79/58.80 | | Case 2:
% 248.79/58.80 | | |
% 248.79/58.80 | | | (228) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 248.79/58.80 | | | e0) = e2)
% 248.79/58.80 | | |
% 248.79/58.80 | | | REF_CLOSE: (32), (34), (140), (146), (186), (228) are inconsistent by
% 248.79/58.80 | | | sub-proof #977.
% 248.79/58.80 | | |
% 248.79/58.80 | | End of split
% 248.79/58.80 | |
% 248.79/58.80 | End of split
% 248.79/58.80 |
% 248.79/58.80 End of proof
% 248.79/58.80
% 248.79/58.80 Sub-proof #83 shows that the following formulas are inconsistent:
% 248.79/58.80 ----------------------------------------------------------------
% 248.79/58.80 (1) ~ (all_244_8 = all_4_2)
% 248.79/58.80 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 248.79/58.80 all_250_23 = e0
% 248.79/58.80 (3) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 248.79/58.80 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 248.79/58.80 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 248.79/58.80 (4) ~ (all_26_2 = e2)
% 248.79/58.80 (5) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 248.79/58.80 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 248.79/58.80 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 248.79/58.80 (6) ~ (all_4_2 = e4)
% 248.79/58.80 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.80 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.80 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.80 (8) op(all_4_2, e2) = e1
% 248.79/58.80 (9) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 248.79/58.80 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 248.79/58.80 (all_252_16 = e3 & op(e4, e0) = e3)
% 248.79/58.80 (10) ~ (all_244_24 = all_34_2)
% 248.79/58.80 (11) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.80 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 248.79/58.80 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 248.79/58.80 (12) ~ (all_244_24 = all_40_2)
% 248.79/58.80 (13) ~ (all_40_2 = all_38_2)
% 248.79/58.80 (14) ~ (all_244_8 = e0)
% 248.79/58.80 (15) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 248.79/58.80 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 248.79/58.80 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 248.79/58.80 (16) op(e4, e0) = all_30_2
% 248.79/58.80 (17) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 248.79/58.80 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 248.79/58.80 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.80 (18) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 248.79/58.80 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 248.79/58.80 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.79/58.81 (19) all_174_2 = all_40_2
% 248.79/58.81 (20) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 248.79/58.81 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 248.79/58.81 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 248.79/58.81 (21) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.79/58.81 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.79/58.81 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.79/58.81 (22) ~ (all_22_2 = e2)
% 248.79/58.81 (23) all_94_2 = all_38_2
% 248.79/58.81 (24) op(all_62_2, all_36_2) = e3
% 248.79/58.81 (25) op(all_38_2, e1) = e2
% 248.79/58.81 (26) all_250_13 = all_38_2
% 248.79/58.81 (27) ~ (all_28_2 = all_6_2)
% 248.79/58.81 (28) ~ (e2 = e0)
% 248.79/58.81 (29) op(all_38_2, all_4_2) = e1
% 248.79/58.81 (30) op(all_64_2, e4) = e2
% 248.79/58.81 (31) ~ (e1 = e0)
% 248.79/58.81 (32) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 248.79/58.81 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 248.79/58.81 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 248.79/58.81 (33) ~ (all_62_2 = e2)
% 248.79/58.81 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.81 (35) ~ (e3 = e2)
% 248.79/58.81 (36) op(e0, e0) = all_244_24
% 248.79/58.81 (37) ~ (e4 = e0)
% 248.79/58.81 (38) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 248.79/58.81 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 248.79/58.81 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 248.79/58.81 (39) op(all_244_8, all_244_8) = e2
% 248.79/58.81 (40) op(e2, e2) = all_244_8
% 248.79/58.81 (41) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 248.79/58.81 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 248.79/58.81 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 248.79/58.81 (42) op(e2, e1) = all_38_2
% 248.79/58.81 (43) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.81 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.81 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.81 (44) ~ (all_36_2 = all_20_2)
% 248.79/58.81 (45) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 248.79/58.81 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 248.79/58.81 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.81 (46) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 248.79/58.81 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 248.79/58.81 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 248.79/58.81 (47) ~ (all_244_3 = all_22_2)
% 248.79/58.81 (48) op(e1, e0) = all_34_2
% 248.79/58.81 (49) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 248.79/58.81 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 248.79/58.81 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 248.79/58.81 (50) all_12_1 = all_6_2
% 248.79/58.81 (51) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 248.79/58.81 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 248.79/58.81 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 248.79/58.81 (52) ~ (all_40_2 = e4)
% 248.79/58.81 (53) op(all_28_2, e2) = e0
% 248.79/58.81 (54) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.79/58.81 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.79/58.81 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.79/58.81 (55) ~ (all_8_2 = all_4_2)
% 248.79/58.81 (56) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 248.79/58.81 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 248.79/58.81 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 248.79/58.81 (57) ~ (e2 = e1)
% 248.79/58.81 (58) op(all_26_2, e1) = e4
% 248.79/58.81 (59) all_252_7 = e4
% 248.79/58.81 (60) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.81 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.81 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.81 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.81 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.81 op(e0, e1) = e0)))
% 248.79/58.81 (61) all_56_2 = all_8_2
% 248.79/58.81 (62) op(e0, e2) = all_28_2
% 248.79/58.81 (63) ~ (e4 = e1)
% 248.79/58.81 (64) ~ (all_244_0 = e2)
% 248.79/58.81 (65) op(all_6_2, all_64_2) = e2
% 248.79/58.81 (66) ~ (all_6_2 = e1)
% 248.79/58.81 (67) ~ (all_62_2 = all_34_2)
% 248.79/58.81 (68) ~ (all_244_8 = all_38_2)
% 248.79/58.81 (69) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 248.79/58.81 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 248.79/58.81 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 248.79/58.81 (70) op(all_244_15, all_244_15) = e1
% 248.79/58.81 (71) all_80_2 = all_6_2
% 248.79/58.81 (72) all_250_21 = all_22_2
% 248.79/58.81 (73) all_50_2 = all_4_2
% 248.79/58.81 (74) op(all_34_2, e0) = e1
% 248.79/58.81 (75) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 248.79/58.81 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 248.79/58.81 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 248.79/58.81 (76) op(e1, e4) = all_16_2
% 248.79/58.81 (77) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 248.79/58.81 all_250_2 = e0
% 248.79/58.81 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.81 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.81 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.81 (79) ~ (all_28_2 = all_20_2)
% 248.79/58.81 (80) op(e1, e3) = all_62_2
% 248.79/58.81 (81) op(all_100_2, e2) = e4
% 248.79/58.81 (82) ~ (all_244_0 = all_26_2)
% 248.79/58.81 (83) ~ (e3 = e0)
% 248.79/58.81 (84) ~ (all_38_2 = e0)
% 248.79/58.81 (85) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 248.79/58.81 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 248.79/58.81 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 248.79/58.81 (86) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 248.79/58.81 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 248.79/58.81 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 248.79/58.81 (87) op(all_20_2, e1) = e0
% 248.79/58.81 (88) ~ (all_30_2 = e2)
% 248.79/58.81 (89) all_252_1 = e2
% 248.79/58.81 (90) ~ (all_6_2 = e2)
% 248.79/58.81 (91) ~ (all_22_2 = e4)
% 248.79/58.81 (92) all_70_2 = all_62_2
% 248.79/58.81 (93) ~ (all_36_2 = all_8_2)
% 248.79/58.81 (94) ~ (e3 = e1)
% 248.79/58.81 (95) op(all_48_2, all_22_2) = e0
% 248.79/58.81 (96) op(e3, e1) = all_36_2
% 248.79/58.81 (97) ~ (all_16_2 = e2)
% 248.79/58.81 (98) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 248.79/58.81 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 248.79/58.81 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 248.79/58.81 (99) ~ (all_8_2 = e1)
% 248.79/58.81 (100) op(all_40_2, e0) = e2
% 248.79/58.81 (101) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 248.79/58.81 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 248.79/58.81 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.81 (102) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 248.79/58.81 all_250_22 = e0
% 248.79/58.81 (103) ~ (all_244_8 = all_40_2)
% 248.79/58.81 (104) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 248.79/58.81 all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) |
% 248.79/58.81 ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.81 (105) ~ (all_28_2 = all_4_2)
% 248.79/58.81 (106) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.81 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.81 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.81 (107) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.79/58.81 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 248.79/58.81 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.81 (108) ~ (all_40_2 = all_34_2)
% 248.79/58.81 (109) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.79/58.81 all_250_13 = e0
% 248.79/58.81 (110) ~ (all_244_15 = all_38_2)
% 248.79/58.81 (111) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 248.79/58.81 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 248.79/58.81 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 248.79/58.81 (112) ~ (all_36_2 = all_26_2)
% 248.79/58.81 (113) op(e4, e3) = e2
% 248.79/58.81 (114) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 248.79/58.81 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 248.79/58.81 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 248.79/58.81 (115) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 248.79/58.81 & op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 248.79/58.81 (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 248.79/58.81 (116) all_74_2 = all_36_2
% 248.79/58.81 (117) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 248.79/58.81 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 248.79/58.81 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 248.79/58.81 (118) ~ (all_38_2 = e4)
% 248.79/58.81 (119) all_182_2 = e2
% 248.79/58.81 (120) ~ (all_26_2 = all_6_2)
% 248.79/58.81 (121) ~ (all_28_2 = e2)
% 248.79/58.81 (122) op(all_22_2, e3) = e0
% 248.79/58.81 (123) op(all_20_2, all_34_2) = e1
% 248.79/58.81 (124) op(e0, e3) = all_22_2
% 248.79/58.81 (125) ~ (all_28_2 = all_22_2)
% 248.79/58.81 (126) ~ (all_40_2 = e0)
% 248.79/58.81 (127) op(all_34_2, all_20_2) = e0
% 248.79/58.81 (128) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 248.79/58.81 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 248.79/58.81 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 248.79/58.81 (129) all_252_20 = e2
% 248.79/58.81 (130) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 248.79/58.81 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 248.79/58.81 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 248.79/58.81 (131) op(e4, e2) = all_12_1
% 248.79/58.81 (132) all_58_2 = all_20_2
% 248.79/58.81 (133) op(e4, e1) = all_26_2
% 248.79/58.81 (134) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 248.79/58.81 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 248.79/58.81 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 248.79/58.81 (135) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 248.79/58.81 all_250_21 = e0
% 248.79/58.81 (136) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 248.79/58.81 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.81 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 248.79/58.81 (137) op(e3, e4) = all_100_2
% 248.79/58.81 (138) op(e4, e4) = all_244_0
% 248.79/58.81 (139) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.79/58.81 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.81 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.81 (140) ~ (e4 = e3)
% 248.79/58.81 (141) op(e1, e1) = all_244_15
% 248.79/58.81 (142) all_64_2 = e0
% 248.79/58.81 (143) op(e0, e1) = all_20_2
% 248.79/58.81 (144) ~ (all_244_15 = all_20_2)
% 248.79/58.81 (145) op(all_48_2, e0) = e3
% 248.79/58.81 (146) ~ (all_38_2 = all_36_2)
% 248.79/58.81 (147) all_82_2 = all_28_2
% 248.79/58.81 (148) ~ (all_244_24 = e2)
% 248.79/58.81 (149) op(e1, e2) = all_4_2
% 248.79/58.81 (150) ~ (all_28_2 = all_8_2)
% 248.79/58.81 (151) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 248.79/58.81 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 248.79/58.81 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 248.79/58.81 (152) op(all_4_2, all_38_2) = e2
% 248.79/58.81 (153) op(e4, e3) = all_84_2
% 248.79/58.81 (154) all_86_2 = all_40_2
% 248.79/58.81 (155) all_116_2 = all_40_2
% 248.79/58.81 (156) ~ (all_6_2 = all_4_2)
% 248.79/58.81 (157) op(all_40_2, all_28_2) = e0
% 248.79/58.81 (158) ~ (e4 = e2)
% 248.79/58.81 (159) ~ (all_22_2 = all_20_2)
% 248.79/58.81 (160) op(e3, e2) = all_8_2
% 248.79/58.81 (161) ~ (all_34_2 = all_16_2)
% 248.79/58.81 (162) op(all_36_2, e1) = e3
% 248.79/58.81 (163) ~ (all_38_2 = all_20_2)
% 248.79/58.81 (164) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 248.79/58.81 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 248.79/58.81 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 248.79/58.81 (165) ~ (all_244_15 = all_36_2)
% 248.79/58.81 (166) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 248.79/58.81 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 248.79/58.81 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 248.79/58.81 (167) op(all_16_2, e4) = e1
% 248.79/58.81 (168) op(e2, e0) = all_40_2
% 248.79/58.81 (169) op(all_8_2, e2) = e3
% 248.79/58.81 (170) ~ (all_244_8 = all_28_2)
% 248.79/58.81 (171) all_24_2 = all_16_2
% 248.79/58.81 (172) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.81 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.81 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.81 (173) all_250_22 = all_28_2
% 248.79/58.81 (174) op(e3, e3) = all_244_3
% 248.79/58.81 (175) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 248.79/58.81 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 248.79/58.81 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 248.79/58.81 (176) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 248.79/58.81 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 248.79/58.81 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.79/58.81 (177) all_188_2 = all_38_2
% 248.79/58.81 (178) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.81 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.81 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.81 (179) ~ (all_62_2 = e4)
% 248.79/58.81 (180) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 248.79/58.81 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 248.79/58.81 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 248.79/58.81 (181) all_250_2 = all_6_2
% 248.79/58.81 (182) all_46_2 = all_36_2
% 248.79/58.81 (183) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 248.79/58.81 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 248.79/58.81 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 248.79/58.81 (184) ~ (all_34_2 = all_4_2)
% 248.79/58.81 (185) ~ (all_16_2 = e0)
% 248.79/58.81 (186) ~ (all_20_2 = e2)
% 248.79/58.81 (187) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 248.79/58.81 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 248.79/58.81 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.81 (188) op(all_64_2, all_6_2) = e4
% 248.79/58.81 (189) all_250_23 = all_20_2
% 248.79/58.81
% 248.79/58.81 Begin of proof
% 248.79/58.81 |
% 248.79/58.81 | REDUCE: (65), (142) imply:
% 248.79/58.81 | (190) op(all_6_2, e0) = e2
% 248.79/58.81 |
% 248.79/58.81 | REDUCE: (50), (131) imply:
% 248.79/58.81 | (191) op(e4, e2) = all_6_2
% 248.79/58.81 |
% 248.79/58.81 | BETA: splitting (18) gives:
% 248.79/58.81 |
% 248.79/58.81 | Case 1:
% 248.79/58.81 | |
% 248.79/58.81 | | (192) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 248.79/58.81 | | e0)
% 248.79/58.81 | |
% 248.79/58.81 | | BETA: splitting (192) gives:
% 248.79/58.81 | |
% 248.79/58.81 | | Case 1:
% 248.79/58.81 | | |
% 248.79/58.81 | | | (193) all_252_6 = e0 & op(e2, e4) = e0
% 248.79/58.81 | | |
% 248.79/58.81 | | | ALPHA: (193) implies:
% 248.79/58.81 | | | (194) all_252_6 = e0
% 248.79/58.81 | | |
% 248.79/58.81 | | | BETA: splitting (56) gives:
% 248.79/58.81 | | |
% 248.79/58.81 | | | Case 1:
% 248.79/58.81 | | | |
% 248.79/58.81 | | | | (195) ~ (all_20_2 = e4)
% 248.79/58.81 | | | |
% 248.79/58.81 | | | | BETA: splitting (151) gives:
% 248.79/58.81 | | | |
% 248.79/58.81 | | | | Case 1:
% 248.79/58.81 | | | | |
% 248.79/58.81 | | | | | (196) ~ (all_24_2 = e3)
% 248.79/58.81 | | | | |
% 248.79/58.81 | | | | | REDUCE: (171), (196) imply:
% 248.79/58.81 | | | | | (197) ~ (all_16_2 = e3)
% 248.79/58.81 | | | | |
% 248.79/58.81 | | | | | BETA: splitting (183) gives:
% 248.79/58.81 | | | | |
% 248.79/58.81 | | | | | Case 1:
% 248.79/58.81 | | | | | |
% 248.79/58.81 | | | | | | (198) ~ (all_22_2 = e1)
% 248.79/58.81 | | | | | |
% 248.79/58.81 | | | | | | BETA: splitting (117) gives:
% 248.79/58.81 | | | | | |
% 248.79/58.81 | | | | | | Case 1:
% 248.79/58.81 | | | | | | |
% 248.79/58.81 | | | | | | | (199) ~ (all_26_2 = e3)
% 248.79/58.81 | | | | | | |
% 248.79/58.81 | | | | | | | BETA: splitting (115) gives:
% 248.79/58.81 | | | | | | |
% 248.79/58.81 | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | |
% 248.79/58.81 | | | | | | | | (200) ~ (all_28_2 = e3)
% 248.79/58.81 | | | | | | | |
% 248.79/58.81 | | | | | | | | BETA: splitting (54) gives:
% 248.79/58.81 | | | | | | | |
% 248.79/58.81 | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | |
% 248.79/58.81 | | | | | | | | | (201) ~ (all_34_2 = e2)
% 248.79/58.81 | | | | | | | | |
% 248.79/58.81 | | | | | | | | | BETA: splitting (21) gives:
% 248.79/58.81 | | | | | | | | |
% 248.79/58.81 | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | (202) ~ (all_36_2 = e4)
% 248.79/58.81 | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | BETA: splitting (107) gives:
% 248.79/58.81 | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | (203) ~ (all_46_2 = e2)
% 248.79/58.81 | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | REDUCE: (182), (203) imply:
% 248.79/58.81 | | | | | | | | | | | (204) ~ (all_36_2 = e2)
% 248.79/58.81 | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | BETA: splitting (187) gives:
% 248.79/58.81 | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | (205) ~ (all_50_2 = e3)
% 248.79/58.81 | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | REDUCE: (73), (205) imply:
% 248.79/58.81 | | | | | | | | | | | | (206) ~ (all_4_2 = e3)
% 248.79/58.81 | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | BETA: splitting (46) gives:
% 248.79/58.81 | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | (207) ~ (all_56_2 = e0)
% 248.79/58.81 | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | REDUCE: (61), (207) imply:
% 248.79/58.81 | | | | | | | | | | | | | (208) ~ (all_8_2 = e0)
% 248.79/58.81 | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | BETA: splitting (98) gives:
% 248.79/58.81 | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | (209) ~ (all_182_2 = e2)
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | REDUCE: (119), (209) imply:
% 248.79/58.81 | | | | | | | | | | | | | | (210) $false
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | Case 2:
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | (211) ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 248.79/58.81 | | | | | | | | | | | | | | op(e2, all_182_1) = all_182_0 & $i(all_182_0) &
% 248.79/58.81 | | | | | | | | | | | | | | $i(all_182_1)) | ( ~ (all_182_1 = e0) & op(e3,
% 248.79/58.81 | | | | | | | | | | | | | | e2) = all_182_1 & $i(all_182_1))
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 248.79/58.81 | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | (212) ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 248.79/58.81 | | | | | | | | | | | | | | | op(e2, all_182_1) = all_182_0 & $i(all_182_0) &
% 248.79/58.81 | | | | | | | | | | | | | | | $i(all_182_1)
% 248.79/58.81 | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 248.79/58.81 | | | | | | | | | | | | | | | (213) op(e3, e2) = all_182_1
% 248.79/58.81 | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_8_2, all_182_1, e2,
% 248.79/58.81 | | | | | | | | | | | | | | | e3, simplifying with (160), (213) gives:
% 248.79/58.81 | | | | | | | | | | | | | | | (214) all_182_1 = all_8_2
% 248.79/58.81 | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 248.79/58.81 | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | Case 1:
% 248.79/58.81 | | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | | (215) ~ (all_58_2 = e3)
% 248.79/58.81 | | | | | | | | | | | | | | | |
% 248.79/58.81 | | | | | | | | | | | | | | | | REDUCE: (132), (215) imply:
% 248.79/58.81 | | | | | | | | | | | | | | | | (216) ~ (all_20_2 = e3)
% 248.79/58.81 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (11), (12), (13),
% 248.79/58.82 | | | | | | | | | | | | | | | | (14), (15), (16), (17), (20), (22), (23), (25),
% 248.79/58.82 | | | | | | | | | | | | | | | | (28), (31), (32), (33), (34), (35), (36), (37),
% 248.79/58.82 | | | | | | | | | | | | | | | | (38), (39), (40), (41), (42), (43), (45), (48),
% 248.79/58.82 | | | | | | | | | | | | | | | | (49), (51), (52), (57), (59), (60), (62), (63),
% 248.79/58.82 | | | | | | | | | | | | | | | | (64), (66), (69), (71), (74), (75), (76), (78),
% 248.79/58.82 | | | | | | | | | | | | | | | | (79), (80), (83), (84), (85), (88), (89), (90),
% 248.79/58.82 | | | | | | | | | | | | | | | | (91), (94), (96), (97), (99), (101), (108), (113),
% 248.79/58.82 | | | | | | | | | | | | | | | | (114), (116), (118), (121), (124), (126), (127),
% 248.79/58.82 | | | | | | | | | | | | | | | | (128), (129), (130), (133), (134), (137), (138),
% 248.79/58.82 | | | | | | | | | | | | | | | | (140), (143), (147), (148), (149), (153), (154),
% 248.79/58.82 | | | | | | | | | | | | | | | | (158), (160), (162), (164), (166), (168), (172),
% 248.79/58.82 | | | | | | | | | | | | | | | | (175), (178), (179), (180), (185), (186), (189),
% 248.79/58.82 | | | | | | | | | | | | | | | | (190), (191), (194), (195), (197), (198), (199),
% 248.79/58.82 | | | | | | | | | | | | | | | | (200), (201), (202), (204), (206), (208), (216)
% 248.79/58.82 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #92.
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | (217) all_58_2 = e3
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (34), (72), (91), (95), (132), (135), (145),
% 248.79/58.82 | | | | | | | | | | | | | | | | (159), (198), (217) are inconsistent by sub-proof
% 248.79/58.82 | | | | | | | | | | | | | | | | #122.
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | (218) ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 &
% 248.79/58.82 | | | | | | | | | | | | | | | $i(all_182_1)
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 248.79/58.82 | | | | | | | | | | | | | | | (219) ~ (all_182_1 = e0)
% 248.79/58.82 | | | | | | | | | | | | | | | (220) op(e3, e2) = all_182_1
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_8_2, all_182_1, e2,
% 248.79/58.82 | | | | | | | | | | | | | | | e3, simplifying with (160), (220) gives:
% 248.79/58.82 | | | | | | | | | | | | | | | (221) all_182_1 = all_8_2
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | (222) ~ (all_58_2 = e3)
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | REDUCE: (132), (222) imply:
% 248.79/58.82 | | | | | | | | | | | | | | | | (223) ~ (all_20_2 = e3)
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (11), (12), (13),
% 248.79/58.82 | | | | | | | | | | | | | | | | (14), (15), (16), (17), (20), (22), (23), (25),
% 248.79/58.82 | | | | | | | | | | | | | | | | (28), (31), (32), (33), (34), (35), (36), (37),
% 248.79/58.82 | | | | | | | | | | | | | | | | (38), (39), (40), (41), (42), (43), (45), (48),
% 248.79/58.82 | | | | | | | | | | | | | | | | (49), (51), (52), (57), (59), (60), (62), (63),
% 248.79/58.82 | | | | | | | | | | | | | | | | (64), (66), (69), (71), (74), (75), (76), (78),
% 248.79/58.82 | | | | | | | | | | | | | | | | (79), (80), (83), (84), (85), (88), (89), (90),
% 248.79/58.82 | | | | | | | | | | | | | | | | (91), (94), (96), (97), (99), (101), (108), (113),
% 248.79/58.82 | | | | | | | | | | | | | | | | (114), (116), (118), (121), (124), (126), (127),
% 248.79/58.82 | | | | | | | | | | | | | | | | (128), (129), (130), (133), (134), (137), (138),
% 248.79/58.82 | | | | | | | | | | | | | | | | (140), (143), (147), (148), (149), (153), (154),
% 248.79/58.82 | | | | | | | | | | | | | | | | (158), (160), (162), (164), (166), (168), (172),
% 248.79/58.82 | | | | | | | | | | | | | | | | (175), (178), (179), (180), (185), (186), (189),
% 248.79/58.82 | | | | | | | | | | | | | | | | (190), (191), (194), (195), (197), (198), (199),
% 248.79/58.82 | | | | | | | | | | | | | | | | (200), (201), (202), (204), (206), (208), (223)
% 248.79/58.82 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #92.
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | (224) all_58_2 = e3
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (34), (72), (91), (95), (132), (135), (145),
% 248.79/58.82 | | | | | | | | | | | | | | | | (159), (198), (224) are inconsistent by sub-proof
% 248.79/58.82 | | | | | | | | | | | | | | | | #122.
% 248.79/58.82 | | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | (225) all_56_2 = e0
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | COMBINE_EQS: (61), (225) imply:
% 248.79/58.82 | | | | | | | | | | | | | (226) all_8_2 = e0
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | REDUCE: (169), (226) imply:
% 248.79/58.82 | | | | | | | | | | | | | (227) op(e0, e2) = e3
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | | REF_CLOSE: (34), (62), (200), (227) are inconsistent by
% 248.79/58.82 | | | | | | | | | | | | | sub-proof #975.
% 248.79/58.82 | | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | (228) all_50_2 = e3
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | COMBINE_EQS: (73), (228) imply:
% 248.79/58.82 | | | | | | | | | | | | (229) all_4_2 = e3
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | REDUCE: (8), (229) imply:
% 248.79/58.82 | | | | | | | | | | | | (230) op(e3, e2) = e1
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | | REF_CLOSE: (34), (99), (160), (230) are inconsistent by
% 248.79/58.82 | | | | | | | | | | | | sub-proof #929.
% 248.79/58.82 | | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | (231) all_46_2 = e2
% 248.79/58.82 | | | | | | | | | | | (232) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 248.79/58.82 | | | | | | | | | | | & op(e1, e2) = all_46_1 & $i(all_46_0) &
% 248.79/58.82 | | | | | | | | | | | $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1, e2)
% 248.79/58.82 | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 248.79/58.82 | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | COMBINE_EQS: (182), (231) imply:
% 248.79/58.82 | | | | | | | | | | | (233) all_36_2 = e2
% 248.79/58.82 | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | | REF_CLOSE: (24), (29), (34), (40), (42), (48), (68), (76),
% 248.79/58.82 | | | | | | | | | | | (80), (92), (97), (99), (111), (141), (149),
% 248.79/58.82 | | | | | | | | | | | (160), (162), (165), (172), (201), (232), (233)
% 248.79/58.82 | | | | | | | | | | | are inconsistent by sub-proof #796.
% 248.79/58.82 | | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | (234) all_36_2 = e4
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | REDUCE: (162), (234) imply:
% 248.79/58.82 | | | | | | | | | | (235) op(e4, e1) = e3
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | REF_CLOSE: (34), (133), (199), (235) are inconsistent by
% 248.79/58.82 | | | | | | | | | | sub-proof #834.
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | (236) all_34_2 = e2
% 248.79/58.82 | | | | | | | | | (237) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.79/58.82 | | | | | | | | | op(e0, e2) = all_34_1 & $i(all_34_0) &
% 248.79/58.82 | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e3) & op(e0, e2) =
% 248.79/58.82 | | | | | | | | | all_34_1 & $i(all_34_1))
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (108), (236) imply:
% 248.79/58.82 | | | | | | | | | (238) ~ (all_40_2 = e2)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (161), (236) imply:
% 248.79/58.82 | | | | | | | | | (239) ~ (all_16_2 = e2)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (184), (236) imply:
% 248.79/58.82 | | | | | | | | | (240) ~ (all_4_2 = e2)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | SIMP: (240) implies:
% 248.79/58.82 | | | | | | | | | (241) ~ (all_4_2 = e2)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (74), (236) imply:
% 248.79/58.82 | | | | | | | | | (242) op(e2, e0) = e1
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | BETA: splitting (237) gives:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | (243) ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.79/58.82 | | | | | | | | | | op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | ALPHA: (243) implies:
% 248.79/58.82 | | | | | | | | | | (244) op(e0, e2) = all_34_1
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (13), (17), (19), (21), (25), (26),
% 248.79/58.82 | | | | | | | | | | (28), (29), (33), (34), (36), (37), (40), (42),
% 248.79/58.82 | | | | | | | | | | (43), (44), (52), (59), (60), (62), (66), (68),
% 248.79/58.82 | | | | | | | | | | (70), (73), (76), (78), (80), (84), (89), (91),
% 248.79/58.82 | | | | | | | | | | (96), (97), (99), (103), (104), (106), (107),
% 248.79/58.82 | | | | | | | | | | (109), (110), (112), (113), (118), (124), (126),
% 248.79/58.82 | | | | | | | | | | (129), (133), (136), (139), (141), (143), (146),
% 248.79/58.82 | | | | | | | | | | (149), (152), (153), (155), (157), (160), (162),
% 248.79/58.82 | | | | | | | | | | (163), (165), (168), (172), (176), (177), (178),
% 248.79/58.82 | | | | | | | | | | (182), (185), (186), (187), (191), (195), (197),
% 248.79/58.82 | | | | | | | | | | (198), (199), (238), (241), (242), (244) are
% 248.79/58.82 | | | | | | | | | | inconsistent by sub-proof #86.
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | (245) ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 &
% 248.79/58.82 | | | | | | | | | | $i(all_34_1)
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | ALPHA: (245) implies:
% 248.79/58.82 | | | | | | | | | | (246) op(e0, e2) = all_34_1
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (13), (17), (19), (21), (25), (26),
% 248.79/58.82 | | | | | | | | | | (28), (29), (33), (34), (36), (37), (40), (42),
% 248.79/58.82 | | | | | | | | | | (43), (44), (52), (59), (60), (62), (66), (68),
% 248.79/58.82 | | | | | | | | | | (70), (73), (76), (78), (80), (84), (89), (91),
% 248.79/58.82 | | | | | | | | | | (96), (97), (99), (103), (104), (106), (107),
% 248.79/58.82 | | | | | | | | | | (109), (110), (112), (113), (118), (124), (126),
% 248.79/58.82 | | | | | | | | | | (129), (133), (136), (139), (141), (143), (146),
% 248.79/58.82 | | | | | | | | | | (149), (152), (153), (155), (157), (160), (162),
% 248.79/58.82 | | | | | | | | | | (163), (165), (168), (172), (176), (177), (178),
% 248.79/58.82 | | | | | | | | | | (182), (185), (186), (187), (191), (195), (197),
% 248.79/58.82 | | | | | | | | | | (198), (199), (238), (241), (242), (246) are
% 248.79/58.82 | | | | | | | | | | inconsistent by sub-proof #86.
% 248.79/58.82 | | | | | | | | | |
% 248.79/58.82 | | | | | | | | | End of split
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | End of split
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | (247) all_28_2 = e3
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | REF_CLOSE: (22), (34), (72), (91), (95), (125), (135), (145),
% 248.79/58.82 | | | | | | | | (198), (247) are inconsistent by sub-proof #115.
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | End of split
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | Case 2:
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | (248) all_26_2 = e3
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | REDUCE: (82), (248) imply:
% 248.79/58.82 | | | | | | | (249) ~ (all_244_0 = e3)
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | REDUCE: (58), (248) imply:
% 248.79/58.82 | | | | | | | (250) op(e3, e1) = e4
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | BETA: splitting (164) gives:
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | (251) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 &
% 248.79/58.82 | | | | | | | | op(e3, e4) = e3)
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | BETA: splitting (251) gives:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | (252) all_252_0 = e3 & op(e4, e4) = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | ALPHA: (252) implies:
% 248.79/58.82 | | | | | | | | | (253) op(e4, e4) = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REF_CLOSE: (34), (138), (249), (253) are inconsistent by
% 248.79/58.82 | | | | | | | | | sub-proof #813.
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | (254) all_252_2 = e3 & op(e3, e4) = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | ALPHA: (254) implies:
% 248.79/58.82 | | | | | | | | | (255) op(e3, e4) = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | GROUND_INST: instantiating (34) with all_36_2, e4, e1, e3,
% 248.79/58.82 | | | | | | | | | simplifying with (96), (250) gives:
% 248.79/58.82 | | | | | | | | | (256) all_36_2 = e4
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | GROUND_INST: instantiating (34) with all_100_2, e3, e4, e3,
% 248.79/58.82 | | | | | | | | | simplifying with (137), (255) gives:
% 248.79/58.82 | | | | | | | | | (257) all_100_2 = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (93), (256) imply:
% 248.79/58.82 | | | | | | | | | (258) ~ (all_8_2 = e4)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | SIMP: (258) implies:
% 248.79/58.82 | | | | | | | | | (259) ~ (all_8_2 = e4)
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (81), (257) imply:
% 248.79/58.82 | | | | | | | | | (260) op(e3, e2) = e4
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REF_CLOSE: (34), (160), (259), (260) are inconsistent by
% 248.79/58.82 | | | | | | | | | sub-proof #502.
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | End of split
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | (261) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 248.79/58.82 | | | | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) =
% 248.79/58.82 | | | | | | | | e3)
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | REF_CLOSE: (34), (35), (76), (83), (129), (194), (197), (261)
% 248.79/58.82 | | | | | | | | are inconsistent by sub-proof #189.
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | End of split
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | End of split
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | Case 2:
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | (262) all_22_2 = e1
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | REDUCE: (47), (262) imply:
% 248.79/58.82 | | | | | | (263) ~ (all_244_3 = e1)
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | REDUCE: (159), (262) imply:
% 248.79/58.82 | | | | | | (264) ~ (all_20_2 = e1)
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | SIMP: (264) implies:
% 248.79/58.82 | | | | | | (265) ~ (all_20_2 = e1)
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | REDUCE: (91), (262) imply:
% 248.79/58.82 | | | | | | (266) ~ (e4 = e1)
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | REDUCE: (22), (262) imply:
% 248.79/58.82 | | | | | | (267) ~ (e2 = e1)
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | REDUCE: (122), (262) imply:
% 248.79/58.82 | | | | | | (268) op(e1, e3) = e0
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | BETA: splitting (178) gives:
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | | Case 1:
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | (269) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 &
% 248.79/58.82 | | | | | | | op(e3, e3) = e1)
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | REF_CLOSE: (34), (57), (89), (174), (263), (269) are inconsistent
% 248.79/58.82 | | | | | | | by sub-proof #120.
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | Case 2:
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | (270) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 &
% 248.79/58.82 | | | | | | | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | BETA: splitting (270) gives:
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | (271) all_252_7 = e1 & op(e2, e3) = e1
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | ALPHA: (271) implies:
% 248.79/58.82 | | | | | | | | (272) all_252_7 = e1
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | COMBINE_EQS: (59), (272) imply:
% 248.79/58.82 | | | | | | | | (273) e4 = e1
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | SIMP: (273) implies:
% 248.79/58.82 | | | | | | | | (274) e4 = e1
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | REDUCE: (63), (274) imply:
% 248.79/58.82 | | | | | | | | (275) $false
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | CLOSE: (275) is inconsistent.
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | (276) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1
% 248.79/58.82 | | | | | | | | & op(e0, e3) = e1)
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | BETA: splitting (276) gives:
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | | Case 1:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | (277) all_252_13 = e1 & op(e1, e3) = e1
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | ALPHA: (277) implies:
% 248.79/58.82 | | | | | | | | | (278) op(e1, e3) = e1
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REF_CLOSE: (31), (34), (80), (268), (278) are inconsistent by
% 248.79/58.82 | | | | | | | | | sub-proof #94.
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | Case 2:
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | GROUND_INST: instantiating (34) with all_62_2, e0, e3, e1,
% 248.79/58.82 | | | | | | | | | simplifying with (80), (268) gives:
% 248.79/58.82 | | | | | | | | | (279) all_62_2 = e0
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REDUCE: (24), (279) imply:
% 248.79/58.82 | | | | | | | | | (280) op(e0, all_36_2) = e3
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | | REF_CLOSE: (2), (8), (10), (17), (34), (36), (48), (73), (74),
% 248.79/58.82 | | | | | | | | | (76), (83), (86), (87), (96), (99), (127), (132),
% 248.79/58.82 | | | | | | | | | (141), (144), (149), (160), (186), (187), (189),
% 248.79/58.82 | | | | | | | | | (195), (197), (265), (268), (280) are inconsistent
% 248.79/58.82 | | | | | | | | | by sub-proof #591.
% 248.79/58.82 | | | | | | | | |
% 248.79/58.82 | | | | | | | | End of split
% 248.79/58.82 | | | | | | | |
% 248.79/58.82 | | | | | | | End of split
% 248.79/58.82 | | | | | | |
% 248.79/58.82 | | | | | | End of split
% 248.79/58.82 | | | | | |
% 248.79/58.82 | | | | | End of split
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | Case 2:
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | (281) all_24_2 = e3
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | COMBINE_EQS: (171), (281) imply:
% 248.79/58.82 | | | | | (282) all_16_2 = e3
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (167), (282) imply:
% 248.79/58.82 | | | | | (283) op(e3, e4) = e1
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | GROUND_INST: instantiating (34) with all_100_2, e1, e4, e3,
% 248.79/58.82 | | | | | simplifying with (137), (283) gives:
% 248.79/58.82 | | | | | (284) all_100_2 = e1
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (81), (284) imply:
% 248.79/58.82 | | | | | (285) op(e1, e2) = e4
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REF_CLOSE: (6), (34), (149), (285) are inconsistent by sub-proof #831.
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | End of split
% 248.79/58.82 | | | |
% 248.79/58.82 | | | Case 2:
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | (286) all_20_2 = e4
% 248.79/58.82 | | | | (287) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4)
% 248.79/58.82 | | | | = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 248.79/58.82 | | | | e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | REDUCE: (79), (286) imply:
% 248.79/58.82 | | | | (288) ~ (all_28_2 = e4)
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | REDUCE: (123), (286) imply:
% 248.79/58.82 | | | | (289) op(e4, all_34_2) = e1
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | REDUCE: (87), (286) imply:
% 248.79/58.82 | | | | (290) op(e4, e1) = e0
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | BETA: splitting (287) gives:
% 248.79/58.82 | | | |
% 248.79/58.82 | | | | Case 1:
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | (291) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4)
% 248.79/58.82 | | | | | = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | ALPHA: (291) implies:
% 248.79/58.82 | | | | | (292) op(e1, e4) = all_20_1
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | GROUND_INST: instantiating (34) with all_16_2, all_20_1, e4, e1,
% 248.79/58.82 | | | | | simplifying with (76), (292) gives:
% 248.79/58.82 | | | | | (293) all_20_1 = all_16_2
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | GROUND_INST: instantiating (34) with all_26_2, e0, e1, e4, simplifying
% 248.79/58.82 | | | | | with (133), (290) gives:
% 248.79/58.82 | | | | | (294) all_26_2 = e0
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (120), (294) imply:
% 248.79/58.82 | | | | | (295) ~ (all_6_2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | SIMP: (295) implies:
% 248.79/58.82 | | | | | (296) ~ (all_6_2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (4), (294) imply:
% 248.79/58.82 | | | | | (297) ~ (e2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REF_CLOSE: (1), (20), (27), (28), (30), (31), (33), (34), (40), (43),
% 248.79/58.82 | | | | | (46), (48), (53), (54), (55), (61), (62), (66), (69), (70),
% 248.79/58.82 | | | | | (77), (80), (90), (97), (98), (100), (102), (105), (115),
% 248.79/58.82 | | | | | (119), (121), (141), (147), (149), (150), (156), (157),
% 248.79/58.82 | | | | | (160), (169), (170), (172), (173), (181), (188), (191),
% 248.79/58.82 | | | | | (288), (289), (292), (293), (296) are inconsistent by
% 248.79/58.82 | | | | | sub-proof #84.
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | Case 2:
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | (298) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | ALPHA: (298) implies:
% 248.79/58.82 | | | | | (299) ~ (all_20_1 = e2)
% 248.79/58.82 | | | | | (300) op(e1, e4) = all_20_1
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | GROUND_INST: instantiating (34) with all_16_2, all_20_1, e4, e1,
% 248.79/58.82 | | | | | simplifying with (76), (300) gives:
% 248.79/58.82 | | | | | (301) all_20_1 = all_16_2
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | GROUND_INST: instantiating (34) with all_26_2, e0, e1, e4, simplifying
% 248.79/58.82 | | | | | with (133), (290) gives:
% 248.79/58.82 | | | | | (302) all_26_2 = e0
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (120), (302) imply:
% 248.79/58.82 | | | | | (303) ~ (all_6_2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | SIMP: (303) implies:
% 248.79/58.82 | | | | | (304) ~ (all_6_2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REDUCE: (4), (302) imply:
% 248.79/58.82 | | | | | (305) ~ (e2 = e0)
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | | REF_CLOSE: (1), (20), (27), (28), (30), (31), (33), (34), (40), (43),
% 248.79/58.82 | | | | | (46), (48), (53), (54), (55), (61), (62), (66), (69), (70),
% 248.79/58.82 | | | | | (77), (80), (90), (97), (98), (100), (102), (105), (115),
% 248.79/58.82 | | | | | (119), (121), (141), (147), (149), (150), (156), (157),
% 248.79/58.82 | | | | | (160), (169), (170), (172), (173), (181), (188), (191),
% 248.79/58.82 | | | | | (288), (289), (300), (301), (304) are inconsistent by
% 248.79/58.82 | | | | | sub-proof #84.
% 248.79/58.82 | | | | |
% 248.79/58.82 | | | | End of split
% 248.79/58.82 | | | |
% 248.79/58.82 | | | End of split
% 248.79/58.82 | | |
% 248.79/58.82 | | Case 2:
% 248.79/58.82 | | |
% 248.79/58.82 | | | (306) all_252_7 = e0 & op(e2, e3) = e0
% 248.79/58.82 | | |
% 248.79/58.82 | | | REF_CLOSE: (37), (59), (306) are inconsistent by sub-proof #125.
% 248.79/58.82 | | |
% 248.79/58.82 | | End of split
% 248.79/58.82 | |
% 248.79/58.82 | Case 2:
% 248.79/58.82 | |
% 248.79/58.82 | | (307) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1)
% 248.79/58.82 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 248.79/58.82 | |
% 248.79/58.82 | | REF_CLOSE: (14), (34), (40), (42), (84), (126), (168), (307) are
% 248.79/58.82 | | inconsistent by sub-proof #879.
% 248.79/58.82 | |
% 248.79/58.82 | End of split
% 248.79/58.82 |
% 248.79/58.82 End of proof
% 248.79/58.82
% 248.79/58.82 Sub-proof #84 shows that the following formulas are inconsistent:
% 248.79/58.82 ----------------------------------------------------------------
% 248.79/58.82 (1) ~ (all_244_8 = all_4_2)
% 248.79/58.82 (2) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 248.79/58.82 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 248.79/58.82 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 248.79/58.82 (3) ~ (all_28_2 = all_6_2)
% 248.79/58.82 (4) ~ (e2 = e0)
% 248.79/58.82 (5) op(all_64_2, e4) = e2
% 248.79/58.82 (6) ~ (e1 = e0)
% 248.79/58.82 (7) op(e4, all_34_2) = e1
% 248.79/58.82 (8) ~ (all_62_2 = e2)
% 248.79/58.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.82 (10) op(e2, e2) = all_244_8
% 248.79/58.82 (11) all_20_1 = all_16_2
% 248.79/58.82 (12) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.82 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.82 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.83 (13) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 248.79/58.83 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 248.79/58.83 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 248.79/58.83 (14) op(e1, e0) = all_34_2
% 248.79/58.83 (15) op(all_28_2, e2) = e0
% 248.79/58.83 (16) op(e4, e2) = all_6_2
% 248.79/58.83 (17) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 248.79/58.83 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 248.79/58.83 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 248.79/58.83 (18) ~ (all_8_2 = all_4_2)
% 248.79/58.83 (19) all_56_2 = all_8_2
% 248.79/58.83 (20) op(e0, e2) = all_28_2
% 248.79/58.83 (21) ~ (all_6_2 = e1)
% 248.79/58.83 (22) op(e1, e4) = all_20_1
% 248.79/58.83 (23) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 248.79/58.83 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 248.79/58.83 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 248.79/58.83 (24) op(all_244_15, all_244_15) = e1
% 248.79/58.83 (25) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 248.79/58.83 all_250_2 = e0
% 248.79/58.83 (26) op(e1, e3) = all_62_2
% 248.79/58.83 (27) ~ (all_6_2 = e2)
% 248.79/58.83 (28) ~ (all_16_2 = e2)
% 248.79/58.83 (29) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 248.79/58.83 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 248.79/58.83 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 248.79/58.83 (30) op(all_40_2, e0) = e2
% 248.79/58.83 (31) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 248.79/58.83 all_250_22 = e0
% 248.79/58.83 (32) ~ (all_28_2 = all_4_2)
% 248.79/58.83 (33) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 248.79/58.83 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 248.79/58.83 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 248.79/58.83 (34) all_182_2 = e2
% 248.79/58.83 (35) ~ (all_28_2 = e4)
% 248.79/58.83 (36) ~ (all_28_2 = e2)
% 248.79/58.83 (37) op(e1, e1) = all_244_15
% 248.79/58.83 (38) all_82_2 = all_28_2
% 248.79/58.83 (39) op(e1, e2) = all_4_2
% 248.79/58.83 (40) ~ (all_28_2 = all_8_2)
% 248.79/58.83 (41) ~ (all_6_2 = all_4_2)
% 248.79/58.83 (42) op(all_40_2, all_28_2) = e0
% 248.79/58.83 (43) ~ (all_6_2 = e0)
% 248.79/58.83 (44) op(e3, e2) = all_8_2
% 248.79/58.83 (45) op(all_8_2, e2) = e3
% 248.79/58.83 (46) ~ (all_244_8 = all_28_2)
% 248.79/58.83 (47) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.83 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.83 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.83 (48) all_250_22 = all_28_2
% 248.79/58.83 (49) all_250_2 = all_6_2
% 248.79/58.83 (50) op(all_64_2, all_6_2) = e4
% 248.79/58.83
% 248.79/58.83 Begin of proof
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (11), (22) imply:
% 248.79/58.83 | (51) op(e1, e4) = all_16_2
% 248.79/58.83 |
% 248.79/58.83 | BETA: splitting (33) gives:
% 248.79/58.83 |
% 248.79/58.83 | Case 1:
% 248.79/58.83 | |
% 248.79/58.83 | | (52) ~ (all_28_2 = e3)
% 248.79/58.83 | |
% 248.79/58.83 | | BETA: splitting (17) gives:
% 248.79/58.83 | |
% 248.79/58.83 | | Case 1:
% 248.79/58.83 | | |
% 248.79/58.83 | | | (53) ~ (all_34_2 = e2)
% 248.79/58.83 | | |
% 248.79/58.83 | | | BETA: splitting (13) gives:
% 248.79/58.83 | | |
% 248.79/58.83 | | | Case 1:
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | (54) ~ (all_56_2 = e0)
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | REDUCE: (19), (54) imply:
% 248.79/58.83 | | | | (55) ~ (all_8_2 = e0)
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | BETA: splitting (29) gives:
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | Case 1:
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | (56) ~ (all_182_2 = e2)
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | REDUCE: (34), (56) imply:
% 248.79/58.83 | | | | | (57) $false
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | CLOSE: (57) is inconsistent.
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | Case 2:
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | (58) ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 & op(e2,
% 248.79/58.83 | | | | | all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) |
% 248.79/58.83 | | | | | ( ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | BETA: splitting (58) gives:
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | | Case 1:
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | (59) ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 & op(e2,
% 248.79/58.83 | | | | | | all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | ALPHA: (59) implies:
% 248.79/58.83 | | | | | | (60) op(e3, e2) = all_182_1
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (14),
% 248.79/58.83 | | | | | | (15), (16), (18), (20), (23), (24), (26), (28), (30),
% 248.79/58.83 | | | | | | (31), (32), (35), (36), (37), (38), (39), (40), (41),
% 248.79/58.83 | | | | | | (42), (43), (44), (46), (47), (48), (51), (52), (53),
% 248.79/58.83 | | | | | | (55), (60) are inconsistent by sub-proof #85.
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | Case 2:
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | (61) ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1)
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | ALPHA: (61) implies:
% 248.79/58.83 | | | | | | (62) op(e3, e2) = all_182_1
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (14),
% 248.79/58.83 | | | | | | (15), (16), (18), (20), (23), (24), (26), (28), (30),
% 248.79/58.83 | | | | | | (31), (32), (35), (36), (37), (38), (39), (40), (41),
% 248.79/58.83 | | | | | | (42), (43), (44), (46), (47), (48), (51), (52), (53),
% 248.79/58.83 | | | | | | (55), (62) are inconsistent by sub-proof #85.
% 248.79/58.83 | | | | | |
% 248.79/58.83 | | | | | End of split
% 248.79/58.83 | | | | |
% 248.79/58.83 | | | | End of split
% 248.79/58.83 | | | |
% 248.79/58.83 | | | Case 2:
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | (63) all_56_2 = e0
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | COMBINE_EQS: (19), (63) imply:
% 248.79/58.83 | | | | (64) all_8_2 = e0
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | REDUCE: (45), (64) imply:
% 248.79/58.83 | | | | (65) op(e0, e2) = e3
% 248.79/58.83 | | | |
% 248.79/58.83 | | | | REF_CLOSE: (9), (20), (52), (65) are inconsistent by sub-proof #975.
% 248.79/58.83 | | | |
% 248.79/58.83 | | | End of split
% 248.79/58.83 | | |
% 248.79/58.83 | | Case 2:
% 248.79/58.83 | | |
% 248.79/58.83 | | | (66) all_34_2 = e2
% 248.79/58.83 | | |
% 248.79/58.83 | | | REDUCE: (7), (66) imply:
% 248.79/58.83 | | | (67) op(e4, e2) = e1
% 248.79/58.83 | | |
% 248.79/58.83 | | | REF_CLOSE: (9), (16), (21), (67) are inconsistent by sub-proof #930.
% 248.79/58.83 | | |
% 248.79/58.83 | | End of split
% 248.79/58.83 | |
% 248.79/58.83 | Case 2:
% 248.79/58.83 | |
% 248.79/58.83 | | (68) all_28_2 = e3
% 248.79/58.83 | |
% 248.79/58.83 | | REF_CLOSE: (3), (5), (9), (21), (25), (27), (43), (49), (50), (68) are
% 248.79/58.83 | | inconsistent by sub-proof #108.
% 248.79/58.83 | |
% 248.79/58.83 | End of split
% 248.79/58.83 |
% 248.79/58.83 End of proof
% 248.79/58.83
% 248.79/58.83 Sub-proof #85 shows that the following formulas are inconsistent:
% 248.79/58.83 ----------------------------------------------------------------
% 248.79/58.83 (1) ~ (all_244_8 = all_4_2)
% 248.79/58.83 (2) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 248.79/58.83 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 248.79/58.83 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 248.79/58.83 (3) ~ (all_28_2 = all_6_2)
% 248.79/58.83 (4) ~ (e2 = e0)
% 248.79/58.83 (5) ~ (e1 = e0)
% 248.79/58.83 (6) ~ (all_28_2 = e3)
% 248.79/58.83 (7) ~ (all_62_2 = e2)
% 248.79/58.83 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.83 (9) op(e2, e2) = all_244_8
% 248.79/58.83 (10) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.83 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.83 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.83 (11) op(e1, e0) = all_34_2
% 248.79/58.83 (12) op(all_28_2, e2) = e0
% 248.79/58.83 (13) op(e4, e2) = all_6_2
% 248.79/58.83 (14) ~ (all_8_2 = all_4_2)
% 248.79/58.83 (15) ~ (all_34_2 = e2)
% 248.79/58.83 (16) op(e0, e2) = all_28_2
% 248.79/58.83 (17) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 248.79/58.83 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 248.79/58.83 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 248.79/58.83 (18) op(all_244_15, all_244_15) = e1
% 248.79/58.83 (19) op(e1, e4) = all_16_2
% 248.79/58.83 (20) op(e1, e3) = all_62_2
% 248.79/58.83 (21) ~ (all_16_2 = e2)
% 248.79/58.83 (22) op(all_40_2, e0) = e2
% 248.79/58.83 (23) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 248.79/58.83 all_250_22 = e0
% 248.79/58.83 (24) ~ (all_28_2 = all_4_2)
% 248.79/58.83 (25) ~ (all_8_2 = e0)
% 248.79/58.83 (26) ~ (all_28_2 = e4)
% 248.79/58.83 (27) ~ (all_28_2 = e2)
% 248.79/58.83 (28) op(e3, e2) = all_182_1
% 248.79/58.83 (29) op(e1, e1) = all_244_15
% 248.79/58.83 (30) all_82_2 = all_28_2
% 248.79/58.83 (31) op(e1, e2) = all_4_2
% 248.79/58.83 (32) ~ (all_28_2 = all_8_2)
% 248.79/58.83 (33) ~ (all_6_2 = all_4_2)
% 248.79/58.83 (34) op(all_40_2, all_28_2) = e0
% 248.79/58.83 (35) ~ (all_6_2 = e0)
% 248.79/58.83 (36) op(e3, e2) = all_8_2
% 248.79/58.83 (37) ~ (all_244_8 = all_28_2)
% 248.79/58.83 (38) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.83 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.83 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.83 (39) all_250_22 = all_28_2
% 248.79/58.83
% 248.79/58.83 Begin of proof
% 248.79/58.83 |
% 248.79/58.83 | GROUND_INST: instantiating (8) with all_8_2, all_182_1, e2, e3, simplifying
% 248.79/58.83 | with (28), (36) gives:
% 248.79/58.83 | (40) all_182_1 = all_8_2
% 248.79/58.83 |
% 248.79/58.83 | BETA: splitting (2) gives:
% 248.79/58.83 |
% 248.79/58.83 | Case 1:
% 248.79/58.83 | |
% 248.79/58.83 | | (41) ~ (all_82_2 = e1)
% 248.79/58.83 | |
% 248.79/58.83 | | REDUCE: (30), (41) imply:
% 248.79/58.83 | | (42) ~ (all_28_2 = e1)
% 248.79/58.83 | |
% 248.79/58.83 | | REF_CLOSE: (6), (8), (22), (23), (26), (27), (34), (39), (42) are
% 248.79/58.83 | | inconsistent by sub-proof #583.
% 248.79/58.83 | |
% 248.79/58.83 | Case 2:
% 248.79/58.83 | |
% 248.79/58.83 | | (43) all_82_2 = e1
% 248.79/58.83 | |
% 248.79/58.83 | | COMBINE_EQS: (30), (43) imply:
% 248.79/58.83 | | (44) all_28_2 = e1
% 248.79/58.83 | |
% 248.79/58.83 | | SIMP: (44) implies:
% 248.79/58.83 | | (45) all_28_2 = e1
% 248.79/58.83 | |
% 248.79/58.83 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 248.79/58.83 | | (15), (16), (17), (18), (19), (20), (21), (24), (25), (29), (31),
% 248.79/58.83 | | (32), (33), (35), (36), (37), (38), (45) are inconsistent by
% 248.79/58.83 | | sub-proof #867.
% 248.79/58.83 | |
% 248.79/58.83 | End of split
% 248.79/58.83 |
% 248.79/58.83 End of proof
% 248.79/58.83
% 248.79/58.83 Sub-proof #86 shows that the following formulas are inconsistent:
% 248.79/58.83 ----------------------------------------------------------------
% 248.79/58.83 (1) ~ (all_26_2 = e2)
% 248.79/58.83 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.83 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.83 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.83 (3) op(all_4_2, e2) = e1
% 248.79/58.83 (4) ~ (all_40_2 = all_38_2)
% 248.79/58.83 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.83 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.83 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.83 (6) all_174_2 = all_40_2
% 248.79/58.83 (7) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.79/58.83 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.79/58.83 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.79/58.83 (8) op(all_38_2, e1) = e2
% 248.79/58.83 (9) all_250_13 = all_38_2
% 248.79/58.83 (10) ~ (e2 = e0)
% 248.79/58.83 (11) op(all_38_2, all_4_2) = e1
% 248.79/58.83 (12) ~ (all_62_2 = e2)
% 248.79/58.83 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.83 (14) op(e0, e0) = all_244_24
% 248.79/58.83 (15) ~ (e4 = e0)
% 248.79/58.83 (16) op(e2, e2) = all_244_8
% 248.79/58.83 (17) op(e2, e1) = all_38_2
% 248.79/58.83 (18) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.83 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.83 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.83 (19) ~ (all_36_2 = all_20_2)
% 248.79/58.83 (20) ~ (all_40_2 = e4)
% 248.79/58.83 (21) op(e4, e2) = all_6_2
% 248.79/58.83 (22) op(e2, e0) = e1
% 248.79/58.83 (23) all_252_7 = e4
% 248.79/58.83 (24) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.83 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.83 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.83 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.83 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.83 op(e0, e1) = e0)))
% 248.79/58.83 (25) op(e0, e2) = all_28_2
% 248.79/58.83 (26) ~ (all_6_2 = e1)
% 248.79/58.83 (27) ~ (all_244_8 = all_38_2)
% 248.79/58.83 (28) op(all_244_15, all_244_15) = e1
% 248.79/58.83 (29) all_50_2 = all_4_2
% 248.79/58.83 (30) op(e1, e4) = all_16_2
% 248.79/58.83 (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.83 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.83 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.83 (32) op(e1, e3) = all_62_2
% 248.79/58.83 (33) ~ (all_38_2 = e0)
% 248.79/58.83 (34) all_252_1 = e2
% 248.79/58.83 (35) ~ (all_22_2 = e4)
% 248.79/58.83 (36) op(e3, e1) = all_36_2
% 248.79/58.83 (37) ~ (all_16_2 = e2)
% 248.79/58.83 (38) ~ (all_8_2 = e1)
% 248.79/58.83 (39) ~ (all_22_2 = e1)
% 248.79/58.83 (40) ~ (all_244_8 = all_40_2)
% 248.79/58.83 (41) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 248.79/58.83 all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) |
% 248.79/58.83 ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.83 (42) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.83 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.83 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.83 (43) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.79/58.83 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.79/58.83 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.83 (44) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.79/58.83 all_250_13 = e0
% 248.79/58.83 (45) ~ (all_244_15 = all_38_2)
% 248.79/58.83 (46) ~ (all_36_2 = all_26_2)
% 248.79/58.83 (47) op(e4, e3) = e2
% 248.79/58.83 (48) ~ (all_38_2 = e4)
% 248.79/58.83 (49) op(e0, e2) = all_34_1
% 248.79/58.83 (50) op(e0, e3) = all_22_2
% 248.79/58.83 (51) ~ (all_40_2 = e0)
% 248.79/58.83 (52) all_252_20 = e2
% 248.79/58.83 (53) op(e4, e1) = all_26_2
% 248.79/58.83 (54) ~ (all_40_2 = e2)
% 248.79/58.83 (55) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 248.79/58.83 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.83 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 248.79/58.83 (56) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.83 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.83 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.83 (57) op(e1, e1) = all_244_15
% 248.79/58.83 (58) op(e0, e1) = all_20_2
% 248.79/58.83 (59) ~ (all_38_2 = all_36_2)
% 248.79/58.83 (60) ~ (all_26_2 = e3)
% 248.79/58.83 (61) op(e1, e2) = all_4_2
% 248.79/58.83 (62) op(all_4_2, all_38_2) = e2
% 248.79/58.83 (63) op(e4, e3) = all_84_2
% 248.79/58.83 (64) all_116_2 = all_40_2
% 248.79/58.83 (65) op(all_40_2, all_28_2) = e0
% 248.79/58.83 (66) op(e3, e2) = all_8_2
% 248.79/58.83 (67) op(all_36_2, e1) = e3
% 248.79/58.83 (68) ~ (all_38_2 = all_20_2)
% 248.79/58.83 (69) ~ (all_244_15 = all_36_2)
% 248.79/58.83 (70) ~ (all_20_2 = e4)
% 248.79/58.83 (71) op(e2, e0) = all_40_2
% 248.79/58.83 (72) ~ (all_16_2 = e3)
% 248.79/58.83 (73) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.83 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.83 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.83 (74) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 248.79/58.83 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 248.79/58.83 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.79/58.83 (75) all_188_2 = all_38_2
% 248.79/58.83 (76) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.83 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.83 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.83 (77) all_46_2 = all_36_2
% 248.79/58.83 (78) ~ (all_4_2 = e2)
% 248.79/58.83 (79) ~ (all_16_2 = e0)
% 248.79/58.83 (80) ~ (all_20_2 = e2)
% 248.79/58.83 (81) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 248.79/58.83 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 248.79/58.83 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.83
% 248.79/58.83 Begin of proof
% 248.79/58.83 |
% 248.79/58.83 | GROUND_INST: instantiating (13) with all_28_2, all_34_1, e2, e0, simplifying
% 248.79/58.83 | with (25), (49) gives:
% 248.79/58.83 | (82) all_34_1 = all_28_2
% 248.79/58.83 |
% 248.79/58.83 | GROUND_INST: instantiating (13) with all_40_2, e1, e0, e2, simplifying with
% 248.79/58.83 | (22), (71) gives:
% 248.79/58.83 | (83) all_40_2 = e1
% 248.79/58.83 |
% 248.79/58.83 | COMBINE_EQS: (64), (83) imply:
% 248.79/58.83 | (84) all_116_2 = e1
% 248.79/58.83 |
% 248.79/58.83 | COMBINE_EQS: (6), (83) imply:
% 248.79/58.83 | (85) all_174_2 = e1
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (40), (83) imply:
% 248.79/58.83 | (86) ~ (all_244_8 = e1)
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (4), (83) imply:
% 248.79/58.83 | (87) ~ (all_38_2 = e1)
% 248.79/58.83 |
% 248.79/58.83 | SIMP: (87) implies:
% 248.79/58.83 | (88) ~ (all_38_2 = e1)
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (20), (83) imply:
% 248.79/58.83 | (89) ~ (e4 = e1)
% 248.79/58.83 |
% 248.79/58.83 | SIMP: (89) implies:
% 248.79/58.83 | (90) ~ (e4 = e1)
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (54), (83) imply:
% 248.79/58.83 | (91) ~ (e2 = e1)
% 248.79/58.83 |
% 248.79/58.83 | SIMP: (91) implies:
% 248.79/58.83 | (92) ~ (e2 = e1)
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (51), (83) imply:
% 248.79/58.83 | (93) ~ (e1 = e0)
% 248.79/58.83 |
% 248.79/58.83 | REDUCE: (65), (83) imply:
% 248.79/58.83 | (94) op(e1, all_28_2) = e0
% 248.79/58.83 |
% 248.79/58.83 | BETA: splitting (74) gives:
% 248.79/58.83 |
% 248.79/58.83 | Case 1:
% 248.79/58.83 | |
% 248.79/58.83 | | (95) ~ (all_174_2 = e1)
% 248.79/58.83 | |
% 248.79/58.83 | | REDUCE: (85), (95) imply:
% 248.79/58.83 | | (96) $false
% 248.79/58.83 | |
% 248.79/58.83 | | CLOSE: (96) is inconsistent.
% 248.79/58.83 | |
% 248.79/58.83 | Case 2:
% 248.79/58.83 | |
% 248.79/58.83 | | (97) ( ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0, e1) =
% 248.79/58.83 | | all_174_1 & $i(all_174_0) & $i(all_174_1)) | ( ~ (all_174_1 = e4)
% 248.79/58.83 | | & op(e0, e1) = all_174_1 & $i(all_174_1))
% 248.79/58.83 | |
% 248.79/58.83 | | BETA: splitting (97) gives:
% 248.79/58.83 | |
% 248.79/58.83 | | Case 1:
% 248.79/58.83 | | |
% 248.79/58.83 | | | (98) ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0, e1) =
% 248.79/58.83 | | | all_174_1 & $i(all_174_0) & $i(all_174_1)
% 248.79/58.83 | | |
% 248.79/58.83 | | | ALPHA: (98) implies:
% 248.79/58.83 | | | (99) op(e0, e1) = all_174_1
% 248.79/58.83 | | |
% 248.79/58.83 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 248.79/58.83 | | | (14), (15), (16), (17), (18), (19), (21), (23), (24), (25),
% 248.79/58.83 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 248.79/58.83 | | | (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 248.79/58.83 | | | (47), (48), (50), (52), (53), (55), (56), (57), (58), (59),
% 248.79/58.83 | | | (60), (61), (62), (63), (66), (67), (68), (69), (70), (72),
% 248.79/58.83 | | | (73), (75), (76), (77), (78), (79), (80), (81), (84), (86),
% 248.79/58.83 | | | (88), (90), (92), (93), (94), (99) are inconsistent by
% 248.79/58.83 | | | sub-proof #87.
% 248.79/58.83 | | |
% 248.79/58.83 | | Case 2:
% 248.79/58.83 | | |
% 248.79/58.83 | | | (100) ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1)
% 248.79/58.83 | | |
% 248.79/58.83 | | | ALPHA: (100) implies:
% 248.79/58.83 | | | (101) op(e0, e1) = all_174_1
% 248.79/58.83 | | |
% 248.79/58.84 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 248.79/58.84 | | | (14), (15), (16), (17), (18), (19), (21), (23), (24), (25),
% 248.79/58.84 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 248.79/58.84 | | | (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 248.79/58.84 | | | (47), (48), (50), (52), (53), (55), (56), (57), (58), (59),
% 248.79/58.84 | | | (60), (61), (62), (63), (66), (67), (68), (69), (70), (72),
% 248.79/58.84 | | | (73), (75), (76), (77), (78), (79), (80), (81), (84), (86),
% 248.79/58.84 | | | (88), (90), (92), (93), (94), (101) are inconsistent by
% 248.79/58.84 | | | sub-proof #87.
% 248.79/58.84 | | |
% 248.79/58.84 | | End of split
% 248.79/58.84 | |
% 248.79/58.84 | End of split
% 248.79/58.84 |
% 248.79/58.84 End of proof
% 248.79/58.84
% 248.79/58.84 Sub-proof #87 shows that the following formulas are inconsistent:
% 248.79/58.84 ----------------------------------------------------------------
% 248.79/58.84 (1) ~ (all_26_2 = e2)
% 248.79/58.84 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.84 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.84 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.84 (3) op(all_4_2, e2) = e1
% 248.79/58.84 (4) ~ (all_38_2 = e1)
% 248.79/58.84 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.84 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.84 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.84 (6) all_116_2 = e1
% 248.79/58.84 (7) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 248.79/58.84 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 248.79/58.84 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 248.79/58.84 (8) op(all_38_2, e1) = e2
% 248.79/58.84 (9) all_250_13 = all_38_2
% 248.79/58.84 (10) op(e0, e1) = all_174_1
% 248.79/58.84 (11) ~ (e2 = e0)
% 248.79/58.84 (12) op(all_38_2, all_4_2) = e1
% 248.79/58.84 (13) ~ (e1 = e0)
% 248.79/58.84 (14) ~ (all_62_2 = e2)
% 248.79/58.84 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.84 (16) op(e0, e0) = all_244_24
% 248.79/58.84 (17) ~ (e4 = e0)
% 248.79/58.84 (18) op(e2, e2) = all_244_8
% 248.79/58.84 (19) op(e2, e1) = all_38_2
% 248.79/58.84 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.84 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.84 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.84 (21) ~ (all_36_2 = all_20_2)
% 248.79/58.84 (22) op(e1, all_28_2) = e0
% 248.79/58.84 (23) op(e4, e2) = all_6_2
% 248.79/58.84 (24) ~ (e2 = e1)
% 248.79/58.84 (25) all_252_7 = e4
% 248.79/58.84 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.84 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.84 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.84 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.84 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.84 op(e0, e1) = e0)))
% 248.79/58.84 (27) op(e0, e2) = all_28_2
% 248.79/58.84 (28) ~ (e4 = e1)
% 248.79/58.84 (29) ~ (all_6_2 = e1)
% 248.79/58.84 (30) ~ (all_244_8 = all_38_2)
% 248.79/58.84 (31) op(all_244_15, all_244_15) = e1
% 248.79/58.84 (32) all_50_2 = all_4_2
% 248.79/58.84 (33) op(e1, e4) = all_16_2
% 248.79/58.84 (34) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.84 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.84 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.84 (35) op(e1, e3) = all_62_2
% 248.79/58.84 (36) ~ (all_38_2 = e0)
% 248.79/58.84 (37) all_252_1 = e2
% 248.79/58.84 (38) ~ (all_22_2 = e4)
% 248.79/58.84 (39) op(e3, e1) = all_36_2
% 248.79/58.84 (40) ~ (all_16_2 = e2)
% 248.79/58.84 (41) ~ (all_8_2 = e1)
% 248.79/58.84 (42) ~ (all_22_2 = e1)
% 248.79/58.84 (43) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 248.79/58.84 all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) |
% 248.79/58.84 ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.84 (44) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.84 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.84 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.84 (45) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 248.79/58.84 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 248.79/58.84 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.84 (46) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 248.79/58.84 all_250_13 = e0
% 248.79/58.84 (47) ~ (all_244_15 = all_38_2)
% 248.79/58.84 (48) ~ (all_36_2 = all_26_2)
% 248.79/58.84 (49) op(e4, e3) = e2
% 248.79/58.84 (50) ~ (all_38_2 = e4)
% 248.79/58.84 (51) op(e0, e3) = all_22_2
% 248.79/58.84 (52) all_252_20 = e2
% 248.79/58.84 (53) op(e4, e1) = all_26_2
% 248.79/58.84 (54) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 248.79/58.84 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.84 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 248.79/58.84 (55) ~ (all_244_8 = e1)
% 248.79/58.84 (56) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.84 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.84 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.84 (57) op(e1, e1) = all_244_15
% 248.79/58.84 (58) op(e0, e1) = all_20_2
% 248.79/58.84 (59) ~ (all_38_2 = all_36_2)
% 248.79/58.84 (60) ~ (all_26_2 = e3)
% 248.79/58.84 (61) op(e1, e2) = all_4_2
% 248.79/58.84 (62) op(all_4_2, all_38_2) = e2
% 248.79/58.84 (63) op(e4, e3) = all_84_2
% 248.79/58.84 (64) op(e3, e2) = all_8_2
% 248.79/58.84 (65) op(all_36_2, e1) = e3
% 248.79/58.84 (66) ~ (all_38_2 = all_20_2)
% 248.79/58.84 (67) ~ (all_244_15 = all_36_2)
% 248.79/58.84 (68) ~ (all_20_2 = e4)
% 248.79/58.84 (69) ~ (all_16_2 = e3)
% 248.79/58.84 (70) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.84 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.84 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.84 (71) all_188_2 = all_38_2
% 248.79/58.84 (72) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.84 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.84 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.84 (73) all_46_2 = all_36_2
% 248.79/58.84 (74) ~ (all_4_2 = e2)
% 248.79/58.84 (75) ~ (all_16_2 = e0)
% 248.79/58.84 (76) ~ (all_20_2 = e2)
% 248.79/58.84 (77) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 248.79/58.84 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 248.79/58.84 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.84
% 248.79/58.84 Begin of proof
% 248.79/58.84 |
% 248.79/58.84 | GROUND_INST: instantiating (15) with all_20_2, all_174_1, e1, e0, simplifying
% 248.79/58.84 | with (10), (58) gives:
% 248.79/58.84 | (78) all_174_1 = all_20_2
% 248.79/58.84 |
% 248.79/58.84 | BETA: splitting (7) gives:
% 248.79/58.84 |
% 248.79/58.84 | Case 1:
% 248.79/58.84 | |
% 248.79/58.84 | | (79) ~ (all_36_2 = e4)
% 248.79/58.84 | |
% 248.79/58.84 | | BETA: splitting (45) gives:
% 248.79/58.84 | |
% 248.79/58.84 | | Case 1:
% 248.79/58.84 | | |
% 248.79/58.84 | | | (80) ~ (all_46_2 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | REF_CLOSE: (1), (3), (4), (15), (18), (19), (31), (39), (53), (55), (56),
% 248.79/58.84 | | | (57), (58), (62), (73), (76), (80) are inconsistent by
% 248.79/58.84 | | | sub-proof #598.
% 248.79/58.84 | | |
% 248.79/58.84 | | Case 2:
% 248.79/58.84 | | |
% 248.79/58.84 | | | (81) all_46_2 = e2
% 248.79/58.84 | | | (82) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 248.79/58.84 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 248.79/58.84 | | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 248.79/58.84 | | |
% 248.79/58.84 | | | COMBINE_EQS: (73), (81) imply:
% 248.79/58.84 | | | (83) all_36_2 = e2
% 248.79/58.84 | | |
% 248.79/58.84 | | | SIMP: (83) implies:
% 248.79/58.84 | | | (84) all_36_2 = e2
% 248.79/58.84 | | |
% 248.79/58.84 | | | REDUCE: (67), (84) imply:
% 248.79/58.84 | | | (85) ~ (all_244_15 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | REDUCE: (59), (84) imply:
% 248.79/58.84 | | | (86) ~ (all_38_2 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | REDUCE: (48), (84) imply:
% 248.79/58.84 | | | (87) ~ (all_26_2 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | REDUCE: (21), (84) imply:
% 248.79/58.84 | | | (88) ~ (all_20_2 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | REDUCE: (79), (84) imply:
% 248.79/58.84 | | | (89) ~ (e4 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | SIMP: (89) implies:
% 248.79/58.84 | | | (90) ~ (e4 = e2)
% 248.79/58.84 | | |
% 248.79/58.84 | | | BETA: splitting (46) gives:
% 248.79/58.84 | | |
% 248.79/58.84 | | | Case 1:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | (91) all_250_13 = e4
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | REF_CLOSE: (9), (50), (91) are inconsistent by sub-proof #992.
% 248.79/58.84 | | | |
% 248.79/58.84 | | | Case 2:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | (92) ~ (all_250_13 = e4)
% 248.79/58.84 | | | | (93) all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 | all_250_13
% 248.79/58.84 | | | | = e0
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | BETA: splitting (93) gives:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | Case 1:
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | (94) all_250_13 = e3
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | COMBINE_EQS: (9), (94) imply:
% 248.79/58.84 | | | | | (95) all_38_2 = e3
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | SIMP: (95) implies:
% 248.79/58.84 | | | | | (96) all_38_2 = e3
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | COMBINE_EQS: (71), (96) imply:
% 248.79/58.84 | | | | | (97) all_188_2 = e3
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (47), (96) imply:
% 248.79/58.84 | | | | | (98) ~ (all_244_15 = e3)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (66), (96) imply:
% 248.79/58.84 | | | | | (99) ~ (all_20_2 = e3)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | SIMP: (99) implies:
% 248.79/58.84 | | | | | (100) ~ (all_20_2 = e3)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (50), (96) imply:
% 248.79/58.84 | | | | | (101) ~ (e4 = e3)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | SIMP: (101) implies:
% 248.79/58.84 | | | | | (102) ~ (e4 = e3)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (86), (96) imply:
% 248.79/58.84 | | | | | (103) ~ (e3 = e2)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (4), (96) imply:
% 248.79/58.84 | | | | | (104) ~ (e3 = e1)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (36), (96) imply:
% 248.79/58.84 | | | | | (105) ~ (e3 = e0)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REDUCE: (12), (96) imply:
% 248.79/58.84 | | | | | (106) op(e3, all_4_2) = e1
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | BETA: splitting (82) gives:
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | Case 1:
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | (107) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1,
% 248.79/58.84 | | | | | | e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | ALPHA: (107) implies:
% 248.79/58.84 | | | | | | (108) op(e1, e2) = all_46_1
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13),
% 248.79/58.84 | | | | | | (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 248.79/58.84 | | | | | | (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 248.79/58.84 | | | | | | (34), (35), (37), (38), (40), (41), (42), (43), (44),
% 248.79/58.84 | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 248.79/58.84 | | | | | | (61), (62), (63), (64), (68), (69), (70), (72), (74),
% 248.79/58.84 | | | | | | (75), (76), (77), (85), (90), (97), (98), (100), (102),
% 248.79/58.84 | | | | | | (103), (104), (105), (106), (108) are inconsistent by
% 248.79/58.84 | | | | | | sub-proof #88.
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | Case 2:
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | (109) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1)
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | ALPHA: (109) implies:
% 248.79/58.84 | | | | | | (110) op(e1, e2) = all_46_1
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13),
% 248.79/58.84 | | | | | | (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 248.79/58.84 | | | | | | (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 248.79/58.84 | | | | | | (34), (35), (37), (38), (40), (41), (42), (43), (44),
% 248.79/58.84 | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 248.79/58.84 | | | | | | (61), (62), (63), (64), (68), (69), (70), (72), (74),
% 248.79/58.84 | | | | | | (75), (76), (77), (85), (90), (97), (98), (100), (102),
% 248.79/58.84 | | | | | | (103), (104), (105), (106), (110) are inconsistent by
% 248.79/58.84 | | | | | | sub-proof #88.
% 248.79/58.84 | | | | | |
% 248.79/58.84 | | | | | End of split
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | Case 2:
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | (111) all_250_13 = e2 | all_250_13 = e1 | all_250_13 = e0
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | REF_CLOSE: (8), (9), (15), (18), (30), (31), (36), (57), (86), (111)
% 248.79/58.84 | | | | | are inconsistent by sub-proof #990.
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | End of split
% 248.79/58.84 | | | |
% 248.79/58.84 | | | End of split
% 248.79/58.84 | | |
% 248.79/58.84 | | End of split
% 248.79/58.84 | |
% 248.79/58.84 | Case 2:
% 248.79/58.84 | |
% 248.79/58.84 | | (112) all_36_2 = e4
% 248.79/58.84 | |
% 248.79/58.84 | | REDUCE: (65), (112) imply:
% 248.79/58.84 | | (113) op(e4, e1) = e3
% 248.79/58.84 | |
% 248.79/58.84 | | REF_CLOSE: (15), (53), (60), (113) are inconsistent by sub-proof #834.
% 248.79/58.84 | |
% 248.79/58.84 | End of split
% 248.79/58.84 |
% 248.79/58.84 End of proof
% 248.79/58.84
% 248.79/58.84 Sub-proof #88 shows that the following formulas are inconsistent:
% 248.79/58.84 ----------------------------------------------------------------
% 248.79/58.84 (1) ~ (all_26_2 = e2)
% 248.79/58.84 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.84 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.84 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.84 (3) op(all_4_2, e2) = e1
% 248.79/58.84 (4) ~ (all_38_2 = e1)
% 248.79/58.84 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.84 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.84 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.84 (6) all_116_2 = e1
% 248.79/58.84 (7) op(all_38_2, e1) = e2
% 248.79/58.84 (8) ~ (e2 = e0)
% 248.79/58.84 (9) op(all_38_2, all_4_2) = e1
% 248.79/58.84 (10) ~ (e1 = e0)
% 248.79/58.84 (11) ~ (all_62_2 = e2)
% 248.79/58.84 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.84 (13) ~ (e3 = e2)
% 248.79/58.84 (14) op(e0, e0) = all_244_24
% 248.79/58.84 (15) ~ (e4 = e0)
% 248.79/58.84 (16) all_188_2 = e3
% 248.79/58.84 (17) op(e2, e2) = all_244_8
% 248.79/58.84 (18) op(e2, e1) = all_38_2
% 248.79/58.84 (19) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.84 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.84 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.84 (20) op(e1, all_28_2) = e0
% 248.79/58.84 (21) op(e4, e2) = all_6_2
% 248.79/58.84 (22) ~ (e2 = e1)
% 248.79/58.84 (23) all_252_7 = e4
% 248.79/58.84 (24) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.84 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.84 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.84 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.84 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.84 op(e0, e1) = e0)))
% 248.79/58.84 (25) op(e0, e2) = all_28_2
% 248.79/58.84 (26) ~ (e4 = e1)
% 248.79/58.84 (27) ~ (all_6_2 = e1)
% 248.79/58.84 (28) op(all_244_15, all_244_15) = e1
% 248.79/58.84 (29) all_50_2 = all_4_2
% 248.79/58.84 (30) op(e1, e4) = all_16_2
% 248.79/58.84 (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.84 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.84 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.84 (32) op(e1, e3) = all_62_2
% 248.79/58.84 (33) ~ (e3 = e0)
% 248.79/58.84 (34) all_252_1 = e2
% 248.79/58.84 (35) ~ (all_22_2 = e4)
% 248.79/58.84 (36) ~ (e3 = e1)
% 248.79/58.84 (37) ~ (all_16_2 = e2)
% 248.79/58.84 (38) ~ (all_8_2 = e1)
% 248.79/58.84 (39) ~ (all_22_2 = e1)
% 248.79/58.84 (40) ~ (all_116_2 = e1) | ( ~ (all_116_0 = e4) & op(e1, all_116_1) =
% 248.79/58.84 all_116_0 & op(e0, e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) |
% 248.79/58.84 ( ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.84 (41) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.84 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.84 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.84 (42) op(e4, e3) = e2
% 248.79/58.84 (43) op(e0, e3) = all_22_2
% 248.79/58.84 (44) all_252_20 = e2
% 248.79/58.84 (45) op(e3, all_4_2) = e1
% 248.79/58.84 (46) op(e4, e1) = all_26_2
% 248.79/58.84 (47) ~ (all_244_15 = e3)
% 248.79/58.84 (48) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 248.79/58.84 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.84 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 248.79/58.84 (49) ~ (all_244_8 = e1)
% 248.79/58.84 (50) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.84 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.84 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.84 (51) ~ (e4 = e3)
% 248.79/58.84 (52) op(e1, e1) = all_244_15
% 248.79/58.84 (53) op(e0, e1) = all_20_2
% 248.79/58.84 (54) op(e1, e2) = all_46_1
% 248.79/58.84 (55) op(e1, e2) = all_4_2
% 248.79/58.84 (56) op(all_4_2, all_38_2) = e2
% 248.79/58.84 (57) op(e4, e3) = all_84_2
% 248.79/58.84 (58) ~ (all_244_15 = e2)
% 248.79/58.84 (59) ~ (e4 = e2)
% 248.79/58.84 (60) op(e3, e2) = all_8_2
% 248.79/58.84 (61) ~ (all_20_2 = e4)
% 248.79/58.84 (62) ~ (all_20_2 = e3)
% 248.79/58.84 (63) ~ (all_16_2 = e3)
% 248.79/58.84 (64) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.84 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.84 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.84 (65) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.84 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.84 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.84 (66) ~ (all_4_2 = e2)
% 248.79/58.84 (67) ~ (all_16_2 = e0)
% 248.79/58.84 (68) ~ (all_20_2 = e2)
% 248.79/58.84 (69) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 248.79/58.84 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 248.79/58.84 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.84
% 248.79/58.84 Begin of proof
% 248.79/58.84 |
% 248.79/58.84 | BETA: splitting (50) gives:
% 248.79/58.84 |
% 248.79/58.84 | Case 1:
% 248.79/58.84 | |
% 248.79/58.84 | | (70) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 248.79/58.84 | | e2)
% 248.79/58.84 | |
% 248.79/58.84 | | BETA: splitting (70) gives:
% 248.79/58.84 | |
% 248.79/58.84 | | Case 1:
% 248.79/58.84 | | |
% 248.79/58.84 | | | (71) all_252_9 = e2 & op(e4, e1) = e2
% 248.79/58.84 | | |
% 248.79/58.84 | | | REF_CLOSE: (1), (12), (46), (71) are inconsistent by sub-proof #970.
% 248.79/58.84 | | |
% 248.79/58.84 | | Case 2:
% 248.79/58.84 | | |
% 248.79/58.84 | | | (72) all_252_10 = e2 & op(e3, e1) = e2
% 248.79/58.84 | | |
% 248.79/58.84 | | | ALPHA: (72) implies:
% 248.79/58.84 | | | (73) all_252_10 = e2
% 248.79/58.84 | | |
% 248.79/58.84 | | | BETA: splitting (40) gives:
% 248.79/58.84 | | |
% 248.79/58.84 | | | Case 1:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | (74) ~ (all_116_2 = e1)
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | REDUCE: (6), (74) imply:
% 248.79/58.84 | | | | (75) $false
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | CLOSE: (75) is inconsistent.
% 248.79/58.84 | | | |
% 248.79/58.84 | | | Case 2:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | (76) ( ~ (all_116_0 = e4) & op(e1, all_116_1) = all_116_0 & op(e0,
% 248.79/58.84 | | | | e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)) | ( ~
% 248.79/58.84 | | | | (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1))
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | BETA: splitting (76) gives:
% 248.79/58.84 | | | |
% 248.79/58.84 | | | | Case 1:
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | (77) ~ (all_116_0 = e4) & op(e1, all_116_1) = all_116_0 & op(e0,
% 248.79/58.84 | | | | | e1) = all_116_1 & $i(all_116_0) & $i(all_116_1)
% 248.79/58.84 | | | | |
% 248.79/58.84 | | | | | ALPHA: (77) implies:
% 248.79/58.84 | | | | | (78) op(e0, e1) = all_116_1
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | BETA: splitting (48) gives:
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | Case 1:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | (79) ~ (all_188_2 = e3)
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | REDUCE: (16), (79) imply:
% 248.79/58.85 | | | | | | (80) $false
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | CLOSE: (80) is inconsistent.
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | Case 2:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | (81) ( ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 248.79/58.85 | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.85 | | | | | | ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 248.79/58.85 | | | | | | $i(all_188_1))
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | BETA: splitting (81) gives:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | Case 1:
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | (82) ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 248.79/58.85 | | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | ALPHA: (82) implies:
% 248.79/58.85 | | | | | | | (83) op(e1, e3) = all_188_1
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 248.79/58.85 | | | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 248.79/58.85 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 248.79/58.85 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 248.79/58.85 | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49), (50),
% 248.79/58.85 | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 248.79/58.85 | | | | | | | (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.79/58.85 | | | | | | | (69), (73), (78), (83) are inconsistent by sub-proof
% 248.79/58.85 | | | | | | | #90.
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | Case 2:
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | (84) ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 248.79/58.85 | | | | | | | $i(all_188_1)
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | ALPHA: (84) implies:
% 248.79/58.85 | | | | | | | (85) op(e1, e3) = all_188_1
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 248.79/58.85 | | | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 248.79/58.85 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 248.79/58.85 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 248.79/58.85 | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49), (50),
% 248.79/58.85 | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 248.79/58.85 | | | | | | | (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 248.79/58.85 | | | | | | | (69), (73), (78), (85) are inconsistent by sub-proof
% 248.79/58.85 | | | | | | | #90.
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | End of split
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | End of split
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | Case 2:
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | (86) ~ (all_116_1 = e3) & op(e0, e1) = all_116_1 & $i(all_116_1)
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | ALPHA: (86) implies:
% 248.79/58.85 | | | | | (87) ~ (all_116_1 = e3)
% 248.79/58.85 | | | | | (88) op(e0, e1) = all_116_1
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | BETA: splitting (48) gives:
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | | Case 1:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | (89) ~ (all_188_2 = e3)
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | REDUCE: (16), (89) imply:
% 248.79/58.85 | | | | | | (90) $false
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | CLOSE: (90) is inconsistent.
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | Case 2:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | (91) ( ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 248.79/58.85 | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 248.79/58.85 | | | | | | ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 248.79/58.85 | | | | | | $i(all_188_1))
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | BETA: splitting (91) gives:
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | | Case 1:
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | (92) ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 248.79/58.85 | | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | ALPHA: (92) implies:
% 248.79/58.85 | | | | | | | (93) op(e1, e3) = all_188_1
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 248.79/58.85 | | | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 248.79/58.85 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 248.79/58.85 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 248.79/58.85 | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49), (50),
% 248.79/58.85 | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 248.79/58.85 | | | | | | | (60), (61), (63), (64), (65), (66), (67), (68), (69),
% 248.79/58.85 | | | | | | | (73), (87), (88), (93) are inconsistent by sub-proof
% 248.79/58.85 | | | | | | | #89.
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | Case 2:
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | (94) ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 248.79/58.85 | | | | | | | $i(all_188_1)
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | ALPHA: (94) implies:
% 248.79/58.85 | | | | | | | (95) op(e1, e3) = all_188_1
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 248.79/58.85 | | | | | | | (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 248.79/58.85 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 248.79/58.85 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 248.79/58.85 | | | | | | | (41), (42), (43), (44), (45), (46), (47), (49), (50),
% 248.79/58.85 | | | | | | | (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 248.79/58.85 | | | | | | | (60), (61), (63), (64), (65), (66), (67), (68), (69),
% 248.79/58.85 | | | | | | | (73), (87), (88), (95) are inconsistent by sub-proof
% 248.79/58.85 | | | | | | | #89.
% 248.79/58.85 | | | | | | |
% 248.79/58.85 | | | | | | End of split
% 248.79/58.85 | | | | | |
% 248.79/58.85 | | | | | End of split
% 248.79/58.85 | | | | |
% 248.79/58.85 | | | | End of split
% 248.79/58.85 | | | |
% 248.79/58.85 | | | End of split
% 248.79/58.85 | | |
% 248.79/58.85 | | End of split
% 248.79/58.85 | |
% 248.79/58.85 | Case 2:
% 248.79/58.85 | |
% 248.79/58.85 | | (96) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 248.79/58.85 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.85 | |
% 248.79/58.85 | | REF_CLOSE: (3), (4), (12), (17), (18), (28), (49), (52), (53), (56), (68),
% 248.79/58.85 | | (96) are inconsistent by sub-proof #737.
% 248.79/58.85 | |
% 248.79/58.85 | End of split
% 248.79/58.85 |
% 248.79/58.85 End of proof
% 248.79/58.85
% 248.79/58.85 Sub-proof #89 shows that the following formulas are inconsistent:
% 248.79/58.85 ----------------------------------------------------------------
% 248.79/58.85 (1) ~ (all_26_2 = e2)
% 248.79/58.85 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.85 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.85 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.85 (3) op(all_4_2, e2) = e1
% 248.79/58.85 (4) ~ (all_38_2 = e1)
% 248.79/58.85 (5) ~ (all_116_1 = e3)
% 248.79/58.85 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.85 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.85 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.85 (7) op(all_38_2, e1) = e2
% 248.79/58.85 (8) ~ (e2 = e0)
% 248.79/58.85 (9) op(all_38_2, all_4_2) = e1
% 248.79/58.85 (10) ~ (e1 = e0)
% 248.79/58.85 (11) ~ (all_62_2 = e2)
% 248.79/58.85 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.85 (13) ~ (e3 = e2)
% 248.79/58.85 (14) op(e0, e0) = all_244_24
% 248.79/58.85 (15) ~ (e4 = e0)
% 248.79/58.85 (16) op(e2, e2) = all_244_8
% 248.79/58.85 (17) op(e2, e1) = all_38_2
% 248.79/58.85 (18) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.85 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.85 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.85 (19) op(e1, all_28_2) = e0
% 248.79/58.85 (20) op(e4, e2) = all_6_2
% 248.79/58.85 (21) ~ (e2 = e1)
% 248.79/58.85 (22) all_252_7 = e4
% 248.79/58.85 (23) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.85 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.85 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.85 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.85 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.85 op(e0, e1) = e0)))
% 248.79/58.85 (24) op(e0, e2) = all_28_2
% 248.79/58.85 (25) ~ (e4 = e1)
% 248.79/58.85 (26) ~ (all_6_2 = e1)
% 248.79/58.85 (27) op(all_244_15, all_244_15) = e1
% 248.79/58.85 (28) all_50_2 = all_4_2
% 248.79/58.85 (29) op(e1, e4) = all_16_2
% 248.79/58.85 (30) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.85 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.85 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.85 (31) op(e1, e3) = all_62_2
% 248.79/58.85 (32) ~ (e3 = e0)
% 248.79/58.85 (33) all_252_1 = e2
% 248.79/58.85 (34) ~ (all_22_2 = e4)
% 248.79/58.85 (35) ~ (e3 = e1)
% 248.79/58.85 (36) ~ (all_16_2 = e2)
% 248.79/58.85 (37) ~ (all_8_2 = e1)
% 248.79/58.85 (38) ~ (all_22_2 = e1)
% 248.79/58.85 (39) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.85 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.85 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.85 (40) op(e0, e1) = all_116_1
% 248.79/58.85 (41) op(e4, e3) = e2
% 248.79/58.85 (42) all_252_10 = e2
% 248.79/58.85 (43) op(e1, e3) = all_188_1
% 248.79/58.85 (44) op(e0, e3) = all_22_2
% 248.79/58.85 (45) all_252_20 = e2
% 248.79/58.85 (46) op(e3, all_4_2) = e1
% 248.79/58.85 (47) op(e4, e1) = all_26_2
% 248.79/58.85 (48) ~ (all_244_15 = e3)
% 248.79/58.85 (49) ~ (all_244_8 = e1)
% 248.79/58.85 (50) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.85 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.85 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.85 (51) ~ (e4 = e3)
% 248.79/58.85 (52) op(e1, e1) = all_244_15
% 248.79/58.85 (53) op(e0, e1) = all_20_2
% 248.79/58.85 (54) op(e1, e2) = all_46_1
% 248.79/58.85 (55) op(e1, e2) = all_4_2
% 248.79/58.85 (56) op(all_4_2, all_38_2) = e2
% 248.79/58.85 (57) op(e4, e3) = all_84_2
% 248.79/58.85 (58) ~ (all_244_15 = e2)
% 248.79/58.85 (59) ~ (e4 = e2)
% 248.79/58.85 (60) op(e3, e2) = all_8_2
% 248.79/58.85 (61) ~ (all_20_2 = e4)
% 248.79/58.85 (62) ~ (all_16_2 = e3)
% 248.79/58.85 (63) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.85 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.85 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.85 (64) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.85 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.85 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.85 (65) ~ (all_4_2 = e2)
% 248.79/58.85 (66) ~ (all_16_2 = e0)
% 248.79/58.85 (67) ~ (all_20_2 = e2)
% 248.79/58.85 (68) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 248.79/58.85 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 248.79/58.85 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.85
% 248.79/58.85 Begin of proof
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (12) with all_20_2, all_116_1, e1, e0, simplifying
% 248.79/58.85 | with (40), (53) gives:
% 248.79/58.85 | (69) all_116_1 = all_20_2
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (12) with all_4_2, all_46_1, e2, e1, simplifying
% 248.79/58.85 | with (54), (55) gives:
% 248.79/58.85 | (70) all_46_1 = all_4_2
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (12) with all_62_2, all_188_1, e3, e1, simplifying
% 248.79/58.85 | with (31), (43) gives:
% 248.79/58.85 | (71) all_188_1 = all_62_2
% 248.79/58.85 |
% 248.79/58.85 | REDUCE: (5), (69) imply:
% 248.79/58.85 | (72) ~ (all_20_2 = e3)
% 248.79/58.85 |
% 248.79/58.85 | BETA: splitting (68) gives:
% 248.79/58.85 |
% 248.79/58.85 | Case 1:
% 248.79/58.85 | |
% 248.79/58.85 | | (73) ~ (all_50_2 = e3)
% 248.79/58.85 | |
% 248.79/58.85 | | REDUCE: (28), (73) imply:
% 248.79/58.85 | | (74) ~ (all_4_2 = e3)
% 248.79/58.85 | |
% 248.79/58.85 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 248.79/58.85 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 248.79/58.85 | | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 248.79/58.85 | | (37), (38), (39), (41), (42), (44), (45), (46), (47), (48), (49),
% 248.79/58.85 | | (50), (51), (52), (53), (55), (56), (57), (58), (59), (60), (61),
% 248.79/58.85 | | (62), (63), (64), (65), (66), (67), (72), (74) are inconsistent
% 248.79/58.85 | | by sub-proof #91.
% 248.79/58.85 | |
% 248.79/58.85 | Case 2:
% 248.79/58.85 | |
% 248.79/58.85 | | (75) all_50_2 = e3
% 248.79/58.85 | |
% 248.79/58.85 | | COMBINE_EQS: (28), (75) imply:
% 248.79/58.85 | | (76) all_4_2 = e3
% 248.79/58.85 | |
% 248.79/58.85 | | REDUCE: (3), (76) imply:
% 248.79/58.85 | | (77) op(e3, e2) = e1
% 248.79/58.85 | |
% 248.79/58.85 | | REF_CLOSE: (12), (37), (60), (77) are inconsistent by sub-proof #929.
% 248.79/58.85 | |
% 248.79/58.85 | End of split
% 248.79/58.85 |
% 248.79/58.85 End of proof
% 248.79/58.85
% 248.79/58.85 Sub-proof #90 shows that the following formulas are inconsistent:
% 248.79/58.85 ----------------------------------------------------------------
% 248.79/58.85 (1) ~ (all_26_2 = e2)
% 248.79/58.85 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.85 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.85 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.85 (3) op(all_4_2, e2) = e1
% 248.79/58.85 (4) ~ (all_38_2 = e1)
% 248.79/58.85 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.85 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.85 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.85 (6) op(all_38_2, e1) = e2
% 248.79/58.85 (7) ~ (e2 = e0)
% 248.79/58.85 (8) op(all_38_2, all_4_2) = e1
% 248.79/58.85 (9) ~ (e1 = e0)
% 248.79/58.85 (10) ~ (all_62_2 = e2)
% 248.79/58.85 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.85 (12) ~ (e3 = e2)
% 248.79/58.85 (13) op(e0, e0) = all_244_24
% 248.79/58.85 (14) ~ (e4 = e0)
% 248.79/58.85 (15) op(e2, e2) = all_244_8
% 248.79/58.85 (16) op(e2, e1) = all_38_2
% 248.79/58.85 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.85 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.85 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.85 (18) op(e1, all_28_2) = e0
% 248.79/58.85 (19) op(e4, e2) = all_6_2
% 248.79/58.85 (20) ~ (e2 = e1)
% 248.79/58.85 (21) all_252_7 = e4
% 248.79/58.85 (22) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.85 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.85 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.85 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.85 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.85 op(e0, e1) = e0)))
% 248.79/58.85 (23) op(e0, e2) = all_28_2
% 248.79/58.85 (24) ~ (e4 = e1)
% 248.79/58.85 (25) ~ (all_6_2 = e1)
% 248.79/58.85 (26) op(all_244_15, all_244_15) = e1
% 248.79/58.85 (27) all_50_2 = all_4_2
% 248.79/58.85 (28) op(e1, e4) = all_16_2
% 248.79/58.85 (29) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.85 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.85 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.85 (30) op(e1, e3) = all_62_2
% 248.79/58.85 (31) ~ (e3 = e0)
% 248.79/58.85 (32) all_252_1 = e2
% 248.79/58.85 (33) ~ (all_22_2 = e4)
% 248.79/58.85 (34) ~ (e3 = e1)
% 248.79/58.85 (35) ~ (all_16_2 = e2)
% 248.79/58.85 (36) ~ (all_8_2 = e1)
% 248.79/58.85 (37) ~ (all_22_2 = e1)
% 248.79/58.85 (38) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.85 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.85 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.85 (39) op(e0, e1) = all_116_1
% 248.79/58.85 (40) op(e4, e3) = e2
% 248.79/58.85 (41) all_252_10 = e2
% 248.79/58.85 (42) op(e1, e3) = all_188_1
% 248.79/58.85 (43) op(e0, e3) = all_22_2
% 248.79/58.85 (44) all_252_20 = e2
% 248.79/58.85 (45) op(e3, all_4_2) = e1
% 248.79/58.85 (46) op(e4, e1) = all_26_2
% 248.79/58.85 (47) ~ (all_244_15 = e3)
% 248.79/58.85 (48) ~ (all_244_8 = e1)
% 248.79/58.85 (49) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.85 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.85 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.85 (50) ~ (e4 = e3)
% 248.79/58.85 (51) op(e1, e1) = all_244_15
% 248.79/58.85 (52) op(e0, e1) = all_20_2
% 248.79/58.85 (53) op(e1, e2) = all_46_1
% 248.79/58.85 (54) op(e1, e2) = all_4_2
% 248.79/58.85 (55) op(all_4_2, all_38_2) = e2
% 248.79/58.85 (56) op(e4, e3) = all_84_2
% 248.79/58.85 (57) ~ (all_244_15 = e2)
% 248.79/58.85 (58) ~ (e4 = e2)
% 248.79/58.85 (59) op(e3, e2) = all_8_2
% 248.79/58.85 (60) ~ (all_20_2 = e4)
% 248.79/58.85 (61) ~ (all_20_2 = e3)
% 248.79/58.85 (62) ~ (all_16_2 = e3)
% 248.79/58.85 (63) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.85 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.85 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.85 (64) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.85 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.85 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.85 (65) ~ (all_4_2 = e2)
% 248.79/58.85 (66) ~ (all_16_2 = e0)
% 248.79/58.85 (67) ~ (all_20_2 = e2)
% 248.79/58.85 (68) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 248.79/58.85 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 248.79/58.85 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 248.79/58.85
% 248.79/58.85 Begin of proof
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (11) with all_20_2, all_116_1, e1, e0, simplifying
% 248.79/58.85 | with (39), (52) gives:
% 248.79/58.85 | (69) all_116_1 = all_20_2
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (11) with all_4_2, all_46_1, e2, e1, simplifying
% 248.79/58.85 | with (53), (54) gives:
% 248.79/58.85 | (70) all_46_1 = all_4_2
% 248.79/58.85 |
% 248.79/58.85 | GROUND_INST: instantiating (11) with all_62_2, all_188_1, e3, e1, simplifying
% 248.79/58.85 | with (30), (42) gives:
% 248.79/58.85 | (71) all_188_1 = all_62_2
% 248.79/58.85 |
% 248.79/58.85 | BETA: splitting (68) gives:
% 248.79/58.85 |
% 248.79/58.85 | Case 1:
% 248.79/58.85 | |
% 248.79/58.85 | | (72) ~ (all_50_2 = e3)
% 248.79/58.85 | |
% 248.79/58.85 | | REDUCE: (27), (72) imply:
% 248.79/58.85 | | (73) ~ (all_4_2 = e3)
% 248.79/58.85 | |
% 248.79/58.85 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 248.79/58.85 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 248.79/58.85 | | (24), (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 248.79/58.85 | | (36), (37), (38), (40), (41), (43), (44), (45), (46), (47), (48),
% 248.79/58.85 | | (49), (50), (51), (52), (54), (55), (56), (57), (58), (59), (60),
% 248.79/58.85 | | (61), (62), (63), (64), (65), (66), (67), (73) are inconsistent
% 248.79/58.85 | | by sub-proof #91.
% 248.79/58.85 | |
% 248.79/58.85 | Case 2:
% 248.79/58.85 | |
% 248.79/58.85 | | (74) all_50_2 = e3
% 248.79/58.85 | |
% 248.79/58.85 | | COMBINE_EQS: (27), (74) imply:
% 248.79/58.85 | | (75) all_4_2 = e3
% 248.79/58.85 | |
% 248.79/58.85 | | REDUCE: (3), (75) imply:
% 248.79/58.85 | | (76) op(e3, e2) = e1
% 248.79/58.85 | |
% 248.79/58.85 | | REF_CLOSE: (11), (36), (59), (76) are inconsistent by sub-proof #929.
% 248.79/58.85 | |
% 248.79/58.85 | End of split
% 248.79/58.85 |
% 248.79/58.85 End of proof
% 248.79/58.85
% 248.79/58.85 Sub-proof #91 shows that the following formulas are inconsistent:
% 248.79/58.85 ----------------------------------------------------------------
% 248.79/58.85 (1) ~ (all_26_2 = e2)
% 248.79/58.85 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 248.79/58.85 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 248.79/58.85 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 248.79/58.85 (3) op(all_4_2, e2) = e1
% 248.79/58.85 (4) ~ (all_38_2 = e1)
% 248.79/58.85 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 248.79/58.85 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 248.79/58.85 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 248.79/58.86 (6) op(all_38_2, e1) = e2
% 248.79/58.86 (7) ~ (e2 = e0)
% 248.79/58.86 (8) op(all_38_2, all_4_2) = e1
% 248.79/58.86 (9) ~ (e1 = e0)
% 248.79/58.86 (10) ~ (all_62_2 = e2)
% 248.79/58.86 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 248.79/58.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 248.79/58.86 (12) ~ (e3 = e2)
% 248.79/58.86 (13) op(e0, e0) = all_244_24
% 248.79/58.86 (14) ~ (e4 = e0)
% 248.79/58.86 (15) op(e2, e2) = all_244_8
% 248.79/58.86 (16) op(e2, e1) = all_38_2
% 248.79/58.86 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 248.79/58.86 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 248.79/58.86 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 248.79/58.86 (18) op(e1, all_28_2) = e0
% 248.79/58.86 (19) op(e4, e2) = all_6_2
% 248.79/58.86 (20) ~ (e2 = e1)
% 248.79/58.86 (21) all_252_7 = e4
% 248.79/58.86 (22) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 248.79/58.86 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 248.79/58.86 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 248.79/58.86 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 248.79/58.86 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 248.79/58.86 op(e0, e1) = e0)))
% 248.79/58.86 (23) op(e0, e2) = all_28_2
% 248.79/58.86 (24) ~ (e4 = e1)
% 248.79/58.86 (25) ~ (all_6_2 = e1)
% 248.79/58.86 (26) op(all_244_15, all_244_15) = e1
% 248.79/58.86 (27) op(e1, e4) = all_16_2
% 248.79/58.86 (28) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 248.79/58.86 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 248.79/58.86 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 248.79/58.86 (29) op(e1, e3) = all_62_2
% 248.79/58.86 (30) ~ (e3 = e0)
% 248.79/58.86 (31) all_252_1 = e2
% 248.79/58.86 (32) ~ (all_22_2 = e4)
% 248.79/58.86 (33) ~ (e3 = e1)
% 248.79/58.86 (34) ~ (all_16_2 = e2)
% 248.79/58.86 (35) ~ (all_8_2 = e1)
% 248.79/58.86 (36) ~ (all_22_2 = e1)
% 248.79/58.86 (37) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 248.79/58.86 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 248.79/58.86 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 248.79/58.86 (38) op(e4, e3) = e2
% 248.79/58.86 (39) all_252_10 = e2
% 248.79/58.86 (40) op(e0, e3) = all_22_2
% 248.79/58.86 (41) all_252_20 = e2
% 248.79/58.86 (42) op(e3, all_4_2) = e1
% 248.79/58.86 (43) op(e4, e1) = all_26_2
% 248.79/58.86 (44) ~ (all_244_15 = e3)
% 248.79/58.86 (45) ~ (all_244_8 = e1)
% 248.79/58.86 (46) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 248.79/58.86 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 248.79/58.86 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 248.79/58.86 (47) ~ (e4 = e3)
% 248.79/58.86 (48) op(e1, e1) = all_244_15
% 248.79/58.86 (49) op(e0, e1) = all_20_2
% 248.79/58.86 (50) op(e1, e2) = all_4_2
% 248.79/58.86 (51) op(all_4_2, all_38_2) = e2
% 248.79/58.86 (52) op(e4, e3) = all_84_2
% 248.79/58.86 (53) ~ (all_244_15 = e2)
% 248.79/58.86 (54) ~ (e4 = e2)
% 248.79/58.86 (55) op(e3, e2) = all_8_2
% 248.79/58.86 (56) ~ (all_20_2 = e4)
% 248.79/58.86 (57) ~ (all_20_2 = e3)
% 248.79/58.86 (58) ~ (all_16_2 = e3)
% 248.79/58.86 (59) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 248.79/58.86 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 248.79/58.86 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 248.79/58.86 (60) ~ (all_4_2 = e3)
% 248.79/58.86 (61) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 248.79/58.86 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 248.79/58.86 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 248.79/58.86 (62) ~ (all_4_2 = e2)
% 248.79/58.86 (63) ~ (all_16_2 = e0)
% 248.79/58.86 (64) ~ (all_20_2 = e2)
% 248.79/58.86
% 248.79/58.86 Begin of proof
% 248.79/58.86 |
% 248.79/58.86 | BETA: splitting (5) gives:
% 248.79/58.86 |
% 248.79/58.86 | Case 1:
% 248.79/58.86 | |
% 248.79/58.86 | | (65) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 248.79/58.86 | | = e3)
% 248.79/58.86 | |
% 248.79/58.86 | | BETA: splitting (65) gives:
% 248.79/58.86 | |
% 248.79/58.86 | | Case 1:
% 248.79/58.86 | | |
% 248.79/58.86 | | | (66) all_252_12 = e3 & op(e1, e4) = e3
% 248.79/58.86 | | |
% 248.79/58.86 | | | REF_CLOSE: (11), (27), (58), (66) are inconsistent by sub-proof #895.
% 248.79/58.86 | | |
% 248.79/58.86 | | Case 2:
% 248.79/58.86 | | |
% 248.79/58.86 | | | (67) all_252_13 = e3 & op(e1, e3) = e3
% 248.79/58.86 | | |
% 248.79/58.86 | | | ALPHA: (67) implies:
% 249.18/58.86 | | | (68) all_252_13 = e3
% 249.18/58.86 | | | (69) op(e1, e3) = e3
% 249.18/58.86 | | |
% 249.18/58.86 | | | BETA: splitting (61) gives:
% 249.18/58.86 | | |
% 249.18/58.86 | | | Case 1:
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | (70) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3,
% 249.18/58.86 | | | | e3) = e1)
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | BETA: splitting (70) gives:
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | Case 1:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | (71) all_252_1 = e1 & op(e4, e3) = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | ALPHA: (71) implies:
% 249.18/58.86 | | | | | (72) all_252_1 = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | COMBINE_EQS: (31), (72) imply:
% 249.18/58.86 | | | | | (73) e2 = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | COMBINE_EQS: (39), (73) imply:
% 249.18/58.86 | | | | | (74) all_252_10 = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | REF_CLOSE: (1), (3), (4), (11), (15), (16), (20), (26), (43), (45),
% 249.18/58.86 | | | | | (46), (48), (49), (51), (64), (74) are inconsistent by
% 249.18/58.86 | | | | | sub-proof #231.
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | Case 2:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | (75) all_252_3 = e1 & op(e3, e3) = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | ALPHA: (75) implies:
% 249.18/58.86 | | | | | (76) all_252_3 = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | BETA: splitting (37) gives:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | Case 1:
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | (77) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 &
% 249.18/58.86 | | | | | | op(e3, e3) = e0)
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | REF_CLOSE: (7), (9), (11), (38), (52), (76), (77) are inconsistent
% 249.18/58.86 | | | | | | by sub-proof #126.
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | Case 2:
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | (78) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 249.18/58.86 | | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | BETA: splitting (78) gives:
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | Case 1:
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | | (79) all_252_7 = e0 & op(e2, e3) = e0
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | | REF_CLOSE: (14), (21), (79) are inconsistent by sub-proof #125.
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | Case 2:
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | | (80) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 249.18/58.86 | | | | | | | op(e0, e3) = e0)
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | | BETA: splitting (80) gives:
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | (81) all_252_13 = e0 & op(e1, e3) = e0
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | ALPHA: (81) implies:
% 249.18/58.86 | | | | | | | | (82) op(e1, e3) = e0
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | REF_CLOSE: (11), (30), (69), (82) are inconsistent by sub-proof
% 249.18/58.86 | | | | | | | | #592.
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | (83) all_252_21 = e0 & op(e0, e3) = e0
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | ALPHA: (83) implies:
% 249.18/58.86 | | | | | | | | (84) all_252_21 = e0
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | BETA: splitting (28) gives:
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | | (85) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3
% 249.18/58.86 | | | | | | | | | & op(e0, e3) = e3)
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | | REF_CLOSE: (12), (30), (41), (84), (85) are inconsistent by
% 249.18/58.86 | | | | | | | | | sub-proof #208.
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | | (86) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3
% 249.18/58.86 | | | | | | | | | & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) =
% 249.18/58.86 | | | | | | | | | e3)
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | | BETA: splitting (86) gives:
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | (87) all_252_22 = e3 & op(e0, e2) = e3
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | ALPHA: (87) implies:
% 249.18/58.86 | | | | | | | | | | (88) op(e0, e2) = e3
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | BETA: splitting (17) gives:
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | (89) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 249.18/58.86 | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | REF_CLOSE: (11), (19), (25), (35), (55), (89) are
% 249.18/58.86 | | | | | | | | | | | inconsistent by sub-proof #928.
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | (90) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 249.18/58.86 | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 249.18/58.86 | | | | | | | | | | | op(e0, e2) = e1)
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | BETA: splitting (90) gives:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | (91) all_252_8 = e1 & op(e2, e2) = e1
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | ALPHA: (91) implies:
% 249.18/58.86 | | | | | | | | | | | | (92) op(e2, e2) = e1
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | REF_CLOSE: (11), (15), (45), (92) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | sub-proof #690.
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | (93) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 249.18/58.86 | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | BETA: splitting (93) gives:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (94) all_252_14 = e1 & op(e1, e2) = e1
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (11), (50), (62), (94) are inconsistent
% 249.18/58.86 | | | | | | | | | | | | | by sub-proof #229.
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (95) all_252_22 = e1 & op(e0, e2) = e1
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | ALPHA: (95) implies:
% 249.18/58.86 | | | | | | | | | | | | | (96) op(e0, e2) = e1
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | REF_CLOSE: (11), (23), (33), (88), (96) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | | sub-proof #641.
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | (97) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 =
% 249.18/58.86 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | BETA: splitting (97) gives:
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | (98) all_252_23 = e3 & op(e0, e1) = e3
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | ALPHA: (98) implies:
% 249.18/58.86 | | | | | | | | | | | (99) op(e0, e1) = e3
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | REF_CLOSE: (11), (49), (57), (99) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | sub-proof #974.
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | (100) all_252_24 = e3 & op(e0, e0) = e3
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | ALPHA: (100) implies:
% 249.18/58.86 | | | | | | | | | | | (101) all_252_24 = e3
% 249.18/58.86 | | | | | | | | | | | (102) op(e0, e0) = e3
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | BETA: splitting (2) gives:
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | (103) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.18/58.86 | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | BETA: splitting (103) gives:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (104) all_252_20 = e4 & op(e0, e4) = e4
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | REF_CLOSE: (41), (54), (104) are inconsistent by sub-proof
% 249.18/58.86 | | | | | | | | | | | | | #543.
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (105) all_252_21 = e4 & op(e0, e3) = e4
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | REF_CLOSE: (11), (32), (40), (105) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | | sub-proof #805.
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | (106) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.18/58.86 | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.18/58.86 | | | | | | | | | | | | op(e0, e0) = e4)
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | BETA: splitting (106) gives:
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (107) all_252_22 = e4 & op(e0, e2) = e4
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | ALPHA: (107) implies:
% 249.18/58.86 | | | | | | | | | | | | | (108) op(e0, e2) = e4
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | BETA: splitting (22) gives:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | (109) all_252_24 = e0 & op(e0, e0) = e0
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | ALPHA: (109) implies:
% 249.18/58.86 | | | | | | | | | | | | | | (110) all_252_24 = e0
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (110) are inconsistent by sub-proof
% 249.18/58.86 | | | | | | | | | | | | | | #343.
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_28_2, e4, e2, e0,
% 249.18/58.86 | | | | | | | | | | | | | | simplifying with (23), (108) gives:
% 249.18/58.86 | | | | | | | | | | | | | | (111) all_28_2 = e4
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | REDUCE: (18), (111) imply:
% 249.18/58.86 | | | | | | | | | | | | | | (112) op(e1, e4) = e0
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | REF_CLOSE: (11), (27), (63), (112) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | | | sub-proof #278.
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | (113) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.18/58.86 | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | BETA: splitting (113) gives:
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | Case 1:
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | (114) all_252_23 = e4 & op(e0, e1) = e4
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | REF_CLOSE: (11), (49), (56), (114) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | | | sub-proof #912.
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | Case 2:
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | (115) all_252_24 = e4 & op(e0, e0) = e4
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | ALPHA: (115) implies:
% 249.18/58.86 | | | | | | | | | | | | | | (116) op(e0, e0) = e4
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (47), (102), (116) are inconsistent by
% 249.18/58.86 | | | | | | | | | | | | | | sub-proof #468.
% 249.18/58.86 | | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | | |
% 249.18/58.86 | | | | | | | | | End of split
% 249.18/58.86 | | | | | | | | |
% 249.18/58.86 | | | | | | | | End of split
% 249.18/58.86 | | | | | | | |
% 249.18/58.86 | | | | | | | End of split
% 249.18/58.86 | | | | | | |
% 249.18/58.86 | | | | | | End of split
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | End of split
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | End of split
% 249.18/58.86 | | | |
% 249.18/58.86 | | | Case 2:
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | (117) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1,
% 249.18/58.86 | | | | e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | BETA: splitting (117) gives:
% 249.18/58.86 | | | |
% 249.18/58.86 | | | | Case 1:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | (118) all_252_7 = e1 & op(e2, e3) = e1
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | REF_CLOSE: (21), (24), (118) are inconsistent by sub-proof #124.
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | Case 2:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | (119) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 249.18/58.86 | | | | | op(e0, e3) = e1)
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | BETA: splitting (119) gives:
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | | Case 1:
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | (120) all_252_13 = e1 & op(e1, e3) = e1
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | REF_CLOSE: (33), (68), (120) are inconsistent by sub-proof #823.
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | Case 2:
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | (121) all_252_21 = e1 & op(e0, e3) = e1
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | ALPHA: (121) implies:
% 249.18/58.86 | | | | | | (122) op(e0, e3) = e1
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | | REF_CLOSE: (11), (36), (40), (122) are inconsistent by sub-proof
% 249.18/58.86 | | | | | | #714.
% 249.18/58.86 | | | | | |
% 249.18/58.86 | | | | | End of split
% 249.18/58.86 | | | | |
% 249.18/58.86 | | | | End of split
% 249.18/58.86 | | | |
% 249.18/58.86 | | | End of split
% 249.18/58.86 | | |
% 249.18/58.86 | | End of split
% 249.18/58.86 | |
% 249.18/58.86 | Case 2:
% 249.18/58.86 | |
% 249.18/58.86 | | (123) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1)
% 249.18/58.86 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.18/58.86 | |
% 249.18/58.86 | | REF_CLOSE: (10), (11), (12), (27), (29), (34), (35), (42), (44), (48), (50),
% 249.18/58.86 | | (53), (55), (59), (60), (123) are inconsistent by sub-proof #734.
% 249.18/58.86 | |
% 249.18/58.86 | End of split
% 249.18/58.86 |
% 249.18/58.86 End of proof
% 249.18/58.86
% 249.18/58.86 Sub-proof #92 shows that the following formulas are inconsistent:
% 249.18/58.86 ----------------------------------------------------------------
% 249.18/58.86 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.18/58.86 all_250_23 = e0
% 249.18/58.86 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.18/58.86 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.18/58.86 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.18/58.86 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.18/58.86 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.18/58.86 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.18/58.86 (4) ~ (all_4_2 = e4)
% 249.18/58.86 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.18/58.86 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.18/58.86 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.18/58.86 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 249.18/58.86 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 249.18/58.86 (all_252_16 = e3 & op(e4, e0) = e3)
% 249.18/58.86 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.18/58.86 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.18/58.86 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.18/58.86 (8) ~ (all_244_24 = all_40_2)
% 249.18/58.86 (9) ~ (all_40_2 = all_38_2)
% 249.18/58.86 (10) ~ (all_244_8 = e0)
% 249.18/58.86 (11) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.18/58.86 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.18/58.86 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.18/58.86 (12) op(e4, e0) = all_30_2
% 249.18/58.86 (13) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.18/58.86 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.18/58.86 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.18/58.86 (14) all_252_6 = e0
% 249.18/58.86 (15) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.18/58.86 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.18/58.86 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.18/58.86 (16) ~ (all_22_2 = e2)
% 249.18/58.86 (17) all_94_2 = all_38_2
% 249.18/58.86 (18) op(all_38_2, e1) = e2
% 249.18/58.86 (19) ~ (e2 = e0)
% 249.18/58.86 (20) ~ (e1 = e0)
% 249.18/58.86 (21) ~ (all_28_2 = e3)
% 249.18/58.86 (22) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.18/58.86 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.18/58.86 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.18/58.86 (23) ~ (all_62_2 = e2)
% 249.18/58.86 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.18/58.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.18/58.86 (25) ~ (e3 = e2)
% 249.18/58.86 (26) op(e0, e0) = all_244_24
% 249.18/58.86 (27) ~ (e4 = e0)
% 249.18/58.86 (28) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.18/58.86 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.18/58.86 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.18/58.86 (29) op(all_244_8, all_244_8) = e2
% 249.18/58.86 (30) op(e2, e2) = all_244_8
% 249.18/58.86 (31) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.18/58.86 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.18/58.86 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.18/58.86 (32) op(e2, e1) = all_38_2
% 249.18/58.86 (33) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.18/58.86 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.18/58.86 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.18/58.86 (34) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.18/58.86 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.18/58.86 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.18/58.86 (35) op(e1, e0) = all_34_2
% 249.18/58.86 (36) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.18/58.86 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.18/58.86 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.18/58.86 (37) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.18/58.86 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.18/58.86 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.18/58.86 (38) ~ (all_40_2 = e4)
% 249.18/58.86 (39) ~ (all_36_2 = e2)
% 249.18/58.86 (40) op(e4, e2) = all_6_2
% 249.18/58.86 (41) ~ (all_34_2 = e2)
% 249.18/58.86 (42) ~ (e2 = e1)
% 249.18/58.86 (43) all_252_7 = e4
% 249.18/58.86 (44) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.18/58.86 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.18/58.86 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.18/58.86 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.18/58.86 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.18/58.86 op(e0, e1) = e0)))
% 249.18/58.86 (45) op(e0, e2) = all_28_2
% 249.18/58.86 (46) ~ (e4 = e1)
% 249.18/58.87 (47) ~ (all_244_0 = e2)
% 249.18/58.87 (48) ~ (all_6_2 = e1)
% 249.18/58.87 (49) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.18/58.87 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.18/58.87 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.18/58.87 (50) all_80_2 = all_6_2
% 249.18/58.87 (51) op(all_34_2, e0) = e1
% 249.18/58.87 (52) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 249.18/58.87 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 249.18/58.87 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 249.18/58.87 (53) op(e1, e4) = all_16_2
% 249.18/58.87 (54) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.18/58.87 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.18/58.87 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.18/58.87 (55) ~ (all_28_2 = all_20_2)
% 249.18/58.87 (56) op(e1, e3) = all_62_2
% 249.18/58.87 (57) ~ (e3 = e0)
% 249.18/58.87 (58) ~ (all_38_2 = e0)
% 249.18/58.87 (59) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.18/58.87 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.18/58.87 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.18/58.87 (60) ~ (all_30_2 = e2)
% 249.18/58.87 (61) all_252_1 = e2
% 249.18/58.87 (62) ~ (all_36_2 = e4)
% 249.18/58.87 (63) ~ (all_6_2 = e2)
% 249.18/58.87 (64) ~ (all_22_2 = e4)
% 249.18/58.87 (65) ~ (e3 = e1)
% 249.18/58.87 (66) op(e3, e1) = all_36_2
% 249.18/58.87 (67) ~ (all_16_2 = e2)
% 249.18/58.87 (68) ~ (all_8_2 = e1)
% 249.18/58.87 (69) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.18/58.87 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.18/58.87 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.18/58.87 (70) ~ (all_22_2 = e1)
% 249.18/58.87 (71) ~ (all_40_2 = all_34_2)
% 249.18/58.87 (72) op(e4, e3) = e2
% 249.18/58.87 (73) ~ (all_8_2 = e0)
% 249.18/58.87 (74) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 249.18/58.87 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 249.18/58.87 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 249.18/58.87 (75) all_74_2 = all_36_2
% 249.18/58.87 (76) ~ (all_38_2 = e4)
% 249.18/58.87 (77) ~ (all_28_2 = e2)
% 249.18/58.87 (78) op(all_6_2, e0) = e2
% 249.18/58.87 (79) op(e0, e3) = all_22_2
% 249.18/58.87 (80) ~ (all_40_2 = e0)
% 249.18/58.87 (81) op(all_34_2, all_20_2) = e0
% 249.18/58.87 (82) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 249.18/58.87 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 249.18/58.87 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.18/58.87 (83) all_252_20 = e2
% 249.18/58.87 (84) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.18/58.87 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.18/58.87 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.18/58.87 (85) op(e4, e1) = all_26_2
% 249.18/58.87 (86) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.18/58.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.18/58.87 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.18/58.87 (87) op(e3, e4) = all_100_2
% 249.18/58.87 (88) op(e4, e4) = all_244_0
% 249.18/58.87 (89) ~ (e4 = e3)
% 249.18/58.87 (90) op(e0, e1) = all_20_2
% 249.18/58.87 (91) ~ (all_26_2 = e3)
% 249.18/58.87 (92) all_82_2 = all_28_2
% 249.18/58.87 (93) ~ (all_244_24 = e2)
% 249.18/58.87 (94) op(e1, e2) = all_4_2
% 249.18/58.87 (95) op(e4, e3) = all_84_2
% 249.18/58.87 (96) all_86_2 = all_40_2
% 249.18/58.87 (97) ~ (e4 = e2)
% 249.18/58.87 (98) op(e3, e2) = all_8_2
% 249.18/58.87 (99) op(all_36_2, e1) = e3
% 249.18/58.87 (100) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.18/58.87 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.18/58.87 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.18/58.87 (101) ~ (all_20_2 = e4)
% 249.18/58.87 (102) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.18/58.87 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.18/58.87 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.18/58.87 (103) op(e2, e0) = all_40_2
% 249.18/58.87 (104) ~ (all_20_2 = e3)
% 249.18/58.87 (105) ~ (all_16_2 = e3)
% 249.18/58.87 (106) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.18/58.87 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.18/58.87 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.18/58.87 (107) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.18/58.87 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.18/58.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.18/58.87 (108) ~ (all_4_2 = e3)
% 249.18/58.87 (109) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.18/58.87 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.18/58.87 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.18/58.87 (110) ~ (all_62_2 = e4)
% 249.18/58.87 (111) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.18/58.87 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.18/58.87 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.18/58.87 (112) ~ (all_16_2 = e0)
% 249.18/58.87 (113) ~ (all_20_2 = e2)
% 249.18/58.87 (114) all_250_23 = all_20_2
% 249.18/58.87
% 249.18/58.87 Begin of proof
% 249.18/58.87 |
% 249.18/58.87 | BETA: splitting (2) gives:
% 249.18/58.87 |
% 249.18/58.87 | Case 1:
% 249.18/58.87 | |
% 249.18/58.87 | | (115) ~ (all_74_2 = e0)
% 249.18/58.87 | |
% 249.18/58.87 | | REDUCE: (75), (115) imply:
% 249.18/58.87 | | (116) ~ (all_36_2 = e0)
% 249.18/58.87 | |
% 249.18/58.87 | | BETA: splitting (15) gives:
% 249.18/58.87 | |
% 249.18/58.87 | | Case 1:
% 249.18/58.87 | | |
% 249.18/58.87 | | | (117) ~ (all_82_2 = e1)
% 249.18/58.87 | | |
% 249.18/58.87 | | | REDUCE: (92), (117) imply:
% 249.18/58.87 | | | (118) ~ (all_28_2 = e1)
% 249.18/58.87 | | |
% 249.18/58.87 | | | BETA: splitting (36) gives:
% 249.18/58.87 | | |
% 249.18/58.87 | | | Case 1:
% 249.18/58.87 | | | |
% 249.18/58.87 | | | | (119) ~ (all_80_2 = e0)
% 249.18/58.87 | | | |
% 249.18/58.87 | | | | REDUCE: (50), (119) imply:
% 249.18/58.87 | | | | (120) ~ (all_6_2 = e0)
% 249.18/58.87 | | | |
% 249.18/58.87 | | | | BETA: splitting (28) gives:
% 249.18/58.87 | | | |
% 249.18/58.87 | | | | Case 1:
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | (121) ~ (all_86_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | REDUCE: (96), (121) imply:
% 249.18/58.87 | | | | | (122) ~ (all_40_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | BETA: splitting (22) gives:
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | Case 1:
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | (123) ~ (all_94_2 = e3)
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | REDUCE: (17), (123) imply:
% 249.18/58.87 | | | | | | (124) ~ (all_38_2 = e3)
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | BETA: splitting (31) gives:
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | Case 1:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | (125) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 &
% 249.18/58.87 | | | | | | | op(e2, e3) = e3)
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | REF_CLOSE: (14), (43), (57), (89), (125) are inconsistent by
% 249.18/58.87 | | | | | | | sub-proof #101.
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | Case 2:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | (126) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 249.18/58.87 | | | | | | | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | BETA: splitting (126) gives:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | (127) all_252_8 = e3 & op(e2, e2) = e3
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | ALPHA: (127) implies:
% 249.18/58.87 | | | | | | | | (128) all_252_8 = e3
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (14), (16), (19), (20),
% 249.18/58.87 | | | | | | | | (21), (23), (24), (25), (26), (27), (29), (30), (32),
% 249.18/58.87 | | | | | | | | (33), (35), (37), (40), (41), (42), (44), (45), (46),
% 249.18/58.87 | | | | | | | | (47), (48), (49), (52), (53), (54), (56), (57), (58),
% 249.18/58.87 | | | | | | | | (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 249.18/58.87 | | | | | | | | (69), (70), (72), (73), (74), (76), (77), (79), (83),
% 249.18/58.87 | | | | | | | | (85), (86), (87), (88), (89), (90), (91), (93), (94),
% 249.18/58.87 | | | | | | | | (95), (97), (98), (100), (101), (102), (104), (105),
% 249.18/58.87 | | | | | | | | (106), (107), (111), (116), (118), (120), (128) are
% 249.18/58.87 | | | | | | | | inconsistent by sub-proof #95.
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | (129) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3
% 249.18/58.87 | | | | | | | | & op(e2, e0) = e3)
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | BETA: splitting (129) gives:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | (130) all_252_11 = e3 & op(e2, e1) = e3
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | REF_CLOSE: (24), (32), (124), (130) are inconsistent by
% 249.18/58.87 | | | | | | | | | sub-proof #900.
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | (131) all_252_18 = e3 & op(e2, e0) = e3
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | REF_CLOSE: (24), (103), (122), (131) are inconsistent by
% 249.18/58.87 | | | | | | | | | sub-proof #899.
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | End of split
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | End of split
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | End of split
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | Case 2:
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | (132) all_94_2 = e3
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | REF_CLOSE: (17), (18), (24), (39), (66), (132) are inconsistent by
% 249.18/58.87 | | | | | | sub-proof #983.
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | End of split
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | Case 2:
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | (133) all_86_2 = e3
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | COMBINE_EQS: (96), (133) imply:
% 249.18/58.87 | | | | | (134) all_40_2 = e3
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | REDUCE: (8), (134) imply:
% 249.18/58.87 | | | | | (135) ~ (all_244_24 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | REDUCE: (9), (134) imply:
% 249.18/58.87 | | | | | (136) ~ (all_38_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | SIMP: (136) implies:
% 249.18/58.87 | | | | | (137) ~ (all_38_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | REDUCE: (71), (134) imply:
% 249.18/58.87 | | | | | (138) ~ (all_34_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | SIMP: (138) implies:
% 249.18/58.87 | | | | | (139) ~ (all_34_2 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | REDUCE: (38), (134) imply:
% 249.18/58.87 | | | | | (140) ~ (e4 = e3)
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | BETA: splitting (54) gives:
% 249.18/58.87 | | | | |
% 249.18/58.87 | | | | | Case 1:
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | (141) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 249.18/58.87 | | | | | | op(e0, e3) = e3)
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | BETA: splitting (141) gives:
% 249.18/58.87 | | | | | |
% 249.18/58.87 | | | | | | Case 1:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | (142) all_252_20 = e3 & op(e0, e4) = e3
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | ALPHA: (142) implies:
% 249.18/58.87 | | | | | | | (143) all_252_20 = e3
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | REF_CLOSE: (25), (83), (143) are inconsistent by sub-proof #520.
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | Case 2:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | (144) all_252_21 = e3 & op(e0, e3) = e3
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | ALPHA: (144) implies:
% 249.18/58.87 | | | | | | | (145) all_252_21 = e3
% 249.18/58.87 | | | | | | | (146) op(e0, e3) = e3
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | BETA: splitting (31) gives:
% 249.18/58.87 | | | | | | |
% 249.18/58.87 | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | (147) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 &
% 249.18/58.87 | | | | | | | | op(e2, e3) = e3)
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | REF_CLOSE: (14), (43), (57), (89), (147) are inconsistent by
% 249.18/58.87 | | | | | | | | sub-proof #101.
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | (148) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 249.18/58.87 | | | | | | | | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) =
% 249.18/58.87 | | | | | | | | e3)
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | BETA: splitting (148) gives:
% 249.18/58.87 | | | | | | | |
% 249.18/58.87 | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | (149) all_252_8 = e3 & op(e2, e2) = e3
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | ALPHA: (149) implies:
% 249.18/58.87 | | | | | | | | | (150) all_252_8 = e3
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (14), (16), (19), (20),
% 249.18/58.87 | | | | | | | | | (21), (23), (24), (25), (26), (27), (29), (30),
% 249.18/58.87 | | | | | | | | | (32), (33), (35), (37), (40), (41), (42), (44),
% 249.18/58.87 | | | | | | | | | (45), (46), (47), (48), (49), (52), (53), (54),
% 249.18/58.87 | | | | | | | | | (56), (57), (58), (59), (61), (62), (63), (64),
% 249.18/58.87 | | | | | | | | | (65), (66), (67), (68), (69), (70), (72), (73),
% 249.18/58.87 | | | | | | | | | (74), (76), (77), (79), (83), (85), (86), (87),
% 249.18/58.87 | | | | | | | | | (88), (89), (90), (91), (93), (94), (95), (97),
% 249.18/58.87 | | | | | | | | | (98), (100), (101), (102), (104), (105), (106),
% 249.18/58.87 | | | | | | | | | (107), (111), (116), (118), (120), (150) are
% 249.18/58.87 | | | | | | | | | inconsistent by sub-proof #95.
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | (151) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 =
% 249.18/58.87 | | | | | | | | | e3 & op(e2, e0) = e3)
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | BETA: splitting (151) gives:
% 249.18/58.87 | | | | | | | | |
% 249.18/58.87 | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | (152) all_252_11 = e3 & op(e2, e1) = e3
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | REF_CLOSE: (24), (32), (137), (152) are inconsistent by
% 249.18/58.87 | | | | | | | | | | sub-proof #900.
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | (153) all_252_18 = e3 & op(e2, e0) = e3
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | ALPHA: (153) implies:
% 249.18/58.87 | | | | | | | | | | (154) all_252_18 = e3
% 249.18/58.87 | | | | | | | | | | (155) op(e2, e0) = e3
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | BETA: splitting (34) gives:
% 249.18/58.87 | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | (156) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 249.18/58.87 | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 249.18/58.87 | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | BETA: splitting (156) gives:
% 249.18/58.87 | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | (157) all_252_16 = e2 & op(e4, e0) = e2
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | ALPHA: (157) implies:
% 249.18/58.87 | | | | | | | | | | | | (158) op(e4, e0) = e2
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | REF_CLOSE: (12), (24), (60), (158) are inconsistent by
% 249.18/58.87 | | | | | | | | | | | | sub-proof #830.
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | (159) all_252_17 = e2 & op(e3, e0) = e2
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | ALPHA: (159) implies:
% 249.18/58.87 | | | | | | | | | | | | (160) all_252_17 = e2
% 249.18/58.87 | | | | | | | | | | | | (161) op(e3, e0) = e2
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | BETA: splitting (7) gives:
% 249.18/58.87 | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | (162) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 =
% 249.18/58.87 | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 249.18/58.87 | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | BETA: splitting (162) gives:
% 249.18/58.87 | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | (163) all_252_2 = e0 & op(e3, e4) = e0
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | ALPHA: (163) implies:
% 249.18/58.87 | | | | | | | | | | | | | | (164) all_252_2 = e0
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (24), (25), (27), (42), (46), (53),
% 249.18/58.87 | | | | | | | | | | | | | | (57), (65), (83), (89), (97), (100), (102), (105),
% 249.18/58.87 | | | | | | | | | | | | | | (111), (164) are inconsistent by sub-proof #538.
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | (165) all_252_3 = e0 & op(e3, e3) = e0
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | ALPHA: (165) implies:
% 249.18/58.87 | | | | | | | | | | | | | | (166) all_252_3 = e0
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 249.18/58.87 | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | (167) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 249.18/58.87 | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | (168) all_252_1 = e1 & op(e4, e3) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (61), (168) are inconsistent by sub-proof
% 249.18/58.87 | | | | | | | | | | | | | | | | #127.
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | (169) all_252_3 = e1 & op(e3, e3) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | (170) all_252_3 = e1
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (170) imply:
% 249.18/58.87 | | | | | | | | | | | | | | | | (171) e1 = e0
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | SIMP: (171) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | (172) e1 = e0
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | REDUCE: (20), (172) imply:
% 249.18/58.87 | | | | | | | | | | | | | | | | (173) $false
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | End of split
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | (174) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 249.18/58.87 | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 249.18/58.87 | | | | | | | | | | | | | | | op(e0, e3) = e1)
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 249.18/58.87 | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | (175) all_252_7 = e1 & op(e2, e3) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (175) are inconsistent by sub-proof
% 249.18/58.87 | | | | | | | | | | | | | | | | #124.
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | (176) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 249.18/58.87 | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | (177) all_252_13 = e1 & op(e1, e3) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | (178) all_252_13 = e1
% 249.18/58.87 | | | | | | | | | | | | | | | | | (179) op(e1, e3) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | (180) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 249.18/58.87 | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | (181) all_252_12 = e3 & op(e1, e4) = e3
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (53), (105), (181) are inconsistent by
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | sub-proof #895.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | (182) all_252_13 = e3 & op(e1, e3) = e3
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (178), (182) are inconsistent by sub-proof
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | #944.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | (183) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 249.18/58.87 | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 249.18/58.87 | | | | | | | | | | | | | | | | | | op(e1, e0) = e3)
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | (184) all_252_14 = e3 & op(e1, e2) = e3
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (94), (108), (184) are inconsistent by
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | sub-proof #858.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | (185) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | (186) all_252_15 = e3 & op(e1, e1) = e3
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | (187) all_252_15 = e3
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | (188) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (24), (53), (56), (67), (188) are
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | (189) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | (190) all_252_14 = e2 & op(e1, e2) = e2
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | (191) all_252_14 = e2
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | (192) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_9 = e4 & op(e4, e1) = e4
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_9 = e4
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | (195) op(e4, e1) = e4
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | (196) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 =
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (20), (24), (25), (27), (42), (46),
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | (53), (57), (65), (72), (83), (87), (89), (95),
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | (97), (100), (102), (105), (111), (196) are
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | (197) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 =
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 &
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e0)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_252_4 = e0 & op(e4, e2) = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (40), (120), (198) are inconsistent by
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (199) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 =
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e0) = e0)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_9 = e0 & op(e4, e1) = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) op(e4, e1) = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (85), (195), (201) are inconsistent by
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #286.
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_16 = e0 & op(e4, e0) = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_16 = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_0 = e1 & op(e4, e4) = e1
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_0 = e1
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0)
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_12 = e0 & op(e1, e4) = e0
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) op(e1, e4) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (53), (112), (209) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #278.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_13 = e0 & op(e1, e3) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) op(e1, e3) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (24), (56), (179), (211) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #94.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_252_14 = e0 & op(e1, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (191), (213) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #93.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_15 = e0 & op(e1, e1) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_252_15 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (187), (216) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #196.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_19 = e0 & op(e1, e0) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_19 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_4 = e0 & op(e4, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (40), (120), (220) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_5 = e0 & op(e3, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (73), (98), (221) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #874.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_8 = e0 & op(e2, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) op(e2, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (24), (30), (224) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_252_14 = e0 & op(e1, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (191), (226) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #93.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_22 = e0 & op(e0, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) op(e0, e2) = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_12 = e4 & op(e1, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_252_12 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) op(e1, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_0 = e3 & op(e4, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (206), (234) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_2 = e3 & op(e3, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_252_2 = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) op(e3, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_252_16 = e1 & op(e4, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_252_16 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (240) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e1 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (241) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_0 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (24), (27), (42), (46), (65), (83),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (87), (89), (97), (102), (111), (236), (237),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) are inconsistent by sub-proof #100.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_252_17 = e1 & op(e3, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) op(e3, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (42), (161), (244) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #427.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_252_18 = e1 & op(e2, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) op(e2, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (65), (155), (247) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #399.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_252_19 = e1 & op(e1, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_252_19 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (250) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e1 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (251) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) e1 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (252) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_252_0 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (24), (27), (42), (46), (65), (83),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (87), (89), (97), (102), (111), (236), (237),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) are inconsistent by sub-proof #100.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_252_24 = e1 & op(e0, e0) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_252_24 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_252_20 = e4 & op(e0, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_252_20 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (258) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) e4 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (259) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e4 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (260) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_252_12 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e4) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_252_0 = e4 & op(e4, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_252_0 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (264) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) e4 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (266) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) $false
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_252_2 = e1 & op(e3, e4) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_252_2 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (236), (269) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #388.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_252_6 = e1 & op(e2, e4) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (271) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #545.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_252_12 = e1 & op(e1, e4) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (261), (273) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #393.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_252_20 = e1 & op(e0, e4) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (83), (274) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #544.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_252_2 = e4 & op(e3, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_252_2 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (236), (276) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #838.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_252_6 = e4 & op(e2, e4) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (27), (278) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #938.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e4) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (260) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) $false
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (97), (257) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #543.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_21 = e4 & op(e0, e3) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) op(e0, e3) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (89), (146), (282) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #964.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_252_22 = e4 & op(e0, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) op(e0, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (45), (228), (285) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #854.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_252_23 = e4 & op(e0, e1) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (90), (101), (287) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_252_24 = e4 & op(e0, e0) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_252_24 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (289) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) e4 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (290) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_252_12 = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (231), (291) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #554.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_252_13 = e4 & op(e1, e3) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (56), (110), (292) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #952.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_252_14 = e4 & op(e1, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) op(e1, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (94), (295) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_252_15 = e4 & op(e1, e1) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_252_15 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (187), (298) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #675.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_252_19 = e4 & op(e1, e0) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_252_19 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (218), (300) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_252_6 = e3 & op(e2, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_252_6 = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (57), (303) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #691.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_252_12 = e3 & op(e1, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) op(e1, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (89), (232), (306) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #603.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_252_20 = e3 & op(e0, e4) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_252_20 = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (308) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) e3 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) e3 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (310) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_252_21 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19), (20), (21), (24), (25), (27), (42),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (54), (57), (64), (65), (69),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (79), (83), (89), (90), (97), (101), (104),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) are inconsistent by sub-proof #524.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_252_13 = e4 & op(e1, e3) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (56), (110), (312) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #952.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_252_14 = e4 & op(e1, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) op(e1, e2) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (94), (315) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_252_15 = e4 & op(e1, e1) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (89), (187), (317) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #678.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_252_19 = e4 & op(e1, e0) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_252_19 = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (319) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) e4 = e0
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (320) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) $false
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_252_1 = e1 & op(e4, e3) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (61), (322) are inconsistent by sub-proof
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #127.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (24), (40), (46), (48), (194), (203), (323)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #96.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | (324) all_252_10 = e4 & op(e3, e1) = e4
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (62), (66), (324) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (325) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (32), (76), (89), (90), (101), (187), (325)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #673.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | (326) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_15 = e2 & op(e1, e1) = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (328) all_252_15 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (328) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (329) e3 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (329) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (330) e3 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (330) imply:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (331) all_252_21 = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19), (20), (21), (24), (25), (27), (42),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (46), (54), (57), (64), (65), (69),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (70), (79), (83), (89), (90), (97), (101), (104),
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (331) are inconsistent by sub-proof #524.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (332) all_252_19 = e2 & op(e1, e0) = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | (333) op(e1, e0) = e2
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (35), (41), (333) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #909.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | (334) all_252_19 = e3 & op(e1, e0) = e3
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (35), (139), (334) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | | sub-proof #836.
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | (335) all_252_21 = e1 & op(e0, e3) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 249.18/58.88 | | | | | | | | | | | | | | | | | (336) op(e0, e3) = e1
% 249.18/58.88 | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (65), (146), (336) are inconsistent by
% 249.18/58.88 | | | | | | | | | | | | | | | | | sub-proof #590.
% 249.18/58.88 | | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | End of split
% 249.18/58.88 | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | Case 2:
% 249.18/58.88 | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | (337) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 =
% 249.18/58.88 | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 &
% 249.18/58.88 | | | | | | | | | | | | | op(e3, e0) = e0)
% 249.18/58.88 | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | BETA: splitting (337) gives:
% 249.18/58.88 | | | | | | | | | | | | |
% 249.18/58.88 | | | | | | | | | | | | | Case 1:
% 249.18/58.88 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (338) all_252_5 = e0 & op(e3, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | REF_CLOSE: (24), (73), (98), (338) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | sub-proof #874.
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (339) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17
% 249.18/58.89 | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | (340) all_252_10 = e0 & op(e3, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | REF_CLOSE: (24), (66), (116), (340) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | | sub-proof #726.
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | (341) all_252_17 = e0 & op(e3, e0) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | REF_CLOSE: (19), (160), (341) are inconsistent by sub-proof
% 249.18/58.89 | | | | | | | | | | | | | | | #180.
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | (342) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 249.18/58.89 | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 249.18/58.89 | | | | | | | | | | | op(e0, e0) = e2)
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | BETA: splitting (342) gives:
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | (343) all_252_18 = e2 & op(e2, e0) = e2
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | ALPHA: (343) implies:
% 249.18/58.89 | | | | | | | | | | | | (344) all_252_18 = e2
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | COMBINE_EQS: (154), (344) imply:
% 249.18/58.89 | | | | | | | | | | | | (345) e3 = e2
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | COMBINE_EQS: (145), (345) imply:
% 249.18/58.89 | | | | | | | | | | | | (346) all_252_21 = e2
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | REF_CLOSE: (5), (19), (20), (21), (24), (25), (27), (42),
% 249.18/58.89 | | | | | | | | | | | | (44), (45), (46), (54), (57), (64), (65), (69),
% 249.18/58.89 | | | | | | | | | | | | (70), (79), (83), (89), (90), (97), (101), (104),
% 249.18/58.89 | | | | | | | | | | | | (346) are inconsistent by sub-proof #524.
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | (347) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 249.18/58.89 | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | REF_CLOSE: (24), (26), (35), (41), (93), (347) are
% 249.18/58.89 | | | | | | | | | | | | inconsistent by sub-proof #652.
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | |
% 249.18/58.89 | | | | | | | | End of split
% 249.18/58.89 | | | | | | | |
% 249.18/58.89 | | | | | | | End of split
% 249.18/58.89 | | | | | | |
% 249.18/58.89 | | | | | | End of split
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | Case 2:
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | (348) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 249.18/58.89 | | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | REF_CLOSE: (21), (24), (26), (45), (90), (104), (135), (348) are
% 249.18/58.89 | | | | | | inconsistent by sub-proof #743.
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | End of split
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | End of split
% 249.18/58.89 | | | |
% 249.18/58.89 | | | Case 2:
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | (349) all_80_2 = e0
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | COMBINE_EQS: (50), (349) imply:
% 249.18/58.89 | | | | (350) all_6_2 = e0
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | REDUCE: (78), (350) imply:
% 249.18/58.89 | | | | (351) op(e0, e0) = e2
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | REF_CLOSE: (24), (26), (93), (351) are inconsistent by sub-proof #978.
% 249.18/58.89 | | | |
% 249.18/58.89 | | | End of split
% 249.18/58.89 | | |
% 249.18/58.89 | | Case 2:
% 249.18/58.89 | | |
% 249.18/58.89 | | | (352) all_82_2 = e1
% 249.18/58.89 | | |
% 249.18/58.89 | | | COMBINE_EQS: (92), (352) imply:
% 249.18/58.89 | | | (353) all_28_2 = e1
% 249.18/58.89 | | |
% 249.18/58.89 | | | REDUCE: (55), (353) imply:
% 249.18/58.89 | | | (354) ~ (all_20_2 = e1)
% 249.18/58.89 | | |
% 249.18/58.89 | | | SIMP: (354) implies:
% 249.18/58.89 | | | (355) ~ (all_20_2 = e1)
% 249.18/58.89 | | |
% 249.18/58.89 | | | REF_CLOSE: (1), (24), (51), (81), (101), (104), (113), (114), (355) are
% 249.18/58.89 | | | inconsistent by sub-proof #780.
% 249.18/58.89 | | |
% 249.18/58.89 | | End of split
% 249.18/58.89 | |
% 249.18/58.89 | Case 2:
% 249.18/58.89 | |
% 249.18/58.89 | | (356) all_74_2 = e0
% 249.18/58.89 | |
% 249.18/58.89 | | COMBINE_EQS: (75), (356) imply:
% 249.18/58.89 | | (357) all_36_2 = e0
% 249.18/58.89 | |
% 249.18/58.89 | | SIMP: (357) implies:
% 249.18/58.89 | | (358) all_36_2 = e0
% 249.18/58.89 | |
% 249.18/58.89 | | REDUCE: (99), (358) imply:
% 249.18/58.89 | | (359) op(e0, e1) = e3
% 249.18/58.89 | |
% 249.18/58.89 | | REF_CLOSE: (24), (90), (104), (359) are inconsistent by sub-proof #974.
% 249.18/58.89 | |
% 249.18/58.89 | End of split
% 249.18/58.89 |
% 249.18/58.89 End of proof
% 249.18/58.89
% 249.18/58.89 Sub-proof #93 shows that the following formulas are inconsistent:
% 249.18/58.89 ----------------------------------------------------------------
% 249.18/58.89 (1) all_252_14 = e0 & op(e1, e2) = e0
% 249.18/58.89 (2) all_252_14 = e2
% 249.18/58.89 (3) ~ (e2 = e0)
% 249.18/58.89
% 249.18/58.89 Begin of proof
% 249.18/58.89 |
% 249.18/58.89 | ALPHA: (1) implies:
% 249.18/58.89 | (4) all_252_14 = e0
% 249.18/58.89 |
% 249.18/58.89 | COMBINE_EQS: (2), (4) imply:
% 249.18/58.89 | (5) e2 = e0
% 249.18/58.89 |
% 249.18/58.89 | SIMP: (5) implies:
% 249.18/58.89 | (6) e2 = e0
% 249.18/58.89 |
% 249.18/58.89 | REDUCE: (3), (6) imply:
% 249.18/58.89 | (7) $false
% 249.18/58.89 |
% 249.18/58.89 | CLOSE: (7) is inconsistent.
% 249.18/58.89 |
% 249.18/58.89 End of proof
% 249.18/58.89
% 249.18/58.89 Sub-proof #94 shows that the following formulas are inconsistent:
% 249.18/58.89 ----------------------------------------------------------------
% 249.18/58.89 (1) op(e1, e3) = e0
% 249.18/58.89 (2) ~ (e1 = e0)
% 249.18/58.89 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.18/58.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.18/58.89 (4) op(e1, e3) = all_62_2
% 249.18/58.89 (5) op(e1, e3) = e1
% 249.18/58.89
% 249.18/58.89 Begin of proof
% 249.18/58.89 |
% 249.18/58.89 | GROUND_INST: instantiating (3) with all_62_2, e0, e3, e1, simplifying with
% 249.18/58.89 | (1), (4) gives:
% 249.18/58.89 | (6) all_62_2 = e0
% 249.18/58.89 |
% 249.18/58.89 | GROUND_INST: instantiating (3) with all_62_2, e1, e3, e1, simplifying with
% 249.18/58.89 | (4), (5) gives:
% 249.18/58.89 | (7) all_62_2 = e1
% 249.18/58.89 |
% 249.18/58.89 | COMBINE_EQS: (6), (7) imply:
% 249.18/58.89 | (8) e1 = e0
% 249.18/58.89 |
% 249.18/58.89 | REDUCE: (2), (8) imply:
% 249.18/58.89 | (9) $false
% 249.18/58.89 |
% 249.18/58.89 | CLOSE: (9) is inconsistent.
% 249.18/58.89 |
% 249.18/58.89 End of proof
% 249.18/58.89
% 249.18/58.89 Sub-proof #95 shows that the following formulas are inconsistent:
% 249.18/58.89 ----------------------------------------------------------------
% 249.18/58.89 (1) ~ (all_4_2 = e4)
% 249.18/58.89 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.18/58.89 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.18/58.89 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.18/58.89 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 249.18/58.89 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 249.18/58.89 (all_252_16 = e3 & op(e4, e0) = e3)
% 249.18/58.89 (4) ~ (all_244_8 = e0)
% 249.18/58.89 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.18/58.89 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.18/58.89 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.18/58.89 (6) all_252_6 = e0
% 249.18/58.89 (7) ~ (all_22_2 = e2)
% 249.18/58.89 (8) ~ (e2 = e0)
% 249.18/58.89 (9) ~ (e1 = e0)
% 249.18/58.89 (10) ~ (all_28_2 = e3)
% 249.18/58.89 (11) ~ (all_62_2 = e2)
% 249.18/58.89 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.18/58.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.18/58.89 (13) ~ (e3 = e2)
% 249.18/58.89 (14) op(e0, e0) = all_244_24
% 249.18/58.89 (15) ~ (e4 = e0)
% 249.18/58.89 (16) op(all_244_8, all_244_8) = e2
% 249.18/58.89 (17) op(e2, e2) = all_244_8
% 249.18/58.89 (18) op(e2, e1) = all_38_2
% 249.18/58.89 (19) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.18/58.89 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.18/58.89 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.18/58.89 (20) op(e1, e0) = all_34_2
% 249.18/58.89 (21) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.18/58.89 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.18/58.89 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.18/58.89 (22) op(e4, e2) = all_6_2
% 249.18/58.89 (23) all_252_8 = e3
% 249.18/58.89 (24) ~ (all_34_2 = e2)
% 249.18/58.89 (25) ~ (e2 = e1)
% 249.18/58.89 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.18/58.89 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.18/58.89 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.18/58.89 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.18/58.89 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.18/58.89 op(e0, e1) = e0)))
% 249.18/58.89 (27) op(e0, e2) = all_28_2
% 249.18/58.89 (28) ~ (e4 = e1)
% 249.18/58.89 (29) ~ (all_244_0 = e2)
% 249.18/58.89 (30) ~ (all_28_2 = e1)
% 249.18/58.89 (31) ~ (all_6_2 = e1)
% 249.18/58.89 (32) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.18/58.89 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.18/58.89 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.18/58.89 (33) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 249.18/58.89 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 249.18/58.89 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 249.18/58.89 (34) op(e1, e4) = all_16_2
% 249.18/58.89 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.18/58.89 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.18/58.89 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.18/58.89 (36) op(e1, e3) = all_62_2
% 249.18/58.89 (37) ~ (e3 = e0)
% 249.18/58.89 (38) ~ (all_38_2 = e0)
% 249.18/58.89 (39) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.18/58.89 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.18/58.89 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.18/58.89 (40) all_252_1 = e2
% 249.18/58.89 (41) ~ (all_36_2 = e4)
% 249.18/58.89 (42) ~ (all_6_2 = e2)
% 249.18/58.89 (43) ~ (all_22_2 = e4)
% 249.18/58.89 (44) ~ (e3 = e1)
% 249.18/58.89 (45) op(e3, e1) = all_36_2
% 249.18/58.89 (46) ~ (all_16_2 = e2)
% 249.18/58.89 (47) ~ (all_8_2 = e1)
% 249.18/58.89 (48) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.18/58.89 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.18/58.89 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.18/58.89 (49) ~ (all_22_2 = e1)
% 249.18/58.89 (50) op(e4, e3) = e2
% 249.18/58.89 (51) ~ (all_8_2 = e0)
% 249.18/58.89 (52) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 249.18/58.89 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 249.18/58.89 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 249.18/58.89 (53) ~ (all_38_2 = e4)
% 249.18/58.89 (54) ~ (all_28_2 = e2)
% 249.18/58.89 (55) op(e0, e3) = all_22_2
% 249.18/58.89 (56) all_252_20 = e2
% 249.18/58.89 (57) op(e4, e1) = all_26_2
% 249.18/58.89 (58) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.18/58.89 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.18/58.89 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.18/58.89 (59) op(e3, e4) = all_100_2
% 249.18/58.89 (60) ~ (all_36_2 = e0)
% 249.18/58.89 (61) op(e4, e4) = all_244_0
% 249.18/58.89 (62) ~ (e4 = e3)
% 249.18/58.89 (63) op(e0, e1) = all_20_2
% 249.18/58.89 (64) ~ (all_26_2 = e3)
% 249.18/58.89 (65) ~ (all_244_24 = e2)
% 249.18/58.89 (66) op(e1, e2) = all_4_2
% 249.18/58.89 (67) op(e4, e3) = all_84_2
% 249.18/58.89 (68) ~ (e4 = e2)
% 249.18/58.89 (69) ~ (all_6_2 = e0)
% 249.18/58.89 (70) op(e3, e2) = all_8_2
% 249.18/58.89 (71) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.18/58.89 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.18/58.89 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.18/58.89 (72) ~ (all_20_2 = e4)
% 249.18/58.89 (73) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.18/58.89 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.18/58.89 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.18/58.89 (74) ~ (all_20_2 = e3)
% 249.18/58.89 (75) ~ (all_16_2 = e3)
% 249.18/58.89 (76) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.18/58.89 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.18/58.89 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.18/58.89 (77) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.18/58.89 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.18/58.89 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.18/58.89 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.18/58.89 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.18/58.89 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.18/58.89
% 249.18/58.89 Begin of proof
% 249.18/58.89 |
% 249.18/58.89 | BETA: splitting (19) gives:
% 249.18/58.89 |
% 249.18/58.89 | Case 1:
% 249.18/58.89 | |
% 249.18/58.89 | | (79) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 249.18/58.89 | | e1)
% 249.18/58.89 | |
% 249.18/58.89 | | REF_CLOSE: (12), (22), (31), (47), (70), (79) are inconsistent by sub-proof
% 249.18/58.89 | | #928.
% 249.18/58.89 | |
% 249.18/58.89 | Case 2:
% 249.18/58.89 | |
% 249.18/58.89 | | (80) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.18/58.89 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.18/58.89 | |
% 249.18/58.89 | | BETA: splitting (80) gives:
% 249.18/58.89 | |
% 249.18/58.89 | | Case 1:
% 249.18/58.89 | | |
% 249.18/58.89 | | | (81) all_252_8 = e1 & op(e2, e2) = e1
% 249.18/58.89 | | |
% 249.18/58.89 | | | REF_CLOSE: (23), (44), (81) are inconsistent by sub-proof #522.
% 249.18/58.89 | | |
% 249.18/58.89 | | Case 2:
% 249.18/58.89 | | |
% 249.18/58.89 | | | (82) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 249.18/58.89 | | | e2) = e1)
% 249.18/58.89 | | |
% 249.18/58.89 | | | BETA: splitting (82) gives:
% 249.18/58.89 | | |
% 249.18/58.89 | | | Case 1:
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | (83) all_252_14 = e1 & op(e1, e2) = e1
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | ALPHA: (83) implies:
% 249.18/58.89 | | | | (84) all_252_14 = e1
% 249.18/58.89 | | | | (85) op(e1, e2) = e1
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | BETA: splitting (76) gives:
% 249.18/58.89 | | | |
% 249.18/58.89 | | | | Case 1:
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | | (86) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 &
% 249.18/58.89 | | | | | op(e1, e3) = e2)
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | | REF_CLOSE: (11), (12), (34), (36), (46), (86) are inconsistent by
% 249.18/58.89 | | | | | sub-proof #925.
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | Case 2:
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | | (87) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 249.18/58.89 | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | | BETA: splitting (87) gives:
% 249.18/58.89 | | | | |
% 249.18/58.89 | | | | | Case 1:
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | (88) all_252_14 = e2 & op(e1, e2) = e2
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | ALPHA: (88) implies:
% 249.18/58.89 | | | | | | (89) all_252_14 = e2
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | REF_CLOSE: (25), (84), (89) are inconsistent by sub-proof #861.
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | Case 2:
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | (90) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 249.18/58.89 | | | | | | op(e1, e0) = e2)
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | BETA: splitting (90) gives:
% 249.18/58.89 | | | | | |
% 249.18/58.89 | | | | | | Case 1:
% 249.18/58.89 | | | | | | |
% 249.18/58.89 | | | | | | | (91) all_252_15 = e2 & op(e1, e1) = e2
% 249.18/58.89 | | | | | | |
% 249.18/58.89 | | | | | | | ALPHA: (91) implies:
% 249.18/58.89 | | | | | | | (92) all_252_15 = e2
% 249.18/58.89 | | | | | | |
% 249.18/58.89 | | | | | | | BETA: splitting (21) gives:
% 249.18/58.89 | | | | | | |
% 249.18/58.89 | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | |
% 249.18/58.89 | | | | | | | | (93) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 &
% 249.18/58.89 | | | | | | | | op(e3, e1) = e4)
% 249.18/58.89 | | | | | | | |
% 249.18/58.89 | | | | | | | | BETA: splitting (93) gives:
% 249.18/58.89 | | | | | | | |
% 249.18/58.89 | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | |
% 249.18/58.89 | | | | | | | | | (94) all_252_9 = e4 & op(e4, e1) = e4
% 249.18/58.89 | | | | | | | | |
% 249.18/58.89 | | | | | | | | | ALPHA: (94) implies:
% 249.18/58.89 | | | | | | | | | (95) all_252_9 = e4
% 249.18/58.89 | | | | | | | | | (96) op(e4, e1) = e4
% 249.18/58.89 | | | | | | | | |
% 249.18/58.89 | | | | | | | | | BETA: splitting (52) gives:
% 249.18/58.89 | | | | | | | | |
% 249.18/58.89 | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | (97) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0
% 249.18/58.89 | | | | | | | | | | & op(e4, e3) = e0)
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (13), (15), (25), (28), (34),
% 249.18/58.89 | | | | | | | | | | (37), (44), (50), (56), (59), (62), (67), (68),
% 249.18/58.89 | | | | | | | | | | (71), (73), (75), (78), (97) are inconsistent by
% 249.18/58.89 | | | | | | | | | | sub-proof #98.
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | (98) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0
% 249.18/58.89 | | | | | | | | | | & op(e4, e1) = e0) | (all_252_16 = e0 & op(e4, e0)
% 249.18/58.89 | | | | | | | | | | = e0)
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | BETA: splitting (98) gives:
% 249.18/58.89 | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | (99) all_252_4 = e0 & op(e4, e2) = e0
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | REF_CLOSE: (12), (22), (69), (99) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | sub-proof #875.
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | (100) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 =
% 249.18/58.89 | | | | | | | | | | | e0 & op(e4, e0) = e0)
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | BETA: splitting (100) gives:
% 249.18/58.89 | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | (101) all_252_9 = e0 & op(e4, e1) = e0
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | ALPHA: (101) implies:
% 249.18/58.89 | | | | | | | | | | | | (102) op(e4, e1) = e0
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | REF_CLOSE: (12), (15), (57), (96), (102) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | sub-proof #286.
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | (103) all_252_16 = e0 & op(e4, e0) = e0
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | ALPHA: (103) implies:
% 249.18/58.89 | | | | | | | | | | | | (104) all_252_16 = e0
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | BETA: splitting (32) gives:
% 249.18/58.89 | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | (105) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 249.18/58.89 | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | BETA: splitting (105) gives:
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (106) all_252_4 = e0 & op(e4, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (69), (106) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | sub-proof #875.
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (107) all_252_5 = e0 & op(e3, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | REF_CLOSE: (12), (51), (70), (107) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | sub-proof #874.
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | (108) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 249.18/58.89 | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 249.18/58.89 | | | | | | | | | | | | | op(e0, e2) = e0)
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 249.18/58.89 | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (109) all_252_8 = e0 & op(e2, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | ALPHA: (109) implies:
% 249.18/58.89 | | | | | | | | | | | | | | (110) op(e2, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (17), (110) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | sub-proof #880.
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | (111) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 249.18/58.89 | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 249.18/58.89 | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | (112) all_252_14 = e0 & op(e1, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 249.18/58.89 | | | | | | | | | | | | | | | (113) op(e1, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (66), (85), (113) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | | sub-proof #870.
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | (114) all_252_22 = e0 & op(e0, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 249.18/58.89 | | | | | | | | | | | | | | | (115) op(e0, e2) = e0
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 249.18/58.89 | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | (116) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 249.18/58.89 | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | (117) all_252_9 = e0 & op(e4, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 249.18/58.89 | | | | | | | | | | | | | | | | | (118) op(e4, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (57), (96), (118) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | | | | sub-proof #286.
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | (119) all_252_10 = e0 & op(e3, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (45), (60), (119) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | | | | sub-proof #726.
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | End of split
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | (120) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15
% 249.18/58.89 | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 249.18/58.89 | | | | | | | | | | | | | | | | op(e0, e1) = e0)
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 249.18/58.89 | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | (121) all_252_11 = e0 & op(e2, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (18), (38), (121) are inconsistent by
% 249.18/58.89 | | | | | | | | | | | | | | | | | sub-proof #904.
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | (122) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23
% 249.18/58.89 | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 249.18/58.89 | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.89 | | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | | (123) all_252_15 = e0 & op(e1, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (92), (123) are inconsistent by sub-proof
% 249.18/58.89 | | | | | | | | | | | | | | | | | | #500.
% 249.18/58.89 | | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.89 | | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | | (124) all_252_23 = e0 & op(e0, e1) = e0
% 249.18/58.89 | | | | | | | | | | | | | | | | | |
% 249.18/58.89 | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | (125) all_252_23 = e0
% 249.18/58.90 | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | (126) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (49), (55), (56), (126) are
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | (127) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | (128) all_252_22 = e1 & op(e0, e2) = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | (129) op(e0, e2) = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (115), (129) are inconsistent by
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | sub-proof #871.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | (130) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | (131) all_252_23 = e1 & op(e0, e1) = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (125), (131) are inconsistent by sub-proof
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | #187.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | (132) all_252_24 = e1 & op(e0, e0) = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | (133) all_252_24 = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | (134) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | (135) all_252_20 = e3 & op(e0, e4) = e3
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | (136) all_252_20 = e3
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (137) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (138) all_252_20 = e2 & op(e0, e4) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (56), (136) are inconsistent by sub-proof
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (139) all_252_21 = e2 & op(e0, e3) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (140) op(e0, e3) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (55), (140) are inconsistent by
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #987.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (141) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (142) all_252_22 = e2 & op(e0, e2) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (54), (142) are inconsistent by
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #979.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (143) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (144) all_252_23 = e2 & op(e0, e1) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (145) all_252_23 = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (145) imply:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (146) e2 = e0
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (146) imply:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (147) $false
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (148) all_252_24 = e2 & op(e0, e0) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (149) op(e0, e0) = e2
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (65), (149) are inconsistent by
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #978.
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | (150) all_252_21 = e3 & op(e0, e3) = e3
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | (151) all_252_21 = e3
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (152) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (153) all_252_0 = e1 & op(e4, e4) = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_0 = e1
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.18/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_0 = e3 & op(e4, e4) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (154), (156) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | #97.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_1 = e3 & op(e4, e3) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_1 = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (158) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) e3 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) e3 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (160) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_21 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (10), (12), (13), (15), (25), (26),
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (35), (37), (43), (44), (48), (49),
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (56), (62), (63), (68), (72), (74), (161)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #524.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (162) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_4 = e3 & op(e4, e2) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_4 = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_4 = e2 & op(e4, e2) = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (42), (166) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #453.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_5 = e2 & op(e3, e2) = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_5 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_4 = e4 & op(e4, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_252_4 = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (171) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) e4 = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (172) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) $false
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_5 = e4 & op(e3, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_5 = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (168), (175) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 &
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_8 = e4 & op(e2, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) op(e2, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (17), (29), (61), (178) are
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_252_14 = e4 & op(e1, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) op(e1, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (66), (181) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_22 = e4 & op(e0, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) op(e0, e2) = e4
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (27), (115), (183) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #854.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_252_8 = e2 & op(e2, e2) = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_8 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (186) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) e3 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) e3 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (188) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_252_21 = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (10), (12), (13), (15), (25), (26),
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (35), (37), (43), (44), (48), (49),
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (56), (62), (63), (68), (72), (74), (189)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #524.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_14 = e2 & op(e1, e2) = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (84), (191) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #924.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_252_22 = e2 & op(e0, e2) = e2
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (54), (192) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #979.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_9 = e3 & op(e4, e1) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) op(e4, e1) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (57), (64), (195) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_16 = e3 & op(e4, e0) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_16 = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (197) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e3 = e0
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (198) imply:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) $false
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_1 = e1 & op(e4, e3) = e1
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (40), (200) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | | #127.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (22), (28), (31), (95), (104), (201)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #96.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | (202) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_22 = e3 & op(e0, e2) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | (204) op(e0, e2) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (37), (115), (204) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #473.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | (205) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_23 = e3 & op(e0, e1) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (207) op(e0, e1) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (63), (74), (207) are inconsistent by
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_24 = e3 & op(e0, e0) = e3
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (133), (208) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | | #266.
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | (209) all_252_10 = e4 & op(e3, e1) = e4
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | REF_CLOSE: (12), (41), (45), (209) are inconsistent by
% 249.33/58.90 | | | | | | | | | sub-proof #914.
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | End of split
% 249.33/58.90 | | | | | | | |
% 249.33/58.90 | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | |
% 249.33/58.90 | | | | | | | | (210) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4
% 249.33/58.90 | | | | | | | | & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.33/58.90 | | | | | | | | e4)
% 249.33/58.90 | | | | | | | |
% 249.33/58.90 | | | | | | | | BETA: splitting (210) gives:
% 249.33/58.90 | | | | | | | |
% 249.33/58.90 | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | (211) all_252_11 = e4 & op(e2, e1) = e4
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | ALPHA: (211) implies:
% 249.33/58.90 | | | | | | | | | (212) op(e2, e1) = e4
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | REF_CLOSE: (12), (18), (53), (212) are inconsistent by
% 249.33/58.90 | | | | | | | | | sub-proof #935.
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | (213) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 =
% 249.33/58.90 | | | | | | | | | e4 & op(e0, e1) = e4)
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | BETA: splitting (213) gives:
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | | Case 1:
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | (214) all_252_15 = e4 & op(e1, e1) = e4
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | ALPHA: (214) implies:
% 249.33/58.90 | | | | | | | | | | (215) all_252_15 = e4
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | REF_CLOSE: (68), (92), (215) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | | | | #470.
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | Case 2:
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | (216) all_252_23 = e4 & op(e0, e1) = e4
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | | REF_CLOSE: (12), (63), (72), (216) are inconsistent by
% 249.33/58.90 | | | | | | | | | | sub-proof #912.
% 249.33/58.90 | | | | | | | | | |
% 249.33/58.90 | | | | | | | | | End of split
% 249.33/58.90 | | | | | | | | |
% 249.33/58.90 | | | | | | | | End of split
% 249.33/58.90 | | | | | | | |
% 249.33/58.90 | | | | | | | End of split
% 249.33/58.90 | | | | | | |
% 249.33/58.90 | | | | | | Case 2:
% 249.33/58.90 | | | | | | |
% 249.33/58.90 | | | | | | | (217) all_252_19 = e2 & op(e1, e0) = e2
% 249.33/58.90 | | | | | | |
% 249.33/58.90 | | | | | | | ALPHA: (217) implies:
% 249.33/58.90 | | | | | | | (218) op(e1, e0) = e2
% 249.33/58.90 | | | | | | |
% 249.33/58.90 | | | | | | | REF_CLOSE: (12), (20), (24), (218) are inconsistent by sub-proof
% 249.33/58.90 | | | | | | | #909.
% 249.33/58.90 | | | | | | |
% 249.33/58.90 | | | | | | End of split
% 249.33/58.90 | | | | | |
% 249.33/58.90 | | | | | End of split
% 249.33/58.90 | | | | |
% 249.33/58.90 | | | | End of split
% 249.33/58.90 | | | |
% 249.33/58.90 | | | Case 2:
% 249.33/58.90 | | | |
% 249.33/58.90 | | | | (219) all_252_22 = e1 & op(e0, e2) = e1
% 249.33/58.90 | | | |
% 249.33/58.90 | | | | ALPHA: (219) implies:
% 249.33/58.90 | | | | (220) op(e0, e2) = e1
% 249.33/58.90 | | | |
% 249.33/58.90 | | | | REF_CLOSE: (12), (27), (30), (220) are inconsistent by sub-proof #907.
% 249.33/58.90 | | | |
% 249.33/58.90 | | | End of split
% 249.33/58.90 | | |
% 249.33/58.90 | | End of split
% 249.33/58.90 | |
% 249.33/58.90 | End of split
% 249.33/58.90 |
% 249.33/58.90 End of proof
% 249.33/58.90
% 249.33/58.90 Sub-proof #96 shows that the following formulas are inconsistent:
% 249.33/58.90 ----------------------------------------------------------------
% 249.33/58.90 (1) ~ (e1 = e0)
% 249.33/58.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.90 (3) op(e4, e2) = all_6_2
% 249.33/58.90 (4) ~ (e4 = e1)
% 249.33/58.90 (5) ~ (all_6_2 = e1)
% 249.33/58.90 (6) all_252_9 = e4
% 249.33/58.90 (7) all_252_16 = e0
% 249.33/58.90 (8) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) |
% 249.33/58.90 (all_252_16 = e1 & op(e4, e0) = e1)
% 249.33/58.90
% 249.33/58.90 Begin of proof
% 249.33/58.90 |
% 249.33/58.90 | BETA: splitting (8) gives:
% 249.33/58.90 |
% 249.33/58.90 | Case 1:
% 249.33/58.90 | |
% 249.33/58.90 | | (9) all_252_4 = e1 & op(e4, e2) = e1
% 249.33/58.90 | |
% 249.33/58.90 | | ALPHA: (9) implies:
% 249.33/58.90 | | (10) op(e4, e2) = e1
% 249.33/58.90 | |
% 249.33/58.90 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #930.
% 249.33/58.90 | |
% 249.33/58.90 | Case 2:
% 249.33/58.90 | |
% 249.33/58.90 | | (11) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 = e1 & op(e4, e0) =
% 249.33/58.90 | | e1)
% 249.33/58.90 | |
% 249.33/58.90 | | BETA: splitting (11) gives:
% 249.33/58.90 | |
% 249.33/58.90 | | Case 1:
% 249.33/58.90 | | |
% 249.33/58.90 | | | (12) all_252_9 = e1 & op(e4, e1) = e1
% 249.33/58.90 | | |
% 249.33/58.90 | | | ALPHA: (12) implies:
% 249.33/58.90 | | | (13) all_252_9 = e1
% 249.33/58.90 | | |
% 249.33/58.90 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #842.
% 249.33/58.90 | | |
% 249.33/58.90 | | Case 2:
% 249.33/58.90 | | |
% 249.33/58.90 | | | (14) all_252_16 = e1 & op(e4, e0) = e1
% 249.33/58.90 | | |
% 249.33/58.90 | | | ALPHA: (14) implies:
% 249.33/58.90 | | | (15) all_252_16 = e1
% 249.33/58.90 | | |
% 249.33/58.90 | | | COMBINE_EQS: (7), (15) imply:
% 249.33/58.90 | | | (16) e1 = e0
% 249.33/58.90 | | |
% 249.33/58.90 | | | REDUCE: (1), (16) imply:
% 249.33/58.90 | | | (17) $false
% 249.33/58.90 | | |
% 249.33/58.90 | | | CLOSE: (17) is inconsistent.
% 249.33/58.90 | | |
% 249.33/58.90 | | End of split
% 249.33/58.90 | |
% 249.33/58.90 | End of split
% 249.33/58.90 |
% 249.33/58.90 End of proof
% 249.33/58.90
% 249.33/58.90 Sub-proof #97 shows that the following formulas are inconsistent:
% 249.33/58.90 ----------------------------------------------------------------
% 249.33/58.90 (1) all_252_0 = e3 & op(e4, e4) = e3
% 249.33/58.90 (2) all_252_0 = e1
% 249.33/58.90 (3) ~ (e3 = e1)
% 249.33/58.90
% 249.33/58.90 Begin of proof
% 249.33/58.90 |
% 249.33/58.90 | ALPHA: (1) implies:
% 249.33/58.90 | (4) all_252_0 = e3
% 249.33/58.90 |
% 249.33/58.90 | COMBINE_EQS: (2), (4) imply:
% 249.33/58.90 | (5) e3 = e1
% 249.33/58.90 |
% 249.33/58.90 | SIMP: (5) implies:
% 249.33/58.90 | (6) e3 = e1
% 249.33/58.90 |
% 249.33/58.90 | REDUCE: (3), (6) imply:
% 249.33/58.90 | (7) $false
% 249.33/58.90 |
% 249.33/58.90 | CLOSE: (7) is inconsistent.
% 249.33/58.90 |
% 249.33/58.90 End of proof
% 249.33/58.90
% 249.33/58.90 Sub-proof #98 shows that the following formulas are inconsistent:
% 249.33/58.90 ----------------------------------------------------------------
% 249.33/58.90 (1) all_252_6 = e0
% 249.33/58.90 (2) ~ (e2 = e0)
% 249.33/58.90 (3) ~ (e1 = e0)
% 249.33/58.90 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.90 (5) ~ (e3 = e2)
% 249.33/58.90 (6) ~ (e4 = e0)
% 249.33/58.90 (7) ~ (e2 = e1)
% 249.33/58.90 (8) ~ (e4 = e1)
% 249.33/58.90 (9) op(e1, e4) = all_16_2
% 249.33/58.90 (10) ~ (e3 = e0)
% 249.33/58.90 (11) ~ (e3 = e1)
% 249.33/58.90 (12) op(e4, e3) = e2
% 249.33/58.90 (13) all_252_20 = e2
% 249.33/58.90 (14) op(e3, e4) = all_100_2
% 249.33/58.90 (15) ~ (e4 = e3)
% 249.33/58.90 (16) op(e4, e3) = all_84_2
% 249.33/58.90 (17) ~ (e4 = e2)
% 249.33/58.90 (18) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.33/58.90 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.33/58.90 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.33/58.90 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.33/58.90 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.33/58.90 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.33/58.90 (20) ~ (all_16_2 = e3)
% 249.33/58.90 (21) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 249.33/58.90 (22) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.33/58.90 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.33/58.90 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.33/58.90
% 249.33/58.90 Begin of proof
% 249.33/58.90 |
% 249.33/58.90 | BETA: splitting (21) gives:
% 249.33/58.90 |
% 249.33/58.90 | Case 1:
% 249.33/58.90 | |
% 249.33/58.90 | | (23) all_252_0 = e0 & op(e4, e4) = e0
% 249.33/58.90 | |
% 249.33/58.90 | | ALPHA: (23) implies:
% 249.33/58.90 | | (24) all_252_0 = e0
% 249.33/58.90 | |
% 249.33/58.90 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 249.33/58.90 | | (15), (17), (18), (19), (20), (22), (24) are inconsistent by
% 249.33/58.90 | | sub-proof #99.
% 249.33/58.90 | |
% 249.33/58.90 | Case 2:
% 249.33/58.90 | |
% 249.33/58.90 | | (25) all_252_1 = e0 & op(e4, e3) = e0
% 249.33/58.90 | |
% 249.33/58.90 | | ALPHA: (25) implies:
% 249.33/58.90 | | (26) op(e4, e3) = e0
% 249.33/58.90 | |
% 249.33/58.90 | | REF_CLOSE: (2), (4), (12), (16), (26) are inconsistent by sub-proof #850.
% 249.33/58.90 | |
% 249.33/58.90 | End of split
% 249.33/58.90 |
% 249.33/58.90 End of proof
% 249.33/58.90
% 249.33/58.90 Sub-proof #99 shows that the following formulas are inconsistent:
% 249.33/58.90 ----------------------------------------------------------------
% 249.33/58.90 (1) all_252_0 = e0
% 249.33/58.90 (2) all_252_6 = e0
% 249.33/58.90 (3) ~ (e1 = e0)
% 249.33/58.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.91 (5) ~ (e3 = e2)
% 249.33/58.91 (6) ~ (e4 = e0)
% 249.33/58.91 (7) ~ (e2 = e1)
% 249.33/58.91 (8) ~ (e4 = e1)
% 249.33/58.91 (9) op(e1, e4) = all_16_2
% 249.33/58.91 (10) ~ (e3 = e0)
% 249.33/58.91 (11) ~ (e3 = e1)
% 249.33/58.91 (12) all_252_20 = e2
% 249.33/58.91 (13) op(e3, e4) = all_100_2
% 249.33/58.91 (14) ~ (e4 = e3)
% 249.33/58.91 (15) ~ (e4 = e2)
% 249.33/58.91 (16) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.33/58.91 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.33/58.91 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.33/58.91 (17) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.33/58.91 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.33/58.91 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.33/58.91 (18) ~ (all_16_2 = e3)
% 249.33/58.91 (19) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.33/58.91 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.33/58.91 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.33/58.91
% 249.33/58.91 Begin of proof
% 249.33/58.91 |
% 249.33/58.91 | BETA: splitting (16) gives:
% 249.33/58.91 |
% 249.33/58.91 | Case 1:
% 249.33/58.91 | |
% 249.33/58.91 | | (20) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 249.33/58.91 | | e3)
% 249.33/58.91 | |
% 249.33/58.91 | | BETA: splitting (20) gives:
% 249.33/58.91 | |
% 249.33/58.91 | | Case 1:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (21) all_252_0 = e3 & op(e4, e4) = e3
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (1), (10), (21) are inconsistent by sub-proof #841.
% 249.33/58.91 | | |
% 249.33/58.91 | | Case 2:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (22) all_252_2 = e3 & op(e3, e4) = e3
% 249.33/58.91 | | |
% 249.33/58.91 | | | ALPHA: (22) implies:
% 249.33/58.91 | | | (23) all_252_2 = e3
% 249.33/58.91 | | | (24) op(e3, e4) = e3
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (13), (14),
% 249.33/58.91 | | | (15), (17), (19), (23), (24) are inconsistent by sub-proof
% 249.33/58.91 | | | #100.
% 249.33/58.91 | | |
% 249.33/58.91 | | End of split
% 249.33/58.91 | |
% 249.33/58.91 | Case 2:
% 249.33/58.91 | |
% 249.33/58.91 | | (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.33/58.91 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.33/58.91 | |
% 249.33/58.91 | | BETA: splitting (25) gives:
% 249.33/58.91 | |
% 249.33/58.91 | | Case 1:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (26) all_252_6 = e3 & op(e2, e4) = e3
% 249.33/58.91 | | |
% 249.33/58.91 | | | ALPHA: (26) implies:
% 249.33/58.91 | | | (27) all_252_6 = e3
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (2), (10), (27) are inconsistent by sub-proof #691.
% 249.33/58.91 | | |
% 249.33/58.91 | | Case 2:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (28) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 249.33/58.91 | | | e4) = e3)
% 249.33/58.91 | | |
% 249.33/58.91 | | | BETA: splitting (28) gives:
% 249.33/58.91 | | |
% 249.33/58.91 | | | Case 1:
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | (29) all_252_12 = e3 & op(e1, e4) = e3
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | REF_CLOSE: (4), (9), (18), (29) are inconsistent by sub-proof #895.
% 249.33/58.91 | | | |
% 249.33/58.91 | | | Case 2:
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | (30) all_252_20 = e3 & op(e0, e4) = e3
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | REF_CLOSE: (5), (12), (30) are inconsistent by sub-proof #539.
% 249.33/58.91 | | | |
% 249.33/58.91 | | | End of split
% 249.33/58.91 | | |
% 249.33/58.91 | | End of split
% 249.33/58.91 | |
% 249.33/58.91 | End of split
% 249.33/58.91 |
% 249.33/58.91 End of proof
% 249.33/58.91
% 249.33/58.91 Sub-proof #100 shows that the following formulas are inconsistent:
% 249.33/58.91 ----------------------------------------------------------------
% 249.33/58.91 (1) all_252_0 = e0
% 249.33/58.91 (2) all_252_6 = e0
% 249.33/58.91 (3) ~ (e1 = e0)
% 249.33/58.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.91 (5) ~ (e4 = e0)
% 249.33/58.91 (6) ~ (e2 = e1)
% 249.33/58.91 (7) ~ (e4 = e1)
% 249.33/58.91 (8) op(e3, e4) = e3
% 249.33/58.91 (9) ~ (e3 = e1)
% 249.33/58.91 (10) all_252_20 = e2
% 249.33/58.91 (11) all_252_2 = e3
% 249.33/58.91 (12) op(e3, e4) = all_100_2
% 249.33/58.91 (13) ~ (e4 = e3)
% 249.33/58.91 (14) ~ (e4 = e2)
% 249.33/58.91 (15) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.33/58.91 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.33/58.91 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.33/58.91 (16) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.33/58.91 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.33/58.91 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.33/58.91
% 249.33/58.91 Begin of proof
% 249.33/58.91 |
% 249.33/58.91 | BETA: splitting (16) gives:
% 249.33/58.91 |
% 249.33/58.91 | Case 1:
% 249.33/58.91 | |
% 249.33/58.91 | | (17) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 249.33/58.91 | | e1)
% 249.33/58.91 | |
% 249.33/58.91 | | BETA: splitting (17) gives:
% 249.33/58.91 | |
% 249.33/58.91 | | Case 1:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (18) all_252_0 = e1 & op(e4, e4) = e1
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (1), (3), (18) are inconsistent by sub-proof #843.
% 249.33/58.91 | | |
% 249.33/58.91 | | Case 2:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (19) all_252_2 = e1 & op(e3, e4) = e1
% 249.33/58.91 | | |
% 249.33/58.91 | | | ALPHA: (19) implies:
% 249.33/58.91 | | | (20) op(e3, e4) = e1
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (4), (8), (9), (12), (20) are inconsistent by sub-proof #896.
% 249.33/58.91 | | |
% 249.33/58.91 | | End of split
% 249.33/58.91 | |
% 249.33/58.91 | Case 2:
% 249.33/58.91 | |
% 249.33/58.91 | | (21) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.33/58.91 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.33/58.91 | |
% 249.33/58.91 | | BETA: splitting (21) gives:
% 249.33/58.91 | |
% 249.33/58.91 | | Case 1:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (22) all_252_6 = e1 & op(e2, e4) = e1
% 249.33/58.91 | | |
% 249.33/58.91 | | | REF_CLOSE: (2), (3), (22) are inconsistent by sub-proof #556.
% 249.33/58.91 | | |
% 249.33/58.91 | | Case 2:
% 249.33/58.91 | | |
% 249.33/58.91 | | | (23) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 249.33/58.91 | | | e4) = e1)
% 249.33/58.91 | | |
% 249.33/58.91 | | | BETA: splitting (23) gives:
% 249.33/58.91 | | |
% 249.33/58.91 | | | Case 1:
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | (24) all_252_12 = e1 & op(e1, e4) = e1
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | ALPHA: (24) implies:
% 249.33/58.91 | | | | (25) all_252_12 = e1
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | BETA: splitting (15) gives:
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | Case 1:
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | (26) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 249.33/58.91 | | | | | e4) = e4)
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | BETA: splitting (26) gives:
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | Case 1:
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | (27) all_252_0 = e4 & op(e4, e4) = e4
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | REF_CLOSE: (1), (5), (27) are inconsistent by sub-proof #570.
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | Case 2:
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | (28) all_252_2 = e4 & op(e3, e4) = e4
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | ALPHA: (28) implies:
% 249.33/58.91 | | | | | | (29) all_252_2 = e4
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | REF_CLOSE: (11), (13), (29) are inconsistent by sub-proof #838.
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | End of split
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | Case 2:
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | (30) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 249.33/58.91 | | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | BETA: splitting (30) gives:
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | | Case 1:
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | (31) all_252_6 = e4 & op(e2, e4) = e4
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | REF_CLOSE: (2), (5), (31) are inconsistent by sub-proof #938.
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | Case 2:
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | (32) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 249.33/58.91 | | | | | | op(e0, e4) = e4)
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | | REF_CLOSE: (7), (10), (14), (25), (32) are inconsistent by sub-proof
% 249.33/58.91 | | | | | | #190.
% 249.33/58.91 | | | | | |
% 249.33/58.91 | | | | | End of split
% 249.33/58.91 | | | | |
% 249.33/58.91 | | | | End of split
% 249.33/58.91 | | | |
% 249.33/58.91 | | | Case 2:
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | (33) all_252_20 = e1 & op(e0, e4) = e1
% 249.33/58.91 | | | |
% 249.33/58.91 | | | | REF_CLOSE: (6), (10), (33) are inconsistent by sub-proof #532.
% 249.33/58.91 | | | |
% 249.33/58.91 | | | End of split
% 249.33/58.91 | | |
% 249.33/58.91 | | End of split
% 249.33/58.91 | |
% 249.33/58.91 | End of split
% 249.33/58.91 |
% 249.33/58.91 End of proof
% 249.33/58.91
% 249.33/58.91 Sub-proof #101 shows that the following formulas are inconsistent:
% 249.33/58.91 ----------------------------------------------------------------
% 249.33/58.91 (1) all_252_6 = e0
% 249.33/58.91 (2) all_252_7 = e4
% 249.33/58.91 (3) ~ (e3 = e0)
% 249.33/58.91 (4) ~ (e4 = e3)
% 249.33/58.91 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.33/58.91
% 249.33/58.91 Begin of proof
% 249.33/58.91 |
% 249.33/58.91 | BETA: splitting (5) gives:
% 249.33/58.91 |
% 249.33/58.91 | Case 1:
% 249.33/58.91 | |
% 249.33/58.91 | | (6) all_252_6 = e3 & op(e2, e4) = e3
% 249.33/58.91 | |
% 249.33/58.91 | | ALPHA: (6) implies:
% 249.33/58.91 | | (7) all_252_6 = e3
% 249.33/58.91 | |
% 249.33/58.91 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #691.
% 249.33/58.91 | |
% 249.33/58.91 | Case 2:
% 249.33/58.91 | |
% 249.33/58.91 | | (8) all_252_7 = e3 & op(e2, e3) = e3
% 249.33/58.91 | |
% 249.33/58.91 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #128.
% 249.33/58.91 | |
% 249.33/58.91 | End of split
% 249.33/58.91 |
% 249.33/58.91 End of proof
% 249.33/58.91
% 249.33/58.91 Sub-proof #102 shows that the following formulas are inconsistent:
% 249.33/58.91 ----------------------------------------------------------------
% 249.33/58.91 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.33/58.91 all_250_23 = e0
% 249.33/58.91 (2) ~ (all_30_2 = all_26_2)
% 249.33/58.91 (3) all_32_2 = all_20_2
% 249.33/58.91 (4) all_18_2 = all_12_2
% 249.33/58.91 (5) ~ (all_26_2 = e2)
% 249.33/58.91 (6) ~ (all_4_2 = e4)
% 249.33/58.91 (7) op(all_4_2, e2) = e1
% 249.33/58.91 (8) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 249.33/58.91 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 249.33/58.91 (all_252_16 = e3 & op(e4, e0) = e3)
% 249.33/58.91 (9) ~ (all_244_24 = all_34_2)
% 249.33/58.91 (10) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.33/58.91 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 249.33/58.91 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.33/58.91 (11) op(all_36_2, all_62_2) = e1
% 249.33/58.91 (12) ~ (all_40_2 = all_38_2)
% 249.33/58.91 (13) op(all_6_2, e2) = e4
% 249.33/58.91 (14) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.33/58.91 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.33/58.91 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.33/58.91 (15) op(e4, e0) = all_30_2
% 249.33/58.91 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.33/58.91 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.33/58.91 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.33/58.91 (17) all_250_8 = all_36_2
% 249.33/58.91 (18) ~ (all_244_8 = all_6_2)
% 249.33/58.91 (19) op(all_28_2, all_40_2) = e2
% 249.33/58.91 (20) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.33/58.91 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.33/58.91 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.33/58.91 (21) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 249.33/58.91 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 249.33/58.91 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 249.33/58.91 (22) ~ (all_22_2 = e2)
% 249.33/58.91 (23) all_94_2 = all_38_2
% 249.33/58.91 (24) op(all_62_2, all_36_2) = e3
% 249.33/58.91 (25) op(all_38_2, e1) = e2
% 249.33/58.91 (26) ~ (all_28_2 = all_6_2)
% 249.33/58.91 (27) ~ (e2 = e0)
% 249.33/58.91 (28) op(all_38_2, all_4_2) = e1
% 249.33/58.91 (29) op(all_64_2, e4) = e2
% 249.33/58.91 (30) ~ (e1 = e0)
% 249.33/58.91 (31) ~ (all_244_24 = all_20_2)
% 249.33/58.91 (32) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 249.33/58.91 all_250_20 = e0
% 249.33/58.91 (33) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.33/58.91 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.33/58.91 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.33/58.91 (34) ~ (all_62_2 = e2)
% 249.33/58.91 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.91 (36) ~ (e3 = e2)
% 249.33/58.91 (37) op(e0, e0) = all_244_24
% 249.33/58.91 (38) ~ (e4 = e0)
% 249.33/58.91 (39) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 249.33/58.91 all_250_17 = e0
% 249.33/58.91 (40) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.33/58.91 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.33/58.91 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.33/58.91 (41) ~ (all_244_8 = all_64_2)
% 249.33/58.91 (42) op(e2, e2) = all_244_8
% 249.33/58.91 (43) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(e4, e3) = all_42_1 &
% 249.33/58.91 op(e3, all_42_1) = all_42_0 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 249.33/58.91 (all_42_1 = e2) & op(e4, e3) = all_42_1 & $i(all_42_1))
% 249.33/58.91 (44) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.33/58.91 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.33/58.91 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.33/58.91 (45) op(e2, e1) = all_38_2
% 249.33/58.91 (46) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.33/58.91 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.33/58.91 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.33/58.91 (47) ~ (all_36_2 = all_20_2)
% 249.33/58.91 (48) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 249.33/58.91 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 249.33/58.91 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 249.33/58.91 (49) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.33/58.91 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.33/58.91 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.33/58.91 (50) ~ (all_244_15 = all_26_2)
% 249.33/58.91 (51) all_216_2 = all_26_2
% 249.33/58.91 (52) op(e1, e0) = all_34_2
% 249.33/58.91 (53) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.33/58.91 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.33/58.91 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.33/58.91 (54) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.33/58.91 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.33/58.91 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.33/58.91 (55) op(e4, e2) = all_6_2
% 249.33/58.91 (56) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.33/58.91 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.33/58.91 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 249.33/58.91 (57) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.33/58.91 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.33/58.91 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.33/58.91 (58) ~ (all_244_0 = all_16_2)
% 249.33/58.91 (59) ~ (all_20_2 = all_12_2)
% 249.33/58.91 (60) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 249.33/58.91 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 249.33/58.91 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 249.33/58.91 (61) ~ (all_18_2 = e3) | ( ~ (all_18_0 = e2) & op(e4, e3) = all_18_1 &
% 249.33/58.91 op(e3, all_18_1) = all_18_0 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 249.33/58.91 (all_18_1 = e1) & op(e4, e3) = all_18_1 & $i(all_18_1))
% 249.33/58.91 (62) ~ (all_66_2 = e3) | ( ~ (all_66_0 = e0) & op(e4, e3) = all_66_1 &
% 249.33/58.91 op(e3, all_66_1) = all_66_0 & $i(all_66_0) & $i(all_66_1)) | ( ~
% 249.33/58.91 (all_66_1 = e2) & op(e4, e3) = all_66_1 & $i(all_66_1))
% 249.33/58.91 (63) ~ (e2 = e1)
% 249.33/58.91 (64) all_252_7 = e4
% 249.33/58.91 (65) ~ (all_100_2 = all_36_2)
% 249.33/58.91 (66) ~ (all_100_2 = all_64_2)
% 249.33/58.91 (67) all_56_2 = all_8_2
% 249.33/58.91 (68) op(e0, e2) = all_28_2
% 249.33/58.91 (69) ~ (e4 = e1)
% 249.33/58.91 (70) ~ (all_244_0 = e2)
% 249.33/58.91 (71) op(all_6_2, all_64_2) = e2
% 249.33/58.91 (72) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.33/58.91 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.33/58.91 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.33/58.91 (73) ~ (all_6_2 = e1)
% 249.33/58.91 (74) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.33/58.91 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.33/58.91 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.33/58.91 (75) ~ (all_244_8 = all_38_2)
% 249.33/58.91 (76) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.33/58.91 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.33/58.91 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.33/58.91 (77) op(all_244_15, all_244_15) = e1
% 249.33/58.91 (78) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 &
% 249.33/58.91 op(e2, all_16_1) = all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 249.33/58.91 (all_16_1 = e0) & op(e4, e2) = all_16_1 & $i(all_16_1))
% 249.33/58.91 (79) all_80_2 = all_6_2
% 249.33/58.91 (80) all_250_21 = all_22_2
% 249.33/58.91 (81) all_50_2 = all_4_2
% 249.33/58.91 (82) op(all_34_2, e0) = e1
% 249.33/58.91 (83) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 249.33/58.91 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 249.33/58.91 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 249.33/58.91 (84) op(e1, e4) = all_16_2
% 249.33/58.91 (85) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 249.33/58.91 all_250_2 = e0
% 249.33/58.91 (86) all_96_2 = all_34_2
% 249.33/58.91 (87) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.33/58.91 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.33/58.91 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.33/58.91 (88) ~ (all_28_2 = all_20_2)
% 249.33/58.91 (89) op(e1, e3) = all_62_2
% 249.33/58.91 (90) op(all_100_2, e2) = e4
% 249.33/58.91 (91) ~ (e3 = e0)
% 249.33/58.91 (92) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 249.33/58.91 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 249.33/58.91 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 249.33/58.91 (93) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 249.33/58.91 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 249.33/58.91 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 249.33/58.91 (94) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.33/58.91 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.33/58.91 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.33/58.91 (95) op(all_20_2, e1) = e0
% 249.33/58.91 (96) ~ (all_48_2 = all_36_2)
% 249.33/58.91 (97) ~ (all_84_2 = e4)
% 249.33/58.91 (98) all_252_1 = e2
% 249.33/58.91 (99) ~ (all_6_2 = e2)
% 249.33/58.91 (100) ~ (all_22_2 = e4)
% 249.33/58.91 (101) all_70_2 = all_62_2
% 249.33/58.91 (102) ~ (e3 = e1)
% 249.33/58.91 (103) op(all_48_2, all_22_2) = e0
% 249.33/58.91 (104) ~ (all_12_2 = e2)
% 249.33/58.91 (105) op(e3, e1) = all_36_2
% 249.33/58.91 (106) ~ (all_28_2 = all_12_2)
% 249.33/58.91 (107) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.33/58.91 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 249.33/58.91 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 249.33/58.91 (108) ~ (all_8_2 = e1)
% 249.33/58.91 (109) ~ (all_244_3 = all_62_2)
% 249.33/58.91 (110) ~ (all_244_8 = all_40_2)
% 249.33/58.91 (111) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 249.33/58.91 all_250_8 = e0
% 249.33/58.91 (112) ~ (all_28_2 = all_4_2)
% 249.33/58.91 (113) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.33/58.91 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.33/58.91 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.33/58.91 (114) op(e2, all_100_2) = e3
% 249.33/58.91 (115) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 249.33/58.91 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 249.33/58.91 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 249.33/58.91 (116) ~ (all_48_2 = all_34_2)
% 249.33/58.91 (117) ~ (all_244_15 = all_38_2)
% 249.33/58.91 (118) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.33/58.91 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.33/58.91 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.33/58.91 (119) ~ (all_36_2 = all_26_2)
% 249.33/58.91 (120) op(e4, e3) = e2
% 249.33/58.91 (121) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 249.33/58.91 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 249.33/58.91 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 249.33/58.91 (122) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 249.33/58.91 & op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 249.33/58.91 (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 249.33/58.91 (123) all_182_2 = e2
% 249.33/58.91 (124) ~ (all_26_2 = all_6_2)
% 249.33/58.91 (125) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 249.33/58.91 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 249.33/58.91 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 249.33/58.91 (126) op(all_22_2, e3) = e0
% 249.33/58.91 (127) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0
% 249.33/58.91 & op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~
% 249.33/58.91 (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 249.33/58.91 (128) op(all_20_2, all_34_2) = e1
% 249.33/58.91 (129) op(e0, e3) = all_22_2
% 249.33/58.91 (130) ~ (all_28_2 = all_22_2)
% 249.33/58.91 (131) op(all_34_2, all_20_2) = e0
% 249.33/58.91 (132) all_58_2 = all_20_2
% 249.33/58.91 (133) op(all_62_2, e3) = e1
% 249.33/58.91 (134) op(e4, e1) = all_26_2
% 249.33/58.91 (135) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.33/58.91 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.33/58.91 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.33/58.91 (136) ~ (all_64_2 = all_38_2)
% 249.33/58.91 (137) ~ (all_100_2 = all_8_2)
% 249.33/58.91 (138) op(all_30_2, all_12_2) = e0
% 249.33/58.91 (139) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 249.33/58.91 all_250_21 = e0
% 249.33/58.91 (140) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 249.33/58.91 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 249.33/58.91 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 249.33/58.91 (141) op(e3, e4) = all_100_2
% 249.33/58.91 (142) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 249.33/58.91 op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~
% 249.33/58.91 (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 249.33/58.91 (143) op(all_8_2, e4) = e2
% 249.33/58.91 (144) op(e4, e4) = all_244_0
% 249.33/58.91 (145) all_230_2 = all_20_2
% 249.33/58.91 (146) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.33/58.91 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 249.33/58.91 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.33/58.92 (147) ~ (e4 = e3)
% 249.33/58.92 (148) op(e1, e1) = all_244_15
% 249.33/58.92 (149) op(e0, e1) = all_20_2
% 249.33/58.92 (150) ~ (all_244_15 = all_20_2)
% 249.33/58.92 (151) op(e3, e0) = all_48_2
% 249.33/58.92 (152) op(all_48_2, e0) = e3
% 249.33/58.92 (153) all_82_2 = all_28_2
% 249.33/58.92 (154) ~ (all_244_3 = all_100_2)
% 249.33/58.92 (155) op(e1, e2) = all_4_2
% 249.33/58.92 (156) ~ (all_100_2 = all_48_2)
% 249.33/58.92 (157) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 249.33/58.92 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 249.33/58.92 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 249.33/58.92 (158) op(all_4_2, all_38_2) = e2
% 249.33/58.92 (159) op(e4, e3) = all_84_2
% 249.33/58.92 (160) all_86_2 = all_40_2
% 249.33/58.92 (161) op(all_244_3, all_244_3) = e3
% 249.33/58.92 (162) op(e2, e4) = all_64_2
% 249.33/58.92 (163) all_250_17 = all_4_2
% 249.33/58.92 (164) all_60_2 = all_20_2
% 249.33/58.92 (165) ~ (all_38_2 = all_26_2)
% 249.33/58.92 (166) ~ (e4 = e2)
% 249.33/58.92 (167) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.33/58.92 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.33/58.92 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.33/58.92 (168) ~ (all_22_2 = all_20_2)
% 249.33/58.92 (169) ~ (all_16_2 = all_4_2)
% 249.33/58.92 (170) op(e3, e2) = all_8_2
% 249.33/58.92 (171) ~ (all_64_2 = all_16_2)
% 249.33/58.92 (172) op(all_36_2, e1) = e3
% 249.33/58.92 (173) ~ (all_38_2 = all_20_2)
% 249.33/58.92 (174) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.33/58.92 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.33/58.92 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.33/58.92 (175) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.33/58.92 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.33/58.92 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.33/58.92 (176) ~ (all_244_15 = all_36_2)
% 249.33/58.92 (177) all_42_2 = all_12_2
% 249.33/58.92 (178) op(all_16_2, e4) = e1
% 249.33/58.92 (179) ~ (all_100_2 = all_16_2)
% 249.33/58.92 (180) op(e2, e0) = all_40_2
% 249.33/58.92 (181) op(all_8_2, e2) = e3
% 249.33/58.92 (182) ~ (all_244_8 = all_28_2)
% 249.33/58.92 (183) ~ (all_244_3 = all_48_2)
% 249.33/58.92 (184) all_24_2 = all_16_2
% 249.33/58.92 (185) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.33/58.92 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.33/58.92 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.33/58.92 (186) all_250_20 = all_12_2
% 249.33/58.92 (187) op(e3, e3) = all_244_3
% 249.33/58.92 (188) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.33/58.92 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.33/58.92 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.33/58.92 (189) ~ (all_16_2 = all_12_2)
% 249.33/58.92 (190) all_188_2 = all_38_2
% 249.33/58.92 (191) ~ (all_26_2 = all_20_2)
% 249.33/58.92 (192) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.33/58.92 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.33/58.92 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.33/58.92 (193) op(all_12_2, e4) = e0
% 249.33/58.92 (194) all_250_2 = all_6_2
% 249.33/58.92 (195) all_46_2 = all_36_2
% 249.33/58.92 (196) ~ (all_62_2 = all_4_2)
% 249.33/58.92 (197) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 249.33/58.92 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 249.33/58.92 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 249.33/58.92 (198) ~ (all_96_2 = e3) | ( ~ (all_96_0 = e2) & op(e3, all_96_1) = all_96_0
% 249.33/58.92 & op(e0, e3) = all_96_1 & $i(all_96_0) & $i(all_96_1)) | ( ~
% 249.33/58.92 (all_96_1 = e4) & op(e0, e3) = all_96_1 & $i(all_96_1))
% 249.33/58.92 (199) op(all_30_2, e0) = e4
% 249.33/58.92 (200) ~ (all_64_2 = e4)
% 249.33/58.92 (201) op(all_244_24, all_244_24) = e0
% 249.33/58.92 (202) op(e0, e4) = all_12_2
% 249.33/58.92 (203) all_66_2 = all_16_2
% 249.33/58.92 (204) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 249.33/58.92 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 249.33/58.92 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 249.33/58.92 (205) op(all_64_2, all_6_2) = e4
% 249.33/58.92 (206) all_250_23 = all_20_2
% 249.33/58.92
% 249.33/58.92 Begin of proof
% 249.33/58.92 |
% 249.33/58.92 | BETA: splitting (78) gives:
% 249.33/58.92 |
% 249.33/58.92 | Case 1:
% 249.33/58.92 | |
% 249.33/58.92 | | (207) ~ (all_16_2 = e2)
% 249.33/58.92 | |
% 249.33/58.92 | | BETA: splitting (61) gives:
% 249.33/58.92 | |
% 249.33/58.92 | | Case 1:
% 249.33/58.92 | | |
% 249.33/58.92 | | | (208) ~ (all_18_2 = e3)
% 249.33/58.92 | | |
% 249.33/58.92 | | | REDUCE: (4), (208) imply:
% 249.33/58.92 | | | (209) ~ (all_12_2 = e3)
% 249.33/58.92 | | |
% 249.33/58.92 | | | BETA: splitting (60) gives:
% 249.33/58.92 | | |
% 249.33/58.92 | | | Case 1:
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | (210) ~ (all_20_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | BETA: splitting (197) gives:
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | Case 1:
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | (211) ~ (all_22_2 = e1)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | BETA: splitting (157) gives:
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | Case 1:
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | (212) ~ (all_24_2 = e3)
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | REDUCE: (184), (212) imply:
% 249.33/58.92 | | | | | | (213) ~ (all_16_2 = e3)
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | BETA: splitting (122) gives:
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | Case 1:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | (214) ~ (all_28_2 = e3)
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | BETA: splitting (92) gives:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | (215) ~ (all_32_2 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (3), (215) imply:
% 249.33/58.92 | | | | | | | | (216) ~ (all_20_2 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | BETA: splitting (57) gives:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | (217) ~ (all_34_2 = e2)
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | BETA: splitting (115) gives:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | (218) ~ (all_46_2 = e2)
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | REDUCE: (195), (218) imply:
% 249.33/58.92 | | | | | | | | | | (219) ~ (all_36_2 = e2)
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | BETA: splitting (125) gives:
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | (220) ~ (all_48_2 = e1)
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | BETA: splitting (204) gives:
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | (221) ~ (all_50_2 = e3)
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | REDUCE: (81), (221) imply:
% 249.33/58.92 | | | | | | | | | | | | (222) ~ (all_4_2 = e3)
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | BETA: splitting (49) gives:
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | (223) ~ (all_56_2 = e0)
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | REDUCE: (67), (223) imply:
% 249.33/58.92 | | | | | | | | | | | | | (224) ~ (all_8_2 = e0)
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | BETA: splitting (107) gives:
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | (225) ~ (all_182_2 = e2)
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | REDUCE: (123), (225) imply:
% 249.33/58.92 | | | | | | | | | | | | | | (226) $false
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | (227) ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.33/58.92 | | | | | | | | | | | | | | op(e2, all_182_1) = all_182_0 & $i(all_182_0) &
% 249.33/58.92 | | | | | | | | | | | | | | $i(all_182_1)) | ( ~ (all_182_1 = e0) & op(e3,
% 249.33/58.92 | | | | | | | | | | | | | | e2) = all_182_1 & $i(all_182_1))
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | (228) ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.33/58.92 | | | | | | | | | | | | | | | op(e2, all_182_1) = all_182_0 & $i(all_182_0) &
% 249.33/58.92 | | | | | | | | | | | | | | | $i(all_182_1)
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 249.33/58.92 | | | | | | | | | | | | | | | (229) op(e3, e2) = all_182_1
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (16), (18), (20), (22), (23), (25),
% 249.33/58.92 | | | | | | | | | | | | | | | (27), (30), (33), (34), (35), (36), (37), (38),
% 249.33/58.92 | | | | | | | | | | | | | | | (40), (41), (42), (44), (45), (46), (52), (53),
% 249.33/58.92 | | | | | | | | | | | | | | | (55), (63), (64), (68), (69), (70), (71), (73),
% 249.33/58.92 | | | | | | | | | | | | | | | (74), (76), (79), (80), (82), (84), (86), (87),
% 249.33/58.92 | | | | | | | | | | | | | | | (88), (89), (91), (94), (98), (100), (102), (103),
% 249.33/58.92 | | | | | | | | | | | | | | | (104), (105), (108), (110), (113), (114), (120),
% 249.33/58.92 | | | | | | | | | | | | | | | (129), (131), (132), (135), (139), (141), (144),
% 249.33/58.92 | | | | | | | | | | | | | | | (147), (149), (151), (152), (153), (155), (159),
% 249.33/58.92 | | | | | | | | | | | | | | | (160), (162), (166), (168), (170), (175), (180),
% 249.33/58.92 | | | | | | | | | | | | | | | (185), (192), (198), (200), (201), (202), (206),
% 249.33/58.92 | | | | | | | | | | | | | | | (207), (209), (210), (211), (213), (216), (217),
% 249.33/58.92 | | | | | | | | | | | | | | | (219), (220), (222), (224), (229) are inconsistent
% 249.33/58.92 | | | | | | | | | | | | | | | by sub-proof #121.
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | (230) ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 &
% 249.33/58.92 | | | | | | | | | | | | | | | $i(all_182_1)
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 249.33/58.92 | | | | | | | | | | | | | | | (231) op(e3, e2) = all_182_1
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (16), (18), (20), (22), (23), (25),
% 249.33/58.92 | | | | | | | | | | | | | | | (27), (30), (33), (34), (35), (36), (37), (38),
% 249.33/58.92 | | | | | | | | | | | | | | | (40), (41), (42), (44), (45), (46), (52), (53),
% 249.33/58.92 | | | | | | | | | | | | | | | (55), (63), (64), (68), (69), (70), (71), (73),
% 249.33/58.92 | | | | | | | | | | | | | | | (74), (76), (79), (80), (82), (84), (86), (87),
% 249.33/58.92 | | | | | | | | | | | | | | | (88), (89), (91), (94), (98), (100), (102), (103),
% 249.33/58.92 | | | | | | | | | | | | | | | (104), (105), (108), (110), (113), (114), (120),
% 249.33/58.92 | | | | | | | | | | | | | | | (129), (131), (132), (135), (139), (141), (144),
% 249.33/58.92 | | | | | | | | | | | | | | | (147), (149), (151), (152), (153), (155), (159),
% 249.33/58.92 | | | | | | | | | | | | | | | (160), (162), (166), (168), (170), (175), (180),
% 249.33/58.92 | | | | | | | | | | | | | | | (185), (192), (198), (200), (201), (202), (206),
% 249.33/58.92 | | | | | | | | | | | | | | | (207), (209), (210), (211), (213), (216), (217),
% 249.33/58.92 | | | | | | | | | | | | | | | (219), (220), (222), (224), (231) are inconsistent
% 249.33/58.92 | | | | | | | | | | | | | | | by sub-proof #121.
% 249.33/58.92 | | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | (232) all_56_2 = e0
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | COMBINE_EQS: (67), (232) imply:
% 249.33/58.92 | | | | | | | | | | | | | (233) all_8_2 = e0
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | REDUCE: (181), (233) imply:
% 249.33/58.92 | | | | | | | | | | | | | (234) op(e0, e2) = e3
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | | REF_CLOSE: (35), (68), (214), (234) are inconsistent by
% 249.33/58.92 | | | | | | | | | | | | | sub-proof #975.
% 249.33/58.92 | | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | (235) all_50_2 = e3
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | | REF_CLOSE: (7), (35), (81), (108), (170), (235) are
% 249.33/58.92 | | | | | | | | | | | | inconsistent by sub-proof #802.
% 249.33/58.92 | | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | (236) all_48_2 = e1
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | REDUCE: (183), (236) imply:
% 249.33/58.92 | | | | | | | | | | | (237) ~ (all_244_3 = e1)
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | REDUCE: (116), (236) imply:
% 249.33/58.92 | | | | | | | | | | | (238) ~ (all_34_2 = e1)
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | SIMP: (238) implies:
% 249.33/58.92 | | | | | | | | | | | (239) ~ (all_34_2 = e1)
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | | REF_CLOSE: (11), (35), (52), (63), (64), (69), (89), (98),
% 249.33/58.92 | | | | | | | | | | | (129), (152), (172), (187), (192), (211), (236),
% 249.33/58.92 | | | | | | | | | | | (237), (239) are inconsistent by sub-proof #119.
% 249.33/58.92 | | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | (240) all_46_2 = e2
% 249.33/58.92 | | | | | | | | | | (241) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 249.33/58.92 | | | | | | | | | | op(e1, e2) = all_46_1 & $i(all_46_0) &
% 249.33/58.92 | | | | | | | | | | $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1, e2)
% 249.33/58.92 | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | COMBINE_EQS: (195), (240) imply:
% 249.33/58.92 | | | | | | | | | | (242) all_36_2 = e2
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | REF_CLOSE: (24), (28), (35), (42), (45), (52), (75), (84),
% 249.33/58.92 | | | | | | | | | | (89), (101), (108), (118), (148), (155), (170),
% 249.33/58.92 | | | | | | | | | | (172), (176), (185), (207), (217), (241), (242)
% 249.33/58.92 | | | | | | | | | | are inconsistent by sub-proof #796.
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | (243) all_34_2 = e2
% 249.33/58.92 | | | | | | | | | (244) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.33/58.92 | | | | | | | | | op(e0, e2) = all_34_1 & $i(all_34_0) &
% 249.33/58.92 | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e3) & op(e0, e2) =
% 249.33/58.92 | | | | | | | | | all_34_1 & $i(all_34_1))
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | REDUCE: (9), (243) imply:
% 249.33/58.92 | | | | | | | | | (245) ~ (all_244_24 = e2)
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | REDUCE: (82), (243) imply:
% 249.33/58.92 | | | | | | | | | (246) op(e2, e0) = e1
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | REF_CLOSE: (7), (12), (19), (22), (35), (37), (45), (68),
% 249.33/58.92 | | | | | | | | | (104), (129), (135), (149), (158), (180), (202),
% 249.33/58.92 | | | | | | | | | (216), (244), (245), (246) are inconsistent by
% 249.33/58.92 | | | | | | | | | sub-proof #117.
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | End of split
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | (247) all_32_2 = e2
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | COMBINE_EQS: (3), (247) imply:
% 249.33/58.92 | | | | | | | | (248) all_20_2 = e2
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | SIMP: (248) implies:
% 249.33/58.92 | | | | | | | | (249) all_20_2 = e2
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | COMBINE_EQS: (145), (249) imply:
% 249.33/58.92 | | | | | | | | (250) all_230_2 = e2
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (150), (249) imply:
% 249.33/58.92 | | | | | | | | (251) ~ (all_244_15 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (31), (249) imply:
% 249.33/58.92 | | | | | | | | (252) ~ (all_244_24 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (88), (249) imply:
% 249.33/58.92 | | | | | | | | (253) ~ (all_28_2 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (59), (249) imply:
% 249.33/58.92 | | | | | | | | (254) ~ (all_12_2 = e2)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (131), (249) imply:
% 249.33/58.92 | | | | | | | | (255) op(all_34_2, e2) = e0
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (95), (249) imply:
% 249.33/58.92 | | | | | | | | (256) op(e2, e1) = e0
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | BETA: splitting (93) gives:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | (257) ~ (all_230_2 = e2)
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | REDUCE: (250), (257) imply:
% 249.33/58.92 | | | | | | | | | (258) $false
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | CLOSE: (258) is inconsistent.
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | (259) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0
% 249.33/58.92 | | | | | | | | | & op(e1, e2) = all_230_1 & $i(all_230_0) &
% 249.33/58.92 | | | | | | | | | $i(all_230_1)) | ( ~ (all_230_1 = e4) & op(e1, e2)
% 249.33/58.92 | | | | | | | | | = all_230_1 & $i(all_230_1))
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | BETA: splitting (259) gives:
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | (260) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0
% 249.33/58.92 | | | | | | | | | | & op(e1, e2) = all_230_1 & $i(all_230_0) &
% 249.33/58.92 | | | | | | | | | | $i(all_230_1)
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | ALPHA: (260) implies:
% 249.33/58.92 | | | | | | | | | | (261) op(e1, e2) = all_230_1
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | REF_CLOSE: (7), (22), (28), (34), (35), (37), (42), (45),
% 249.33/58.92 | | | | | | | | | | (52), (57), (68), (75), (84), (89), (104), (129),
% 249.33/58.92 | | | | | | | | | | (135), (148), (155), (182), (185), (202), (207),
% 249.33/58.92 | | | | | | | | | | (251), (252), (253), (255), (256), (261) are
% 249.33/58.92 | | | | | | | | | | inconsistent by sub-proof #116.
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | (262) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 &
% 249.33/58.92 | | | | | | | | | | $i(all_230_1)
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | ALPHA: (262) implies:
% 249.33/58.92 | | | | | | | | | | (263) op(e1, e2) = all_230_1
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | | REF_CLOSE: (7), (22), (28), (34), (35), (37), (42), (45),
% 249.33/58.92 | | | | | | | | | | (52), (57), (68), (75), (84), (89), (104), (129),
% 249.33/58.92 | | | | | | | | | | (135), (148), (155), (182), (185), (202), (207),
% 249.33/58.92 | | | | | | | | | | (251), (252), (253), (255), (256), (263) are
% 249.33/58.92 | | | | | | | | | | inconsistent by sub-proof #116.
% 249.33/58.92 | | | | | | | | | |
% 249.33/58.92 | | | | | | | | | End of split
% 249.33/58.92 | | | | | | | | |
% 249.33/58.92 | | | | | | | | End of split
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | End of split
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | Case 2:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | (264) all_28_2 = e3
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | REF_CLOSE: (22), (35), (80), (100), (103), (130), (139), (152),
% 249.33/58.92 | | | | | | | (211), (264) are inconsistent by sub-proof #115.
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | End of split
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | Case 2:
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | (265) all_24_2 = e3
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | COMBINE_EQS: (184), (265) imply:
% 249.33/58.92 | | | | | | (266) all_16_2 = e3
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | COMBINE_EQS: (203), (266) imply:
% 249.33/58.92 | | | | | | (267) all_66_2 = e3
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | REDUCE: (178), (266) imply:
% 249.33/58.92 | | | | | | (268) op(e3, e4) = e1
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | BETA: splitting (62) gives:
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | | Case 1:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | (269) ~ (all_66_2 = e3)
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | REDUCE: (267), (269) imply:
% 249.33/58.92 | | | | | | | (270) $false
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | CLOSE: (270) is inconsistent.
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | Case 2:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | (271) ( ~ (all_66_0 = e0) & op(e4, e3) = all_66_1 & op(e3,
% 249.33/58.92 | | | | | | | all_66_1) = all_66_0 & $i(all_66_0) & $i(all_66_1)) |
% 249.33/58.92 | | | | | | | ( ~ (all_66_1 = e2) & op(e4, e3) = all_66_1 &
% 249.33/58.92 | | | | | | | $i(all_66_1))
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | BETA: splitting (271) gives:
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | | Case 1:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | GROUND_INST: instantiating (35) with all_100_2, e1, e4, e3,
% 249.33/58.92 | | | | | | | | simplifying with (141), (268) gives:
% 249.33/58.92 | | | | | | | | (272) all_100_2 = e1
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (90), (272) imply:
% 249.33/58.92 | | | | | | | | (273) op(e1, e2) = e4
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REF_CLOSE: (6), (35), (155), (273) are inconsistent by sub-proof
% 249.33/58.92 | | | | | | | | #831.
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | Case 2:
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | (274) ~ (all_66_1 = e2) & op(e4, e3) = all_66_1 &
% 249.33/58.92 | | | | | | | | $i(all_66_1)
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | ALPHA: (274) implies:
% 249.33/58.92 | | | | | | | | (275) ~ (all_66_1 = e2)
% 249.33/58.92 | | | | | | | | (276) op(e4, e3) = all_66_1
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | GROUND_INST: instantiating (35) with e2, all_66_1, e3, e4,
% 249.33/58.92 | | | | | | | | simplifying with (120), (276) gives:
% 249.33/58.92 | | | | | | | | (277) all_66_1 = e2
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | REDUCE: (275), (277) imply:
% 249.33/58.92 | | | | | | | | (278) $false
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | | CLOSE: (278) is inconsistent.
% 249.33/58.92 | | | | | | | |
% 249.33/58.92 | | | | | | | End of split
% 249.33/58.92 | | | | | | |
% 249.33/58.92 | | | | | | End of split
% 249.33/58.92 | | | | | |
% 249.33/58.92 | | | | | End of split
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | Case 2:
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | (279) all_22_2 = e1
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (130), (279) imply:
% 249.33/58.92 | | | | | (280) ~ (all_28_2 = e1)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (168), (279) imply:
% 249.33/58.92 | | | | | (281) ~ (all_20_2 = e1)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | SIMP: (281) implies:
% 249.33/58.92 | | | | | (282) ~ (all_20_2 = e1)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (126), (279) imply:
% 249.33/58.92 | | | | | (283) op(e1, e3) = e0
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | GROUND_INST: instantiating (35) with all_62_2, e0, e3, e1, simplifying
% 249.33/58.92 | | | | | with (89), (283) gives:
% 249.33/58.92 | | | | | (284) all_62_2 = e0
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (109), (284) imply:
% 249.33/58.92 | | | | | (285) ~ (all_244_3 = e0)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (196), (284) imply:
% 249.33/58.92 | | | | | (286) ~ (all_4_2 = e0)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | SIMP: (286) implies:
% 249.33/58.92 | | | | | (287) ~ (all_4_2 = e0)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REDUCE: (34), (284) imply:
% 249.33/58.92 | | | | | (288) ~ (e2 = e0)
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | | REF_CLOSE: (1), (3), (6), (7), (9), (16), (17), (21), (24), (25),
% 249.33/58.92 | | | | | (27), (28), (31), (35), (36), (37), (39), (45), (47), (52),
% 249.33/58.92 | | | | | (58), (65), (68), (81), (82), (84), (87), (88), (89), (91),
% 249.33/58.92 | | | | | (92), (94), (95), (102), (105), (108), (111), (112), (115),
% 249.33/58.92 | | | | | (122), (131), (132), (133), (134), (141), (144), (146),
% 249.33/58.92 | | | | | (148), (150), (155), (157), (162), (163), (170), (171),
% 249.33/58.92 | | | | | (174), (178), (179), (184), (187), (189), (191), (195),
% 249.33/58.92 | | | | | (201), (202), (204), (206), (207), (209), (210), (280),
% 249.33/58.92 | | | | | (282), (284), (285), (287) are inconsistent by sub-proof
% 249.33/58.92 | | | | | #586.
% 249.33/58.92 | | | | |
% 249.33/58.92 | | | | End of split
% 249.33/58.92 | | | |
% 249.33/58.92 | | | Case 2:
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | (289) all_20_2 = e4
% 249.33/58.92 | | | | (290) ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4)
% 249.33/58.92 | | | | = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 249.33/58.92 | | | | e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | COMBINE_EQS: (164), (289) imply:
% 249.33/58.92 | | | | (291) all_60_2 = e4
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (150), (289) imply:
% 249.33/58.92 | | | | (292) ~ (all_244_15 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (173), (289) imply:
% 249.33/58.92 | | | | (293) ~ (all_38_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (47), (289) imply:
% 249.33/58.92 | | | | (294) ~ (all_36_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (191), (289) imply:
% 249.33/58.92 | | | | (295) ~ (all_26_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (59), (289) imply:
% 249.33/58.92 | | | | (296) ~ (all_12_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | SIMP: (296) implies:
% 249.33/58.92 | | | | (297) ~ (all_12_2 = e4)
% 249.33/58.92 | | | |
% 249.33/58.92 | | | | REDUCE: (128), (289) imply:
% 249.33/58.93 | | | | (298) op(e4, all_34_2) = e1
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (95), (289) imply:
% 249.33/58.93 | | | | (299) op(e4, e1) = e0
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | BETA: splitting (290) gives:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | Case 1:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (300) ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 & op(e1, e4)
% 249.33/58.93 | | | | | = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | ALPHA: (300) implies:
% 249.33/58.93 | | | | | (301) op(e1, e4) = all_20_1
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REF_CLOSE: (2), (5), (8), (13), (14), (15), (20), (23), (24), (25),
% 249.33/58.93 | | | | | (26), (28), (29), (30), (32), (33), (34), (35), (36), (40),
% 249.33/58.93 | | | | | (41), (42), (44), (45), (46), (48), (49), (50), (51), (52),
% 249.33/58.93 | | | | | (54), (55), (57), (63), (64), (67), (68), (69), (70), (71),
% 249.33/58.93 | | | | | (72), (73), (74), (75), (76), (83), (84), (85), (89), (91),
% 249.33/58.93 | | | | | (97), (98), (99), (101), (102), (104), (105), (106), (107),
% 249.33/58.93 | | | | | (108), (110), (114), (115), (118), (119), (120), (121),
% 249.33/58.93 | | | | | (122), (123), (124), (127), (134), (138), (141), (142),
% 249.33/58.93 | | | | | (143), (144), (146), (147), (148), (153), (155), (159),
% 249.33/58.93 | | | | | (160), (162), (165), (166), (167), (170), (172), (175),
% 249.33/58.93 | | | | | (176), (180), (181), (185), (186), (188), (194), (195),
% 249.33/58.93 | | | | | (199), (200), (202), (205), (207), (209), (291), (292),
% 249.33/58.93 | | | | | (293), (294), (295), (297), (298), (299), (301) are
% 249.33/58.93 | | | | | inconsistent by sub-proof #106.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | Case 2:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (302) ~ (all_20_1 = e2) & op(e1, e4) = all_20_1 & $i(all_20_1)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | ALPHA: (302) implies:
% 249.33/58.93 | | | | | (303) op(e1, e4) = all_20_1
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REF_CLOSE: (2), (5), (8), (13), (14), (15), (20), (23), (24), (25),
% 249.33/58.93 | | | | | (26), (28), (29), (30), (32), (33), (34), (35), (36), (40),
% 249.33/58.93 | | | | | (41), (42), (44), (45), (46), (48), (49), (50), (51), (52),
% 249.33/58.93 | | | | | (54), (55), (57), (63), (64), (67), (68), (69), (70), (71),
% 249.33/58.93 | | | | | (72), (73), (74), (75), (76), (83), (84), (85), (89), (91),
% 249.33/58.93 | | | | | (97), (98), (99), (101), (102), (104), (105), (106), (107),
% 249.33/58.93 | | | | | (108), (110), (114), (115), (118), (119), (120), (121),
% 249.33/58.93 | | | | | (122), (123), (124), (127), (134), (138), (141), (142),
% 249.33/58.93 | | | | | (143), (144), (146), (147), (148), (153), (155), (159),
% 249.33/58.93 | | | | | (160), (162), (165), (166), (167), (170), (172), (175),
% 249.33/58.93 | | | | | (176), (180), (181), (185), (186), (188), (194), (195),
% 249.33/58.93 | | | | | (199), (200), (202), (205), (207), (209), (291), (292),
% 249.33/58.93 | | | | | (293), (294), (295), (297), (298), (299), (303) are
% 249.33/58.93 | | | | | inconsistent by sub-proof #106.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | End of split
% 249.33/58.93 | | | |
% 249.33/58.93 | | | End of split
% 249.33/58.93 | | |
% 249.33/58.93 | | Case 2:
% 249.33/58.93 | | |
% 249.33/58.93 | | | (304) all_18_2 = e3
% 249.33/58.93 | | |
% 249.33/58.93 | | | COMBINE_EQS: (4), (304) imply:
% 249.33/58.93 | | | (305) all_12_2 = e3
% 249.33/58.93 | | |
% 249.33/58.93 | | | SIMP: (305) implies:
% 249.33/58.93 | | | (306) all_12_2 = e3
% 249.33/58.93 | | |
% 249.33/58.93 | | | COMBINE_EQS: (177), (306) imply:
% 249.33/58.93 | | | (307) all_42_2 = e3
% 249.33/58.93 | | |
% 249.33/58.93 | | | REDUCE: (193), (306) imply:
% 249.33/58.93 | | | (308) op(e3, e4) = e0
% 249.33/58.93 | | |
% 249.33/58.93 | | | BETA: splitting (43) gives:
% 249.33/58.93 | | |
% 249.33/58.93 | | | Case 1:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | (309) ~ (all_42_2 = e3)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (307), (309) imply:
% 249.33/58.93 | | | | (310) $false
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | CLOSE: (310) is inconsistent.
% 249.33/58.93 | | | |
% 249.33/58.93 | | | Case 2:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | GROUND_INST: instantiating (35) with all_100_2, e0, e4, e3, simplifying
% 249.33/58.93 | | | | with (141), (308) gives:
% 249.33/58.93 | | | | (311) all_100_2 = e0
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (154), (311) imply:
% 249.33/58.93 | | | | (312) ~ (all_244_3 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (156), (311) imply:
% 249.33/58.93 | | | | (313) ~ (all_48_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | SIMP: (313) implies:
% 249.33/58.93 | | | | (314) ~ (all_48_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (65), (311) imply:
% 249.33/58.93 | | | | (315) ~ (all_36_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | SIMP: (315) implies:
% 249.33/58.93 | | | | (316) ~ (all_36_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (137), (311) imply:
% 249.33/58.93 | | | | (317) ~ (all_8_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | SIMP: (317) implies:
% 249.33/58.93 | | | | (318) ~ (all_8_2 = e0)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | BETA: splitting (175) gives:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | Case 1:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (319) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3,
% 249.33/58.93 | | | | | e4) = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REF_CLOSE: (10), (27), (35), (70), (105), (144), (151), (170), (187),
% 249.33/58.93 | | | | | (312), (314), (316), (318), (319) are inconsistent by
% 249.33/58.93 | | | | | sub-proof #459.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | Case 2:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (320) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 249.33/58.93 | | | | | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REF_CLOSE: (13), (35), (71), (84), (104), (162), (200), (202), (207),
% 249.33/58.93 | | | | | (320) are inconsistent by sub-proof #758.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | End of split
% 249.33/58.93 | | | |
% 249.33/58.93 | | | End of split
% 249.33/58.93 | | |
% 249.33/58.93 | | End of split
% 249.33/58.93 | |
% 249.33/58.93 | Case 2:
% 249.33/58.93 | |
% 249.33/58.93 | | (321) all_16_2 = e2
% 249.33/58.93 | | (322) ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 & op(e2, all_16_1) =
% 249.33/58.93 | | all_16_0 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e0) &
% 249.33/58.93 | | op(e4, e2) = all_16_1 & $i(all_16_1))
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (171), (321) imply:
% 249.33/58.93 | | (323) ~ (all_64_2 = e2)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (169), (321) imply:
% 249.33/58.93 | | (324) ~ (all_4_2 = e2)
% 249.33/58.93 | |
% 249.33/58.93 | | SIMP: (324) implies:
% 249.33/58.93 | | (325) ~ (all_4_2 = e2)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (178), (321) imply:
% 249.33/58.93 | | (326) op(e2, e4) = e1
% 249.33/58.93 | |
% 249.33/58.93 | | GROUND_INST: instantiating (35) with all_64_2, e1, e4, e2, simplifying with
% 249.33/58.93 | | (162), (326) gives:
% 249.33/58.93 | | (327) all_64_2 = e1
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (41), (327) imply:
% 249.33/58.93 | | (328) ~ (all_244_8 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (66), (327) imply:
% 249.33/58.93 | | (329) ~ (all_100_2 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (136), (327) imply:
% 249.33/58.93 | | (330) ~ (all_38_2 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | SIMP: (330) implies:
% 249.33/58.93 | | (331) ~ (all_38_2 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (200), (327) imply:
% 249.33/58.93 | | (332) ~ (e4 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (323), (327) imply:
% 249.33/58.93 | | (333) ~ (e2 = e1)
% 249.33/58.93 | |
% 249.33/58.93 | | BETA: splitting (197) gives:
% 249.33/58.93 | |
% 249.33/58.93 | | Case 1:
% 249.33/58.93 | | |
% 249.33/58.93 | | | (334) ~ (all_22_2 = e1)
% 249.33/58.93 | | |
% 249.33/58.93 | | | BETA: splitting (92) gives:
% 249.33/58.93 | | |
% 249.33/58.93 | | | Case 1:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | (335) ~ (all_32_2 = e2)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (3), (335) imply:
% 249.33/58.93 | | | | (336) ~ (all_20_2 = e2)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | BETA: splitting (115) gives:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | Case 1:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (337) ~ (all_46_2 = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REF_CLOSE: (5), (7), (35), (42), (45), (77), (105), (134), (146),
% 249.33/58.93 | | | | | (148), (149), (158), (195), (328), (331), (336), (337) are
% 249.33/58.93 | | | | | inconsistent by sub-proof #598.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | Case 2:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (338) all_46_2 = e2
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | COMBINE_EQS: (195), (338) imply:
% 249.33/58.93 | | | | | (339) all_36_2 = e2
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | SIMP: (339) implies:
% 249.33/58.93 | | | | | (340) all_36_2 = e2
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (96), (340) imply:
% 249.33/58.93 | | | | | (341) ~ (all_48_2 = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (119), (340) imply:
% 249.33/58.93 | | | | | (342) ~ (all_26_2 = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (47), (340) imply:
% 249.33/58.93 | | | | | (343) ~ (all_20_2 = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (172), (340) imply:
% 249.33/58.93 | | | | | (344) op(e2, e1) = e3
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | GROUND_INST: instantiating (35) with all_38_2, e3, e1, e2, simplifying
% 249.33/58.93 | | | | | with (45), (344) gives:
% 249.33/58.93 | | | | | (345) all_38_2 = e3
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | COMBINE_EQS: (190), (345) imply:
% 249.33/58.93 | | | | | (346) all_188_2 = e3
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (117), (345) imply:
% 249.33/58.93 | | | | | (347) ~ (all_244_15 = e3)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | BETA: splitting (140) gives:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | Case 1:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | (348) ~ (all_188_2 = e3)
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | REDUCE: (346), (348) imply:
% 249.33/58.93 | | | | | | (349) $false
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | CLOSE: (349) is inconsistent.
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | Case 2:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | (350) ( ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 249.33/58.93 | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 249.33/58.93 | | | | | | ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 249.33/58.93 | | | | | | $i(all_188_1))
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | BETA: splitting (350) gives:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | Case 1:
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | (351) ~ (all_188_0 = e0) & op(e3, all_188_1) = all_188_0 &
% 249.33/58.93 | | | | | | | op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | ALPHA: (351) implies:
% 249.33/58.93 | | | | | | | (352) op(e1, e3) = all_188_1
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | REF_CLOSE: (5), (7), (11), (35), (42), (45), (52), (56), (63),
% 249.33/58.93 | | | | | | | (64), (69), (77), (89), (98), (108), (116), (125),
% 249.33/58.93 | | | | | | | (129), (134), (141), (146), (148), (149), (151), (152),
% 249.33/58.93 | | | | | | | (158), (161), (170), (172), (183), (187), (192), (328),
% 249.33/58.93 | | | | | | | (329), (331), (334), (336), (341), (347), (352) are
% 249.33/58.93 | | | | | | | inconsistent by sub-proof #105.
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | Case 2:
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | (353) ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 &
% 249.33/58.93 | | | | | | | $i(all_188_1)
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | ALPHA: (353) implies:
% 249.33/58.93 | | | | | | | (354) op(e1, e3) = all_188_1
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | REF_CLOSE: (5), (7), (11), (35), (42), (45), (52), (56), (63),
% 249.33/58.93 | | | | | | | (64), (69), (77), (89), (98), (108), (116), (125),
% 249.33/58.93 | | | | | | | (129), (134), (141), (146), (148), (149), (151), (152),
% 249.33/58.93 | | | | | | | (158), (161), (170), (172), (183), (187), (192), (328),
% 249.33/58.93 | | | | | | | (329), (331), (334), (336), (341), (347), (354) are
% 249.33/58.93 | | | | | | | inconsistent by sub-proof #105.
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | End of split
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | End of split
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | End of split
% 249.33/58.93 | | | |
% 249.33/58.93 | | | Case 2:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | (355) all_32_2 = e2
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | COMBINE_EQS: (3), (355) imply:
% 249.33/58.93 | | | | (356) all_20_2 = e2
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | COMBINE_EQS: (145), (356) imply:
% 249.33/58.93 | | | | (357) all_230_2 = e2
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (31), (356) imply:
% 249.33/58.93 | | | | (358) ~ (all_244_24 = e2)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (88), (356) imply:
% 249.33/58.93 | | | | (359) ~ (all_28_2 = e2)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (59), (356) imply:
% 249.33/58.93 | | | | (360) ~ (all_12_2 = e2)
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | REDUCE: (95), (356) imply:
% 249.33/58.93 | | | | (361) op(e2, e1) = e0
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | BETA: splitting (93) gives:
% 249.33/58.93 | | | |
% 249.33/58.93 | | | | Case 1:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (362) ~ (all_230_2 = e2)
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | REDUCE: (357), (362) imply:
% 249.33/58.93 | | | | | (363) $false
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | CLOSE: (363) is inconsistent.
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | Case 2:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | (364) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1,
% 249.33/58.93 | | | | | e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) | ( ~
% 249.33/58.93 | | | | | (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | BETA: splitting (364) gives:
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | | Case 1:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | (365) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 &
% 249.33/58.93 | | | | | | op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | ALPHA: (365) implies:
% 249.33/58.93 | | | | | | (366) op(e1, e2) = all_230_1
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | GROUND_INST: instantiating (35) with all_4_2, all_230_1, e2, e1,
% 249.33/58.93 | | | | | | simplifying with (155), (366) gives:
% 249.33/58.93 | | | | | | (367) all_230_1 = all_4_2
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | GROUND_INST: instantiating (35) with all_38_2, e0, e1, e2,
% 249.33/58.93 | | | | | | simplifying with (45), (361) gives:
% 249.33/58.93 | | | | | | (368) all_38_2 = e0
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | REF_CLOSE: (6), (20), (25), (28), (35), (37), (39), (42), (46),
% 249.33/58.93 | | | | | | (55), (68), (73), (81), (108), (112), (129), (153),
% 249.33/58.93 | | | | | | (158), (163), (170), (204), (322), (325), (328), (334),
% 249.33/58.93 | | | | | | (358), (366), (367), (368) are inconsistent by sub-proof
% 249.33/58.93 | | | | | | #103.
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | Case 2:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | (369) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 &
% 249.33/58.93 | | | | | | $i(all_230_1)
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | ALPHA: (369) implies:
% 249.33/58.93 | | | | | | (370) ~ (all_230_1 = e4)
% 249.33/58.93 | | | | | | (371) op(e1, e2) = all_230_1
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | BETA: splitting (135) gives:
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | | Case 1:
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | (372) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 249.33/58.93 | | | | | | | op(e0, e3) = e2)
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | REF_CLOSE: (22), (35), (104), (129), (202), (372) are inconsistent
% 249.33/58.93 | | | | | | | by sub-proof #727.
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | Case 2:
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | (373) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 249.33/58.93 | | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | BETA: splitting (373) gives:
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | | Case 1:
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | | (374) all_252_22 = e2 & op(e0, e2) = e2
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | | REF_CLOSE: (35), (68), (359), (374) are inconsistent by
% 249.33/58.93 | | | | | | | | sub-proof #979.
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | Case 2:
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | | (375) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2
% 249.33/58.93 | | | | | | | | & op(e0, e0) = e2)
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | | BETA: splitting (375) gives:
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | | Case 1:
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | GROUND_INST: instantiating (35) with all_4_2, all_230_1, e2,
% 249.33/58.93 | | | | | | | | | e1, simplifying with (155), (371) gives:
% 249.33/58.93 | | | | | | | | | (376) all_230_1 = all_4_2
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | GROUND_INST: instantiating (35) with all_38_2, e0, e1, e2,
% 249.33/58.93 | | | | | | | | | simplifying with (45), (361) gives:
% 249.33/58.93 | | | | | | | | | (377) all_38_2 = e0
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | REF_CLOSE: (6), (20), (25), (28), (35), (37), (39), (42),
% 249.33/58.93 | | | | | | | | | (46), (55), (68), (73), (81), (108), (112), (129),
% 249.33/58.93 | | | | | | | | | (153), (158), (163), (170), (204), (322), (325),
% 249.33/58.93 | | | | | | | | | (328), (334), (358), (371), (376), (377) are
% 249.33/58.93 | | | | | | | | | inconsistent by sub-proof #103.
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | Case 2:
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | (378) all_252_24 = e2 & op(e0, e0) = e2
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | ALPHA: (378) implies:
% 249.33/58.93 | | | | | | | | | (379) op(e0, e0) = e2
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | | REF_CLOSE: (35), (37), (358), (379) are inconsistent by
% 249.33/58.93 | | | | | | | | | sub-proof #978.
% 249.33/58.93 | | | | | | | | |
% 249.33/58.93 | | | | | | | | End of split
% 249.33/58.93 | | | | | | | |
% 249.33/58.93 | | | | | | | End of split
% 249.33/58.93 | | | | | | |
% 249.33/58.93 | | | | | | End of split
% 249.33/58.93 | | | | | |
% 249.33/58.93 | | | | | End of split
% 249.33/58.93 | | | | |
% 249.33/58.93 | | | | End of split
% 249.33/58.93 | | | |
% 249.33/58.93 | | | End of split
% 249.33/58.93 | | |
% 249.33/58.93 | | Case 2:
% 249.33/58.93 | | |
% 249.33/58.93 | | | (380) all_22_2 = e1
% 249.33/58.93 | | |
% 249.33/58.93 | | | REDUCE: (130), (380) imply:
% 249.33/58.93 | | | (381) ~ (all_28_2 = e1)
% 249.33/58.93 | | |
% 249.33/58.93 | | | REF_CLOSE: (25), (28), (35), (42), (46), (55), (68), (73), (108), (155),
% 249.33/58.93 | | | (170), (325), (328), (381) are inconsistent by sub-proof #228.
% 249.33/58.93 | | |
% 249.33/58.93 | | End of split
% 249.33/58.93 | |
% 249.33/58.93 | End of split
% 249.33/58.93 |
% 249.33/58.93 End of proof
% 249.33/58.93
% 249.33/58.93 Sub-proof #103 shows that the following formulas are inconsistent:
% 249.33/58.93 ----------------------------------------------------------------
% 249.33/58.93 (1) ~ (all_4_2 = e4)
% 249.33/58.93 (2) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.33/58.93 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.33/58.93 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.33/58.93 (3) op(all_38_2, e1) = e2
% 249.33/58.93 (4) op(all_38_2, all_4_2) = e1
% 249.33/58.93 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.93 (6) op(e0, e0) = all_244_24
% 249.33/58.93 (7) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 249.33/58.93 all_250_17 = e0
% 249.33/58.93 (8) op(e2, e2) = all_244_8
% 249.33/58.93 (9) ( ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 & op(e2, all_16_1) = all_16_0
% 249.33/58.93 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e0) & op(e4, e2) =
% 249.33/58.93 all_16_1 & $i(all_16_1))
% 249.33/58.93 (10) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.33/58.93 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.33/58.93 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.33/58.93 (11) op(e4, e2) = all_6_2
% 249.33/58.93 (12) op(e0, e2) = all_28_2
% 249.33/58.93 (13) ~ (all_6_2 = e1)
% 249.33/58.93 (14) all_50_2 = all_4_2
% 249.33/58.93 (15) all_38_2 = e0
% 249.33/58.93 (16) ~ (all_8_2 = e1)
% 249.33/58.93 (17) ~ (all_22_2 = e1)
% 249.33/58.93 (18) ~ (all_28_2 = all_4_2)
% 249.33/58.93 (19) op(e0, e3) = all_22_2
% 249.33/58.93 (20) ~ (all_244_8 = e1)
% 249.33/58.93 (21) all_230_1 = all_4_2
% 249.33/58.93 (22) all_82_2 = all_28_2
% 249.33/58.93 (23) ~ (all_244_24 = e2)
% 249.33/58.93 (24) op(all_4_2, all_38_2) = e2
% 249.33/58.93 (25) all_250_17 = all_4_2
% 249.33/58.93 (26) op(e3, e2) = all_8_2
% 249.33/58.93 (27) op(e1, e2) = all_230_1
% 249.33/58.93 (28) ~ (all_4_2 = e2)
% 249.33/58.93 (29) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 249.33/58.93 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 249.33/58.93 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 249.33/58.93
% 249.33/58.93 Begin of proof
% 249.33/58.93 |
% 249.33/58.93 | REDUCE: (4), (15) imply:
% 249.33/58.93 | (30) op(e0, all_4_2) = e1
% 249.33/58.93 |
% 249.33/58.93 | REDUCE: (15), (24) imply:
% 249.33/58.93 | (31) op(all_4_2, e0) = e2
% 249.33/58.93 |
% 249.33/58.93 | REDUCE: (21), (27) imply:
% 249.33/58.93 | (32) op(e1, e2) = all_4_2
% 249.33/58.93 |
% 249.33/58.93 | BETA: splitting (29) gives:
% 249.33/58.93 |
% 249.33/58.93 | Case 1:
% 249.33/58.93 | |
% 249.33/58.93 | | (33) ~ (all_50_2 = e3)
% 249.33/58.93 | |
% 249.33/58.93 | | REDUCE: (14), (33) imply:
% 249.33/58.93 | | (34) ~ (all_4_2 = e3)
% 249.33/58.93 | |
% 249.33/58.93 | | BETA: splitting (9) gives:
% 249.33/58.93 | |
% 249.33/58.93 | | Case 1:
% 249.33/58.93 | | |
% 249.33/58.93 | | | (35) ~ (all_16_0 = e3) & op(e4, e2) = all_16_1 & op(e2, all_16_1) =
% 249.33/58.93 | | | all_16_0 & $i(all_16_0) & $i(all_16_1)
% 249.33/58.93 | | |
% 249.33/58.93 | | | ALPHA: (35) implies:
% 249.33/58.93 | | | (36) op(e4, e2) = all_16_1
% 249.33/58.93 | | |
% 249.33/58.93 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 249.33/58.93 | | | (16), (18), (20), (22), (23), (25), (26), (28), (31), (32),
% 249.33/58.93 | | | (34), (36) are inconsistent by sub-proof #104.
% 249.33/58.93 | | |
% 249.33/58.93 | | Case 2:
% 249.33/58.93 | | |
% 249.33/58.93 | | | (37) ~ (all_16_1 = e0) & op(e4, e2) = all_16_1 & $i(all_16_1)
% 249.33/58.93 | | |
% 249.33/58.93 | | | ALPHA: (37) implies:
% 249.33/58.93 | | | (38) op(e4, e2) = all_16_1
% 249.33/58.93 | | |
% 249.33/58.93 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 249.33/58.93 | | | (16), (18), (20), (22), (23), (25), (26), (28), (31), (32),
% 249.33/58.93 | | | (34), (38) are inconsistent by sub-proof #104.
% 249.33/58.93 | | |
% 249.33/58.93 | | End of split
% 249.33/58.93 | |
% 249.33/58.93 | Case 2:
% 249.33/58.93 | |
% 249.33/58.93 | | (39) all_50_2 = e3
% 249.33/58.93 | |
% 249.33/58.93 | | REF_CLOSE: (5), (14), (17), (19), (30), (39) are inconsistent by sub-proof
% 249.33/58.93 | | #713.
% 249.33/58.93 | |
% 249.33/58.93 | End of split
% 249.33/58.93 |
% 249.33/58.93 End of proof
% 249.33/58.93
% 249.33/58.93 Sub-proof #104 shows that the following formulas are inconsistent:
% 249.33/58.93 ----------------------------------------------------------------
% 249.33/58.93 (1) op(e4, e2) = all_16_1
% 249.33/58.93 (2) ~ (all_4_2 = e4)
% 249.33/58.93 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.33/58.93 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.33/58.93 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.33/58.93 (4) op(all_38_2, e1) = e2
% 249.33/58.93 (5) op(all_38_2, all_4_2) = e1
% 249.33/58.93 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.93 (7) op(e0, e0) = all_244_24
% 249.33/58.93 (8) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 249.33/58.93 all_250_17 = e0
% 249.33/58.93 (9) op(e2, e2) = all_244_8
% 249.33/58.93 (10) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.33/58.93 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.33/58.93 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.33/58.93 (11) op(e4, e2) = all_6_2
% 249.33/58.93 (12) op(e0, e2) = all_28_2
% 249.33/58.93 (13) ~ (all_6_2 = e1)
% 249.33/58.93 (14) ~ (all_8_2 = e1)
% 249.33/58.94 (15) ~ (all_28_2 = all_4_2)
% 249.33/58.94 (16) op(all_4_2, e0) = e2
% 249.33/58.94 (17) ~ (all_244_8 = e1)
% 249.33/58.94 (18) all_82_2 = all_28_2
% 249.33/58.94 (19) ~ (all_244_24 = e2)
% 249.33/58.94 (20) op(e1, e2) = all_4_2
% 249.33/58.94 (21) all_250_17 = all_4_2
% 249.33/58.94 (22) op(e3, e2) = all_8_2
% 249.33/58.94 (23) ~ (all_4_2 = e3)
% 249.33/58.94 (24) ~ (all_4_2 = e2)
% 249.33/58.94
% 249.33/58.94 Begin of proof
% 249.33/58.94 |
% 249.33/58.94 | GROUND_INST: instantiating (6) with all_6_2, all_16_1, e2, e4, simplifying
% 249.33/58.94 | with (1), (11) gives:
% 249.33/58.94 | (25) all_16_1 = all_6_2
% 249.33/58.94 |
% 249.33/58.94 | BETA: splitting (3) gives:
% 249.33/58.94 |
% 249.33/58.94 | Case 1:
% 249.33/58.94 | |
% 249.33/58.94 | | (26) ~ (all_82_2 = e1)
% 249.33/58.94 | |
% 249.33/58.94 | | REDUCE: (18), (26) imply:
% 249.33/58.94 | | (27) ~ (all_28_2 = e1)
% 249.33/58.94 | |
% 249.33/58.94 | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (12), (13), (14), (17), (20),
% 249.33/58.94 | | (22), (24), (27) are inconsistent by sub-proof #228.
% 249.33/58.94 | |
% 249.33/58.94 | Case 2:
% 249.33/58.94 | |
% 249.33/58.94 | | (28) all_82_2 = e1
% 249.33/58.94 | |
% 249.33/58.94 | | COMBINE_EQS: (18), (28) imply:
% 249.33/58.94 | | (29) all_28_2 = e1
% 249.33/58.94 | |
% 249.33/58.94 | | SIMP: (29) implies:
% 249.33/58.94 | | (30) all_28_2 = e1
% 249.33/58.94 | |
% 249.33/58.94 | | REDUCE: (15), (30) imply:
% 249.33/58.94 | | (31) ~ (all_4_2 = e1)
% 249.33/58.94 | |
% 249.33/58.94 | | SIMP: (31) implies:
% 249.33/58.94 | | (32) ~ (all_4_2 = e1)
% 249.33/58.94 | |
% 249.33/58.94 | | REF_CLOSE: (2), (6), (7), (8), (16), (19), (21), (23), (24), (32) are
% 249.33/58.94 | | inconsistent by sub-proof #718.
% 249.33/58.94 | |
% 249.33/58.94 | End of split
% 249.33/58.94 |
% 249.33/58.94 End of proof
% 249.33/58.94
% 249.33/58.94 Sub-proof #105 shows that the following formulas are inconsistent:
% 249.33/58.94 ----------------------------------------------------------------
% 249.33/58.94 (1) ~ (all_26_2 = e2)
% 249.33/58.94 (2) op(all_4_2, e2) = e1
% 249.33/58.94 (3) ~ (all_38_2 = e1)
% 249.33/58.94 (4) op(all_36_2, all_62_2) = e1
% 249.33/58.94 (5) ~ (all_48_2 = e2)
% 249.33/58.94 (6) ~ (all_100_2 = e1)
% 249.33/58.94 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.33/58.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.33/58.94 (8) op(e2, e2) = all_244_8
% 249.33/58.94 (9) op(e2, e1) = all_38_2
% 249.33/58.94 (10) op(e1, e0) = all_34_2
% 249.33/58.94 (11) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.33/58.94 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.33/58.94 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 249.33/58.94 (12) ~ (e2 = e1)
% 249.33/58.94 (13) all_252_7 = e4
% 249.33/58.94 (14) ~ (e4 = e1)
% 249.33/58.94 (15) op(all_244_15, all_244_15) = e1
% 249.33/58.94 (16) op(e1, e3) = all_62_2
% 249.33/58.94 (17) all_252_1 = e2
% 249.33/58.94 (18) ~ (all_8_2 = e1)
% 249.33/58.94 (19) ~ (all_22_2 = e1)
% 249.33/58.94 (20) ~ (all_48_2 = all_34_2)
% 249.33/58.94 (21) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 249.33/58.94 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 249.33/58.94 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 249.33/58.94 (22) op(e1, e3) = all_188_1
% 249.33/58.94 (23) op(e0, e3) = all_22_2
% 249.33/58.94 (24) op(e4, e1) = all_26_2
% 249.33/58.94 (25) ~ (all_244_15 = e3)
% 249.33/58.94 (26) op(e3, e4) = all_100_2
% 249.33/58.94 (27) ~ (all_244_8 = e1)
% 249.33/58.94 (28) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 249.33/58.94 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 249.33/58.94 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.33/58.94 (29) op(e1, e1) = all_244_15
% 249.33/58.94 (30) op(e0, e1) = all_20_2
% 249.49/58.94 (31) op(e3, e0) = all_48_2
% 249.49/58.94 (32) op(all_48_2, e0) = e3
% 249.49/58.94 (33) op(all_4_2, all_38_2) = e2
% 249.49/58.94 (34) op(all_244_3, all_244_3) = e3
% 249.49/58.94 (35) op(e3, e2) = all_8_2
% 249.49/58.94 (36) op(all_36_2, e1) = e3
% 249.49/58.94 (37) ~ (all_244_3 = all_48_2)
% 249.49/58.94 (38) op(e3, e3) = all_244_3
% 249.49/58.94 (39) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/58.94 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/58.94 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/58.94 (40) ~ (all_20_2 = e2)
% 249.49/58.94
% 249.49/58.94 Begin of proof
% 249.49/58.94 |
% 249.49/58.94 | GROUND_INST: instantiating (7) with all_62_2, all_188_1, e3, e1, simplifying
% 249.49/58.94 | with (16), (22) gives:
% 249.49/58.94 | (41) all_188_1 = all_62_2
% 249.49/58.94 |
% 249.49/58.94 | BETA: splitting (21) gives:
% 249.49/58.94 |
% 249.49/58.94 | Case 1:
% 249.49/58.94 | |
% 249.49/58.94 | | (42) ~ (all_48_2 = e1)
% 249.49/58.94 | |
% 249.49/58.94 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (12), (15), (18), (24),
% 249.49/58.94 | | (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (38),
% 249.49/58.94 | | (40), (42) are inconsistent by sub-proof #230.
% 249.49/58.94 | |
% 249.49/58.94 | Case 2:
% 249.49/58.94 | |
% 249.49/58.94 | | (43) all_48_2 = e1
% 249.49/58.94 | |
% 249.49/58.94 | | REDUCE: (37), (43) imply:
% 249.49/58.94 | | (44) ~ (all_244_3 = e1)
% 249.49/58.94 | |
% 249.49/58.94 | | REDUCE: (20), (43) imply:
% 249.49/58.94 | | (45) ~ (all_34_2 = e1)
% 249.49/58.94 | |
% 249.49/58.94 | | SIMP: (45) implies:
% 249.49/58.94 | | (46) ~ (all_34_2 = e1)
% 249.49/58.94 | |
% 249.49/58.94 | | REDUCE: (5), (43) imply:
% 249.49/58.94 | | (47) ~ (e2 = e1)
% 249.49/58.94 | |
% 249.49/58.94 | | REF_CLOSE: (4), (7), (10), (12), (13), (14), (16), (17), (19), (23), (32),
% 249.49/58.94 | | (36), (38), (39), (43), (44), (46) are inconsistent by sub-proof
% 249.49/58.94 | | #119.
% 249.49/58.94 | |
% 249.49/58.94 | End of split
% 249.49/58.94 |
% 249.49/58.94 End of proof
% 249.49/58.94
% 249.49/58.94 Sub-proof #106 shows that the following formulas are inconsistent:
% 249.49/58.94 ----------------------------------------------------------------
% 249.49/58.94 (1) ~ (all_30_2 = all_26_2)
% 249.49/58.94 (2) ~ (all_26_2 = e2)
% 249.49/58.94 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 249.49/58.94 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 249.49/58.94 (all_252_16 = e3 & op(e4, e0) = e3)
% 249.49/58.94 (4) op(all_6_2, e2) = e4
% 249.49/58.94 (5) op(e4, e1) = e0
% 249.49/58.94 (6) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/58.94 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/58.94 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.94 (7) op(e4, e0) = all_30_2
% 249.49/58.94 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/58.94 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/58.94 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/58.94 (9) all_94_2 = all_38_2
% 249.49/58.94 (10) op(all_62_2, all_36_2) = e3
% 249.49/58.94 (11) op(all_38_2, e1) = e2
% 249.49/58.94 (12) ~ (all_28_2 = all_6_2)
% 249.49/58.94 (13) op(all_38_2, all_4_2) = e1
% 249.49/58.94 (14) op(all_64_2, e4) = e2
% 249.49/58.94 (15) ~ (e1 = e0)
% 249.49/58.94 (16) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 249.49/58.94 all_250_20 = e0
% 249.49/58.94 (17) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.49/58.94 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.49/58.94 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.49/58.94 (18) op(e4, all_34_2) = e1
% 249.49/58.94 (19) ~ (all_62_2 = e2)
% 249.49/58.94 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.94 (21) ~ (e3 = e2)
% 249.49/58.94 (22) ~ (all_12_2 = e3)
% 249.49/58.94 (23) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.49/58.94 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.49/58.94 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.49/58.94 (24) ~ (all_244_8 = all_64_2)
% 249.49/58.94 (25) op(e2, e2) = all_244_8
% 249.49/58.94 (26) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/58.94 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/58.94 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.94 (27) op(e2, e1) = all_38_2
% 249.49/58.94 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/58.94 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/58.94 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.94 (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 249.49/58.94 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 249.49/58.94 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 249.49/58.94 (30) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/58.94 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/58.94 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/58.94 (31) ~ (all_244_15 = all_26_2)
% 249.49/58.94 (32) all_216_2 = all_26_2
% 249.49/58.94 (33) op(e1, e0) = all_34_2
% 249.49/58.94 (34) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.49/58.94 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.49/58.94 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.49/58.94 (35) op(e4, e2) = all_6_2
% 249.49/58.94 (36) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.49/58.94 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.49/58.94 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.49/58.94 (37) ~ (all_244_15 = e4)
% 249.49/58.94 (38) ~ (e2 = e1)
% 249.49/58.94 (39) all_252_7 = e4
% 249.49/58.94 (40) all_56_2 = all_8_2
% 249.49/58.94 (41) op(e0, e2) = all_28_2
% 249.49/58.94 (42) ~ (e4 = e1)
% 249.49/58.94 (43) ~ (all_244_0 = e2)
% 249.49/58.94 (44) op(all_6_2, all_64_2) = e2
% 249.49/58.94 (45) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/58.94 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/58.94 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/58.94 (46) ~ (all_6_2 = e1)
% 249.49/58.94 (47) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.49/58.94 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.49/58.94 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.49/58.94 (48) op(e1, e4) = all_20_1
% 249.49/58.94 (49) ~ (all_244_8 = all_38_2)
% 249.49/58.94 (50) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/58.94 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/58.94 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/58.94 (51) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 249.49/58.94 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 249.49/58.94 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 249.49/58.94 (52) op(e1, e4) = all_16_2
% 249.49/58.94 (53) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 249.49/58.94 all_250_2 = e0
% 249.49/58.94 (54) op(e1, e3) = all_62_2
% 249.49/58.94 (55) ~ (e3 = e0)
% 249.49/58.94 (56) ~ (all_84_2 = e4)
% 249.49/58.94 (57) all_252_1 = e2
% 249.49/58.94 (58) ~ (all_36_2 = e4)
% 249.49/58.94 (59) ~ (all_6_2 = e2)
% 249.49/58.94 (60) all_70_2 = all_62_2
% 249.49/58.94 (61) ~ (e3 = e1)
% 249.49/58.94 (62) ~ (all_12_2 = e2)
% 249.49/58.94 (63) op(e3, e1) = all_36_2
% 249.49/58.94 (64) ~ (all_28_2 = all_12_2)
% 249.49/58.94 (65) ~ (all_16_2 = e2)
% 249.49/58.94 (66) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.49/58.94 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 249.49/58.94 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 249.49/58.94 (67) ~ (all_8_2 = e1)
% 249.49/58.94 (68) ~ (all_244_8 = all_40_2)
% 249.49/58.94 (69) op(e2, all_100_2) = e3
% 249.49/58.94 (70) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 249.49/58.94 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 249.49/58.94 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 249.49/58.94 (71) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/58.94 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/58.94 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/58.94 (72) ~ (all_36_2 = all_26_2)
% 249.49/58.94 (73) op(e4, e3) = e2
% 249.49/58.94 (74) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 249.49/58.94 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 249.49/58.94 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 249.49/58.94 (75) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 249.49/58.94 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 249.49/58.94 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 249.49/58.94 (76) all_60_2 = e4
% 249.49/58.94 (77) ~ (all_38_2 = e4)
% 249.49/58.94 (78) all_182_2 = e2
% 249.49/58.94 (79) ~ (all_26_2 = all_6_2)
% 249.49/58.94 (80) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 249.49/58.94 op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 =
% 249.49/58.94 e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 249.49/58.94 (81) ~ (all_26_2 = e4)
% 249.49/58.94 (82) op(e4, e1) = all_26_2
% 249.49/58.94 (83) op(all_30_2, all_12_2) = e0
% 249.49/58.94 (84) ~ (all_12_2 = e4)
% 249.49/58.94 (85) op(e3, e4) = all_100_2
% 249.49/58.94 (86) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 249.49/58.94 op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~
% 249.49/58.94 (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 249.49/58.94 (87) op(all_8_2, e4) = e2
% 249.49/58.94 (88) op(e4, e4) = all_244_0
% 249.49/58.94 (89) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 249.49/58.94 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 249.49/58.94 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.49/58.94 (90) ~ (e4 = e3)
% 249.49/58.94 (91) op(e1, e1) = all_244_15
% 249.49/58.94 (92) all_82_2 = all_28_2
% 249.49/58.94 (93) op(e1, e2) = all_4_2
% 249.49/58.94 (94) op(e4, e3) = all_84_2
% 249.49/58.94 (95) all_86_2 = all_40_2
% 249.49/58.94 (96) op(e2, e4) = all_64_2
% 249.49/58.94 (97) ~ (all_38_2 = all_26_2)
% 249.49/58.94 (98) ~ (e4 = e2)
% 249.49/58.94 (99) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/58.94 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/58.94 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/58.94 (100) op(e3, e2) = all_8_2
% 249.49/58.94 (101) op(all_36_2, e1) = e3
% 249.49/58.94 (102) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/58.94 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/58.94 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/58.94 (103) ~ (all_244_15 = all_36_2)
% 249.49/58.94 (104) op(e2, e0) = all_40_2
% 249.49/58.94 (105) op(all_8_2, e2) = e3
% 249.49/58.94 (106) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.94 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.94 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.94 (107) all_250_20 = all_12_2
% 249.49/58.94 (108) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/58.94 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/58.94 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/58.94 (109) all_250_2 = all_6_2
% 249.49/58.94 (110) all_46_2 = all_36_2
% 249.49/58.94 (111) op(all_30_2, e0) = e4
% 249.49/58.94 (112) ~ (all_64_2 = e4)
% 249.49/58.94 (113) op(e0, e4) = all_12_2
% 249.49/58.94 (114) op(all_64_2, all_6_2) = e4
% 249.49/58.94
% 249.49/58.94 Begin of proof
% 249.49/58.94 |
% 249.49/58.94 | BETA: splitting (34) gives:
% 249.49/58.94 |
% 249.49/58.94 | Case 1:
% 249.49/58.94 | |
% 249.49/58.94 | | (115) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1)
% 249.49/58.94 | | = e4)
% 249.49/58.94 | |
% 249.49/58.94 | | BETA: splitting (115) gives:
% 249.49/58.94 | |
% 249.49/58.94 | | Case 1:
% 249.49/58.94 | | |
% 249.49/58.94 | | | (116) all_252_9 = e4 & op(e4, e1) = e4
% 249.49/58.94 | | |
% 249.49/58.94 | | | REF_CLOSE: (20), (81), (82), (116) are inconsistent by sub-proof #114.
% 249.49/58.94 | | |
% 249.49/58.94 | | Case 2:
% 249.49/58.94 | | |
% 249.49/58.94 | | | (117) all_252_10 = e4 & op(e3, e1) = e4
% 249.49/58.94 | | |
% 249.49/58.94 | | | REF_CLOSE: (20), (58), (63), (117) are inconsistent by sub-proof #914.
% 249.49/58.94 | | |
% 249.49/58.94 | | End of split
% 249.49/58.94 | |
% 249.49/58.94 | Case 2:
% 249.49/58.94 | |
% 249.49/58.94 | | (118) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 249.49/58.94 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.49/58.94 | |
% 249.49/58.94 | | BETA: splitting (118) gives:
% 249.49/58.94 | |
% 249.49/58.94 | | Case 1:
% 249.49/58.94 | | |
% 249.49/58.94 | | | (119) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/58.94 | | |
% 249.49/58.94 | | | ALPHA: (119) implies:
% 249.49/58.94 | | | (120) op(e2, e1) = e4
% 249.49/58.94 | | |
% 249.49/58.94 | | | REF_CLOSE: (20), (27), (77), (120) are inconsistent by sub-proof #935.
% 249.49/58.94 | | |
% 249.49/58.94 | | Case 2:
% 249.49/58.94 | | |
% 249.49/58.94 | | | (121) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0,
% 249.49/58.94 | | | e1) = e4)
% 249.49/58.94 | | |
% 249.49/58.94 | | | BETA: splitting (121) gives:
% 249.49/58.94 | | |
% 249.49/58.94 | | | Case 1:
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | (122) all_252_15 = e4 & op(e1, e1) = e4
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | ALPHA: (122) implies:
% 249.49/58.94 | | | | (123) op(e1, e1) = e4
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REF_CLOSE: (20), (37), (91), (123) are inconsistent by sub-proof #756.
% 249.49/58.94 | | | |
% 249.49/58.94 | | | Case 2:
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | (124) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | ALPHA: (124) implies:
% 249.49/58.94 | | | | (125) all_252_23 = e4
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | GROUND_INST: instantiating (20) with all_16_2, all_20_1, e4, e1,
% 249.49/58.94 | | | | simplifying with (48), (52) gives:
% 249.49/58.94 | | | | (126) all_20_1 = all_16_2
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | GROUND_INST: instantiating (20) with all_26_2, e0, e1, e4, simplifying
% 249.49/58.94 | | | | with (5), (82) gives:
% 249.49/58.94 | | | | (127) all_26_2 = e0
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | COMBINE_EQS: (32), (127) imply:
% 249.49/58.94 | | | | (128) all_216_2 = e0
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (31), (127) imply:
% 249.49/58.94 | | | | (129) ~ (all_244_15 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (97), (127) imply:
% 249.49/58.94 | | | | (130) ~ (all_38_2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (72), (127) imply:
% 249.49/58.94 | | | | (131) ~ (all_36_2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (1), (127) imply:
% 249.49/58.94 | | | | (132) ~ (all_30_2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (79), (127) imply:
% 249.49/58.94 | | | | (133) ~ (all_6_2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | SIMP: (133) implies:
% 249.49/58.94 | | | | (134) ~ (all_6_2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (81), (127) imply:
% 249.49/58.94 | | | | (135) ~ (e4 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | SIMP: (135) implies:
% 249.49/58.94 | | | | (136) ~ (e4 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | REDUCE: (2), (127) imply:
% 249.49/58.94 | | | | (137) ~ (e2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | SIMP: (137) implies:
% 249.49/58.94 | | | | (138) ~ (e2 = e0)
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | BETA: splitting (74) gives:
% 249.49/58.94 | | | |
% 249.49/58.94 | | | | Case 1:
% 249.49/58.94 | | | | |
% 249.49/58.94 | | | | | (139) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4,
% 249.49/58.94 | | | | | e3) = e0)
% 249.49/58.94 | | | | |
% 249.49/58.94 | | | | | BETA: splitting (139) gives:
% 249.49/58.94 | | | | |
% 249.49/58.94 | | | | | Case 1:
% 249.49/58.94 | | | | | |
% 249.49/58.94 | | | | | | (140) all_252_0 = e0 & op(e4, e4) = e0
% 249.49/58.94 | | | | | |
% 249.49/58.94 | | | | | | ALPHA: (140) implies:
% 249.49/58.94 | | | | | | (141) all_252_0 = e0
% 249.49/58.94 | | | | | |
% 249.49/58.94 | | | | | | BETA: splitting (51) gives:
% 249.49/58.94 | | | | | |
% 249.49/58.94 | | | | | | Case 1:
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | (142) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 &
% 249.49/58.94 | | | | | | | op(e4, e3) = e1)
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | BETA: splitting (142) gives:
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | Case 1:
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | (143) all_252_0 = e1 & op(e4, e4) = e1
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | REF_CLOSE: (15), (141), (143) are inconsistent by sub-proof
% 249.49/58.94 | | | | | | | | #843.
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | Case 2:
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | (144) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | REF_CLOSE: (38), (57), (144) are inconsistent by sub-proof #127.
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | End of split
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | Case 2:
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | (145) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 &
% 249.49/58.94 | | | | | | | op(e4, e1) = e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | BETA: splitting (145) gives:
% 249.49/58.94 | | | | | | |
% 249.49/58.94 | | | | | | | Case 1:
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | (146) all_252_4 = e1 & op(e4, e2) = e1
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | ALPHA: (146) implies:
% 249.49/58.94 | | | | | | | | (147) op(e4, e2) = e1
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | REF_CLOSE: (20), (35), (46), (147) are inconsistent by sub-proof
% 249.49/58.94 | | | | | | | | #930.
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | Case 2:
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | (148) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 249.49/58.94 | | | | | | | | op(e4, e0) = e1)
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | BETA: splitting (148) gives:
% 249.49/58.94 | | | | | | | |
% 249.49/58.94 | | | | | | | | Case 1:
% 249.49/58.94 | | | | | | | | |
% 249.49/58.94 | | | | | | | | | (149) all_252_9 = e1 & op(e4, e1) = e1
% 249.49/58.94 | | | | | | | | |
% 249.49/58.94 | | | | | | | | | ALPHA: (149) implies:
% 249.49/58.94 | | | | | | | | | (150) all_252_9 = e1
% 249.49/58.94 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | REF_CLOSE: (6), (15), (20), (27), (63), (91), (125), (129),
% 249.49/58.95 | | | | | | | | | (130), (131), (136), (150) are inconsistent by
% 249.49/58.95 | | | | | | | | | sub-proof #112.
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | (151) all_252_16 = e1 & op(e4, e0) = e1
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | ALPHA: (151) implies:
% 249.49/58.95 | | | | | | | | | (152) all_252_16 = e1
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | BETA: splitting (6) gives:
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | (153) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 249.49/58.95 | | | | | | | | | | e0 & op(e3, e1) = e0)
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | BETA: splitting (153) gives:
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | (154) all_252_9 = e0 & op(e4, e1) = e0
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | ALPHA: (154) implies:
% 249.49/58.95 | | | | | | | | | | | (155) all_252_9 = e0
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | BETA: splitting (29) gives:
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | (156) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 249.49/58.95 | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | BETA: splitting (156) gives:
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | (157) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | REF_CLOSE: (136), (141), (157) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | | | | | | | #570.
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | (158) all_252_1 = e4 & op(e4, e3) = e4
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | REF_CLOSE: (20), (56), (94), (158) are inconsistent by
% 249.49/58.95 | | | | | | | | | | | | | sub-proof #815.
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | (159) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 249.49/58.95 | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 249.49/58.95 | | | | | | | | | | | | op(e4, e0) = e4)
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | BETA: splitting (159) gives:
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | (160) all_252_4 = e4 & op(e4, e2) = e4
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | ALPHA: (160) implies:
% 249.49/58.95 | | | | | | | | | | | | | (161) all_252_4 = e4
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | (162) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 249.49/58.95 | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | (163) all_252_0 = e3 & op(e4, e4) = e3
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | REF_CLOSE: (55), (141), (163) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | | | | | | | | | #841.
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | (164) all_252_1 = e3 & op(e4, e3) = e3
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 249.49/58.95 | | | | | | | | | | | | | | | (165) all_252_1 = e3
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | COMBINE_EQS: (57), (165) imply:
% 249.49/58.95 | | | | | | | | | | | | | | | (166) e3 = e2
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | SIMP: (166) implies:
% 249.49/58.95 | | | | | | | | | | | | | | | (167) e3 = e2
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | REDUCE: (21), (167) imply:
% 249.49/58.95 | | | | | | | | | | | | | | | (168) $false
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | (169) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 249.49/58.95 | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 249.49/58.95 | | | | | | | | | | | | | | op(e4, e0) = e3)
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | (170) all_252_4 = e3 & op(e4, e2) = e3
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 249.49/58.95 | | | | | | | | | | | | | | | (171) all_252_4 = e3
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | REF_CLOSE: (90), (161), (171) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | | | | | | | | | #479.
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | (172) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 249.49/58.95 | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | | (173) all_252_9 = e3 & op(e4, e1) = e3
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | | REF_CLOSE: (55), (155), (173) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | | | | | | | | | | #251.
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | | (174) all_252_16 = e3 & op(e4, e0) = e3
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (152), (174) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | | | | | | | | | | #839.
% 249.49/58.95 | | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | (175) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 249.49/58.95 | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | BETA: splitting (175) gives:
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | (176) all_252_9 = e4 & op(e4, e1) = e4
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | ALPHA: (176) implies:
% 249.49/58.95 | | | | | | | | | | | | | | (177) op(e4, e1) = e4
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | REF_CLOSE: (5), (20), (82), (136), (177) are inconsistent by
% 249.49/58.95 | | | | | | | | | | | | | | sub-proof #286.
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | (178) all_252_16 = e4 & op(e4, e0) = e4
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | ALPHA: (178) implies:
% 249.49/58.95 | | | | | | | | | | | | | | (179) all_252_16 = e4
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | COMBINE_EQS: (152), (179) imply:
% 249.49/58.95 | | | | | | | | | | | | | | (180) e4 = e1
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | REDUCE: (42), (180) imply:
% 249.49/58.95 | | | | | | | | | | | | | | (181) $false
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 249.49/58.95 | | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | (182) all_252_10 = e0 & op(e3, e1) = e0
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | | REF_CLOSE: (20), (63), (131), (182) are inconsistent by
% 249.49/58.95 | | | | | | | | | | | sub-proof #726.
% 249.49/58.95 | | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | (183) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 =
% 249.49/58.95 | | | | | | | | | | e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0,
% 249.49/58.95 | | | | | | | | | | e1) = e0)
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | | REF_CLOSE: (20), (27), (91), (125), (129), (130), (136),
% 249.49/58.95 | | | | | | | | | | (183) are inconsistent by sub-proof #113.
% 249.49/58.95 | | | | | | | | | |
% 249.49/58.95 | | | | | | | | | End of split
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | End of split
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | End of split
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | End of split
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | Case 2:
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | (184) all_252_1 = e0 & op(e4, e3) = e0
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | ALPHA: (184) implies:
% 249.49/58.95 | | | | | | (185) op(e4, e3) = e0
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | REF_CLOSE: (20), (73), (94), (138), (185) are inconsistent by
% 249.49/58.95 | | | | | | sub-proof #850.
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | End of split
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | Case 2:
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | (186) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4,
% 249.49/58.95 | | | | | e1) = e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | BETA: splitting (186) gives:
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | Case 1:
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | (187) all_252_4 = e0 & op(e4, e2) = e0
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | REF_CLOSE: (20), (35), (134), (187) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | #875.
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | Case 2:
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | (188) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 = e0 &
% 249.49/58.95 | | | | | | op(e4, e0) = e0)
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | BETA: splitting (188) gives:
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | | Case 1:
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | (189) all_252_9 = e0 & op(e4, e1) = e0
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | ALPHA: (189) implies:
% 249.49/58.95 | | | | | | | (190) all_252_9 = e0
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | BETA: splitting (80) gives:
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | (191) ~ (all_60_2 = e4)
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | REDUCE: (76), (191) imply:
% 249.49/58.95 | | | | | | | | (192) $false
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | CLOSE: (192) is inconsistent.
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | (193) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 249.49/58.95 | | | | | | | | op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1))
% 249.49/58.95 | | | | | | | | | ( ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 &
% 249.49/58.95 | | | | | | | | $i(all_60_1))
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | BETA: splitting (193) gives:
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | | Case 1:
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | (194) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 249.49/58.95 | | | | | | | | | op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | ALPHA: (194) implies:
% 249.49/58.95 | | | | | | | | | (195) op(e1, e4) = all_60_1
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 249.49/58.95 | | | | | | | | | (15), (16), (17), (18), (19), (20), (21), (22),
% 249.49/58.95 | | | | | | | | | (23), (24), (25), (26), (27), (28), (30), (33),
% 249.49/58.95 | | | | | | | | | (35), (36), (38), (39), (40), (41), (42), (43),
% 249.49/58.95 | | | | | | | | | (44), (45), (46), (47), (49), (50), (52), (53),
% 249.49/58.95 | | | | | | | | | (54), (55), (59), (60), (61), (62), (63), (64),
% 249.49/58.95 | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (75),
% 249.49/58.95 | | | | | | | | | (78), (83), (84), (85), (86), (87), (88), (89),
% 249.49/58.95 | | | | | | | | | (90), (91), (92), (93), (95), (96), (98), (99),
% 249.49/58.95 | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 249.49/58.95 | | | | | | | | | (107), (108), (109), (110), (111), (112), (113),
% 249.49/58.95 | | | | | | | | | (114), (125), (128), (129), (130), (131), (134),
% 249.49/58.95 | | | | | | | | | (136), (138), (190), (195) are inconsistent by
% 249.49/58.95 | | | | | | | | | sub-proof #107.
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | Case 2:
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | (196) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 &
% 249.49/58.95 | | | | | | | | | $i(all_60_1)
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | ALPHA: (196) implies:
% 249.49/58.95 | | | | | | | | | (197) op(e1, e4) = all_60_1
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 249.49/58.95 | | | | | | | | | (15), (16), (17), (18), (19), (20), (21), (22),
% 249.49/58.95 | | | | | | | | | (23), (24), (25), (26), (27), (28), (30), (33),
% 249.49/58.95 | | | | | | | | | (35), (36), (38), (39), (40), (41), (42), (43),
% 249.49/58.95 | | | | | | | | | (44), (45), (46), (47), (49), (50), (52), (53),
% 249.49/58.95 | | | | | | | | | (54), (55), (59), (60), (61), (62), (63), (64),
% 249.49/58.95 | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (75),
% 249.49/58.95 | | | | | | | | | (78), (83), (84), (85), (86), (87), (88), (89),
% 249.49/58.95 | | | | | | | | | (90), (91), (92), (93), (95), (96), (98), (99),
% 249.49/58.95 | | | | | | | | | (100), (101), (102), (103), (104), (105), (106),
% 249.49/58.95 | | | | | | | | | (107), (108), (109), (110), (111), (112), (113),
% 249.49/58.95 | | | | | | | | | (114), (125), (128), (129), (130), (131), (134),
% 249.49/58.95 | | | | | | | | | (136), (138), (190), (197) are inconsistent by
% 249.49/58.95 | | | | | | | | | sub-proof #107.
% 249.49/58.95 | | | | | | | | |
% 249.49/58.95 | | | | | | | | End of split
% 249.49/58.95 | | | | | | | |
% 249.49/58.95 | | | | | | | End of split
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | Case 2:
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | (198) all_252_16 = e0 & op(e4, e0) = e0
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | | REF_CLOSE: (7), (20), (132), (198) are inconsistent by sub-proof
% 249.49/58.95 | | | | | | | #469.
% 249.49/58.95 | | | | | | |
% 249.49/58.95 | | | | | | End of split
% 249.49/58.95 | | | | | |
% 249.49/58.95 | | | | | End of split
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | End of split
% 249.49/58.95 | | | |
% 249.49/58.95 | | | End of split
% 249.49/58.95 | | |
% 249.49/58.95 | | End of split
% 249.49/58.95 | |
% 249.49/58.95 | End of split
% 249.49/58.95 |
% 249.49/58.95 End of proof
% 249.49/58.95
% 249.49/58.95 Sub-proof #107 shows that the following formulas are inconsistent:
% 249.49/58.95 ----------------------------------------------------------------
% 249.49/58.95 (1) op(all_6_2, e2) = e4
% 249.49/58.95 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/58.95 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/58.95 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.95 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/58.95 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/58.95 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/58.95 (4) all_94_2 = all_38_2
% 249.49/58.95 (5) op(all_62_2, all_36_2) = e3
% 249.49/58.95 (6) op(all_38_2, e1) = e2
% 249.49/58.95 (7) ~ (all_28_2 = all_6_2)
% 249.49/58.95 (8) all_216_2 = e0
% 249.49/58.95 (9) ~ (e2 = e0)
% 249.49/58.95 (10) op(all_38_2, all_4_2) = e1
% 249.49/58.95 (11) op(all_64_2, e4) = e2
% 249.49/58.95 (12) ~ (e1 = e0)
% 249.49/58.95 (13) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 249.49/58.95 all_250_20 = e0
% 249.49/58.95 (14) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.49/58.95 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.49/58.95 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.49/58.95 (15) op(e4, all_34_2) = e1
% 249.49/58.95 (16) ~ (all_62_2 = e2)
% 249.49/58.95 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.95 (18) ~ (e3 = e2)
% 249.49/58.95 (19) ~ (e4 = e0)
% 249.49/58.95 (20) ~ (all_12_2 = e3)
% 249.49/58.95 (21) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.49/58.95 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.49/58.95 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.49/58.95 (22) ~ (all_244_8 = all_64_2)
% 249.49/58.95 (23) op(e2, e2) = all_244_8
% 249.49/58.95 (24) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/58.95 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/58.95 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.95 (25) op(e2, e1) = all_38_2
% 249.49/58.95 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/58.95 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/58.95 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.95 (27) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/58.95 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/58.95 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/58.95 (28) op(e1, e0) = all_34_2
% 249.49/58.95 (29) op(e4, e2) = all_6_2
% 249.49/58.95 (30) ~ (all_244_15 = e0)
% 249.49/58.95 (31) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.49/58.95 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.49/58.95 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.49/58.95 (32) ~ (e2 = e1)
% 249.49/58.95 (33) all_252_7 = e4
% 249.49/58.95 (34) all_56_2 = all_8_2
% 249.49/58.95 (35) op(e0, e2) = all_28_2
% 249.49/58.95 (36) ~ (e4 = e1)
% 249.49/58.95 (37) ~ (all_244_0 = e2)
% 249.49/58.95 (38) op(all_6_2, all_64_2) = e2
% 249.49/58.95 (39) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/58.95 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/58.95 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/58.95 (40) ~ (all_6_2 = e1)
% 249.49/58.95 (41) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.49/58.95 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.49/58.95 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.49/58.95 (42) ~ (all_244_8 = all_38_2)
% 249.49/58.95 (43) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/58.95 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/58.95 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/58.95 (44) op(e1, e4) = all_16_2
% 249.49/58.95 (45) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 249.49/58.95 all_250_2 = e0
% 249.49/58.95 (46) op(e1, e3) = all_62_2
% 249.49/58.95 (47) ~ (e3 = e0)
% 249.49/58.95 (48) ~ (all_38_2 = e0)
% 249.49/58.95 (49) ~ (all_6_2 = e2)
% 249.49/58.95 (50) all_70_2 = all_62_2
% 249.49/58.95 (51) ~ (e3 = e1)
% 249.49/58.95 (52) ~ (all_12_2 = e2)
% 249.49/58.95 (53) op(e3, e1) = all_36_2
% 249.49/58.95 (54) ~ (all_28_2 = all_12_2)
% 249.49/58.95 (55) ~ (all_16_2 = e2)
% 249.49/58.95 (56) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.49/58.95 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 249.49/58.95 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 249.49/58.95 (57) ~ (all_8_2 = e1)
% 249.49/58.95 (58) all_252_9 = e0
% 249.49/58.95 (59) ~ (all_244_8 = all_40_2)
% 249.49/58.95 (60) op(e2, all_100_2) = e3
% 249.49/58.95 (61) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 249.49/58.95 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 249.49/58.95 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 249.49/58.95 (62) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/58.95 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/58.95 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/58.95 (63) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 249.49/58.95 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 249.49/58.95 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 249.49/58.95 (64) all_182_2 = e2
% 249.49/58.95 (65) op(e1, e4) = all_60_1
% 249.49/58.95 (66) op(all_30_2, all_12_2) = e0
% 249.49/58.95 (67) ~ (all_12_2 = e4)
% 249.49/58.95 (68) op(e3, e4) = all_100_2
% 249.49/58.95 (69) ~ (all_36_2 = e0)
% 249.49/58.95 (70) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 249.49/58.95 op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~
% 249.49/58.95 (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 249.49/58.95 (71) op(all_8_2, e4) = e2
% 249.49/58.95 (72) op(e4, e4) = all_244_0
% 249.49/58.95 (73) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 249.49/58.95 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 249.49/58.95 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.49/58.95 (74) ~ (e4 = e3)
% 249.49/58.95 (75) op(e1, e1) = all_244_15
% 249.49/58.95 (76) all_82_2 = all_28_2
% 249.49/58.95 (77) op(e1, e2) = all_4_2
% 249.49/58.95 (78) all_86_2 = all_40_2
% 249.49/58.95 (79) op(e2, e4) = all_64_2
% 249.49/58.95 (80) ~ (e4 = e2)
% 249.49/58.95 (81) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/58.95 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/58.95 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/58.95 (82) ~ (all_6_2 = e0)
% 249.49/58.95 (83) op(e3, e2) = all_8_2
% 249.49/58.95 (84) op(all_36_2, e1) = e3
% 249.49/58.95 (85) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/58.95 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/58.95 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/58.95 (86) ~ (all_244_15 = all_36_2)
% 249.49/58.95 (87) op(e2, e0) = all_40_2
% 249.49/58.95 (88) op(all_8_2, e2) = e3
% 249.49/58.95 (89) all_252_23 = e4
% 249.49/58.95 (90) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.95 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.95 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.95 (91) all_250_20 = all_12_2
% 249.49/58.95 (92) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/58.95 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/58.95 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/58.95 (93) all_250_2 = all_6_2
% 249.49/58.95 (94) all_46_2 = all_36_2
% 249.49/58.95 (95) op(all_30_2, e0) = e4
% 249.49/58.95 (96) ~ (all_64_2 = e4)
% 249.49/58.95 (97) op(e0, e4) = all_12_2
% 249.49/58.95 (98) op(all_64_2, all_6_2) = e4
% 249.49/58.95
% 249.49/58.95 Begin of proof
% 249.49/58.95 |
% 249.49/58.95 | GROUND_INST: instantiating (17) with all_16_2, all_60_1, e4, e1, simplifying
% 249.49/58.95 | with (44), (65) gives:
% 249.49/58.95 | (99) all_60_1 = all_16_2
% 249.49/58.95 |
% 249.49/58.95 | BETA: splitting (63) gives:
% 249.49/58.95 |
% 249.49/58.95 | Case 1:
% 249.49/58.95 | |
% 249.49/58.95 | | (100) ~ (all_28_2 = e3)
% 249.49/58.95 | |
% 249.49/58.95 | | BETA: splitting (31) gives:
% 249.49/58.95 | |
% 249.49/58.95 | | Case 1:
% 249.49/58.95 | | |
% 249.49/58.95 | | | (101) ~ (all_34_2 = e2)
% 249.49/58.95 | | |
% 249.49/58.95 | | | BETA: splitting (70) gives:
% 249.49/58.95 | | |
% 249.49/58.95 | | | Case 1:
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | (102) ~ (all_216_2 = e0)
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | REDUCE: (8), (102) imply:
% 249.49/58.95 | | | | (103) $false
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | CLOSE: (103) is inconsistent.
% 249.49/58.95 | | | |
% 249.49/58.95 | | | Case 2:
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | (104) ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 249.49/58.95 | | | | all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | (
% 249.49/58.95 | | | | ~ (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | BETA: splitting (104) gives:
% 249.49/58.95 | | | |
% 249.49/58.95 | | | | Case 1:
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | (105) ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 249.49/58.95 | | | | | all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | ALPHA: (105) implies:
% 249.49/58.95 | | | | | (106) op(e1, e0) = all_216_1
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | GROUND_INST: instantiating (17) with all_34_2, all_216_1, e0, e1,
% 249.49/58.95 | | | | | simplifying with (28), (106) gives:
% 249.49/58.95 | | | | | (107) all_216_1 = all_34_2
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (13), (14),
% 249.49/58.95 | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 249.49/58.95 | | | | | (26), (27), (29), (30), (32), (33), (34), (35), (36), (37),
% 249.49/58.95 | | | | | (38), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 249.49/58.95 | | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 249.49/58.95 | | | | | (59), (60), (61), (62), (64), (66), (67), (68), (69), (71),
% 249.49/58.95 | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 249.49/58.95 | | | | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 249.49/58.95 | | | | | (92), (94), (95), (96), (97), (100), (101), (106), (107)
% 249.49/58.95 | | | | | are inconsistent by sub-proof #109.
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | Case 2:
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | (108) ~ (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1)
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | ALPHA: (108) implies:
% 249.49/58.95 | | | | | (109) ~ (all_216_1 = e2)
% 249.49/58.95 | | | | | (110) op(e1, e0) = all_216_1
% 249.49/58.95 | | | | |
% 249.49/58.95 | | | | | GROUND_INST: instantiating (17) with all_34_2, all_216_1, e0, e1,
% 249.49/58.95 | | | | | simplifying with (28), (110) gives:
% 249.49/58.95 | | | | | (111) all_216_1 = all_34_2
% 249.49/58.95 | | | | |
% 249.49/58.96 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (13), (14),
% 249.49/58.96 | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 249.49/58.96 | | | | | (26), (27), (29), (30), (32), (33), (34), (35), (36), (37),
% 249.49/58.96 | | | | | (38), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 249.49/58.96 | | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 249.49/58.96 | | | | | (59), (60), (61), (62), (64), (66), (67), (68), (69), (71),
% 249.49/58.96 | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 249.49/58.96 | | | | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 249.49/58.96 | | | | | (92), (94), (95), (96), (97), (100), (101), (110), (111)
% 249.49/58.96 | | | | | are inconsistent by sub-proof #109.
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | End of split
% 249.49/58.96 | | | |
% 249.49/58.96 | | | End of split
% 249.49/58.96 | | |
% 249.49/58.96 | | Case 2:
% 249.49/58.96 | | |
% 249.49/58.96 | | | (112) all_34_2 = e2
% 249.49/58.96 | | |
% 249.49/58.96 | | | REDUCE: (15), (112) imply:
% 249.49/58.96 | | | (113) op(e4, e2) = e1
% 249.49/58.96 | | |
% 249.49/58.96 | | | REF_CLOSE: (17), (29), (40), (113) are inconsistent by sub-proof #930.
% 249.49/58.96 | | |
% 249.49/58.96 | | End of split
% 249.49/58.96 | |
% 249.49/58.96 | Case 2:
% 249.49/58.96 | |
% 249.49/58.96 | | (114) all_28_2 = e3
% 249.49/58.96 | |
% 249.49/58.96 | | REF_CLOSE: (7), (11), (17), (40), (45), (49), (82), (93), (98), (114) are
% 249.49/58.96 | | inconsistent by sub-proof #108.
% 249.49/58.96 | |
% 249.49/58.96 | End of split
% 249.49/58.96 |
% 249.49/58.96 End of proof
% 249.49/58.96
% 249.49/58.96 Sub-proof #108 shows that the following formulas are inconsistent:
% 249.49/58.96 ----------------------------------------------------------------
% 249.49/58.96 (1) ~ (all_28_2 = all_6_2)
% 249.49/58.96 (2) op(all_64_2, e4) = e2
% 249.49/58.96 (3) all_28_2 = e3
% 249.49/58.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.96 (5) ~ (all_6_2 = e1)
% 249.49/58.96 (6) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 249.49/58.96 all_250_2 = e0
% 249.49/58.96 (7) ~ (all_6_2 = e2)
% 249.49/58.96 (8) ~ (all_6_2 = e0)
% 249.49/58.96 (9) all_250_2 = all_6_2
% 249.49/58.96 (10) op(all_64_2, all_6_2) = e4
% 249.49/58.96
% 249.49/58.96 Begin of proof
% 249.49/58.96 |
% 249.49/58.96 | REDUCE: (1), (3) imply:
% 249.49/58.96 | (11) ~ (all_6_2 = e3)
% 249.49/58.96 |
% 249.49/58.96 | SIMP: (11) implies:
% 249.49/58.96 | (12) ~ (all_6_2 = e3)
% 249.49/58.96 |
% 249.49/58.96 | BETA: splitting (6) gives:
% 249.49/58.96 |
% 249.49/58.96 | Case 1:
% 249.49/58.96 | |
% 249.49/58.96 | | (13) all_250_2 = e4
% 249.49/58.96 | |
% 249.49/58.96 | | COMBINE_EQS: (9), (13) imply:
% 249.49/58.96 | | (14) all_6_2 = e4
% 249.49/58.96 | |
% 249.49/58.96 | | REDUCE: (7), (14) imply:
% 249.49/58.96 | | (15) ~ (e4 = e2)
% 249.49/58.96 | |
% 249.49/58.96 | | REF_CLOSE: (2), (4), (10), (14), (15) are inconsistent by sub-proof #646.
% 249.49/58.96 | |
% 249.49/58.96 | Case 2:
% 249.49/58.96 | |
% 249.49/58.96 | | (16) all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0
% 249.49/58.96 | |
% 249.49/58.96 | | BETA: splitting (16) gives:
% 249.49/58.96 | |
% 249.49/58.96 | | Case 1:
% 249.49/58.96 | | |
% 249.49/58.96 | | | (17) all_250_2 = e3
% 249.49/58.96 | | |
% 249.49/58.96 | | | COMBINE_EQS: (9), (17) imply:
% 249.49/58.96 | | | (18) all_6_2 = e3
% 249.49/58.96 | | |
% 249.49/58.96 | | | REDUCE: (12), (18) imply:
% 249.49/58.96 | | | (19) $false
% 249.49/58.96 | | |
% 249.49/58.96 | | | CLOSE: (19) is inconsistent.
% 249.49/58.96 | | |
% 249.49/58.96 | | Case 2:
% 249.49/58.96 | | |
% 249.49/58.96 | | | (20) all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0
% 249.49/58.96 | | |
% 249.49/58.96 | | | REF_CLOSE: (5), (7), (8), (9), (20) are inconsistent by sub-proof #243.
% 249.49/58.96 | | |
% 249.49/58.96 | | End of split
% 249.49/58.96 | |
% 249.49/58.96 | End of split
% 249.49/58.96 |
% 249.49/58.96 End of proof
% 249.49/58.96
% 249.49/58.96 Sub-proof #109 shows that the following formulas are inconsistent:
% 249.49/58.96 ----------------------------------------------------------------
% 249.49/58.96 (1) op(all_6_2, e2) = e4
% 249.49/58.96 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/58.96 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/58.96 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.96 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/58.96 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/58.96 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/58.96 (4) all_94_2 = all_38_2
% 249.49/58.96 (5) op(all_62_2, all_36_2) = e3
% 249.49/58.96 (6) op(all_38_2, e1) = e2
% 249.49/58.96 (7) ~ (e2 = e0)
% 249.49/58.96 (8) op(all_38_2, all_4_2) = e1
% 249.49/58.96 (9) ~ (e1 = e0)
% 249.49/58.96 (10) ~ (all_28_2 = e3)
% 249.49/58.96 (11) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 249.49/58.96 all_250_20 = e0
% 249.49/58.96 (12) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.49/58.96 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.49/58.96 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.49/58.96 (13) ~ (all_62_2 = e2)
% 249.49/58.96 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.96 (15) ~ (e3 = e2)
% 249.49/58.96 (16) ~ (e4 = e0)
% 249.49/58.96 (17) ~ (all_12_2 = e3)
% 249.49/58.96 (18) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.49/58.96 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.49/58.96 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.49/58.96 (19) ~ (all_244_8 = all_64_2)
% 249.49/58.96 (20) op(e2, e2) = all_244_8
% 249.49/58.96 (21) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/58.96 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/58.96 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.96 (22) op(e2, e1) = all_38_2
% 249.49/58.96 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/58.96 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/58.96 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.96 (24) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/58.96 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/58.96 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/58.96 (25) op(e4, e2) = all_6_2
% 249.49/58.96 (26) ~ (all_244_15 = e0)
% 249.49/58.96 (27) ~ (all_34_2 = e2)
% 249.49/58.96 (28) ~ (e2 = e1)
% 249.49/58.96 (29) all_252_7 = e4
% 249.49/58.96 (30) all_56_2 = all_8_2
% 249.49/58.96 (31) op(e0, e2) = all_28_2
% 249.49/58.96 (32) ~ (e4 = e1)
% 249.49/58.96 (33) ~ (all_244_0 = e2)
% 249.49/58.96 (34) op(all_6_2, all_64_2) = e2
% 249.49/58.96 (35) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/58.96 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/58.96 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/58.96 (36) ~ (all_6_2 = e1)
% 249.49/58.96 (37) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.49/58.96 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.49/58.96 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.49/58.96 (38) ~ (all_244_8 = all_38_2)
% 249.49/58.96 (39) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/58.96 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/58.96 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/58.96 (40) op(e1, e4) = all_16_2
% 249.49/58.96 (41) op(e1, e3) = all_62_2
% 249.49/58.96 (42) ~ (e3 = e0)
% 249.49/58.96 (43) ~ (all_38_2 = e0)
% 249.49/58.96 (44) ~ (all_6_2 = e2)
% 249.49/58.96 (45) all_70_2 = all_62_2
% 249.49/58.96 (46) ~ (e3 = e1)
% 249.49/58.96 (47) ~ (all_12_2 = e2)
% 249.49/58.96 (48) op(e3, e1) = all_36_2
% 249.49/58.96 (49) all_216_1 = all_34_2
% 249.49/58.96 (50) ~ (all_28_2 = all_12_2)
% 249.49/58.96 (51) ~ (all_16_2 = e2)
% 249.49/58.96 (52) ~ (all_182_2 = e2) | ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 &
% 249.49/58.96 op(e2, all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | ( ~
% 249.49/58.96 (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 249.49/58.96 (53) ~ (all_8_2 = e1)
% 249.49/58.96 (54) all_252_9 = e0
% 249.49/58.96 (55) ~ (all_244_8 = all_40_2)
% 249.49/58.96 (56) op(e2, all_100_2) = e3
% 249.49/58.96 (57) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 249.49/58.96 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 249.49/58.96 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 249.49/58.96 (58) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/58.96 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/58.96 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/58.96 (59) all_182_2 = e2
% 249.49/58.96 (60) op(all_30_2, all_12_2) = e0
% 249.49/58.96 (61) ~ (all_12_2 = e4)
% 249.49/58.96 (62) op(e3, e4) = all_100_2
% 249.49/58.96 (63) ~ (all_36_2 = e0)
% 249.49/58.96 (64) op(all_8_2, e4) = e2
% 249.49/58.96 (65) op(e4, e4) = all_244_0
% 249.49/58.96 (66) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 249.49/58.96 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 249.49/58.96 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.49/58.96 (67) ~ (e4 = e3)
% 249.49/58.96 (68) op(e1, e1) = all_244_15
% 249.49/58.96 (69) op(e1, e0) = all_216_1
% 249.49/58.96 (70) all_82_2 = all_28_2
% 249.49/58.96 (71) op(e1, e2) = all_4_2
% 249.49/58.96 (72) all_86_2 = all_40_2
% 249.49/58.96 (73) op(e2, e4) = all_64_2
% 249.49/58.96 (74) ~ (e4 = e2)
% 249.49/58.96 (75) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/58.96 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/58.96 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/58.96 (76) ~ (all_6_2 = e0)
% 249.49/58.96 (77) op(e3, e2) = all_8_2
% 249.49/58.96 (78) op(all_36_2, e1) = e3
% 249.49/58.96 (79) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/58.96 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/58.96 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/58.96 (80) ~ (all_244_15 = all_36_2)
% 249.49/58.96 (81) op(e2, e0) = all_40_2
% 249.49/58.96 (82) op(all_8_2, e2) = e3
% 249.49/58.96 (83) all_252_23 = e4
% 249.49/58.96 (84) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.96 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.96 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.96 (85) all_250_20 = all_12_2
% 249.49/58.96 (86) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/58.96 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/58.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/58.96 (87) all_46_2 = all_36_2
% 249.49/58.96 (88) op(all_30_2, e0) = e4
% 249.49/58.96 (89) ~ (all_64_2 = e4)
% 249.49/58.96 (90) op(e0, e4) = all_12_2
% 249.49/58.96
% 249.49/58.96 Begin of proof
% 249.49/58.96 |
% 249.49/58.96 | REDUCE: (49), (69) imply:
% 249.49/58.96 | (91) op(e1, e0) = all_34_2
% 249.49/58.96 |
% 249.49/58.96 | BETA: splitting (57) gives:
% 249.49/58.96 |
% 249.49/58.96 | Case 1:
% 249.49/58.96 | |
% 249.49/58.96 | | (92) ~ (all_46_2 = e2)
% 249.49/58.96 | |
% 249.49/58.96 | | REDUCE: (87), (92) imply:
% 249.49/58.96 | | (93) ~ (all_36_2 = e2)
% 249.49/58.96 | |
% 249.49/58.96 | | BETA: splitting (24) gives:
% 249.49/58.96 | |
% 249.49/58.96 | | Case 1:
% 249.49/58.96 | | |
% 249.49/58.96 | | | (94) ~ (all_56_2 = e0)
% 249.49/58.96 | | |
% 249.49/58.96 | | | REDUCE: (30), (94) imply:
% 249.49/58.96 | | | (95) ~ (all_8_2 = e0)
% 249.49/58.96 | | |
% 249.49/58.96 | | | BETA: splitting (52) gives:
% 249.49/58.96 | | |
% 249.49/58.96 | | | Case 1:
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | (96) ~ (all_182_2 = e2)
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | REDUCE: (59), (96) imply:
% 249.49/58.96 | | | | (97) $false
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | CLOSE: (97) is inconsistent.
% 249.49/58.96 | | | |
% 249.49/58.96 | | | Case 2:
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | (98) ( ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 & op(e2,
% 249.49/58.96 | | | | all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)) | (
% 249.49/58.96 | | | | ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1))
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | BETA: splitting (98) gives:
% 249.49/58.96 | | | |
% 249.49/58.96 | | | | Case 1:
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | (99) ~ (all_182_0 = e1) & op(e3, e2) = all_182_1 & op(e2,
% 249.49/58.96 | | | | | all_182_1) = all_182_0 & $i(all_182_0) & $i(all_182_1)
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | ALPHA: (99) implies:
% 249.49/58.96 | | | | | (100) op(e3, e2) = all_182_1
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (13), (14),
% 249.49/58.96 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 249.49/58.96 | | | | | (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 249.49/58.96 | | | | | (37), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 249.49/58.96 | | | | | (50), (51), (53), (54), (55), (56), (60), (61), (62), (63),
% 249.49/58.96 | | | | | (64), (65), (66), (67), (68), (70), (71), (72), (73), (74),
% 249.49/58.96 | | | | | (75), (76), (77), (79), (81), (83), (84), (85), (86), (88),
% 249.49/58.96 | | | | | (89), (90), (91), (93), (95), (100) are inconsistent by
% 249.49/58.96 | | | | | sub-proof #110.
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | Case 2:
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | (101) ~ (all_182_1 = e0) & op(e3, e2) = all_182_1 & $i(all_182_1)
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | ALPHA: (101) implies:
% 249.49/58.96 | | | | | (102) op(e3, e2) = all_182_1
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (13), (14),
% 249.49/58.96 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 249.49/58.96 | | | | | (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 249.49/58.96 | | | | | (37), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 249.49/58.96 | | | | | (50), (51), (53), (54), (55), (56), (60), (61), (62), (63),
% 249.49/58.96 | | | | | (64), (65), (66), (67), (68), (70), (71), (72), (73), (74),
% 249.49/58.96 | | | | | (75), (76), (77), (79), (81), (83), (84), (85), (86), (88),
% 249.49/58.96 | | | | | (89), (90), (91), (93), (95), (102) are inconsistent by
% 249.49/58.96 | | | | | sub-proof #110.
% 249.49/58.96 | | | | |
% 249.49/58.96 | | | | End of split
% 249.49/58.96 | | | |
% 249.49/58.96 | | | End of split
% 249.49/58.96 | | |
% 249.49/58.96 | | Case 2:
% 249.49/58.96 | | |
% 249.49/58.96 | | | (103) all_56_2 = e0
% 249.49/58.96 | | |
% 249.49/58.96 | | | REF_CLOSE: (10), (14), (30), (31), (82), (103) are inconsistent by
% 249.49/58.96 | | | sub-proof #668.
% 249.49/58.96 | | |
% 249.49/58.96 | | End of split
% 249.49/58.96 | |
% 249.49/58.96 | Case 2:
% 249.49/58.96 | |
% 249.49/58.96 | | (104) all_46_2 = e2
% 249.49/58.96 | | (105) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 249.49/58.96 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 249.49/58.96 | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 249.49/58.96 | |
% 249.49/58.96 | | COMBINE_EQS: (87), (104) imply:
% 249.49/58.96 | | (106) all_36_2 = e2
% 249.49/58.96 | |
% 249.49/58.96 | | SIMP: (106) implies:
% 249.49/58.96 | | (107) all_36_2 = e2
% 249.49/58.96 | |
% 249.49/58.96 | | REF_CLOSE: (5), (8), (14), (20), (22), (27), (38), (40), (41), (45), (51),
% 249.49/58.96 | | (53), (58), (68), (71), (77), (78), (80), (84), (91), (105),
% 249.49/58.96 | | (107) are inconsistent by sub-proof #796.
% 249.49/58.96 | |
% 249.49/58.96 | End of split
% 249.49/58.96 |
% 249.49/58.96 End of proof
% 249.49/58.96
% 249.49/58.96 Sub-proof #110 shows that the following formulas are inconsistent:
% 249.49/58.96 ----------------------------------------------------------------
% 249.49/58.96 (1) op(all_6_2, e2) = e4
% 249.49/58.96 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/58.96 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/58.96 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.96 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/58.96 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/58.96 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/58.96 (4) all_94_2 = all_38_2
% 249.49/58.96 (5) op(all_38_2, e1) = e2
% 249.49/58.96 (6) ~ (e2 = e0)
% 249.49/58.96 (7) ~ (e1 = e0)
% 249.49/58.96 (8) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 249.49/58.96 all_250_20 = e0
% 249.49/58.96 (9) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.49/58.96 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.49/58.96 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.49/58.96 (10) ~ (all_62_2 = e2)
% 249.49/58.96 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.96 (12) ~ (e3 = e2)
% 249.49/58.96 (13) ~ (e4 = e0)
% 249.49/58.96 (14) ~ (all_12_2 = e3)
% 249.49/58.96 (15) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.49/58.96 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.49/58.96 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.49/58.96 (16) ~ (all_244_8 = all_64_2)
% 249.49/58.96 (17) op(e2, e2) = all_244_8
% 249.49/58.96 (18) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/58.96 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/58.96 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.96 (19) op(e2, e1) = all_38_2
% 249.49/58.96 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/58.96 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/58.96 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.96 (21) op(e1, e0) = all_34_2
% 249.49/58.96 (22) ~ (all_36_2 = e2)
% 249.49/58.96 (23) op(e4, e2) = all_6_2
% 249.49/58.96 (24) ~ (all_244_15 = e0)
% 249.49/58.96 (25) ~ (all_34_2 = e2)
% 249.49/58.96 (26) ~ (e2 = e1)
% 249.49/58.96 (27) all_252_7 = e4
% 249.49/58.96 (28) op(e0, e2) = all_28_2
% 249.49/58.96 (29) ~ (e4 = e1)
% 249.49/58.96 (30) ~ (all_244_0 = e2)
% 249.49/58.96 (31) op(all_6_2, all_64_2) = e2
% 249.49/58.96 (32) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/58.96 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/58.96 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/58.96 (33) ~ (all_6_2 = e1)
% 249.49/58.96 (34) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.49/58.96 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.49/58.96 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.49/58.96 (35) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/58.96 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/58.96 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/58.96 (36) op(e1, e4) = all_16_2
% 249.49/58.96 (37) op(e1, e3) = all_62_2
% 249.49/58.96 (38) ~ (e3 = e0)
% 249.49/58.96 (39) ~ (all_38_2 = e0)
% 249.49/58.96 (40) ~ (all_6_2 = e2)
% 249.49/58.96 (41) ~ (e3 = e1)
% 249.49/58.96 (42) ~ (all_12_2 = e2)
% 249.49/58.96 (43) op(e3, e1) = all_36_2
% 249.49/58.96 (44) ~ (all_28_2 = all_12_2)
% 249.49/58.96 (45) ~ (all_16_2 = e2)
% 249.49/58.96 (46) ~ (all_8_2 = e1)
% 249.49/58.96 (47) all_252_9 = e0
% 249.49/58.96 (48) ~ (all_244_8 = all_40_2)
% 249.49/58.96 (49) op(e2, all_100_2) = e3
% 249.49/58.96 (50) ~ (all_8_2 = e0)
% 249.49/58.96 (51) op(all_30_2, all_12_2) = e0
% 249.49/58.96 (52) ~ (all_12_2 = e4)
% 249.49/58.96 (53) op(e3, e4) = all_100_2
% 249.49/58.96 (54) ~ (all_36_2 = e0)
% 249.49/58.96 (55) op(e3, e2) = all_182_1
% 249.49/58.96 (56) op(all_8_2, e4) = e2
% 249.49/58.96 (57) op(e4, e4) = all_244_0
% 249.49/58.96 (58) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 249.49/58.96 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 249.49/58.96 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 249.49/58.96 (59) ~ (e4 = e3)
% 249.49/58.96 (60) op(e1, e1) = all_244_15
% 249.49/58.96 (61) all_82_2 = all_28_2
% 249.49/58.96 (62) op(e1, e2) = all_4_2
% 249.49/58.96 (63) all_86_2 = all_40_2
% 249.49/58.96 (64) op(e2, e4) = all_64_2
% 249.49/58.96 (65) ~ (e4 = e2)
% 249.49/58.96 (66) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/58.96 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/58.96 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/58.96 (67) ~ (all_6_2 = e0)
% 249.49/58.96 (68) op(e3, e2) = all_8_2
% 249.49/58.96 (69) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/58.96 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/58.96 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/58.96 (70) op(e2, e0) = all_40_2
% 249.49/58.96 (71) all_252_23 = e4
% 249.49/58.96 (72) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.96 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.96 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.96 (73) all_250_20 = all_12_2
% 249.49/58.96 (74) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/58.96 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/58.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/58.96 (75) op(all_30_2, e0) = e4
% 249.49/58.97 (76) ~ (all_64_2 = e4)
% 249.49/58.97 (77) op(e0, e4) = all_12_2
% 249.49/58.97
% 249.49/58.97 Begin of proof
% 249.49/58.97 |
% 249.49/58.97 | GROUND_INST: instantiating (11) with all_8_2, all_182_1, e2, e3, simplifying
% 249.49/58.97 | with (55), (68) gives:
% 249.49/58.97 | (78) all_182_1 = all_8_2
% 249.49/58.97 |
% 249.49/58.97 | BETA: splitting (34) gives:
% 249.49/58.97 |
% 249.49/58.97 | Case 1:
% 249.49/58.97 | |
% 249.49/58.97 | | (79) ~ (all_64_2 = e3)
% 249.49/58.97 | |
% 249.49/58.97 | | BETA: splitting (3) gives:
% 249.49/58.97 | |
% 249.49/58.97 | | Case 1:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (80) ~ (all_82_2 = e1)
% 249.49/58.97 | | |
% 249.49/58.97 | | | REDUCE: (61), (80) imply:
% 249.49/58.97 | | | (81) ~ (all_28_2 = e1)
% 249.49/58.97 | | |
% 249.49/58.97 | | | BETA: splitting (15) gives:
% 249.49/58.97 | | |
% 249.49/58.97 | | | Case 1:
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | (82) ~ (all_86_2 = e3)
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | REDUCE: (63), (82) imply:
% 249.49/58.97 | | | | (83) ~ (all_40_2 = e3)
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | BETA: splitting (9) gives:
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | Case 1:
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | (84) ~ (all_94_2 = e3)
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | REDUCE: (4), (84) imply:
% 249.49/58.97 | | | | | (85) ~ (all_38_2 = e3)
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | BETA: splitting (18) gives:
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | Case 1:
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | (86) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 &
% 249.49/58.97 | | | | | | op(e2, e3) = e3)
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | BETA: splitting (86) gives:
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | Case 1:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | (87) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | REF_CLOSE: (11), (64), (79), (87) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | #940.
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | Case 2:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | (88) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | REF_CLOSE: (27), (59), (88) are inconsistent by sub-proof #128.
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | End of split
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | Case 2:
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | (89) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 249.49/58.97 | | | | | | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | BETA: splitting (89) gives:
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | | Case 1:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | (90) all_252_8 = e3 & op(e2, e2) = e3
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | ALPHA: (90) implies:
% 249.49/58.97 | | | | | | | (91) all_252_8 = e3
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | BETA: splitting (20) gives:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | (92) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 249.49/58.97 | | | | | | | | op(e3, e2) = e1)
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | REF_CLOSE: (11), (23), (33), (46), (68), (92) are inconsistent
% 249.49/58.97 | | | | | | | | by sub-proof #928.
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | (93) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 249.49/58.97 | | | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | BETA: splitting (93) gives:
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | (94) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | ALPHA: (94) implies:
% 249.49/58.97 | | | | | | | | | (95) all_252_8 = e1
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | REF_CLOSE: (41), (91), (95) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | #927.
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | (96) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1
% 249.49/58.97 | | | | | | | | | & op(e0, e2) = e1)
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | BETA: splitting (96) gives:
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | (97) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | ALPHA: (97) implies:
% 249.49/58.97 | | | | | | | | | | (98) all_252_14 = e1
% 249.49/58.97 | | | | | | | | | | (99) op(e1, e2) = e1
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | BETA: splitting (72) gives:
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | (100) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 249.49/58.97 | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | REF_CLOSE: (10), (11), (36), (37), (45), (100) are
% 249.49/58.97 | | | | | | | | | | | inconsistent by sub-proof #925.
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | (101) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 249.49/58.97 | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 249.49/58.97 | | | | | | | | | | | op(e1, e0) = e2)
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | BETA: splitting (101) gives:
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | (102) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | REF_CLOSE: (26), (98), (102) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | #924.
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | (103) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 249.49/58.97 | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | BETA: splitting (103) gives:
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | (104) all_252_15 = e2 & op(e1, e1) = e2
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | ALPHA: (104) implies:
% 249.49/58.97 | | | | | | | | | | | | | (105) all_252_15 = e2
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | (106) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 249.49/58.97 | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | (107) all_252_9 = e3 & op(e4, e1) = e3
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | REF_CLOSE: (38), (47), (107) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | #248.
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | (108) all_252_10 = e3 & op(e3, e1) = e3
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | (109) all_252_10 = e3
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | (110) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 249.49/58.97 | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | (111) all_252_4 = e0 & op(e4, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (67), (111) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | | | sub-proof #875.
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | (112) all_252_5 = e0 & op(e3, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (50), (68), (112) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | | | sub-proof #874.
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | (113) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 249.49/58.97 | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 249.49/58.97 | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | (114) all_252_8 = e0 & op(e2, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | (115) all_252_8 = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (91), (115) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | #905.
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | (116) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 249.49/58.97 | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | (117) all_252_14 = e0 & op(e1, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | (118) op(e1, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (62), (99), (118) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | | | | sub-proof #870.
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | (119) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | (120) all_252_22 = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | (121) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 =
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (122) all_252_9 = e1 & op(e4, e1) = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (123) all_252_9 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (11), (13), (19), (24), (39), (43),
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (54), (60), (71), (123) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | sub-proof #112.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (124) all_252_10 = e1 & op(e3, e1) = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (125) all_252_10 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (109), (125) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | #693.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | (126) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (127) all_252_11 = e1 & op(e2, e1) = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (128) all_252_11 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (129) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | (130) all_252_4 = e2 & op(e4, e2) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (40), (130) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | sub-proof #453.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | (131) all_252_5 = e2 & op(e3, e2) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (11), (31), (56), (64), (68), (76), (131) are
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (132) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | (133) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | (134) all_252_8 = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (91), (134) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | #920.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | (135) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | (136) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | (137) all_252_14 = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (137) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | (138) e2 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (138) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | (139) all_252_15 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | (140) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (141) all_252_9 = e2 & op(e4, e1) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (142) all_252_9 = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (142) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (143) e2 = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (143) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (144) e2 = e0
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (144) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (145) $false
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (146) all_252_10 = e2 & op(e3, e1) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (147) all_252_10 = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (147) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (148) e3 = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (148) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (149) $false
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | (150) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (151) all_252_11 = e2 & op(e2, e1) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (128), (151) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | (152) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (104), (139) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | | #246.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (153) all_252_23 = e2 & op(e0, e1) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (71), (153) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | | #274.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (120), (154) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | | #261.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | (155) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1)
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (156) all_252_15 = e1 & op(e1, e1) = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (105), (156) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | #916.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (157) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (158) all_252_23 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (158) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (159) e4 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (160) e4 = e1
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (160) imply:
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | (161) $false
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | (162) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 249.49/58.97 | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 249.49/58.97 | | | | | | | | | | | | | | op(e0, e1) = e3)
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | (163) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | REF_CLOSE: (11), (19), (85), (163) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | | | sub-proof #900.
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | (164) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 249.49/58.97 | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | (165) all_252_15 = e3 & op(e1, e1) = e3
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (105), (165) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | #405.
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | (166) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | | REF_CLOSE: (59), (71), (166) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | | | | | | | | | #240.
% 249.49/58.97 | | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | (167) all_252_19 = e2 & op(e1, e0) = e2
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | ALPHA: (167) implies:
% 249.49/58.97 | | | | | | | | | | | | | (168) op(e1, e0) = e2
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | | REF_CLOSE: (11), (21), (25), (168) are inconsistent by
% 249.49/58.97 | | | | | | | | | | | | | sub-proof #909.
% 249.49/58.97 | | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | (169) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | ALPHA: (169) implies:
% 249.49/58.97 | | | | | | | | | | (170) op(e0, e2) = e1
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | | REF_CLOSE: (11), (28), (81), (170) are inconsistent by
% 249.49/58.97 | | | | | | | | | | sub-proof #907.
% 249.49/58.97 | | | | | | | | | |
% 249.49/58.97 | | | | | | | | | End of split
% 249.49/58.97 | | | | | | | | |
% 249.49/58.97 | | | | | | | | End of split
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | End of split
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | Case 2:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | (171) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 249.49/58.97 | | | | | | | op(e2, e0) = e3)
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | BETA: splitting (171) gives:
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | | Case 1:
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | (172) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | REF_CLOSE: (11), (19), (85), (172) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | #900.
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | Case 2:
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | (173) all_252_18 = e3 & op(e2, e0) = e3
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | | REF_CLOSE: (11), (70), (83), (173) are inconsistent by sub-proof
% 249.49/58.97 | | | | | | | | #899.
% 249.49/58.97 | | | | | | | |
% 249.49/58.97 | | | | | | | End of split
% 249.49/58.97 | | | | | | |
% 249.49/58.97 | | | | | | End of split
% 249.49/58.97 | | | | | |
% 249.49/58.97 | | | | | End of split
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | Case 2:
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | (174) all_94_2 = e3
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | | REF_CLOSE: (4), (5), (11), (22), (43), (174) are inconsistent by
% 249.49/58.97 | | | | | sub-proof #983.
% 249.49/58.97 | | | | |
% 249.49/58.97 | | | | End of split
% 249.49/58.97 | | | |
% 249.49/58.97 | | | Case 2:
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | (175) all_86_2 = e3
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | COMBINE_EQS: (63), (175) imply:
% 249.49/58.97 | | | | (176) all_40_2 = e3
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | SIMP: (176) implies:
% 249.49/58.97 | | | | (177) all_40_2 = e3
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | REDUCE: (48), (177) imply:
% 249.49/58.97 | | | | (178) ~ (all_244_8 = e3)
% 249.49/58.97 | | | |
% 249.49/58.97 | | | | REF_CLOSE: (1), (11), (17), (30), (31), (36), (42), (45), (49), (53),
% 249.49/58.97 | | | | (57), (64), (69), (76), (77), (178) are inconsistent by
% 249.49/58.97 | | | | sub-proof #123.
% 249.49/58.97 | | | |
% 249.49/58.97 | | | End of split
% 249.49/58.97 | | |
% 249.49/58.97 | | Case 2:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (179) all_82_2 = e1
% 249.49/58.97 | | |
% 249.49/58.97 | | | COMBINE_EQS: (61), (179) imply:
% 249.49/58.97 | | | (180) all_28_2 = e1
% 249.49/58.97 | | |
% 249.49/58.97 | | | REDUCE: (44), (180) imply:
% 249.49/58.97 | | | (181) ~ (all_12_2 = e1)
% 249.49/58.97 | | |
% 249.49/58.97 | | | SIMP: (181) implies:
% 249.49/58.97 | | | (182) ~ (all_12_2 = e1)
% 249.49/58.97 | | |
% 249.49/58.97 | | | REF_CLOSE: (8), (11), (14), (42), (51), (52), (73), (75), (182) are
% 249.49/58.97 | | | inconsistent by sub-proof #582.
% 249.49/58.97 | | |
% 249.49/58.97 | | End of split
% 249.49/58.97 | |
% 249.49/58.97 | Case 2:
% 249.49/58.97 | |
% 249.49/58.97 | | (183) all_64_2 = e3
% 249.49/58.97 | |
% 249.49/58.97 | | REDUCE: (16), (183) imply:
% 249.49/58.97 | | (184) ~ (all_244_8 = e3)
% 249.49/58.97 | |
% 249.49/58.97 | | REF_CLOSE: (1), (11), (17), (30), (31), (36), (42), (45), (49), (53), (57),
% 249.49/58.97 | | (64), (69), (76), (77), (184) are inconsistent by sub-proof #123.
% 249.49/58.97 | |
% 249.49/58.97 | End of split
% 249.49/58.97 |
% 249.49/58.97 End of proof
% 249.49/58.97
% 249.49/58.97 Sub-proof #111 shows that the following formulas are inconsistent:
% 249.49/58.97 ----------------------------------------------------------------
% 249.49/58.97 (1) op(all_6_2, e2) = e4
% 249.49/58.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.97 (3) all_252_5 = e2 & op(e3, e2) = e2
% 249.49/58.97 (4) op(all_6_2, all_64_2) = e2
% 249.49/58.97 (5) op(all_8_2, e4) = e2
% 249.49/58.97 (6) op(e2, e4) = all_64_2
% 249.49/58.97 (7) op(e3, e2) = all_8_2
% 249.49/58.97 (8) ~ (all_64_2 = e4)
% 249.49/58.97
% 249.49/58.97 Begin of proof
% 249.49/58.97 |
% 249.49/58.97 | ALPHA: (3) implies:
% 249.49/58.97 | (9) op(e3, e2) = e2
% 249.49/58.97 |
% 249.49/58.97 | GROUND_INST: instantiating (2) with all_8_2, e2, e2, e3, simplifying with (7),
% 249.49/58.97 | (9) gives:
% 249.49/58.97 | (10) all_8_2 = e2
% 249.49/58.97 |
% 249.49/58.97 | REDUCE: (5), (10) imply:
% 249.49/58.97 | (11) op(e2, e4) = e2
% 249.49/58.97 |
% 249.49/58.97 | REF_CLOSE: (1), (2), (4), (6), (8), (11) are inconsistent by sub-proof #790.
% 249.49/58.97 |
% 249.49/58.97 End of proof
% 249.49/58.97
% 249.49/58.97 Sub-proof #112 shows that the following formulas are inconsistent:
% 249.49/58.97 ----------------------------------------------------------------
% 249.49/58.97 (1) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/58.97 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/58.97 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.97 (2) ~ (e1 = e0)
% 249.49/58.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.97 (4) ~ (e4 = e0)
% 249.49/58.97 (5) op(e2, e1) = all_38_2
% 249.49/58.97 (6) ~ (all_244_15 = e0)
% 249.49/58.97 (7) all_252_9 = e1
% 249.49/58.97 (8) ~ (all_38_2 = e0)
% 249.49/58.97 (9) op(e3, e1) = all_36_2
% 249.49/58.97 (10) ~ (all_36_2 = e0)
% 249.49/58.97 (11) op(e1, e1) = all_244_15
% 249.49/58.97 (12) all_252_23 = e4
% 249.49/58.97
% 249.49/58.97 Begin of proof
% 249.49/58.97 |
% 249.49/58.97 | BETA: splitting (1) gives:
% 249.49/58.97 |
% 249.49/58.97 | Case 1:
% 249.49/58.97 | |
% 249.49/58.97 | | (13) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 249.49/58.97 | | e0)
% 249.49/58.97 | |
% 249.49/58.97 | | BETA: splitting (13) gives:
% 249.49/58.97 | |
% 249.49/58.97 | | Case 1:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (14) all_252_9 = e0 & op(e4, e1) = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | ALPHA: (14) implies:
% 249.49/58.97 | | | (15) all_252_9 = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | COMBINE_EQS: (7), (15) imply:
% 249.49/58.97 | | | (16) e1 = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | REDUCE: (2), (16) imply:
% 249.49/58.97 | | | (17) $false
% 249.49/58.97 | | |
% 249.49/58.97 | | | CLOSE: (17) is inconsistent.
% 249.49/58.97 | | |
% 249.49/58.97 | | Case 2:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (18) all_252_10 = e0 & op(e3, e1) = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | REF_CLOSE: (3), (9), (10), (18) are inconsistent by sub-proof #726.
% 249.49/58.97 | | |
% 249.49/58.97 | | End of split
% 249.49/58.97 | |
% 249.49/58.97 | Case 2:
% 249.49/58.97 | |
% 249.49/58.97 | | (19) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1)
% 249.49/58.97 | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.97 | |
% 249.49/58.97 | | REF_CLOSE: (3), (4), (5), (6), (8), (11), (12), (19) are inconsistent by
% 249.49/58.97 | | sub-proof #113.
% 249.49/58.97 | |
% 249.49/58.97 | End of split
% 249.49/58.97 |
% 249.49/58.97 End of proof
% 249.49/58.97
% 249.49/58.97 Sub-proof #113 shows that the following formulas are inconsistent:
% 249.49/58.97 ----------------------------------------------------------------
% 249.49/58.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.97 (2) ~ (e4 = e0)
% 249.49/58.97 (3) op(e2, e1) = all_38_2
% 249.49/58.97 (4) ~ (all_244_15 = e0)
% 249.49/58.97 (5) ~ (all_38_2 = e0)
% 249.49/58.97 (6) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = e0)
% 249.49/58.97 | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/58.97 (7) op(e1, e1) = all_244_15
% 249.49/58.97 (8) all_252_23 = e4
% 249.49/58.97
% 249.49/58.97 Begin of proof
% 249.49/58.97 |
% 249.49/58.97 | BETA: splitting (6) gives:
% 249.49/58.97 |
% 249.49/58.97 | Case 1:
% 249.49/58.97 | |
% 249.49/58.97 | | (9) all_252_11 = e0 & op(e2, e1) = e0
% 249.49/58.97 | |
% 249.49/58.97 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #904.
% 249.49/58.97 | |
% 249.49/58.97 | Case 2:
% 249.49/58.97 | |
% 249.49/58.97 | | (10) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1)
% 249.49/58.97 | | = e0)
% 249.49/58.97 | |
% 249.49/58.97 | | BETA: splitting (10) gives:
% 249.49/58.97 | |
% 249.49/58.97 | | Case 1:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (11) all_252_15 = e0 & op(e1, e1) = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | ALPHA: (11) implies:
% 249.49/58.97 | | | (12) op(e1, e1) = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | REF_CLOSE: (1), (4), (7), (12) are inconsistent by sub-proof #712.
% 249.49/58.97 | | |
% 249.49/58.97 | | Case 2:
% 249.49/58.97 | | |
% 249.49/58.97 | | | (13) all_252_23 = e0 & op(e0, e1) = e0
% 249.49/58.97 | | |
% 249.49/58.97 | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #259.
% 249.49/58.97 | | |
% 249.49/58.97 | | End of split
% 249.49/58.97 | |
% 249.49/58.97 | End of split
% 249.49/58.97 |
% 249.49/58.97 End of proof
% 249.49/58.97
% 249.49/58.97 Sub-proof #114 shows that the following formulas are inconsistent:
% 249.49/58.97 ----------------------------------------------------------------
% 249.49/58.97 (1) all_252_9 = e4 & op(e4, e1) = e4
% 249.49/58.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.97 (3) op(e4, e1) = all_26_2
% 249.49/58.97 (4) ~ (all_26_2 = e4)
% 249.49/58.97
% 249.49/58.97 Begin of proof
% 249.49/58.97 |
% 249.49/58.97 | ALPHA: (1) implies:
% 249.49/58.97 | (5) op(e4, e1) = e4
% 249.49/58.97 |
% 249.49/58.97 | GROUND_INST: instantiating (2) with all_26_2, e4, e1, e4, simplifying with
% 249.49/58.97 | (3), (5) gives:
% 249.49/58.97 | (6) all_26_2 = e4
% 249.49/58.97 |
% 249.49/58.97 | REDUCE: (4), (6) imply:
% 249.49/58.97 | (7) $false
% 249.49/58.97 |
% 249.49/58.97 | CLOSE: (7) is inconsistent.
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #115 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) ~ (all_22_2 = e2)
% 249.49/58.98 (2) all_28_2 = e3
% 249.49/58.98 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (4) all_250_21 = all_22_2
% 249.49/58.98 (5) ~ (all_22_2 = e4)
% 249.49/58.98 (6) op(all_48_2, all_22_2) = e0
% 249.49/58.98 (7) ~ (all_22_2 = e1)
% 249.49/58.98 (8) ~ (all_28_2 = all_22_2)
% 249.49/58.98 (9) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 249.49/58.98 all_250_21 = e0
% 249.49/58.98 (10) op(all_48_2, e0) = e3
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | REDUCE: (2), (8) imply:
% 249.49/58.98 | (11) ~ (all_22_2 = e3)
% 249.49/58.98 |
% 249.49/58.98 | SIMP: (11) implies:
% 249.49/58.98 | (12) ~ (all_22_2 = e3)
% 249.49/58.98 |
% 249.49/58.98 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12) are inconsistent by
% 249.49/58.98 | sub-proof #957.
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #116 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) op(all_4_2, e2) = e1
% 249.49/58.98 (2) ~ (all_22_2 = e2)
% 249.49/58.98 (3) op(all_38_2, all_4_2) = e1
% 249.49/58.98 (4) ~ (all_62_2 = e2)
% 249.49/58.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (6) op(e0, e0) = all_244_24
% 249.49/58.98 (7) op(e2, e2) = all_244_8
% 249.49/58.98 (8) op(e2, e1) = all_38_2
% 249.49/58.98 (9) op(e1, e0) = all_34_2
% 249.49/58.98 (10) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.49/58.98 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.49/58.98 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.49/58.98 (11) op(e0, e2) = all_28_2
% 249.49/58.98 (12) ~ (all_244_8 = all_38_2)
% 249.49/58.98 (13) op(e1, e4) = all_16_2
% 249.49/58.98 (14) op(e1, e3) = all_62_2
% 249.49/58.98 (15) ~ (all_12_2 = e2)
% 249.49/58.98 (16) ~ (all_16_2 = e2)
% 249.49/58.98 (17) ~ (all_28_2 = e2)
% 249.49/58.98 (18) op(e0, e3) = all_22_2
% 249.49/58.98 (19) op(all_34_2, e2) = e0
% 249.49/58.98 (20) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.49/58.98 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.49/58.98 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.98 (21) op(e1, e1) = all_244_15
% 249.49/58.98 (22) ~ (all_244_24 = e2)
% 249.49/58.98 (23) op(e1, e2) = all_4_2
% 249.49/58.98 (24) ~ (all_244_15 = e2)
% 249.49/58.98 (25) ~ (all_244_8 = all_28_2)
% 249.49/58.98 (26) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.98 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.98 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.98 (27) op(e1, e2) = all_230_1
% 249.49/58.98 (28) op(e2, e1) = e0
% 249.49/58.98 (29) op(e0, e4) = all_12_2
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | BETA: splitting (20) gives:
% 249.49/58.98 |
% 249.49/58.98 | Case 1:
% 249.49/58.98 | |
% 249.49/58.98 | | (30) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 249.49/58.98 | | = e2)
% 249.49/58.98 | |
% 249.49/58.98 | | REF_CLOSE: (2), (5), (15), (18), (29), (30) are inconsistent by sub-proof
% 249.49/58.98 | | #727.
% 249.49/58.98 | |
% 249.49/58.98 | Case 2:
% 249.49/58.98 | |
% 249.49/58.98 | | (31) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1)
% 249.49/58.98 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.98 | |
% 249.49/58.98 | | BETA: splitting (31) gives:
% 249.49/58.98 | |
% 249.49/58.98 | | Case 1:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (32) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/58.98 | | |
% 249.49/58.98 | | | REF_CLOSE: (5), (11), (17), (32) are inconsistent by sub-proof #979.
% 249.49/58.98 | | |
% 249.49/58.98 | | Case 2:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (33) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 249.49/58.98 | | | e0) = e2)
% 249.49/58.98 | | |
% 249.49/58.98 | | | BETA: splitting (33) gives:
% 249.49/58.98 | | |
% 249.49/58.98 | | | Case 1:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | GROUND_INST: instantiating (5) with all_4_2, all_230_1, e2, e1,
% 249.49/58.98 | | | | simplifying with (23), (27) gives:
% 249.49/58.98 | | | | (34) all_230_1 = all_4_2
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | GROUND_INST: instantiating (5) with all_38_2, e0, e1, e2, simplifying
% 249.49/58.98 | | | | with (8), (28) gives:
% 249.49/58.98 | | | | (35) all_38_2 = e0
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REDUCE: (12), (35) imply:
% 249.49/58.98 | | | | (36) ~ (all_244_8 = e0)
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REDUCE: (3), (35) imply:
% 249.49/58.98 | | | | (37) op(e0, all_4_2) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | BETA: splitting (10) gives:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | Case 1:
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | | (38) ~ (all_34_2 = e2)
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | | REF_CLOSE: (1), (4), (5), (7), (9), (11), (13), (14), (16), (21),
% 249.49/58.98 | | | | | (23), (24), (25), (26), (37), (38) are inconsistent by
% 249.49/58.98 | | | | | sub-proof #709.
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | Case 2:
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | | (39) all_34_2 = e2
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | | REDUCE: (19), (39) imply:
% 249.49/58.98 | | | | | (40) op(e2, e2) = e0
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | | REF_CLOSE: (5), (7), (36), (40) are inconsistent by sub-proof #880.
% 249.49/58.98 | | | | |
% 249.49/58.98 | | | | End of split
% 249.49/58.98 | | | |
% 249.49/58.98 | | | Case 2:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | (41) all_252_24 = e2 & op(e0, e0) = e2
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | ALPHA: (41) implies:
% 249.49/58.98 | | | | (42) op(e0, e0) = e2
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REF_CLOSE: (5), (6), (22), (42) are inconsistent by sub-proof #978.
% 249.49/58.98 | | | |
% 249.49/58.98 | | | End of split
% 249.49/58.98 | | |
% 249.49/58.98 | | End of split
% 249.49/58.98 | |
% 249.49/58.98 | End of split
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #117 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) op(all_4_2, e2) = e1
% 249.49/58.98 (2) ~ (all_40_2 = all_38_2)
% 249.49/58.98 (3) op(all_28_2, all_40_2) = e2
% 249.49/58.98 (4) ~ (all_22_2 = e2)
% 249.49/58.98 (5) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) = all_34_1
% 249.49/58.98 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e3) & op(e0, e2) =
% 249.49/58.98 all_34_1 & $i(all_34_1))
% 249.49/58.98 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (7) op(e0, e0) = all_244_24
% 249.49/58.98 (8) op(e2, e1) = all_38_2
% 249.49/58.98 (9) op(e2, e0) = e1
% 249.49/58.98 (10) op(e0, e2) = all_28_2
% 249.49/58.98 (11) ~ (all_12_2 = e2)
% 249.49/58.98 (12) op(e0, e3) = all_22_2
% 249.49/58.98 (13) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.49/58.98 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.49/58.98 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.98 (14) op(e0, e1) = all_20_2
% 249.49/58.98 (15) ~ (all_244_24 = e2)
% 249.49/58.98 (16) op(all_4_2, all_38_2) = e2
% 249.49/58.98 (17) op(e2, e0) = all_40_2
% 249.49/58.98 (18) op(e0, e4) = all_12_2
% 249.49/58.98 (19) ~ (all_20_2 = e2)
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | BETA: splitting (13) gives:
% 249.49/58.98 |
% 249.49/58.98 | Case 1:
% 249.49/58.98 | |
% 249.49/58.98 | | (20) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 249.49/58.98 | | = e2)
% 249.49/58.98 | |
% 249.49/58.98 | | REF_CLOSE: (4), (6), (11), (12), (18), (20) are inconsistent by sub-proof
% 249.49/58.98 | | #727.
% 249.49/58.98 | |
% 249.49/58.98 | Case 2:
% 249.49/58.98 | |
% 249.49/58.98 | | (21) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1)
% 249.49/58.98 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.98 | |
% 249.49/58.98 | | BETA: splitting (21) gives:
% 249.49/58.98 | |
% 249.49/58.98 | | Case 1:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (22) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/58.98 | | |
% 249.49/58.98 | | | ALPHA: (22) implies:
% 249.49/58.98 | | | (23) op(e0, e2) = e2
% 249.49/58.98 | | |
% 249.49/58.98 | | | BETA: splitting (5) gives:
% 249.49/58.98 | | |
% 249.49/58.98 | | | Case 1:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | (24) ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) =
% 249.49/58.98 | | | | all_34_1 & $i(all_34_0) & $i(all_34_1)
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | ALPHA: (24) implies:
% 249.49/58.98 | | | | (25) op(e0, e2) = all_34_1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (16), (17), (23), (25)
% 249.49/58.98 | | | | are inconsistent by sub-proof #118.
% 249.49/58.98 | | | |
% 249.49/58.98 | | | Case 2:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | (26) ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 & $i(all_34_1)
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | ALPHA: (26) implies:
% 249.49/58.98 | | | | (27) op(e0, e2) = all_34_1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (16), (17), (23), (27)
% 249.49/58.98 | | | | are inconsistent by sub-proof #118.
% 249.49/58.98 | | | |
% 249.49/58.98 | | | End of split
% 249.49/58.98 | | |
% 249.49/58.98 | | Case 2:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (28) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 249.49/58.98 | | | e0) = e2)
% 249.49/58.98 | | |
% 249.49/58.98 | | | REF_CLOSE: (6), (7), (14), (15), (19), (28) are inconsistent by sub-proof
% 249.49/58.98 | | | #977.
% 249.49/58.98 | | |
% 249.49/58.98 | | End of split
% 249.49/58.98 | |
% 249.49/58.98 | End of split
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #118 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) op(all_4_2, e2) = e1
% 249.49/58.98 (2) op(e0, e2) = e2
% 249.49/58.98 (3) ~ (all_40_2 = all_38_2)
% 249.49/58.98 (4) op(all_28_2, all_40_2) = e2
% 249.49/58.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (6) op(e2, e1) = all_38_2
% 249.49/58.98 (7) op(e2, e0) = e1
% 249.49/58.98 (8) op(e0, e2) = all_28_2
% 249.49/58.98 (9) op(e0, e2) = all_34_1
% 249.49/58.98 (10) op(all_4_2, all_38_2) = e2
% 249.49/58.98 (11) op(e2, e0) = all_40_2
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | GROUND_INST: instantiating (5) with all_28_2, all_34_1, e2, e0, simplifying
% 249.49/58.98 | with (8), (9) gives:
% 249.49/58.98 | (12) all_34_1 = all_28_2
% 249.49/58.98 |
% 249.49/58.98 | GROUND_INST: instantiating (5) with e2, all_34_1, e2, e0, simplifying with
% 249.49/58.98 | (2), (9) gives:
% 249.49/58.98 | (13) all_34_1 = e2
% 249.49/58.98 |
% 249.49/58.98 | GROUND_INST: instantiating (5) with all_40_2, e1, e0, e2, simplifying with
% 249.49/58.98 | (7), (11) gives:
% 249.49/58.98 | (14) all_40_2 = e1
% 249.49/58.98 |
% 249.49/58.98 | COMBINE_EQS: (12), (13) imply:
% 249.49/58.98 | (15) all_28_2 = e2
% 249.49/58.98 |
% 249.49/58.98 | SIMP: (15) implies:
% 249.49/58.98 | (16) all_28_2 = e2
% 249.49/58.98 |
% 249.49/58.98 | REDUCE: (3), (14) imply:
% 249.49/58.98 | (17) ~ (all_38_2 = e1)
% 249.49/58.98 |
% 249.49/58.98 | SIMP: (17) implies:
% 249.49/58.98 | (18) ~ (all_38_2 = e1)
% 249.49/58.98 |
% 249.49/58.98 | REDUCE: (4), (14), (16) imply:
% 249.49/58.98 | (19) op(e2, e1) = e2
% 249.49/58.98 |
% 249.49/58.98 | REF_CLOSE: (1), (5), (6), (10), (18), (19) are inconsistent by sub-proof #739.
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #119 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) ~ (all_34_2 = e1)
% 249.49/58.98 (2) op(all_36_2, all_62_2) = e1
% 249.49/58.98 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (4) ~ (all_244_3 = e1)
% 249.49/58.98 (5) op(e1, e0) = all_34_2
% 249.49/58.98 (6) ~ (e2 = e1)
% 249.49/58.98 (7) all_252_7 = e4
% 249.49/58.98 (8) ~ (e4 = e1)
% 249.49/58.98 (9) op(e1, e3) = all_62_2
% 249.49/58.98 (10) all_252_1 = e2
% 249.49/58.98 (11) ~ (all_22_2 = e1)
% 249.49/58.98 (12) op(e0, e3) = all_22_2
% 249.49/58.98 (13) op(all_48_2, e0) = e3
% 249.49/58.98 (14) all_48_2 = e1
% 249.49/58.98 (15) op(all_36_2, e1) = e3
% 249.49/58.98 (16) op(e3, e3) = all_244_3
% 249.49/58.98 (17) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/58.98 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/58.98 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | REDUCE: (13), (14) imply:
% 249.49/58.98 | (18) op(e1, e0) = e3
% 249.49/58.98 |
% 249.49/58.98 | BETA: splitting (17) gives:
% 249.49/58.98 |
% 249.49/58.98 | Case 1:
% 249.49/58.98 | |
% 249.49/58.98 | | (19) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 249.49/58.98 | | e1)
% 249.49/58.98 | |
% 249.49/58.98 | | REF_CLOSE: (3), (4), (6), (10), (16), (19) are inconsistent by sub-proof
% 249.49/58.98 | | #120.
% 249.49/58.98 | |
% 249.49/58.98 | Case 2:
% 249.49/58.98 | |
% 249.49/58.98 | | (20) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/58.98 | | e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/58.98 | |
% 249.49/58.98 | | BETA: splitting (20) gives:
% 249.49/58.98 | |
% 249.49/58.98 | | Case 1:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (21) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/58.98 | | |
% 249.49/58.98 | | | REF_CLOSE: (7), (8), (21) are inconsistent by sub-proof #124.
% 249.49/58.98 | | |
% 249.49/58.98 | | Case 2:
% 249.49/58.98 | | |
% 249.49/58.98 | | | (22) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0,
% 249.49/58.98 | | | e3) = e1)
% 249.49/58.98 | | |
% 249.49/58.98 | | | BETA: splitting (22) gives:
% 249.49/58.98 | | |
% 249.49/58.98 | | | Case 1:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | (23) all_252_13 = e1 & op(e1, e3) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | ALPHA: (23) implies:
% 249.49/58.98 | | | | (24) op(e1, e3) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | GROUND_INST: instantiating (3) with all_34_2, e3, e0, e1, simplifying
% 249.49/58.98 | | | | with (5), (18) gives:
% 249.49/58.98 | | | | (25) all_34_2 = e3
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | GROUND_INST: instantiating (3) with all_62_2, e1, e3, e1, simplifying
% 249.49/58.98 | | | | with (9), (24) gives:
% 249.49/58.98 | | | | (26) all_62_2 = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REDUCE: (1), (25) imply:
% 249.49/58.98 | | | | (27) ~ (e3 = e1)
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REDUCE: (2), (26) imply:
% 249.49/58.98 | | | | (28) op(all_36_2, e1) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | GROUND_INST: instantiating (3) with e3, e1, e1, all_36_2, simplifying
% 249.49/58.98 | | | | with (15), (28) gives:
% 249.49/58.98 | | | | (29) e3 = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REDUCE: (27), (29) imply:
% 249.49/58.98 | | | | (30) $false
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | CLOSE: (30) is inconsistent.
% 249.49/58.98 | | | |
% 249.49/58.98 | | | Case 2:
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | (31) all_252_21 = e1 & op(e0, e3) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | ALPHA: (31) implies:
% 249.49/58.98 | | | | (32) op(e0, e3) = e1
% 249.49/58.98 | | | |
% 249.49/58.98 | | | | REF_CLOSE: (3), (11), (12), (32) are inconsistent by sub-proof #714.
% 249.49/58.98 | | | |
% 249.49/58.98 | | | End of split
% 249.49/58.98 | | |
% 249.49/58.98 | | End of split
% 249.49/58.98 | |
% 249.49/58.98 | End of split
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #120 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (2) ~ (all_244_3 = e1)
% 249.49/58.98 (3) ~ (e2 = e1)
% 249.49/58.98 (4) all_252_1 = e2
% 249.49/58.98 (5) op(e3, e3) = all_244_3
% 249.49/58.98 (6) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/58.98
% 249.49/58.98 Begin of proof
% 249.49/58.98 |
% 249.49/58.98 | BETA: splitting (6) gives:
% 249.49/58.98 |
% 249.49/58.98 | Case 1:
% 249.49/58.98 | |
% 249.49/58.98 | | (7) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/58.98 | |
% 249.49/58.98 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #127.
% 249.49/58.98 | |
% 249.49/58.98 | Case 2:
% 249.49/58.98 | |
% 249.49/58.98 | | (8) all_252_3 = e1 & op(e3, e3) = e1
% 249.49/58.98 | |
% 249.49/58.98 | | ALPHA: (8) implies:
% 249.49/58.98 | | (9) op(e3, e3) = e1
% 249.49/58.98 | |
% 249.49/58.98 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #801.
% 249.49/58.98 | |
% 249.49/58.98 | End of split
% 249.49/58.98 |
% 249.49/58.98 End of proof
% 249.49/58.98
% 249.49/58.98 Sub-proof #121 shows that the following formulas are inconsistent:
% 249.49/58.98 ----------------------------------------------------------------
% 249.49/58.98 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/58.98 all_250_23 = e0
% 249.49/58.98 (2) op(all_6_2, e2) = e4
% 249.49/58.98 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 249.49/58.98 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/58.98 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/58.98 (4) ~ (all_244_8 = all_6_2)
% 249.49/58.98 (5) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/58.98 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/58.98 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/58.98 (6) ~ (all_22_2 = e2)
% 249.49/58.98 (7) all_94_2 = all_38_2
% 249.49/58.98 (8) op(all_38_2, e1) = e2
% 249.49/58.98 (9) ~ (e2 = e0)
% 249.49/58.98 (10) ~ (e1 = e0)
% 249.49/58.98 (11) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 249.49/58.98 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 249.49/58.98 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 249.49/58.98 (12) ~ (all_62_2 = e2)
% 249.49/58.98 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.98 (14) ~ (e3 = e2)
% 249.49/58.98 (15) op(e0, e0) = all_244_24
% 249.49/58.98 (16) ~ (e4 = e0)
% 249.49/58.98 (17) ~ (all_12_2 = e3)
% 249.49/58.98 (18) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 249.49/58.98 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 249.49/58.98 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 249.49/58.98 (19) ~ (all_244_8 = all_64_2)
% 249.49/58.98 (20) op(e2, e2) = all_244_8
% 249.49/58.98 (21) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/58.98 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/58.98 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/58.98 (22) op(e2, e1) = all_38_2
% 249.49/58.98 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/58.98 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/58.98 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/58.98 (24) op(e1, e0) = all_34_2
% 249.49/58.98 (25) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/58.98 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/58.98 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/58.98 (26) ~ (all_36_2 = e2)
% 249.49/58.98 (27) op(e4, e2) = all_6_2
% 249.49/58.98 (28) ~ (all_34_2 = e2)
% 249.49/58.98 (29) ~ (e2 = e1)
% 249.49/58.98 (30) all_252_7 = e4
% 249.49/58.98 (31) op(e0, e2) = all_28_2
% 249.49/58.98 (32) ~ (e4 = e1)
% 249.49/58.98 (33) ~ (all_244_0 = e2)
% 249.49/58.98 (34) op(all_6_2, all_64_2) = e2
% 249.49/58.98 (35) ~ (all_6_2 = e1)
% 249.49/58.98 (36) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 249.49/58.98 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 249.49/58.98 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 249.49/58.98 (37) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/58.98 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/58.98 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/58.98 (38) all_80_2 = all_6_2
% 249.49/58.98 (39) all_250_21 = all_22_2
% 249.49/58.98 (40) op(all_34_2, e0) = e1
% 249.49/58.98 (41) op(e1, e4) = all_16_2
% 249.49/58.98 (42) all_96_2 = all_34_2
% 249.49/58.98 (43) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/58.98 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/58.98 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/58.98 (44) ~ (all_28_2 = all_20_2)
% 249.49/58.98 (45) op(e1, e3) = all_62_2
% 249.49/58.98 (46) ~ (e3 = e0)
% 249.49/58.98 (47) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/58.98 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/58.98 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/58.98 (48) all_252_1 = e2
% 249.49/58.98 (49) ~ (all_22_2 = e4)
% 249.49/58.98 (50) ~ (e3 = e1)
% 249.49/58.98 (51) op(all_48_2, all_22_2) = e0
% 249.49/58.98 (52) ~ (all_12_2 = e2)
% 249.49/58.98 (53) op(e3, e1) = all_36_2
% 249.49/58.98 (54) ~ (all_16_2 = e2)
% 249.49/58.98 (55) ~ (all_8_2 = e1)
% 249.49/58.98 (56) ~ (all_22_2 = e1)
% 249.49/58.98 (57) ~ (all_244_8 = all_40_2)
% 249.49/58.98 (58) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/58.98 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/58.98 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/58.98 (59) op(e2, all_100_2) = e3
% 249.49/58.98 (60) op(e4, e3) = e2
% 249.49/58.98 (61) ~ (all_8_2 = e0)
% 249.49/58.98 (62) op(e0, e3) = all_22_2
% 249.49/58.98 (63) op(all_34_2, all_20_2) = e0
% 249.49/58.98 (64) all_58_2 = all_20_2
% 249.49/58.98 (65) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.49/58.98 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.49/58.98 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.98 (66) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 249.49/58.98 all_250_21 = e0
% 249.49/58.98 (67) op(e3, e4) = all_100_2
% 249.49/58.98 (68) op(e3, e2) = all_182_1
% 249.49/58.98 (69) op(e4, e4) = all_244_0
% 249.49/58.98 (70) ~ (e4 = e3)
% 249.49/58.98 (71) op(e0, e1) = all_20_2
% 249.49/58.98 (72) op(e3, e0) = all_48_2
% 249.49/58.99 (73) op(all_48_2, e0) = e3
% 249.49/58.99 (74) all_82_2 = all_28_2
% 249.49/58.99 (75) op(e1, e2) = all_4_2
% 249.49/58.99 (76) ~ (all_48_2 = e1)
% 249.49/58.99 (77) op(e4, e3) = all_84_2
% 249.49/58.99 (78) all_86_2 = all_40_2
% 249.49/58.99 (79) op(e2, e4) = all_64_2
% 249.49/58.99 (80) ~ (e4 = e2)
% 249.49/58.99 (81) ~ (all_22_2 = all_20_2)
% 249.49/58.99 (82) op(e3, e2) = all_8_2
% 249.49/58.99 (83) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/58.99 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/58.99 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/58.99 (84) ~ (all_20_2 = e4)
% 249.49/58.99 (85) op(e2, e0) = all_40_2
% 249.49/58.99 (86) ~ (all_16_2 = e3)
% 249.49/58.99 (87) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/58.99 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/58.99 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/58.99 (88) ~ (all_4_2 = e3)
% 249.49/58.99 (89) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/58.99 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/58.99 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/58.99 (90) ~ (all_96_2 = e3) | ( ~ (all_96_0 = e2) & op(e3, all_96_1) = all_96_0 &
% 249.49/58.99 op(e0, e3) = all_96_1 & $i(all_96_0) & $i(all_96_1)) | ( ~ (all_96_1 =
% 249.49/58.99 e4) & op(e0, e3) = all_96_1 & $i(all_96_1))
% 249.49/58.99 (91) ~ (all_64_2 = e4)
% 249.49/58.99 (92) op(all_244_24, all_244_24) = e0
% 249.49/58.99 (93) op(e0, e4) = all_12_2
% 249.49/58.99 (94) ~ (all_20_2 = e2)
% 249.49/58.99 (95) all_250_23 = all_20_2
% 249.49/58.99
% 249.49/58.99 Begin of proof
% 249.49/58.99 |
% 249.49/58.99 | GROUND_INST: instantiating (13) with all_8_2, all_182_1, e2, e3, simplifying
% 249.49/58.99 | with (68), (82) gives:
% 249.49/58.99 | (96) all_182_1 = all_8_2
% 249.49/58.99 |
% 249.49/58.99 | BETA: splitting (47) gives:
% 249.49/58.99 |
% 249.49/58.99 | Case 1:
% 249.49/58.99 | |
% 249.49/58.99 | | (97) ~ (all_58_2 = e3)
% 249.49/58.99 | |
% 249.49/58.99 | | REDUCE: (64), (97) imply:
% 249.49/58.99 | | (98) ~ (all_20_2 = e3)
% 249.49/58.99 | |
% 249.49/58.99 | | BETA: splitting (36) gives:
% 249.49/58.99 | |
% 249.49/58.99 | | Case 1:
% 249.49/58.99 | | |
% 249.49/58.99 | | | (99) ~ (all_64_2 = e3)
% 249.49/58.99 | | |
% 249.49/58.99 | | | BETA: splitting (5) gives:
% 249.49/58.99 | | |
% 249.49/58.99 | | | Case 1:
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | (100) ~ (all_82_2 = e1)
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | REDUCE: (74), (100) imply:
% 249.49/58.99 | | | | (101) ~ (all_28_2 = e1)
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | BETA: splitting (25) gives:
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | Case 1:
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | (102) ~ (all_80_2 = e0)
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | REDUCE: (38), (102) imply:
% 249.49/58.99 | | | | | (103) ~ (all_6_2 = e0)
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | BETA: splitting (18) gives:
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | Case 1:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | (104) ~ (all_86_2 = e3)
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | REDUCE: (78), (104) imply:
% 249.49/58.99 | | | | | | (105) ~ (all_40_2 = e3)
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | BETA: splitting (90) gives:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | Case 1:
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | (106) ~ (all_96_2 = e3)
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | REDUCE: (42), (106) imply:
% 249.49/58.99 | | | | | | | (107) ~ (all_34_2 = e3)
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | BETA: splitting (11) gives:
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | (108) ~ (all_94_2 = e3)
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | REDUCE: (7), (108) imply:
% 249.49/58.99 | | | | | | | | (109) ~ (all_38_2 = e3)
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | BETA: splitting (21) gives:
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | (110) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3
% 249.49/58.99 | | | | | | | | | & op(e2, e3) = e3)
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | BETA: splitting (110) gives:
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | (111) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | REF_CLOSE: (13), (79), (99), (111) are inconsistent by
% 249.49/58.99 | | | | | | | | | | sub-proof #940.
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | (112) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | REF_CLOSE: (30), (70), (112) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | #128.
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | (113) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3
% 249.49/58.99 | | | | | | | | | & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0)
% 249.49/58.99 | | | | | | | | | = e3)
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | BETA: splitting (113) gives:
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | (114) all_252_8 = e3 & op(e2, e2) = e3
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | ALPHA: (114) implies:
% 249.49/58.99 | | | | | | | | | | (115) all_252_8 = e3
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | BETA: splitting (23) gives:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | (116) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 249.49/58.99 | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | REF_CLOSE: (13), (27), (35), (55), (82), (116) are
% 249.49/58.99 | | | | | | | | | | | inconsistent by sub-proof #928.
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | (117) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 249.49/58.99 | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 249.49/58.99 | | | | | | | | | | | op(e0, e2) = e1)
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | BETA: splitting (117) gives:
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | (118) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | ALPHA: (118) implies:
% 249.49/58.99 | | | | | | | | | | | | (119) all_252_8 = e1
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | REF_CLOSE: (50), (115), (119) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | #927.
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | (120) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 249.49/58.99 | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | BETA: splitting (120) gives:
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | (121) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | ALPHA: (121) implies:
% 249.49/58.99 | | | | | | | | | | | | | (122) all_252_14 = e1
% 249.49/58.99 | | | | | | | | | | | | | (123) op(e1, e2) = e1
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | BETA: splitting (37) gives:
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | (124) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 249.49/58.99 | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | (125) all_252_4 = e0 & op(e4, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | REF_CLOSE: (13), (27), (103), (125) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | sub-proof #875.
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | (126) all_252_5 = e0 & op(e3, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | REF_CLOSE: (13), (61), (82), (126) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | sub-proof #874.
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | (127) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 249.49/58.99 | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 249.49/58.99 | | | | | | | | | | | | | | op(e0, e2) = e0)
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | (128) all_252_8 = e0 & op(e2, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | (129) all_252_8 = e0
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | REF_CLOSE: (46), (115), (129) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | #905.
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | (130) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 249.49/58.99 | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | (131) all_252_14 = e0 & op(e1, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | (132) op(e1, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (75), (123), (132) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | sub-proof #870.
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | (133) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | (134) all_252_22 = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | (135) op(e0, e2) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | (136) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 249.49/58.99 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (41), (45), (54), (136) are
% 249.49/58.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | (137) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 249.49/58.99 | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | (138) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | (139) all_252_14 = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (122), (139) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | #861.
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | (140) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 249.49/58.99 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | (141) all_252_15 = e2 & op(e1, e1) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | (142) all_252_15 = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | (143) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (52), (62), (93), (143) are
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #727.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | (144) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | (145) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (134), (145) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | #261.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | (146) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | (147) all_252_23 = e2 & op(e0, e1) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | (148) op(e0, e1) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (71), (94), (148) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | sub-proof #985.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | (149) all_252_24 = e2 & op(e0, e0) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | (150) all_252_24 = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | (151) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (152) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (153) op(e0, e4) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (93), (153) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #981.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (155) all_252_21 = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (156) op(e0, e3) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (157) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_12 = e3 & op(e1, e4) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (41), (86), (158) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #895.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_13 = e3 & op(e1, e3) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_13 = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (161) op(e1, e3) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (48), (163) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #127.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_3 = e1 & op(e3, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_252_3 = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (13), (60), (77), (165), (166) are
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_7 = e0 & op(e2, e3) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (168) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #125.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_13 = e0 & op(e1, e3) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) op(e1, e3) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (46), (161), (171) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #592.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_21 = e0 & op(e0, e3) = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_21 = e0
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (155), (173) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #773.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (32), (175) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #124.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_13 = e1 & op(e1, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_13 = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (178) imply:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) e3 = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) e3 = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (180) imply:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) $false
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_21 = e1 & op(e0, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) op(e0, e3) = e1
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (156), (183) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #590.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (184) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_252_14 = e3 & op(e1, e2) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (75), (88), (185) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #858.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (186) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_15 = e3 & op(e1, e1) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (142), (187) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | #405.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_252_19 = e3 & op(e1, e0) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (107), (188) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #836.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | (189) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (191) op(e0, e2) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (31), (46), (135), (191) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #473.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | (192) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (194) op(e0, e1) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (71), (98), (194) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_24 = e3
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (196) imply:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (198) e3 = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (198) imply:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | (199) $false
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | (200) all_252_19 = e2 & op(e1, e0) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | (201) op(e1, e0) = e2
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (28), (201) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | | | | | | | sub-proof #909.
% 249.49/58.99 | | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | (202) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | ALPHA: (202) implies:
% 249.49/58.99 | | | | | | | | | | | | | (203) op(e0, e2) = e1
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | | REF_CLOSE: (13), (31), (101), (203) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | | | sub-proof #907.
% 249.49/58.99 | | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | (204) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 =
% 249.49/58.99 | | | | | | | | | | e3 & op(e2, e0) = e3)
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | BETA: splitting (204) gives:
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | Case 1:
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | (205) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | REF_CLOSE: (13), (22), (109), (205) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | sub-proof #900.
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | (206) all_252_18 = e3 & op(e2, e0) = e3
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | | REF_CLOSE: (13), (85), (105), (206) are inconsistent by
% 249.49/58.99 | | | | | | | | | | | sub-proof #899.
% 249.49/58.99 | | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | | |
% 249.49/58.99 | | | | | | | | | End of split
% 249.49/58.99 | | | | | | | | |
% 249.49/58.99 | | | | | | | | End of split
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | Case 2:
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | (207) all_94_2 = e3
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | | REF_CLOSE: (7), (8), (13), (26), (53), (207) are inconsistent by
% 249.49/58.99 | | | | | | | | sub-proof #983.
% 249.49/58.99 | | | | | | | |
% 249.49/58.99 | | | | | | | End of split
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | Case 2:
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | (208) all_96_2 = e3
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | COMBINE_EQS: (42), (208) imply:
% 249.49/58.99 | | | | | | | (209) all_34_2 = e3
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | REDUCE: (40), (209) imply:
% 249.49/58.99 | | | | | | | (210) op(e3, e0) = e1
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | REF_CLOSE: (13), (72), (76), (210) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | #889.
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | End of split
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | Case 2:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | (211) all_86_2 = e3
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | COMBINE_EQS: (78), (211) imply:
% 249.49/58.99 | | | | | | (212) all_40_2 = e3
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | REDUCE: (57), (212) imply:
% 249.49/58.99 | | | | | | (213) ~ (all_244_8 = e3)
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | REF_CLOSE: (2), (13), (20), (33), (34), (41), (52), (54), (59),
% 249.49/58.99 | | | | | | (67), (69), (79), (83), (91), (93), (213) are
% 249.49/58.99 | | | | | | inconsistent by sub-proof #123.
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | End of split
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | Case 2:
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | (214) all_80_2 = e0
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | COMBINE_EQS: (38), (214) imply:
% 249.49/58.99 | | | | | (215) all_6_2 = e0
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | REDUCE: (4), (215) imply:
% 249.49/58.99 | | | | | (216) ~ (all_244_8 = e0)
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | REDUCE: (2), (215) imply:
% 249.49/58.99 | | | | | (217) op(e0, e2) = e4
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | BETA: splitting (65) gives:
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | | Case 1:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | (218) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 249.49/58.99 | | | | | | op(e0, e3) = e2)
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | REF_CLOSE: (6), (13), (52), (62), (93), (218) are inconsistent by
% 249.49/58.99 | | | | | | sub-proof #727.
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | Case 2:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | (219) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 249.49/58.99 | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | BETA: splitting (219) gives:
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | | Case 1:
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | (220) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | REF_CLOSE: (13), (80), (217), (220) are inconsistent by sub-proof
% 249.49/58.99 | | | | | | | #860.
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | Case 2:
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | (221) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 249.49/58.99 | | | | | | | op(e0, e0) = e2)
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | | REF_CLOSE: (13), (15), (20), (71), (92), (94), (216), (221) are
% 249.49/58.99 | | | | | | | inconsistent by sub-proof #648.
% 249.49/58.99 | | | | | | |
% 249.49/58.99 | | | | | | End of split
% 249.49/58.99 | | | | | |
% 249.49/58.99 | | | | | End of split
% 249.49/58.99 | | | | |
% 249.49/58.99 | | | | End of split
% 249.49/58.99 | | | |
% 249.49/58.99 | | | Case 2:
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | (222) all_82_2 = e1
% 249.49/58.99 | | | |
% 249.49/58.99 | | | | REF_CLOSE: (1), (13), (40), (44), (63), (74), (84), (94), (95), (98),
% 249.49/58.99 | | | | (222) are inconsistent by sub-proof #779.
% 249.49/58.99 | | | |
% 249.49/58.99 | | | End of split
% 249.49/58.99 | | |
% 249.49/58.99 | | Case 2:
% 249.49/58.99 | | |
% 249.49/58.99 | | | (223) all_64_2 = e3
% 249.49/58.99 | | |
% 249.49/58.99 | | | REDUCE: (19), (223) imply:
% 249.49/58.99 | | | (224) ~ (all_244_8 = e3)
% 249.49/58.99 | | |
% 249.49/58.99 | | | REF_CLOSE: (2), (13), (20), (33), (34), (41), (52), (54), (59), (67),
% 249.49/58.99 | | | (69), (79), (83), (91), (93), (224) are inconsistent by
% 249.49/58.99 | | | sub-proof #123.
% 249.49/58.99 | | |
% 249.49/58.99 | | End of split
% 249.49/58.99 | |
% 249.49/58.99 | Case 2:
% 249.49/58.99 | |
% 249.49/58.99 | | (225) all_58_2 = e3
% 249.49/58.99 | |
% 249.49/58.99 | | REF_CLOSE: (6), (13), (39), (49), (51), (56), (64), (66), (73), (81), (225)
% 249.49/58.99 | | are inconsistent by sub-proof #122.
% 249.49/58.99 | |
% 249.49/58.99 | End of split
% 249.49/58.99 |
% 249.49/58.99 End of proof
% 249.49/58.99
% 249.49/58.99 Sub-proof #122 shows that the following formulas are inconsistent:
% 249.49/58.99 ----------------------------------------------------------------
% 249.49/58.99 (1) ~ (all_22_2 = e2)
% 249.49/58.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/58.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/58.99 (3) all_58_2 = e3
% 249.49/58.99 (4) all_250_21 = all_22_2
% 249.49/58.99 (5) ~ (all_22_2 = e4)
% 249.49/59.00 (6) op(all_48_2, all_22_2) = e0
% 249.49/59.00 (7) ~ (all_22_2 = e1)
% 249.49/59.00 (8) all_58_2 = all_20_2
% 249.49/59.00 (9) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 249.49/59.00 all_250_21 = e0
% 249.49/59.00 (10) op(all_48_2, e0) = e3
% 249.49/59.00 (11) ~ (all_22_2 = all_20_2)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | COMBINE_EQS: (3), (8) imply:
% 249.49/59.00 | (12) all_20_2 = e3
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (11), (12) imply:
% 249.49/59.00 | (13) ~ (all_22_2 = e3)
% 249.49/59.00 |
% 249.49/59.00 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (13) are inconsistent by
% 249.49/59.00 | sub-proof #957.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #123 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) op(all_6_2, e2) = e4
% 249.49/59.00 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.00 (3) op(e2, e2) = all_244_8
% 249.49/59.00 (4) ~ (all_244_0 = e2)
% 249.49/59.00 (5) op(all_6_2, all_64_2) = e2
% 249.49/59.00 (6) op(e1, e4) = all_16_2
% 249.49/59.00 (7) ~ (all_12_2 = e2)
% 249.49/59.00 (8) ~ (all_16_2 = e2)
% 249.49/59.00 (9) op(e2, all_100_2) = e3
% 249.49/59.00 (10) ~ (all_244_8 = e3)
% 249.49/59.00 (11) op(e3, e4) = all_100_2
% 249.49/59.00 (12) op(e4, e4) = all_244_0
% 249.49/59.00 (13) op(e2, e4) = all_64_2
% 249.49/59.00 (14) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 249.49/59.00 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/59.00 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/59.00 (15) ~ (all_64_2 = e4)
% 249.49/59.00 (16) op(e0, e4) = all_12_2
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | BETA: splitting (14) gives:
% 249.49/59.00 |
% 249.49/59.00 | Case 1:
% 249.49/59.00 | |
% 249.49/59.00 | | (17) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 249.49/59.00 | | e2)
% 249.49/59.00 | |
% 249.49/59.00 | | BETA: splitting (17) gives:
% 249.49/59.00 | |
% 249.49/59.00 | | Case 1:
% 249.49/59.00 | | |
% 249.49/59.00 | | | (18) all_252_0 = e2 & op(e4, e4) = e2
% 249.49/59.00 | | |
% 249.49/59.00 | | | ALPHA: (18) implies:
% 249.49/59.00 | | | (19) op(e4, e4) = e2
% 249.49/59.00 | | |
% 249.49/59.00 | | | REF_CLOSE: (2), (4), (12), (19) are inconsistent by sub-proof #809.
% 249.49/59.00 | | |
% 249.49/59.00 | | Case 2:
% 249.49/59.00 | | |
% 249.49/59.00 | | | (20) all_252_2 = e2 & op(e3, e4) = e2
% 249.49/59.00 | | |
% 249.49/59.00 | | | ALPHA: (20) implies:
% 249.49/59.00 | | | (21) op(e3, e4) = e2
% 249.49/59.00 | | |
% 249.49/59.00 | | | GROUND_INST: instantiating (2) with all_100_2, e2, e4, e3, simplifying
% 249.49/59.00 | | | with (11), (21) gives:
% 249.49/59.00 | | | (22) all_100_2 = e2
% 249.49/59.00 | | |
% 249.49/59.00 | | | REDUCE: (9), (22) imply:
% 249.49/59.00 | | | (23) op(e2, e2) = e3
% 249.49/59.00 | | |
% 249.49/59.00 | | | REF_CLOSE: (2), (3), (10), (23) are inconsistent by sub-proof #877.
% 249.49/59.00 | | |
% 249.49/59.00 | | End of split
% 249.49/59.00 | |
% 249.49/59.00 | Case 2:
% 249.49/59.00 | |
% 249.49/59.00 | | (24) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 249.49/59.00 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 249.49/59.00 | |
% 249.49/59.00 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (13), (15), (16), (24) are
% 249.49/59.00 | | inconsistent by sub-proof #758.
% 249.49/59.00 | |
% 249.49/59.00 | End of split
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #124 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/59.00 (2) all_252_7 = e4
% 249.49/59.00 (3) ~ (e4 = e1)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | ALPHA: (1) implies:
% 249.49/59.00 | (4) all_252_7 = e1
% 249.49/59.00 |
% 249.49/59.00 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.00 | (5) e4 = e1
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (3), (5) imply:
% 249.49/59.00 | (6) $false
% 249.49/59.00 |
% 249.49/59.00 | CLOSE: (6) is inconsistent.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #125 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) all_252_7 = e0 & op(e2, e3) = e0
% 249.49/59.00 (2) all_252_7 = e4
% 249.49/59.00 (3) ~ (e4 = e0)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | ALPHA: (1) implies:
% 249.49/59.00 | (4) all_252_7 = e0
% 249.49/59.00 |
% 249.49/59.00 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.00 | (5) e4 = e0
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (3), (5) imply:
% 249.49/59.00 | (6) $false
% 249.49/59.00 |
% 249.49/59.00 | CLOSE: (6) is inconsistent.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #126 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) ~ (e2 = e0)
% 249.49/59.00 (2) ~ (e1 = e0)
% 249.49/59.00 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.00 (4) all_252_3 = e1
% 249.49/59.00 (5) op(e4, e3) = e2
% 249.49/59.00 (6) op(e4, e3) = all_84_2
% 249.49/59.00 (7) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | BETA: splitting (7) gives:
% 249.49/59.00 |
% 249.49/59.00 | Case 1:
% 249.49/59.00 | |
% 249.49/59.00 | | (8) all_252_1 = e0 & op(e4, e3) = e0
% 249.49/59.00 | |
% 249.49/59.00 | | ALPHA: (8) implies:
% 249.49/59.00 | | (9) op(e4, e3) = e0
% 249.49/59.00 | |
% 249.49/59.00 | | REF_CLOSE: (1), (3), (5), (6), (9) are inconsistent by sub-proof #850.
% 249.49/59.00 | |
% 249.49/59.00 | Case 2:
% 249.49/59.00 | |
% 249.49/59.00 | | (10) all_252_3 = e0 & op(e3, e3) = e0
% 249.49/59.00 | |
% 249.49/59.00 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #777.
% 249.49/59.00 | |
% 249.49/59.00 | End of split
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #127 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/59.00 (2) all_252_1 = e2
% 249.49/59.00 (3) ~ (e2 = e1)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | ALPHA: (1) implies:
% 249.49/59.00 | (4) all_252_1 = e1
% 249.49/59.00 |
% 249.49/59.00 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.00 | (5) e2 = e1
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (3), (5) imply:
% 249.49/59.00 | (6) $false
% 249.49/59.00 |
% 249.49/59.00 | CLOSE: (6) is inconsistent.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #128 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/59.00 (2) all_252_7 = e4
% 249.49/59.00 (3) ~ (e4 = e3)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | ALPHA: (1) implies:
% 249.49/59.00 | (4) all_252_7 = e3
% 249.49/59.00 |
% 249.49/59.00 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.00 | (5) e4 = e3
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (3), (5) imply:
% 249.49/59.00 | (6) $false
% 249.49/59.00 |
% 249.49/59.00 | CLOSE: (6) is inconsistent.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #129 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.00 (2) op(e2, e4) = all_64_2
% 249.49/59.00 (3) op(e2, e4) = e4
% 249.49/59.00 (4) ~ (all_64_2 = e4)
% 249.49/59.00
% 249.49/59.00 Begin of proof
% 249.49/59.00 |
% 249.49/59.00 | GROUND_INST: instantiating (1) with all_64_2, e4, e4, e2, simplifying with
% 249.49/59.00 | (2), (3) gives:
% 249.49/59.00 | (5) all_64_2 = e4
% 249.49/59.00 |
% 249.49/59.00 | REDUCE: (4), (5) imply:
% 249.49/59.00 | (6) $false
% 249.49/59.00 |
% 249.49/59.00 | CLOSE: (6) is inconsistent.
% 249.49/59.00 |
% 249.49/59.00 End of proof
% 249.49/59.00
% 249.49/59.00 Sub-proof #130 shows that the following formulas are inconsistent:
% 249.49/59.00 ----------------------------------------------------------------
% 249.49/59.00 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) |
% 249.49/59.00 (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = e2) |
% 249.49/59.00 (all_252_16 = e2 & op(e4, e0) = e2)
% 249.49/59.00 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.00 all_250_23 = e0
% 249.49/59.00 (3) ~ (all_30_2 = all_26_2)
% 249.49/59.00 (4) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.00 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.00 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.00 (5) ~ (all_244_0 = all_84_2)
% 249.49/59.00 (6) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.00 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.00 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.00 (7) ~ (all_4_2 = e4)
% 249.49/59.00 (8) ~ (all_10_2 = e4)
% 249.49/59.00 (9) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.00 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.00 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.00 (10) ~ (all_244_0 = all_30_2)
% 249.49/59.00 (11) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.00 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.00 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 249.49/59.00 (12) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.00 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 249.49/59.00 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.00 (13) ~ (all_40_2 = all_38_2)
% 249.49/59.00 (14) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.00 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.00 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.00 (15) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 249.49/59.00 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.00 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.00 (16) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.00 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.00 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.00 (17) op(e4, e0) = all_30_2
% 249.49/59.00 (18) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.00 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.00 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.00 (19) all_172_2 = all_10_2
% 249.49/59.00 (20) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 249.49/59.00 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 249.49/59.00 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 249.49/59.00 (21) all_14_2 = e2
% 249.49/59.00 (22) ~ (all_244_8 = all_6_2)
% 249.49/59.00 (23) ~ (all_84_2 = all_10_2)
% 249.49/59.00 (24) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 249.49/59.00 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 249.49/59.00 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 249.49/59.00 (25) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.00 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.00 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.00 (26) ~ (all_22_2 = e2)
% 249.49/59.00 (27) op(all_100_2, e4) = e3
% 249.49/59.00 (28) op(all_38_2, e1) = e2
% 249.49/59.00 (29) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.00 all_250_15 = e0
% 249.49/59.00 (30) ~ (all_28_2 = all_6_2)
% 249.49/59.00 (31) op(all_38_2, all_4_2) = e1
% 249.49/59.00 (32) ~ (e1 = e0)
% 249.49/59.00 (33) ~ (all_244_24 = all_20_2)
% 249.49/59.00 (34) ~ (all_62_2 = all_22_2)
% 249.49/59.00 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.00 (36) op(e2, e3) = all_10_2
% 249.49/59.00 (37) ~ (e3 = e2)
% 249.49/59.00 (38) op(e0, e0) = all_244_24
% 249.49/59.00 (39) ~ (e4 = e0)
% 249.49/59.00 (40) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.00 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.00 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.00 (41) ~ (all_244_8 = all_64_2)
% 249.49/59.00 (42) op(all_244_8, all_244_8) = e2
% 249.49/59.00 (43) op(e2, e2) = all_244_8
% 249.49/59.00 (44) ~ (all_64_2 = e2)
% 249.49/59.00 (45) ~ (all_108_2 = e1) | ( ~ (all_108_0 = e4) & op(e2, e1) = all_108_1 &
% 249.49/59.00 op(e1, all_108_1) = all_108_0 & $i(all_108_0) & $i(all_108_1)) | ( ~
% 249.49/59.00 (all_108_1 = e3) & op(e2, e1) = all_108_1 & $i(all_108_1))
% 249.49/59.00 (46) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.00 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.00 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.00 (47) op(all_84_2, all_100_2) = e3
% 249.49/59.00 (48) op(e2, e1) = all_38_2
% 249.49/59.00 (49) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.00 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.00 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.00 (50) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.00 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.00 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.00 (51) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.00 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.00 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.00 (52) ~ (all_64_2 = all_40_2)
% 249.49/59.00 (53) all_250_0 = all_244_0
% 249.49/59.00 (54) ~ (all_84_2 = all_62_2)
% 249.49/59.00 (55) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.00 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.00 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.00 (56) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 249.49/59.00 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 249.49/59.00 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 249.49/59.00 (57) ~ (all_244_15 = all_16_2)
% 249.49/59.00 (58) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/59.00 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/59.00 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/59.00 (59) ~ (all_244_15 = all_26_2)
% 249.49/59.00 (60) op(e1, e0) = all_34_2
% 249.49/59.00 (61) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.00 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.00 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.00 (62) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.49/59.00 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.49/59.00 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.49/59.00 (63) op(all_28_2, e2) = e0
% 249.49/59.00 (64) op(e4, e2) = all_6_2
% 249.49/59.00 (65) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.49/59.00 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.49/59.00 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.49/59.00 (66) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.00 all_250_18 = e0
% 249.49/59.00 (67) ~ (all_244_0 = all_16_2)
% 249.49/59.00 (68) all_78_2 = all_10_2
% 249.49/59.00 (69) ~ (all_8_2 = all_4_2)
% 249.49/59.00 (70) ~ (all_20_2 = e4) | ( ~ (all_20_0 = e3) & op(e4, all_20_1) = all_20_0 &
% 249.49/59.00 op(e1, e4) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 249.49/59.00 e2) & op(e1, e4) = all_20_1 & $i(all_20_1))
% 249.49/59.00 (71) ~ (e2 = e1)
% 249.49/59.00 (72) op(all_26_2, e1) = e4
% 249.49/59.00 (73) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.00 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.00 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.00 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.00 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.00 op(e0, e1) = e0)))
% 249.49/59.00 (74) ~ (all_100_2 = all_36_2)
% 249.49/59.00 (75) ~ (all_100_2 = all_64_2)
% 249.49/59.00 (76) all_56_2 = all_8_2
% 249.49/59.00 (77) op(e0, e2) = all_28_2
% 249.49/59.00 (78) ~ (e4 = e1)
% 249.49/59.00 (79) ~ (all_244_0 = e2)
% 249.49/59.00 (80) op(all_6_2, all_64_2) = e2
% 249.49/59.00 (81) ~ (all_64_2 = all_10_2)
% 249.49/59.00 (82) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.00 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.00 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.00 (83) ~ (all_6_2 = e1)
% 249.49/59.00 (84) ~ (all_62_2 = all_34_2)
% 249.49/59.00 (85) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.00 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.00 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.00 (86) all_80_2 = all_6_2
% 249.49/59.00 (87) op(all_34_2, e0) = e1
% 249.49/59.00 (88) ~ (all_244_3 = all_84_2)
% 249.49/59.00 (89) op(e1, e4) = all_16_2
% 249.49/59.00 (90) ~ (all_244_0 = all_64_2)
% 249.49/59.00 (91) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.00 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.00 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.00 (92) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.00 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.00 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.00 (93) ~ (all_28_2 = all_20_2)
% 249.49/59.00 (94) op(e1, e3) = all_62_2
% 249.49/59.00 (95) op(all_16_2, all_26_2) = e4
% 249.49/59.00 (96) ~ (e3 = e0)
% 249.49/59.00 (97) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.00 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.00 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.00 (98) all_112_2 = all_62_2
% 249.49/59.00 (99) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/59.00 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/59.00 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/59.00 (100) op(all_20_2, e1) = e0
% 249.49/59.00 (101) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0
% 249.49/59.00 & op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 249.49/59.00 (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.00 (102) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 249.49/59.00 all_250_1 = e0
% 249.49/59.00 (103) all_70_2 = all_62_2
% 249.49/59.00 (104) ~ (e3 = e1)
% 249.49/59.00 (105) op(e3, e1) = all_36_2
% 249.49/59.00 (106) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.00 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.00 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.00 (107) ~ (all_16_2 = e2)
% 249.49/59.00 (108) ~ (all_8_2 = e1)
% 249.49/59.00 (109) ~ (all_244_3 = all_62_2)
% 249.49/59.00 (110) op(all_40_2, e0) = e2
% 249.49/59.00 (111) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.00 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.00 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.00 (112) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 249.49/59.00 all_250_22 = e0
% 249.49/59.00 (113) ~ (all_14_2 = e2) | ( ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 &
% 249.49/59.00 op(e2, all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 249.49/59.00 (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1))
% 249.49/59.00 (114) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.00 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.00 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.00 (115) ~ (all_28_2 = all_4_2)
% 249.49/59.00 (116) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.00 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.00 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.00 (117) ~ (all_84_2 = all_26_2)
% 249.49/59.00 (118) ~ (all_148_2 = e0) | ( ~ (all_148_0 = e1) & op(e4, e0) = all_148_1 &
% 249.49/59.00 op(e0, all_148_1) = all_148_0 & $i(all_148_0) & $i(all_148_1)) | ( ~
% 249.49/59.00 (all_148_1 = e3) & op(e4, e0) = all_148_1 & $i(all_148_1))
% 249.49/59.00 (119) ~ (all_244_15 = all_38_2)
% 249.49/59.00 (120) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/59.00 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/59.00 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/59.00 (121) ~ (all_36_2 = all_26_2)
% 249.49/59.00 (122) all_44_2 = all_26_2
% 249.49/59.00 (123) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 249.49/59.00 & op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 249.49/59.00 (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 249.49/59.00 (124) all_92_2 = all_20_2
% 249.49/59.00 (125) all_130_2 = all_62_2
% 249.49/59.00 (126) all_74_2 = all_36_2
% 249.49/59.00 (127) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.00 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.00 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.00 (128) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0
% 249.49/59.00 & op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 249.49/59.00 (all_26_1 = e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 249.49/59.00 (129) ~ (all_26_2 = all_6_2)
% 249.49/59.00 (130) ~ (all_28_2 = e2)
% 249.49/59.00 (131) op(all_22_2, e3) = e0
% 249.49/59.00 (132) all_68_2 = all_22_2
% 249.49/59.00 (133) op(e0, e3) = all_22_2
% 249.49/59.00 (134) ~ (all_244_0 = all_100_2)
% 249.49/59.00 (135) ~ (all_28_2 = all_22_2)
% 249.49/59.00 (136) all_242_2 = all_38_2
% 249.49/59.00 (137) all_250_18 = all_244_15
% 249.49/59.00 (138) op(all_34_2, all_20_2) = e0
% 249.49/59.00 (139) op(e2, all_30_2) = e4
% 249.49/59.01 (140) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.01 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.01 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.01 (141) op(e4, e2) = all_12_1
% 249.49/59.01 (142) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.01 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.01 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.01 (143) all_58_2 = all_20_2
% 249.49/59.01 (144) op(all_62_2, e3) = e1
% 249.49/59.01 (145) all_148_2 = all_64_2
% 249.49/59.01 (146) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.01 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 249.49/59.01 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 249.49/59.01 (147) op(e4, e1) = all_26_2
% 249.49/59.01 (148) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 249.49/59.01 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 249.49/59.01 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.01 (149) ~ (all_64_2 = all_38_2)
% 249.49/59.01 (150) ~ (all_100_2 = all_8_2)
% 249.49/59.01 (151) ~ (all_244_15 = all_62_2)
% 249.49/59.01 (152) all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 249.49/59.01 all_250_0 = e0
% 249.49/59.01 (153) ~ (all_62_2 = all_16_2)
% 249.49/59.01 (154) ~ (all_8_2 = all_6_2)
% 249.49/59.01 (155) op(e3, e4) = all_100_2
% 249.49/59.01 (156) ~ (all_100_2 = e2)
% 249.49/59.01 (157) all_250_15 = all_16_2
% 249.49/59.01 (158) op(e4, e4) = all_244_0
% 249.49/59.01 (159) all_108_2 = all_28_2
% 249.49/59.01 (160) ~ (e4 = e3)
% 249.49/59.01 (161) ~ (all_112_2 = e0) | ( ~ (all_112_0 = e2) & op(e3, e0) = all_112_1 &
% 249.49/59.01 op(e0, all_112_1) = all_112_0 & $i(all_112_0) & $i(all_112_1)) | ( ~
% 249.49/59.01 (all_112_1 = e4) & op(e3, e0) = all_112_1 & $i(all_112_1))
% 249.49/59.01 (162) op(e1, e1) = all_244_15
% 249.49/59.01 (163) all_202_2 = all_26_2
% 249.49/59.01 (164) op(e0, e1) = all_20_2
% 249.49/59.01 (165) ~ (all_244_15 = all_20_2)
% 249.49/59.01 (166) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 249.49/59.01 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 249.49/59.01 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 249.49/59.01 (167) ~ (all_38_2 = all_36_2)
% 249.49/59.01 (168) op(e2, e4) = e0
% 249.49/59.01 (169) all_82_2 = all_28_2
% 249.49/59.01 (170) ~ (all_244_24 = e2)
% 249.49/59.01 (171) ~ (all_244_3 = all_100_2)
% 249.49/59.01 (172) op(e1, e2) = all_4_2
% 249.49/59.01 (173) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.01 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.01 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.01 (174) ~ (all_28_2 = all_8_2)
% 249.49/59.01 (175) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 249.49/59.01 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 249.49/59.01 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 249.49/59.01 (176) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.01 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.01 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.01 (177) op(e4, e3) = all_84_2
% 249.49/59.01 (178) op(all_244_3, all_244_3) = e3
% 249.49/59.01 (179) ~ (all_62_2 = all_10_2)
% 249.49/59.01 (180) op(e2, e4) = all_64_2
% 249.49/59.01 (181) ~ (all_22_2 = all_10_2)
% 249.49/59.01 (182) ~ (all_38_2 = all_26_2)
% 249.49/59.01 (183) op(all_40_2, all_28_2) = e0
% 249.49/59.01 (184) ~ (e4 = e2)
% 249.49/59.01 (185) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.49/59.01 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.01 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.01 (186) ~ (all_22_2 = all_20_2)
% 249.49/59.01 (187) op(e3, e2) = all_8_2
% 249.49/59.01 (188) ~ (all_64_2 = all_16_2)
% 249.49/59.01 (189) op(all_36_2, e1) = e3
% 249.49/59.01 (190) ~ (all_38_2 = all_20_2)
% 249.49/59.01 (191) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.01 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.01 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.01 (192) ~ (all_38_2 = all_10_2)
% 249.49/59.01 (193) ~ (all_244_15 = all_36_2)
% 249.49/59.01 (194) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.01 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.01 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.01 (195) all_250_1 = all_84_2
% 249.49/59.01 (196) op(all_16_2, e4) = e1
% 249.49/59.01 (197) ~ (all_100_2 = all_16_2)
% 249.49/59.01 (198) op(e2, e0) = all_40_2
% 249.49/59.01 (199) op(all_8_2, e2) = e3
% 249.49/59.01 (200) ~ (all_244_8 = all_28_2)
% 249.49/59.01 (201) all_24_2 = all_16_2
% 249.49/59.01 (202) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.01 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.01 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.01 (203) all_250_22 = all_28_2
% 249.49/59.01 (204) op(e3, e3) = all_244_3
% 249.49/59.01 (205) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.01 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.01 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.01 (206) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.01 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.01 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.01 (207) ~ (all_26_2 = all_20_2)
% 249.49/59.01 (208) ~ (all_92_2 = e3) | ( ~ (all_92_0 = e4) & op(e3, all_92_1) = all_92_0
% 249.49/59.01 & op(e1, e3) = all_92_1 & $i(all_92_0) & $i(all_92_1)) | ( ~
% 249.49/59.01 (all_92_1 = e2) & op(e1, e3) = all_92_1 & $i(all_92_1))
% 249.49/59.01 (209) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.01 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.01 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.01 (210) op(all_26_2, all_16_2) = e1
% 249.49/59.01 (211) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.01 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.01 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.01 (212) ~ (all_202_2 = e2) | ( ~ (all_202_0 = e3) & op(e2, all_202_1) =
% 249.49/59.01 all_202_0 & op(e1, e2) = all_202_1 & $i(all_202_0) & $i(all_202_1)) |
% 249.49/59.01 ( ~ (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1))
% 249.49/59.01 (213) ~ (all_62_2 = all_4_2)
% 249.49/59.01 (214) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 249.49/59.01 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 249.49/59.01 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 249.49/59.01 (215) op(all_244_24, all_244_24) = e0
% 249.49/59.01 (216) ~ (all_34_2 = all_4_2)
% 249.49/59.01 (217) ~ (all_20_2 = e2)
% 249.49/59.01 (218) all_250_23 = all_20_2
% 249.49/59.01
% 249.49/59.01 Begin of proof
% 249.49/59.01 |
% 249.49/59.01 | BETA: splitting (148) gives:
% 249.49/59.01 |
% 249.49/59.01 | Case 1:
% 249.49/59.01 | |
% 249.49/59.01 | | (219) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 249.49/59.01 | | = e2)
% 249.49/59.01 | |
% 249.49/59.01 | | BETA: splitting (219) gives:
% 249.49/59.01 | |
% 249.49/59.01 | | Case 1:
% 249.49/59.01 | | |
% 249.49/59.01 | | | (220) all_252_20 = e2 & op(e0, e4) = e2
% 249.49/59.01 | | |
% 249.49/59.01 | | | ALPHA: (220) implies:
% 249.49/59.01 | | | (221) all_252_20 = e2
% 249.49/59.01 | | |
% 249.49/59.01 | | | GROUND_INST: instantiating (35) with all_64_2, e0, e4, e2, simplifying
% 249.49/59.01 | | | with (168), (180) gives:
% 249.49/59.01 | | | (222) all_64_2 = e0
% 249.49/59.01 | | |
% 249.49/59.01 | | | GROUND_INST: instantiating (35) with all_6_2, all_12_1, e2, e4,
% 249.49/59.01 | | | simplifying with (64), (141) gives:
% 249.49/59.01 | | | (223) all_12_1 = all_6_2
% 249.49/59.01 | | |
% 249.49/59.01 | | | COMBINE_EQS: (145), (222) imply:
% 249.49/59.01 | | | (224) all_148_2 = e0
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (90), (222) imply:
% 249.49/59.01 | | | (225) ~ (all_244_0 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (41), (222) imply:
% 249.49/59.01 | | | (226) ~ (all_244_8 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (75), (222) imply:
% 249.49/59.01 | | | (227) ~ (all_100_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (52), (222) imply:
% 249.49/59.01 | | | (228) ~ (all_40_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | SIMP: (228) implies:
% 249.49/59.01 | | | (229) ~ (all_40_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (149), (222) imply:
% 249.49/59.01 | | | (230) ~ (all_38_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | SIMP: (230) implies:
% 249.49/59.01 | | | (231) ~ (all_38_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (188), (222) imply:
% 249.49/59.01 | | | (232) ~ (all_16_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | SIMP: (232) implies:
% 249.49/59.01 | | | (233) ~ (all_16_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (81), (222) imply:
% 249.49/59.01 | | | (234) ~ (all_10_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | SIMP: (234) implies:
% 249.49/59.01 | | | (235) ~ (all_10_2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (44), (222) imply:
% 249.49/59.01 | | | (236) ~ (e2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | SIMP: (236) implies:
% 249.49/59.01 | | | (237) ~ (e2 = e0)
% 249.49/59.01 | | |
% 249.49/59.01 | | | REDUCE: (80), (222) imply:
% 249.49/59.01 | | | (238) op(all_6_2, e0) = e2
% 249.49/59.01 | | |
% 249.49/59.01 | | | BETA: splitting (20) gives:
% 249.49/59.01 | | |
% 249.49/59.01 | | | Case 1:
% 249.49/59.01 | | | |
% 249.49/59.01 | | | | (239) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2,
% 249.49/59.01 | | | | e3) = e0)
% 249.49/59.01 | | | |
% 249.49/59.01 | | | | BETA: splitting (239) gives:
% 249.49/59.01 | | | |
% 249.49/59.01 | | | | Case 1:
% 249.49/59.01 | | | | |
% 249.49/59.01 | | | | | (240) all_252_6 = e0 & op(e2, e4) = e0
% 249.49/59.01 | | | | |
% 249.49/59.01 | | | | | ALPHA: (240) implies:
% 249.49/59.01 | | | | | (241) all_252_6 = e0
% 249.49/59.01 | | | | |
% 249.49/59.01 | | | | | BETA: splitting (113) gives:
% 249.49/59.01 | | | | |
% 249.49/59.01 | | | | | Case 1:
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | (242) ~ (all_14_2 = e2)
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | REDUCE: (21), (242) imply:
% 249.49/59.01 | | | | | | (243) $false
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | CLOSE: (243) is inconsistent.
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | Case 2:
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | (244) ( ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2,
% 249.49/59.01 | | | | | | all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1)) | (
% 249.49/59.01 | | | | | | ~ (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1))
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | BETA: splitting (70) gives:
% 249.49/59.01 | | | | | |
% 249.49/59.01 | | | | | | Case 1:
% 249.49/59.01 | | | | | | |
% 249.49/59.01 | | | | | | | (245) ~ (all_20_2 = e4)
% 249.49/59.01 | | | | | | |
% 249.49/59.01 | | | | | | | BETA: splitting (214) gives:
% 249.49/59.01 | | | | | | |
% 249.49/59.01 | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | |
% 249.49/59.01 | | | | | | | | (246) ~ (all_22_2 = e1)
% 249.49/59.01 | | | | | | | |
% 249.49/59.01 | | | | | | | | BETA: splitting (175) gives:
% 249.49/59.01 | | | | | | | |
% 249.49/59.01 | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | |
% 249.49/59.01 | | | | | | | | | (247) ~ (all_24_2 = e3)
% 249.49/59.01 | | | | | | | | |
% 249.49/59.01 | | | | | | | | | REDUCE: (201), (247) imply:
% 249.49/59.01 | | | | | | | | | (248) ~ (all_16_2 = e3)
% 249.49/59.01 | | | | | | | | |
% 249.49/59.01 | | | | | | | | | BETA: splitting (128) gives:
% 249.49/59.01 | | | | | | | | |
% 249.49/59.01 | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | (249) ~ (all_26_2 = e3)
% 249.49/59.01 | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | BETA: splitting (123) gives:
% 249.49/59.01 | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | (250) ~ (all_28_2 = e3)
% 249.49/59.01 | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | BETA: splitting (51) gives:
% 249.49/59.01 | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | (251) ~ (all_30_2 = e2)
% 249.49/59.01 | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | BETA: splitting (50) gives:
% 249.49/59.01 | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | (252) ~ (all_38_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REF_CLOSE: (8), (17), (35), (36), (39), (42), (43), (48),
% 249.49/59.01 | | | | | | | | | | | | | (79), (101), (110), (142), (158), (198), (241),
% 249.49/59.01 | | | | | | | | | | | | | (251), (252) are inconsistent by sub-proof #216.
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | (253) all_38_2 = e4
% 249.49/59.01 | | | | | | | | | | | | | (254) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0
% 249.49/59.01 | | | | | | | | | | | | | & op(e1, e4) = all_38_1 & $i(all_38_0) &
% 249.49/59.01 | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e4)
% 249.49/59.01 | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | COMBINE_EQS: (136), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (255) all_242_2 = e4
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (119), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (256) ~ (all_244_15 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (167), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (257) ~ (all_36_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | SIMP: (257) implies:
% 249.49/59.01 | | | | | | | | | | | | | (258) ~ (all_36_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (182), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (259) ~ (all_26_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | SIMP: (259) implies:
% 249.49/59.01 | | | | | | | | | | | | | (260) ~ (all_26_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (190), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (261) ~ (all_20_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (192), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (262) ~ (all_10_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (31), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (263) op(e4, all_4_2) = e1
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | REDUCE: (28), (253) imply:
% 249.49/59.01 | | | | | | | | | | | | | (264) op(e4, e1) = e2
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | BETA: splitting (254) gives:
% 249.49/59.01 | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | (265) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.01 | | | | | | | | | | | | | | op(e1, e4) = all_38_1 & $i(all_38_0) &
% 249.49/59.01 | | | | | | | | | | | | | | $i(all_38_1)
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | ALPHA: (265) implies:
% 249.49/59.01 | | | | | | | | | | | | | | (266) op(e1, e4) = all_38_1
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | (267) ~ (all_242_2 = e4)
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | REDUCE: (255), (267) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | (268) $false
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | (269) ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.01 | | | | | | | | | | | | | | | all_242_0 & op(e1, e4) = all_242_1 &
% 249.49/59.01 | | | | | | | | | | | | | | | $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1
% 249.49/59.01 | | | | | | | | | | | | | | | = e0) & op(e1, e4) = all_242_1 &
% 249.49/59.01 | | | | | | | | | | | | | | | $i(all_242_1))
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | (270) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 249.49/59.01 | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (105), (147), (184), (258), (264), (270) are
% 249.49/59.01 | | | | | | | | | | | | | | | | inconsistent by sub-proof #795.
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | (271) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 249.49/59.01 | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 249.49/59.01 | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | (272) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (273) all_252_11 = e4
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_16_2, all_38_1, e4,
% 249.49/59.01 | | | | | | | | | | | | | | | | | e1, simplifying with (89), (266) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (274) all_38_1 = all_16_2
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_26_2, e2, e1, e4,
% 249.49/59.01 | | | | | | | | | | | | | | | | | simplifying with (147), (264) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (275) all_26_2 = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (276) all_44_2 = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (59), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (277) ~ (all_244_15 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (117), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (278) ~ (all_84_2 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (121), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (279) ~ (all_36_2 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (207), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (280) ~ (all_20_2 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (129), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (281) ~ (all_6_2 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | SIMP: (281) implies:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (282) ~ (all_6_2 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (260), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (283) ~ (e4 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (249), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (284) ~ (e3 = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (210), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (285) op(e2, all_16_2) = e1
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REDUCE: (95), (275) imply:
% 249.49/59.01 | | | | | | | | | | | | | | | | | (286) op(all_16_2, e2) = e4
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | (287) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 =
% 249.49/59.01 | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (35), (37), (39), (71), (78), (96), (104),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | (160), (177), (184), (191), (194), (211), (221),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | (241), (278), (287) are inconsistent by sub-proof
% 249.49/59.01 | | | | | | | | | | | | | | | | | | #215.
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | (288) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 =
% 249.49/59.01 | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 &
% 249.49/59.01 | | | | | | | | | | | | | | | | | | op(e4, e0) = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | (289) all_252_4 = e2 & op(e4, e2) = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (64), (282), (289) are inconsistent by
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | sub-proof #453.
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | (290) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 =
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2)
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (291) all_252_9 = e2 & op(e4, e1) = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (292) all_252_9 = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (12), (14), (15),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (16), (17), (18), (19), (24), (25), (29), (32),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (35), (36), (37), (38), (39), (40), (46), (49),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (64), (66),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (68), (71), (73), (76), (77), (78), (82), (83),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (88), (89), (91), (92), (93),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (94), (96), (99), (100), (103), (104), (105),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (106), (107), (108), (111), (116), (120), (125),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (126), (127), (131), (132), (133), (137), (138),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (140), (143), (144), (146), (151), (153), (157),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (160), (162), (164), (165), (166), (168), (169),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (170), (172), (173), (176), (177), (179), (181),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (184), (185), (186), (187), (189), (191), (193),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (194), (198), (199), (202), (204), (206), (209),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (211), (213), (215), (217), (218), (221), (233),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (235), (237), (238), (241), (245), (246), (248),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (250), (251), (256), (263), (264), (269), (273),
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (276), (277), (279), (285), (286), (292) are
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #164.
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (293) all_252_16 = e2 & op(e4, e0) = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | (294) op(e4, e0) = e2
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (251), (294) are inconsistent by
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | | sub-proof #830.
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | (295) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 249.49/59.01 | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (162), (164), (245), (256), (295) are
% 249.49/59.01 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 249.49/59.01 | | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | End of split
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | Case 2:
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | (296) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 &
% 249.49/59.01 | | | | | | | | | | | | | | $i(all_38_1)
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | ALPHA: (296) implies:
% 249.49/59.01 | | | | | | | | | | | | | | (297) ~ (all_38_1 = e3)
% 249.49/59.01 | | | | | | | | | | | | | | (298) op(e1, e4) = all_38_1
% 249.49/59.01 | | | | | | | | | | | | | |
% 249.49/59.01 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (12),
% 249.49/59.01 | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (24), (25),
% 249.49/59.01 | | | | | | | | | | | | | | (29), (32), (35), (36), (38), (39), (40), (46),
% 249.49/59.01 | | | | | | | | | | | | | | (49), (54), (55), (56), (57), (58), (59), (61),
% 249.49/59.01 | | | | | | | | | | | | | | (62), (64), (66), (68), (71), (73), (76), (77),
% 249.49/59.01 | | | | | | | | | | | | | | (78), (82), (83), (85), (86), (87), (88), (89),
% 249.49/59.01 | | | | | | | | | | | | | | (91), (92), (93), (94), (95), (96), (99), (100),
% 249.49/59.01 | | | | | | | | | | | | | | (103), (104), (105), (106), (107), (108), (111),
% 249.49/59.01 | | | | | | | | | | | | | | (114), (116), (117), (120), (121), (122), (125),
% 249.49/59.01 | | | | | | | | | | | | | | (126), (127), (129), (131), (132), (133), (137),
% 249.49/59.01 | | | | | | | | | | | | | | (138), (140), (143), (144), (146), (147), (151),
% 249.49/59.01 | | | | | | | | | | | | | | (153), (157), (160), (162), (164), (165), (166),
% 249.49/59.01 | | | | | | | | | | | | | | (168), (169), (170), (172), (173), (176), (177),
% 249.49/59.01 | | | | | | | | | | | | | | (179), (181), (184), (185), (186), (187), (189),
% 249.49/59.01 | | | | | | | | | | | | | | (191), (193), (194), (198), (199), (202), (204),
% 249.49/59.02 | | | | | | | | | | | | | | (206), (207), (209), (210), (211), (213), (215),
% 249.49/59.02 | | | | | | | | | | | | | | (218), (221), (233), (235), (237), (238), (241),
% 249.49/59.02 | | | | | | | | | | | | | | (245), (246), (249), (250), (255), (256), (258),
% 249.49/59.02 | | | | | | | | | | | | | | (260), (263), (264), (297), (298) are inconsistent
% 249.49/59.02 | | | | | | | | | | | | | | by sub-proof #163.
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | (299) all_30_2 = e2
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REF_CLOSE: (10), (35), (42), (43), (139), (158), (299) are
% 249.49/59.02 | | | | | | | | | | | | inconsistent by sub-proof #162.
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | (300) all_28_2 = e3
% 249.49/59.02 | | | | | | | | | | | (301) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 249.49/59.02 | | | | | | | | | | | & op(e2, e3) = all_28_1 & $i(all_28_0) &
% 249.49/59.02 | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3)
% 249.49/59.02 | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (200), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (302) ~ (all_244_8 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (135), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (303) ~ (all_22_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | SIMP: (303) implies:
% 249.49/59.02 | | | | | | | | | | | (304) ~ (all_22_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (93), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (305) ~ (all_20_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | SIMP: (305) implies:
% 249.49/59.02 | | | | | | | | | | | (306) ~ (all_20_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (174), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (307) ~ (all_8_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | SIMP: (307) implies:
% 249.49/59.02 | | | | | | | | | | | (308) ~ (all_8_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (30), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (309) ~ (all_6_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | SIMP: (309) implies:
% 249.49/59.02 | | | | | | | | | | | (310) ~ (all_6_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (115), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (311) ~ (all_4_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | SIMP: (311) implies:
% 249.49/59.02 | | | | | | | | | | | (312) ~ (all_4_2 = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (63), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (313) op(e3, e2) = e0
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REDUCE: (77), (300) imply:
% 249.49/59.02 | | | | | | | | | | | (314) op(e0, e2) = e3
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (9), (10), (17), (28), (31), (32),
% 249.49/59.02 | | | | | | | | | | | (35), (36), (37), (39), (42), (43), (48), (49),
% 249.49/59.02 | | | | | | | | | | | (50), (51), (64), (69), (71), (73), (77), (78),
% 249.49/59.02 | | | | | | | | | | | (79), (83), (85), (91), (96), (97), (101), (104),
% 249.49/59.02 | | | | | | | | | | | (108), (110), (111), (114), (130), (133), (136),
% 249.49/59.02 | | | | | | | | | | | (139), (142), (147), (154), (158), (160), (164),
% 249.49/59.02 | | | | | | | | | | | (172), (176), (184), (187), (198), (199), (205),
% 249.49/59.02 | | | | | | | | | | | (221), (231), (237), (238), (241), (244), (245),
% 249.49/59.02 | | | | | | | | | | | (246), (301), (302), (304), (306), (308), (310),
% 249.49/59.02 | | | | | | | | | | | (312), (313), (314) are inconsistent by sub-proof
% 249.49/59.02 | | | | | | | | | | | #154.
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | (315) all_26_2 = e3
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | REDUCE: (72), (315) imply:
% 249.49/59.02 | | | | | | | | | | (316) op(e3, e1) = e4
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | REF_CLOSE: (8), (10), (17), (35), (36), (39), (42), (43),
% 249.49/59.02 | | | | | | | | | | (48), (51), (79), (101), (105), (110), (118),
% 249.49/59.02 | | | | | | | | | | (139), (142), (158), (167), (198), (224), (241),
% 249.49/59.02 | | | | | | | | | | (316) are inconsistent by sub-proof #151.
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | (317) all_24_2 = e3
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | COMBINE_EQS: (201), (317) imply:
% 249.49/59.02 | | | | | | | | | (318) all_16_2 = e3
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (67), (318) imply:
% 249.49/59.02 | | | | | | | | | (319) ~ (all_244_0 = e3)
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (197), (318) imply:
% 249.49/59.02 | | | | | | | | | (320) ~ (all_100_2 = e3)
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (210), (318) imply:
% 249.49/59.02 | | | | | | | | | (321) op(all_26_2, e3) = e1
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (95), (318) imply:
% 249.49/59.02 | | | | | | | | | (322) op(e3, all_26_2) = e4
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (196), (318) imply:
% 249.49/59.02 | | | | | | | | | (323) op(e3, e4) = e1
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | REDUCE: (89), (318) imply:
% 249.49/59.02 | | | | | | | | | (324) op(e1, e4) = e3
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | BETA: splitting (191) gives:
% 249.49/59.02 | | | | | | | | |
% 249.49/59.02 | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | (325) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 249.49/59.02 | | | | | | | | | | e3 & op(e3, e4) = e3)
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | REF_CLOSE: (32), (35), (39), (71), (78), (104), (155), (160),
% 249.49/59.02 | | | | | | | | | | (184), (194), (211), (221), (241), (323), (324),
% 249.49/59.02 | | | | | | | | | | (325) are inconsistent by sub-proof #146.
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | (326) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 249.49/59.02 | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 249.49/59.02 | | | | | | | | | | e4) = e3)
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | BETA: splitting (326) gives:
% 249.49/59.02 | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | (327) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | ALPHA: (327) implies:
% 249.49/59.02 | | | | | | | | | | | (328) all_252_6 = e3
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | REF_CLOSE: (96), (241), (328) are inconsistent by sub-proof
% 249.49/59.02 | | | | | | | | | | | #691.
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | (329) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 249.49/59.02 | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | BETA: splitting (329) gives:
% 249.49/59.02 | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | (330) all_252_12 = e3 & op(e1, e4) = e3
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | ALPHA: (330) implies:
% 249.49/59.02 | | | | | | | | | | | | (331) all_252_12 = e3
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_100_2, e1, e4, e3,
% 249.49/59.02 | | | | | | | | | | | | simplifying with (155), (323) gives:
% 249.49/59.02 | | | | | | | | | | | | (332) all_100_2 = e1
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (134), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (333) ~ (all_244_0 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (74), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (334) ~ (all_36_2 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | SIMP: (334) implies:
% 249.49/59.02 | | | | | | | | | | | | (335) ~ (all_36_2 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (150), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (336) ~ (all_8_2 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (320), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (337) ~ (e3 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (156), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (338) ~ (e2 = e1)
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | REDUCE: (47), (332) imply:
% 249.49/59.02 | | | | | | | | | | | | (339) op(all_84_2, e1) = e3
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | BETA: splitting (211) gives:
% 249.49/59.02 | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | (340) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 249.49/59.02 | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 249.49/59.02 | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | BETA: splitting (340) gives:
% 249.49/59.02 | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | (341) all_252_0 = e1 & op(e4, e4) = e1
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | REF_CLOSE: (35), (53), (79), (152), (158), (194), (221),
% 249.49/59.02 | | | | | | | | | | | | | | (225), (241), (319), (324), (331), (333), (341)
% 249.49/59.02 | | | | | | | | | | | | | | are inconsistent by sub-proof #143.
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | (342) all_252_2 = e1 & op(e3, e4) = e1
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | ALPHA: (342) implies:
% 249.49/59.02 | | | | | | | | | | | | | | (343) all_252_2 = e1
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 249.49/59.02 | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | (344) all_250_0 = e4
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | COMBINE_EQS: (53), (344) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | (345) all_244_0 = e4
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | REDUCE: (5), (345) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | (346) ~ (all_84_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | SIMP: (346) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | (347) ~ (all_84_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 249.49/59.02 | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | (348) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 =
% 249.49/59.02 | | | | | | | | | | | | | | | | e4 & op(e3, e4) = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | (349) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | (350) all_252_0 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | (351) ~ (all_28_2 = e3)
% 249.49/59.02 | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | (352) ~ (all_26_2 = e3)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | (353) ~ (all_30_2 = e2)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_38_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (35), (36), (39), (42), (43), (48),
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (79), (101), (110), (142), (158), (198), (241),
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (353), (354) are inconsistent by sub-proof #216.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (355) all_38_2 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (356) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | & op(e1, e4) = all_38_1 & $i(all_38_0) &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (357) all_242_2 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (358) ~ (all_244_15 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (359) ~ (all_36_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | SIMP: (359) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_36_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (361) ~ (all_26_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | SIMP: (361) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (362) ~ (all_26_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (190), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (363) ~ (all_20_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (364) ~ (all_10_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (365) op(e4, all_4_2) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (355) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | (366) op(e4, e1) = e2
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | op(e1, e4) = all_38_1 & $i(all_38_0) &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_38_0 = e0)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | (369) op(e1, e4) = all_38_1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | (370) op(e4, all_38_1) = all_38_0
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | (371) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (105), (147), (184), (360), (366), (371) are
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #795.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | (372) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | (373) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | (374) all_252_11 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (375) ~ (all_242_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (357), (375) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (376) $false
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (376) is inconsistent.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e3, all_38_1, e4, e1,
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (324), (369) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_38_1 = e3
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_26_2, e2, e1, e4,
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (147), (366) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_26_2 = e2
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (379) ~ (all_84_2 = e2)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_20_2 = e2)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (381) ~ (e4 = e2)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (382) ~ (e3 = e2)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (321), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (383) op(e2, e3) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (377) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (384) op(e4, e3) = all_38_0
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (378) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | (385) op(e3, e2) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (386) ~ (all_68_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (386) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_22_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) ~ (all_82_2 = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (388) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) ~ (all_28_2 = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_8_2, e4, e2, e3,
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (187), (385) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) all_8_2 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (390) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) ~ (all_28_2 = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (110), (112), (130), (183), (203), (351),
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (391) are inconsistent by sub-proof #583.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_82_2 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (392) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_28_2 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (393) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_108_2 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (393) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_22_2 = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (393) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_20_2 = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (396) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) ~ (all_20_2 = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (393) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) op(e0, e2) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 =
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_252_9 = e1 & op(e4, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) op(e4, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (71), (366), (401) are inconsistent by
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #785.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_252_10 = e1 & op(e3, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (402) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) op(e3, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_36_2, e1, e1, e3,
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (105), (403) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_36_2 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (335), (404) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) $false
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_252_11 = e1 & op(e2, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_252_11 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (408) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) e4 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (409) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_252_0 = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (78), (160), (184), (194), (221), (241),
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (343), (410) are inconsistent by sub-proof
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_252_15 = e1 & op(e1, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) op(e1, e1) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_252_20 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (416) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) e4 = e2
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (417) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) e4 = e2
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (418) imply:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_252_0 = e2
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (39), (78), (96), (104), (160), (184),
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (194), (221), (241), (343), (419) are
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #386.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (133), (387), (420) are inconsistent by
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_252_22 = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) op(e0, e2) = e4
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (71), (133), (221), (246), (425) are
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 249.49/59.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_252_22 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (423), (428) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) e4 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (429) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_252_0 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (78), (160), (184), (194), (221), (241),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (343), (430) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (164), (397), (432) are inconsistent by
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #287.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e1, e4, e2, e0,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (398), (424) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) e4 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (433) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_252_0 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (78), (160), (184), (194), (221), (241),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331), (343), (434) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (164), (245), (436) are inconsistent by
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) op(e0, e0) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_108_2 = e1)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (439) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_244_24, e4, e0, e0,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (38), (438) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_244_24 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_244_15, e1, e1, e1,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (162), (413) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_244_15 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_10_2, e1, e3, e2,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (36), (383) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_10_2 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_84_2, all_38_0, e3,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, simplifying with (177), (384) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_84_2 = all_38_0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (444) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_250_1 = all_38_0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (443), (444) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) ~ (all_38_0 = e1)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (444) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) ~ (all_38_0 = e4)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (444) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ (all_38_0 = e2)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (444) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) op(all_38_0, e1) = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) ~ (all_92_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (450) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) ~ (all_20_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (35), (87), (138), (217), (218), (245),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (451) are inconsistent by sub-proof #780.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) all_92_2 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (452) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_20_2 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (453) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) op(e3, e1) = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_250_1 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (455) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_38_0 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (447), (456) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (457) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_1 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_250_1 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (459) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_38_0 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (460) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) op(e3, e1) = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (96), (105), (454), (461) are inconsistent
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #748.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_250_1 = e2 | all_250_1 = e1 | all_250_1 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_250_1 = e2
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (463) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_38_0 = e2
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (448), (464) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_250_1 = e1 | all_250_1 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_250_1 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (467) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_38_0 = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (446), (468) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (469) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_250_1 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (445), (470) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_38_0 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (471) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (472) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (164), (397), (473) are inconsistent by
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #287.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_68_2 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (474) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_22_2 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (475) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (476) op(e4, e3) = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_84_2, e0, e3, e4,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (177), (476) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_84_2 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_84_2, all_38_0, e3,
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | e4, simplifying with (177), (384) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_84_2 = all_38_0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (478) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_38_0 = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (479) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (480) $false
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (480) is inconsistent.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | (481) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (162), (164), (245), (358), (481) are
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (482) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 &
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (483) ~ (all_38_1 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (484) op(e1, e4) = all_38_1
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (12),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (24), (25),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (29), (32), (35), (36), (38), (39), (40), (46),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (49), (54), (55), (56), (57), (58), (59), (61),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (62), (64), (66), (68), (71), (73), (76), (77),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (78), (82), (83), (85), (86), (87), (88), (89),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (91), (92), (93), (94), (95), (96), (99), (100),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (103), (104), (105), (106), (107), (108), (111),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (114), (116), (117), (120), (121), (122), (125),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (126), (127), (129), (131), (132), (133), (137),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (138), (140), (143), (144), (146), (147), (151),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (153), (157), (160), (162), (164), (165), (166),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (172), (173), (176), (177),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (179), (181), (184), (185), (186), (187), (189),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (191), (193), (194), (198), (199), (202), (204),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (206), (207), (209), (210), (211), (213), (215),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (218), (221), (233), (235), (237), (238), (241),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (245), (246), (351), (352), (357), (358), (360),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | (362), (365), (366), (483), (484) are inconsistent
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #163.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | (485) all_30_2 = e2
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (485) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | (486) op(e2, e2) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (42), (43), (79), (158), (486) are
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | (487) all_26_2 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | REDUCE: (72), (487) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | (488) op(e3, e1) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (17), (35), (36), (39), (42), (43),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | (48), (51), (79), (101), (105), (110), (118),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | (139), (142), (158), (167), (198), (224), (241),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | | (488) are inconsistent by sub-proof #151.
% 249.49/59.03 | | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (489) all_28_2 = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (490) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0
% 249.49/59.03 | | | | | | | | | | | | | | | | | | & op(e2, e3) = all_28_1 & $i(all_28_0) &
% 249.49/59.03 | | | | | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (200), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (491) ~ (all_244_8 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (135), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (492) ~ (all_22_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | SIMP: (492) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (493) ~ (all_22_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (93), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (494) ~ (all_20_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | SIMP: (494) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (495) ~ (all_20_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (174), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (496) ~ (all_8_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | SIMP: (496) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (497) ~ (all_8_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (30), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (498) ~ (all_6_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | SIMP: (498) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (499) ~ (all_6_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (115), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (500) ~ (all_4_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | SIMP: (500) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (501) ~ (all_4_2 = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (63), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (502) op(e3, e2) = e0
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REDUCE: (77), (489) imply:
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (503) op(e0, e2) = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (9), (10), (17), (28), (31), (32),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (35), (36), (37), (39), (42), (43), (48), (49),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (50), (51), (64), (69), (71), (73), (77), (78),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (79), (83), (85), (91), (96), (97), (101), (104),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (108), (110), (111), (114), (130), (133), (136),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (139), (142), (147), (154), (158), (160), (164),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (172), (176), (184), (187), (198), (199), (205),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (221), (231), (237), (238), (241), (244), (245),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (246), (490), (491), (493), (495), (497), (499),
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (501), (502), (503) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | | #154.
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | (504) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | ALPHA: (504) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | | (505) all_252_2 = e4
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (343), (505) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | #605.
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | (506) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 =
% 249.49/59.03 | | | | | | | | | | | | | | | | e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 249.49/59.03 | | | | | | | | | | | | | | | | op(e0, e4) = e4)
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (39), (160), (184), (221), (241), (324),
% 249.49/59.03 | | | | | | | | | | | | | | | | (506) are inconsistent by sub-proof #142.
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | (507) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 249.49/59.03 | | | | | | | | | | | | | | | all_250_0 = e0
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | REF_CLOSE: (53), (79), (225), (319), (333), (507) are
% 249.49/59.03 | | | | | | | | | | | | | | | inconsistent by sub-proof #217.
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | (508) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 249.49/59.03 | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 249.49/59.03 | | | | | | | | | | | | | op(e0, e4) = e1)
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | REF_CLOSE: (32), (71), (104), (221), (241), (331), (508) are
% 249.49/59.03 | | | | | | | | | | | | | inconsistent by sub-proof #141.
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | (509) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | ALPHA: (509) implies:
% 249.49/59.03 | | | | | | | | | | | | (510) all_252_20 = e3
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | REF_CLOSE: (37), (221), (510) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | #520.
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | |
% 249.49/59.03 | | | | | | | | End of split
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | (511) all_22_2 = e1
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (34), (511) imply:
% 249.49/59.03 | | | | | | | | (512) ~ (all_62_2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (186), (511) imply:
% 249.49/59.03 | | | | | | | | (513) ~ (all_20_2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | SIMP: (513) implies:
% 249.49/59.03 | | | | | | | | (514) ~ (all_20_2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (181), (511) imply:
% 249.49/59.03 | | | | | | | | (515) ~ (all_10_2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | SIMP: (515) implies:
% 249.49/59.03 | | | | | | | | (516) ~ (all_10_2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (26), (511) imply:
% 249.49/59.03 | | | | | | | | (517) ~ (e2 = e1)
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (131), (511) imply:
% 249.49/59.03 | | | | | | | | (518) op(e1, e3) = e0
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | REDUCE: (133), (511) imply:
% 249.49/59.03 | | | | | | | | (519) op(e0, e3) = e1
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | BETA: splitting (111) gives:
% 249.49/59.03 | | | | | | | |
% 249.49/59.03 | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | |
% 249.49/59.03 | | | | | | | | | (520) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 =
% 249.49/59.03 | | | | | | | | | e1 & op(e0, e3) = e1)
% 249.49/59.03 | | | | | | | | |
% 249.49/59.03 | | | | | | | | | BETA: splitting (520) gives:
% 249.49/59.03 | | | | | | | | |
% 249.49/59.03 | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | (521) all_252_20 = e1 & op(e0, e4) = e1
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | REF_CLOSE: (71), (221), (521) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | #544.
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | (522) all_252_21 = e1 & op(e0, e3) = e1
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | ALPHA: (522) implies:
% 249.49/59.03 | | | | | | | | | | (523) all_252_21 = e1
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | GROUND_INST: instantiating (35) with all_62_2, e0, e3, e1,
% 249.49/59.03 | | | | | | | | | | simplifying with (94), (518) gives:
% 249.49/59.03 | | | | | | | | | | (524) all_62_2 = e0
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | COMBINE_EQS: (98), (524) imply:
% 249.49/59.03 | | | | | | | | | | (525) all_112_2 = e0
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | REDUCE: (109), (524) imply:
% 249.49/59.03 | | | | | | | | | | (526) ~ (all_244_3 = e0)
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | REDUCE: (84), (524) imply:
% 249.49/59.03 | | | | | | | | | | (527) ~ (all_34_2 = e0)
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | SIMP: (527) implies:
% 249.49/59.03 | | | | | | | | | | (528) ~ (all_34_2 = e0)
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | REDUCE: (512), (524) imply:
% 249.49/59.03 | | | | | | | | | | (529) ~ (e1 = e0)
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | BETA: splitting (116) gives:
% 249.49/59.03 | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | (530) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 249.49/59.03 | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 249.49/59.03 | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | BETA: splitting (530) gives:
% 249.49/59.03 | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | (531) all_252_1 = e0 & op(e4, e3) = e0
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | ALPHA: (531) implies:
% 249.49/59.03 | | | | | | | | | | | | (532) all_252_1 = e0
% 249.49/59.03 | | | | | | | | | | | | (533) op(e4, e3) = e0
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | BETA: splitting (15) gives:
% 249.49/59.03 | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | (534) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 249.49/59.03 | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | BETA: splitting (534) gives:
% 249.49/59.03 | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | (535) all_252_1 = e4 & op(e4, e3) = e4
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | REF_CLOSE: (39), (532), (535) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | #898.
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | (536) all_252_3 = e4 & op(e3, e3) = e4
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | ALPHA: (536) implies:
% 249.49/59.03 | | | | | | | | | | | | | | (537) all_252_3 = e4
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 249.49/59.03 | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | (538) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 249.49/59.03 | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | REF_CLOSE: (35), (177), (184), (237), (533), (537), (538) are
% 249.49/59.03 | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | (539) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 249.49/59.03 | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 249.49/59.03 | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | BETA: splitting (539) gives:
% 249.49/59.03 | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | (540) all_252_7 = e2 & op(e2, e3) = e2
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | ALPHA: (540) implies:
% 249.49/59.03 | | | | | | | | | | | | | | | | (541) all_252_7 = e2
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | (542) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 249.49/59.03 | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | BETA: splitting (542) gives:
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (543) all_252_1 = e3 & op(e4, e3) = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (532), (543) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | | #840.
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | (544) all_252_3 = e3 & op(e3, e3) = e3
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (537), (544) are inconsistent by sub-proof
% 249.49/59.03 | | | | | | | | | | | | | | | | | | #685.
% 249.49/59.03 | | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.03 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.03 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | (545) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 249.49/59.04 | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 249.49/59.04 | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | (546) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | ALPHA: (546) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | (547) all_252_7 = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (541), (547) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | #939.
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | (548) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | BETA: splitting (548) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (549) all_252_13 = e3 & op(e1, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | ALPHA: (549) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (550) all_252_13 = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (551) op(e1, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, e3, e3, e1,
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | simplifying with (518), (551) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (552) e3 = e0
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (552) imply:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (553) all_252_13 = e0
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (13), (14),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (15), (17), (18), (22), (27), (28), (31), (32),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (35), (36), (37), (39), (40), (42), (43), (46),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (48), (49), (50), (51), (53), (60), (64), (65),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (67), (71), (73), (78), (79), (82), (83), (87),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (89), (91), (96), (101), (104), (107), (108),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (110), (114), (127), (128), (134), (136), (138),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (139), (140), (142), (147), (152), (155), (156),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (158), (160), (161), (163), (164), (171), (172),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (175), (177), (178), (182), (184), (185), (187),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (191), (192), (194), (196), (197), (198), (201),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (202), (204), (207), (211), (212), (216), (217),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (218), (221), (225), (227), (231), (233), (237),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (241), (245), (514), (516), (519), (523), (525),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (526), (528), (553) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | #131.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (554) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (555) op(e0, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (104), (519), (555) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | sub-proof #590.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | (556) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 249.49/59.04 | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | BETA: splitting (556) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | (557) all_252_13 = e2 & op(e1, e3) = e2
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | ALPHA: (557) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | | | (558) all_252_13 = e2
% 249.49/59.04 | | | | | | | | | | | | | | | | | (559) op(e1, e3) = e2
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | (560) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 249.49/59.04 | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | BETA: splitting (560) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (561) all_252_1 = e3 & op(e4, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (532), (561) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | #840.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (562) all_252_3 = e3 & op(e3, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (537), (562) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | #685.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | (563) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 249.49/59.04 | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 249.49/59.04 | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | BETA: splitting (563) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, e2, e3, e1,
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | simplifying with (518), (559) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (564) e2 = e0
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (558), (564) imply:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (565) all_252_13 = e0
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (13), (14),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (15), (17), (18), (22), (27), (28), (31), (32),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (35), (36), (37), (39), (40), (42), (43), (46),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (48), (49), (50), (51), (53), (60), (64), (65),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (67), (71), (73), (78), (79), (82), (83), (87),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (89), (91), (96), (101), (104), (107), (108),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (110), (114), (127), (128), (134), (136), (138),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (139), (140), (142), (147), (152), (155), (156),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (158), (160), (161), (163), (164), (171), (172),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (175), (177), (178), (182), (184), (185), (187),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (191), (192), (194), (196), (197), (198), (201),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (202), (204), (207), (211), (212), (216), (217),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (218), (221), (225), (227), (231), (233), (237),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (241), (245), (514), (516), (519), (523), (525),
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (526), (528), (565) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | #131.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | (566) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | (567) all_252_13 = e3 & op(e1, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (558), (567) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | #774.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | (568) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | ALPHA: (568) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | (569) op(e0, e3) = e3
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (104), (519), (569) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | | sub-proof #590.
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | (570) all_252_21 = e2 & op(e0, e3) = e2
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (523), (570) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | | | #375.
% 249.49/59.04 | | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (571) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 249.49/59.04 | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 249.49/59.04 | | | | | | | | | | | | | op(e0, e3) = e4)
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | BETA: splitting (571) gives:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | (572) all_252_7 = e4 & op(e2, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | ALPHA: (572) implies:
% 249.49/59.04 | | | | | | | | | | | | | | (573) op(e2, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | REF_CLOSE: (8), (35), (36), (573) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | | | sub-proof #953.
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | (574) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | BETA: splitting (574) gives:
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | (575) all_252_13 = e4 & op(e1, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | ALPHA: (575) implies:
% 249.49/59.04 | | | | | | | | | | | | | | | (576) all_252_13 = e4
% 249.49/59.04 | | | | | | | | | | | | | | | (577) op(e1, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, e4, e3, e1,
% 249.49/59.04 | | | | | | | | | | | | | | | simplifying with (518), (577) gives:
% 249.49/59.04 | | | | | | | | | | | | | | | (578) e4 = e0
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | COMBINE_EQS: (576), (578) imply:
% 249.49/59.04 | | | | | | | | | | | | | | | (579) all_252_13 = e0
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (13), (14),
% 249.49/59.04 | | | | | | | | | | | | | | | (15), (17), (18), (22), (27), (28), (31), (32),
% 249.49/59.04 | | | | | | | | | | | | | | | (35), (36), (37), (39), (40), (42), (43), (46),
% 249.49/59.04 | | | | | | | | | | | | | | | (48), (49), (50), (51), (53), (60), (64), (65),
% 249.49/59.04 | | | | | | | | | | | | | | | (67), (71), (73), (78), (79), (82), (83), (87),
% 249.49/59.04 | | | | | | | | | | | | | | | (89), (91), (96), (101), (104), (107), (108),
% 249.49/59.04 | | | | | | | | | | | | | | | (110), (114), (127), (128), (134), (136), (138),
% 249.49/59.04 | | | | | | | | | | | | | | | (139), (140), (142), (147), (152), (155), (156),
% 249.49/59.04 | | | | | | | | | | | | | | | (158), (160), (161), (163), (164), (171), (172),
% 249.49/59.04 | | | | | | | | | | | | | | | (175), (177), (178), (182), (184), (185), (187),
% 249.49/59.04 | | | | | | | | | | | | | | | (191), (192), (194), (196), (197), (198), (201),
% 249.49/59.04 | | | | | | | | | | | | | | | (202), (204), (207), (211), (212), (216), (217),
% 249.49/59.04 | | | | | | | | | | | | | | | (218), (221), (225), (227), (231), (233), (237),
% 249.49/59.04 | | | | | | | | | | | | | | | (241), (245), (514), (516), (519), (523), (525),
% 249.49/59.04 | | | | | | | | | | | | | | | (526), (528), (579) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | #131.
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | (580) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | | REF_CLOSE: (78), (523), (580) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | | #367.
% 249.49/59.04 | | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (581) all_252_3 = e0 & op(e3, e3) = e0
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | ALPHA: (581) implies:
% 249.49/59.04 | | | | | | | | | | | | (582) all_252_3 = e0
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | REF_CLOSE: (8), (15), (16), (35), (36), (37), (39), (71),
% 249.49/59.04 | | | | | | | | | | | | (78), (96), (104), (160), (173), (184), (237),
% 249.49/59.04 | | | | | | | | | | | | (518), (519), (523), (582) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | sub-proof #288.
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | (583) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 249.49/59.04 | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 249.49/59.04 | | | | | | | | | | | op(e0, e3) = e0)
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | BETA: splitting (583) gives:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (584) all_252_7 = e0 & op(e2, e3) = e0
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | REF_CLOSE: (35), (36), (235), (584) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | sub-proof #816.
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (585) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | BETA: splitting (585) gives:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (586) all_252_13 = e0 & op(e1, e3) = e0
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | ALPHA: (586) implies:
% 249.49/59.04 | | | | | | | | | | | | | (587) all_252_13 = e0
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (11), (13), (14),
% 249.49/59.04 | | | | | | | | | | | | | (15), (17), (18), (22), (27), (28), (31), (32),
% 249.49/59.04 | | | | | | | | | | | | | (35), (36), (37), (39), (40), (42), (43), (46),
% 249.49/59.04 | | | | | | | | | | | | | (48), (49), (50), (51), (53), (60), (64), (65),
% 249.49/59.04 | | | | | | | | | | | | | (67), (71), (73), (78), (79), (82), (83), (87),
% 249.49/59.04 | | | | | | | | | | | | | (89), (91), (96), (101), (104), (107), (108),
% 249.49/59.04 | | | | | | | | | | | | | (110), (114), (127), (128), (134), (136), (138),
% 249.49/59.04 | | | | | | | | | | | | | (139), (140), (142), (147), (152), (155), (156),
% 249.49/59.04 | | | | | | | | | | | | | (158), (160), (161), (163), (164), (171), (172),
% 249.49/59.04 | | | | | | | | | | | | | (175), (177), (178), (182), (184), (185), (187),
% 249.49/59.04 | | | | | | | | | | | | | (191), (192), (194), (196), (197), (198), (201),
% 249.49/59.04 | | | | | | | | | | | | | (202), (204), (207), (211), (212), (216), (217),
% 249.49/59.04 | | | | | | | | | | | | | (218), (221), (225), (227), (231), (233), (237),
% 249.49/59.04 | | | | | | | | | | | | | (241), (245), (514), (516), (519), (523), (525),
% 249.49/59.04 | | | | | | | | | | | | | (526), (528), (587) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | #131.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (588) all_252_21 = e0 & op(e0, e3) = e0
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | ALPHA: (588) implies:
% 249.49/59.04 | | | | | | | | | | | | | (589) op(e0, e3) = e0
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (32), (35), (519), (589) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | | sub-proof #320.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | |
% 249.49/59.04 | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | |
% 249.49/59.04 | | | | | | | | | (590) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 =
% 249.49/59.04 | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 249.49/59.04 | | | | | | | | | e0) = e1)
% 249.49/59.04 | | | | | | | | |
% 249.49/59.04 | | | | | | | | | BETA: splitting (590) gives:
% 249.49/59.04 | | | | | | | | |
% 249.49/59.04 | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | (591) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | ALPHA: (591) implies:
% 249.49/59.04 | | | | | | | | | | (592) all_252_22 = e1
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | BETA: splitting (9) gives:
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | (593) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | BETA: splitting (593) gives:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (594) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | REF_CLOSE: (184), (221), (594) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | #543.
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (595) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | ALPHA: (595) implies:
% 249.49/59.04 | | | | | | | | | | | | (596) all_252_21 = e4
% 249.49/59.04 | | | | | | | | | | | | (597) op(e0, e3) = e4
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | GROUND_INST: instantiating (35) with e1, e4, e3, e0,
% 249.49/59.04 | | | | | | | | | | | | simplifying with (519), (597) gives:
% 249.49/59.04 | | | | | | | | | | | | (598) e4 = e1
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | COMBINE_EQS: (596), (598) imply:
% 249.49/59.04 | | | | | | | | | | | | (599) all_252_21 = e1
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | REF_CLOSE: (9), (32), (35), (37), (39), (73), (78), (91),
% 249.49/59.04 | | | | | | | | | | | | (96), (104), (160), (184), (221), (237), (519),
% 249.49/59.04 | | | | | | | | | | | | (592), (599) are inconsistent by sub-proof #137.
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | (600) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.49/59.04 | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.49/59.04 | | | | | | | | | | | op(e0, e0) = e4)
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | BETA: splitting (600) gives:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (601) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | ALPHA: (601) implies:
% 249.49/59.04 | | | | | | | | | | | | (602) all_252_22 = e4
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | REF_CLOSE: (78), (592), (602) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | #530.
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (603) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.49/59.04 | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | BETA: splitting (603) gives:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (604) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (32), (35), (37), (39), (73), (91), (96), (104),
% 249.49/59.04 | | | | | | | | | | | | | (160), (221), (237), (519), (592), (604) are
% 249.49/59.04 | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (605) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | ALPHA: (605) implies:
% 249.49/59.04 | | | | | | | | | | | | | (606) all_252_24 = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (32), (35), (37), (39), (73), (91), (96), (104),
% 249.49/59.04 | | | | | | | | | | | | | (160), (221), (237), (519), (592), (606) are
% 249.49/59.04 | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | (607) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 =
% 249.49/59.04 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | BETA: splitting (607) gives:
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | (608) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | REF_CLOSE: (35), (164), (514), (608) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | sub-proof #287.
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | (609) all_252_24 = e1 & op(e0, e0) = e1
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | ALPHA: (609) implies:
% 249.49/59.04 | | | | | | | | | | | (610) all_252_24 = e1
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | BETA: splitting (9) gives:
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (611) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.49/59.04 | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | BETA: splitting (611) gives:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (612) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (184), (221), (612) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | #543.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (613) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | ALPHA: (613) implies:
% 249.49/59.04 | | | | | | | | | | | | | (614) op(e0, e3) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (35), (78), (519), (614) are inconsistent by
% 249.49/59.04 | | | | | | | | | | | | | sub-proof #828.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | (615) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.49/59.04 | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.49/59.04 | | | | | | | | | | | | op(e0, e0) = e4)
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | BETA: splitting (615) gives:
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (616) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | ALPHA: (616) implies:
% 249.49/59.04 | | | | | | | | | | | | | (617) all_252_22 = e4
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | REF_CLOSE: (32), (35), (37), (39), (73), (91), (96), (104),
% 249.49/59.04 | | | | | | | | | | | | | (160), (221), (237), (519), (610), (617) are
% 249.49/59.04 | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | (618) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.49/59.04 | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | BETA: splitting (618) gives:
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | Case 1:
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | (619) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | ALPHA: (619) implies:
% 249.49/59.04 | | | | | | | | | | | | | | (620) all_252_23 = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | REF_CLOSE: (32), (35), (37), (39), (73), (91), (96), (104),
% 249.49/59.04 | | | | | | | | | | | | | | (160), (221), (237), (519), (610), (620) are
% 249.49/59.04 | | | | | | | | | | | | | | inconsistent by sub-proof #239.
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | Case 2:
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | (621) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | ALPHA: (621) implies:
% 249.49/59.04 | | | | | | | | | | | | | | (622) all_252_24 = e4
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | | REF_CLOSE: (78), (610), (622) are inconsistent by sub-proof
% 249.49/59.04 | | | | | | | | | | | | | | #514.
% 249.49/59.04 | | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | | |
% 249.49/59.04 | | | | | | | | | End of split
% 249.49/59.04 | | | | | | | | |
% 249.49/59.04 | | | | | | | | End of split
% 249.49/59.04 | | | | | | | |
% 249.49/59.04 | | | | | | | End of split
% 249.49/59.04 | | | | | | |
% 249.49/59.04 | | | | | | Case 2:
% 249.49/59.04 | | | | | | |
% 249.49/59.04 | | | | | | | (623) all_20_2 = e4
% 249.49/59.04 | | | | | | |
% 249.49/59.04 | | | | | | | REDUCE: (190), (623) imply:
% 249.49/59.04 | | | | | | | (624) ~ (all_38_2 = e4)
% 249.49/59.04 | | | | | | |
% 249.49/59.04 | | | | | | | REF_CLOSE: (8), (10), (17), (35), (36), (39), (42), (43), (48),
% 249.49/59.04 | | | | | | | (51), (79), (101), (110), (139), (142), (158), (198),
% 249.49/59.04 | | | | | | | (241), (624) are inconsistent by sub-proof #153.
% 249.49/59.04 | | | | | | |
% 249.49/59.04 | | | | | | End of split
% 249.49/59.04 | | | | | |
% 249.49/59.04 | | | | | End of split
% 249.49/59.04 | | | | |
% 249.49/59.04 | | | | Case 2:
% 249.49/59.04 | | | | |
% 249.49/59.04 | | | | | (625) all_252_7 = e0 & op(e2, e3) = e0
% 249.49/59.04 | | | | |
% 249.49/59.04 | | | | | REF_CLOSE: (35), (36), (235), (625) are inconsistent by sub-proof
% 249.49/59.04 | | | | | #816.
% 249.49/59.04 | | | | |
% 249.49/59.04 | | | | End of split
% 249.49/59.04 | | | |
% 249.49/59.04 | | | Case 2:
% 249.49/59.04 | | | |
% 249.49/59.04 | | | | (626) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2,
% 249.49/59.04 | | | | e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 249.49/59.04 | | | |
% 249.49/59.04 | | | | REF_CLOSE: (35), (43), (48), (198), (226), (229), (231), (626) are
% 249.49/59.04 | | | | inconsistent by sub-proof #879.
% 249.49/59.04 | | | |
% 249.49/59.04 | | | End of split
% 249.49/59.04 | | |
% 249.49/59.04 | | Case 2:
% 249.49/59.04 | | |
% 249.49/59.04 | | | (627) all_252_21 = e2 & op(e0, e3) = e2
% 249.49/59.04 | | |
% 249.49/59.04 | | | ALPHA: (627) implies:
% 249.49/59.04 | | | (628) op(e0, e3) = e2
% 249.49/59.04 | | |
% 249.49/59.04 | | | REF_CLOSE: (26), (35), (133), (628) are inconsistent by sub-proof #987.
% 249.49/59.04 | | |
% 249.49/59.04 | | End of split
% 249.49/59.04 | |
% 249.49/59.04 | Case 2:
% 249.49/59.04 | |
% 249.49/59.04 | | (629) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1)
% 249.49/59.04 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.04 | |
% 249.49/59.04 | | BETA: splitting (629) gives:
% 249.49/59.04 | |
% 249.49/59.04 | | Case 1:
% 249.49/59.04 | | |
% 249.49/59.04 | | | (630) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/59.04 | | |
% 249.49/59.04 | | | REF_CLOSE: (35), (77), (130), (630) are inconsistent by sub-proof #979.
% 249.49/59.04 | | |
% 249.49/59.04 | | Case 2:
% 249.49/59.04 | | |
% 249.49/59.05 | | | (631) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 249.49/59.05 | | | e0) = e2)
% 249.49/59.05 | | |
% 249.49/59.05 | | | REF_CLOSE: (35), (38), (164), (170), (217), (631) are inconsistent by
% 249.49/59.05 | | | sub-proof #977.
% 249.49/59.05 | | |
% 249.49/59.05 | | End of split
% 249.49/59.05 | |
% 249.49/59.05 | End of split
% 249.49/59.05 |
% 249.49/59.05 End of proof
% 249.49/59.05
% 249.49/59.05 Sub-proof #131 shows that the following formulas are inconsistent:
% 249.49/59.05 ----------------------------------------------------------------
% 249.49/59.05 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.05 all_250_23 = e0
% 249.49/59.05 (2) ~ (all_244_0 = all_84_2)
% 249.49/59.05 (3) ~ (all_10_2 = e1)
% 249.49/59.05 (4) op(e0, e3) = e1
% 249.49/59.05 (5) ~ (all_4_2 = e4)
% 249.49/59.05 (6) ~ (all_10_2 = e4)
% 249.49/59.05 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.05 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.05 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.05 (8) ~ (all_244_0 = all_30_2)
% 249.49/59.05 (9) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 249.49/59.05 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.05 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 249.49/59.05 (10) all_252_21 = e1
% 249.49/59.05 (11) ~ (all_40_2 = all_38_2)
% 249.49/59.05 (12) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.05 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.05 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.05 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 249.49/59.05 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.05 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.05 (14) op(e4, e0) = all_30_2
% 249.49/59.05 (15) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.05 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.05 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.05 (16) ~ (all_244_8 = all_6_2)
% 249.49/59.05 (17) all_252_6 = e0
% 249.49/59.05 (18) op(all_100_2, e4) = e3
% 249.49/59.05 (19) op(all_38_2, e1) = e2
% 249.49/59.05 (20) ~ (e2 = e0)
% 249.49/59.05 (21) op(all_38_2, all_4_2) = e1
% 249.49/59.05 (22) ~ (all_34_2 = e0)
% 249.49/59.05 (23) ~ (e1 = e0)
% 249.49/59.05 (24) all_252_13 = e0
% 249.49/59.05 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.05 (26) op(e2, e3) = all_10_2
% 249.49/59.05 (27) ~ (e3 = e2)
% 249.49/59.05 (28) ~ (e4 = e0)
% 249.49/59.05 (29) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.05 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.05 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.05 (30) op(all_244_8, all_244_8) = e2
% 249.49/59.05 (31) op(e2, e2) = all_244_8
% 249.49/59.05 (32) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.05 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.05 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.05 (33) op(e2, e1) = all_38_2
% 249.49/59.05 (34) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.05 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.05 (35) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.05 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.05 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.05 (36) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.05 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.05 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.05 (37) all_250_0 = all_244_0
% 249.49/59.05 (38) op(e1, e0) = all_34_2
% 249.49/59.05 (39) op(e4, e2) = all_6_2
% 249.49/59.05 (40) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 249.49/59.05 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 249.49/59.05 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 249.49/59.05 (41) ~ (all_244_0 = all_16_2)
% 249.49/59.05 (42) ~ (e2 = e1)
% 249.49/59.05 (43) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.05 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.05 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.05 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.05 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.05 op(e0, e1) = e0)))
% 249.49/59.05 (44) ~ (e4 = e1)
% 249.49/59.05 (45) ~ (all_244_0 = e2)
% 249.49/59.05 (46) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.05 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.05 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.05 (47) ~ (all_6_2 = e1)
% 249.49/59.05 (48) ~ (all_20_2 = e1)
% 249.49/59.05 (49) op(all_34_2, e0) = e1
% 249.49/59.05 (50) op(e1, e4) = all_16_2
% 249.49/59.05 (51) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.05 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.05 (52) ~ (all_100_2 = e0)
% 249.49/59.05 (53) ~ (e3 = e0)
% 249.49/59.05 (54) ~ (all_38_2 = e0)
% 249.49/59.05 (55) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.05 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.05 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.05 (56) ~ (e3 = e1)
% 249.49/59.05 (57) ~ (all_16_2 = e2)
% 249.49/59.05 (58) ~ (all_8_2 = e1)
% 249.49/59.05 (59) op(all_40_2, e0) = e2
% 249.49/59.05 (60) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.05 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.05 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.05 (61) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.05 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.05 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.05 (62) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(e3, all_26_1) = all_26_0 &
% 249.49/59.05 op(e1, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 249.49/59.05 e2) & op(e1, e3) = all_26_1 & $i(all_26_1))
% 249.49/59.05 (63) ~ (all_244_0 = all_100_2)
% 249.49/59.05 (64) all_242_2 = all_38_2
% 249.49/59.05 (65) op(all_34_2, all_20_2) = e0
% 249.49/59.05 (66) all_252_20 = e2
% 249.49/59.05 (67) op(e2, all_30_2) = e4
% 249.49/59.05 (68) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.05 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.05 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.05 (69) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.05 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.05 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.05 (70) all_112_2 = e0
% 249.49/59.05 (71) op(e4, e1) = all_26_2
% 249.49/59.05 (72) all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 249.49/59.05 all_250_0 = e0
% 249.49/59.05 (73) op(e3, e4) = all_100_2
% 249.49/59.05 (74) ~ (all_100_2 = e2)
% 249.49/59.05 (75) op(e4, e4) = all_244_0
% 249.49/59.05 (76) ~ (e4 = e3)
% 249.49/59.05 (77) ~ (all_112_2 = e0) | ( ~ (all_112_0 = e2) & op(e3, e0) = all_112_1 &
% 249.49/59.05 op(e0, all_112_1) = all_112_0 & $i(all_112_0) & $i(all_112_1)) | ( ~
% 249.49/59.05 (all_112_1 = e4) & op(e3, e0) = all_112_1 & $i(all_112_1))
% 249.49/59.05 (78) all_202_2 = all_26_2
% 249.49/59.05 (79) op(e0, e1) = all_20_2
% 249.49/59.05 (80) ~ (all_244_3 = all_100_2)
% 249.49/59.05 (81) op(e1, e2) = all_4_2
% 249.49/59.05 (82) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 249.49/59.05 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 249.49/59.05 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 249.49/59.05 (83) op(e4, e3) = all_84_2
% 249.49/59.05 (84) op(all_244_3, all_244_3) = e3
% 249.49/59.05 (85) ~ (all_38_2 = all_26_2)
% 249.49/59.05 (86) ~ (e4 = e2)
% 249.49/59.05 (87) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.05 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.05 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.05 (88) op(e3, e2) = all_8_2
% 249.49/59.05 (89) ~ (all_244_0 = e0)
% 249.49/59.05 (90) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.05 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.05 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.05 (91) ~ (all_38_2 = all_10_2)
% 249.49/59.05 (92) ~ (all_20_2 = e4)
% 249.49/59.05 (93) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.05 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.05 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.05 (94) op(all_16_2, e4) = e1
% 249.49/59.05 (95) ~ (all_100_2 = all_16_2)
% 249.49/59.05 (96) ~ (all_244_3 = e0)
% 249.49/59.05 (97) op(e2, e0) = all_40_2
% 249.49/59.05 (98) all_24_2 = all_16_2
% 249.49/59.05 (99) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.05 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.05 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.05 (100) op(e3, e3) = all_244_3
% 249.49/59.05 (101) ~ (all_26_2 = all_20_2)
% 249.49/59.05 (102) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.05 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.05 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.05 (103) ~ (all_202_2 = e2) | ( ~ (all_202_0 = e3) & op(e2, all_202_1) =
% 249.49/59.05 all_202_0 & op(e1, e2) = all_202_1 & $i(all_202_0) & $i(all_202_1)) |
% 249.49/59.05 ( ~ (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1))
% 249.49/59.05 (104) ~ (all_34_2 = all_4_2)
% 249.49/59.05 (105) ~ (all_16_2 = e0)
% 249.49/59.05 (106) ~ (all_20_2 = e2)
% 249.49/59.05 (107) all_250_23 = all_20_2
% 249.49/59.05
% 249.49/59.05 Begin of proof
% 249.49/59.05 |
% 249.49/59.05 | BETA: splitting (82) gives:
% 249.49/59.05 |
% 249.49/59.05 | Case 1:
% 249.49/59.05 | |
% 249.49/59.05 | | (108) ~ (all_24_2 = e3)
% 249.49/59.05 | |
% 249.49/59.05 | | REDUCE: (98), (108) imply:
% 249.49/59.05 | | (109) ~ (all_16_2 = e3)
% 249.49/59.05 | |
% 249.49/59.05 | | BETA: splitting (62) gives:
% 249.49/59.05 | |
% 249.49/59.05 | | Case 1:
% 249.49/59.05 | | |
% 249.49/59.05 | | | (110) ~ (all_26_2 = e3)
% 249.49/59.05 | | |
% 249.49/59.05 | | | BETA: splitting (36) gives:
% 249.49/59.05 | | |
% 249.49/59.05 | | | Case 1:
% 249.49/59.05 | | | |
% 249.49/59.05 | | | | (111) ~ (all_30_2 = e2)
% 249.49/59.05 | | | |
% 249.49/59.05 | | | | BETA: splitting (40) gives:
% 249.49/59.05 | | | |
% 249.49/59.05 | | | | Case 1:
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | (112) ~ (all_34_2 = e2)
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | BETA: splitting (35) gives:
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | Case 1:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | (113) ~ (all_38_2 = e4)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REF_CLOSE: (6), (14), (17), (25), (26), (28), (30), (31), (33),
% 249.49/59.05 | | | | | | (45), (55), (59), (69), (75), (97), (111), (113) are
% 249.49/59.05 | | | | | | inconsistent by sub-proof #216.
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | Case 2:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | (114) all_38_2 = e4
% 249.49/59.05 | | | | | | (115) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1,
% 249.49/59.05 | | | | | | e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 249.49/59.05 | | | | | | (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | COMBINE_EQS: (64), (114) imply:
% 249.49/59.05 | | | | | | (116) all_242_2 = e4
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REDUCE: (11), (114) imply:
% 249.49/59.05 | | | | | | (117) ~ (all_40_2 = e4)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REDUCE: (85), (114) imply:
% 249.49/59.05 | | | | | | (118) ~ (all_26_2 = e4)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | SIMP: (118) implies:
% 249.49/59.05 | | | | | | (119) ~ (all_26_2 = e4)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REDUCE: (91), (114) imply:
% 249.49/59.05 | | | | | | (120) ~ (all_10_2 = e4)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REDUCE: (21), (114) imply:
% 249.49/59.05 | | | | | | (121) op(e4, all_4_2) = e1
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | REDUCE: (19), (114) imply:
% 249.49/59.05 | | | | | | (122) op(e4, e1) = e2
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | BETA: splitting (60) gives:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | Case 1:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | (123) ~ (all_242_2 = e4)
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | REDUCE: (116), (123) imply:
% 249.49/59.05 | | | | | | | (124) $false
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | CLOSE: (124) is inconsistent.
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | Case 2:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | (125) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 &
% 249.49/59.05 | | | | | | | op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1))
% 249.49/59.05 | | | | | | | | ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 &
% 249.49/59.05 | | | | | | | $i(all_242_1))
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | BETA: splitting (115) gives:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | (126) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.05 | | | | | | | | op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | ALPHA: (126) implies:
% 249.49/59.05 | | | | | | | | (127) op(e1, e4) = all_38_1
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (12), (16), (17), (20), (23),
% 249.49/59.05 | | | | | | | | (24), (25), (26), (28), (30), (31), (34), (38), (39),
% 249.49/59.05 | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 249.49/59.05 | | | | | | | | (53), (56), (57), (58), (66), (69), (71), (75), (76),
% 249.49/59.05 | | | | | | | | (78), (79), (81), (87), (88), (97), (99), (103),
% 249.49/59.05 | | | | | | | | (110), (112), (117), (119), (121), (122), (125),
% 249.49/59.05 | | | | | | | | (127) are inconsistent by sub-proof #134.
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | (128) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 &
% 249.49/59.05 | | | | | | | | $i(all_38_1)
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | ALPHA: (128) implies:
% 249.49/59.05 | | | | | | | | (129) op(e1, e4) = all_38_1
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (12), (16), (17), (20), (23),
% 249.49/59.05 | | | | | | | | (24), (25), (26), (28), (30), (31), (34), (38), (39),
% 249.49/59.05 | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 249.49/59.05 | | | | | | | | (53), (56), (57), (58), (66), (69), (71), (75), (76),
% 249.49/59.05 | | | | | | | | (78), (79), (81), (87), (88), (97), (99), (103),
% 249.49/59.05 | | | | | | | | (110), (112), (117), (119), (121), (122), (125),
% 249.49/59.05 | | | | | | | | (129) are inconsistent by sub-proof #134.
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | End of split
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | End of split
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | End of split
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | Case 2:
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | (130) all_34_2 = e2
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | REDUCE: (104), (130) imply:
% 249.49/59.05 | | | | | (131) ~ (all_4_2 = e2)
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | SIMP: (131) implies:
% 249.49/59.05 | | | | | (132) ~ (all_4_2 = e2)
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | REDUCE: (49), (130) imply:
% 249.49/59.05 | | | | | (133) op(e2, e0) = e1
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | REDUCE: (38), (130) imply:
% 249.49/59.05 | | | | | (134) op(e1, e0) = e2
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | BETA: splitting (29) gives:
% 249.49/59.05 | | | | |
% 249.49/59.05 | | | | | Case 1:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | (135) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 &
% 249.49/59.05 | | | | | | op(e2, e3) = e1)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | BETA: splitting (135) gives:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | Case 1:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | (136) all_252_6 = e1 & op(e2, e4) = e1
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | REF_CLOSE: (17), (23), (136) are inconsistent by sub-proof #545.
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | Case 2:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | (137) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | ALPHA: (137) implies:
% 249.49/59.05 | | | | | | | (138) op(e2, e3) = e1
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | REF_CLOSE: (3), (25), (26), (138) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | #948.
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | End of split
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | Case 2:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | (139) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 &
% 249.49/59.05 | | | | | | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | BETA: splitting (139) gives:
% 249.49/59.05 | | | | | |
% 249.49/59.05 | | | | | | Case 1:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | (140) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | ALPHA: (140) implies:
% 249.49/59.05 | | | | | | | (141) all_252_8 = e1
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | BETA: splitting (69) gives:
% 249.49/59.05 | | | | | | |
% 249.49/59.05 | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | (142) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 249.49/59.05 | | | | | | | | op(e2, e3) = e4)
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | REF_CLOSE: (6), (17), (25), (26), (28), (142) are inconsistent
% 249.49/59.05 | | | | | | | | by sub-proof #937.
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | (143) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 249.49/59.05 | | | | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) =
% 249.49/59.05 | | | | | | | | e4)
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | BETA: splitting (143) gives:
% 249.49/59.05 | | | | | | | |
% 249.49/59.05 | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | (144) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | ALPHA: (144) implies:
% 249.49/59.05 | | | | | | | | | (145) op(e2, e2) = e4
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | REF_CLOSE: (25), (30), (31), (45), (75), (145) are
% 249.49/59.05 | | | | | | | | | inconsistent by sub-proof #626.
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | (146) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 =
% 249.49/59.05 | | | | | | | | | e4 & op(e2, e0) = e4)
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | BETA: splitting (146) gives:
% 249.49/59.05 | | | | | | | | |
% 249.49/59.05 | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | (147) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.05 | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | ALPHA: (147) implies:
% 249.49/59.05 | | | | | | | | | | (148) all_252_11 = e4
% 249.49/59.05 | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | BETA: splitting (32) gives:
% 249.49/59.05 | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | (149) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 249.49/59.05 | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | BETA: splitting (149) gives:
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | (150) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | ALPHA: (150) implies:
% 249.49/59.05 | | | | | | | | | | | | (151) all_252_6 = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | REF_CLOSE: (17), (53), (151) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | #691.
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | (152) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | ALPHA: (152) implies:
% 249.49/59.05 | | | | | | | | | | | | (153) all_252_7 = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | BETA: splitting (61) gives:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | (154) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 249.49/59.05 | | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | (155) all_252_6 = e2 & op(e2, e4) = e2
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (155) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | | | #892.
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | (156) all_252_7 = e2 & op(e2, e3) = e2
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | REF_CLOSE: (27), (153), (156) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | | | #666.
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | End of split
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | (157) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 249.49/59.05 | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 249.49/59.05 | | | | | | | | | | | | | op(e2, e0) = e2)
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | BETA: splitting (157) gives:
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | (158) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | REF_CLOSE: (42), (141), (158) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | | | #339.
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | (159) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 249.49/59.05 | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | (160) all_252_11 = e2 & op(e2, e1) = e2
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | REF_CLOSE: (86), (148), (160) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | | | | #787.
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | (161) all_252_18 = e2 & op(e2, e0) = e2
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 249.49/59.05 | | | | | | | | | | | | | | | (162) all_252_18 = e2
% 249.49/59.05 | | | | | | | | | | | | | | | (163) op(e2, e0) = e2
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with e1, e2, e0, e2,
% 249.49/59.05 | | | | | | | | | | | | | | | simplifying with (133), (163) gives:
% 249.49/59.05 | | | | | | | | | | | | | | | (164) e2 = e1
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | COMBINE_EQS: (162), (164) imply:
% 249.49/59.05 | | | | | | | | | | | | | | | (165) all_252_18 = e1
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (20), (25), (26), (27), (28), (30),
% 249.49/59.05 | | | | | | | | | | | | | | | (31), (32), (42), (44), (45), (53), (56), (61),
% 249.49/59.05 | | | | | | | | | | | | | | | (69), (75), (76), (86), (141), (165) are
% 249.49/59.05 | | | | | | | | | | | | | | | inconsistent by sub-proof #133.
% 249.49/59.05 | | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | | End of split
% 249.49/59.05 | | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | End of split
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | End of split
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | End of split
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | (166) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 249.49/59.05 | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 249.49/59.05 | | | | | | | | | | | op(e2, e0) = e3)
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | BETA: splitting (166) gives:
% 249.49/59.05 | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | (167) all_252_8 = e3 & op(e2, e2) = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | ALPHA: (167) implies:
% 249.49/59.05 | | | | | | | | | | | | (168) all_252_8 = e3
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | REF_CLOSE: (56), (141), (168) are inconsistent by sub-proof
% 249.49/59.05 | | | | | | | | | | | | #927.
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | Case 2:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | (169) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 249.49/59.05 | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | BETA: splitting (169) gives:
% 249.49/59.05 | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | Case 1:
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.05 | | | | | | | | | | | | | (170) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/59.05 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | REF_CLOSE: (76), (148), (170) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | #768.
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | (171) all_252_18 = e3 & op(e2, e0) = e3
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | ALPHA: (171) implies:
% 249.49/59.06 | | | | | | | | | | | | | (172) all_252_18 = e3
% 249.49/59.06 | | | | | | | | | | | | | (173) op(e2, e0) = e3
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | BETA: splitting (61) gives:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (174) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 249.49/59.06 | | | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (175) all_252_6 = e2 & op(e2, e4) = e2
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (175) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | #892.
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (176) all_252_7 = e2 & op(e2, e3) = e2
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | (177) all_252_7 = e2
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with e1, e3, e0, e2,
% 249.49/59.06 | | | | | | | | | | | | | | | simplifying with (133), (173) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | (178) e3 = e1
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | COMBINE_EQS: (172), (178) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | (179) all_252_18 = e1
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | REF_CLOSE: (17), (27), (32), (53), (56), (76), (141), (148),
% 249.49/59.06 | | | | | | | | | | | | | | | (177), (179) are inconsistent by sub-proof #303.
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (180) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 249.49/59.06 | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 249.49/59.06 | | | | | | | | | | | | | | op(e2, e0) = e2)
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (181) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | REF_CLOSE: (42), (141), (181) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | #788.
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (182) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 249.49/59.06 | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (183) all_252_11 = e2 & op(e2, e1) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (86), (148), (183) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #302.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (184) all_252_18 = e2 & op(e2, e0) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | (185) all_252_18 = e2
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (172), (185) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #786.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | (186) all_252_18 = e4 & op(e2, e0) = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | ALPHA: (186) implies:
% 249.49/59.06 | | | | | | | | | | (187) all_252_18 = e4
% 249.49/59.06 | | | | | | | | | | (188) op(e2, e0) = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | GROUND_INST: instantiating (25) with e1, e4, e0, e2,
% 249.49/59.06 | | | | | | | | | | simplifying with (133), (188) gives:
% 249.49/59.06 | | | | | | | | | | (189) e4 = e1
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | COMBINE_EQS: (187), (189) imply:
% 249.49/59.06 | | | | | | | | | | (190) all_252_18 = e1
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | REF_CLOSE: (6), (17), (20), (25), (26), (27), (28), (30),
% 249.49/59.06 | | | | | | | | | | (31), (32), (42), (44), (45), (53), (56), (61),
% 249.49/59.06 | | | | | | | | | | (69), (75), (76), (86), (141), (190) are
% 249.49/59.06 | | | | | | | | | | inconsistent by sub-proof #133.
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | End of split
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | End of split
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | Case 2:
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | (191) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 249.49/59.06 | | | | | | | op(e2, e0) = e1)
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | BETA: splitting (191) gives:
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | (192) all_252_11 = e1 & op(e2, e1) = e1
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | ALPHA: (192) implies:
% 249.49/59.06 | | | | | | | | (193) all_252_11 = e1
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | BETA: splitting (69) gives:
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | (194) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4
% 249.49/59.06 | | | | | | | | | & op(e2, e3) = e4)
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | REF_CLOSE: (6), (17), (25), (26), (28), (194) are inconsistent
% 249.49/59.06 | | | | | | | | | by sub-proof #937.
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | (195) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4
% 249.49/59.06 | | | | | | | | | & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0)
% 249.49/59.06 | | | | | | | | | = e4)
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | BETA: splitting (195) gives:
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | (196) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | ALPHA: (196) implies:
% 249.49/59.06 | | | | | | | | | | (197) op(e2, e2) = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | REF_CLOSE: (25), (30), (31), (45), (75), (197) are
% 249.49/59.06 | | | | | | | | | | inconsistent by sub-proof #626.
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | (198) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 =
% 249.49/59.06 | | | | | | | | | | e4 & op(e2, e0) = e4)
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | BETA: splitting (198) gives:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | (199) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | ALPHA: (199) implies:
% 249.49/59.06 | | | | | | | | | | | (200) all_252_11 = e4
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | REF_CLOSE: (44), (193), (200) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | #188.
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | (201) all_252_18 = e4 & op(e2, e0) = e4
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | ALPHA: (201) implies:
% 249.49/59.06 | | | | | | | | | | | (202) all_252_18 = e4
% 249.49/59.06 | | | | | | | | | | | (203) op(e2, e0) = e4
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | BETA: splitting (34) gives:
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | (204) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 249.49/59.06 | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | REF_CLOSE: (25), (39), (47), (58), (88), (204) are
% 249.49/59.06 | | | | | | | | | | | | inconsistent by sub-proof #928.
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | (205) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 249.49/59.06 | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 249.49/59.06 | | | | | | | | | | | | op(e0, e2) = e1)
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | BETA: splitting (205) gives:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | (206) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | ALPHA: (206) implies:
% 249.49/59.06 | | | | | | | | | | | | | (207) all_252_8 = e1
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (208) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 249.49/59.06 | | | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (209) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | (210) all_252_6 = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | REF_CLOSE: (17), (53), (210) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | #691.
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (211) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | (212) all_252_7 = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (213) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 249.49/59.06 | | | | | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (214) all_252_6 = e2 & op(e2, e4) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (214) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | #892.
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (215) all_252_7 = e2 & op(e2, e3) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (212), (215) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | #666.
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (216) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 249.49/59.06 | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 249.49/59.06 | | | | | | | | | | | | | | | | op(e2, e0) = e2)
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (217) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (207), (217) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | #339.
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (218) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 249.49/59.06 | | | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (219) all_252_11 = e2 & op(e2, e1) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (193), (219) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | | #330.
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (220) all_252_18 = e2 & op(e2, e0) = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (221) all_252_18 = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (221) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (222) e4 = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (223) e4 = e2
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | REDUCE: (86), (223) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (224) $false
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (225) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 249.49/59.06 | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 249.49/59.06 | | | | | | | | | | | | | | op(e2, e0) = e3)
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (226) all_252_8 = e3 & op(e2, e2) = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | (227) all_252_8 = e3
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | REF_CLOSE: (56), (207), (227) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | #927.
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (228) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 249.49/59.06 | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (229) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (193), (229) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #329.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (230) all_252_18 = e3 & op(e2, e0) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (76), (202), (230) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #663.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | (231) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 249.49/59.06 | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | BETA: splitting (231) gives:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (232) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | ALPHA: (232) implies:
% 249.49/59.06 | | | | | | | | | | | | | | (233) all_252_14 = e1
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (234) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 249.49/59.06 | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (235) all_252_12 = e3 & op(e1, e4) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (25), (50), (109), (235) are inconsistent by
% 249.49/59.06 | | | | | | | | | | | | | | | | sub-proof #895.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (236) all_252_13 = e3 & op(e1, e3) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (24), (53), (236) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #883.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | (237) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 249.49/59.06 | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 249.49/59.06 | | | | | | | | | | | | | | | op(e1, e0) = e3)
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (238) all_252_14 = e3 & op(e1, e2) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | REF_CLOSE: (56), (233), (238) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | #299.
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | (239) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 249.49/59.06 | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (240) all_252_15 = e3 & op(e1, e1) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | (241) all_252_15 = e3
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (242) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 249.49/59.06 | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | (243) all_252_12 = e4 & op(e1, e4) = e4
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | (244) all_252_12 = e4
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | (245) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1)
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (246) all_252_12 = e1 & op(e1, e4) = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (247) all_252_12 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (247) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (248) e4 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (249) e4 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (249) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (250) all_252_18 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (17), (19), (20), (21), (23),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (30), (31), (32), (34),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (39), (42), (43), (44), (45), (47), (51), (53),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (56), (58), (61), (66), (69), (75), (76), (81),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (86), (88), (132), (250) are inconsistent by
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | sub-proof #132.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (251) all_252_13 = e1 & op(e1, e3) = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (252) all_252_13 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (24), (252) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | #943.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | (253) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 &
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1)
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with e1, e4, e0, e2,
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | simplifying with (133), (203) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (254) e4 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (254) imply:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (255) all_252_18 = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (17), (19), (20), (21), (23),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (30), (31), (32), (34),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (39), (42), (43), (44), (45), (47), (51), (53),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (56), (58), (61), (66), (69), (75), (76), (81),
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (86), (88), (132), (255) are inconsistent by
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | sub-proof #132.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | (256) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1)
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | (257) all_252_15 = e1 & op(e1, e1) = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (241), (257) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | #752.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | (258) all_252_19 = e1 & op(e1, e0) = e1
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (42), (134), (258) are inconsistent by
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | | sub-proof #408.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | (259) all_252_13 = e4 & op(e1, e3) = e4
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (28), (259) are inconsistent by sub-proof
% 249.49/59.06 | | | | | | | | | | | | | | | | | | | #413.
% 249.49/59.06 | | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | (260) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 249.49/59.06 | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 249.49/59.06 | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (25), (76), (81), (86), (134), (241), (260)
% 249.49/59.06 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #357.
% 249.49/59.06 | | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | (261) all_252_19 = e3 & op(e1, e0) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 249.49/59.06 | | | | | | | | | | | | | | | | | (262) op(e1, e0) = e3
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (27), (134), (262) are inconsistent by
% 249.49/59.06 | | | | | | | | | | | | | | | | | sub-proof #736.
% 249.49/59.06 | | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | (263) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | ALPHA: (263) implies:
% 249.49/59.06 | | | | | | | | | | | | | | (264) all_252_22 = e1
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (10), (20), (23), (25), (27), (28),
% 249.49/59.06 | | | | | | | | | | | | | | (43), (44), (51), (53), (56), (66), (76), (86),
% 249.49/59.06 | | | | | | | | | | | | | | (264) are inconsistent by sub-proof #137.
% 249.49/59.06 | | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | End of split
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | End of split
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | (265) all_252_18 = e1 & op(e2, e0) = e1
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | ALPHA: (265) implies:
% 249.49/59.06 | | | | | | | | (266) all_252_18 = e1
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (17), (19), (20), (21), (23),
% 249.49/59.06 | | | | | | | | (25), (26), (27), (28), (30), (31), (32), (34), (39),
% 249.49/59.06 | | | | | | | | (42), (43), (44), (45), (47), (51), (53), (56), (58),
% 249.49/59.06 | | | | | | | | (61), (66), (69), (75), (76), (81), (86), (88),
% 249.49/59.06 | | | | | | | | (132), (266) are inconsistent by sub-proof #132.
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | End of split
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | End of split
% 249.49/59.06 | | | | | |
% 249.49/59.06 | | | | | End of split
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | End of split
% 249.49/59.06 | | | |
% 249.49/59.06 | | | Case 2:
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | (267) all_30_2 = e2
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | REF_CLOSE: (8), (25), (30), (31), (67), (75), (267) are inconsistent by
% 249.49/59.06 | | | | sub-proof #162.
% 249.49/59.06 | | | |
% 249.49/59.06 | | | End of split
% 249.49/59.06 | | |
% 249.49/59.06 | | Case 2:
% 249.49/59.06 | | |
% 249.49/59.06 | | | (268) all_26_2 = e3
% 249.49/59.06 | | |
% 249.49/59.06 | | | REDUCE: (101), (268) imply:
% 249.49/59.06 | | | (269) ~ (all_20_2 = e3)
% 249.49/59.06 | | |
% 249.49/59.06 | | | SIMP: (269) implies:
% 249.49/59.06 | | | (270) ~ (all_20_2 = e3)
% 249.49/59.06 | | |
% 249.49/59.06 | | | REF_CLOSE: (1), (25), (48), (49), (65), (92), (106), (107), (270) are
% 249.49/59.06 | | | inconsistent by sub-proof #780.
% 249.49/59.06 | | |
% 249.49/59.06 | | End of split
% 249.49/59.06 | |
% 249.49/59.06 | Case 2:
% 249.49/59.06 | |
% 249.49/59.06 | | (271) all_24_2 = e3
% 249.49/59.06 | |
% 249.49/59.06 | | COMBINE_EQS: (98), (271) imply:
% 249.49/59.06 | | (272) all_16_2 = e3
% 249.49/59.06 | |
% 249.49/59.06 | | REDUCE: (41), (272) imply:
% 249.49/59.06 | | (273) ~ (all_244_0 = e3)
% 249.49/59.06 | |
% 249.49/59.06 | | REDUCE: (95), (272) imply:
% 249.49/59.06 | | (274) ~ (all_100_2 = e3)
% 249.49/59.06 | |
% 249.49/59.06 | | REDUCE: (94), (272) imply:
% 249.49/59.06 | | (275) op(e3, e4) = e1
% 249.49/59.06 | |
% 249.49/59.06 | | REDUCE: (50), (272) imply:
% 249.49/59.06 | | (276) op(e1, e4) = e3
% 249.49/59.06 | |
% 249.49/59.06 | | BETA: splitting (90) gives:
% 249.49/59.06 | |
% 249.49/59.06 | | Case 1:
% 249.49/59.06 | | |
% 249.49/59.06 | | | (277) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4)
% 249.49/59.06 | | | = e3)
% 249.49/59.06 | | |
% 249.49/59.06 | | | REF_CLOSE: (17), (23), (25), (28), (42), (44), (56), (66), (73), (76),
% 249.49/59.06 | | | (86), (93), (102), (275), (276), (277) are inconsistent by
% 249.49/59.06 | | | sub-proof #146.
% 249.49/59.06 | | |
% 249.49/59.06 | | Case 2:
% 249.49/59.06 | | |
% 249.49/59.06 | | | (278) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1,
% 249.49/59.06 | | | e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.06 | | |
% 249.49/59.06 | | | BETA: splitting (278) gives:
% 249.49/59.06 | | |
% 249.49/59.06 | | | Case 1:
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | (279) all_252_6 = e3 & op(e2, e4) = e3
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | ALPHA: (279) implies:
% 249.49/59.06 | | | | (280) all_252_6 = e3
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | REF_CLOSE: (17), (53), (280) are inconsistent by sub-proof #691.
% 249.49/59.06 | | | |
% 249.49/59.06 | | | Case 2:
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | (281) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 249.49/59.06 | | | | e4) = e3)
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | BETA: splitting (281) gives:
% 249.49/59.06 | | | |
% 249.49/59.06 | | | | Case 1:
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | (282) all_252_12 = e3 & op(e1, e4) = e3
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | ALPHA: (282) implies:
% 249.49/59.06 | | | | | (283) all_252_12 = e3
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | GROUND_INST: instantiating (25) with all_100_2, e1, e4, e3,
% 249.49/59.06 | | | | | simplifying with (73), (275) gives:
% 249.49/59.06 | | | | | (284) all_100_2 = e1
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | REDUCE: (63), (284) imply:
% 249.49/59.06 | | | | | (285) ~ (all_244_0 = e1)
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | REDUCE: (80), (284) imply:
% 249.49/59.06 | | | | | (286) ~ (all_244_3 = e1)
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | REDUCE: (274), (284) imply:
% 249.49/59.06 | | | | | (287) ~ (e3 = e1)
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | REDUCE: (74), (284) imply:
% 249.49/59.06 | | | | | (288) ~ (e2 = e1)
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | BETA: splitting (102) gives:
% 249.49/59.06 | | | | |
% 249.49/59.06 | | | | | Case 1:
% 249.49/59.06 | | | | | |
% 249.49/59.06 | | | | | | (289) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 249.49/59.06 | | | | | | op(e3, e4) = e1)
% 249.49/59.06 | | | | | |
% 249.49/59.06 | | | | | | BETA: splitting (289) gives:
% 249.49/59.06 | | | | | |
% 249.49/59.06 | | | | | | Case 1:
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | (290) all_252_0 = e1 & op(e4, e4) = e1
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | REF_CLOSE: (17), (25), (37), (45), (66), (72), (75), (89), (93),
% 249.49/59.06 | | | | | | | (273), (276), (283), (285), (290) are inconsistent by
% 249.49/59.06 | | | | | | | sub-proof #143.
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | Case 2:
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | (291) all_252_2 = e1 & op(e3, e4) = e1
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | ALPHA: (291) implies:
% 249.49/59.06 | | | | | | | (292) all_252_2 = e1
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | BETA: splitting (93) gives:
% 249.49/59.06 | | | | | | |
% 249.49/59.06 | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | (293) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 &
% 249.49/59.06 | | | | | | | | op(e3, e4) = e4)
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | BETA: splitting (293) gives:
% 249.49/59.06 | | | | | | | |
% 249.49/59.06 | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | (294) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | ALPHA: (294) implies:
% 249.49/59.06 | | | | | | | | | (295) all_252_0 = e4
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | BETA: splitting (72) gives:
% 249.49/59.06 | | | | | | | | |
% 249.49/59.06 | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | (296) all_250_0 = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | COMBINE_EQS: (37), (296) imply:
% 249.49/59.06 | | | | | | | | | | (297) all_244_0 = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | REDUCE: (2), (297) imply:
% 249.49/59.06 | | | | | | | | | | (298) ~ (all_84_2 = e4)
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | SIMP: (298) implies:
% 249.49/59.06 | | | | | | | | | | (299) ~ (all_84_2 = e4)
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | REDUCE: (75), (297) imply:
% 249.49/59.06 | | | | | | | | | | (300) op(e4, e4) = e4
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | BETA: splitting (13) gives:
% 249.49/59.06 | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | (301) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 249.49/59.06 | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | BETA: splitting (301) gives:
% 249.49/59.06 | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | (302) all_252_1 = e4 & op(e4, e3) = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | ALPHA: (302) implies:
% 249.49/59.06 | | | | | | | | | | | | (303) op(e4, e3) = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_84_2, e4, e3, e4,
% 249.49/59.06 | | | | | | | | | | | | simplifying with (83), (303) gives:
% 249.49/59.06 | | | | | | | | | | | | (304) all_84_2 = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | REDUCE: (299), (304) imply:
% 249.49/59.06 | | | | | | | | | | | | (305) $false
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | Case 2:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | (306) all_252_3 = e4 & op(e3, e3) = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | ALPHA: (306) implies:
% 249.49/59.06 | | | | | | | | | | | | (307) op(e3, e3) = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_244_3, e4, e3, e3,
% 249.49/59.06 | | | | | | | | | | | | simplifying with (100), (307) gives:
% 249.49/59.06 | | | | | | | | | | | | (308) all_244_3 = e4
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | REDUCE: (84), (308) imply:
% 249.49/59.06 | | | | | | | | | | | | (309) op(e4, e4) = e3
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | BETA: splitting (77) gives:
% 249.49/59.06 | | | | | | | | | | | |
% 249.49/59.06 | | | | | | | | | | | | Case 1:
% 249.49/59.06 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | (310) ~ (all_112_2 = e0)
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | REDUCE: (70), (310) imply:
% 249.49/59.07 | | | | | | | | | | | | | (311) $false
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | CLOSE: (311) is inconsistent.
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with e4, e3, e4, e4,
% 249.49/59.07 | | | | | | | | | | | | | simplifying with (300), (309) gives:
% 249.49/59.07 | | | | | | | | | | | | | (312) e4 = e3
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | COMBINE_EQS: (295), (312) imply:
% 249.49/59.07 | | | | | | | | | | | | | (313) all_252_0 = e3
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | REF_CLOSE: (17), (25), (28), (44), (66), (76), (86), (93),
% 249.49/59.07 | | | | | | | | | | | | | (276), (292), (313) are inconsistent by sub-proof
% 249.49/59.07 | | | | | | | | | | | | | #149.
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | (314) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 249.49/59.07 | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 249.49/59.07 | | | | | | | | | | | op(e0, e3) = e4)
% 249.49/59.07 | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | BETA: splitting (314) gives:
% 249.49/59.07 | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | Case 1:
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | (315) all_252_7 = e4 & op(e2, e3) = e4
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | ALPHA: (315) implies:
% 249.49/59.07 | | | | | | | | | | | | (316) op(e2, e3) = e4
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | REF_CLOSE: (6), (25), (26), (316) are inconsistent by
% 249.49/59.07 | | | | | | | | | | | | sub-proof #953.
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | (317) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 249.49/59.07 | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | BETA: splitting (317) gives:
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | Case 1:
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | (318) all_252_13 = e4 & op(e1, e3) = e4
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | ALPHA: (318) implies:
% 249.49/59.07 | | | | | | | | | | | | | (319) all_252_13 = e4
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | REF_CLOSE: (24), (28), (319) are inconsistent by sub-proof
% 249.49/59.07 | | | | | | | | | | | | | #407.
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | (320) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | ALPHA: (320) implies:
% 249.49/59.07 | | | | | | | | | | | | | (321) all_252_21 = e4
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | COMBINE_EQS: (10), (321) imply:
% 249.49/59.07 | | | | | | | | | | | | | (322) e4 = e1
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | COMBINE_EQS: (295), (322) imply:
% 249.49/59.07 | | | | | | | | | | | | | (323) all_252_0 = e1
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | | REF_CLOSE: (17), (28), (44), (66), (76), (86), (93), (283),
% 249.49/59.07 | | | | | | | | | | | | | (292), (323) are inconsistent by sub-proof #144.
% 249.49/59.07 | | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | (324) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 249.49/59.07 | | | | | | | | | | all_250_0 = e0
% 249.49/59.07 | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | | REF_CLOSE: (37), (45), (89), (273), (285), (324) are
% 249.49/59.07 | | | | | | | | | | inconsistent by sub-proof #217.
% 249.49/59.07 | | | | | | | | | |
% 249.49/59.07 | | | | | | | | | End of split
% 249.49/59.07 | | | | | | | | |
% 249.49/59.07 | | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | | |
% 249.49/59.07 | | | | | | | | | (325) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.07 | | | | | | | | |
% 249.49/59.07 | | | | | | | | | ALPHA: (325) implies:
% 249.49/59.07 | | | | | | | | | (326) all_252_2 = e4
% 249.49/59.07 | | | | | | | | |
% 249.49/59.07 | | | | | | | | | REF_CLOSE: (44), (292), (326) are inconsistent by sub-proof
% 249.49/59.07 | | | | | | | | | #605.
% 249.49/59.07 | | | | | | | | |
% 249.49/59.07 | | | | | | | | End of split
% 249.49/59.07 | | | | | | | |
% 249.49/59.07 | | | | | | | Case 2:
% 249.49/59.07 | | | | | | | |
% 249.49/59.07 | | | | | | | | (327) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 &
% 249.49/59.07 | | | | | | | | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) =
% 249.49/59.07 | | | | | | | | e4)
% 249.49/59.07 | | | | | | | |
% 249.49/59.07 | | | | | | | | REF_CLOSE: (17), (25), (28), (66), (76), (86), (276), (327) are
% 249.49/59.07 | | | | | | | | inconsistent by sub-proof #142.
% 249.49/59.07 | | | | | | | |
% 249.49/59.07 | | | | | | | End of split
% 249.49/59.07 | | | | | | |
% 249.49/59.07 | | | | | | End of split
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | Case 2:
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | (328) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 249.49/59.07 | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | REF_CLOSE: (17), (23), (42), (56), (66), (283), (328) are
% 249.49/59.07 | | | | | | inconsistent by sub-proof #141.
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | End of split
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | Case 2:
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | (329) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | REF_CLOSE: (27), (66), (329) are inconsistent by sub-proof #539.
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | End of split
% 249.49/59.07 | | | |
% 249.49/59.07 | | | End of split
% 249.49/59.07 | | |
% 249.49/59.07 | | End of split
% 249.49/59.07 | |
% 249.49/59.07 | End of split
% 249.49/59.07 |
% 249.49/59.07 End of proof
% 249.49/59.07
% 249.49/59.07 Sub-proof #132 shows that the following formulas are inconsistent:
% 249.49/59.07 ----------------------------------------------------------------
% 249.49/59.07 (1) op(e0, e3) = e1
% 249.49/59.07 (2) ~ (all_10_2 = e4)
% 249.49/59.07 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.07 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.07 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.07 (4) all_252_21 = e1
% 249.49/59.07 (5) all_252_6 = e0
% 249.49/59.07 (6) op(all_38_2, e1) = e2
% 249.49/59.07 (7) ~ (e2 = e0)
% 249.49/59.07 (8) op(all_38_2, all_4_2) = e1
% 249.49/59.07 (9) ~ (e1 = e0)
% 249.49/59.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.07 (11) op(e2, e3) = all_10_2
% 249.49/59.07 (12) ~ (e3 = e2)
% 249.49/59.07 (13) ~ (e4 = e0)
% 249.49/59.07 (14) op(all_244_8, all_244_8) = e2
% 249.49/59.07 (15) op(e2, e2) = all_244_8
% 249.49/59.07 (16) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.07 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.07 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.07 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.07 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.07 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.07 (18) op(e4, e2) = all_6_2
% 249.49/59.07 (19) ~ (e2 = e1)
% 249.49/59.07 (20) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.07 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.07 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.07 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.07 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.07 op(e0, e1) = e0)))
% 249.49/59.07 (21) ~ (e4 = e1)
% 249.49/59.07 (22) ~ (all_244_0 = e2)
% 249.49/59.07 (23) ~ (all_6_2 = e1)
% 249.49/59.07 (24) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.07 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.07 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.07 (25) ~ (e3 = e0)
% 249.49/59.07 (26) ~ (e3 = e1)
% 249.49/59.07 (27) ~ (all_8_2 = e1)
% 249.49/59.07 (28) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.07 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.07 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.07 (29) all_252_20 = e2
% 249.49/59.07 (30) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.07 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.07 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.07 (31) op(e4, e4) = all_244_0
% 249.49/59.07 (32) ~ (e4 = e3)
% 249.49/59.07 (33) all_252_18 = e1
% 249.49/59.07 (34) op(e1, e2) = all_4_2
% 249.49/59.07 (35) ~ (e4 = e2)
% 249.49/59.07 (36) op(e3, e2) = all_8_2
% 249.49/59.07 (37) ~ (all_4_2 = e2)
% 249.49/59.07
% 249.49/59.07 Begin of proof
% 249.49/59.07 |
% 249.49/59.07 | BETA: splitting (17) gives:
% 249.49/59.07 |
% 249.49/59.07 | Case 1:
% 249.49/59.07 | |
% 249.49/59.07 | | (38) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 249.49/59.07 | | e1)
% 249.49/59.07 | |
% 249.49/59.07 | | REF_CLOSE: (10), (18), (23), (27), (36), (38) are inconsistent by sub-proof
% 249.49/59.07 | | #928.
% 249.49/59.07 | |
% 249.49/59.07 | Case 2:
% 249.49/59.07 | |
% 249.49/59.07 | | (39) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.07 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.07 | |
% 249.49/59.07 | | BETA: splitting (39) gives:
% 249.49/59.07 | |
% 249.49/59.07 | | Case 1:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (40) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.07 | | |
% 249.49/59.07 | | | ALPHA: (40) implies:
% 249.49/59.07 | | | (41) all_252_8 = e1
% 249.49/59.07 | | |
% 249.49/59.07 | | | REF_CLOSE: (2), (5), (7), (10), (11), (12), (13), (14), (15), (16), (19),
% 249.49/59.07 | | | (21), (22), (25), (26), (28), (30), (31), (32), (33), (35),
% 249.49/59.07 | | | (41) are inconsistent by sub-proof #133.
% 249.49/59.07 | | |
% 249.49/59.07 | | Case 2:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (42) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 249.49/59.07 | | | e2) = e1)
% 249.49/59.07 | | |
% 249.49/59.07 | | | BETA: splitting (42) gives:
% 249.49/59.07 | | |
% 249.49/59.07 | | | Case 1:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (43) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REF_CLOSE: (6), (8), (10), (34), (37), (43) are inconsistent by
% 249.49/59.07 | | | | sub-proof #229.
% 249.49/59.07 | | | |
% 249.49/59.07 | | | Case 2:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (44) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | ALPHA: (44) implies:
% 249.49/59.07 | | | | (45) all_252_22 = e1
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REF_CLOSE: (1), (3), (4), (7), (9), (10), (12), (13), (20), (21), (24),
% 249.49/59.07 | | | | (25), (26), (29), (32), (35), (45) are inconsistent by
% 249.49/59.07 | | | | sub-proof #137.
% 249.49/59.07 | | | |
% 249.49/59.07 | | | End of split
% 249.49/59.07 | | |
% 249.49/59.07 | | End of split
% 249.49/59.07 | |
% 249.49/59.07 | End of split
% 249.49/59.07 |
% 249.49/59.07 End of proof
% 249.49/59.07
% 249.49/59.07 Sub-proof #133 shows that the following formulas are inconsistent:
% 249.49/59.07 ----------------------------------------------------------------
% 249.49/59.07 (1) ~ (all_10_2 = e4)
% 249.49/59.07 (2) all_252_6 = e0
% 249.49/59.07 (3) ~ (e2 = e0)
% 249.49/59.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.07 (5) op(e2, e3) = all_10_2
% 249.49/59.07 (6) ~ (e3 = e2)
% 249.49/59.07 (7) ~ (e4 = e0)
% 249.49/59.07 (8) op(all_244_8, all_244_8) = e2
% 249.49/59.07 (9) op(e2, e2) = all_244_8
% 249.49/59.07 (10) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.07 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.07 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.07 (11) ~ (e2 = e1)
% 249.49/59.07 (12) ~ (e4 = e1)
% 249.49/59.07 (13) ~ (all_244_0 = e2)
% 249.49/59.07 (14) ~ (e3 = e0)
% 249.49/59.07 (15) ~ (e3 = e1)
% 249.49/59.07 (16) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.07 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.07 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.07 (17) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.07 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.07 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.07 (18) op(e4, e4) = all_244_0
% 249.49/59.07 (19) ~ (e4 = e3)
% 249.49/59.07 (20) all_252_18 = e1
% 249.49/59.07 (21) ~ (e4 = e2)
% 249.49/59.07 (22) all_252_8 = e1
% 249.49/59.07
% 249.49/59.07 Begin of proof
% 249.49/59.07 |
% 249.49/59.07 | BETA: splitting (17) gives:
% 249.49/59.07 |
% 249.49/59.07 | Case 1:
% 249.49/59.07 | |
% 249.49/59.07 | | (23) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 249.49/59.07 | | e4)
% 249.49/59.07 | |
% 249.49/59.07 | | REF_CLOSE: (1), (2), (4), (5), (7), (23) are inconsistent by sub-proof #937.
% 249.49/59.07 | |
% 249.49/59.07 | Case 2:
% 249.49/59.07 | |
% 249.49/59.07 | | (24) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.07 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.07 | |
% 249.49/59.07 | | BETA: splitting (24) gives:
% 249.49/59.07 | |
% 249.49/59.07 | | Case 1:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (25) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.07 | | |
% 249.49/59.07 | | | ALPHA: (25) implies:
% 249.49/59.07 | | | (26) op(e2, e2) = e4
% 249.49/59.07 | | |
% 249.49/59.07 | | | REF_CLOSE: (4), (8), (9), (13), (18), (26) are inconsistent by sub-proof
% 249.49/59.07 | | | #626.
% 249.49/59.07 | | |
% 249.49/59.07 | | Case 2:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (27) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 249.49/59.07 | | | e0) = e4)
% 249.49/59.07 | | |
% 249.49/59.07 | | | BETA: splitting (27) gives:
% 249.49/59.07 | | |
% 249.49/59.07 | | | Case 1:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (28) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | ALPHA: (28) implies:
% 249.49/59.07 | | | | (29) all_252_11 = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REF_CLOSE: (2), (3), (6), (10), (11), (14), (15), (16), (19), (20),
% 249.49/59.07 | | | | (21), (22), (29) are inconsistent by sub-proof #301.
% 249.49/59.07 | | | |
% 249.49/59.07 | | | Case 2:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (30) all_252_18 = e4 & op(e2, e0) = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | ALPHA: (30) implies:
% 249.49/59.07 | | | | (31) all_252_18 = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REF_CLOSE: (12), (20), (31) are inconsistent by sub-proof #448.
% 249.49/59.07 | | | |
% 249.49/59.07 | | | End of split
% 249.49/59.07 | | |
% 249.49/59.07 | | End of split
% 249.49/59.07 | |
% 249.49/59.07 | End of split
% 249.49/59.07 |
% 249.49/59.07 End of proof
% 249.49/59.07
% 249.49/59.07 Sub-proof #134 shows that the following formulas are inconsistent:
% 249.49/59.07 ----------------------------------------------------------------
% 249.49/59.07 (1) op(e0, e3) = e1
% 249.49/59.07 (2) ~ (all_10_2 = e4)
% 249.49/59.07 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.07 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.07 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.07 (4) all_252_21 = e1
% 249.49/59.07 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.07 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.07 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.07 (6) ~ (all_244_8 = all_6_2)
% 249.49/59.07 (7) all_252_6 = e0
% 249.49/59.07 (8) ~ (e2 = e0)
% 249.49/59.07 (9) ~ (e1 = e0)
% 249.49/59.07 (10) all_252_13 = e0
% 249.49/59.07 (11) op(e4, e1) = e2
% 249.49/59.07 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.07 (13) op(e2, e3) = all_10_2
% 249.49/59.07 (14) ~ (e4 = e0)
% 249.49/59.07 (15) op(all_244_8, all_244_8) = e2
% 249.49/59.07 (16) op(e2, e2) = all_244_8
% 249.49/59.07 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.07 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.07 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.07 (18) op(e1, e0) = all_34_2
% 249.49/59.07 (19) ~ (all_40_2 = e4)
% 249.49/59.07 (20) op(e4, e2) = all_6_2
% 249.49/59.07 (21) ~ (all_34_2 = e2)
% 249.49/59.07 (22) ~ (e2 = e1)
% 249.49/59.07 (23) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.07 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.07 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.07 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.07 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.07 op(e0, e1) = e0)))
% 249.49/59.07 (24) ~ (e4 = e1)
% 249.49/59.07 (25) ~ (all_244_0 = e2)
% 249.49/59.07 (26) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.07 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.07 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.07 (27) ~ (all_6_2 = e1)
% 249.49/59.07 (28) ~ (all_20_2 = e1)
% 249.49/59.07 (29) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 249.49/59.07 all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0) &
% 249.49/59.07 op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.07 (30) op(e1, e4) = all_16_2
% 249.49/59.07 (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.07 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.07 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.07 (32) ~ (e3 = e0)
% 249.49/59.07 (33) ~ (e3 = e1)
% 249.49/59.07 (34) ~ (all_16_2 = e2)
% 249.49/59.07 (35) ~ (all_8_2 = e1)
% 249.49/59.07 (36) op(e1, e4) = all_38_1
% 249.49/59.07 (37) op(e4, all_4_2) = e1
% 249.49/59.07 (38) ~ (all_26_2 = e4)
% 249.49/59.07 (39) all_252_20 = e2
% 249.49/59.07 (40) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.07 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.07 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.07 (41) op(e4, e1) = all_26_2
% 249.49/59.07 (42) op(e4, e4) = all_244_0
% 249.49/59.07 (43) ~ (e4 = e3)
% 249.49/59.07 (44) all_202_2 = all_26_2
% 249.49/59.07 (45) op(e0, e1) = all_20_2
% 249.49/59.07 (46) ~ (all_26_2 = e3)
% 249.49/59.07 (47) op(e1, e2) = all_4_2
% 249.49/59.07 (48) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.07 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.07 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.07 (49) op(e3, e2) = all_8_2
% 249.49/59.07 (50) op(e2, e0) = all_40_2
% 249.49/59.07 (51) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.07 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.07 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.07 (52) ~ (all_202_2 = e2) | ( ~ (all_202_0 = e3) & op(e2, all_202_1) =
% 249.49/59.07 all_202_0 & op(e1, e2) = all_202_1 & $i(all_202_0) & $i(all_202_1)) |
% 249.49/59.07 ( ~ (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1))
% 249.49/59.07
% 249.49/59.07 Begin of proof
% 249.49/59.07 |
% 249.49/59.07 | BETA: splitting (40) gives:
% 249.49/59.07 |
% 249.49/59.07 | Case 1:
% 249.49/59.07 | |
% 249.49/59.07 | | (53) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 249.49/59.07 | | e4)
% 249.49/59.07 | |
% 249.49/59.07 | | REF_CLOSE: (2), (7), (12), (13), (14), (53) are inconsistent by sub-proof
% 249.49/59.07 | | #937.
% 249.49/59.07 | |
% 249.49/59.07 | Case 2:
% 249.49/59.07 | |
% 249.49/59.07 | | (54) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.07 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.07 | |
% 249.49/59.07 | | BETA: splitting (54) gives:
% 249.49/59.07 | |
% 249.49/59.07 | | Case 1:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (55) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.07 | | |
% 249.49/59.07 | | | ALPHA: (55) implies:
% 249.49/59.07 | | | (56) op(e2, e2) = e4
% 249.49/59.07 | | |
% 249.49/59.07 | | | REF_CLOSE: (12), (15), (16), (25), (42), (56) are inconsistent by
% 249.49/59.07 | | | sub-proof #626.
% 249.49/59.07 | | |
% 249.49/59.07 | | Case 2:
% 249.49/59.07 | | |
% 249.49/59.07 | | | (57) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 249.49/59.07 | | | e0) = e4)
% 249.49/59.07 | | |
% 249.49/59.07 | | | BETA: splitting (57) gives:
% 249.49/59.07 | | |
% 249.49/59.07 | | | Case 1:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (58) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | ALPHA: (58) implies:
% 249.49/59.07 | | | | (59) all_252_11 = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | GROUND_INST: instantiating (12) with all_16_2, all_38_1, e4, e1,
% 249.49/59.07 | | | | simplifying with (30), (36) gives:
% 249.49/59.07 | | | | (60) all_38_1 = all_16_2
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | GROUND_INST: instantiating (12) with all_26_2, e2, e1, e4, simplifying
% 249.49/59.07 | | | | with (11), (41) gives:
% 249.49/59.07 | | | | (61) all_26_2 = e2
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | COMBINE_EQS: (44), (61) imply:
% 249.49/59.07 | | | | (62) all_202_2 = e2
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REDUCE: (38), (61) imply:
% 249.49/59.07 | | | | (63) ~ (e4 = e2)
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | SIMP: (63) implies:
% 249.49/59.07 | | | | (64) ~ (e4 = e2)
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REDUCE: (46), (61) imply:
% 249.49/59.07 | | | | (65) ~ (e3 = e2)
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | SIMP: (65) implies:
% 249.49/59.07 | | | | (66) ~ (e3 = e2)
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | BETA: splitting (52) gives:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | Case 1:
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | (67) ~ (all_202_2 = e2)
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | REDUCE: (62), (67) imply:
% 249.49/59.07 | | | | | (68) $false
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | CLOSE: (68) is inconsistent.
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | Case 2:
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | (69) ( ~ (all_202_0 = e3) & op(e2, all_202_1) = all_202_0 & op(e1,
% 249.49/59.07 | | | | | e2) = all_202_1 & $i(all_202_0) & $i(all_202_1)) | ( ~
% 249.49/59.07 | | | | | (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1))
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | BETA: splitting (69) gives:
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | | Case 1:
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | (70) ~ (all_202_0 = e3) & op(e2, all_202_1) = all_202_0 & op(e1,
% 249.49/59.07 | | | | | | e2) = all_202_1 & $i(all_202_0) & $i(all_202_1)
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | ALPHA: (70) implies:
% 249.49/59.07 | | | | | | (71) op(e1, e2) = all_202_1
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 249.49/59.07 | | | | | | (14), (16), (17), (18), (20), (21), (22), (23), (24),
% 249.49/59.07 | | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.07 | | | | | | (35), (37), (39), (43), (45), (47), (48), (49), (51),
% 249.49/59.07 | | | | | | (59), (64), (66), (71) are inconsistent by sub-proof
% 249.49/59.07 | | | | | | #135.
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | Case 2:
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | (72) ~ (all_202_1 = e0) & op(e1, e2) = all_202_1 & $i(all_202_1)
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | ALPHA: (72) implies:
% 249.49/59.07 | | | | | | (73) op(e1, e2) = all_202_1
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 249.49/59.07 | | | | | | (14), (16), (17), (18), (20), (21), (22), (23), (24),
% 249.49/59.07 | | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.07 | | | | | | (35), (37), (39), (43), (45), (47), (48), (49), (51),
% 249.49/59.07 | | | | | | (59), (64), (66), (73) are inconsistent by sub-proof
% 249.49/59.07 | | | | | | #135.
% 249.49/59.07 | | | | | |
% 249.49/59.07 | | | | | End of split
% 249.49/59.07 | | | | |
% 249.49/59.07 | | | | End of split
% 249.49/59.07 | | | |
% 249.49/59.07 | | | Case 2:
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | (74) all_252_18 = e4 & op(e2, e0) = e4
% 249.49/59.07 | | | |
% 249.49/59.07 | | | | REF_CLOSE: (12), (19), (50), (74) are inconsistent by sub-proof #934.
% 249.49/59.07 | | | |
% 249.49/59.07 | | | End of split
% 249.49/59.07 | | |
% 249.49/59.07 | | End of split
% 249.49/59.07 | |
% 249.49/59.07 | End of split
% 249.49/59.07 |
% 249.49/59.07 End of proof
% 249.49/59.07
% 249.49/59.07 Sub-proof #135 shows that the following formulas are inconsistent:
% 249.49/59.07 ----------------------------------------------------------------
% 249.49/59.07 (1) op(e0, e3) = e1
% 249.49/59.07 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.07 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.07 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.07 (3) all_252_21 = e1
% 249.49/59.07 (4) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.07 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.07 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.07 (5) ~ (all_244_8 = all_6_2)
% 249.49/59.07 (6) ~ (e2 = e0)
% 249.49/59.07 (7) ~ (e1 = e0)
% 249.49/59.07 (8) all_252_13 = e0
% 249.49/59.07 (9) op(e4, e1) = e2
% 249.49/59.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.07 (11) ~ (e3 = e2)
% 249.49/59.07 (12) ~ (e4 = e0)
% 249.49/59.07 (13) op(e2, e2) = all_244_8
% 249.49/59.07 (14) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.07 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.07 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.07 (15) op(e1, e0) = all_34_2
% 249.49/59.08 (16) op(e4, e2) = all_6_2
% 249.49/59.08 (17) ~ (all_34_2 = e2)
% 249.49/59.08 (18) ~ (e2 = e1)
% 249.49/59.08 (19) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.08 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.08 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.08 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.08 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.08 op(e0, e1) = e0)))
% 249.49/59.08 (20) ~ (e4 = e1)
% 249.49/59.08 (21) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.08 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.08 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.08 (22) ~ (all_6_2 = e1)
% 249.49/59.08 (23) ~ (all_20_2 = e1)
% 249.49/59.08 (24) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 249.49/59.08 all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0) &
% 249.49/59.08 op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.08 (25) op(e1, e4) = all_16_2
% 249.49/59.08 (26) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.08 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.08 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.08 (27) ~ (e3 = e0)
% 249.49/59.08 (28) ~ (e3 = e1)
% 249.49/59.08 (29) ~ (all_16_2 = e2)
% 249.49/59.08 (30) all_252_11 = e4
% 249.49/59.08 (31) ~ (all_8_2 = e1)
% 249.49/59.08 (32) op(e1, e2) = all_202_1
% 249.49/59.08 (33) op(e4, all_4_2) = e1
% 249.49/59.08 (34) all_252_20 = e2
% 249.49/59.08 (35) ~ (e4 = e3)
% 249.49/59.08 (36) op(e0, e1) = all_20_2
% 249.49/59.08 (37) op(e1, e2) = all_4_2
% 249.49/59.08 (38) ~ (e4 = e2)
% 249.49/59.08 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.08 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.08 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.08 (40) op(e3, e2) = all_8_2
% 249.49/59.08 (41) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.08 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.08 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.08
% 249.49/59.08 Begin of proof
% 249.49/59.08 |
% 249.49/59.08 | BETA: splitting (41) gives:
% 249.49/59.08 |
% 249.49/59.08 | Case 1:
% 249.49/59.08 | |
% 249.49/59.08 | | (42) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 249.49/59.08 | | = e2)
% 249.49/59.08 | |
% 249.49/59.08 | | BETA: splitting (42) gives:
% 249.49/59.08 | |
% 249.49/59.08 | | Case 1:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (43) all_252_12 = e2 & op(e1, e4) = e2
% 249.49/59.08 | | |
% 249.49/59.08 | | | ALPHA: (43) implies:
% 249.49/59.08 | | | (44) op(e1, e4) = e2
% 249.49/59.08 | | |
% 249.49/59.08 | | | BETA: splitting (24) gives:
% 249.49/59.08 | | |
% 249.49/59.08 | | | Case 1:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (45) ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4)
% 249.49/59.08 | | | | = all_242_1 & $i(all_242_0) & $i(all_242_1)
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | ALPHA: (45) implies:
% 249.49/59.08 | | | | (46) op(e1, e4) = all_242_1
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | REF_CLOSE: (10), (25), (29), (44), (46) are inconsistent by sub-proof
% 249.49/59.08 | | | | #600.
% 249.49/59.08 | | | |
% 249.49/59.08 | | | Case 2:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (47) ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1)
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | ALPHA: (47) implies:
% 249.49/59.08 | | | | (48) op(e1, e4) = all_242_1
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | REF_CLOSE: (10), (25), (29), (44), (48) are inconsistent by sub-proof
% 249.49/59.08 | | | | #600.
% 249.49/59.08 | | | |
% 249.49/59.08 | | | End of split
% 249.49/59.08 | | |
% 249.49/59.08 | | Case 2:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (49) all_252_13 = e2 & op(e1, e3) = e2
% 249.49/59.08 | | |
% 249.49/59.08 | | | REF_CLOSE: (6), (8), (49) are inconsistent by sub-proof #376.
% 249.49/59.08 | | |
% 249.49/59.08 | | End of split
% 249.49/59.08 | |
% 249.49/59.08 | Case 2:
% 249.49/59.08 | |
% 249.49/59.08 | | (50) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 249.49/59.08 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.08 | |
% 249.49/59.08 | | BETA: splitting (50) gives:
% 249.49/59.08 | |
% 249.49/59.08 | | Case 1:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (51) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/59.08 | | |
% 249.49/59.08 | | | ALPHA: (51) implies:
% 249.49/59.08 | | | (52) all_252_14 = e2
% 249.49/59.08 | | | (53) op(e1, e2) = e2
% 249.49/59.08 | | |
% 249.49/59.08 | | | BETA: splitting (14) gives:
% 249.49/59.08 | | |
% 249.49/59.08 | | | Case 1:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (54) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 249.49/59.08 | | | | e2) = e1)
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | REF_CLOSE: (10), (16), (22), (31), (40), (54) are inconsistent by
% 249.49/59.08 | | | | sub-proof #928.
% 249.49/59.08 | | | |
% 249.49/59.08 | | | Case 2:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (55) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1,
% 249.49/59.08 | | | | e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | BETA: splitting (55) gives:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | Case 1:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | (56) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | ALPHA: (56) implies:
% 249.49/59.08 | | | | | (57) op(e2, e2) = e1
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | GROUND_INST: instantiating (10) with all_4_2, all_202_1, e2, e1,
% 249.49/59.08 | | | | | simplifying with (32), (37) gives:
% 249.49/59.08 | | | | | (58) all_202_1 = all_4_2
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | GROUND_INST: instantiating (10) with e2, all_202_1, e2, e1,
% 249.49/59.08 | | | | | simplifying with (32), (53) gives:
% 249.49/59.08 | | | | | (59) all_202_1 = e2
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | GROUND_INST: instantiating (10) with all_244_8, e1, e2, e2,
% 249.49/59.08 | | | | | simplifying with (13), (57) gives:
% 249.49/59.08 | | | | | (60) all_244_8 = e1
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | COMBINE_EQS: (58), (59) imply:
% 249.49/59.08 | | | | | (61) all_4_2 = e2
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | SIMP: (61) implies:
% 249.49/59.08 | | | | | (62) all_4_2 = e2
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | REDUCE: (5), (60) imply:
% 249.49/59.08 | | | | | (63) ~ (all_6_2 = e1)
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | REDUCE: (33), (62) imply:
% 249.49/59.08 | | | | | (64) op(e4, e2) = e1
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | REF_CLOSE: (10), (16), (22), (64) are inconsistent by sub-proof #930.
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | Case 2:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | (65) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 249.49/59.08 | | | | | op(e0, e2) = e1)
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | BETA: splitting (65) gives:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | Case 1:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (66) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | REF_CLOSE: (18), (52), (66) are inconsistent by sub-proof #753.
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | Case 2:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (67) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | ALPHA: (67) implies:
% 249.49/59.08 | | | | | | (68) all_252_22 = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (11), (12), (19), (20),
% 249.49/59.08 | | | | | | (26), (27), (28), (34), (35), (38), (68) are inconsistent
% 249.49/59.08 | | | | | | by sub-proof #137.
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | End of split
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | End of split
% 249.49/59.08 | | | |
% 249.49/59.08 | | | End of split
% 249.49/59.08 | | |
% 249.49/59.08 | | Case 2:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (69) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.08 | | | e0) = e2)
% 249.49/59.08 | | |
% 249.49/59.08 | | | BETA: splitting (69) gives:
% 249.49/59.08 | | |
% 249.49/59.08 | | | Case 1:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (70) all_252_15 = e2 & op(e1, e1) = e2
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | ALPHA: (70) implies:
% 249.49/59.08 | | | | (71) all_252_15 = e2
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | BETA: splitting (39) gives:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | Case 1:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | (72) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3,
% 249.49/59.08 | | | | | e1) = e1)
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | BETA: splitting (72) gives:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | Case 1:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (73) all_252_9 = e1 & op(e4, e1) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | ALPHA: (73) implies:
% 249.49/59.08 | | | | | | (74) op(e4, e1) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | REF_CLOSE: (9), (10), (18), (74) are inconsistent by sub-proof #785.
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | Case 2:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (75) all_252_10 = e1 & op(e3, e1) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | ALPHA: (75) implies:
% 249.49/59.08 | | | | | | (76) all_252_10 = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | BETA: splitting (4) gives:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | Case 1:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | (77) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 &
% 249.49/59.08 | | | | | | | op(e3, e1) = e0)
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | BETA: splitting (77) gives:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | (78) all_252_9 = e0 & op(e4, e1) = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | ALPHA: (78) implies:
% 249.49/59.08 | | | | | | | | (79) op(e4, e1) = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | REF_CLOSE: (6), (9), (10), (79) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | #767.
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | (80) all_252_10 = e0 & op(e3, e1) = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | ALPHA: (80) implies:
% 249.49/59.08 | | | | | | | | (81) all_252_10 = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | COMBINE_EQS: (76), (81) imply:
% 249.49/59.08 | | | | | | | | (82) e1 = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | SIMP: (82) implies:
% 249.49/59.08 | | | | | | | | (83) e1 = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | REDUCE: (7), (83) imply:
% 249.49/59.08 | | | | | | | | (84) $false
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | CLOSE: (84) is inconsistent.
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | End of split
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | Case 2:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | (85) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 &
% 249.49/59.08 | | | | | | | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | BETA: splitting (85) gives:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | (86) all_252_11 = e0 & op(e2, e1) = e0
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | REF_CLOSE: (12), (30), (86) are inconsistent by sub-proof #197.
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | (87) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 249.49/59.08 | | | | | | | | op(e0, e1) = e0)
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | BETA: splitting (87) gives:
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | (88) all_252_15 = e0 & op(e1, e1) = e0
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | REF_CLOSE: (6), (71), (88) are inconsistent by sub-proof #500.
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | (89) all_252_23 = e0 & op(e0, e1) = e0
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | ALPHA: (89) implies:
% 249.49/59.08 | | | | | | | | | (90) all_252_23 = e0
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | BETA: splitting (21) gives:
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | (91) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 249.49/59.08 | | | | | | | | | | e3 & op(e3, e1) = e3)
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | BETA: splitting (91) gives:
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | (92) all_252_9 = e3 & op(e4, e1) = e3
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | ALPHA: (92) implies:
% 249.49/59.08 | | | | | | | | | | | (93) all_252_9 = e3
% 249.49/59.08 | | | | | | | | | | | (94) op(e4, e1) = e3
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | BETA: splitting (26) gives:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | (95) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 249.49/59.08 | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | BETA: splitting (95) gives:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | (96) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | ALPHA: (96) implies:
% 249.49/59.08 | | | | | | | | | | | | | (97) all_252_20 = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | COMBINE_EQS: (34), (97) imply:
% 249.49/59.08 | | | | | | | | | | | | | (98) e3 = e2
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | SIMP: (98) implies:
% 249.49/59.08 | | | | | | | | | | | | | (99) e3 = e2
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | REF_CLOSE: (11), (21), (27), (28), (30), (35), (71), (76),
% 249.49/59.08 | | | | | | | | | | | | | (90), (93), (99) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | #136.
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | (100) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | ALPHA: (100) implies:
% 249.49/59.08 | | | | | | | | | | | | | (101) op(e0, e3) = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | REF_CLOSE: (1), (10), (28), (101) are inconsistent by
% 249.49/59.08 | | | | | | | | | | | | | sub-proof #590.
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | (102) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 249.49/59.08 | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 249.49/59.08 | | | | | | | | | | | | op(e0, e0) = e3)
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | BETA: splitting (102) gives:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | (103) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | ALPHA: (103) implies:
% 249.49/59.08 | | | | | | | | | | | | | (104) all_252_22 = e3
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | BETA: splitting (2) gives:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (105) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 249.49/59.08 | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (106) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (34), (38), (106) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #543.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (107) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (3), (20), (107) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #367.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (108) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 249.49/59.08 | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.49/59.08 | | | | | | | | | | | | | | op(e0, e0) = e4)
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (109) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (35), (104), (109) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #321.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (110) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 249.49/59.08 | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | (111) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 249.49/59.08 | | | | | | | | | | | | | | | | (112) all_252_23 = e4
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (112) imply:
% 249.49/59.08 | | | | | | | | | | | | | | | | (113) e4 = e0
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | REDUCE: (12), (113) imply:
% 249.49/59.08 | | | | | | | | | | | | | | | | (114) $false
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | (115) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 249.49/59.08 | | | | | | | | | | | | | | | | (116) all_252_24 = e4
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | | (117) all_252_24 = e0 & op(e0, e0) = e0
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 249.49/59.08 | | | | | | | | | | | | | | | | | (118) all_252_24 = e0
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (116), (118) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | | | #401.
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with e2, e3, e1, e4,
% 249.49/59.08 | | | | | | | | | | | | | | | | | simplifying with (9), (94) gives:
% 249.49/59.08 | | | | | | | | | | | | | | | | | (119) e3 = e2
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (21), (27), (28), (30), (35), (71), (76),
% 249.49/59.08 | | | | | | | | | | | | | | | | | (90), (93), (119) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | | | #136.
% 249.49/59.08 | | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | (120) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 249.49/59.08 | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | BETA: splitting (120) gives:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (121) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | ALPHA: (121) implies:
% 249.49/59.08 | | | | | | | | | | | | | | (122) all_252_23 = e3
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | COMBINE_EQS: (90), (122) imply:
% 249.49/59.08 | | | | | | | | | | | | | | (123) e3 = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | REDUCE: (27), (123) imply:
% 249.49/59.08 | | | | | | | | | | | | | | (124) $false
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (125) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | ALPHA: (125) implies:
% 249.49/59.08 | | | | | | | | | | | | | | (126) all_252_24 = e3
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (127) all_252_24 = e0 & op(e0, e0) = e0
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 249.49/59.08 | | | | | | | | | | | | | | | (128) all_252_24 = e0
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (27), (126), (128) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #343.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with e2, e3, e1, e4,
% 249.49/59.08 | | | | | | | | | | | | | | | simplifying with (9), (94) gives:
% 249.49/59.08 | | | | | | | | | | | | | | | (129) e3 = e2
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (11), (21), (27), (28), (30), (35), (71), (76),
% 249.49/59.08 | | | | | | | | | | | | | | | (90), (93), (129) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #136.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | (130) all_252_10 = e3 & op(e3, e1) = e3
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | REF_CLOSE: (28), (76), (130) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | #769.
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | (131) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 =
% 249.49/59.08 | | | | | | | | | | e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.08 | | | | | | | | | | e1) = e3)
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | BETA: splitting (131) gives:
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | (132) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | REF_CLOSE: (30), (35), (132) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | #791.
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | (133) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 249.49/59.08 | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | BETA: splitting (133) gives:
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | (134) all_252_15 = e3 & op(e1, e1) = e3
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | REF_CLOSE: (11), (71), (134) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | #501.
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | (135) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | ALPHA: (135) implies:
% 249.49/59.08 | | | | | | | | | | | | (136) all_252_23 = e3
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | BETA: splitting (4) gives:
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | (137) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 249.49/59.08 | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | BETA: splitting (137) gives:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (138) all_252_9 = e0 & op(e4, e1) = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | ALPHA: (138) implies:
% 249.49/59.08 | | | | | | | | | | | | | | (139) op(e4, e1) = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with e2, e0, e1, e4,
% 249.49/59.08 | | | | | | | | | | | | | | simplifying with (9), (139) gives:
% 249.49/59.08 | | | | | | | | | | | | | | (140) e2 = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | REDUCE: (6), (140) imply:
% 249.49/59.08 | | | | | | | | | | | | | | (141) $false
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (142) all_252_10 = e0 & op(e3, e1) = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | ALPHA: (142) implies:
% 249.49/59.08 | | | | | | | | | | | | | | (143) all_252_10 = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | COMBINE_EQS: (76), (143) imply:
% 249.49/59.08 | | | | | | | | | | | | | | (144) e1 = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | REDUCE: (7), (144) imply:
% 249.49/59.08 | | | | | | | | | | | | | | (145) $false
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | (146) all_252_11 = e0 & op(e2, e1) = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | ALPHA: (146) implies:
% 249.49/59.08 | | | | | | | | | | | | | | (147) all_252_11 = e0
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | REF_CLOSE: (12), (30), (147) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | #766.
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 1:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | (148) all_252_15 = e0 & op(e1, e1) = e0
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 249.49/59.08 | | | | | | | | | | | | | | | (149) all_252_15 = e0
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (149) imply:
% 249.49/59.08 | | | | | | | | | | | | | | | (150) e2 = e0
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REDUCE: (6), (150) imply:
% 249.49/59.08 | | | | | | | | | | | | | | | (151) $false
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | Case 2:
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | | REF_CLOSE: (27), (89), (136) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | | | | | | | | | #316.
% 249.49/59.08 | | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | | |
% 249.49/59.08 | | | | | | | | | End of split
% 249.49/59.08 | | | | | | | | |
% 249.49/59.08 | | | | | | | | End of split
% 249.49/59.08 | | | | | | | |
% 249.49/59.08 | | | | | | | End of split
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | End of split
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | End of split
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | Case 2:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | (152) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 &
% 249.49/59.08 | | | | | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | BETA: splitting (152) gives:
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | | Case 1:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (153) all_252_11 = e1 & op(e2, e1) = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | ALPHA: (153) implies:
% 249.49/59.08 | | | | | | (154) all_252_11 = e1
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | REF_CLOSE: (20), (30), (154) are inconsistent by sub-proof #188.
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | Case 2:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | (155) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 249.49/59.08 | | | | | | op(e0, e1) = e1)
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | BETA: splitting (155) gives:
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | | Case 1:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | (156) all_252_15 = e1 & op(e1, e1) = e1
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | REF_CLOSE: (18), (71), (156) are inconsistent by sub-proof #409.
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | Case 2:
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | (157) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | | REF_CLOSE: (10), (23), (36), (157) are inconsistent by sub-proof
% 249.49/59.08 | | | | | | | #287.
% 249.49/59.08 | | | | | | |
% 249.49/59.08 | | | | | | End of split
% 249.49/59.08 | | | | | |
% 249.49/59.08 | | | | | End of split
% 249.49/59.08 | | | | |
% 249.49/59.08 | | | | End of split
% 249.49/59.08 | | | |
% 249.49/59.08 | | | Case 2:
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | (158) all_252_19 = e2 & op(e1, e0) = e2
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | ALPHA: (158) implies:
% 249.49/59.08 | | | | (159) op(e1, e0) = e2
% 249.49/59.08 | | | |
% 249.49/59.08 | | | | REF_CLOSE: (10), (15), (17), (159) are inconsistent by sub-proof #909.
% 249.49/59.08 | | | |
% 249.49/59.08 | | | End of split
% 249.49/59.08 | | |
% 249.49/59.08 | | End of split
% 249.49/59.08 | |
% 249.49/59.08 | End of split
% 249.49/59.08 |
% 249.49/59.08 End of proof
% 249.49/59.08
% 249.49/59.08 Sub-proof #136 shows that the following formulas are inconsistent:
% 249.49/59.08 ----------------------------------------------------------------
% 249.49/59.08 (1) ~ (e3 = e2)
% 249.49/59.08 (2) e3 = e2
% 249.49/59.08 (3) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.08 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.08 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.08 (4) ~ (e3 = e0)
% 249.49/59.08 (5) ~ (e3 = e1)
% 249.49/59.08 (6) all_252_11 = e4
% 249.49/59.08 (7) all_252_23 = e0
% 249.49/59.08 (8) all_252_15 = e2
% 249.49/59.08 (9) all_252_9 = e3
% 249.49/59.08 (10) ~ (e4 = e3)
% 249.49/59.08 (11) all_252_10 = e1
% 249.49/59.08
% 249.49/59.08 Begin of proof
% 249.49/59.08 |
% 249.49/59.08 | COMBINE_EQS: (2), (9) imply:
% 249.49/59.08 | (12) all_252_9 = e2
% 249.49/59.08 |
% 249.49/59.08 | BETA: splitting (3) gives:
% 249.49/59.08 |
% 249.49/59.08 | Case 1:
% 249.49/59.08 | |
% 249.49/59.08 | | (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 249.49/59.08 | | e3)
% 249.49/59.08 | |
% 249.49/59.08 | | BETA: splitting (13) gives:
% 249.49/59.08 | |
% 249.49/59.08 | | Case 1:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (14) all_252_9 = e3 & op(e4, e1) = e3
% 249.49/59.08 | | |
% 249.49/59.08 | | | REF_CLOSE: (1), (9), (12) are inconsistent by sub-proof #186.
% 249.49/59.08 | | |
% 249.49/59.08 | | Case 2:
% 249.49/59.08 | | |
% 249.49/59.08 | | | (15) all_252_10 = e3 & op(e3, e1) = e3
% 249.49/59.08 | | |
% 249.49/59.08 | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #769.
% 249.49/59.08 | | |
% 249.49/59.08 | | End of split
% 249.49/59.08 | |
% 249.49/59.08 | Case 2:
% 249.49/59.08 | |
% 249.49/59.09 | | (16) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1)
% 249.49/59.09 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (16) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (17) all_252_11 = e3 & op(e2, e1) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #791.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (18) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.09 | | | e1) = e3)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (18) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (19) all_252_15 = e3 & op(e1, e1) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (1), (8), (19) are inconsistent by sub-proof #405.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (20) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (20) implies:
% 249.49/59.09 | | | | (21) all_252_23 = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (4), (7), (21) are inconsistent by sub-proof #183.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #137 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) op(e0, e3) = e1
% 249.49/59.09 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.09 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.09 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.09 (3) all_252_21 = e1
% 249.49/59.09 (4) ~ (e2 = e0)
% 249.49/59.09 (5) ~ (e1 = e0)
% 249.49/59.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.09 (7) ~ (e3 = e2)
% 249.49/59.09 (8) ~ (e4 = e0)
% 249.49/59.09 (9) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.09 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.09 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.09 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.09 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 op(e0, e1) = e0)))
% 249.49/59.09 (10) ~ (e4 = e1)
% 249.49/59.09 (11) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.09 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.09 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.09 (12) all_252_22 = e1
% 249.49/59.09 (13) ~ (e3 = e0)
% 249.49/59.09 (14) ~ (e3 = e1)
% 249.49/59.09 (15) all_252_20 = e2
% 249.49/59.09 (16) ~ (e4 = e3)
% 249.49/59.09 (17) ~ (e4 = e2)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (2) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (18) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3)
% 249.49/59.09 | | = e4)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (18) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (19) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (15), (17), (19) are inconsistent by sub-proof #534.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (20) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (3), (10), (20) are inconsistent by sub-proof #344.
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (21) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1)
% 249.49/59.09 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (21) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (22) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | ALPHA: (22) implies:
% 249.49/59.09 | | | (23) all_252_22 = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (10), (12), (23) are inconsistent by sub-proof #530.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (24) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 249.49/59.09 | | | e0) = e4)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (24) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (25) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 249.49/59.09 | | | | (15), (16), (25) are inconsistent by sub-proof #139.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (26) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (26) implies:
% 249.49/59.09 | | | | (27) all_252_24 = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 249.49/59.09 | | | | (15), (16), (27) are inconsistent by sub-proof #138.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #138 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) op(e0, e3) = e1
% 249.49/59.09 (2) ~ (e2 = e0)
% 249.49/59.09 (3) ~ (e1 = e0)
% 249.49/59.09 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.09 (5) ~ (e3 = e2)
% 249.49/59.09 (6) ~ (e4 = e0)
% 249.49/59.09 (7) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.09 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.09 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.09 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.09 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 op(e0, e1) = e0)))
% 249.49/59.09 (8) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.09 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 249.49/59.09 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.09 (9) all_252_22 = e1
% 249.49/59.09 (10) ~ (e3 = e0)
% 249.49/59.09 (11) ~ (e3 = e1)
% 249.49/59.09 (12) all_252_20 = e2
% 249.49/59.09 (13) ~ (e4 = e3)
% 249.49/59.09 (14) all_252_24 = e4
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (8) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (15) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 249.49/59.09 | | = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (15) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (16) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (5), (12), (16) are inconsistent by sub-proof #539.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (17) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | ALPHA: (17) implies:
% 249.49/59.09 | | | (18) op(e0, e3) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (1), (4), (11), (18) are inconsistent by sub-proof #590.
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (19) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 249.49/59.09 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (19) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (20) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (9), (11), (20) are inconsistent by sub-proof #140.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (21) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 249.49/59.09 | | | e0) = e3)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (21) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (22) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (22) implies:
% 249.49/59.09 | | | | (23) all_252_23 = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | BETA: splitting (7) gives:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | Case 1:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | (24) all_252_24 = e0 & op(e0, e0) = e0
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | ALPHA: (24) implies:
% 249.49/59.09 | | | | | (25) all_252_24 = e0
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | REF_CLOSE: (6), (14), (25) are inconsistent by sub-proof #401.
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | Case 2:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | (26) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 249.49/59.09 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 249.49/59.09 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 249.49/59.09 | | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 249.49/59.09 | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 | | | | | op(e0, e1) = e0))
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | ALPHA: (26) implies:
% 249.49/59.09 | | | | | (27) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 249.49/59.09 | | | | | op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 249.49/59.09 | | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | BETA: splitting (27) gives:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | Case 1:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | (28) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 249.49/59.09 | | | | | | op(e0, e3) = e0)
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | BETA: splitting (28) gives:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | Case 1:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (29) all_252_20 = e0 & op(e0, e4) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (2), (12), (29) are inconsistent by sub-proof #185.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | Case 2:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (30) all_252_21 = e0 & op(e0, e3) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | ALPHA: (30) implies:
% 249.49/59.09 | | | | | | | (31) op(e0, e3) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (1), (3), (4), (31) are inconsistent by sub-proof #320.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | End of split
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | Case 2:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | (32) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 | | | | | | op(e0, e1) = e0)
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | BETA: splitting (32) gives:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | Case 1:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (33) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (3), (9), (33) are inconsistent by sub-proof #869.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | Case 2:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (34) all_252_23 = e0 & op(e0, e1) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | ALPHA: (34) implies:
% 249.49/59.09 | | | | | | | (35) all_252_23 = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (10), (23), (35) are inconsistent by sub-proof #183.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | End of split
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | End of split
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | End of split
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (36) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (13), (14), (36) are inconsistent by sub-proof #194.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #139 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.09 (2) op(e0, e3) = e1
% 249.49/59.09 (3) ~ (e2 = e0)
% 249.49/59.09 (4) ~ (e1 = e0)
% 249.49/59.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.09 (6) ~ (e3 = e2)
% 249.49/59.09 (7) ~ (e4 = e0)
% 249.49/59.09 (8) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.09 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.09 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.09 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.09 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 op(e0, e1) = e0)))
% 249.49/59.09 (9) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.09 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 249.49/59.09 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.09 (10) all_252_22 = e1
% 249.49/59.09 (11) ~ (e3 = e0)
% 249.49/59.09 (12) ~ (e3 = e1)
% 249.49/59.09 (13) all_252_20 = e2
% 249.49/59.09 (14) ~ (e4 = e3)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | ALPHA: (1) implies:
% 249.49/59.09 | (15) all_252_23 = e4
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (9) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (16) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 249.49/59.09 | | = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | REF_CLOSE: (2), (5), (6), (12), (13), (16) are inconsistent by sub-proof
% 249.49/59.09 | | #322.
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (17) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 249.49/59.09 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (17) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (18) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (10), (12), (18) are inconsistent by sub-proof #140.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (19) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 249.49/59.09 | | | e0) = e3)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (19) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (20) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (14), (15), (20) are inconsistent by sub-proof #240.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (21) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (21) implies:
% 249.49/59.09 | | | | (22) all_252_24 = e3
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | BETA: splitting (8) gives:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | Case 1:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | (23) all_252_24 = e0 & op(e0, e0) = e0
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | ALPHA: (23) implies:
% 249.49/59.09 | | | | | (24) all_252_24 = e0
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | REF_CLOSE: (11), (22), (24) are inconsistent by sub-proof #343.
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | Case 2:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | (25) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 249.49/59.09 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 249.49/59.09 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 249.49/59.09 | | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 249.49/59.09 | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 | | | | | op(e0, e1) = e0))
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | ALPHA: (25) implies:
% 249.49/59.09 | | | | | (26) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 249.49/59.09 | | | | | op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 249.49/59.09 | | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | BETA: splitting (26) gives:
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | | Case 1:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | (27) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 249.49/59.09 | | | | | | op(e0, e3) = e0)
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | REF_CLOSE: (2), (3), (4), (5), (13), (27) are inconsistent by
% 249.49/59.09 | | | | | | sub-proof #319.
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | Case 2:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | (28) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.09 | | | | | | op(e0, e1) = e0)
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | BETA: splitting (28) gives:
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | | Case 1:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (29) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (4), (10), (29) are inconsistent by sub-proof #869.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | Case 2:
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | (30) all_252_23 = e0 & op(e0, e1) = e0
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | | REF_CLOSE: (7), (15), (30) are inconsistent by sub-proof #317.
% 249.49/59.09 | | | | | | |
% 249.49/59.09 | | | | | | End of split
% 249.49/59.09 | | | | | |
% 249.49/59.09 | | | | | End of split
% 249.49/59.09 | | | | |
% 249.49/59.09 | | | | End of split
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #140 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.09 (2) all_252_22 = e1
% 249.49/59.09 (3) ~ (e3 = e1)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | ALPHA: (1) implies:
% 249.49/59.09 | (4) all_252_22 = e3
% 249.49/59.09 |
% 249.49/59.09 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.09 | (5) e3 = e1
% 249.49/59.09 |
% 249.49/59.09 | SIMP: (5) implies:
% 249.49/59.09 | (6) e3 = e1
% 249.49/59.09 |
% 249.49/59.09 | REDUCE: (3), (6) imply:
% 249.49/59.09 | (7) $false
% 249.49/59.09 |
% 249.49/59.09 | CLOSE: (7) is inconsistent.
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #141 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_6 = e0
% 249.49/59.09 (2) ~ (e1 = e0)
% 249.49/59.09 (3) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = e1)
% 249.49/59.09 | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.09 (4) ~ (e2 = e1)
% 249.49/59.09 (5) ~ (e3 = e1)
% 249.49/59.09 (6) all_252_12 = e3
% 249.49/59.09 (7) all_252_20 = e2
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (3) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (8) all_252_6 = e1 & op(e2, e4) = e1
% 249.49/59.09 | |
% 249.49/59.09 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #545.
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (9) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) =
% 249.49/59.09 | | e1)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (9) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (10) all_252_12 = e1 & op(e1, e4) = e1
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #594.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (11) all_252_20 = e1 & op(e0, e4) = e1
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #544.
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #142 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_6 = e0
% 249.49/59.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.09 (3) ~ (e4 = e0)
% 249.49/59.09 (4) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4)
% 249.49/59.09 | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.09 (5) op(e1, e4) = e3
% 249.49/59.09 (6) all_252_20 = e2
% 249.49/59.09 (7) ~ (e4 = e3)
% 249.49/59.09 (8) ~ (e4 = e2)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (4) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (9) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.09 | |
% 249.49/59.09 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #938.
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (10) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4)
% 249.49/59.09 | | = e4)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (10) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (11) all_252_12 = e4 & op(e1, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | ALPHA: (11) implies:
% 249.49/59.09 | | | (12) op(e1, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (2), (5), (7), (12) are inconsistent by sub-proof #603.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (13) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #543.
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #143 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_6 = e0
% 249.49/59.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.09 (3) all_250_0 = all_244_0
% 249.49/59.09 (4) ~ (all_244_0 = e2)
% 249.49/59.09 (5) all_252_12 = e3
% 249.49/59.09 (6) op(e1, e4) = e3
% 249.49/59.09 (7) all_252_0 = e1 & op(e4, e4) = e1
% 249.49/59.09 (8) all_252_20 = e2
% 249.49/59.09 (9) all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 |
% 249.49/59.09 all_250_0 = e0
% 249.49/59.09 (10) op(e4, e4) = all_244_0
% 249.49/59.09 (11) ~ (all_244_0 = e1)
% 249.49/59.09 (12) ~ (all_244_0 = e0)
% 249.49/59.09 (13) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.09 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.09 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.09 (14) ~ (all_244_0 = e3)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | ALPHA: (7) implies:
% 249.49/59.09 | (15) all_252_0 = e1
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (9) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (16) all_250_0 = e4
% 249.49/59.09 | |
% 249.49/59.09 | | COMBINE_EQS: (3), (16) imply:
% 249.49/59.09 | | (17) all_244_0 = e4
% 249.49/59.09 | |
% 249.49/59.09 | | REDUCE: (14), (17) imply:
% 249.49/59.09 | | (18) ~ (e4 = e3)
% 249.49/59.09 | |
% 249.49/59.09 | | REDUCE: (4), (17) imply:
% 249.49/59.09 | | (19) ~ (e4 = e2)
% 249.49/59.09 | |
% 249.49/59.09 | | REDUCE: (11), (17) imply:
% 249.49/59.09 | | (20) ~ (e4 = e1)
% 249.49/59.09 | |
% 249.49/59.09 | | REDUCE: (12), (17) imply:
% 249.49/59.09 | | (21) ~ (e4 = e0)
% 249.49/59.09 | |
% 249.49/59.09 | | REDUCE: (10), (17) imply:
% 249.49/59.09 | | (22) op(e4, e4) = e4
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (13) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4)
% 249.49/59.09 | | | = e4)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (23) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (24) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (15), (20), (24) are inconsistent by sub-proof #145.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (25) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (25) implies:
% 249.49/59.09 | | | | (26) all_252_2 = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | ALPHA: (7) implies:
% 249.49/59.09 | | | | (27) op(e4, e4) = e1
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | GROUND_INST: instantiating (2) with e1, e4, e4, e4, simplifying with
% 249.49/59.09 | | | | (22), (27) gives:
% 249.49/59.09 | | | | (28) e4 = e1
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | COMBINE_EQS: (26), (28) imply:
% 249.49/59.09 | | | | (29) all_252_2 = e1
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (1), (5), (8), (13), (15), (18), (19), (20), (21), (29) are
% 249.49/59.09 | | | | inconsistent by sub-proof #144.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (30) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4)
% 249.49/59.09 | | | = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.09 | | |
% 249.49/59.09 | | | BETA: splitting (30) gives:
% 249.49/59.09 | | |
% 249.49/59.09 | | | Case 1:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (31) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (1), (21), (31) are inconsistent by sub-proof #387.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | Case 2:
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | (32) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 249.49/59.09 | | | | e4) = e4)
% 249.49/59.09 | | | |
% 249.49/59.09 | | | | REF_CLOSE: (2), (6), (8), (18), (19), (32) are inconsistent by sub-proof
% 249.49/59.09 | | | | #147.
% 249.49/59.09 | | | |
% 249.49/59.09 | | | End of split
% 249.49/59.09 | | |
% 249.49/59.09 | | End of split
% 249.49/59.09 | |
% 249.49/59.09 | Case 2:
% 249.49/59.09 | |
% 249.49/59.09 | | (33) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 | all_250_0 = e0
% 249.49/59.09 | |
% 249.49/59.09 | | REF_CLOSE: (3), (4), (11), (12), (14), (33) are inconsistent by sub-proof
% 249.49/59.09 | | #217.
% 249.49/59.09 | |
% 249.49/59.09 | End of split
% 249.49/59.09 |
% 249.49/59.09 End of proof
% 249.49/59.09
% 249.49/59.09 Sub-proof #144 shows that the following formulas are inconsistent:
% 249.49/59.09 ----------------------------------------------------------------
% 249.49/59.09 (1) all_252_6 = e0
% 249.49/59.09 (2) ~ (e4 = e0)
% 249.49/59.09 (3) all_252_2 = e1
% 249.49/59.09 (4) ~ (e4 = e1)
% 249.49/59.09 (5) all_252_12 = e3
% 249.49/59.09 (6) all_252_0 = e1
% 249.49/59.09 (7) all_252_20 = e2
% 249.49/59.09 (8) ~ (e4 = e3)
% 249.49/59.09 (9) ~ (e4 = e2)
% 249.49/59.09 (10) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.09 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.09 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.09
% 249.49/59.09 Begin of proof
% 249.49/59.09 |
% 249.49/59.09 | BETA: splitting (10) gives:
% 249.49/59.09 |
% 249.49/59.09 | Case 1:
% 249.49/59.09 | |
% 249.49/59.09 | | (11) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 249.49/59.09 | | e4)
% 249.49/59.09 | |
% 249.49/59.09 | | BETA: splitting (11) gives:
% 249.49/59.09 | |
% 249.49/59.09 | | Case 1:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (12) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #145.
% 249.49/59.09 | | |
% 249.49/59.09 | | Case 2:
% 249.49/59.09 | | |
% 249.49/59.09 | | | (13) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | ALPHA: (13) implies:
% 249.49/59.09 | | | (14) all_252_2 = e4
% 249.49/59.09 | | |
% 249.49/59.09 | | | COMBINE_EQS: (3), (14) imply:
% 249.49/59.10 | | | (15) e4 = e1
% 249.49/59.10 | | |
% 249.49/59.10 | | | REDUCE: (4), (15) imply:
% 249.49/59.10 | | | (16) $false
% 249.49/59.10 | | |
% 249.49/59.10 | | | CLOSE: (16) is inconsistent.
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (17) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 | |
% 249.49/59.10 | | BETA: splitting (17) gives:
% 249.49/59.10 | |
% 249.49/59.10 | | Case 1:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (18) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #387.
% 249.49/59.10 | | |
% 249.49/59.10 | | Case 2:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (19) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 249.49/59.10 | | | e4) = e4)
% 249.49/59.10 | | |
% 249.49/59.10 | | | BETA: splitting (19) gives:
% 249.49/59.10 | | |
% 249.49/59.10 | | | Case 1:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (20) all_252_12 = e4 & op(e1, e4) = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | ALPHA: (20) implies:
% 249.49/59.10 | | | | (21) all_252_12 = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | COMBINE_EQS: (5), (21) imply:
% 249.49/59.10 | | | | (22) e4 = e3
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REDUCE: (8), (22) imply:
% 249.49/59.10 | | | | (23) $false
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | CLOSE: (23) is inconsistent.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | Case 2:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (24) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REF_CLOSE: (7), (9), (24) are inconsistent by sub-proof #543.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | End of split
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #145 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.10 (2) all_252_0 = e1
% 249.49/59.10 (3) ~ (e4 = e1)
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | ALPHA: (1) implies:
% 249.49/59.10 | (4) all_252_0 = e4
% 249.49/59.10 |
% 249.49/59.10 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.10 | (5) e4 = e1
% 249.49/59.10 |
% 249.49/59.10 | SIMP: (5) implies:
% 249.49/59.10 | (6) e4 = e1
% 249.49/59.10 |
% 249.49/59.10 | REDUCE: (3), (6) imply:
% 249.49/59.10 | (7) $false
% 249.49/59.10 |
% 249.49/59.10 | CLOSE: (7) is inconsistent.
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #146 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) all_252_6 = e0
% 249.49/59.10 (2) ~ (e1 = e0)
% 249.49/59.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (4) ~ (e4 = e0)
% 249.49/59.10 (5) ~ (e2 = e1)
% 249.49/59.10 (6) op(e3, e4) = e1
% 249.49/59.10 (7) ~ (e4 = e1)
% 249.49/59.10 (8) ~ (e3 = e1)
% 249.49/59.10 (9) op(e1, e4) = e3
% 249.49/59.10 (10) all_252_20 = e2
% 249.49/59.10 (11) op(e3, e4) = all_100_2
% 249.49/59.10 (12) ~ (e4 = e3)
% 249.49/59.10 (13) ~ (e4 = e2)
% 249.49/59.10 (14) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.10 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 (15) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.10 (16) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.10 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.10 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (15) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (17) all_252_0 = e3 & op(e4, e4) = e3
% 249.49/59.10 | |
% 249.49/59.10 | | ALPHA: (17) implies:
% 249.49/59.10 | | (18) all_252_0 = e3
% 249.49/59.10 | |
% 249.49/59.10 | | BETA: splitting (16) gives:
% 249.49/59.10 | |
% 249.49/59.10 | | Case 1:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (19) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4)
% 249.49/59.10 | | | = e1)
% 249.49/59.10 | | |
% 249.49/59.10 | | | BETA: splitting (19) gives:
% 249.49/59.10 | | |
% 249.49/59.10 | | | Case 1:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (20) all_252_0 = e1 & op(e4, e4) = e1
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REF_CLOSE: (8), (18), (20) are inconsistent by sub-proof #546.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | Case 2:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (21) all_252_2 = e1 & op(e3, e4) = e1
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | ALPHA: (21) implies:
% 249.49/59.10 | | | | (22) all_252_2 = e1
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REF_CLOSE: (1), (3), (4), (7), (9), (10), (12), (13), (14), (18), (22)
% 249.49/59.10 | | | | are inconsistent by sub-proof #149.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | End of split
% 249.49/59.10 | | |
% 249.49/59.10 | | Case 2:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (23) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4)
% 249.49/59.10 | | | = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.10 | | |
% 249.49/59.10 | | | BETA: splitting (23) gives:
% 249.49/59.10 | | |
% 249.49/59.10 | | | Case 1:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (24) all_252_6 = e1 & op(e2, e4) = e1
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REF_CLOSE: (1), (2), (24) are inconsistent by sub-proof #545.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | Case 2:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (25) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 249.49/59.10 | | | | e4) = e1)
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | BETA: splitting (25) gives:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | Case 1:
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | (26) all_252_12 = e1 & op(e1, e4) = e1
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | ALPHA: (26) implies:
% 249.49/59.10 | | | | | (27) all_252_12 = e1
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | BETA: splitting (14) gives:
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | Case 1:
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | (28) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 &
% 249.49/59.10 | | | | | | op(e3, e4) = e4)
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | BETA: splitting (28) gives:
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | Case 1:
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | (29) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | REF_CLOSE: (12), (18), (29) are inconsistent by sub-proof #547.
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | Case 2:
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | (30) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | ALPHA: (30) implies:
% 249.49/59.10 | | | | | | | (31) all_252_2 = e4
% 249.49/59.10 | | | | | | | (32) op(e3, e4) = e4
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | GROUND_INST: instantiating (3) with all_100_2, e1, e4, e3,
% 249.49/59.10 | | | | | | | simplifying with (6), (11) gives:
% 249.49/59.10 | | | | | | | (33) all_100_2 = e1
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | GROUND_INST: instantiating (3) with all_100_2, e4, e4, e3,
% 249.49/59.10 | | | | | | | simplifying with (11), (32) gives:
% 249.49/59.10 | | | | | | | (34) all_100_2 = e4
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | COMBINE_EQS: (33), (34) imply:
% 249.49/59.10 | | | | | | | (35) e4 = e1
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | REF_CLOSE: (1), (4), (7), (10), (12), (13), (14), (18), (27),
% 249.49/59.10 | | | | | | | (31), (35) are inconsistent by sub-proof #148.
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | End of split
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | Case 2:
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | (36) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 &
% 249.49/59.10 | | | | | | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | BETA: splitting (36) gives:
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | | Case 1:
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | (37) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | REF_CLOSE: (1), (4), (37) are inconsistent by sub-proof #938.
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | Case 2:
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | (38) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 249.49/59.10 | | | | | | | op(e0, e4) = e4)
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | | REF_CLOSE: (3), (9), (10), (12), (13), (38) are inconsistent by
% 249.49/59.10 | | | | | | | sub-proof #147.
% 249.49/59.10 | | | | | | |
% 249.49/59.10 | | | | | | End of split
% 249.49/59.10 | | | | | |
% 249.49/59.10 | | | | | End of split
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | Case 2:
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | (39) all_252_20 = e1 & op(e0, e4) = e1
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | | REF_CLOSE: (5), (10), (39) are inconsistent by sub-proof #544.
% 249.49/59.10 | | | | |
% 249.49/59.10 | | | | End of split
% 249.49/59.10 | | | |
% 249.49/59.10 | | | End of split
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (40) all_252_2 = e3 & op(e3, e4) = e3
% 249.49/59.10 | |
% 249.49/59.10 | | ALPHA: (40) implies:
% 249.49/59.10 | | (41) op(e3, e4) = e3
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (3), (6), (8), (11), (41) are inconsistent by sub-proof #896.
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #147 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (2) op(e1, e4) = e3
% 249.49/59.10 (3) all_252_20 = e2
% 249.49/59.10 (4) ~ (e4 = e3)
% 249.49/59.10 (5) ~ (e4 = e2)
% 249.49/59.10 (6) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (6) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (7) all_252_12 = e4 & op(e1, e4) = e4
% 249.49/59.10 | |
% 249.49/59.10 | | ALPHA: (7) implies:
% 249.49/59.10 | | (8) op(e1, e4) = e4
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #603.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (9) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #534.
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #148 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) all_252_6 = e0
% 249.49/59.10 (2) ~ (e4 = e0)
% 249.49/59.10 (3) ~ (e4 = e1)
% 249.49/59.10 (4) all_252_2 = e4
% 249.49/59.10 (5) all_252_0 = e3
% 249.49/59.10 (6) e4 = e1
% 249.49/59.10 (7) all_252_20 = e2
% 249.49/59.10 (8) ~ (e4 = e3)
% 249.49/59.10 (9) ~ (e4 = e2)
% 249.49/59.10 (10) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.10 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 (11) all_252_12 = e1
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | SIMP: (6) implies:
% 249.49/59.10 | (12) e4 = e1
% 249.49/59.10 |
% 249.49/59.10 | COMBINE_EQS: (4), (12) imply:
% 249.49/59.10 | (13) all_252_2 = e1
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (10) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (14) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 249.49/59.10 | | e4)
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (3), (5), (8), (13), (14) are inconsistent by sub-proof #150.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (15) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 | |
% 249.49/59.10 | | BETA: splitting (15) gives:
% 249.49/59.10 | |
% 249.49/59.10 | | Case 1:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (16) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (1), (2), (16) are inconsistent by sub-proof #387.
% 249.49/59.10 | | |
% 249.49/59.10 | | Case 2:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (17) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 249.49/59.10 | | | e4) = e4)
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (3), (7), (9), (11), (17) are inconsistent by sub-proof #190.
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #149 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) all_252_6 = e0
% 249.49/59.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (3) ~ (e4 = e0)
% 249.49/59.10 (4) all_252_2 = e1
% 249.49/59.10 (5) ~ (e4 = e1)
% 249.49/59.10 (6) all_252_0 = e3
% 249.49/59.10 (7) op(e1, e4) = e3
% 249.49/59.10 (8) all_252_20 = e2
% 249.49/59.10 (9) ~ (e4 = e3)
% 249.49/59.10 (10) ~ (e4 = e2)
% 249.49/59.10 (11) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.10 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (11) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (12) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 249.49/59.10 | | e4)
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (4), (5), (6), (9), (12) are inconsistent by sub-proof #150.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (13) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.10 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.10 | |
% 249.49/59.10 | | BETA: splitting (13) gives:
% 249.49/59.10 | |
% 249.49/59.10 | | Case 1:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (14) all_252_6 = e4 & op(e2, e4) = e4
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #387.
% 249.49/59.10 | | |
% 249.49/59.10 | | Case 2:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (15) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 249.49/59.10 | | | e4) = e4)
% 249.49/59.10 | | |
% 249.49/59.10 | | | BETA: splitting (15) gives:
% 249.49/59.10 | | |
% 249.49/59.10 | | | Case 1:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (16) all_252_12 = e4 & op(e1, e4) = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | ALPHA: (16) implies:
% 249.49/59.10 | | | | (17) op(e1, e4) = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | GROUND_INST: instantiating (2) with e3, e4, e4, e1, simplifying with
% 249.49/59.10 | | | | (7), (17) gives:
% 249.49/59.10 | | | | (18) e4 = e3
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REDUCE: (9), (18) imply:
% 249.49/59.10 | | | | (19) $false
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | CLOSE: (19) is inconsistent.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | Case 2:
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | (20) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.10 | | | |
% 249.49/59.10 | | | | REF_CLOSE: (8), (10), (20) are inconsistent by sub-proof #534.
% 249.49/59.10 | | | |
% 249.49/59.10 | | | End of split
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #150 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) all_252_2 = e1
% 249.49/59.10 (2) ~ (e4 = e1)
% 249.49/59.10 (3) all_252_0 = e3
% 249.49/59.10 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.10 (5) ~ (e4 = e3)
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (4) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (6) all_252_0 = e4 & op(e4, e4) = e4
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #547.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (7) all_252_2 = e4 & op(e3, e4) = e4
% 249.49/59.10 | |
% 249.49/59.10 | | ALPHA: (7) implies:
% 249.49/59.10 | | (8) all_252_2 = e4
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #605.
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #151 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) ~ (all_10_2 = e4)
% 249.49/59.10 (2) ~ (all_244_0 = all_30_2)
% 249.49/59.10 (3) op(e4, e0) = all_30_2
% 249.49/59.10 (4) all_252_6 = e0
% 249.49/59.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (6) op(e2, e3) = all_10_2
% 249.49/59.10 (7) ~ (e4 = e0)
% 249.49/59.10 (8) op(all_244_8, all_244_8) = e2
% 249.49/59.10 (9) op(e2, e2) = all_244_8
% 249.49/59.10 (10) op(e2, e1) = all_38_2
% 249.49/59.10 (11) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.10 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.10 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.10 (12) ~ (all_244_0 = e2)
% 249.49/59.10 (13) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.10 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.10 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.10 (14) op(e3, e1) = all_36_2
% 249.49/59.10 (15) all_148_2 = e0
% 249.49/59.10 (16) op(all_40_2, e0) = e2
% 249.49/59.10 (17) ~ (all_148_2 = e0) | ( ~ (all_148_0 = e1) & op(e4, e0) = all_148_1 &
% 249.49/59.10 op(e0, all_148_1) = all_148_0 & $i(all_148_0) & $i(all_148_1)) | ( ~
% 249.49/59.10 (all_148_1 = e3) & op(e4, e0) = all_148_1 & $i(all_148_1))
% 249.49/59.10 (18) op(e2, all_30_2) = e4
% 249.49/59.10 (19) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.10 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.10 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.10 (20) op(e3, e1) = e4
% 249.49/59.10 (21) op(e4, e4) = all_244_0
% 249.49/59.10 (22) ~ (all_38_2 = all_36_2)
% 249.49/59.10 (23) op(e2, e0) = all_40_2
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (17) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (24) ~ (all_148_2 = e0)
% 249.49/59.10 | |
% 249.49/59.10 | | REDUCE: (15), (24) imply:
% 249.49/59.10 | | (25) $false
% 249.49/59.10 | |
% 249.49/59.10 | | CLOSE: (25) is inconsistent.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (26) ( ~ (all_148_0 = e1) & op(e4, e0) = all_148_1 & op(e0, all_148_1) =
% 249.49/59.10 | | all_148_0 & $i(all_148_0) & $i(all_148_1)) | ( ~ (all_148_1 = e3)
% 249.49/59.10 | | & op(e4, e0) = all_148_1 & $i(all_148_1))
% 249.49/59.10 | |
% 249.49/59.10 | | BETA: splitting (26) gives:
% 249.49/59.10 | |
% 249.49/59.10 | | Case 1:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (27) ~ (all_148_0 = e1) & op(e4, e0) = all_148_1 & op(e0, all_148_1) =
% 249.49/59.10 | | | all_148_0 & $i(all_148_0) & $i(all_148_1)
% 249.49/59.10 | | |
% 249.49/59.10 | | | ALPHA: (27) implies:
% 249.49/59.10 | | | (28) op(e4, e0) = all_148_1
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.10 | | | (13), (14), (16), (18), (19), (20), (21), (22), (23), (28) are
% 249.49/59.10 | | | inconsistent by sub-proof #152.
% 249.49/59.10 | | |
% 249.49/59.10 | | Case 2:
% 249.49/59.10 | | |
% 249.49/59.10 | | | (29) ~ (all_148_1 = e3) & op(e4, e0) = all_148_1 & $i(all_148_1)
% 249.49/59.10 | | |
% 249.49/59.10 | | | ALPHA: (29) implies:
% 249.49/59.10 | | | (30) op(e4, e0) = all_148_1
% 249.49/59.10 | | |
% 249.49/59.10 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.10 | | | (13), (14), (16), (18), (19), (20), (21), (22), (23), (30) are
% 249.49/59.10 | | | inconsistent by sub-proof #152.
% 249.49/59.10 | | |
% 249.49/59.10 | | End of split
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #152 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) ~ (all_10_2 = e4)
% 249.49/59.10 (2) ~ (all_244_0 = all_30_2)
% 249.49/59.10 (3) op(e4, e0) = all_30_2
% 249.49/59.10 (4) op(e4, e0) = all_148_1
% 249.49/59.10 (5) all_252_6 = e0
% 249.49/59.10 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (7) op(e2, e3) = all_10_2
% 249.49/59.10 (8) ~ (e4 = e0)
% 249.49/59.10 (9) op(all_244_8, all_244_8) = e2
% 249.49/59.10 (10) op(e2, e2) = all_244_8
% 249.49/59.10 (11) op(e2, e1) = all_38_2
% 249.49/59.10 (12) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.10 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.10 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.10 (13) ~ (all_244_0 = e2)
% 249.49/59.10 (14) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.10 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.10 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.10 (15) op(e3, e1) = all_36_2
% 249.49/59.10 (16) op(all_40_2, e0) = e2
% 249.49/59.10 (17) op(e2, all_30_2) = e4
% 249.49/59.10 (18) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.10 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.10 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.10 (19) op(e3, e1) = e4
% 249.49/59.10 (20) op(e4, e4) = all_244_0
% 249.49/59.10 (21) ~ (all_38_2 = all_36_2)
% 249.49/59.10 (22) op(e2, e0) = all_40_2
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | GROUND_INST: instantiating (6) with all_36_2, e4, e1, e3, simplifying with
% 249.49/59.10 | (15), (19) gives:
% 249.49/59.10 | (23) all_36_2 = e4
% 249.49/59.10 |
% 249.49/59.10 | GROUND_INST: instantiating (6) with all_30_2, all_148_1, e0, e4, simplifying
% 249.49/59.10 | with (3), (4) gives:
% 249.49/59.10 | (24) all_148_1 = all_30_2
% 249.49/59.10 |
% 249.49/59.10 | REDUCE: (21), (23) imply:
% 249.49/59.10 | (25) ~ (all_38_2 = e4)
% 249.49/59.10 |
% 249.49/59.10 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 249.49/59.10 | (14), (16), (17), (18), (20), (22), (25) are inconsistent by
% 249.49/59.10 | sub-proof #153.
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #153 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) ~ (all_10_2 = e4)
% 249.49/59.10 (2) ~ (all_244_0 = all_30_2)
% 249.49/59.10 (3) op(e4, e0) = all_30_2
% 249.49/59.10 (4) all_252_6 = e0
% 249.49/59.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (6) op(e2, e3) = all_10_2
% 249.49/59.10 (7) ~ (e4 = e0)
% 249.49/59.10 (8) op(all_244_8, all_244_8) = e2
% 249.49/59.10 (9) op(e2, e2) = all_244_8
% 249.49/59.10 (10) op(e2, e1) = all_38_2
% 249.49/59.10 (11) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.10 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.10 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.10 (12) ~ (all_244_0 = e2)
% 249.49/59.10 (13) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.10 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.10 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.10 (14) op(all_40_2, e0) = e2
% 249.49/59.10 (15) ~ (all_38_2 = e4)
% 249.49/59.10 (16) op(e2, all_30_2) = e4
% 249.49/59.10 (17) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.10 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.10 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.10 (18) op(e4, e4) = all_244_0
% 249.49/59.10 (19) op(e2, e0) = all_40_2
% 249.49/59.10
% 249.49/59.10 Begin of proof
% 249.49/59.10 |
% 249.49/59.10 | BETA: splitting (11) gives:
% 249.49/59.10 |
% 249.49/59.10 | Case 1:
% 249.49/59.10 | |
% 249.49/59.10 | | (20) ~ (all_30_2 = e2)
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 249.49/59.10 | | (15), (17), (18), (19), (20) are inconsistent by sub-proof #216.
% 249.49/59.10 | |
% 249.49/59.10 | Case 2:
% 249.49/59.10 | |
% 249.49/59.10 | | (21) all_30_2 = e2
% 249.49/59.10 | |
% 249.49/59.10 | | REF_CLOSE: (2), (5), (8), (9), (16), (18), (21) are inconsistent by
% 249.49/59.10 | | sub-proof #162.
% 249.49/59.10 | |
% 249.49/59.10 | End of split
% 249.49/59.10 |
% 249.49/59.10 End of proof
% 249.49/59.10
% 249.49/59.10 Sub-proof #154 shows that the following formulas are inconsistent:
% 249.49/59.10 ----------------------------------------------------------------
% 249.49/59.10 (1) ~ (all_6_2 = e3)
% 249.49/59.10 (2) ~ (all_30_2 = all_26_2)
% 249.49/59.10 (3) ~ (all_4_2 = e4)
% 249.49/59.10 (4) ~ (all_10_2 = e4)
% 249.49/59.10 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.10 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.10 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.10 (6) ~ (all_244_0 = all_30_2)
% 249.49/59.10 (7) op(e4, e0) = all_30_2
% 249.49/59.10 (8) op(e0, e2) = e3
% 249.49/59.10 (9) all_252_6 = e0
% 249.49/59.10 (10) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 249.49/59.10 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2,
% 249.49/59.10 e3) = all_28_1 & $i(all_28_1))
% 249.49/59.10 (11) op(all_38_2, e1) = e2
% 249.49/59.10 (12) ~ (e2 = e0)
% 249.49/59.10 (13) op(all_38_2, all_4_2) = e1
% 249.49/59.10 (14) ~ (e1 = e0)
% 249.49/59.10 (15) ~ (all_22_2 = e3)
% 249.49/59.10 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.10 (17) op(e2, e3) = all_10_2
% 249.49/59.10 (18) ~ (e3 = e2)
% 249.49/59.10 (19) ~ (e4 = e0)
% 249.49/59.10 (20) op(all_244_8, all_244_8) = e2
% 249.49/59.10 (21) op(e2, e2) = all_244_8
% 249.49/59.10 (22) op(e2, e1) = all_38_2
% 249.49/59.10 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.10 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.10 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.10 (24) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.10 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.10 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.11 (25) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.11 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.11 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.11 (26) op(e4, e2) = all_6_2
% 249.49/59.11 (27) ~ (all_8_2 = all_4_2)
% 249.49/59.11 (28) ~ (e2 = e1)
% 249.49/59.11 (29) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.11 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.11 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.11 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.11 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.11 op(e0, e1) = e0)))
% 249.49/59.11 (30) op(e3, e2) = e0
% 249.49/59.11 (31) op(e0, e2) = all_28_2
% 249.49/59.11 (32) ~ (e4 = e1)
% 249.49/59.11 (33) ~ (all_244_0 = e2)
% 249.49/59.11 (34) ~ (all_6_2 = e1)
% 249.49/59.11 (35) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.11 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.11 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.11 (36) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.11 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.11 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.11 (37) ~ (all_8_2 = e3)
% 249.49/59.11 (38) ~ (e3 = e0)
% 249.49/59.11 (39) ~ (all_38_2 = e0)
% 249.49/59.11 (40) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.11 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.11 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.11 (41) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.11 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.11 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.11 (42) ~ (e3 = e1)
% 249.49/59.11 (43) ~ (all_8_2 = e1)
% 249.49/59.11 (44) op(all_40_2, e0) = e2
% 249.49/59.11 (45) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.11 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.11 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.11 (46) ~ (all_22_2 = e1)
% 249.49/59.11 (47) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.11 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.11 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.11 (48) ~ (all_28_2 = e2)
% 249.49/59.11 (49) op(all_6_2, e0) = e2
% 249.49/59.11 (50) op(e0, e3) = all_22_2
% 249.49/59.11 (51) all_242_2 = all_38_2
% 249.49/59.11 (52) ( ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2, all_14_1) =
% 249.49/59.11 all_14_0 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e4,
% 249.49/59.11 e2) = all_14_1 & $i(all_14_1))
% 249.49/59.11 (53) all_252_20 = e2
% 249.49/59.11 (54) op(e2, all_30_2) = e4
% 249.49/59.11 (55) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.11 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.11 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.11 (56) ~ (all_244_8 = e3)
% 249.49/59.11 (57) op(e4, e1) = all_26_2
% 249.49/59.11 (58) ~ (all_8_2 = all_6_2)
% 249.49/59.11 (59) op(e4, e4) = all_244_0
% 249.49/59.11 (60) ~ (e4 = e3)
% 249.49/59.11 (61) op(e0, e1) = all_20_2
% 249.49/59.11 (62) op(e1, e2) = all_4_2
% 249.49/59.11 (63) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.11 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.11 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.11 (64) ~ (e4 = e2)
% 249.49/59.11 (65) op(e3, e2) = all_8_2
% 249.49/59.11 (66) ~ (all_20_2 = e4)
% 249.49/59.11 (67) op(e2, e0) = all_40_2
% 249.49/59.11 (68) ~ (all_20_2 = e3)
% 249.49/59.11 (69) op(all_8_2, e2) = e3
% 249.49/59.11 (70) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.11 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.11 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.11 (71) ~ (all_4_2 = e3)
% 249.49/59.11
% 249.49/59.11 Begin of proof
% 249.49/59.11 |
% 249.49/59.11 | BETA: splitting (10) gives:
% 249.49/59.11 |
% 249.49/59.11 | Case 1:
% 249.49/59.11 | |
% 249.49/59.11 | | (72) ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 249.49/59.11 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 249.49/59.11 | |
% 249.49/59.11 | | ALPHA: (72) implies:
% 249.49/59.11 | | (73) op(e2, e3) = all_28_1
% 249.49/59.11 | |
% 249.49/59.11 | | BETA: splitting (63) gives:
% 249.49/59.11 | |
% 249.49/59.11 | | Case 1:
% 249.49/59.11 | | |
% 249.49/59.11 | | | (74) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2)
% 249.49/59.11 | | | = e3)
% 249.49/59.11 | | |
% 249.49/59.11 | | | BETA: splitting (74) gives:
% 249.49/59.11 | | |
% 249.49/59.11 | | | Case 1:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (75) all_252_4 = e3 & op(e4, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | ALPHA: (75) implies:
% 249.49/59.11 | | | | (76) op(e4, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | BETA: splitting (52) gives:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | Case 1:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (77) ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2, all_14_1)
% 249.49/59.11 | | | | | = all_14_0 & $i(all_14_0) & $i(all_14_1)
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (77) implies:
% 249.49/59.11 | | | | | (78) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (1), (16), (26), (76), (78) are inconsistent by sub-proof
% 249.49/59.11 | | | | | #161.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | Case 2:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (79) ~ (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1)
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (79) implies:
% 249.49/59.11 | | | | | (80) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (1), (16), (26), (76), (80) are inconsistent by sub-proof
% 249.49/59.11 | | | | | #161.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | End of split
% 249.49/59.11 | | | |
% 249.49/59.11 | | | Case 2:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (81) all_252_5 = e3 & op(e3, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | REF_CLOSE: (16), (30), (38), (65), (81) are inconsistent by sub-proof
% 249.49/59.11 | | | | #576.
% 249.49/59.11 | | | |
% 249.49/59.11 | | | End of split
% 249.49/59.11 | | |
% 249.49/59.11 | | Case 2:
% 249.49/59.11 | | |
% 249.49/59.11 | | | (82) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2)
% 249.49/59.11 | | | = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.11 | | |
% 249.49/59.11 | | | BETA: splitting (82) gives:
% 249.49/59.11 | | |
% 249.49/59.11 | | | Case 1:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (83) all_252_8 = e3 & op(e2, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | ALPHA: (83) implies:
% 249.49/59.11 | | | | (84) op(e2, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | REF_CLOSE: (16), (21), (56), (84) are inconsistent by sub-proof #877.
% 249.49/59.11 | | | |
% 249.49/59.11 | | | Case 2:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (85) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0,
% 249.49/59.11 | | | | e2) = e3)
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | BETA: splitting (85) gives:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | Case 1:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (86) all_252_14 = e3 & op(e1, e2) = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (16), (62), (71), (86) are inconsistent by sub-proof #858.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | Case 2:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (87) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (87) implies:
% 249.49/59.11 | | | | | (88) all_252_22 = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | BETA: splitting (52) gives:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | Case 1:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | (89) ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2,
% 249.49/59.11 | | | | | | all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1)
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | ALPHA: (89) implies:
% 249.49/59.11 | | | | | | (90) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (11), (12), (13), (16),
% 249.49/59.11 | | | | | | (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 249.49/59.11 | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (37),
% 249.49/59.11 | | | | | | (39), (40), (41), (42), (43), (44), (47), (48), (49),
% 249.49/59.11 | | | | | | (51), (54), (55), (57), (58), (59), (60), (62), (64),
% 249.49/59.11 | | | | | | (65), (67), (69), (70), (73), (88), (90) are inconsistent
% 249.49/59.11 | | | | | | by sub-proof #156.
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | Case 2:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | (91) ~ (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1)
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | ALPHA: (91) implies:
% 249.49/59.11 | | | | | | (92) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (11), (12), (13), (16),
% 249.49/59.11 | | | | | | (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 249.49/59.11 | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (37),
% 249.49/59.11 | | | | | | (39), (40), (41), (42), (43), (44), (47), (48), (49),
% 249.49/59.11 | | | | | | (51), (54), (55), (57), (58), (59), (60), (62), (64),
% 249.49/59.11 | | | | | | (65), (67), (69), (70), (73), (88), (92) are inconsistent
% 249.49/59.11 | | | | | | by sub-proof #156.
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | End of split
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | End of split
% 249.49/59.11 | | | |
% 249.49/59.11 | | | End of split
% 249.49/59.11 | | |
% 249.49/59.11 | | End of split
% 249.49/59.11 | |
% 249.49/59.11 | Case 2:
% 249.49/59.11 | |
% 249.49/59.11 | | (93) ~ (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1)
% 249.49/59.11 | |
% 249.49/59.11 | | ALPHA: (93) implies:
% 249.49/59.11 | | (94) ~ (all_28_1 = e4)
% 249.49/59.11 | | (95) op(e2, e3) = all_28_1
% 249.49/59.11 | |
% 249.49/59.11 | | BETA: splitting (36) gives:
% 249.49/59.11 | |
% 249.49/59.11 | | Case 1:
% 249.49/59.11 | | |
% 249.49/59.11 | | | (96) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0,
% 249.49/59.11 | | | e3) = e3)
% 249.49/59.11 | | |
% 249.49/59.11 | | | REF_CLOSE: (15), (16), (18), (50), (53), (96) are inconsistent by
% 249.49/59.11 | | | sub-proof #167.
% 249.49/59.11 | | |
% 249.49/59.11 | | Case 2:
% 249.49/59.11 | | |
% 249.49/59.11 | | | (97) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.11 | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.11 | | |
% 249.49/59.11 | | | BETA: splitting (97) gives:
% 249.49/59.11 | | |
% 249.49/59.11 | | | Case 1:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (98) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | ALPHA: (98) implies:
% 249.49/59.11 | | | | (99) all_252_22 = e3
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | BETA: splitting (52) gives:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | Case 1:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (100) ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2, all_14_1)
% 249.49/59.11 | | | | | = all_14_0 & $i(all_14_0) & $i(all_14_1)
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (100) implies:
% 249.49/59.11 | | | | | (101) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (2), (3), (6), (7), (9), (11), (12), (13), (16), (17),
% 249.49/59.11 | | | | | (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 249.49/59.11 | | | | | (30), (31), (32), (33), (34), (35), (37), (39), (40), (41),
% 249.49/59.11 | | | | | (42), (43), (44), (47), (48), (49), (51), (54), (55), (57),
% 249.49/59.11 | | | | | (58), (59), (60), (62), (64), (65), (67), (69), (70), (94),
% 249.49/59.11 | | | | | (95), (99), (101) are inconsistent by sub-proof #155.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | Case 2:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (102) ~ (all_14_1 = e3) & op(e4, e2) = all_14_1 & $i(all_14_1)
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (102) implies:
% 249.49/59.11 | | | | | (103) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (2), (3), (6), (7), (9), (11), (12), (13), (16), (17),
% 249.49/59.11 | | | | | (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 249.49/59.11 | | | | | (30), (31), (32), (33), (34), (35), (37), (39), (40), (41),
% 249.49/59.11 | | | | | (42), (43), (44), (47), (48), (49), (51), (54), (55), (57),
% 249.49/59.11 | | | | | (58), (59), (60), (62), (64), (65), (67), (69), (70), (94),
% 249.49/59.11 | | | | | (95), (99), (103) are inconsistent by sub-proof #155.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | End of split
% 249.49/59.11 | | | |
% 249.49/59.11 | | | Case 2:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | (104) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 249.49/59.11 | | | | e0) = e3)
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | BETA: splitting (104) gives:
% 249.49/59.11 | | | |
% 249.49/59.11 | | | | Case 1:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (105) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (105) implies:
% 249.49/59.11 | | | | | (106) op(e0, e1) = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | REF_CLOSE: (16), (61), (68), (106) are inconsistent by sub-proof #974.
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | Case 2:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | (107) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | ALPHA: (107) implies:
% 249.49/59.11 | | | | | (108) all_252_24 = e3
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | BETA: splitting (5) gives:
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | | Case 1:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | (109) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 249.49/59.11 | | | | | | op(e0, e3) = e4)
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | BETA: splitting (109) gives:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | Case 1:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | (110) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | REF_CLOSE: (53), (64), (110) are inconsistent by sub-proof #543.
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | Case 2:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | (111) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | ALPHA: (111) implies:
% 249.49/59.11 | | | | | | | (112) all_252_21 = e4
% 249.49/59.11 | | | | | | | (113) op(e0, e3) = e4
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | BETA: splitting (29) gives:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (114) all_252_24 = e0 & op(e0, e0) = e0
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | REF_CLOSE: (38), (108), (114) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | #533.
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (115) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0
% 249.49/59.11 | | | | | | | | & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0)
% 249.49/59.11 | | | | | | | | = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.11 | | | | | | | | ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 249.49/59.11 | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2)
% 249.49/59.11 | | | | | | | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | ALPHA: (115) implies:
% 249.49/59.11 | | | | | | | | (116) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 249.49/59.11 | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) =
% 249.49/59.11 | | | | | | | | e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | BETA: splitting (116) gives:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | (117) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 =
% 249.49/59.11 | | | | | | | | | e0 & op(e0, e3) = e0)
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | REF_CLOSE: (12), (19), (53), (112), (117) are inconsistent by
% 249.49/59.11 | | | | | | | | | sub-proof #184.
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | (118) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 =
% 249.49/59.11 | | | | | | | | | e0 & op(e0, e1) = e0)
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | BETA: splitting (118) gives:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | (119) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | ALPHA: (119) implies:
% 249.49/59.11 | | | | | | | | | | (120) op(e0, e2) = e0
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | REF_CLOSE: (8), (16), (31), (38), (120) are inconsistent by
% 249.49/59.11 | | | | | | | | | | sub-proof #473.
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | (121) all_252_23 = e0 & op(e0, e1) = e0
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | ALPHA: (121) implies:
% 249.49/59.11 | | | | | | | | | | (122) all_252_23 = e0
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | BETA: splitting (45) gives:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | (123) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 249.49/59.11 | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | BETA: splitting (123) gives:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | (124) all_252_20 = e1 & op(e0, e4) = e1
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | REF_CLOSE: (28), (53), (124) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | | | | | #544.
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | (125) all_252_21 = e1 & op(e0, e3) = e1
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | ALPHA: (125) implies:
% 249.49/59.11 | | | | | | | | | | | | (126) op(e0, e3) = e1
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | REF_CLOSE: (16), (32), (113), (126) are inconsistent by
% 249.49/59.11 | | | | | | | | | | | | sub-proof #828.
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | (127) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 249.49/59.11 | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 249.49/59.11 | | | | | | | | | | | op(e0, e0) = e1)
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | BETA: splitting (127) gives:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | (128) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | ALPHA: (128) implies:
% 249.49/59.11 | | | | | | | | | | | | (129) op(e0, e2) = e1
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | REF_CLOSE: (8), (16), (31), (42), (129) are inconsistent by
% 249.49/59.11 | | | | | | | | | | | | sub-proof #641.
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | (130) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 249.49/59.11 | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | BETA: splitting (130) gives:
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | | (131) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | | ALPHA: (131) implies:
% 249.49/59.11 | | | | | | | | | | | | | (132) all_252_23 = e1
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | | REF_CLOSE: (14), (122), (132) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | | | | | | #515.
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | | (133) all_252_24 = e1 & op(e0, e0) = e1
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | | REF_CLOSE: (42), (108), (133) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | | | | | | #526.
% 249.49/59.11 | | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | End of split
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | End of split
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | End of split
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | Case 2:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | (134) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 249.49/59.11 | | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | BETA: splitting (134) gives:
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | | Case 1:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | (135) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | ALPHA: (135) implies:
% 249.49/59.11 | | | | | | | (136) all_252_22 = e4
% 249.49/59.11 | | | | | | | (137) op(e0, e2) = e4
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | BETA: splitting (52) gives:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (138) ~ (all_14_0 = e1) & op(e4, e2) = all_14_1 & op(e2,
% 249.49/59.11 | | | | | | | | all_14_1) = all_14_0 & $i(all_14_0) & $i(all_14_1)
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | ALPHA: (138) implies:
% 249.49/59.11 | | | | | | | | (139) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | GROUND_INST: instantiating (16) with e3, e4, e2, e0, simplifying
% 249.49/59.11 | | | | | | | | with (8), (137) gives:
% 249.49/59.11 | | | | | | | | (140) e4 = e3
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | COMBINE_EQS: (136), (140) imply:
% 249.49/59.11 | | | | | | | | (141) all_252_22 = e3
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (9), (11), (12), (13), (16),
% 249.49/59.11 | | | | | | | | (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 249.49/59.11 | | | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (37),
% 249.49/59.11 | | | | | | | | (39), (40), (41), (42), (43), (44), (47), (48), (49),
% 249.49/59.11 | | | | | | | | (51), (54), (55), (57), (58), (59), (60), (62), (64),
% 249.49/59.11 | | | | | | | | (65), (67), (69), (70), (94), (95), (139), (141) are
% 249.49/59.11 | | | | | | | | inconsistent by sub-proof #155.
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (142) ~ (all_14_1 = e3) & op(e4, e2) = all_14_1 &
% 249.49/59.11 | | | | | | | | $i(all_14_1)
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | ALPHA: (142) implies:
% 249.49/59.11 | | | | | | | | (143) op(e4, e2) = all_14_1
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | BETA: splitting (45) gives:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | (144) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 =
% 249.49/59.11 | | | | | | | | | e1 & op(e0, e3) = e1)
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | REF_CLOSE: (16), (28), (46), (50), (53), (144) are
% 249.49/59.11 | | | | | | | | | inconsistent by sub-proof #199.
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | (145) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 =
% 249.49/59.11 | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 249.49/59.11 | | | | | | | | | e0) = e1)
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | BETA: splitting (145) gives:
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | (146) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | ALPHA: (146) implies:
% 249.49/59.11 | | | | | | | | | | (147) op(e0, e2) = e1
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | REF_CLOSE: (8), (16), (31), (42), (147) are inconsistent by
% 249.49/59.11 | | | | | | | | | | sub-proof #641.
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | (148) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 =
% 249.49/59.11 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | BETA: splitting (148) gives:
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | GROUND_INST: instantiating (16) with e3, e4, e2, e0,
% 249.49/59.11 | | | | | | | | | | | simplifying with (8), (137) gives:
% 249.49/59.11 | | | | | | | | | | | (149) e4 = e3
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | COMBINE_EQS: (136), (149) imply:
% 249.49/59.11 | | | | | | | | | | | (150) all_252_22 = e3
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (9), (11), (12), (13), (16),
% 249.49/59.11 | | | | | | | | | | | (17), (19), (20), (21), (22), (23), (24), (25),
% 249.49/59.11 | | | | | | | | | | | (26), (27), (28), (30), (31), (32), (33), (34),
% 249.49/59.11 | | | | | | | | | | | (35), (37), (39), (40), (41), (42), (43), (44),
% 249.49/59.11 | | | | | | | | | | | (47), (48), (49), (51), (54), (55), (57), (58),
% 249.49/59.11 | | | | | | | | | | | (59), (60), (62), (64), (65), (67), (69), (70),
% 249.49/59.11 | | | | | | | | | | | (94), (95), (143), (150) are inconsistent by
% 249.49/59.11 | | | | | | | | | | | sub-proof #155.
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | (151) all_252_24 = e1 & op(e0, e0) = e1
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | | REF_CLOSE: (42), (108), (151) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | | | | #526.
% 249.49/59.11 | | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | | |
% 249.49/59.11 | | | | | | | | | End of split
% 249.49/59.11 | | | | | | | | |
% 249.49/59.11 | | | | | | | | End of split
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | End of split
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | Case 2:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | (152) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 249.49/59.11 | | | | | | | op(e0, e0) = e4)
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | BETA: splitting (152) gives:
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | | Case 1:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (153) all_252_23 = e4 & op(e0, e1) = e4
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | REF_CLOSE: (16), (61), (66), (153) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | #912.
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | Case 2:
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | (154) all_252_24 = e4 & op(e0, e0) = e4
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | | REF_CLOSE: (60), (108), (154) are inconsistent by sub-proof
% 249.49/59.11 | | | | | | | | #421.
% 249.49/59.11 | | | | | | | |
% 249.49/59.11 | | | | | | | End of split
% 249.49/59.11 | | | | | | |
% 249.49/59.11 | | | | | | End of split
% 249.49/59.11 | | | | | |
% 249.49/59.11 | | | | | End of split
% 249.49/59.11 | | | | |
% 249.49/59.11 | | | | End of split
% 249.49/59.11 | | | |
% 249.49/59.11 | | | End of split
% 249.49/59.11 | | |
% 249.49/59.11 | | End of split
% 249.49/59.11 | |
% 249.49/59.11 | End of split
% 249.49/59.11 |
% 249.49/59.11 End of proof
% 249.49/59.11
% 249.49/59.11 Sub-proof #155 shows that the following formulas are inconsistent:
% 249.49/59.11 ----------------------------------------------------------------
% 249.49/59.11 (1) ~ (all_30_2 = all_26_2)
% 249.49/59.11 (2) ~ (all_4_2 = e4)
% 249.49/59.11 (3) ~ (all_244_0 = all_30_2)
% 249.49/59.11 (4) op(e4, e0) = all_30_2
% 249.49/59.11 (5) all_252_6 = e0
% 249.49/59.11 (6) op(all_38_2, e1) = e2
% 249.49/59.11 (7) ~ (e2 = e0)
% 249.49/59.11 (8) op(all_38_2, all_4_2) = e1
% 249.49/59.11 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.11 (10) op(e2, e3) = all_10_2
% 249.49/59.11 (11) ~ (e4 = e0)
% 249.49/59.11 (12) op(all_244_8, all_244_8) = e2
% 249.49/59.11 (13) op(e2, e2) = all_244_8
% 249.49/59.11 (14) op(e2, e1) = all_38_2
% 249.49/59.11 (15) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.11 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.11 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.11 (16) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.11 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.11 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.11 (17) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.11 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.11 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.11 (18) op(e4, e2) = all_6_2
% 249.49/59.11 (19) ~ (all_8_2 = all_4_2)
% 249.49/59.11 (20) ~ (e2 = e1)
% 249.49/59.11 (21) op(e3, e2) = e0
% 249.49/59.11 (22) op(e0, e2) = all_28_2
% 249.49/59.11 (23) ~ (e4 = e1)
% 249.49/59.11 (24) ~ (all_244_0 = e2)
% 249.49/59.11 (25) ~ (all_6_2 = e1)
% 249.49/59.11 (26) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.11 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.11 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.11 (27) all_252_22 = e3
% 249.49/59.11 (28) ~ (all_8_2 = e3)
% 249.49/59.11 (29) ~ (all_38_2 = e0)
% 249.49/59.11 (30) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.11 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.11 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.12 (31) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.12 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.12 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.12 (32) ~ (e3 = e1)
% 249.49/59.12 (33) ~ (all_8_2 = e1)
% 249.49/59.12 (34) op(all_40_2, e0) = e2
% 249.49/59.12 (35) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.12 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.12 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.12 (36) ~ (all_28_2 = e2)
% 249.49/59.12 (37) op(all_6_2, e0) = e2
% 249.49/59.12 (38) all_242_2 = all_38_2
% 249.49/59.12 (39) op(e2, all_30_2) = e4
% 249.49/59.12 (40) op(e4, e2) = all_14_1
% 249.49/59.12 (41) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.12 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.12 (42) op(e4, e1) = all_26_2
% 249.49/59.12 (43) ~ (all_8_2 = all_6_2)
% 249.49/59.12 (44) op(e4, e4) = all_244_0
% 249.49/59.12 (45) ~ (e4 = e3)
% 249.49/59.12 (46) ~ (all_28_1 = e4)
% 249.49/59.12 (47) op(e2, e3) = all_28_1
% 249.49/59.12 (48) op(e1, e2) = all_4_2
% 249.49/59.12 (49) ~ (e4 = e2)
% 249.49/59.12 (50) op(e3, e2) = all_8_2
% 249.49/59.12 (51) op(e2, e0) = all_40_2
% 249.49/59.12 (52) op(all_8_2, e2) = e3
% 249.49/59.12 (53) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.12 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.12 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.12
% 249.49/59.12 Begin of proof
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (9) with all_10_2, all_28_1, e3, e2, simplifying
% 249.49/59.12 | with (10), (47) gives:
% 249.49/59.12 | (54) all_28_1 = all_10_2
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (9) with all_8_2, e0, e2, e3, simplifying with
% 249.49/59.12 | (21), (50) gives:
% 249.49/59.12 | (55) all_8_2 = e0
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (9) with all_6_2, all_14_1, e2, e4, simplifying
% 249.49/59.12 | with (18), (40) gives:
% 249.49/59.12 | (56) all_14_1 = all_6_2
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (46), (54) imply:
% 249.49/59.12 | (57) ~ (all_10_2 = e4)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (43), (55) imply:
% 249.49/59.12 | (58) ~ (all_6_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (58) implies:
% 249.49/59.12 | (59) ~ (all_6_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (19), (55) imply:
% 249.49/59.12 | (60) ~ (all_4_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (60) implies:
% 249.49/59.12 | (61) ~ (all_4_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (28), (55) imply:
% 249.49/59.12 | (62) ~ (e3 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (62) implies:
% 249.49/59.12 | (63) ~ (e3 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (33), (55) imply:
% 249.49/59.12 | (64) ~ (e1 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (64) implies:
% 249.49/59.12 | (65) ~ (e1 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (52), (55) imply:
% 249.49/59.12 | (66) op(e0, e2) = e3
% 249.49/59.12 |
% 249.49/59.12 | BETA: splitting (26) gives:
% 249.49/59.12 |
% 249.49/59.12 | Case 1:
% 249.49/59.12 | |
% 249.49/59.12 | | (67) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 249.49/59.12 | | e0)
% 249.49/59.12 | |
% 249.49/59.12 | | BETA: splitting (67) gives:
% 249.49/59.12 | |
% 249.49/59.12 | | Case 1:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (68) all_252_4 = e0 & op(e4, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (9), (18), (59), (68) are inconsistent by sub-proof #875.
% 249.49/59.12 | | |
% 249.49/59.12 | | Case 2:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (69) all_252_5 = e0 & op(e3, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | ALPHA: (69) implies:
% 249.49/59.12 | | | (70) all_252_5 = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.12 | | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 249.49/59.12 | | | (24), (25), (27), (29), (30), (31), (32), (34), (35), (36),
% 249.49/59.12 | | | (37), (38), (39), (41), (42), (44), (45), (48), (49), (51),
% 249.49/59.12 | | | (53), (57), (65), (70) are inconsistent by sub-proof #158.
% 249.49/59.12 | | |
% 249.49/59.12 | | End of split
% 249.49/59.12 | |
% 249.49/59.12 | Case 2:
% 249.49/59.12 | |
% 249.49/59.12 | | (71) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.12 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.12 | |
% 249.49/59.12 | | REF_CLOSE: (2), (7), (9), (11), (12), (13), (15), (18), (20), (21), (22),
% 249.49/59.12 | | (24), (25), (27), (30), (32), (33), (36), (44), (45), (48), (49),
% 249.49/59.12 | | (50), (53), (61), (63), (65), (66), (71) are inconsistent by
% 249.49/59.12 | | sub-proof #157.
% 249.49/59.12 | |
% 249.49/59.12 | End of split
% 249.49/59.12 |
% 249.49/59.12 End of proof
% 249.49/59.12
% 249.49/59.12 Sub-proof #156 shows that the following formulas are inconsistent:
% 249.49/59.12 ----------------------------------------------------------------
% 249.49/59.12 (1) ~ (all_30_2 = all_26_2)
% 249.49/59.12 (2) ~ (all_4_2 = e4)
% 249.49/59.12 (3) ~ (all_10_2 = e4)
% 249.49/59.12 (4) ~ (all_244_0 = all_30_2)
% 249.49/59.12 (5) op(e4, e0) = all_30_2
% 249.49/59.12 (6) all_252_6 = e0
% 249.49/59.12 (7) op(all_38_2, e1) = e2
% 249.49/59.12 (8) ~ (e2 = e0)
% 249.49/59.12 (9) op(all_38_2, all_4_2) = e1
% 249.49/59.12 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.12 (11) op(e2, e3) = all_10_2
% 249.49/59.12 (12) ~ (e4 = e0)
% 249.49/59.12 (13) op(all_244_8, all_244_8) = e2
% 249.49/59.12 (14) op(e2, e2) = all_244_8
% 249.49/59.12 (15) op(e2, e1) = all_38_2
% 249.49/59.12 (16) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.12 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.12 (17) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.12 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.12 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.12 (18) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.12 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.12 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.12 (19) op(e4, e2) = all_6_2
% 249.49/59.12 (20) ~ (all_8_2 = all_4_2)
% 249.49/59.12 (21) ~ (e2 = e1)
% 249.49/59.12 (22) op(e3, e2) = e0
% 249.49/59.12 (23) op(e0, e2) = all_28_2
% 249.49/59.12 (24) ~ (e4 = e1)
% 249.49/59.12 (25) ~ (all_244_0 = e2)
% 249.49/59.12 (26) ~ (all_6_2 = e1)
% 249.49/59.12 (27) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.12 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.12 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.12 (28) all_252_22 = e3
% 249.49/59.12 (29) ~ (all_8_2 = e3)
% 249.49/59.12 (30) ~ (all_38_2 = e0)
% 249.49/59.12 (31) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.12 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.12 (32) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.12 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.12 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.12 (33) ~ (e3 = e1)
% 249.49/59.12 (34) ~ (all_8_2 = e1)
% 249.49/59.12 (35) op(all_40_2, e0) = e2
% 249.49/59.12 (36) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.12 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.12 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.12 (37) ~ (all_28_2 = e2)
% 249.49/59.12 (38) op(all_6_2, e0) = e2
% 249.49/59.12 (39) all_242_2 = all_38_2
% 249.49/59.12 (40) op(e2, all_30_2) = e4
% 249.49/59.12 (41) op(e4, e2) = all_14_1
% 249.49/59.12 (42) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.12 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.12 (43) op(e4, e1) = all_26_2
% 249.49/59.12 (44) ~ (all_8_2 = all_6_2)
% 249.49/59.12 (45) op(e4, e4) = all_244_0
% 249.49/59.12 (46) ~ (e4 = e3)
% 249.49/59.12 (47) op(e2, e3) = all_28_1
% 249.49/59.12 (48) op(e1, e2) = all_4_2
% 249.49/59.12 (49) ~ (e4 = e2)
% 249.49/59.12 (50) op(e3, e2) = all_8_2
% 249.49/59.12 (51) op(e2, e0) = all_40_2
% 249.49/59.12 (52) op(all_8_2, e2) = e3
% 249.49/59.12 (53) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.12 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.12 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.12
% 249.49/59.12 Begin of proof
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (10) with all_10_2, all_28_1, e3, e2, simplifying
% 249.49/59.12 | with (11), (47) gives:
% 249.49/59.12 | (54) all_28_1 = all_10_2
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (10) with all_8_2, e0, e2, e3, simplifying with
% 249.49/59.12 | (22), (50) gives:
% 249.49/59.12 | (55) all_8_2 = e0
% 249.49/59.12 |
% 249.49/59.12 | GROUND_INST: instantiating (10) with all_6_2, all_14_1, e2, e4, simplifying
% 249.49/59.12 | with (19), (41) gives:
% 249.49/59.12 | (56) all_14_1 = all_6_2
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (44), (55) imply:
% 249.49/59.12 | (57) ~ (all_6_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (57) implies:
% 249.49/59.12 | (58) ~ (all_6_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (20), (55) imply:
% 249.49/59.12 | (59) ~ (all_4_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (59) implies:
% 249.49/59.12 | (60) ~ (all_4_2 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (29), (55) imply:
% 249.49/59.12 | (61) ~ (e3 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (61) implies:
% 249.49/59.12 | (62) ~ (e3 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (34), (55) imply:
% 249.49/59.12 | (63) ~ (e1 = e0)
% 249.49/59.12 |
% 249.49/59.12 | SIMP: (63) implies:
% 249.49/59.12 | (64) ~ (e1 = e0)
% 249.49/59.12 |
% 249.49/59.12 | REDUCE: (52), (55) imply:
% 249.49/59.12 | (65) op(e0, e2) = e3
% 249.49/59.12 |
% 249.49/59.12 | BETA: splitting (27) gives:
% 249.49/59.12 |
% 249.49/59.12 | Case 1:
% 249.49/59.12 | |
% 249.49/59.12 | | (66) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 249.49/59.12 | | e0)
% 249.49/59.12 | |
% 249.49/59.12 | | BETA: splitting (66) gives:
% 249.49/59.12 | |
% 249.49/59.12 | | Case 1:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (67) all_252_4 = e0 & op(e4, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (10), (19), (58), (67) are inconsistent by sub-proof #875.
% 249.49/59.12 | | |
% 249.49/59.12 | | Case 2:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (68) all_252_5 = e0 & op(e3, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | ALPHA: (68) implies:
% 249.49/59.12 | | | (69) all_252_5 = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.12 | | | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 249.49/59.12 | | | (24), (25), (26), (28), (30), (31), (32), (33), (35), (36),
% 249.49/59.12 | | | (37), (38), (39), (40), (42), (43), (45), (46), (48), (49),
% 249.49/59.12 | | | (51), (53), (64), (69) are inconsistent by sub-proof #158.
% 249.49/59.12 | | |
% 249.49/59.12 | | End of split
% 249.49/59.12 | |
% 249.49/59.12 | Case 2:
% 249.49/59.12 | |
% 249.49/59.12 | | (70) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.12 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.12 | |
% 249.49/59.12 | | REF_CLOSE: (2), (8), (10), (12), (13), (14), (16), (19), (21), (22), (23),
% 249.49/59.12 | | (25), (26), (28), (31), (33), (34), (37), (45), (46), (48), (49),
% 249.49/59.12 | | (50), (53), (60), (62), (64), (65), (70) are inconsistent by
% 249.49/59.12 | | sub-proof #157.
% 249.49/59.12 | |
% 249.49/59.12 | End of split
% 249.49/59.12 |
% 249.49/59.12 End of proof
% 249.49/59.12
% 249.49/59.12 Sub-proof #157 shows that the following formulas are inconsistent:
% 249.49/59.12 ----------------------------------------------------------------
% 249.49/59.12 (1) ~ (all_4_2 = e4)
% 249.49/59.12 (2) op(e0, e2) = e3
% 249.49/59.12 (3) ~ (e2 = e0)
% 249.49/59.12 (4) ~ (e1 = e0)
% 249.49/59.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.12 (6) ~ (e4 = e0)
% 249.49/59.12 (7) op(all_244_8, all_244_8) = e2
% 249.49/59.12 (8) op(e2, e2) = all_244_8
% 249.49/59.12 (9) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 249.49/59.12 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 249.49/59.12 | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.12 (10) op(e4, e2) = all_6_2
% 249.49/59.12 (11) ~ (e2 = e1)
% 249.49/59.12 (12) op(e3, e2) = e0
% 249.49/59.12 (13) op(e0, e2) = all_28_2
% 249.49/59.12 (14) ~ (all_244_0 = e2)
% 249.49/59.12 (15) ~ (all_6_2 = e1)
% 249.49/59.12 (16) all_252_22 = e3
% 249.49/59.12 (17) ~ (e3 = e0)
% 249.49/59.12 (18) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.12 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.12 (19) ~ (e3 = e1)
% 249.49/59.12 (20) ~ (all_8_2 = e1)
% 249.49/59.12 (21) ~ (all_28_2 = e2)
% 249.49/59.12 (22) op(e4, e4) = all_244_0
% 249.49/59.12 (23) ~ (e4 = e3)
% 249.49/59.12 (24) op(e1, e2) = all_4_2
% 249.49/59.12 (25) ~ (e4 = e2)
% 249.49/59.12 (26) op(e3, e2) = all_8_2
% 249.49/59.12 (27) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = e0)
% 249.49/59.12 | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.12 (28) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.12 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.12 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.12 (29) ~ (all_4_2 = e0)
% 249.49/59.12
% 249.49/59.12 Begin of proof
% 249.49/59.12 |
% 249.49/59.12 | BETA: splitting (27) gives:
% 249.49/59.12 |
% 249.49/59.12 | Case 1:
% 249.49/59.12 | |
% 249.49/59.12 | | (30) all_252_8 = e0 & op(e2, e2) = e0
% 249.49/59.12 | |
% 249.49/59.12 | | ALPHA: (30) implies:
% 249.49/59.12 | | (31) all_252_8 = e0
% 249.49/59.12 | |
% 249.49/59.12 | | BETA: splitting (18) gives:
% 249.49/59.12 | |
% 249.49/59.12 | | Case 1:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (32) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2)
% 249.49/59.12 | | | = e4)
% 249.49/59.12 | | |
% 249.49/59.12 | | | BETA: splitting (32) gives:
% 249.49/59.12 | | |
% 249.49/59.12 | | | Case 1:
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | (33) all_252_4 = e4 & op(e4, e2) = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | ALPHA: (33) implies:
% 249.49/59.12 | | | | (34) all_252_4 = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | BETA: splitting (28) gives:
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | Case 1:
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | (35) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3,
% 249.49/59.12 | | | | | e2) = e2)
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | BETA: splitting (35) gives:
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | Case 1:
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | (36) all_252_4 = e2 & op(e4, e2) = e2
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | REF_CLOSE: (25), (34), (36) are inconsistent by sub-proof #280.
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | Case 2:
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | (37) all_252_5 = e2 & op(e3, e2) = e2
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | ALPHA: (37) implies:
% 249.49/59.12 | | | | | | (38) op(e3, e2) = e2
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | REF_CLOSE: (3), (5), (12), (38) are inconsistent by sub-proof #643.
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | End of split
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | Case 2:
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | (39) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1,
% 249.49/59.12 | | | | | e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | BETA: splitting (39) gives:
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | | Case 1:
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | (40) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | REF_CLOSE: (3), (31), (40) are inconsistent by sub-proof #201.
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | Case 2:
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | (41) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 249.49/59.12 | | | | | | op(e0, e2) = e2)
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | BETA: splitting (41) gives:
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | | Case 1:
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | (42) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | ALPHA: (42) implies:
% 249.49/59.12 | | | | | | | (43) all_252_14 = e2
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | BETA: splitting (9) gives:
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | Case 1:
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | | (44) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 249.49/59.12 | | | | | | | | op(e3, e2) = e1)
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | | REF_CLOSE: (5), (10), (15), (20), (26), (44) are inconsistent by
% 249.49/59.12 | | | | | | | | sub-proof #928.
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | Case 2:
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | | (45) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 249.49/59.12 | | | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | | BETA: splitting (45) gives:
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | | Case 1:
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | (46) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | ALPHA: (46) implies:
% 249.49/59.12 | | | | | | | | | (47) all_252_8 = e1
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | COMBINE_EQS: (31), (47) imply:
% 249.49/59.12 | | | | | | | | | (48) e1 = e0
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | REDUCE: (4), (48) imply:
% 249.49/59.12 | | | | | | | | | (49) $false
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | CLOSE: (49) is inconsistent.
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | Case 2:
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | (50) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1
% 249.49/59.12 | | | | | | | | | & op(e0, e2) = e1)
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | BETA: splitting (50) gives:
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | | Case 1:
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | | (51) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | | ALPHA: (51) implies:
% 249.49/59.12 | | | | | | | | | | (52) all_252_14 = e1
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | | REF_CLOSE: (11), (43), (52) are inconsistent by sub-proof
% 249.49/59.12 | | | | | | | | | | #861.
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | Case 2:
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | | (53) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | | REF_CLOSE: (16), (19), (53) are inconsistent by sub-proof
% 249.49/59.12 | | | | | | | | | | #160.
% 249.49/59.12 | | | | | | | | | |
% 249.49/59.12 | | | | | | | | | End of split
% 249.49/59.12 | | | | | | | | |
% 249.49/59.12 | | | | | | | | End of split
% 249.49/59.12 | | | | | | | |
% 249.49/59.12 | | | | | | | End of split
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | Case 2:
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | (54) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | | REF_CLOSE: (5), (13), (21), (54) are inconsistent by sub-proof
% 249.49/59.12 | | | | | | | #979.
% 249.49/59.12 | | | | | | |
% 249.49/59.12 | | | | | | End of split
% 249.49/59.12 | | | | | |
% 249.49/59.12 | | | | | End of split
% 249.49/59.12 | | | | |
% 249.49/59.12 | | | | End of split
% 249.49/59.12 | | | |
% 249.49/59.12 | | | Case 2:
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | (55) all_252_5 = e4 & op(e3, e2) = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | ALPHA: (55) implies:
% 249.49/59.12 | | | | (56) op(e3, e2) = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | REF_CLOSE: (5), (6), (12), (56) are inconsistent by sub-proof #645.
% 249.49/59.12 | | | |
% 249.49/59.12 | | | End of split
% 249.49/59.12 | | |
% 249.49/59.12 | | Case 2:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (57) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2)
% 249.49/59.12 | | | = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.12 | | |
% 249.49/59.12 | | | BETA: splitting (57) gives:
% 249.49/59.12 | | |
% 249.49/59.12 | | | Case 1:
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | (58) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | ALPHA: (58) implies:
% 249.49/59.12 | | | | (59) op(e2, e2) = e4
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | REF_CLOSE: (5), (7), (8), (14), (22), (59) are inconsistent by sub-proof
% 249.49/59.12 | | | | #626.
% 249.49/59.12 | | | |
% 249.49/59.12 | | | Case 2:
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | (60) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 = e4 & op(e0,
% 249.49/59.12 | | | | e2) = e4)
% 249.49/59.12 | | | |
% 249.49/59.12 | | | | REF_CLOSE: (1), (5), (16), (23), (24), (60) are inconsistent by
% 249.49/59.12 | | | | sub-proof #159.
% 249.49/59.12 | | | |
% 249.49/59.12 | | | End of split
% 249.49/59.12 | | |
% 249.49/59.12 | | End of split
% 249.49/59.12 | |
% 249.49/59.12 | Case 2:
% 249.49/59.12 | |
% 249.49/59.12 | | (61) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2)
% 249.49/59.12 | | = e0)
% 249.49/59.12 | |
% 249.49/59.12 | | BETA: splitting (61) gives:
% 249.49/59.12 | |
% 249.49/59.12 | | Case 1:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (62) all_252_14 = e0 & op(e1, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (5), (24), (29), (62) are inconsistent by sub-proof #855.
% 249.49/59.12 | | |
% 249.49/59.12 | | Case 2:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (63) all_252_22 = e0 & op(e0, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | ALPHA: (63) implies:
% 249.49/59.12 | | | (64) op(e0, e2) = e0
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (2), (5), (13), (17), (64) are inconsistent by sub-proof #473.
% 249.49/59.12 | | |
% 249.49/59.12 | | End of split
% 249.49/59.12 | |
% 249.49/59.12 | End of split
% 249.49/59.12 |
% 249.49/59.12 End of proof
% 249.49/59.12
% 249.49/59.12 Sub-proof #158 shows that the following formulas are inconsistent:
% 249.49/59.12 ----------------------------------------------------------------
% 249.49/59.12 (1) ~ (all_30_2 = all_26_2)
% 249.49/59.12 (2) ~ (all_4_2 = e4)
% 249.49/59.12 (3) ~ (all_10_2 = e4)
% 249.49/59.12 (4) ~ (all_244_0 = all_30_2)
% 249.49/59.12 (5) op(e4, e0) = all_30_2
% 249.49/59.12 (6) all_252_6 = e0
% 249.49/59.12 (7) op(all_38_2, e1) = e2
% 249.49/59.12 (8) ~ (e2 = e0)
% 249.49/59.12 (9) op(all_38_2, all_4_2) = e1
% 249.49/59.12 (10) ~ (e1 = e0)
% 249.49/59.12 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.12 (12) op(e2, e3) = all_10_2
% 249.49/59.12 (13) ~ (e4 = e0)
% 249.49/59.12 (14) op(all_244_8, all_244_8) = e2
% 249.49/59.12 (15) op(e2, e2) = all_244_8
% 249.49/59.12 (16) op(e2, e1) = all_38_2
% 249.49/59.12 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.12 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.12 (18) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 249.49/59.12 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 249.49/59.12 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 249.49/59.12 (19) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 249.49/59.12 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 249.49/59.12 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 249.49/59.12 (20) op(e4, e2) = all_6_2
% 249.49/59.12 (21) ~ (e2 = e1)
% 249.49/59.12 (22) op(e3, e2) = e0
% 249.49/59.12 (23) op(e0, e2) = all_28_2
% 249.49/59.12 (24) ~ (e4 = e1)
% 249.49/59.12 (25) ~ (all_244_0 = e2)
% 249.49/59.12 (26) ~ (all_6_2 = e1)
% 249.49/59.12 (27) all_252_22 = e3
% 249.49/59.12 (28) ~ (all_38_2 = e0)
% 249.49/59.12 (29) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 249.49/59.12 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.12 (30) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 249.49/59.12 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 249.49/59.12 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 249.49/59.12 (31) ~ (e3 = e1)
% 249.49/59.12 (32) op(all_40_2, e0) = e2
% 249.49/59.12 (33) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.12 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.12 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.12 (34) ~ (all_28_2 = e2)
% 249.49/59.12 (35) op(all_6_2, e0) = e2
% 249.49/59.12 (36) all_242_2 = all_38_2
% 249.49/59.12 (37) op(e2, all_30_2) = e4
% 249.49/59.12 (38) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 249.49/59.12 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 249.49/59.12 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 249.49/59.12 (39) op(e4, e1) = all_26_2
% 249.49/59.12 (40) op(e4, e4) = all_244_0
% 249.49/59.12 (41) ~ (e4 = e3)
% 249.49/59.12 (42) all_252_5 = e0
% 249.49/59.12 (43) op(e1, e2) = all_4_2
% 249.49/59.12 (44) ~ (e4 = e2)
% 249.49/59.12 (45) op(e2, e0) = all_40_2
% 249.49/59.12 (46) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 249.49/59.12 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 249.49/59.12 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 249.49/59.12
% 249.49/59.12 Begin of proof
% 249.49/59.12 |
% 249.49/59.12 | BETA: splitting (19) gives:
% 249.49/59.12 |
% 249.49/59.12 | Case 1:
% 249.49/59.12 | |
% 249.49/59.12 | | (47) ~ (all_30_2 = e2)
% 249.49/59.12 | |
% 249.49/59.12 | | BETA: splitting (18) gives:
% 249.49/59.12 | |
% 249.49/59.12 | | Case 1:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (48) ~ (all_38_2 = e4)
% 249.49/59.12 | | |
% 249.49/59.12 | | | REF_CLOSE: (3), (5), (6), (11), (12), (13), (14), (15), (16), (25), (30),
% 249.49/59.12 | | | (32), (38), (40), (45), (47), (48) are inconsistent by
% 249.49/59.12 | | | sub-proof #216.
% 249.49/59.12 | | |
% 249.49/59.12 | | Case 2:
% 249.49/59.12 | | |
% 249.49/59.12 | | | (49) all_38_2 = e4
% 249.49/59.12 | | |
% 249.49/59.13 | | | COMBINE_EQS: (36), (49) imply:
% 249.49/59.13 | | | (50) all_242_2 = e4
% 249.49/59.13 | | |
% 249.49/59.13 | | | REDUCE: (7), (49) imply:
% 249.49/59.13 | | | (51) op(e4, e1) = e2
% 249.49/59.13 | | |
% 249.49/59.13 | | | BETA: splitting (29) gives:
% 249.49/59.13 | | |
% 249.49/59.13 | | | Case 1:
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | (52) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3,
% 249.49/59.13 | | | | e2) = e4)
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | BETA: splitting (52) gives:
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | Case 1:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | (53) all_252_4 = e4 & op(e4, e2) = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | ALPHA: (53) implies:
% 249.49/59.13 | | | | | (54) op(e4, e2) = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | BETA: splitting (33) gives:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | Case 1:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | (55) ~ (all_242_2 = e4)
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | REDUCE: (50), (55) imply:
% 249.49/59.13 | | | | | | (56) $false
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | CLOSE: (56) is inconsistent.
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | Case 2:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | GROUND_INST: instantiating (11) with all_26_2, e2, e1, e4,
% 249.49/59.13 | | | | | | simplifying with (39), (51) gives:
% 249.49/59.13 | | | | | | (57) all_26_2 = e2
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | GROUND_INST: instantiating (11) with all_6_2, e4, e2, e4,
% 249.49/59.13 | | | | | | simplifying with (20), (54) gives:
% 249.49/59.13 | | | | | | (58) all_6_2 = e4
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | REDUCE: (35), (58) imply:
% 249.49/59.13 | | | | | | (59) op(e4, e0) = e2
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | REF_CLOSE: (5), (11), (47), (59) are inconsistent by sub-proof #830.
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | End of split
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | Case 2:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | (60) all_252_5 = e4 & op(e3, e2) = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | ALPHA: (60) implies:
% 249.49/59.13 | | | | | (61) op(e3, e2) = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | REF_CLOSE: (11), (13), (22), (61) are inconsistent by sub-proof #645.
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | End of split
% 249.49/59.13 | | | |
% 249.49/59.13 | | | Case 2:
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | (62) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1,
% 249.49/59.13 | | | | e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | BETA: splitting (62) gives:
% 249.49/59.13 | | | |
% 249.49/59.13 | | | | Case 1:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | (63) all_252_8 = e4 & op(e2, e2) = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | ALPHA: (63) implies:
% 249.49/59.13 | | | | | (64) all_252_8 = e4
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | BETA: splitting (17) gives:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | Case 1:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | (65) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 249.49/59.13 | | | | | | op(e3, e2) = e1)
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | BETA: splitting (65) gives:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | Case 1:
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | (66) all_252_4 = e1 & op(e4, e2) = e1
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | ALPHA: (66) implies:
% 249.49/59.13 | | | | | | | (67) op(e4, e2) = e1
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | REF_CLOSE: (11), (20), (26), (67) are inconsistent by sub-proof
% 249.49/59.13 | | | | | | | #930.
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | Case 2:
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | (68) all_252_5 = e1 & op(e3, e2) = e1
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | ALPHA: (68) implies:
% 249.49/59.13 | | | | | | | (69) all_252_5 = e1
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | COMBINE_EQS: (42), (69) imply:
% 249.49/59.13 | | | | | | | (70) e1 = e0
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | SIMP: (70) implies:
% 249.49/59.13 | | | | | | | (71) e1 = e0
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | REDUCE: (10), (71) imply:
% 249.49/59.13 | | | | | | | (72) $false
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | CLOSE: (72) is inconsistent.
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | End of split
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | Case 2:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | (73) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 249.49/59.13 | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | BETA: splitting (73) gives:
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | | Case 1:
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | (74) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | REF_CLOSE: (24), (64), (74) are inconsistent by sub-proof #644.
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | Case 2:
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | (75) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 249.49/59.13 | | | | | | | op(e0, e2) = e1)
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | BETA: splitting (75) gives:
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | | Case 1:
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | (76) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | ALPHA: (76) implies:
% 249.49/59.13 | | | | | | | | (77) all_252_14 = e1
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | BETA: splitting (46) gives:
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | Case 1:
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | (78) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 &
% 249.49/59.13 | | | | | | | | | op(e3, e2) = e2)
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | BETA: splitting (78) gives:
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | Case 1:
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | (79) all_252_4 = e2 & op(e4, e2) = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | ALPHA: (79) implies:
% 249.49/59.13 | | | | | | | | | | (80) op(e4, e2) = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | ALPHA: (76) implies:
% 249.49/59.13 | | | | | | | | | | (81) op(e1, e2) = e1
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | GROUND_INST: instantiating (11) with all_4_2, e1, e2, e1,
% 249.49/59.13 | | | | | | | | | | simplifying with (43), (81) gives:
% 249.49/59.13 | | | | | | | | | | (82) all_4_2 = e1
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | GROUND_INST: instantiating (11) with all_6_2, e2, e2, e4,
% 249.49/59.13 | | | | | | | | | | simplifying with (20), (80) gives:
% 249.49/59.13 | | | | | | | | | | (83) all_6_2 = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | REF_CLOSE: (7), (9), (11), (21), (82) are inconsistent by
% 249.49/59.13 | | | | | | | | | | sub-proof #640.
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | Case 2:
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | (84) all_252_5 = e2 & op(e3, e2) = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | ALPHA: (84) implies:
% 249.49/59.13 | | | | | | | | | | (85) all_252_5 = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | COMBINE_EQS: (42), (85) imply:
% 249.49/59.13 | | | | | | | | | | (86) e2 = e0
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | SIMP: (86) implies:
% 249.49/59.13 | | | | | | | | | | (87) e2 = e0
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | REDUCE: (8), (87) imply:
% 249.49/59.13 | | | | | | | | | | (88) $false
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | CLOSE: (88) is inconsistent.
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | End of split
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | Case 2:
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | (89) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2
% 249.49/59.13 | | | | | | | | | & op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) =
% 249.49/59.13 | | | | | | | | | e2)
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | BETA: splitting (89) gives:
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | | Case 1:
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | (90) all_252_8 = e2 & op(e2, e2) = e2
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | REF_CLOSE: (44), (64), (90) are inconsistent by sub-proof
% 249.49/59.13 | | | | | | | | | | #642.
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | Case 2:
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | (91) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 =
% 249.49/59.13 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | BETA: splitting (91) gives:
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | Case 1:
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | | (92) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | | ALPHA: (92) implies:
% 249.49/59.13 | | | | | | | | | | | (93) all_252_14 = e2
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | | REF_CLOSE: (21), (77), (93) are inconsistent by sub-proof
% 249.49/59.13 | | | | | | | | | | | #861.
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | Case 2:
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | | (94) all_252_22 = e2 & op(e0, e2) = e2
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | | REF_CLOSE: (11), (23), (34), (94) are inconsistent by
% 249.49/59.13 | | | | | | | | | | | sub-proof #979.
% 249.49/59.13 | | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | | End of split
% 249.49/59.13 | | | | | | | | | |
% 249.49/59.13 | | | | | | | | | End of split
% 249.49/59.13 | | | | | | | | |
% 249.49/59.13 | | | | | | | | End of split
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | Case 2:
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | (95) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | | REF_CLOSE: (27), (31), (95) are inconsistent by sub-proof #160.
% 249.49/59.13 | | | | | | | |
% 249.49/59.13 | | | | | | | End of split
% 249.49/59.13 | | | | | | |
% 249.49/59.13 | | | | | | End of split
% 249.49/59.13 | | | | | |
% 249.49/59.13 | | | | | End of split
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | Case 2:
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | (96) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 = e4 &
% 249.49/59.13 | | | | | op(e0, e2) = e4)
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | | REF_CLOSE: (2), (11), (27), (41), (43), (96) are inconsistent by
% 249.49/59.13 | | | | | sub-proof #159.
% 249.49/59.13 | | | | |
% 249.49/59.13 | | | | End of split
% 249.49/59.13 | | | |
% 249.49/59.13 | | | End of split
% 249.49/59.13 | | |
% 249.49/59.13 | | End of split
% 249.49/59.13 | |
% 249.49/59.13 | Case 2:
% 249.49/59.13 | |
% 249.49/59.13 | | (97) all_30_2 = e2
% 249.49/59.13 | |
% 249.49/59.13 | | REF_CLOSE: (4), (11), (14), (15), (37), (40), (97) are inconsistent by
% 249.49/59.13 | | sub-proof #162.
% 249.49/59.13 | |
% 249.49/59.13 | End of split
% 249.49/59.13 |
% 249.49/59.13 End of proof
% 249.49/59.13
% 249.49/59.13 Sub-proof #159 shows that the following formulas are inconsistent:
% 249.49/59.13 ----------------------------------------------------------------
% 249.49/59.13 (1) ~ (all_4_2 = e4)
% 249.49/59.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.13 (3) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 249.49/59.13 (4) all_252_22 = e3
% 249.49/59.13 (5) ~ (e4 = e3)
% 249.49/59.13 (6) op(e1, e2) = all_4_2
% 249.49/59.13
% 249.49/59.13 Begin of proof
% 249.49/59.13 |
% 249.49/59.13 | BETA: splitting (3) gives:
% 249.49/59.13 |
% 249.49/59.13 | Case 1:
% 249.49/59.13 | |
% 249.49/59.13 | | (7) all_252_14 = e4 & op(e1, e2) = e4
% 249.49/59.13 | |
% 249.49/59.13 | | ALPHA: (7) implies:
% 249.49/59.13 | | (8) op(e1, e2) = e4
% 249.49/59.13 | |
% 249.49/59.13 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #831.
% 249.49/59.13 | |
% 249.49/59.13 | Case 2:
% 249.49/59.13 | |
% 249.49/59.13 | | (9) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.13 | |
% 249.49/59.13 | | ALPHA: (9) implies:
% 249.49/59.13 | | (10) all_252_22 = e4
% 249.49/59.13 | |
% 249.49/59.13 | | COMBINE_EQS: (4), (10) imply:
% 249.49/59.13 | | (11) e4 = e3
% 249.49/59.13 | |
% 249.49/59.13 | | SIMP: (11) implies:
% 249.49/59.13 | | (12) e4 = e3
% 249.49/59.13 | |
% 249.49/59.13 | | REDUCE: (5), (12) imply:
% 249.49/59.13 | | (13) $false
% 249.49/59.13 | |
% 249.49/59.13 | | CLOSE: (13) is inconsistent.
% 249.49/59.13 | |
% 249.49/59.13 | End of split
% 249.49/59.13 |
% 249.49/59.13 End of proof
% 249.49/59.13
% 249.49/59.13 Sub-proof #160 shows that the following formulas are inconsistent:
% 249.49/59.13 ----------------------------------------------------------------
% 249.49/59.13 (1) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.13 (2) all_252_22 = e3
% 249.49/59.13 (3) ~ (e3 = e1)
% 249.49/59.13
% 249.49/59.13 Begin of proof
% 249.49/59.13 |
% 249.49/59.13 | ALPHA: (1) implies:
% 249.49/59.13 | (4) all_252_22 = e1
% 249.49/59.13 |
% 249.49/59.13 | COMBINE_EQS: (2), (4) imply:
% 249.49/59.13 | (5) e3 = e1
% 249.49/59.13 |
% 249.49/59.13 | REDUCE: (3), (5) imply:
% 249.49/59.13 | (6) $false
% 249.49/59.13 |
% 249.49/59.13 | CLOSE: (6) is inconsistent.
% 249.49/59.13 |
% 249.49/59.13 End of proof
% 249.49/59.13
% 249.49/59.13 Sub-proof #161 shows that the following formulas are inconsistent:
% 249.49/59.13 ----------------------------------------------------------------
% 249.49/59.13 (1) ~ (all_6_2 = e3)
% 249.49/59.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.13 (3) op(e4, e2) = all_6_2
% 249.49/59.13 (4) op(e4, e2) = e3
% 249.49/59.13 (5) op(e4, e2) = all_14_1
% 249.49/59.13
% 249.49/59.13 Begin of proof
% 249.49/59.13 |
% 249.49/59.13 | GROUND_INST: instantiating (2) with all_6_2, all_14_1, e2, e4, simplifying
% 249.49/59.13 | with (3), (5) gives:
% 249.49/59.13 | (6) all_14_1 = all_6_2
% 249.49/59.13 |
% 249.49/59.13 | GROUND_INST: instantiating (2) with e3, all_14_1, e2, e4, simplifying with
% 249.49/59.13 | (4), (5) gives:
% 249.49/59.13 | (7) all_14_1 = e3
% 249.49/59.13 |
% 249.49/59.13 | COMBINE_EQS: (6), (7) imply:
% 249.49/59.13 | (8) all_6_2 = e3
% 249.49/59.13 |
% 249.49/59.13 | SIMP: (8) implies:
% 249.49/59.13 | (9) all_6_2 = e3
% 249.49/59.13 |
% 249.49/59.13 | REDUCE: (1), (9) imply:
% 249.49/59.13 | (10) $false
% 249.49/59.13 |
% 249.49/59.13 | CLOSE: (10) is inconsistent.
% 249.49/59.13 |
% 249.49/59.13 End of proof
% 249.49/59.13
% 249.49/59.13 Sub-proof #162 shows that the following formulas are inconsistent:
% 249.49/59.13 ----------------------------------------------------------------
% 249.49/59.13 (1) ~ (all_244_0 = all_30_2)
% 249.49/59.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.13 (3) op(all_244_8, all_244_8) = e2
% 249.49/59.13 (4) op(e2, e2) = all_244_8
% 249.49/59.13 (5) all_30_2 = e2
% 249.49/59.13 (6) op(e2, all_30_2) = e4
% 249.49/59.13 (7) op(e4, e4) = all_244_0
% 249.49/59.13
% 249.49/59.13 Begin of proof
% 249.49/59.13 |
% 249.49/59.13 | REDUCE: (1), (5) imply:
% 249.49/59.13 | (8) ~ (all_244_0 = e2)
% 249.49/59.13 |
% 249.49/59.13 | REDUCE: (5), (6) imply:
% 249.49/59.13 | (9) op(e2, e2) = e4
% 249.49/59.13 |
% 249.49/59.13 | REF_CLOSE: (2), (3), (4), (7), (8), (9) are inconsistent by sub-proof #626.
% 249.49/59.13 |
% 249.49/59.13 End of proof
% 249.49/59.13
% 249.49/59.13 Sub-proof #163 shows that the following formulas are inconsistent:
% 249.49/59.13 ----------------------------------------------------------------
% 249.49/59.13 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) |
% 249.49/59.13 (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = e2) |
% 249.49/59.13 (all_252_16 = e2 & op(e4, e0) = e2)
% 249.49/59.13 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.13 all_250_23 = e0
% 249.49/59.13 (3) ~ (all_30_2 = all_26_2)
% 249.49/59.13 (4) all_242_2 = e4
% 249.49/59.13 (5) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.13 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.13 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.13 (6) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.13 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.13 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.13 (7) ~ (all_4_2 = e4)
% 249.49/59.13 (8) ~ (all_10_2 = e4)
% 249.49/59.13 (9) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.13 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.13 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.13 (10) ~ (all_38_1 = e3)
% 249.49/59.13 (11) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.13 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 249.49/59.13 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.13 (12) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.13 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.13 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.13 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 249.49/59.13 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.13 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.13 (14) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.13 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.13 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.13 (15) op(e4, e0) = all_30_2
% 249.49/59.13 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.13 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.13 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.13 (17) all_172_2 = all_10_2
% 249.49/59.13 (18) all_252_6 = e0
% 249.49/59.13 (19) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 249.49/59.13 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 249.49/59.13 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 249.49/59.13 (20) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.13 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.13 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.13 (21) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.13 all_250_15 = e0
% 249.49/59.13 (22) ~ (e2 = e0)
% 249.49/59.13 (23) ~ (e1 = e0)
% 249.49/59.13 (24) ~ (all_28_2 = e3)
% 249.49/59.13 (25) op(e4, e1) = e2
% 249.49/59.13 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.13 (27) op(e2, e3) = all_10_2
% 249.49/59.13 (28) op(e0, e0) = all_244_24
% 249.49/59.13 (29) ~ (e4 = e0)
% 249.49/59.13 (30) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.13 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.13 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.13 (31) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.13 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.13 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.13 (32) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.13 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.13 (33) ~ (all_84_2 = all_62_2)
% 249.49/59.13 (34) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.13 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.13 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.13 (35) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 249.49/59.13 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 249.49/59.13 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 249.49/59.13 (36) ~ (all_244_15 = all_16_2)
% 249.49/59.13 (37) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/59.13 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/59.13 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/59.13 (38) ~ (all_244_15 = all_26_2)
% 249.49/59.13 (39) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.13 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.13 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.13 (40) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 249.49/59.13 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 249.49/59.13 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.49/59.13 (41) op(e4, e2) = all_6_2
% 249.49/59.13 (42) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.13 all_250_18 = e0
% 249.49/59.13 (43) all_78_2 = all_10_2
% 249.49/59.13 (44) ~ (all_244_15 = e4)
% 249.49/59.13 (45) ~ (e2 = e1)
% 249.49/59.13 (46) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.13 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.13 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.13 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.13 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.13 op(e0, e1) = e0)))
% 249.49/59.13 (47) all_56_2 = all_8_2
% 249.49/59.13 (48) op(e0, e2) = all_28_2
% 249.49/59.13 (49) ~ (e4 = e1)
% 249.49/59.13 (50) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.13 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.13 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.13 (51) ~ (all_6_2 = e1)
% 249.49/59.13 (52) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.13 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.13 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.13 (53) all_80_2 = all_6_2
% 249.49/59.13 (54) op(all_34_2, e0) = e1
% 249.49/59.13 (55) ~ (all_244_3 = all_84_2)
% 249.49/59.13 (56) op(e1, e4) = all_16_2
% 249.49/59.13 (57) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.13 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.13 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.13 (58) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.13 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.13 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.13 (59) ~ (all_28_2 = all_20_2)
% 249.49/59.13 (60) op(e1, e3) = all_62_2
% 249.49/59.13 (61) op(all_16_2, all_26_2) = e4
% 249.49/59.13 (62) ~ (e3 = e0)
% 249.49/59.13 (63) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/59.13 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/59.13 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/59.13 (64) op(all_20_2, e1) = e0
% 249.49/59.13 (65) ~ (all_36_2 = e4)
% 249.49/59.13 (66) all_70_2 = all_62_2
% 249.49/59.13 (67) ~ (e3 = e1)
% 249.49/59.13 (68) op(e3, e1) = all_36_2
% 249.49/59.13 (69) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.13 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.13 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.13 (70) ~ (all_16_2 = e2)
% 249.49/59.13 (71) ~ (all_8_2 = e1)
% 249.49/59.13 (72) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.13 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.13 (73) ~ (all_22_2 = e1)
% 249.49/59.13 (74) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 249.49/59.13 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 249.49/59.13 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.13 (75) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.13 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.13 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.13 (76) ~ (all_84_2 = all_26_2)
% 249.49/59.13 (77) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/59.13 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/59.13 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/59.13 (78) ~ (all_36_2 = all_26_2)
% 249.49/59.13 (79) all_44_2 = all_26_2
% 249.49/59.13 (80) all_130_2 = all_62_2
% 249.49/59.13 (81) all_74_2 = all_36_2
% 249.49/59.13 (82) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.13 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.13 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.13 (83) op(e1, e4) = all_38_1
% 249.49/59.13 (84) op(e4, all_4_2) = e1
% 249.49/59.13 (85) ~ (all_26_2 = all_6_2)
% 249.49/59.13 (86) op(all_22_2, e3) = e0
% 249.49/59.13 (87) all_68_2 = all_22_2
% 249.49/59.13 (88) op(all_6_2, e0) = e2
% 249.49/59.13 (89) op(e0, e3) = all_22_2
% 249.49/59.13 (90) ~ (all_26_2 = e4)
% 249.49/59.13 (91) all_250_18 = all_244_15
% 249.49/59.13 (92) op(all_34_2, all_20_2) = e0
% 249.49/59.13 (93) all_252_20 = e2
% 249.49/59.13 (94) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.13 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.13 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.13 (95) all_58_2 = all_20_2
% 249.49/59.13 (96) op(all_62_2, e3) = e1
% 249.49/59.13 (97) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.13 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 249.49/59.13 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 249.49/59.13 (98) op(e4, e1) = all_26_2
% 249.49/59.13 (99) ~ (all_244_15 = all_62_2)
% 249.49/59.13 (100) ~ (all_62_2 = all_16_2)
% 249.49/59.13 (101) all_250_15 = all_16_2
% 249.49/59.13 (102) ~ (e4 = e3)
% 249.49/59.13 (103) op(e1, e1) = all_244_15
% 249.49/59.13 (104) op(e0, e1) = all_20_2
% 249.49/59.13 (105) ~ (all_244_15 = all_20_2)
% 249.49/59.13 (106) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 249.49/59.13 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 249.49/59.13 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 249.49/59.13 (107) ~ (all_26_2 = e3)
% 249.49/59.13 (108) op(e2, e4) = e0
% 249.49/59.13 (109) all_82_2 = all_28_2
% 249.49/59.13 (110) ~ (all_244_24 = e2)
% 249.49/59.13 (111) op(e1, e2) = all_4_2
% 249.49/59.14 (112) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.14 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.14 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.14 (113) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.14 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.14 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.14 (114) op(e4, e3) = all_84_2
% 249.49/59.14 (115) ~ (all_62_2 = all_10_2)
% 249.49/59.14 (116) ~ (all_22_2 = all_10_2)
% 249.49/59.14 (117) ~ (e4 = e2)
% 249.49/59.14 (118) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.49/59.14 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.14 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.14 (119) ~ (all_22_2 = all_20_2)
% 249.49/59.14 (120) op(e3, e2) = all_8_2
% 249.49/59.14 (121) op(all_36_2, e1) = e3
% 249.49/59.14 (122) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.14 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.14 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.14 (123) ~ (all_244_15 = all_36_2)
% 249.49/59.14 (124) ~ (all_20_2 = e4)
% 249.49/59.14 (125) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.14 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.14 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.14 (126) op(e2, e0) = all_40_2
% 249.49/59.14 (127) op(all_8_2, e2) = e3
% 249.49/59.14 (128) ~ (all_10_2 = e0)
% 249.49/59.14 (129) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.14 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.14 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.14 (130) op(e3, e3) = all_244_3
% 249.49/59.14 (131) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.14 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.14 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.14 (132) ~ (all_26_2 = all_20_2)
% 249.49/59.14 (133) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.14 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.14 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.14 (134) op(all_26_2, all_16_2) = e1
% 249.49/59.14 (135) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.14 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.14 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.14 (136) ~ (all_62_2 = all_4_2)
% 249.49/59.14 (137) op(all_244_24, all_244_24) = e0
% 249.49/59.14 (138) ~ (all_16_2 = e0)
% 249.49/59.14 (139) all_250_23 = all_20_2
% 249.49/59.14
% 249.49/59.14 Begin of proof
% 249.49/59.14 |
% 249.49/59.14 | BETA: splitting (74) gives:
% 249.49/59.14 |
% 249.49/59.14 | Case 1:
% 249.49/59.14 | |
% 249.49/59.14 | | (140) ~ (all_242_2 = e4)
% 249.49/59.14 | |
% 249.49/59.14 | | REDUCE: (4), (140) imply:
% 249.49/59.14 | | (141) $false
% 249.49/59.14 | |
% 249.49/59.14 | | CLOSE: (141) is inconsistent.
% 249.49/59.14 | |
% 249.49/59.14 | Case 2:
% 249.49/59.14 | |
% 249.49/59.14 | | (142) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 249.49/59.14 | | all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0)
% 249.49/59.14 | | & op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.14 | |
% 249.49/59.14 | | BETA: splitting (40) gives:
% 249.49/59.14 | |
% 249.49/59.14 | | Case 1:
% 249.49/59.14 | | |
% 249.49/59.14 | | | (143) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3,
% 249.49/59.14 | | | e1) = e4)
% 249.49/59.14 | | |
% 249.49/59.14 | | | REF_CLOSE: (25), (26), (65), (68), (98), (117), (143) are inconsistent by
% 249.49/59.14 | | | sub-proof #795.
% 249.49/59.14 | | |
% 249.49/59.14 | | Case 2:
% 249.49/59.14 | | |
% 249.49/59.14 | | | (144) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.14 | | | e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 249.49/59.14 | | |
% 249.49/59.14 | | | BETA: splitting (144) gives:
% 249.49/59.14 | | |
% 249.49/59.14 | | | Case 1:
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | (145) all_252_11 = e4 & op(e2, e1) = e4
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | ALPHA: (145) implies:
% 249.49/59.14 | | | | (146) all_252_11 = e4
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | GROUND_INST: instantiating (26) with all_16_2, all_38_1, e4, e1,
% 249.49/59.14 | | | | simplifying with (56), (83) gives:
% 249.49/59.14 | | | | (147) all_38_1 = all_16_2
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | GROUND_INST: instantiating (26) with all_26_2, e2, e1, e4, simplifying
% 249.49/59.14 | | | | with (25), (98) gives:
% 249.49/59.14 | | | | (148) all_26_2 = e2
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | COMBINE_EQS: (79), (148) imply:
% 249.49/59.14 | | | | (149) all_44_2 = e2
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (38), (148) imply:
% 249.49/59.14 | | | | (150) ~ (all_244_15 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (76), (148) imply:
% 249.49/59.14 | | | | (151) ~ (all_84_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (10), (147) imply:
% 249.49/59.14 | | | | (152) ~ (all_16_2 = e3)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (78), (148) imply:
% 249.49/59.14 | | | | (153) ~ (all_36_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (3), (148) imply:
% 249.49/59.14 | | | | (154) ~ (all_30_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (132), (148) imply:
% 249.49/59.14 | | | | (155) ~ (all_20_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | SIMP: (155) implies:
% 249.49/59.14 | | | | (156) ~ (all_20_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (85), (148) imply:
% 249.49/59.14 | | | | (157) ~ (all_6_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | SIMP: (157) implies:
% 249.49/59.14 | | | | (158) ~ (all_6_2 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (90), (148) imply:
% 249.49/59.14 | | | | (159) ~ (e4 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (107), (148) imply:
% 249.49/59.14 | | | | (160) ~ (e3 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | SIMP: (160) implies:
% 249.49/59.14 | | | | (161) ~ (e3 = e2)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (134), (148) imply:
% 249.49/59.14 | | | | (162) op(e2, all_16_2) = e1
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REDUCE: (61), (148) imply:
% 249.49/59.14 | | | | (163) op(all_16_2, e2) = e4
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | BETA: splitting (1) gives:
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | Case 1:
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | | (164) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4,
% 249.49/59.14 | | | | | e3) = e2)
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | | REF_CLOSE: (18), (23), (26), (29), (45), (49), (62), (67), (93),
% 249.49/59.14 | | | | | (102), (114), (117), (122), (125), (135), (151), (161),
% 249.49/59.14 | | | | | (164) are inconsistent by sub-proof #215.
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | Case 2:
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | | (165) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4,
% 249.49/59.14 | | | | | e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2)
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | | BETA: splitting (165) gives:
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | | Case 1:
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | | (166) all_252_4 = e2 & op(e4, e2) = e2
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | | REF_CLOSE: (26), (41), (158), (166) are inconsistent by sub-proof
% 249.49/59.14 | | | | | | #453.
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | Case 2:
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | | (167) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = e2 &
% 249.49/59.14 | | | | | | op(e4, e0) = e2)
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | | BETA: splitting (167) gives:
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | | Case 1:
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | (168) all_252_9 = e2 & op(e4, e1) = e2
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | ALPHA: (168) implies:
% 249.49/59.14 | | | | | | | (169) all_252_9 = e2
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 249.49/59.14 | | | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 249.49/59.14 | | | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 249.49/59.14 | | | | | | | (33), (34), (35), (36), (37), (39), (41), (42), (43),
% 249.49/59.14 | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 249.49/59.14 | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60), (62),
% 249.49/59.14 | | | | | | | (63), (64), (66), (67), (68), (69), (70), (71), (72),
% 249.49/59.14 | | | | | | | (73), (75), (77), (80), (81), (82), (84), (86), (87),
% 249.49/59.14 | | | | | | | (88), (89), (91), (92), (93), (94), (95), (96), (97),
% 249.49/59.14 | | | | | | | (99), (100), (101), (102), (103), (104), (105), (106),
% 249.49/59.14 | | | | | | | (108), (109), (110), (111), (112), (113), (114), (115),
% 249.49/59.14 | | | | | | | (116), (117), (118), (119), (120), (121), (122), (123),
% 249.49/59.14 | | | | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 249.49/59.14 | | | | | | | (133), (135), (136), (137), (138), (139), (142), (146),
% 249.49/59.14 | | | | | | | (149), (150), (152), (153), (154), (156), (161), (162),
% 249.49/59.14 | | | | | | | (163), (169) are inconsistent by sub-proof #164.
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | Case 2:
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | (170) all_252_16 = e2 & op(e4, e0) = e2
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | ALPHA: (170) implies:
% 249.49/59.14 | | | | | | | (171) op(e4, e0) = e2
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | | REF_CLOSE: (15), (26), (154), (171) are inconsistent by sub-proof
% 249.49/59.14 | | | | | | | #830.
% 249.49/59.14 | | | | | | |
% 249.49/59.14 | | | | | | End of split
% 249.49/59.14 | | | | | |
% 249.49/59.14 | | | | | End of split
% 249.49/59.14 | | | | |
% 249.49/59.14 | | | | End of split
% 249.49/59.14 | | | |
% 249.49/59.14 | | | Case 2:
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | (172) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0,
% 249.49/59.14 | | | | e1) = e4)
% 249.49/59.14 | | | |
% 249.49/59.14 | | | | REF_CLOSE: (26), (44), (103), (104), (124), (172) are inconsistent by
% 249.49/59.14 | | | | sub-proof #750.
% 249.49/59.14 | | | |
% 249.49/59.14 | | | End of split
% 249.49/59.14 | | |
% 249.49/59.14 | | End of split
% 249.49/59.14 | |
% 249.49/59.14 | End of split
% 249.49/59.14 |
% 249.49/59.14 End of proof
% 249.49/59.14
% 249.49/59.14 Sub-proof #164 shows that the following formulas are inconsistent:
% 249.49/59.14 ----------------------------------------------------------------
% 249.49/59.14 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.14 all_250_23 = e0
% 249.49/59.14 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.14 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.14 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.14 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.14 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.14 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.14 (4) ~ (all_4_2 = e4)
% 249.49/59.14 (5) ~ (all_10_2 = e4)
% 249.49/59.14 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.14 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.14 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.14 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.14 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.14 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.14 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.14 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.14 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.14 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 249.49/59.14 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 249.49/59.14 | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.14 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.14 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.14 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.14 (11) op(e4, e0) = all_30_2
% 249.49/59.14 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.14 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.14 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.14 (13) all_172_2 = all_10_2
% 249.49/59.14 (14) all_252_6 = e0
% 249.49/59.14 (15) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 249.49/59.14 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 249.49/59.14 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 249.49/59.14 (16) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.14 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.14 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.14 (17) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.14 all_250_15 = e0
% 249.49/59.14 (18) ~ (e2 = e0)
% 249.49/59.14 (19) ~ (e1 = e0)
% 249.49/59.14 (20) ~ (all_28_2 = e3)
% 249.49/59.14 (21) op(e4, e1) = e2
% 249.49/59.14 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.14 (23) op(e2, e3) = all_10_2
% 249.49/59.14 (24) ~ (e3 = e2)
% 249.49/59.14 (25) op(e0, e0) = all_244_24
% 249.49/59.14 (26) ~ (e4 = e0)
% 249.49/59.14 (27) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.14 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.14 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.14 (28) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.14 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.14 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.14 (29) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.14 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.14 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.14 (30) ~ (all_84_2 = all_62_2)
% 249.49/59.14 (31) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.14 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.14 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.14 (32) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 249.49/59.14 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 249.49/59.14 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 249.49/59.14 (33) ~ (all_244_15 = all_16_2)
% 249.49/59.14 (34) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/59.14 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/59.14 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/59.14 (35) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.14 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.14 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.14 (36) ~ (all_36_2 = e2)
% 249.49/59.14 (37) op(e4, e2) = all_6_2
% 249.49/59.14 (38) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.14 all_250_18 = e0
% 249.49/59.14 (39) all_78_2 = all_10_2
% 249.49/59.14 (40) ~ (all_244_15 = e4)
% 249.49/59.14 (41) ~ (e2 = e1)
% 249.49/59.14 (42) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.14 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.14 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.14 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.14 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.14 op(e0, e1) = e0)))
% 249.49/59.14 (43) all_56_2 = all_8_2
% 249.49/59.14 (44) op(e0, e2) = all_28_2
% 249.49/59.14 (45) ~ (e4 = e1)
% 249.49/59.14 (46) all_252_9 = e2
% 249.49/59.14 (47) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.14 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.14 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.14 (48) ~ (all_6_2 = e1)
% 249.49/59.14 (49) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.14 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.14 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.14 (50) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 249.49/59.14 all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0) &
% 249.49/59.14 op(e1, e4) = all_242_1 & $i(all_242_1))
% 249.49/59.14 (51) all_80_2 = all_6_2
% 249.49/59.14 (52) op(all_34_2, e0) = e1
% 249.49/59.14 (53) ~ (all_244_3 = all_84_2)
% 249.49/59.14 (54) op(e1, e4) = all_16_2
% 249.49/59.14 (55) op(e2, all_16_2) = e1
% 249.49/59.14 (56) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.14 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.14 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.14 (57) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.14 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.14 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.14 (58) ~ (all_28_2 = all_20_2)
% 249.49/59.14 (59) op(e1, e3) = all_62_2
% 249.49/59.14 (60) ~ (e3 = e0)
% 249.49/59.14 (61) all_44_2 = e2
% 249.49/59.14 (62) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/59.14 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/59.14 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/59.14 (63) op(all_20_2, e1) = e0
% 249.49/59.14 (64) ~ (all_30_2 = e2)
% 249.49/59.14 (65) all_70_2 = all_62_2
% 249.49/59.14 (66) ~ (e3 = e1)
% 249.49/59.14 (67) op(e3, e1) = all_36_2
% 249.49/59.14 (68) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.14 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.14 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.14 (69) ~ (all_16_2 = e2)
% 249.49/59.14 (70) all_252_11 = e4
% 249.49/59.14 (71) ~ (all_8_2 = e1)
% 249.49/59.14 (72) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.14 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.14 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.14 (73) ~ (all_22_2 = e1)
% 249.49/59.14 (74) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.14 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.14 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.14 (75) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/59.14 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/59.14 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/59.14 (76) all_130_2 = all_62_2
% 249.49/59.14 (77) all_74_2 = all_36_2
% 249.49/59.14 (78) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.14 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.14 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.14 (79) op(e4, all_4_2) = e1
% 249.49/59.14 (80) op(all_16_2, e2) = e4
% 249.49/59.14 (81) op(all_22_2, e3) = e0
% 249.49/59.14 (82) all_68_2 = all_22_2
% 249.49/59.14 (83) op(all_6_2, e0) = e2
% 249.49/59.14 (84) op(e0, e3) = all_22_2
% 249.49/59.14 (85) all_250_18 = all_244_15
% 249.49/59.14 (86) op(all_34_2, all_20_2) = e0
% 249.49/59.14 (87) all_252_20 = e2
% 249.49/59.14 (88) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.14 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.14 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.14 (89) all_58_2 = all_20_2
% 249.49/59.14 (90) op(all_62_2, e3) = e1
% 249.49/59.14 (91) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.14 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 249.49/59.14 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 249.49/59.14 (92) ~ (all_244_15 = all_62_2)
% 249.49/59.14 (93) ~ (all_62_2 = all_16_2)
% 249.49/59.14 (94) all_250_15 = all_16_2
% 249.49/59.14 (95) ~ (e4 = e3)
% 249.49/59.14 (96) op(e1, e1) = all_244_15
% 249.49/59.14 (97) op(e0, e1) = all_20_2
% 249.49/59.14 (98) ~ (all_244_15 = all_20_2)
% 249.49/59.14 (99) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 249.49/59.14 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 249.49/59.14 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 249.49/59.14 (100) op(e2, e4) = e0
% 249.49/59.14 (101) all_82_2 = all_28_2
% 249.49/59.14 (102) ~ (all_244_24 = e2)
% 249.49/59.14 (103) op(e1, e2) = all_4_2
% 249.49/59.14 (104) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.14 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.14 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.14 (105) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.14 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.14 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.14 (106) op(e4, e3) = all_84_2
% 249.49/59.14 (107) ~ (all_62_2 = all_10_2)
% 249.49/59.14 (108) ~ (all_22_2 = all_10_2)
% 249.49/59.14 (109) ~ (all_244_15 = e2)
% 249.49/59.14 (110) ~ (e4 = e2)
% 249.49/59.14 (111) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.49/59.14 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.14 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.14 (112) ~ (all_22_2 = all_20_2)
% 249.49/59.14 (113) op(e3, e2) = all_8_2
% 249.49/59.14 (114) op(all_36_2, e1) = e3
% 249.49/59.14 (115) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.14 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.14 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.14 (116) ~ (all_244_15 = all_36_2)
% 249.49/59.14 (117) ~ (all_20_2 = e4)
% 249.49/59.14 (118) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.14 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.14 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.14 (119) op(e2, e0) = all_40_2
% 249.49/59.14 (120) ~ (all_16_2 = e3)
% 249.49/59.14 (121) op(all_8_2, e2) = e3
% 249.49/59.14 (122) ~ (all_10_2 = e0)
% 249.49/59.14 (123) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.14 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.14 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.14 (124) op(e3, e3) = all_244_3
% 249.49/59.14 (125) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.14 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.14 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.14 (126) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.14 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.14 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.14 (127) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.14 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.14 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.14 (128) ~ (all_62_2 = all_4_2)
% 249.49/59.14 (129) op(all_244_24, all_244_24) = e0
% 249.49/59.14 (130) ~ (all_16_2 = e0)
% 249.49/59.14 (131) ~ (all_20_2 = e2)
% 249.49/59.14 (132) all_250_23 = all_20_2
% 249.49/59.14
% 249.49/59.14 Begin of proof
% 249.49/59.14 |
% 249.49/59.14 | BETA: splitting (50) gives:
% 249.49/59.14 |
% 249.49/59.14 | Case 1:
% 249.49/59.14 | |
% 249.49/59.14 | | (133) ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 249.49/59.14 | | all_242_1 & $i(all_242_0) & $i(all_242_1)
% 249.49/59.14 | |
% 249.49/59.14 | | ALPHA: (133) implies:
% 249.49/59.14 | | (134) op(e1, e4) = all_242_1
% 249.49/59.14 | |
% 249.49/59.14 | | GROUND_INST: instantiating (22) with all_16_2, all_242_1, e4, e1,
% 249.49/59.14 | | simplifying with (54), (134) gives:
% 249.49/59.14 | | (135) all_242_1 = all_16_2
% 249.49/59.14 | |
% 249.49/59.14 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.14 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 249.49/59.14 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.14 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 249.49/59.14 | | (46), (47), (48), (49), (51), (52), (53), (55), (56), (57), (58),
% 249.49/59.14 | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 249.49/59.14 | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 249.49/59.14 | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 249.49/59.14 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 249.49/59.14 | | (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 249.49/59.14 | | (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 249.49/59.14 | | (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 249.49/59.14 | | (129), (130), (131), (132), (134), (135) are inconsistent by
% 249.49/59.14 | | sub-proof #165.
% 249.49/59.14 | |
% 249.49/59.14 | Case 2:
% 249.49/59.14 | |
% 249.49/59.15 | | (136) ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1)
% 249.49/59.15 | |
% 249.49/59.15 | | ALPHA: (136) implies:
% 249.49/59.15 | | (137) ~ (all_242_1 = e0)
% 249.49/59.15 | | (138) op(e1, e4) = all_242_1
% 249.49/59.15 | |
% 249.49/59.15 | | GROUND_INST: instantiating (22) with all_16_2, all_242_1, e4, e1,
% 249.49/59.15 | | simplifying with (54), (138) gives:
% 249.49/59.15 | | (139) all_242_1 = all_16_2
% 249.49/59.15 | |
% 249.49/59.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.15 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 249.49/59.15 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.15 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 249.49/59.15 | | (46), (47), (48), (49), (51), (52), (53), (55), (56), (57), (58),
% 249.49/59.15 | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 249.49/59.15 | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 249.49/59.15 | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 249.49/59.15 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 249.49/59.15 | | (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 249.49/59.15 | | (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 249.49/59.15 | | (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 249.49/59.15 | | (129), (130), (131), (132), (138), (139) are inconsistent by
% 249.49/59.15 | | sub-proof #165.
% 249.49/59.15 | |
% 249.49/59.15 | End of split
% 249.49/59.15 |
% 249.49/59.15 End of proof
% 249.49/59.15
% 249.49/59.15 Sub-proof #165 shows that the following formulas are inconsistent:
% 249.49/59.15 ----------------------------------------------------------------
% 249.49/59.15 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.15 all_250_23 = e0
% 249.49/59.15 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.15 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.15 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.15 (3) all_242_1 = all_16_2
% 249.49/59.15 (4) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.15 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.15 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.15 (5) ~ (all_4_2 = e4)
% 249.49/59.15 (6) ~ (all_10_2 = e4)
% 249.49/59.15 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.15 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.15 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.15 (8) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.15 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.15 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.15 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.15 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.15 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.15 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 249.49/59.15 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.15 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.15 (11) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.15 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.15 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.15 (12) op(e4, e0) = all_30_2
% 249.49/59.15 (13) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.15 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.15 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.15 (14) all_172_2 = all_10_2
% 249.49/59.15 (15) all_252_6 = e0
% 249.49/59.15 (16) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 249.49/59.15 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 249.49/59.15 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 249.49/59.15 (17) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.15 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.15 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.15 (18) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.15 all_250_15 = e0
% 249.49/59.15 (19) ~ (e2 = e0)
% 249.49/59.15 (20) ~ (e1 = e0)
% 249.49/59.15 (21) ~ (all_28_2 = e3)
% 249.49/59.15 (22) op(e4, e1) = e2
% 249.49/59.15 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.15 (24) op(e2, e3) = all_10_2
% 249.49/59.15 (25) ~ (e3 = e2)
% 249.49/59.15 (26) op(e0, e0) = all_244_24
% 249.49/59.15 (27) ~ (e4 = e0)
% 249.49/59.15 (28) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.15 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.15 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.15 (29) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.15 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.15 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.15 (30) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.15 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.15 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.15 (31) ~ (all_84_2 = all_62_2)
% 249.49/59.15 (32) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.15 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.15 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.15 (33) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 249.49/59.15 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 249.49/59.15 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 249.49/59.15 (34) ~ (all_244_15 = all_16_2)
% 249.49/59.15 (35) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/59.15 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/59.15 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/59.15 (36) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.15 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.15 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.15 (37) ~ (all_36_2 = e2)
% 249.49/59.15 (38) op(e4, e2) = all_6_2
% 249.49/59.15 (39) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.15 all_250_18 = e0
% 249.49/59.15 (40) all_78_2 = all_10_2
% 249.49/59.15 (41) ~ (all_244_15 = e4)
% 249.49/59.15 (42) ~ (e2 = e1)
% 249.49/59.15 (43) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.15 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.15 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.15 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.15 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.15 op(e0, e1) = e0)))
% 249.49/59.15 (44) all_56_2 = all_8_2
% 249.49/59.15 (45) op(e0, e2) = all_28_2
% 249.49/59.15 (46) ~ (e4 = e1)
% 249.49/59.15 (47) all_252_9 = e2
% 249.49/59.15 (48) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.15 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.15 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.15 (49) ~ (all_6_2 = e1)
% 249.49/59.15 (50) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.15 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.15 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.15 (51) all_80_2 = all_6_2
% 249.49/59.15 (52) op(all_34_2, e0) = e1
% 249.49/59.15 (53) ~ (all_244_3 = all_84_2)
% 249.49/59.15 (54) op(e2, all_16_2) = e1
% 249.49/59.15 (55) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.15 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.15 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.15 (56) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.15 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.15 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.15 (57) ~ (all_28_2 = all_20_2)
% 249.49/59.15 (58) op(e1, e3) = all_62_2
% 249.49/59.15 (59) ~ (e3 = e0)
% 249.49/59.15 (60) all_44_2 = e2
% 249.49/59.15 (61) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/59.15 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/59.15 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/59.15 (62) op(all_20_2, e1) = e0
% 249.49/59.15 (63) ~ (all_30_2 = e2)
% 249.49/59.15 (64) all_70_2 = all_62_2
% 249.49/59.15 (65) ~ (e3 = e1)
% 249.49/59.15 (66) op(e3, e1) = all_36_2
% 249.49/59.15 (67) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.15 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.15 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.15 (68) ~ (all_16_2 = e2)
% 249.49/59.15 (69) all_252_11 = e4
% 249.49/59.15 (70) ~ (all_8_2 = e1)
% 249.49/59.15 (71) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.15 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.15 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.15 (72) ~ (all_22_2 = e1)
% 249.49/59.15 (73) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.15 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.15 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.15 (74) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/59.15 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/59.15 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/59.15 (75) all_130_2 = all_62_2
% 249.49/59.15 (76) all_74_2 = all_36_2
% 249.49/59.15 (77) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.15 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.15 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.15 (78) op(e4, all_4_2) = e1
% 249.49/59.15 (79) op(all_16_2, e2) = e4
% 249.49/59.15 (80) op(all_22_2, e3) = e0
% 249.49/59.15 (81) all_68_2 = all_22_2
% 249.49/59.15 (82) op(e1, e4) = all_242_1
% 249.49/59.15 (83) op(all_6_2, e0) = e2
% 249.49/59.15 (84) op(e0, e3) = all_22_2
% 249.49/59.15 (85) all_250_18 = all_244_15
% 249.49/59.15 (86) op(all_34_2, all_20_2) = e0
% 249.49/59.15 (87) all_252_20 = e2
% 249.49/59.15 (88) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.15 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.15 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.15 (89) all_58_2 = all_20_2
% 249.49/59.15 (90) op(all_62_2, e3) = e1
% 249.49/59.15 (91) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.15 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 249.49/59.15 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 249.49/59.15 (92) ~ (all_244_15 = all_62_2)
% 249.49/59.15 (93) ~ (all_62_2 = all_16_2)
% 249.49/59.15 (94) all_250_15 = all_16_2
% 249.49/59.15 (95) ~ (e4 = e3)
% 249.49/59.15 (96) op(e1, e1) = all_244_15
% 249.49/59.15 (97) op(e0, e1) = all_20_2
% 249.49/59.15 (98) ~ (all_244_15 = all_20_2)
% 249.49/59.15 (99) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 249.49/59.15 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 249.49/59.15 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 249.49/59.15 (100) op(e2, e4) = e0
% 249.49/59.15 (101) all_82_2 = all_28_2
% 249.49/59.15 (102) ~ (all_244_24 = e2)
% 249.49/59.15 (103) op(e1, e2) = all_4_2
% 249.49/59.15 (104) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.15 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.15 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.15 (105) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.15 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.15 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.15 (106) op(e4, e3) = all_84_2
% 249.49/59.15 (107) ~ (all_62_2 = all_10_2)
% 249.49/59.15 (108) ~ (all_22_2 = all_10_2)
% 249.49/59.15 (109) ~ (all_244_15 = e2)
% 249.49/59.15 (110) ~ (e4 = e2)
% 249.49/59.15 (111) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.49/59.15 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.15 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.15 (112) ~ (all_22_2 = all_20_2)
% 249.49/59.15 (113) op(e3, e2) = all_8_2
% 249.49/59.15 (114) op(all_36_2, e1) = e3
% 249.49/59.15 (115) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.15 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.15 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.15 (116) ~ (all_244_15 = all_36_2)
% 249.49/59.15 (117) ~ (all_20_2 = e4)
% 249.49/59.15 (118) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.15 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.15 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.15 (119) op(e2, e0) = all_40_2
% 249.49/59.15 (120) ~ (all_16_2 = e3)
% 249.49/59.15 (121) op(all_8_2, e2) = e3
% 249.49/59.15 (122) ~ (all_10_2 = e0)
% 249.49/59.15 (123) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.15 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.15 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.15 (124) op(e3, e3) = all_244_3
% 249.49/59.15 (125) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.15 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.15 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.15 (126) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.15 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.15 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.15 (127) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.15 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.15 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.15 (128) ~ (all_62_2 = all_4_2)
% 249.49/59.15 (129) op(all_244_24, all_244_24) = e0
% 249.49/59.15 (130) ~ (all_16_2 = e0)
% 249.49/59.15 (131) ~ (all_20_2 = e2)
% 249.49/59.15 (132) all_250_23 = all_20_2
% 249.49/59.15
% 249.49/59.15 Begin of proof
% 249.49/59.15 |
% 249.49/59.15 | REDUCE: (3), (82) imply:
% 249.49/59.15 | (133) op(e1, e4) = all_16_2
% 249.49/59.15 |
% 249.49/59.15 | BETA: splitting (16) gives:
% 249.49/59.15 |
% 249.49/59.15 | Case 1:
% 249.49/59.15 | |
% 249.49/59.15 | | (134) ~ (all_44_2 = e2)
% 249.49/59.15 | |
% 249.49/59.15 | | REDUCE: (60), (134) imply:
% 249.49/59.15 | | (135) $false
% 249.49/59.15 | |
% 249.49/59.15 | | CLOSE: (135) is inconsistent.
% 249.49/59.15 | |
% 249.49/59.15 | Case 2:
% 249.49/59.15 | |
% 249.49/59.15 | | (136) ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 & op(e1, e2) =
% 249.49/59.15 | | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e3) &
% 249.49/59.15 | | op(e1, e2) = all_44_1 & $i(all_44_1))
% 249.49/59.15 | |
% 249.49/59.15 | | BETA: splitting (136) gives:
% 249.49/59.15 | |
% 249.49/59.15 | | Case 1:
% 249.49/59.15 | | |
% 249.49/59.15 | | | (137) ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 & op(e1, e2) =
% 249.49/59.15 | | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 249.49/59.15 | | |
% 249.49/59.15 | | | ALPHA: (137) implies:
% 249.49/59.15 | | | (138) op(e1, e2) = all_44_1
% 249.49/59.15 | | |
% 249.49/59.15 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 249.49/59.15 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 249.49/59.15 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.15 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 249.49/59.15 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 249.49/59.15 | | | (55), (56), (57), (58), (59), (61), (62), (63), (64), (65),
% 249.49/59.15 | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 249.49/59.15 | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 249.49/59.15 | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 249.49/59.15 | | | (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 249.49/59.15 | | | (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 249.49/59.15 | | | (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 249.49/59.15 | | | (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 249.49/59.15 | | | (132), (133), (138) are inconsistent by sub-proof #166.
% 249.49/59.15 | | |
% 249.49/59.15 | | Case 2:
% 249.49/59.15 | | |
% 249.49/59.15 | | | (139) ~ (all_44_1 = e3) & op(e1, e2) = all_44_1 & $i(all_44_1)
% 249.49/59.15 | | |
% 249.49/59.15 | | | ALPHA: (139) implies:
% 249.49/59.15 | | | (140) op(e1, e2) = all_44_1
% 249.49/59.15 | | |
% 249.49/59.15 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 249.49/59.15 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 249.49/59.15 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.15 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 249.49/59.15 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 249.49/59.15 | | | (55), (56), (57), (58), (59), (61), (62), (63), (64), (65),
% 249.49/59.15 | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 249.49/59.15 | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 249.49/59.15 | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 249.49/59.15 | | | (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 249.49/59.15 | | | (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 249.49/59.15 | | | (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 249.49/59.15 | | | (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 249.49/59.15 | | | (132), (133), (140) are inconsistent by sub-proof #166.
% 249.49/59.15 | | |
% 249.49/59.15 | | End of split
% 249.49/59.15 | |
% 249.49/59.15 | End of split
% 249.49/59.15 |
% 249.49/59.15 End of proof
% 249.49/59.15
% 249.49/59.15 Sub-proof #166 shows that the following formulas are inconsistent:
% 249.49/59.15 ----------------------------------------------------------------
% 249.49/59.15 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.15 all_250_23 = e0
% 249.49/59.15 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.15 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.15 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.15 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.15 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.15 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.15 (4) ~ (all_4_2 = e4)
% 249.49/59.15 (5) ~ (all_10_2 = e4)
% 249.49/59.15 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.15 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.15 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.15 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.15 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.15 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.15 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.15 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.15 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.15 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 249.49/59.15 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 249.49/59.15 | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.15 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.15 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.15 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.15 (11) op(e4, e0) = all_30_2
% 249.49/59.15 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.15 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.15 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.15 (13) all_172_2 = all_10_2
% 249.49/59.15 (14) all_252_6 = e0
% 249.49/59.15 (15) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.15 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.15 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.15 (16) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.15 all_250_15 = e0
% 249.49/59.15 (17) ~ (e2 = e0)
% 249.49/59.15 (18) ~ (e1 = e0)
% 249.49/59.15 (19) ~ (all_28_2 = e3)
% 249.49/59.15 (20) op(e4, e1) = e2
% 249.49/59.15 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.15 (22) op(e2, e3) = all_10_2
% 249.49/59.15 (23) ~ (e3 = e2)
% 249.49/59.15 (24) op(e0, e0) = all_244_24
% 249.49/59.15 (25) ~ (e4 = e0)
% 249.49/59.15 (26) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.15 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.15 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.15 (27) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.15 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.15 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.15 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.15 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.15 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.15 (29) ~ (all_84_2 = all_62_2)
% 249.49/59.15 (30) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.15 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.15 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.15 (31) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 249.49/59.15 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 249.49/59.15 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 249.49/59.15 (32) ~ (all_244_15 = all_16_2)
% 249.49/59.15 (33) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 249.49/59.15 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 249.49/59.15 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 249.49/59.15 (34) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.15 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.15 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.15 (35) ~ (all_36_2 = e2)
% 249.49/59.15 (36) op(e4, e2) = all_6_2
% 249.49/59.16 (37) all_250_18 = e4 | all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.16 all_250_18 = e0
% 249.49/59.16 (38) all_78_2 = all_10_2
% 249.49/59.16 (39) ~ (all_244_15 = e4)
% 249.49/59.16 (40) ~ (e2 = e1)
% 249.49/59.16 (41) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.16 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.16 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.16 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.16 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.16 op(e0, e1) = e0)))
% 249.49/59.16 (42) all_56_2 = all_8_2
% 249.49/59.16 (43) op(e0, e2) = all_28_2
% 249.49/59.16 (44) ~ (e4 = e1)
% 249.49/59.16 (45) all_252_9 = e2
% 249.49/59.16 (46) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.16 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.16 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.16 (47) ~ (all_6_2 = e1)
% 249.49/59.16 (48) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.16 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.16 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.16 (49) all_80_2 = all_6_2
% 249.49/59.16 (50) op(all_34_2, e0) = e1
% 249.49/59.16 (51) ~ (all_244_3 = all_84_2)
% 249.49/59.16 (52) op(e1, e4) = all_16_2
% 249.49/59.16 (53) op(e2, all_16_2) = e1
% 249.49/59.16 (54) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.16 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.16 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.16 (55) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.16 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.16 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.16 (56) ~ (all_28_2 = all_20_2)
% 249.49/59.16 (57) op(e1, e3) = all_62_2
% 249.49/59.16 (58) ~ (e3 = e0)
% 249.49/59.16 (59) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 249.49/59.16 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 249.49/59.16 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 249.49/59.16 (60) op(all_20_2, e1) = e0
% 249.49/59.16 (61) ~ (all_30_2 = e2)
% 249.49/59.16 (62) all_70_2 = all_62_2
% 249.49/59.16 (63) ~ (e3 = e1)
% 249.49/59.16 (64) op(e3, e1) = all_36_2
% 249.49/59.16 (65) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.16 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.16 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.16 (66) ~ (all_16_2 = e2)
% 249.49/59.16 (67) all_252_11 = e4
% 249.49/59.16 (68) ~ (all_8_2 = e1)
% 249.49/59.16 (69) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.16 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.16 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.16 (70) ~ (all_22_2 = e1)
% 249.49/59.16 (71) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.16 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.16 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.16 (72) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 249.49/59.16 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 249.49/59.16 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 249.49/59.16 (73) all_130_2 = all_62_2
% 249.49/59.16 (74) all_74_2 = all_36_2
% 249.49/59.16 (75) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.16 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.16 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.16 (76) op(e4, all_4_2) = e1
% 249.49/59.16 (77) op(all_16_2, e2) = e4
% 249.49/59.16 (78) op(all_22_2, e3) = e0
% 249.49/59.16 (79) all_68_2 = all_22_2
% 249.49/59.16 (80) op(e1, e4) = all_242_1
% 249.49/59.16 (81) op(all_6_2, e0) = e2
% 249.49/59.16 (82) op(e0, e3) = all_22_2
% 249.49/59.16 (83) all_250_18 = all_244_15
% 249.49/59.16 (84) op(all_34_2, all_20_2) = e0
% 249.49/59.16 (85) all_252_20 = e2
% 249.49/59.16 (86) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.16 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.16 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.16 (87) all_58_2 = all_20_2
% 249.49/59.16 (88) op(e1, e2) = all_44_1
% 249.49/59.16 (89) op(all_62_2, e3) = e1
% 249.49/59.16 (90) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.16 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 249.49/59.16 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 249.49/59.16 (91) ~ (all_244_15 = all_62_2)
% 249.49/59.16 (92) ~ (all_62_2 = all_16_2)
% 249.49/59.16 (93) all_250_15 = all_16_2
% 249.49/59.16 (94) ~ (e4 = e3)
% 249.49/59.16 (95) op(e1, e1) = all_244_15
% 249.49/59.16 (96) op(e0, e1) = all_20_2
% 249.49/59.16 (97) ~ (all_244_15 = all_20_2)
% 249.49/59.16 (98) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 249.49/59.16 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 249.49/59.16 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 249.49/59.16 (99) op(e2, e4) = e0
% 249.49/59.16 (100) all_82_2 = all_28_2
% 249.49/59.16 (101) ~ (all_244_24 = e2)
% 249.49/59.16 (102) op(e1, e2) = all_4_2
% 249.49/59.16 (103) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.16 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.16 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.16 (104) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.16 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.16 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.16 (105) op(e4, e3) = all_84_2
% 249.49/59.16 (106) ~ (all_62_2 = all_10_2)
% 249.49/59.16 (107) ~ (all_22_2 = all_10_2)
% 249.49/59.16 (108) ~ (all_244_15 = e2)
% 249.49/59.16 (109) ~ (e4 = e2)
% 249.49/59.16 (110) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 249.49/59.16 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 249.49/59.16 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.16 (111) ~ (all_22_2 = all_20_2)
% 249.49/59.16 (112) op(e3, e2) = all_8_2
% 249.49/59.16 (113) op(all_36_2, e1) = e3
% 249.49/59.16 (114) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.16 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.16 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.16 (115) ~ (all_244_15 = all_36_2)
% 249.49/59.16 (116) ~ (all_20_2 = e4)
% 249.49/59.16 (117) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.16 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.16 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.16 (118) op(e2, e0) = all_40_2
% 249.49/59.16 (119) ~ (all_16_2 = e3)
% 249.49/59.16 (120) op(all_8_2, e2) = e3
% 249.49/59.16 (121) ~ (all_10_2 = e0)
% 249.49/59.16 (122) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.16 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.16 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.16 (123) op(e3, e3) = all_244_3
% 249.49/59.16 (124) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.16 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.16 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.16 (125) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.16 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.16 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.16 (126) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.16 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.16 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.16 (127) ~ (all_62_2 = all_4_2)
% 249.49/59.16 (128) op(all_244_24, all_244_24) = e0
% 249.49/59.16 (129) ~ (all_16_2 = e0)
% 249.49/59.16 (130) ~ (all_20_2 = e2)
% 249.49/59.16 (131) all_250_23 = all_20_2
% 249.49/59.16
% 249.49/59.16 Begin of proof
% 249.49/59.16 |
% 249.49/59.16 | GROUND_INST: instantiating (21) with all_4_2, all_44_1, e2, e1, simplifying
% 249.49/59.16 | with (88), (102) gives:
% 249.49/59.16 | (132) all_44_1 = all_4_2
% 249.49/59.16 |
% 249.49/59.16 | BETA: splitting (33) gives:
% 249.49/59.16 |
% 249.49/59.16 | Case 1:
% 249.49/59.16 | |
% 249.49/59.16 | | (133) ~ (all_56_2 = e0)
% 249.49/59.16 | |
% 249.49/59.16 | | REDUCE: (42), (133) imply:
% 249.49/59.16 | | (134) ~ (all_8_2 = e0)
% 249.49/59.16 | |
% 249.49/59.16 | | BETA: splitting (59) gives:
% 249.49/59.16 | |
% 249.49/59.16 | | Case 1:
% 249.49/59.16 | | |
% 249.49/59.16 | | | (135) ~ (all_58_2 = e3)
% 249.49/59.16 | | |
% 249.49/59.16 | | | REDUCE: (87), (135) imply:
% 249.49/59.16 | | | (136) ~ (all_20_2 = e3)
% 249.49/59.16 | | |
% 249.49/59.16 | | | BETA: splitting (98) gives:
% 249.49/59.16 | | |
% 249.49/59.16 | | | Case 1:
% 249.49/59.16 | | | |
% 249.49/59.16 | | | | (137) ~ (all_62_2 = e4)
% 249.49/59.16 | | | |
% 249.49/59.16 | | | | BETA: splitting (31) gives:
% 249.49/59.16 | | | |
% 249.49/59.16 | | | | Case 1:
% 249.49/59.16 | | | | |
% 249.49/59.16 | | | | | (138) ~ (all_68_2 = e4)
% 249.49/59.16 | | | | |
% 249.49/59.16 | | | | | REDUCE: (79), (138) imply:
% 249.49/59.16 | | | | | (139) ~ (all_22_2 = e4)
% 249.49/59.16 | | | | |
% 249.49/59.16 | | | | | BETA: splitting (72) gives:
% 249.49/59.16 | | | | |
% 249.49/59.16 | | | | | Case 1:
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | (140) ~ (all_70_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (62), (140) imply:
% 249.49/59.16 | | | | | | (141) ~ (all_62_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | BETA: splitting (122) gives:
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | Case 1:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | (142) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 &
% 249.49/59.16 | | | | | | | op(e1, e3) = e2)
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | BETA: splitting (142) gives:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (143) all_252_12 = e2 & op(e1, e4) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | ALPHA: (143) implies:
% 249.49/59.16 | | | | | | | | (144) op(e1, e4) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (21), (52), (66), (80), (144) are inconsistent by
% 249.49/59.16 | | | | | | | | sub-proof #600.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (145) all_252_13 = e2 & op(e1, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | ALPHA: (145) implies:
% 249.49/59.16 | | | | | | | | (146) op(e1, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (21), (57), (141), (146) are inconsistent by
% 249.49/59.16 | | | | | | | | sub-proof #972.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | End of split
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | Case 2:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | (147) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 249.49/59.16 | | | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | BETA: splitting (147) gives:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (148) all_252_14 = e2 & op(e1, e2) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (21), (36), (47), (76), (102), (148) are inconsistent
% 249.49/59.16 | | | | | | | | by sub-proof #794.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (149) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2
% 249.49/59.16 | | | | | | | | & op(e1, e0) = e2)
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | BETA: splitting (149) gives:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | (150) all_252_15 = e2 & op(e1, e1) = e2
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | REF_CLOSE: (21), (95), (108), (150) are inconsistent by
% 249.49/59.16 | | | | | | | | | sub-proof #966.
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | (151) all_252_19 = e2 & op(e1, e0) = e2
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | REF_CLOSE: (4), (18), (21), (39), (52), (53), (57), (86),
% 249.49/59.16 | | | | | | | | | (95), (99), (102), (109), (137), (151) are
% 249.49/59.16 | | | | | | | | | inconsistent by sub-proof #213.
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | End of split
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | End of split
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | End of split
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | Case 2:
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | (152) all_70_2 = e2
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | COMBINE_EQS: (62), (152) imply:
% 249.49/59.16 | | | | | | (153) all_62_2 = e2
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | SIMP: (153) implies:
% 249.49/59.16 | | | | | | (154) all_62_2 = e2
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | COMBINE_EQS: (73), (154) imply:
% 249.49/59.16 | | | | | | (155) all_130_2 = e2
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (29), (154) imply:
% 249.49/59.16 | | | | | | (156) ~ (all_84_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (92), (154) imply:
% 249.49/59.16 | | | | | | (157) ~ (all_16_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (106), (154) imply:
% 249.49/59.16 | | | | | | (158) ~ (all_10_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | SIMP: (158) implies:
% 249.49/59.16 | | | | | | (159) ~ (all_10_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (127), (154) imply:
% 249.49/59.16 | | | | | | (160) ~ (all_4_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | SIMP: (160) implies:
% 249.49/59.16 | | | | | | (161) ~ (all_4_2 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (137), (154) imply:
% 249.49/59.16 | | | | | | (162) ~ (e4 = e2)
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | REDUCE: (89), (154) imply:
% 249.49/59.16 | | | | | | (163) op(e2, e3) = e1
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | BETA: splitting (10) gives:
% 249.49/59.16 | | | | | |
% 249.49/59.16 | | | | | | Case 1:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | (164) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 &
% 249.49/59.16 | | | | | | | op(e3, e3) = e2)
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | BETA: splitting (164) gives:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (165) all_252_1 = e2 & op(e4, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (21), (105), (156), (165) are inconsistent by
% 249.49/59.16 | | | | | | | | sub-proof #956.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (166) all_252_3 = e2 & op(e3, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | ALPHA: (166) implies:
% 249.49/59.16 | | | | | | | | (167) all_252_3 = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (4), (5), (9), (17), (18), (21), (22), (23), (25),
% 249.49/59.16 | | | | | | | | (39), (40), (44), (52), (53), (57), (58), (63), (66),
% 249.49/59.16 | | | | | | | | (70), (71), (80), (82), (86), (94), (95), (99),
% 249.49/59.16 | | | | | | | | (102), (103), (108), (109), (121), (122), (125),
% 249.49/59.16 | | | | | | | | (137), (139), (161), (167) are inconsistent by
% 249.49/59.16 | | | | | | | | sub-proof #209.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | End of split
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | Case 2:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | (168) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 &
% 249.49/59.16 | | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | BETA: splitting (168) gives:
% 249.49/59.16 | | | | | | |
% 249.49/59.16 | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (169) all_252_7 = e2 & op(e2, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | ALPHA: (169) implies:
% 249.49/59.16 | | | | | | | | (170) op(e2, e3) = e2
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | REF_CLOSE: (21), (22), (40), (163), (170) are inconsistent by
% 249.49/59.16 | | | | | | | | sub-proof #902.
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | (171) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2
% 249.49/59.16 | | | | | | | | & op(e0, e3) = e2)
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | BETA: splitting (171) gives:
% 249.49/59.16 | | | | | | | |
% 249.49/59.16 | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | (172) all_252_13 = e2 & op(e1, e3) = e2
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | ALPHA: (172) implies:
% 249.49/59.16 | | | | | | | | | (173) all_252_13 = e2
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | BETA: splitting (90) gives:
% 249.49/59.16 | | | | | | | | |
% 249.49/59.16 | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | (174) ~ (all_130_2 = e2)
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | REDUCE: (155), (174) imply:
% 249.49/59.16 | | | | | | | | | | (175) $false
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | CLOSE: (175) is inconsistent.
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | (176) ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.16 | | | | | | | | | | op(e2, all_130_1) = all_130_0 & $i(all_130_0) &
% 249.49/59.16 | | | | | | | | | | $i(all_130_1)) | ( ~ (all_130_1 = e0) & op(e3,
% 249.49/59.16 | | | | | | | | | | e2) = all_130_1 & $i(all_130_1))
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | BETA: splitting (176) gives:
% 249.49/59.16 | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | (177) ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 249.49/59.16 | | | | | | | | | | | op(e2, all_130_1) = all_130_0 & $i(all_130_0) &
% 249.49/59.16 | | | | | | | | | | | $i(all_130_1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | ALPHA: (177) implies:
% 249.49/59.16 | | | | | | | | | | | (178) op(e3, e2) = all_130_1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_10_2, e1, e3, e2,
% 249.49/59.16 | | | | | | | | | | | simplifying with (22), (163) gives:
% 249.49/59.16 | | | | | | | | | | | (179) all_10_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_8_2, all_130_1, e2,
% 249.49/59.16 | | | | | | | | | | | e3, simplifying with (112), (178) gives:
% 249.49/59.16 | | | | | | | | | | | (180) all_130_1 = all_8_2
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | COMBINE_EQS: (38), (179) imply:
% 249.49/59.16 | | | | | | | | | | | (181) all_78_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | COMBINE_EQS: (13), (179) imply:
% 249.49/59.16 | | | | | | | | | | | (182) all_172_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | REDUCE: (5), (179) imply:
% 249.49/59.16 | | | | | | | | | | | (183) ~ (e4 = e1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | REDUCE: (159), (179) imply:
% 249.49/59.16 | | | | | | | | | | | (184) ~ (e2 = e1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | BETA: splitting (125) gives:
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | (185) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 249.49/59.16 | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | BETA: splitting (185) gives:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | (186) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | ALPHA: (186) implies:
% 249.49/59.16 | | | | | | | | | | | | | (187) all_252_1 = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 249.49/59.16 | | | | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 249.49/59.16 | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (30),
% 249.49/59.16 | | | | | | | | | | | | | (34), (35), (36), (39), (40), (41), (43), (44),
% 249.49/59.16 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 249.49/59.16 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (63), (64),
% 249.49/59.16 | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (74),
% 249.49/59.16 | | | | | | | | | | | | | (75), (80), (81), (82), (84), (85), (86), (94),
% 249.49/59.16 | | | | | | | | | | | | | (95), (96), (99), (100), (101), (102), (103),
% 249.49/59.16 | | | | | | | | | | | | | (104), (108), (109), (110), (112), (113), (114),
% 249.49/59.16 | | | | | | | | | | | | | (116), (117), (118), (119), (121), (122), (124),
% 249.49/59.16 | | | | | | | | | | | | | (125), (126), (129), (130), (131), (134), (136),
% 249.49/59.16 | | | | | | | | | | | | | (137), (139), (161), (163), (173), (181), (182),
% 249.49/59.16 | | | | | | | | | | | | | (187) are inconsistent by sub-proof #172.
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | (188) all_252_3 = e1 & op(e3, e3) = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | ALPHA: (188) implies:
% 249.49/59.16 | | | | | | | | | | | | | (189) all_252_3 = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 249.49/59.16 | | | | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 249.49/59.16 | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (30),
% 249.49/59.16 | | | | | | | | | | | | | (34), (35), (36), (39), (40), (41), (43), (44),
% 249.49/59.16 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 249.49/59.16 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (63), (64),
% 249.49/59.16 | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (74),
% 249.49/59.16 | | | | | | | | | | | | | (75), (80), (81), (82), (84), (85), (86), (94),
% 249.49/59.16 | | | | | | | | | | | | | (95), (96), (99), (100), (101), (102), (103),
% 249.49/59.16 | | | | | | | | | | | | | (104), (108), (109), (110), (112), (113), (114),
% 249.49/59.16 | | | | | | | | | | | | | (116), (117), (118), (119), (121), (122), (124),
% 249.49/59.16 | | | | | | | | | | | | | (125), (126), (129), (130), (131), (134), (136),
% 249.49/59.16 | | | | | | | | | | | | | (137), (139), (161), (163), (173), (181), (182),
% 249.49/59.16 | | | | | | | | | | | | | (189) are inconsistent by sub-proof #171.
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | End of split
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | (190) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 249.49/59.16 | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 249.49/59.16 | | | | | | | | | | | | op(e0, e3) = e1)
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | BETA: splitting (190) gives:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | (191) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | ALPHA: (191) implies:
% 249.49/59.16 | | | | | | | | | | | | | (192) all_252_7 = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (12), (14), (15), (17),
% 249.49/59.16 | | | | | | | | | | | | | (18), (19), (20), (21), (22), (23), (24), (25),
% 249.49/59.16 | | | | | | | | | | | | | (26), (27), (28), (34), (36), (39), (40), (41),
% 249.49/59.16 | | | | | | | | | | | | | (43), (44), (47), (48), (49), (50), (52), (53),
% 249.49/59.16 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (63), (64), (65),
% 249.49/59.16 | | | | | | | | | | | | | (67), (68), (69), (70), (74), (75), (81), (82),
% 249.49/59.16 | | | | | | | | | | | | | (84), (85), (86), (94), (95), (96), (99), (100),
% 249.49/59.16 | | | | | | | | | | | | | (101), (102), (109), (112), (113), (116), (118),
% 249.49/59.16 | | | | | | | | | | | | | (119), (130), (131), (134), (136), (137), (139),
% 249.49/59.16 | | | | | | | | | | | | | (163), (173), (181), (182), (192) are inconsistent
% 249.49/59.16 | | | | | | | | | | | | | by sub-proof #170.
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | (193) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 249.49/59.16 | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | REF_CLOSE: (21), (40), (70), (82), (173), (193) are
% 249.49/59.16 | | | | | | | | | | | | | inconsistent by sub-proof #169.
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | End of split
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | End of split
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | Case 2:
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | (194) ~ (all_130_1 = e0) & op(e3, e2) = all_130_1 &
% 249.49/59.16 | | | | | | | | | | | $i(all_130_1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | ALPHA: (194) implies:
% 249.49/59.16 | | | | | | | | | | | (195) ~ (all_130_1 = e0)
% 249.49/59.16 | | | | | | | | | | | (196) op(e3, e2) = all_130_1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_10_2, e1, e3, e2,
% 249.49/59.16 | | | | | | | | | | | simplifying with (22), (163) gives:
% 249.49/59.16 | | | | | | | | | | | (197) all_10_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | GROUND_INST: instantiating (21) with all_8_2, all_130_1, e2,
% 249.49/59.16 | | | | | | | | | | | e3, simplifying with (112), (196) gives:
% 249.49/59.16 | | | | | | | | | | | (198) all_130_1 = all_8_2
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | COMBINE_EQS: (38), (197) imply:
% 249.49/59.16 | | | | | | | | | | | (199) all_78_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | COMBINE_EQS: (13), (197) imply:
% 249.49/59.16 | | | | | | | | | | | (200) all_172_2 = e1
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | REDUCE: (5), (197) imply:
% 249.49/59.16 | | | | | | | | | | | (201) ~ (e4 = e1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | REDUCE: (159), (197) imply:
% 249.49/59.16 | | | | | | | | | | | (202) ~ (e2 = e1)
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | BETA: splitting (125) gives:
% 249.49/59.16 | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | (203) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 249.49/59.16 | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | BETA: splitting (203) gives:
% 249.49/59.16 | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | Case 1:
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | (204) all_252_1 = e1 & op(e4, e3) = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.16 | | | | | | | | | | | | | ALPHA: (204) implies:
% 249.49/59.16 | | | | | | | | | | | | | (205) all_252_1 = e1
% 249.49/59.16 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 249.49/59.17 | | | | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 249.49/59.17 | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (30),
% 249.49/59.17 | | | | | | | | | | | | | (34), (35), (36), (39), (40), (41), (43), (44),
% 249.49/59.17 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 249.49/59.17 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (63), (64),
% 249.49/59.17 | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (74),
% 249.49/59.17 | | | | | | | | | | | | | (75), (80), (81), (82), (84), (85), (86), (94),
% 249.49/59.17 | | | | | | | | | | | | | (95), (96), (99), (100), (101), (102), (103),
% 249.49/59.17 | | | | | | | | | | | | | (104), (108), (109), (110), (112), (113), (114),
% 249.49/59.17 | | | | | | | | | | | | | (116), (117), (118), (119), (121), (122), (124),
% 249.49/59.17 | | | | | | | | | | | | | (125), (126), (129), (130), (131), (134), (136),
% 249.49/59.17 | | | | | | | | | | | | | (137), (139), (161), (163), (173), (199), (200),
% 249.49/59.17 | | | | | | | | | | | | | (205) are inconsistent by sub-proof #172.
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | (206) all_252_3 = e1 & op(e3, e3) = e1
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | ALPHA: (206) implies:
% 249.49/59.17 | | | | | | | | | | | | | (207) all_252_3 = e1
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 249.49/59.17 | | | | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 249.49/59.17 | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (30),
% 249.49/59.17 | | | | | | | | | | | | | (34), (35), (36), (39), (40), (41), (43), (44),
% 249.49/59.17 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (52), (53),
% 249.49/59.17 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (61), (63), (64),
% 249.49/59.17 | | | | | | | | | | | | | (65), (66), (67), (68), (69), (70), (71), (74),
% 249.49/59.17 | | | | | | | | | | | | | (75), (80), (81), (82), (84), (85), (86), (94),
% 249.49/59.17 | | | | | | | | | | | | | (95), (96), (99), (100), (101), (102), (103),
% 249.49/59.17 | | | | | | | | | | | | | (104), (108), (109), (110), (112), (113), (114),
% 249.49/59.17 | | | | | | | | | | | | | (116), (117), (118), (119), (121), (122), (124),
% 249.49/59.17 | | | | | | | | | | | | | (125), (126), (129), (130), (131), (134), (136),
% 249.49/59.17 | | | | | | | | | | | | | (137), (139), (161), (163), (173), (199), (200),
% 249.49/59.17 | | | | | | | | | | | | | (207) are inconsistent by sub-proof #171.
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | (208) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 249.49/59.17 | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 249.49/59.17 | | | | | | | | | | | | op(e0, e3) = e1)
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | BETA: splitting (208) gives:
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | (209) all_252_7 = e1 & op(e2, e3) = e1
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | ALPHA: (209) implies:
% 249.49/59.17 | | | | | | | | | | | | | (210) all_252_7 = e1
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (12), (14), (15), (17),
% 249.49/59.17 | | | | | | | | | | | | | (18), (19), (20), (21), (22), (23), (24), (25),
% 249.49/59.17 | | | | | | | | | | | | | (26), (27), (28), (34), (36), (39), (40), (41),
% 249.49/59.17 | | | | | | | | | | | | | (43), (44), (47), (48), (49), (50), (52), (53),
% 249.49/59.17 | | | | | | | | | | | | | (54), (55), (56), (57), (58), (63), (64), (65),
% 249.49/59.17 | | | | | | | | | | | | | (67), (68), (69), (70), (74), (75), (81), (82),
% 249.49/59.17 | | | | | | | | | | | | | (84), (85), (86), (94), (95), (96), (99), (100),
% 249.49/59.17 | | | | | | | | | | | | | (101), (102), (109), (112), (113), (116), (118),
% 249.49/59.17 | | | | | | | | | | | | | (119), (130), (131), (134), (136), (137), (139),
% 249.49/59.17 | | | | | | | | | | | | | (163), (173), (199), (200), (210) are inconsistent
% 249.49/59.17 | | | | | | | | | | | | | by sub-proof #170.
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | (211) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 249.49/59.17 | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | REF_CLOSE: (21), (40), (70), (82), (173), (211) are
% 249.49/59.17 | | | | | | | | | | | | | inconsistent by sub-proof #169.
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | (212) all_252_21 = e2 & op(e0, e3) = e2
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | ALPHA: (212) implies:
% 249.49/59.17 | | | | | | | | | (213) all_252_21 = e2
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | REF_CLOSE: (6), (17), (18), (19), (21), (23), (25), (40),
% 249.49/59.17 | | | | | | | | | (41), (43), (44), (54), (58), (63), (69), (70),
% 249.49/59.17 | | | | | | | | | (82), (85), (94), (96), (109), (116), (136), (139),
% 249.49/59.17 | | | | | | | | | (213) are inconsistent by sub-proof #524.
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | End of split
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | End of split
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | End of split
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | End of split
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | Case 2:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | (214) all_68_2 = e4
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | COMBINE_EQS: (79), (214) imply:
% 249.49/59.17 | | | | | (215) all_22_2 = e4
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | REDUCE: (78), (215) imply:
% 249.49/59.17 | | | | | (216) op(e4, e3) = e0
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | REDUCE: (82), (215) imply:
% 249.49/59.17 | | | | | (217) op(e0, e3) = e4
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | BETA: splitting (54) gives:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | Case 1:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | (218) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 249.49/59.17 | | | | | | op(e0, e3) = e3)
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | BETA: splitting (218) gives:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | Case 1:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (219) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | ALPHA: (219) implies:
% 249.49/59.17 | | | | | | | (220) all_252_20 = e3
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | REF_CLOSE: (23), (85), (220) are inconsistent by sub-proof #520.
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | Case 2:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (221) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | ALPHA: (221) implies:
% 249.49/59.17 | | | | | | | (222) op(e0, e3) = e3
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | REF_CLOSE: (21), (94), (217), (222) are inconsistent by sub-proof
% 249.49/59.17 | | | | | | | #964.
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | End of split
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | Case 2:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | (223) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 249.49/59.17 | | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | REF_CLOSE: (19), (21), (24), (43), (51), (96), (105), (123), (128),
% 249.49/59.17 | | | | | | (136), (216), (223) are inconsistent by sub-proof #961.
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | End of split
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | End of split
% 249.49/59.17 | | | |
% 249.49/59.17 | | | Case 2:
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | (224) all_62_2 = e4
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | REDUCE: (92), (224) imply:
% 249.49/59.17 | | | | (225) ~ (all_16_2 = e4)
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | SIMP: (225) implies:
% 249.49/59.17 | | | | (226) ~ (all_16_2 = e4)
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | REDUCE: (127), (224) imply:
% 249.49/59.17 | | | | (227) ~ (all_4_2 = e4)
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | BETA: splitting (16) gives:
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | Case 1:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | (228) all_250_15 = e4
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | COMBINE_EQS: (93), (228) imply:
% 249.49/59.17 | | | | | (229) all_16_2 = e4
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | REDUCE: (226), (229) imply:
% 249.49/59.17 | | | | | (230) $false
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | CLOSE: (230) is inconsistent.
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | Case 2:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | (231) all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 249.49/59.17 | | | | | all_250_15 = e0
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | BETA: splitting (231) gives:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | Case 1:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | (232) all_250_15 = e3
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | COMBINE_EQS: (93), (232) imply:
% 249.49/59.17 | | | | | | (233) all_16_2 = e3
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | REDUCE: (119), (233) imply:
% 249.49/59.17 | | | | | | (234) $false
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | CLOSE: (234) is inconsistent.
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | Case 2:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | (235) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = e0
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | BETA: splitting (235) gives:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | Case 1:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (236) all_250_15 = e2
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | COMBINE_EQS: (93), (236) imply:
% 249.49/59.17 | | | | | | | (237) all_16_2 = e2
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | REDUCE: (66), (237) imply:
% 249.49/59.17 | | | | | | | (238) $false
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | CLOSE: (238) is inconsistent.
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | Case 2:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (239) all_250_15 = e1 | all_250_15 = e0
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | BETA: splitting (239) gives:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | (240) all_250_15 = e1
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | COMBINE_EQS: (93), (240) imply:
% 249.49/59.17 | | | | | | | | (241) all_16_2 = e1
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | SIMP: (241) implies:
% 249.49/59.17 | | | | | | | | (242) all_16_2 = e1
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | REDUCE: (77), (242) imply:
% 249.49/59.17 | | | | | | | | (243) op(e1, e2) = e4
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | REF_CLOSE: (4), (21), (102), (243) are inconsistent by sub-proof
% 249.49/59.17 | | | | | | | | #831.
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | (244) all_250_15 = e0
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | REF_CLOSE: (93), (129), (244) are inconsistent by sub-proof
% 249.49/59.17 | | | | | | | | #168.
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | End of split
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | End of split
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | End of split
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | End of split
% 249.49/59.17 | | | |
% 249.49/59.17 | | | End of split
% 249.49/59.17 | | |
% 249.49/59.17 | | Case 2:
% 249.49/59.17 | | |
% 249.49/59.17 | | | (245) all_58_2 = e3
% 249.49/59.17 | | |
% 249.49/59.17 | | | COMBINE_EQS: (87), (245) imply:
% 249.49/59.17 | | | (246) all_20_2 = e3
% 249.49/59.17 | | |
% 249.49/59.17 | | | SIMP: (246) implies:
% 249.49/59.17 | | | (247) all_20_2 = e3
% 249.49/59.17 | | |
% 249.49/59.17 | | | REDUCE: (97), (247) imply:
% 249.49/59.17 | | | (248) ~ (all_244_15 = e3)
% 249.49/59.17 | | |
% 249.49/59.17 | | | REDUCE: (111), (247) imply:
% 249.49/59.17 | | | (249) ~ (all_22_2 = e3)
% 249.49/59.17 | | |
% 249.49/59.17 | | | REDUCE: (116), (247) imply:
% 249.49/59.17 | | | (250) ~ (e4 = e3)
% 249.49/59.17 | | |
% 249.49/59.17 | | | REDUCE: (60), (247) imply:
% 249.49/59.17 | | | (251) op(e3, e1) = e0
% 249.49/59.17 | | |
% 249.49/59.17 | | | REDUCE: (96), (247) imply:
% 249.49/59.17 | | | (252) op(e0, e1) = e3
% 249.49/59.17 | | |
% 249.49/59.17 | | | BETA: splitting (54) gives:
% 249.49/59.17 | | |
% 249.49/59.17 | | | Case 1:
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | (253) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0,
% 249.49/59.17 | | | | e3) = e3)
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | REF_CLOSE: (21), (23), (82), (85), (249), (253) are inconsistent by
% 249.49/59.17 | | | | sub-proof #167.
% 249.49/59.17 | | | |
% 249.49/59.17 | | | Case 2:
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | (254) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.17 | | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | BETA: splitting (254) gives:
% 249.49/59.17 | | | |
% 249.49/59.17 | | | | Case 1:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | (255) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | ALPHA: (255) implies:
% 249.49/59.17 | | | | | (256) op(e0, e2) = e3
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | REF_CLOSE: (19), (21), (43), (256) are inconsistent by sub-proof #975.
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | Case 2:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | (257) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 249.49/59.17 | | | | | op(e0, e0) = e3)
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | BETA: splitting (257) gives:
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | | Case 1:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | GROUND_INST: instantiating (21) with all_36_2, e0, e1, e3,
% 249.49/59.17 | | | | | | simplifying with (64), (251) gives:
% 249.49/59.17 | | | | | | (258) all_36_2 = e0
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | REDUCE: (115), (258) imply:
% 249.49/59.17 | | | | | | (259) ~ (all_244_15 = e0)
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | BETA: splitting (37) gives:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | Case 1:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (260) all_250_18 = e4
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | COMBINE_EQS: (83), (260) imply:
% 249.49/59.17 | | | | | | | (261) all_244_15 = e4
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | SIMP: (261) implies:
% 249.49/59.17 | | | | | | | (262) all_244_15 = e4
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | REDUCE: (39), (262) imply:
% 249.49/59.17 | | | | | | | (263) $false
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | CLOSE: (263) is inconsistent.
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | Case 2:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | (264) all_250_18 = e3 | all_250_18 = e2 | all_250_18 = e1 |
% 249.49/59.17 | | | | | | | all_250_18 = e0
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | BETA: splitting (264) gives:
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | (265) all_250_18 = e3
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | COMBINE_EQS: (83), (265) imply:
% 249.49/59.17 | | | | | | | | (266) all_244_15 = e3
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | SIMP: (266) implies:
% 249.49/59.17 | | | | | | | | (267) all_244_15 = e3
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | REDUCE: (248), (267) imply:
% 249.49/59.17 | | | | | | | | (268) $false
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | CLOSE: (268) is inconsistent.
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | (269) all_250_18 = e2 | all_250_18 = e1 | all_250_18 = e0
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | BETA: splitting (269) gives:
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | (270) all_250_18 = e2
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | COMBINE_EQS: (83), (270) imply:
% 249.49/59.17 | | | | | | | | | (271) all_244_15 = e2
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | SIMP: (271) implies:
% 249.49/59.17 | | | | | | | | | (272) all_244_15 = e2
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | REDUCE: (108), (272) imply:
% 249.49/59.17 | | | | | | | | | (273) $false
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | CLOSE: (273) is inconsistent.
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | (274) all_250_18 = e1 | all_250_18 = e0
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | BETA: splitting (274) gives:
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | (275) all_250_18 = e1
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | COMBINE_EQS: (83), (275) imply:
% 249.49/59.17 | | | | | | | | | | (276) all_244_15 = e1
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | SIMP: (276) implies:
% 249.49/59.17 | | | | | | | | | | (277) all_244_15 = e1
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | REDUCE: (32), (277) imply:
% 249.49/59.17 | | | | | | | | | | (278) ~ (all_16_2 = e1)
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | SIMP: (278) implies:
% 249.49/59.17 | | | | | | | | | | (279) ~ (all_16_2 = e1)
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | BETA: splitting (16) gives:
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | (280) all_250_15 = e4
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | COMBINE_EQS: (93), (280) imply:
% 249.49/59.17 | | | | | | | | | | | (281) all_16_2 = e4
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | REDUCE: (52), (281) imply:
% 249.49/59.17 | | | | | | | | | | | (282) op(e1, e4) = e4
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | REF_CLOSE: (18), (21), (52), (53), (99), (282) are
% 249.49/59.17 | | | | | | | | | | | inconsistent by sub-proof #214.
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | (283) all_250_15 = e3 | all_250_15 = e2 | all_250_15 =
% 249.49/59.17 | | | | | | | | | | | e1 | all_250_15 = e0
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | BETA: splitting (283) gives:
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | (284) all_250_15 = e3
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | COMBINE_EQS: (93), (284) imply:
% 249.49/59.17 | | | | | | | | | | | | (285) all_16_2 = e3
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | SIMP: (285) implies:
% 249.49/59.17 | | | | | | | | | | | | (286) all_16_2 = e3
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | REDUCE: (119), (286) imply:
% 249.49/59.17 | | | | | | | | | | | | (287) $false
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | (288) all_250_15 = e2 | all_250_15 = e1 | all_250_15 =
% 249.49/59.17 | | | | | | | | | | | | e0
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | BETA: splitting (288) gives:
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | (289) all_250_15 = e2
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | COMBINE_EQS: (93), (289) imply:
% 249.49/59.17 | | | | | | | | | | | | | (290) all_16_2 = e2
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | SIMP: (290) implies:
% 249.49/59.17 | | | | | | | | | | | | | (291) all_16_2 = e2
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | REDUCE: (66), (291) imply:
% 249.49/59.17 | | | | | | | | | | | | | (292) $false
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | (293) all_250_15 = e1 | all_250_15 = e0
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | BETA: splitting (293) gives:
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | Case 1:
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | (294) all_250_15 = e1
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | COMBINE_EQS: (93), (294) imply:
% 249.49/59.17 | | | | | | | | | | | | | | (295) all_16_2 = e1
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | SIMP: (295) implies:
% 249.49/59.17 | | | | | | | | | | | | | | (296) all_16_2 = e1
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | REDUCE: (279), (296) imply:
% 249.49/59.17 | | | | | | | | | | | | | | (297) $false
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | (298) all_250_15 = e0
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | | REF_CLOSE: (93), (129), (298) are inconsistent by sub-proof
% 249.49/59.17 | | | | | | | | | | | | | | #168.
% 249.49/59.17 | | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | Case 2:
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | (299) all_250_18 = e0
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | COMBINE_EQS: (83), (299) imply:
% 249.49/59.17 | | | | | | | | | | (300) all_244_15 = e0
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | SIMP: (300) implies:
% 249.49/59.17 | | | | | | | | | | (301) all_244_15 = e0
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | REDUCE: (259), (301) imply:
% 249.49/59.17 | | | | | | | | | | (302) $false
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | | CLOSE: (302) is inconsistent.
% 249.49/59.17 | | | | | | | | | |
% 249.49/59.17 | | | | | | | | | End of split
% 249.49/59.17 | | | | | | | | |
% 249.49/59.17 | | | | | | | | End of split
% 249.49/59.17 | | | | | | | |
% 249.49/59.17 | | | | | | | End of split
% 249.49/59.17 | | | | | | |
% 249.49/59.17 | | | | | | End of split
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | Case 2:
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | (303) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | ALPHA: (303) implies:
% 249.49/59.17 | | | | | | (304) all_252_24 = e3
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | | REF_CLOSE: (6), (17), (18), (20), (21), (23), (25), (40), (41),
% 249.49/59.17 | | | | | | (44), (45), (46), (58), (63), (64), (67), (69), (70),
% 249.49/59.17 | | | | | | (82), (85), (94), (96), (109), (110), (116), (251),
% 249.49/59.17 | | | | | | (252), (304) are inconsistent by sub-proof #182.
% 249.49/59.17 | | | | | |
% 249.49/59.17 | | | | | End of split
% 249.49/59.17 | | | | |
% 249.49/59.17 | | | | End of split
% 249.49/59.17 | | | |
% 249.49/59.17 | | | End of split
% 249.49/59.17 | | |
% 249.49/59.17 | | End of split
% 249.49/59.17 | |
% 249.49/59.17 | Case 2:
% 249.49/59.17 | |
% 249.49/59.17 | | (305) all_56_2 = e0
% 249.49/59.17 | |
% 249.49/59.17 | | COMBINE_EQS: (42), (305) imply:
% 249.49/59.17 | | (306) all_8_2 = e0
% 249.49/59.17 | |
% 249.49/59.17 | | REDUCE: (120), (306) imply:
% 249.49/59.17 | | (307) op(e0, e2) = e3
% 249.49/59.17 | |
% 249.49/59.17 | | REF_CLOSE: (19), (21), (43), (307) are inconsistent by sub-proof #975.
% 249.49/59.17 | |
% 249.49/59.17 | End of split
% 249.49/59.17 |
% 249.49/59.17 End of proof
% 249.49/59.17
% 249.49/59.17 Sub-proof #167 shows that the following formulas are inconsistent:
% 249.49/59.17 ----------------------------------------------------------------
% 249.49/59.17 (1) ~ (all_22_2 = e3)
% 249.49/59.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.17 (3) ~ (e3 = e2)
% 249.49/59.17 (4) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.17 (5) op(e0, e3) = all_22_2
% 249.49/59.17 (6) all_252_20 = e2
% 249.49/59.17
% 249.49/59.17 Begin of proof
% 249.49/59.17 |
% 249.49/59.17 | BETA: splitting (4) gives:
% 249.49/59.17 |
% 249.49/59.17 | Case 1:
% 249.49/59.17 | |
% 249.49/59.17 | | (7) all_252_20 = e3 & op(e0, e4) = e3
% 249.49/59.17 | |
% 249.49/59.17 | | ALPHA: (7) implies:
% 249.49/59.17 | | (8) all_252_20 = e3
% 249.49/59.17 | |
% 249.49/59.17 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #520.
% 249.49/59.17 | |
% 249.49/59.17 | Case 2:
% 249.49/59.17 | |
% 249.49/59.17 | | (9) all_252_21 = e3 & op(e0, e3) = e3
% 249.49/59.17 | |
% 249.49/59.17 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #959.
% 249.49/59.17 | |
% 249.49/59.17 | End of split
% 249.49/59.17 |
% 249.49/59.17 End of proof
% 249.49/59.17
% 249.49/59.17 Sub-proof #168 shows that the following formulas are inconsistent:
% 249.49/59.17 ----------------------------------------------------------------
% 249.49/59.17 (1) all_250_15 = all_16_2
% 249.49/59.17 (2) all_250_15 = e0
% 249.49/59.17 (3) ~ (all_16_2 = e0)
% 249.49/59.17
% 249.49/59.17 Begin of proof
% 249.49/59.17 |
% 249.49/59.17 | COMBINE_EQS: (1), (2) imply:
% 249.49/59.17 | (4) all_16_2 = e0
% 249.49/59.17 |
% 249.49/59.17 | SIMP: (4) implies:
% 249.49/59.17 | (5) all_16_2 = e0
% 249.49/59.17 |
% 249.49/59.17 | REDUCE: (3), (5) imply:
% 249.49/59.17 | (6) $false
% 249.49/59.17 |
% 249.49/59.17 | CLOSE: (6) is inconsistent.
% 249.49/59.17 |
% 249.49/59.17 End of proof
% 249.49/59.17
% 249.49/59.17 Sub-proof #169 shows that the following formulas are inconsistent:
% 249.49/59.17 ----------------------------------------------------------------
% 249.49/59.17 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.17 (2) ~ (e2 = e1)
% 249.49/59.17 (3) all_252_13 = e2
% 249.49/59.17 (4) ~ (all_22_2 = e1)
% 249.49/59.17 (5) op(e0, e3) = all_22_2
% 249.49/59.17 (6) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.17
% 249.49/59.17 Begin of proof
% 249.49/59.17 |
% 249.49/59.17 | BETA: splitting (6) gives:
% 249.49/59.17 |
% 249.49/59.17 | Case 1:
% 249.49/59.17 | |
% 249.49/59.17 | | (7) all_252_13 = e1 & op(e1, e3) = e1
% 249.49/59.17 | |
% 249.49/59.17 | | ALPHA: (7) implies:
% 249.49/59.17 | | (8) all_252_13 = e1
% 249.49/59.17 | |
% 249.49/59.17 | | COMBINE_EQS: (3), (8) imply:
% 249.49/59.17 | | (9) e2 = e1
% 249.49/59.17 | |
% 249.49/59.17 | | REDUCE: (2), (9) imply:
% 249.49/59.17 | | (10) $false
% 249.49/59.17 | |
% 249.49/59.17 | | CLOSE: (10) is inconsistent.
% 249.49/59.17 | |
% 249.49/59.17 | Case 2:
% 249.49/59.17 | |
% 249.49/59.17 | | (11) all_252_21 = e1 & op(e0, e3) = e1
% 249.49/59.17 | |
% 249.49/59.17 | | ALPHA: (11) implies:
% 249.49/59.17 | | (12) op(e0, e3) = e1
% 249.49/59.17 | |
% 249.49/59.17 | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #714.
% 249.49/59.17 | |
% 249.49/59.17 | End of split
% 249.49/59.17 |
% 249.49/59.17 End of proof
% 249.49/59.17
% 249.49/59.17 Sub-proof #170 shows that the following formulas are inconsistent:
% 249.49/59.17 ----------------------------------------------------------------
% 249.49/59.17 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.17 all_250_23 = e0
% 249.49/59.17 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.17 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.17 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.17 (3) ~ (all_4_2 = e4)
% 249.49/59.17 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.17 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.17 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.17 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.17 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.17 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.17 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 249.49/59.17 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.17 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.17 (7) all_252_6 = e0
% 249.49/59.17 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 249.49/59.17 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 249.49/59.17 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.17 (9) ~ (e2 = e0)
% 249.49/59.17 (10) ~ (e1 = e0)
% 249.49/59.17 (11) ~ (all_28_2 = e3)
% 249.49/59.17 (12) op(e4, e1) = e2
% 249.49/59.17 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.17 (14) op(e2, e3) = all_10_2
% 249.49/59.17 (15) ~ (e3 = e2)
% 249.49/59.17 (16) op(e0, e0) = all_244_24
% 249.49/59.17 (17) ~ (e4 = e0)
% 249.49/59.17 (18) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.17 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.17 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.17 (19) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.17 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.17 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.17 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.17 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.17 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.17 (21) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.17 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.17 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.17 (22) op(e4, e2) = all_6_2
% 249.49/59.17 (23) ~ (all_244_15 = e4)
% 249.49/59.17 (24) ~ (e2 = e1)
% 249.49/59.17 (25) all_252_13 = e2
% 249.49/59.17 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.17 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.17 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.17 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.17 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.17 op(e0, e1) = e0)))
% 249.49/59.17 (27) op(e0, e2) = all_28_2
% 249.49/59.17 (28) ~ (e4 = e1)
% 249.49/59.17 (29) ~ (all_6_2 = e1)
% 249.49/59.17 (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.17 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.17 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.17 (31) all_80_2 = all_6_2
% 249.49/59.17 (32) op(all_34_2, e0) = e1
% 249.49/59.17 (33) op(e1, e4) = all_16_2
% 249.49/59.17 (34) op(e2, all_16_2) = e1
% 249.49/59.17 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.17 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.17 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.18 (36) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.18 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.18 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.18 (37) ~ (all_28_2 = all_20_2)
% 249.49/59.18 (38) op(e1, e3) = all_62_2
% 249.49/59.18 (39) ~ (e3 = e0)
% 249.49/59.18 (40) op(e2, e3) = e1
% 249.49/59.18 (41) ~ (all_22_2 = e4)
% 249.49/59.18 (42) ~ (e3 = e1)
% 249.49/59.18 (43) op(e3, e1) = all_36_2
% 249.49/59.18 (44) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.18 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.18 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.18 (45) all_252_11 = e4
% 249.49/59.18 (46) ~ (all_8_2 = e1)
% 249.49/59.18 (47) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.18 (48) ~ (all_22_2 = e1)
% 249.49/59.18 (49) ~ (all_8_2 = e0)
% 249.49/59.18 (50) all_74_2 = all_36_2
% 249.49/59.18 (51) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.18 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.18 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.18 (52) op(all_6_2, e0) = e2
% 249.49/59.18 (53) op(e0, e3) = all_22_2
% 249.49/59.18 (54) op(all_34_2, all_20_2) = e0
% 249.49/59.18 (55) all_252_20 = e2
% 249.49/59.18 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.18 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.18 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.18 (57) ~ (e4 = e3)
% 249.49/59.18 (58) op(e1, e1) = all_244_15
% 249.49/59.18 (59) op(e0, e1) = all_20_2
% 249.49/59.18 (60) op(e2, e4) = e0
% 249.49/59.18 (61) all_82_2 = all_28_2
% 249.49/59.18 (62) ~ (all_244_24 = e2)
% 249.49/59.18 (63) op(e1, e2) = all_4_2
% 249.49/59.18 (64) all_252_7 = e1
% 249.49/59.18 (65) ~ (e4 = e2)
% 249.49/59.18 (66) op(e3, e2) = all_8_2
% 249.49/59.18 (67) op(all_36_2, e1) = e3
% 249.49/59.18 (68) ~ (all_20_2 = e4)
% 249.49/59.18 (69) op(e2, e0) = all_40_2
% 249.49/59.18 (70) all_78_2 = e1
% 249.49/59.18 (71) ~ (all_20_2 = e3)
% 249.49/59.18 (72) ~ (all_16_2 = e3)
% 249.49/59.18 (73) all_172_2 = e1
% 249.49/59.18 (74) ~ (all_62_2 = e4)
% 249.49/59.18 (75) ~ (all_20_2 = e2)
% 249.49/59.18 (76) all_250_23 = all_20_2
% 249.49/59.18
% 249.49/59.18 Begin of proof
% 249.49/59.18 |
% 249.49/59.18 | BETA: splitting (36) gives:
% 249.49/59.18 |
% 249.49/59.18 | Case 1:
% 249.49/59.18 | |
% 249.49/59.18 | | (77) ~ (all_172_2 = e1)
% 249.49/59.18 | |
% 249.49/59.18 | | REDUCE: (73), (77) imply:
% 249.49/59.18 | | (78) $false
% 249.49/59.18 | |
% 249.49/59.18 | | CLOSE: (78) is inconsistent.
% 249.49/59.18 | |
% 249.49/59.18 | Case 2:
% 249.49/59.18 | |
% 249.49/59.18 | | (79) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 249.49/59.18 | | all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4)
% 249.49/59.18 | | & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.18 | |
% 249.49/59.18 | | BETA: splitting (79) gives:
% 249.49/59.18 | |
% 249.49/59.18 | | Case 1:
% 249.49/59.18 | | |
% 249.49/59.18 | | | (80) ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 249.49/59.18 | | | all_172_0 & $i(all_172_0) & $i(all_172_1)
% 249.49/59.18 | | |
% 249.49/59.18 | | | ALPHA: (80) implies:
% 249.49/59.18 | | | (81) op(e3, e1) = all_172_1
% 249.49/59.18 | | |
% 249.49/59.18 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.18 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 249.49/59.18 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 249.49/59.18 | | | (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 249.49/59.18 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 249.49/59.18 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 249.49/59.18 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (74),
% 249.49/59.18 | | | (75), (76), (81) are inconsistent by sub-proof #192.
% 249.49/59.18 | | |
% 249.49/59.18 | | Case 2:
% 249.49/59.18 | | |
% 249.49/59.18 | | | (82) ~ (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1)
% 249.49/59.18 | | |
% 249.49/59.18 | | | ALPHA: (82) implies:
% 249.49/59.18 | | | (83) op(e3, e1) = all_172_1
% 249.49/59.18 | | |
% 249.49/59.18 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.18 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 249.49/59.18 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 249.49/59.18 | | | (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 249.49/59.18 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 249.49/59.18 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 249.49/59.18 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (74),
% 249.49/59.18 | | | (75), (76), (83) are inconsistent by sub-proof #192.
% 249.49/59.18 | | |
% 249.49/59.18 | | End of split
% 249.49/59.18 | |
% 249.49/59.18 | End of split
% 249.49/59.18 |
% 249.49/59.18 End of proof
% 249.49/59.18
% 249.49/59.18 Sub-proof #171 shows that the following formulas are inconsistent:
% 249.49/59.18 ----------------------------------------------------------------
% 249.49/59.18 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.18 all_250_23 = e0
% 249.49/59.18 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.18 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.18 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.18 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.18 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.18 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.18 (4) ~ (all_4_2 = e4)
% 249.49/59.18 (5) ~ (all_10_2 = e4)
% 249.49/59.18 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.18 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.18 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.18 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.18 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.18 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.18 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.18 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.18 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.18 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 249.49/59.18 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 249.49/59.18 | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.18 (10) op(e4, e0) = all_30_2
% 249.49/59.18 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.18 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.18 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.18 (12) all_252_6 = e0
% 249.49/59.18 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.18 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.18 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.18 (14) ~ (e2 = e0)
% 249.49/59.18 (15) ~ (e1 = e0)
% 249.49/59.18 (16) ~ (all_28_2 = e3)
% 249.49/59.18 (17) op(e4, e1) = e2
% 249.49/59.18 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.18 (19) all_252_3 = e1
% 249.49/59.18 (20) op(e2, e3) = all_10_2
% 249.49/59.18 (21) ~ (e3 = e2)
% 249.49/59.18 (22) op(e0, e0) = all_244_24
% 249.49/59.18 (23) ~ (e4 = e0)
% 249.49/59.18 (24) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.18 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.18 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.18 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.18 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.18 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.18 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.18 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.18 (27) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.18 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.18 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.18 (28) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.18 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.18 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.18 (29) ~ (all_36_2 = e2)
% 249.49/59.18 (30) op(e4, e2) = all_6_2
% 249.49/59.18 (31) ~ (all_244_15 = e4)
% 249.49/59.18 (32) ~ (e2 = e1)
% 249.49/59.18 (33) all_252_13 = e2
% 249.49/59.18 (34) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.18 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.18 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.18 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.18 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.18 op(e0, e1) = e0)))
% 249.49/59.18 (35) op(e0, e2) = all_28_2
% 249.49/59.18 (36) ~ (e4 = e1)
% 249.49/59.18 (37) all_252_9 = e2
% 249.49/59.18 (38) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.18 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.18 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.18 (39) ~ (all_6_2 = e1)
% 249.49/59.18 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.18 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.18 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.18 (41) all_80_2 = all_6_2
% 249.49/59.18 (42) op(all_34_2, e0) = e1
% 249.49/59.18 (43) op(e1, e4) = all_16_2
% 249.49/59.18 (44) op(e2, all_16_2) = e1
% 249.49/59.18 (45) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.18 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.18 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.18 (46) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.18 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.18 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.18 (47) ~ (all_28_2 = all_20_2)
% 249.49/59.18 (48) op(e1, e3) = all_62_2
% 249.49/59.18 (49) ~ (e3 = e0)
% 249.49/59.18 (50) op(e2, e3) = e1
% 249.49/59.18 (51) ~ (all_30_2 = e2)
% 249.49/59.18 (52) ~ (all_22_2 = e4)
% 249.49/59.18 (53) ~ (e3 = e1)
% 249.49/59.18 (54) op(e3, e1) = all_36_2
% 249.49/59.18 (55) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.18 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.18 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.18 (56) ~ (all_16_2 = e2)
% 249.49/59.18 (57) all_252_11 = e4
% 249.49/59.18 (58) ~ (all_8_2 = e1)
% 249.49/59.18 (59) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.18 (60) ~ (all_22_2 = e1)
% 249.49/59.18 (61) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.18 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.18 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.18 (62) ~ (all_8_2 = e0)
% 249.49/59.18 (63) all_74_2 = all_36_2
% 249.49/59.18 (64) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.18 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.18 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.18 (65) op(e1, e4) = all_242_1
% 249.49/59.18 (66) op(all_6_2, e0) = e2
% 249.49/59.18 (67) op(e0, e3) = all_22_2
% 249.49/59.18 (68) op(all_34_2, all_20_2) = e0
% 249.49/59.18 (69) all_252_20 = e2
% 249.49/59.18 (70) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.18 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.18 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.18 (71) ~ (e4 = e3)
% 249.49/59.18 (72) op(e1, e1) = all_244_15
% 249.49/59.18 (73) op(e0, e1) = all_20_2
% 249.49/59.18 (74) op(e2, e4) = e0
% 249.49/59.18 (75) all_82_2 = all_28_2
% 249.49/59.18 (76) ~ (all_244_24 = e2)
% 249.49/59.18 (77) op(e1, e2) = all_4_2
% 249.49/59.18 (78) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.18 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.18 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.18 (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.18 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.18 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.18 (80) ~ (all_244_15 = e2)
% 249.49/59.18 (81) ~ (e4 = e2)
% 249.49/59.18 (82) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.18 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.18 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.18 (83) op(e3, e2) = all_8_2
% 249.49/59.18 (84) op(all_36_2, e1) = e3
% 249.49/59.18 (85) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.18 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.18 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.18 (86) ~ (all_20_2 = e4)
% 249.49/59.18 (87) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.18 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.18 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.18 (88) op(e2, e0) = all_40_2
% 249.49/59.18 (89) all_78_2 = e1
% 249.49/59.18 (90) ~ (all_20_2 = e3)
% 249.49/59.18 (91) ~ (all_16_2 = e3)
% 249.49/59.18 (92) all_172_2 = e1
% 249.49/59.18 (93) ~ (all_10_2 = e0)
% 249.49/59.18 (94) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.18 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.18 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.18 (95) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.18 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.18 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.18 (96) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.18 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.18 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.18 (97) ~ (all_62_2 = e4)
% 249.49/59.18 (98) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.18 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.18 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.18 (99) ~ (all_4_2 = e2)
% 249.49/59.18 (100) ~ (all_16_2 = e0)
% 249.49/59.18 (101) ~ (all_20_2 = e2)
% 249.49/59.18 (102) all_250_23 = all_20_2
% 249.49/59.18
% 249.49/59.18 Begin of proof
% 249.49/59.18 |
% 249.49/59.18 | BETA: splitting (46) gives:
% 249.49/59.18 |
% 249.49/59.18 | Case 1:
% 249.49/59.18 | |
% 249.49/59.18 | | (103) ~ (all_172_2 = e1)
% 249.49/59.18 | |
% 249.49/59.18 | | REDUCE: (92), (103) imply:
% 249.49/59.18 | | (104) $false
% 249.49/59.18 | |
% 249.49/59.18 | | CLOSE: (104) is inconsistent.
% 249.49/59.18 | |
% 249.49/59.18 | Case 2:
% 249.49/59.18 | |
% 249.49/59.18 | | (105) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 249.49/59.18 | | all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4)
% 249.49/59.18 | | & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.18 | |
% 249.49/59.18 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 249.49/59.18 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 249.49/59.18 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 249.49/59.18 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 249.49/59.18 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 249.49/59.18 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 249.49/59.18 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 249.49/59.18 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 249.49/59.18 | | (91), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 249.49/59.18 | | (102), (105) are inconsistent by sub-proof #175.
% 249.49/59.18 | |
% 249.49/59.18 | End of split
% 249.49/59.18 |
% 249.49/59.18 End of proof
% 249.49/59.18
% 249.49/59.18 Sub-proof #172 shows that the following formulas are inconsistent:
% 249.49/59.18 ----------------------------------------------------------------
% 249.49/59.18 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.18 all_250_23 = e0
% 249.49/59.18 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.18 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.18 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.18 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.18 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.18 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.18 (4) ~ (all_4_2 = e4)
% 249.49/59.18 (5) ~ (all_10_2 = e4)
% 249.49/59.18 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.18 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.18 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.18 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.18 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.18 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.18 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.18 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.18 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.18 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 249.49/59.18 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 249.49/59.18 | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.18 (10) op(e4, e0) = all_30_2
% 249.49/59.18 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.18 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.18 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.18 (12) all_252_6 = e0
% 249.49/59.18 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.18 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.18 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.18 (14) ~ (e2 = e0)
% 249.49/59.18 (15) ~ (e1 = e0)
% 249.49/59.18 (16) ~ (all_28_2 = e3)
% 249.49/59.18 (17) op(e4, e1) = e2
% 249.49/59.18 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.18 (19) op(e2, e3) = all_10_2
% 249.49/59.18 (20) ~ (e3 = e2)
% 249.49/59.18 (21) op(e0, e0) = all_244_24
% 249.49/59.18 (22) ~ (e4 = e0)
% 249.49/59.18 (23) all_252_1 = e1
% 249.49/59.18 (24) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.18 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.18 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.18 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.18 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.18 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.18 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.18 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.18 (27) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.18 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.18 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.18 (28) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.18 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.18 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.18 (29) ~ (all_36_2 = e2)
% 249.49/59.18 (30) op(e4, e2) = all_6_2
% 249.49/59.18 (31) ~ (all_244_15 = e4)
% 249.49/59.18 (32) ~ (e2 = e1)
% 249.49/59.18 (33) all_252_13 = e2
% 249.49/59.18 (34) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.18 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.18 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.18 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.18 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.18 op(e0, e1) = e0)))
% 249.49/59.18 (35) op(e0, e2) = all_28_2
% 249.49/59.18 (36) ~ (e4 = e1)
% 249.49/59.18 (37) all_252_9 = e2
% 249.49/59.18 (38) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.18 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.18 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.18 (39) ~ (all_6_2 = e1)
% 249.49/59.18 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.18 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.18 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.18 (41) all_80_2 = all_6_2
% 249.49/59.18 (42) op(all_34_2, e0) = e1
% 249.49/59.18 (43) op(e1, e4) = all_16_2
% 249.49/59.18 (44) op(e2, all_16_2) = e1
% 249.49/59.18 (45) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.18 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.18 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.18 (46) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 249.49/59.18 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 249.49/59.18 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.18 (47) ~ (all_28_2 = all_20_2)
% 249.49/59.18 (48) op(e1, e3) = all_62_2
% 249.49/59.18 (49) ~ (e3 = e0)
% 249.49/59.18 (50) op(e2, e3) = e1
% 249.49/59.18 (51) ~ (all_30_2 = e2)
% 249.49/59.18 (52) ~ (all_22_2 = e4)
% 249.49/59.18 (53) ~ (e3 = e1)
% 249.49/59.18 (54) op(e3, e1) = all_36_2
% 249.49/59.18 (55) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.18 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.18 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.18 (56) ~ (all_16_2 = e2)
% 249.49/59.18 (57) all_252_11 = e4
% 249.49/59.18 (58) ~ (all_8_2 = e1)
% 249.49/59.18 (59) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.18 (60) ~ (all_22_2 = e1)
% 249.49/59.18 (61) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.18 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.18 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.18 (62) ~ (all_8_2 = e0)
% 249.49/59.18 (63) all_74_2 = all_36_2
% 249.49/59.18 (64) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.18 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.18 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.18 (65) op(e1, e4) = all_242_1
% 249.49/59.18 (66) op(all_6_2, e0) = e2
% 249.49/59.18 (67) op(e0, e3) = all_22_2
% 249.49/59.18 (68) op(all_34_2, all_20_2) = e0
% 249.49/59.19 (69) all_252_20 = e2
% 249.49/59.19 (70) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.19 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.19 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.19 (71) ~ (e4 = e3)
% 249.49/59.19 (72) op(e1, e1) = all_244_15
% 249.49/59.19 (73) op(e0, e1) = all_20_2
% 249.49/59.19 (74) op(e2, e4) = e0
% 249.49/59.19 (75) all_82_2 = all_28_2
% 249.49/59.19 (76) ~ (all_244_24 = e2)
% 249.49/59.19 (77) op(e1, e2) = all_4_2
% 249.49/59.19 (78) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.19 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.19 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.19 (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.19 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.19 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.19 (80) ~ (all_244_15 = e2)
% 249.49/59.19 (81) ~ (e4 = e2)
% 249.49/59.19 (82) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.19 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.19 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.19 (83) op(e3, e2) = all_8_2
% 249.49/59.19 (84) op(all_36_2, e1) = e3
% 249.49/59.19 (85) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.19 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.19 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.19 (86) ~ (all_20_2 = e4)
% 249.49/59.19 (87) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.19 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.19 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.19 (88) op(e2, e0) = all_40_2
% 249.49/59.19 (89) all_78_2 = e1
% 249.49/59.19 (90) ~ (all_20_2 = e3)
% 249.49/59.19 (91) ~ (all_16_2 = e3)
% 249.49/59.19 (92) all_172_2 = e1
% 249.49/59.19 (93) ~ (all_10_2 = e0)
% 249.49/59.19 (94) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.19 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.19 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.19 (95) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.19 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.19 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.19 (96) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.19 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.19 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.19 (97) ~ (all_62_2 = e4)
% 249.49/59.19 (98) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.19 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.19 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.19 (99) ~ (all_4_2 = e2)
% 249.49/59.19 (100) ~ (all_16_2 = e0)
% 249.49/59.19 (101) ~ (all_20_2 = e2)
% 249.49/59.19 (102) all_250_23 = all_20_2
% 249.49/59.19
% 249.49/59.19 Begin of proof
% 249.49/59.19 |
% 249.49/59.19 | BETA: splitting (46) gives:
% 249.49/59.19 |
% 249.49/59.19 | Case 1:
% 249.49/59.19 | |
% 249.49/59.19 | | (103) ~ (all_172_2 = e1)
% 249.49/59.19 | |
% 249.49/59.19 | | REDUCE: (92), (103) imply:
% 249.49/59.19 | | (104) $false
% 249.49/59.19 | |
% 249.49/59.19 | | CLOSE: (104) is inconsistent.
% 249.49/59.19 | |
% 249.49/59.19 | Case 2:
% 249.49/59.19 | |
% 249.49/59.19 | | (105) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 249.49/59.19 | | all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4)
% 249.49/59.19 | | & op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.19 | |
% 249.49/59.19 | | BETA: splitting (9) gives:
% 249.49/59.19 | |
% 249.49/59.19 | | Case 1:
% 249.49/59.19 | | |
% 249.49/59.19 | | | (106) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3)
% 249.49/59.19 | | | = e4)
% 249.49/59.19 | | |
% 249.49/59.19 | | | BETA: splitting (106) gives:
% 249.49/59.19 | | |
% 249.49/59.19 | | | Case 1:
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | (107) all_252_1 = e4 & op(e4, e3) = e4
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | REF_CLOSE: (23), (36), (107) are inconsistent by sub-proof #955.
% 249.49/59.19 | | | |
% 249.49/59.19 | | | Case 2:
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | (108) all_252_3 = e4 & op(e3, e3) = e4
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | ALPHA: (108) implies:
% 249.49/59.19 | | | | (109) all_252_3 = e4
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | BETA: splitting (61) gives:
% 249.49/59.19 | | | |
% 249.49/59.19 | | | | Case 1:
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | | (110) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 249.49/59.19 | | | | | e3) = e0)
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | | REF_CLOSE: (15), (22), (23), (109), (110) are inconsistent by
% 249.49/59.19 | | | | | sub-proof #683.
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | Case 2:
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | | (111) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 249.49/59.19 | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | | BETA: splitting (111) gives:
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | | Case 1:
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | | (112) all_252_7 = e0 & op(e2, e3) = e0
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | | REF_CLOSE: (18), (19), (93), (112) are inconsistent by sub-proof
% 249.49/59.19 | | | | | | #816.
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | Case 2:
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | | (113) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 249.49/59.19 | | | | | | op(e0, e3) = e0)
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | | BETA: splitting (113) gives:
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | | Case 1:
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | (114) all_252_13 = e0 & op(e1, e3) = e0
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | ALPHA: (114) implies:
% 249.49/59.19 | | | | | | | (115) all_252_13 = e0
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | REF_CLOSE: (14), (33), (115) are inconsistent by sub-proof #418.
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | Case 2:
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | (116) all_252_21 = e0 & op(e0, e3) = e0
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | ALPHA: (116) implies:
% 249.49/59.19 | | | | | | | (117) all_252_21 = e0
% 249.49/59.19 | | | | | | | (118) op(e0, e3) = e0
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | BETA: splitting (105) gives:
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | | Case 1:
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | (119) ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1,
% 249.49/59.19 | | | | | | | | all_172_1) = all_172_0 & $i(all_172_0) &
% 249.49/59.19 | | | | | | | | $i(all_172_1)
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | ALPHA: (119) implies:
% 249.49/59.19 | | | | | | | | (120) op(e3, e1) = all_172_1
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 249.49/59.19 | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 249.49/59.19 | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 249.49/59.19 | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 249.49/59.19 | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 249.49/59.19 | | | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 249.49/59.19 | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 249.49/59.19 | | | | | | | | (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 249.49/59.19 | | | | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 249.49/59.19 | | | | | | | | (84), (85), (86), (87), (88), (89), (90), (91), (93),
% 249.49/59.19 | | | | | | | | (94), (95), (96), (97), (98), (99), (100), (101),
% 249.49/59.19 | | | | | | | | (102), (105), (109), (117), (118), (120) are
% 249.49/59.19 | | | | | | | | inconsistent by sub-proof #173.
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | Case 2:
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | (121) ~ (all_172_1 = e4) & op(e3, e1) = all_172_1 &
% 249.49/59.19 | | | | | | | | $i(all_172_1)
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | ALPHA: (121) implies:
% 249.49/59.19 | | | | | | | | (122) op(e3, e1) = all_172_1
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 249.49/59.19 | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 249.49/59.19 | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 249.49/59.19 | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 249.49/59.19 | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 249.49/59.19 | | | | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 249.49/59.19 | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 249.49/59.19 | | | | | | | | (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 249.49/59.19 | | | | | | | | (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 249.49/59.19 | | | | | | | | (84), (85), (86), (87), (88), (89), (90), (91), (93),
% 249.49/59.19 | | | | | | | | (94), (95), (96), (97), (98), (99), (100), (101),
% 249.49/59.19 | | | | | | | | (102), (105), (109), (117), (118), (122) are
% 249.49/59.19 | | | | | | | | inconsistent by sub-proof #173.
% 249.49/59.19 | | | | | | | |
% 249.49/59.19 | | | | | | | End of split
% 249.49/59.19 | | | | | | |
% 249.49/59.19 | | | | | | End of split
% 249.49/59.19 | | | | | |
% 249.49/59.19 | | | | | End of split
% 249.49/59.19 | | | | |
% 249.49/59.19 | | | | End of split
% 249.49/59.19 | | | |
% 249.49/59.19 | | | End of split
% 249.49/59.19 | | |
% 249.49/59.19 | | Case 2:
% 249.49/59.19 | | |
% 249.49/59.19 | | | (123) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1,
% 249.49/59.19 | | | e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.19 | | |
% 249.49/59.19 | | | REF_CLOSE: (5), (18), (19), (48), (52), (67), (97), (123) are inconsistent
% 249.49/59.19 | | | by sub-proof #771.
% 249.49/59.19 | | |
% 249.49/59.19 | | End of split
% 249.49/59.19 | |
% 249.49/59.19 | End of split
% 249.49/59.19 |
% 249.49/59.19 End of proof
% 249.49/59.19
% 249.49/59.19 Sub-proof #173 shows that the following formulas are inconsistent:
% 249.49/59.19 ----------------------------------------------------------------
% 249.49/59.19 (1) all_252_3 = e4
% 249.49/59.19 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 249.49/59.19 all_250_23 = e0
% 249.49/59.19 (3) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 249.49/59.19 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 249.49/59.19 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 249.49/59.19 (4) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 249.49/59.19 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.19 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 249.49/59.19 (5) ~ (all_4_2 = e4)
% 249.49/59.19 (6) ~ (all_10_2 = e4)
% 249.49/59.19 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.19 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 249.49/59.19 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.19 (8) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 249.49/59.19 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.19 | (all_252_17 = e0 & op(e3, e0) = e0)
% 249.49/59.19 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 249.49/59.19 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 249.49/59.19 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 249.49/59.19 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 249.49/59.19 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.19 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 249.49/59.19 (11) op(e4, e0) = all_30_2
% 249.49/59.20 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.20 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 249.49/59.20 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 249.49/59.20 (13) all_252_6 = e0
% 249.49/59.20 (14) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 249.49/59.20 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 249.49/59.20 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 249.49/59.20 (15) ~ (e2 = e0)
% 249.49/59.20 (16) ~ (e1 = e0)
% 249.49/59.20 (17) ~ (all_28_2 = e3)
% 249.49/59.20 (18) op(e4, e1) = e2
% 249.49/59.20 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 249.49/59.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 249.49/59.20 (20) op(e2, e3) = all_10_2
% 249.49/59.20 (21) ~ (e3 = e2)
% 249.49/59.20 (22) op(e0, e0) = all_244_24
% 249.49/59.20 (23) ~ (e4 = e0)
% 249.49/59.20 (24) all_252_1 = e1
% 249.49/59.20 (25) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 249.49/59.20 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 249.49/59.20 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 249.49/59.20 (26) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 249.49/59.20 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 249.49/59.20 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 249.49/59.20 (27) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 249.49/59.20 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 249.49/59.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 249.49/59.20 (28) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 249.49/59.20 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 249.49/59.20 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 249.49/59.20 (29) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 249.49/59.20 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 249.49/59.20 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 249.49/59.20 (30) ~ (all_36_2 = e2)
% 249.49/59.20 (31) op(e4, e2) = all_6_2
% 249.49/59.20 (32) op(e0, e3) = e0
% 249.49/59.20 (33) ~ (all_244_15 = e4)
% 249.49/59.20 (34) ~ (e2 = e1)
% 249.49/59.20 (35) all_252_13 = e2
% 249.49/59.20 (36) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 249.49/59.20 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 249.49/59.20 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 249.49/59.20 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 249.49/59.20 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 249.49/59.20 op(e0, e1) = e0)))
% 249.49/59.20 (37) op(e0, e2) = all_28_2
% 249.49/59.20 (38) ~ (e4 = e1)
% 249.49/59.20 (39) all_252_9 = e2
% 249.49/59.20 (40) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 249.49/59.20 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 249.49/59.20 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 249.49/59.20 (41) ~ (all_6_2 = e1)
% 249.49/59.20 (42) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 249.49/59.20 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 249.49/59.20 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 249.49/59.20 (43) all_80_2 = all_6_2
% 249.49/59.20 (44) op(all_34_2, e0) = e1
% 249.49/59.20 (45) op(e1, e4) = all_16_2
% 249.49/59.20 (46) op(e2, all_16_2) = e1
% 249.49/59.20 (47) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 249.49/59.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.20 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.20 (48) ~ (all_28_2 = all_20_2)
% 249.49/59.20 (49) op(e1, e3) = all_62_2
% 249.49/59.20 (50) ~ (e3 = e0)
% 249.49/59.20 (51) op(e2, e3) = e1
% 249.49/59.20 (52) ~ (all_30_2 = e2)
% 249.49/59.20 (53) ~ (all_22_2 = e4)
% 249.49/59.20 (54) ~ (e3 = e1)
% 249.49/59.20 (55) op(e3, e1) = all_36_2
% 249.49/59.20 (56) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 249.49/59.20 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 249.49/59.20 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 249.49/59.20 (57) ~ (all_16_2 = e2)
% 249.49/59.20 (58) all_252_11 = e4
% 249.49/59.20 (59) ~ (all_8_2 = e1)
% 249.49/59.20 (60) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 249.49/59.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 249.49/59.20 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 249.49/59.20 (61) ~ (all_22_2 = e1)
% 249.49/59.20 (62) all_252_21 = e0
% 249.49/59.20 (63) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 249.49/59.20 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 249.49/59.20 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 249.49/59.20 (64) op(e3, e1) = all_172_1
% 249.49/59.20 (65) ~ (all_8_2 = e0)
% 249.49/59.20 (66) all_74_2 = all_36_2
% 249.49/59.20 (67) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 249.49/59.20 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 249.49/59.20 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 249.49/59.20 (68) op(e1, e4) = all_242_1
% 249.49/59.20 (69) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 249.49/59.20 all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4) &
% 249.49/59.20 op(e3, e1) = all_172_1 & $i(all_172_1))
% 249.49/59.20 (70) op(all_6_2, e0) = e2
% 249.49/59.20 (71) op(e0, e3) = all_22_2
% 249.49/59.20 (72) op(all_34_2, all_20_2) = e0
% 249.49/59.20 (73) all_252_20 = e2
% 249.49/59.20 (74) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 249.49/59.20 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 249.49/59.20 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 249.49/59.20 (75) ~ (e4 = e3)
% 249.49/59.20 (76) op(e1, e1) = all_244_15
% 249.49/59.20 (77) op(e0, e1) = all_20_2
% 249.49/59.20 (78) op(e2, e4) = e0
% 249.49/59.20 (79) all_82_2 = all_28_2
% 249.49/59.20 (80) ~ (all_244_24 = e2)
% 249.49/59.20 (81) op(e1, e2) = all_4_2
% 249.49/59.20 (82) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 249.49/59.20 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 249.49/59.20 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.20 (83) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 249.49/59.20 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 249.49/59.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 249.49/59.20 (84) ~ (all_244_15 = e2)
% 249.49/59.20 (85) ~ (e4 = e2)
% 249.49/59.20 (86) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 249.49/59.20 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 249.49/59.20 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 249.49/59.20 (87) op(e3, e2) = all_8_2
% 249.49/59.20 (88) op(all_36_2, e1) = e3
% 249.49/59.20 (89) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 249.49/59.20 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 249.49/59.20 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 249.49/59.20 (90) ~ (all_20_2 = e4)
% 249.49/59.20 (91) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 249.49/59.20 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 249.49/59.20 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 249.49/59.20 (92) op(e2, e0) = all_40_2
% 249.49/59.20 (93) all_78_2 = e1
% 249.49/59.20 (94) ~ (all_20_2 = e3)
% 249.49/59.20 (95) ~ (all_16_2 = e3)
% 249.49/59.20 (96) ~ (all_10_2 = e0)
% 249.49/59.20 (97) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 249.49/59.20 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 249.49/59.20 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 249.49/59.20 (98) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 249.49/59.20 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 249.49/59.20 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 249.49/59.20 (99) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 249.49/59.20 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 249.49/59.20 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 249.49/59.20 (100) ~ (all_62_2 = e4)
% 249.49/59.20 (101) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 249.49/59.20 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 249.49/59.20 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 249.49/59.20 (102) ~ (all_4_2 = e2)
% 249.49/59.20 (103) ~ (all_16_2 = e0)
% 249.49/59.20 (104) ~ (all_20_2 = e2)
% 249.49/59.20 (105) all_250_23 = all_20_2
% 249.49/59.20
% 249.49/59.20 Begin of proof
% 249.49/59.20 |
% 249.49/59.20 | BETA: splitting (82) gives:
% 249.49/59.20 |
% 249.49/59.20 | Case 1:
% 249.49/59.20 | |
% 249.49/59.20 | | (106) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 249.49/59.20 | | e3)
% 249.49/59.20 | |
% 249.49/59.20 | | BETA: splitting (106) gives:
% 249.49/59.20 | |
% 249.49/59.20 | | Case 1:
% 249.49/59.20 | | |
% 249.49/59.20 | | | (107) all_252_1 = e3 & op(e4, e3) = e3
% 249.49/59.20 | | |
% 249.49/59.20 | | | REF_CLOSE: (24), (54), (107) are inconsistent by sub-proof #686.
% 249.49/59.20 | | |
% 249.49/59.20 | | Case 2:
% 249.49/59.20 | | |
% 249.49/59.20 | | | (108) all_252_3 = e3 & op(e3, e3) = e3
% 249.49/59.20 | | |
% 249.49/59.20 | | | REF_CLOSE: (1), (75), (108) are inconsistent by sub-proof #685.
% 249.49/59.20 | | |
% 249.49/59.20 | | End of split
% 249.49/59.20 | |
% 249.49/59.20 | Case 2:
% 249.49/59.20 | |
% 249.49/59.20 | | (109) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3)
% 249.49/59.20 | | = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 249.49/59.20 | |
% 249.49/59.20 | | BETA: splitting (109) gives:
% 249.49/59.20 | |
% 249.49/59.20 | | Case 1:
% 249.49/59.20 | | |
% 249.49/59.20 | | | (110) all_252_7 = e3 & op(e2, e3) = e3
% 249.49/59.20 | | |
% 249.49/59.20 | | | ALPHA: (110) implies:
% 249.49/59.20 | | | (111) all_252_7 = e3
% 249.49/59.20 | | |
% 249.49/59.20 | | | BETA: splitting (47) gives:
% 249.49/59.20 | | |
% 249.49/59.20 | | | Case 1:
% 249.49/59.20 | | | |
% 249.49/59.20 | | | | (112) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0,
% 249.49/59.20 | | | | e3) = e3)
% 249.49/59.20 | | | |
% 249.49/59.20 | | | | REF_CLOSE: (21), (50), (62), (73), (112) are inconsistent by sub-proof
% 249.49/59.20 | | | | #208.
% 249.49/59.20 | | | |
% 249.49/59.20 | | | Case 2:
% 249.49/59.20 | | | |
% 249.49/59.20 | | | | (113) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 249.49/59.20 | | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 249.49/59.20 | | | |
% 249.49/59.20 | | | | BETA: splitting (113) gives:
% 249.49/59.20 | | | |
% 249.49/59.20 | | | | Case 1:
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | (114) all_252_22 = e3 & op(e0, e2) = e3
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | ALPHA: (114) implies:
% 249.49/59.20 | | | | | (115) op(e0, e2) = e3
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | REF_CLOSE: (17), (19), (37), (115) are inconsistent by sub-proof #975.
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | Case 2:
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | (116) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 249.49/59.20 | | | | | op(e0, e0) = e3)
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | BETA: splitting (116) gives:
% 249.49/59.20 | | | | |
% 249.49/59.20 | | | | | Case 1:
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | (117) all_252_23 = e3 & op(e0, e1) = e3
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | ALPHA: (117) implies:
% 249.49/59.20 | | | | | | (118) op(e0, e1) = e3
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | REF_CLOSE: (19), (77), (94), (118) are inconsistent by sub-proof
% 249.49/59.20 | | | | | | #974.
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | Case 2:
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | (119) all_252_24 = e3 & op(e0, e0) = e3
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | ALPHA: (119) implies:
% 249.49/59.20 | | | | | | (120) all_252_24 = e3
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | BETA: splitting (7) gives:
% 249.49/59.20 | | | | | |
% 249.49/59.20 | | | | | | Case 1:
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | (121) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 249.49/59.20 | | | | | | | op(e0, e3) = e4)
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | BETA: splitting (121) gives:
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | (122) all_252_20 = e4 & op(e0, e4) = e4
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | ALPHA: (122) implies:
% 249.49/59.20 | | | | | | | | (123) all_252_20 = e4
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | COMBINE_EQS: (73), (123) imply:
% 249.49/59.20 | | | | | | | | (124) e4 = e2
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | SIMP: (124) implies:
% 249.49/59.20 | | | | | | | | (125) e4 = e2
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | COMBINE_EQS: (1), (125) imply:
% 249.49/59.20 | | | | | | | | (126) all_252_3 = e2
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | REF_CLOSE: (5), (6), (10), (15), (16), (19), (20), (21), (23),
% 249.49/59.20 | | | | | | | | (33), (34), (38), (45), (46), (49), (50), (53), (54),
% 249.49/59.20 | | | | | | | | (57), (61), (63), (68), (71), (74), (75), (76), (78),
% 249.49/59.20 | | | | | | | | (81), (82), (84), (85), (96), (97), (99), (100),
% 249.49/59.20 | | | | | | | | (102), (126) are inconsistent by sub-proof #209.
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | (127) all_252_21 = e4 & op(e0, e3) = e4
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | REF_CLOSE: (19), (53), (71), (127) are inconsistent by sub-proof
% 249.49/59.20 | | | | | | | | #805.
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | End of split
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | Case 2:
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | (128) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 249.49/59.20 | | | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | BETA: splitting (128) gives:
% 249.49/59.20 | | | | | | |
% 249.49/59.20 | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | (129) all_252_22 = e4 & op(e0, e2) = e4
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | ALPHA: (129) implies:
% 249.49/59.20 | | | | | | | | (130) all_252_22 = e4
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | BETA: splitting (27) gives:
% 249.49/59.20 | | | | | | | |
% 249.49/59.20 | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | | (131) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1
% 249.49/59.20 | | | | | | | | | & op(e3, e2) = e1)
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | | REF_CLOSE: (19), (31), (41), (59), (87), (131) are
% 249.49/59.20 | | | | | | | | | inconsistent by sub-proof #928.
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | | (132) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1
% 249.49/59.20 | | | | | | | | | & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2)
% 249.49/59.20 | | | | | | | | | = e1)
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | | BETA: splitting (132) gives:
% 249.49/59.20 | | | | | | | | |
% 249.49/59.20 | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | (133) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | ALPHA: (133) implies:
% 249.49/59.20 | | | | | | | | | | (134) all_252_8 = e1
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | REF_CLOSE: (13), (15), (19), (20), (21), (26), (34), (50),
% 249.49/59.20 | | | | | | | | | | (51), (54), (58), (67), (75), (85), (111), (133),
% 249.49/59.20 | | | | | | | | | | (134) are inconsistent by sub-proof #205.
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | (135) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 =
% 249.49/59.20 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | BETA: splitting (135) gives:
% 249.49/59.20 | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | (136) all_252_14 = e1 & op(e1, e2) = e1
% 249.49/59.20 | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | ALPHA: (136) implies:
% 249.49/59.20 | | | | | | | | | | | (137) all_252_14 = e1
% 249.49/59.20 | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | BETA: splitting (60) gives:
% 249.49/59.20 | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | (138) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 249.49/59.20 | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | REF_CLOSE: (16), (19), (32), (34), (73), (138) are
% 249.49/59.20 | | | | | | | | | | | | inconsistent by sub-proof #204.
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | (139) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 249.49/59.20 | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 249.49/59.20 | | | | | | | | | | | | op(e0, e0) = e1)
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | BETA: splitting (139) gives:
% 249.49/59.20 | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | (140) all_252_22 = e1 & op(e0, e2) = e1
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | ALPHA: (140) implies:
% 249.49/59.20 | | | | | | | | | | | | | (141) all_252_22 = e1
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | COMBINE_EQS: (130), (141) imply:
% 249.49/59.20 | | | | | | | | | | | | | (142) e4 = e1
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 249.49/59.20 | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 249.49/59.20 | | | | | | | | | | | | | (19), (20), (21), (22), (23), (25), (26), (27),
% 249.49/59.20 | | | | | | | | | | | | | (28), (29), (30), (31), (33), (34), (35), (36),
% 249.49/59.20 | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 249.49/59.20 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 249.49/59.20 | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 249.49/59.20 | | | | | | | | | | | | | (61), (63), (65), (66), (67), (68), (69), (70),
% 249.49/59.20 | | | | | | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78),
% 249.49/59.20 | | | | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86),
% 249.49/59.20 | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94),
% 249.49/59.20 | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 249.49/59.20 | | | | | | | | | | | | | (103), (104), (105), (142) are inconsistent by
% 249.49/59.20 | | | | | | | | | | | | | sub-proof #174.
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | (143) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 249.49/59.20 | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | BETA: splitting (143) gives:
% 249.49/59.20 | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | (144) all_252_23 = e1 & op(e0, e1) = e1
% 249.49/59.20 | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | ALPHA: (144) implies:
% 249.49/59.20 | | | | | | | | | | | | | | (145) all_252_23 = e1
% 249.49/59.20 | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 249.49/59.20 | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | (146) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 249.49/59.20 | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (12), (13), (14), (15),
% 249.49/59.20 | | | | | | | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 249.49/59.20 | | | | | | | | | | | | | | | (25), (26), (27), (29), (31), (33), (34), (35),
% 249.49/59.20 | | | | | | | | | | | | | | | (36), (37), (38), (41), (42), (43), (44), (45),
% 249.49/59.20 | | | | | | | | | | | | | | | (46), (47), (48), (49), (50), (53), (54), (55),
% 249.49/59.20 | | | | | | | | | | | | | | | (56), (58), (59), (60), (61), (64), (65), (66),
% 249.49/59.20 | | | | | | | | | | | | | | | (67), (70), (71), (72), (73), (74), (75), (76),
% 249.49/59.20 | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (85), (87), (88),
% 249.49/59.20 | | | | | | | | | | | | | | | (90), (92), (93), (94), (95), (100), (104), (105),
% 249.49/59.20 | | | | | | | | | | | | | | | (146) are inconsistent by sub-proof #191.
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | (147) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 249.49/59.20 | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 249.49/59.20 | | | | | | | | | | | | | | | op(e2, e0) = e1)
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 249.49/59.20 | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | (148) all_252_8 = e1 & op(e2, e2) = e1
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 249.49/59.20 | | | | | | | | | | | | | | | | (149) all_252_8 = e1
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (19), (20), (21), (26), (34), (50),
% 249.49/59.20 | | | | | | | | | | | | | | | | (51), (54), (58), (67), (75), (85), (111), (148),
% 249.49/59.20 | | | | | | | | | | | | | | | | (149) are inconsistent by sub-proof #205.
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | (150) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 249.49/59.20 | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 249.49/59.20 | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | (151) all_252_11 = e1 & op(e2, e1) = e1
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 249.49/59.20 | | | | | | | | | | | | | | | | | (152) all_252_11 = e1
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (152) imply:
% 249.49/59.20 | | | | | | | | | | | | | | | | | (153) e4 = e1
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (19), (20), (21), (22), (23), (25), (26), (27),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (28), (29), (30), (31), (33), (34), (35), (36),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (61), (63), (65), (66), (67), (68), (69), (70),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 249.49/59.20 | | | | | | | | | | | | | | | | | (103), (104), (105), (153) are inconsistent by
% 249.49/59.20 | | | | | | | | | | | | | | | | | sub-proof #174.
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | Case 2:
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | (154) all_252_18 = e1 & op(e2, e0) = e1
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 249.49/59.20 | | | | | | | | | | | | | | | | | (155) op(e2, e0) = e1
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 249.49/59.20 | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | | (156) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 249.49/59.20 | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 249.49/59.20 | | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 249.49/59.20 | | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | | Case 1:
% 249.49/59.20 | | | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | | | (157) all_252_16 = e2 & op(e4, e0) = e2
% 249.49/59.20 | | | | | | | | | | | | | | | | | | |
% 249.49/59.20 | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | (158) op(e4, e0) = e2
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (19), (52), (158) are inconsistent by
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | sub-proof #830.
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | (159) all_252_17 = e2 & op(e3, e0) = e2
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | (160) all_252_17 = e2
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | (161) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 =
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (162) all_252_2 = e0 & op(e3, e4) = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (163) all_252_2 = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (19), (21), (23), (34), (38), (45),
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (50), (54), (73), (75), (85), (89), (91), (95),
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (101), (163) are inconsistent by sub-proof #538.
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (164) all_252_3 = e0 & op(e3, e3) = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (23), (164) are inconsistent by sub-proof
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | #688.
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | (165) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 =
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 &
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0)
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (166) all_252_5 = e0 & op(e3, e2) = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (65), (87), (166) are inconsistent by
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #874.
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | (167) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | | (168) all_252_10 = e0 & op(e3, e1) = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | | (169) op(e3, e1) = e0
% 250.02/59.20 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (15), (16), (18), (19), (21), (23),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (33), (34), (35), (36), (38), (39), (40), (45),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (46), (49), (50), (54), (55), (58), (60), (61),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (71), (73), (74), (75), (76), (77), (78), (81),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (85), (86), (90), (100), (103), (120), (137),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (145), (169) are inconsistent by sub-proof #181.
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | (170) all_252_17 = e0 & op(e3, e0) = e0
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (160), (170) are inconsistent by sub-proof
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | | #180.
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | (171) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 250.02/59.21 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 250.02/59.21 | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.02/59.21 | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (19), (22), (33), (34), (45), (46),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | (49), (74), (76), (78), (80), (81), (85), (92),
% 250.02/59.21 | | | | | | | | | | | | | | | | | | (100), (155), (171) are inconsistent by sub-proof
% 250.02/59.21 | | | | | | | | | | | | | | | | | | #178.
% 250.02/59.21 | | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | (172) all_252_24 = e1 & op(e0, e0) = e1
% 250.02/59.21 | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (12), (13), (14), (15),
% 250.02/59.21 | | | | | | | | | | | | | | (16), (17), (18), (19), (20), (21), (22), (23),
% 250.02/59.21 | | | | | | | | | | | | | | (25), (26), (27), (29), (31), (33), (34), (35),
% 250.02/59.21 | | | | | | | | | | | | | | (36), (37), (38), (41), (42), (43), (44), (45),
% 250.02/59.21 | | | | | | | | | | | | | | (46), (47), (48), (49), (50), (51), (53), (54),
% 250.02/59.21 | | | | | | | | | | | | | | (55), (56), (58), (59), (60), (61), (64), (65),
% 250.02/59.21 | | | | | | | | | | | | | | (66), (67), (70), (71), (72), (73), (74), (75),
% 250.02/59.21 | | | | | | | | | | | | | | (76), (77), (78), (79), (80), (81), (85), (87),
% 250.02/59.21 | | | | | | | | | | | | | | (88), (90), (92), (93), (94), (95), (100), (104),
% 250.02/59.21 | | | | | | | | | | | | | | (105), (111), (120), (172) are inconsistent by
% 250.02/59.21 | | | | | | | | | | | | | | sub-proof #177.
% 250.02/59.21 | | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | (173) all_252_22 = e1 & op(e0, e2) = e1
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | ALPHA: (173) implies:
% 250.02/59.21 | | | | | | | | | | | (174) all_252_22 = e1
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | COMBINE_EQS: (130), (174) imply:
% 250.02/59.21 | | | | | | | | | | | (175) e4 = e1
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | COMBINE_EQS: (1), (175) imply:
% 250.02/59.21 | | | | | | | | | | | (176) all_252_3 = e1
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 250.02/59.21 | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 250.02/59.21 | | | | | | | | | | | (19), (20), (21), (22), (23), (25), (26), (27),
% 250.02/59.21 | | | | | | | | | | | (28), (29), (30), (31), (33), (34), (35), (36),
% 250.02/59.21 | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44),
% 250.02/59.21 | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 250.02/59.21 | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (59), (60),
% 250.02/59.21 | | | | | | | | | | | (61), (63), (65), (66), (67), (68), (69), (70),
% 250.02/59.21 | | | | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78),
% 250.02/59.21 | | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86),
% 250.02/59.21 | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94),
% 250.02/59.21 | | | | | | | | | | | (95), (96), (97), (98), (99), (100), (101), (102),
% 250.02/59.21 | | | | | | | | | | | (103), (104), (105), (176) are inconsistent by
% 250.02/59.21 | | | | | | | | | | | sub-proof #175.
% 250.02/59.21 | | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | | |
% 250.02/59.21 | | | | | | | | | End of split
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | End of split
% 250.02/59.21 | | | | | | | |
% 250.02/59.21 | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | |
% 250.02/59.21 | | | | | | | | (177) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4
% 250.02/59.21 | | | | | | | | & op(e0, e0) = e4)
% 250.02/59.21 | | | | | | | |
% 250.02/59.21 | | | | | | | | BETA: splitting (177) gives:
% 250.02/59.21 | | | | | | | |
% 250.02/59.21 | | | | | | | | Case 1:
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | | (178) all_252_23 = e4 & op(e0, e1) = e4
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | | REF_CLOSE: (19), (77), (90), (178) are inconsistent by
% 250.02/59.21 | | | | | | | | | sub-proof #912.
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | Case 2:
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | | (179) all_252_24 = e4 & op(e0, e0) = e4
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | | REF_CLOSE: (75), (120), (179) are inconsistent by sub-proof
% 250.02/59.21 | | | | | | | | | #525.
% 250.02/59.21 | | | | | | | | |
% 250.02/59.21 | | | | | | | | End of split
% 250.02/59.21 | | | | | | | |
% 250.02/59.21 | | | | | | | End of split
% 250.02/59.21 | | | | | | |
% 250.02/59.21 | | | | | | End of split
% 250.02/59.21 | | | | | |
% 250.02/59.21 | | | | | End of split
% 250.02/59.21 | | | | |
% 250.02/59.21 | | | | End of split
% 250.02/59.21 | | | |
% 250.02/59.21 | | | End of split
% 250.02/59.21 | | |
% 250.02/59.21 | | Case 2:
% 250.02/59.21 | | |
% 250.02/59.21 | | | (180) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0,
% 250.02/59.21 | | | e3) = e3)
% 250.02/59.21 | | |
% 250.02/59.21 | | | REF_CLOSE: (21), (35), (50), (62), (180) are inconsistent by sub-proof
% 250.02/59.21 | | | #211.
% 250.02/59.21 | | |
% 250.02/59.21 | | End of split
% 250.02/59.21 | |
% 250.02/59.21 | End of split
% 250.02/59.21 |
% 250.02/59.21 End of proof
% 250.02/59.21
% 250.02/59.21 Sub-proof #174 shows that the following formulas are inconsistent:
% 250.02/59.21 ----------------------------------------------------------------
% 250.02/59.21 (1) all_252_3 = e4
% 250.02/59.21 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.21 all_250_23 = e0
% 250.02/59.21 (3) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.21 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.21 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.21 (4) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.02/59.21 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.21 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.21 (5) ~ (all_4_2 = e4)
% 250.02/59.21 (6) ~ (all_10_2 = e4)
% 250.02/59.21 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.21 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.21 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.21 (8) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.02/59.21 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.21 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.02/59.21 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.21 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.21 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.21 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.02/59.21 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.21 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.21 (11) op(e4, e0) = all_30_2
% 250.02/59.21 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.02/59.21 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.02/59.21 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.21 (13) all_252_6 = e0
% 250.02/59.21 (14) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.02/59.21 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.02/59.21 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.21 (15) ~ (e2 = e0)
% 250.02/59.21 (16) ~ (e1 = e0)
% 250.02/59.21 (17) ~ (all_28_2 = e3)
% 250.02/59.21 (18) op(e4, e1) = e2
% 250.02/59.21 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.21 (20) op(e2, e3) = all_10_2
% 250.02/59.21 (21) ~ (e3 = e2)
% 250.02/59.21 (22) op(e0, e0) = all_244_24
% 250.02/59.21 (23) ~ (e4 = e0)
% 250.02/59.21 (24) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.21 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.21 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.21 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.21 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.21 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.21 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.21 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.21 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.21 (27) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.02/59.21 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.02/59.21 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.02/59.21 (28) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.21 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.21 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.21 (29) ~ (all_36_2 = e2)
% 250.02/59.21 (30) op(e4, e2) = all_6_2
% 250.02/59.21 (31) ~ (all_244_15 = e4)
% 250.02/59.21 (32) ~ (e2 = e1)
% 250.02/59.21 (33) all_252_13 = e2
% 250.02/59.21 (34) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.21 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.21 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.21 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.21 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.21 op(e0, e1) = e0)))
% 250.02/59.21 (35) op(e0, e2) = all_28_2
% 250.02/59.21 (36) ~ (e4 = e1)
% 250.02/59.21 (37) all_252_9 = e2
% 250.02/59.21 (38) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.21 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.21 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.21 (39) ~ (all_6_2 = e1)
% 250.02/59.21 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.21 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.21 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.21 (41) all_80_2 = all_6_2
% 250.02/59.21 (42) op(all_34_2, e0) = e1
% 250.02/59.21 (43) op(e1, e4) = all_16_2
% 250.02/59.21 (44) op(e2, all_16_2) = e1
% 250.02/59.21 (45) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.21 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.21 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.21 (46) ~ (all_28_2 = all_20_2)
% 250.02/59.21 (47) op(e1, e3) = all_62_2
% 250.02/59.21 (48) ~ (e3 = e0)
% 250.02/59.21 (49) op(e2, e3) = e1
% 250.02/59.21 (50) ~ (all_30_2 = e2)
% 250.02/59.21 (51) ~ (all_22_2 = e4)
% 250.02/59.21 (52) ~ (e3 = e1)
% 250.02/59.21 (53) op(e3, e1) = all_36_2
% 250.02/59.21 (54) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.21 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.21 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.21 (55) ~ (all_16_2 = e2)
% 250.02/59.21 (56) all_252_11 = e4
% 250.02/59.21 (57) ~ (all_8_2 = e1)
% 250.02/59.21 (58) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.21 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.21 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.21 (59) ~ (all_22_2 = e1)
% 250.02/59.21 (60) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.02/59.21 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.02/59.21 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.02/59.21 (61) ~ (all_8_2 = e0)
% 250.02/59.21 (62) all_74_2 = all_36_2
% 250.02/59.21 (63) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.21 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.21 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.21 (64) e4 = e1
% 250.02/59.21 (65) op(e1, e4) = all_242_1
% 250.02/59.21 (66) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 250.02/59.21 all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4) &
% 250.02/59.21 op(e3, e1) = all_172_1 & $i(all_172_1))
% 250.02/59.21 (67) op(all_6_2, e0) = e2
% 250.02/59.21 (68) op(e0, e3) = all_22_2
% 250.02/59.21 (69) op(all_34_2, all_20_2) = e0
% 250.02/59.21 (70) all_252_20 = e2
% 250.02/59.21 (71) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.21 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.21 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.21 (72) ~ (e4 = e3)
% 250.02/59.21 (73) op(e1, e1) = all_244_15
% 250.02/59.21 (74) op(e0, e1) = all_20_2
% 250.02/59.21 (75) op(e2, e4) = e0
% 250.02/59.21 (76) all_82_2 = all_28_2
% 250.02/59.21 (77) ~ (all_244_24 = e2)
% 250.02/59.21 (78) op(e1, e2) = all_4_2
% 250.02/59.21 (79) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.02/59.21 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.02/59.21 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.02/59.21 (80) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.02/59.21 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.02/59.21 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.02/59.21 (81) ~ (all_244_15 = e2)
% 250.02/59.21 (82) ~ (e4 = e2)
% 250.02/59.21 (83) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.21 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.21 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.21 (84) op(e3, e2) = all_8_2
% 250.02/59.21 (85) op(all_36_2, e1) = e3
% 250.02/59.21 (86) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.02/59.21 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.02/59.21 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.02/59.21 (87) ~ (all_20_2 = e4)
% 250.02/59.21 (88) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.02/59.21 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.02/59.21 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.02/59.21 (89) op(e2, e0) = all_40_2
% 250.02/59.21 (90) all_78_2 = e1
% 250.02/59.21 (91) ~ (all_20_2 = e3)
% 250.02/59.21 (92) ~ (all_16_2 = e3)
% 250.02/59.21 (93) ~ (all_10_2 = e0)
% 250.02/59.21 (94) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.02/59.21 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.02/59.21 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.02/59.21 (95) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.02/59.21 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.02/59.21 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.02/59.21 (96) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.02/59.21 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.02/59.21 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.02/59.21 (97) ~ (all_62_2 = e4)
% 250.02/59.21 (98) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.02/59.21 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.02/59.21 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.02/59.21 (99) ~ (all_4_2 = e2)
% 250.02/59.21 (100) ~ (all_16_2 = e0)
% 250.02/59.21 (101) ~ (all_20_2 = e2)
% 250.02/59.21 (102) all_250_23 = all_20_2
% 250.02/59.21
% 250.02/59.21 Begin of proof
% 250.02/59.21 |
% 250.02/59.21 | SIMP: (64) implies:
% 250.02/59.21 | (103) e4 = e1
% 250.02/59.21 |
% 250.02/59.21 | COMBINE_EQS: (1), (103) imply:
% 250.02/59.21 | (104) all_252_3 = e1
% 250.02/59.21 |
% 250.02/59.21 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.02/59.21 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.02/59.21 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.02/59.21 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 250.02/59.21 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.02/59.21 | (58), (59), (60), (61), (62), (63), (65), (66), (67), (68), (69),
% 250.02/59.21 | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 250.02/59.21 | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 250.02/59.21 | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 250.02/59.21 | (102), (104) are inconsistent by sub-proof #175.
% 250.02/59.21 |
% 250.02/59.21 End of proof
% 250.02/59.21
% 250.02/59.21 Sub-proof #175 shows that the following formulas are inconsistent:
% 250.02/59.21 ----------------------------------------------------------------
% 250.02/59.21 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.21 all_250_23 = e0
% 250.02/59.21 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.21 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.21 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.21 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.02/59.21 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.21 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.21 (4) ~ (all_4_2 = e4)
% 250.02/59.21 (5) ~ (all_10_2 = e4)
% 250.02/59.21 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.21 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.21 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.21 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.02/59.21 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.21 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.02/59.21 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.21 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.21 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.21 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.02/59.21 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.02/59.21 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.21 (10) op(e4, e0) = all_30_2
% 250.02/59.21 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.02/59.21 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.02/59.21 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.21 (12) all_252_6 = e0
% 250.02/59.21 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.02/59.21 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.02/59.21 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.21 (14) ~ (e2 = e0)
% 250.02/59.21 (15) ~ (e1 = e0)
% 250.02/59.21 (16) ~ (all_28_2 = e3)
% 250.02/59.21 (17) op(e4, e1) = e2
% 250.02/59.21 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.21 (19) all_252_3 = e1
% 250.02/59.21 (20) op(e2, e3) = all_10_2
% 250.02/59.21 (21) ~ (e3 = e2)
% 250.02/59.21 (22) op(e0, e0) = all_244_24
% 250.02/59.21 (23) ~ (e4 = e0)
% 250.02/59.21 (24) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.21 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.21 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.21 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.21 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.21 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.21 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.21 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.21 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.21 (27) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.02/59.21 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.02/59.21 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.02/59.21 (28) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.21 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.21 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.21 (29) ~ (all_36_2 = e2)
% 250.02/59.21 (30) op(e4, e2) = all_6_2
% 250.02/59.21 (31) ~ (all_244_15 = e4)
% 250.02/59.21 (32) ~ (e2 = e1)
% 250.02/59.21 (33) all_252_13 = e2
% 250.02/59.21 (34) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.21 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.21 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.21 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.21 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.21 op(e0, e1) = e0)))
% 250.02/59.21 (35) op(e0, e2) = all_28_2
% 250.02/59.21 (36) ~ (e4 = e1)
% 250.02/59.21 (37) all_252_9 = e2
% 250.02/59.21 (38) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.21 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.21 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.21 (39) ~ (all_6_2 = e1)
% 250.02/59.21 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.21 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.21 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.21 (41) all_80_2 = all_6_2
% 250.02/59.21 (42) op(all_34_2, e0) = e1
% 250.02/59.21 (43) op(e1, e4) = all_16_2
% 250.02/59.21 (44) op(e2, all_16_2) = e1
% 250.02/59.21 (45) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.21 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.21 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.21 (46) ~ (all_28_2 = all_20_2)
% 250.02/59.21 (47) op(e1, e3) = all_62_2
% 250.02/59.21 (48) ~ (e3 = e0)
% 250.02/59.21 (49) op(e2, e3) = e1
% 250.02/59.21 (50) ~ (all_30_2 = e2)
% 250.02/59.21 (51) ~ (all_22_2 = e4)
% 250.02/59.21 (52) ~ (e3 = e1)
% 250.02/59.21 (53) op(e3, e1) = all_36_2
% 250.02/59.21 (54) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.21 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.21 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.21 (55) ~ (all_16_2 = e2)
% 250.02/59.21 (56) all_252_11 = e4
% 250.02/59.21 (57) ~ (all_8_2 = e1)
% 250.02/59.21 (58) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.21 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.21 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.21 (59) ~ (all_22_2 = e1)
% 250.02/59.21 (60) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.02/59.21 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.02/59.21 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.02/59.21 (61) ~ (all_8_2 = e0)
% 250.02/59.21 (62) all_74_2 = all_36_2
% 250.02/59.21 (63) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.21 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.21 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.21 (64) op(e1, e4) = all_242_1
% 250.02/59.21 (65) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 250.02/59.21 all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4) &
% 250.02/59.21 op(e3, e1) = all_172_1 & $i(all_172_1))
% 250.02/59.21 (66) op(all_6_2, e0) = e2
% 250.02/59.21 (67) op(e0, e3) = all_22_2
% 250.02/59.21 (68) op(all_34_2, all_20_2) = e0
% 250.02/59.21 (69) all_252_20 = e2
% 250.02/59.22 (70) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.22 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.22 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.22 (71) ~ (e4 = e3)
% 250.02/59.22 (72) op(e1, e1) = all_244_15
% 250.02/59.22 (73) op(e0, e1) = all_20_2
% 250.02/59.22 (74) op(e2, e4) = e0
% 250.02/59.22 (75) all_82_2 = all_28_2
% 250.02/59.22 (76) ~ (all_244_24 = e2)
% 250.02/59.22 (77) op(e1, e2) = all_4_2
% 250.02/59.22 (78) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.02/59.22 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.02/59.22 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.02/59.22 (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.02/59.22 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.02/59.22 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.02/59.22 (80) ~ (all_244_15 = e2)
% 250.02/59.22 (81) ~ (e4 = e2)
% 250.02/59.22 (82) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.22 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.22 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.22 (83) op(e3, e2) = all_8_2
% 250.02/59.22 (84) op(all_36_2, e1) = e3
% 250.02/59.22 (85) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.02/59.22 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.02/59.22 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.02/59.22 (86) ~ (all_20_2 = e4)
% 250.02/59.22 (87) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.02/59.22 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.02/59.22 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.02/59.22 (88) op(e2, e0) = all_40_2
% 250.02/59.22 (89) all_78_2 = e1
% 250.02/59.22 (90) ~ (all_20_2 = e3)
% 250.02/59.22 (91) ~ (all_16_2 = e3)
% 250.02/59.22 (92) ~ (all_10_2 = e0)
% 250.02/59.22 (93) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.02/59.22 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.02/59.22 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.02/59.22 (94) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.02/59.22 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.02/59.22 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.02/59.22 (95) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.02/59.22 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.02/59.22 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.02/59.22 (96) ~ (all_62_2 = e4)
% 250.02/59.22 (97) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.02/59.22 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.02/59.22 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.02/59.22 (98) ~ (all_4_2 = e2)
% 250.02/59.22 (99) ~ (all_16_2 = e0)
% 250.02/59.22 (100) ~ (all_20_2 = e2)
% 250.02/59.22 (101) all_250_23 = all_20_2
% 250.02/59.22
% 250.02/59.22 Begin of proof
% 250.02/59.22 |
% 250.02/59.22 | BETA: splitting (9) gives:
% 250.02/59.22 |
% 250.02/59.22 | Case 1:
% 250.02/59.22 | |
% 250.02/59.22 | | (102) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.02/59.22 | | e4)
% 250.02/59.22 | |
% 250.02/59.22 | | BETA: splitting (102) gives:
% 250.02/59.22 | |
% 250.02/59.22 | | Case 1:
% 250.02/59.22 | | |
% 250.02/59.22 | | | (103) all_252_1 = e4 & op(e4, e3) = e4
% 250.02/59.22 | | |
% 250.02/59.22 | | | ALPHA: (103) implies:
% 250.02/59.22 | | | (104) all_252_1 = e4
% 250.02/59.22 | | |
% 250.02/59.22 | | | BETA: splitting (60) gives:
% 250.02/59.22 | | |
% 250.02/59.22 | | | Case 1:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | (105) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 250.02/59.22 | | | | e3) = e0)
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | BETA: splitting (105) gives:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | Case 1:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (106) all_252_1 = e0 & op(e4, e3) = e0
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | REF_CLOSE: (23), (104), (106) are inconsistent by sub-proof #947.
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | Case 2:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (107) all_252_3 = e0 & op(e3, e3) = e0
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | REF_CLOSE: (15), (19), (107) are inconsistent by sub-proof #777.
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | End of split
% 250.02/59.22 | | | |
% 250.02/59.22 | | | Case 2:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | (108) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1,
% 250.02/59.22 | | | | e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | BETA: splitting (108) gives:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | Case 1:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (109) all_252_7 = e0 & op(e2, e3) = e0
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | REF_CLOSE: (18), (20), (92), (109) are inconsistent by sub-proof #816.
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | Case 2:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (110) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 250.02/59.22 | | | | | op(e0, e3) = e0)
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | BETA: splitting (110) gives:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | Case 1:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | (111) all_252_13 = e0 & op(e1, e3) = e0
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | ALPHA: (111) implies:
% 250.02/59.22 | | | | | | (112) all_252_13 = e0
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | REF_CLOSE: (14), (33), (112) are inconsistent by sub-proof #418.
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | Case 2:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | (113) all_252_21 = e0 & op(e0, e3) = e0
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | ALPHA: (113) implies:
% 250.02/59.22 | | | | | | (114) all_252_21 = e0
% 250.02/59.22 | | | | | | (115) op(e0, e3) = e0
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | BETA: splitting (65) gives:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | Case 1:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | (116) ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1,
% 250.02/59.22 | | | | | | | all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | ALPHA: (116) implies:
% 250.02/59.22 | | | | | | | (117) op(e3, e1) = all_172_1
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12),
% 250.02/59.22 | | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 250.02/59.22 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 250.02/59.22 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 250.02/59.22 | | | | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 250.02/59.22 | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.02/59.22 | | | | | | | (58), (59), (60), (61), (62), (63), (64), (66), (67),
% 250.02/59.22 | | | | | | | (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 250.02/59.22 | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 250.02/59.22 | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 250.02/59.22 | | | | | | | (95), (96), (97), (98), (99), (100), (101), (104),
% 250.02/59.22 | | | | | | | (114), (115), (117) are inconsistent by sub-proof #176.
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | Case 2:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | (118) ~ (all_172_1 = e4) & op(e3, e1) = all_172_1 &
% 250.02/59.22 | | | | | | | $i(all_172_1)
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | ALPHA: (118) implies:
% 250.02/59.22 | | | | | | | (119) op(e3, e1) = all_172_1
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12),
% 250.02/59.22 | | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 250.02/59.22 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 250.02/59.22 | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 250.02/59.22 | | | | | | | (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 250.02/59.22 | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.02/59.22 | | | | | | | (58), (59), (60), (61), (62), (63), (64), (66), (67),
% 250.02/59.22 | | | | | | | (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 250.02/59.22 | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 250.02/59.22 | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 250.02/59.22 | | | | | | | (95), (96), (97), (98), (99), (100), (101), (104),
% 250.02/59.22 | | | | | | | (114), (115), (119) are inconsistent by sub-proof #176.
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | End of split
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | End of split
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | End of split
% 250.02/59.22 | | | |
% 250.02/59.22 | | | End of split
% 250.02/59.22 | | |
% 250.02/59.22 | | Case 2:
% 250.02/59.22 | | |
% 250.02/59.22 | | | (120) all_252_3 = e4 & op(e3, e3) = e4
% 250.02/59.22 | | |
% 250.02/59.22 | | | ALPHA: (120) implies:
% 250.02/59.22 | | | (121) all_252_3 = e4
% 250.02/59.22 | | |
% 250.02/59.22 | | | REF_CLOSE: (19), (36), (121) are inconsistent by sub-proof #772.
% 250.02/59.22 | | |
% 250.02/59.22 | | End of split
% 250.02/59.22 | |
% 250.02/59.22 | Case 2:
% 250.02/59.22 | |
% 250.02/59.22 | | (122) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3)
% 250.02/59.22 | | = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.22 | |
% 250.02/59.22 | | REF_CLOSE: (5), (18), (20), (47), (51), (67), (96), (122) are inconsistent
% 250.02/59.22 | | by sub-proof #771.
% 250.02/59.22 | |
% 250.02/59.22 | End of split
% 250.02/59.22 |
% 250.02/59.22 End of proof
% 250.02/59.22
% 250.02/59.22 Sub-proof #176 shows that the following formulas are inconsistent:
% 250.02/59.22 ----------------------------------------------------------------
% 250.02/59.22 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.22 all_250_23 = e0
% 250.02/59.22 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.22 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.22 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.22 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.02/59.22 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.22 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.22 (4) ~ (all_4_2 = e4)
% 250.02/59.22 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.22 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.22 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.22 (6) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.02/59.22 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.22 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.02/59.22 (7) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.22 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.22 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.22 (8) op(e4, e0) = all_30_2
% 250.02/59.22 (9) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.02/59.22 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.22 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.22 (10) all_252_6 = e0
% 250.02/59.22 (11) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.02/59.22 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.02/59.22 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.22 (12) ~ (e2 = e0)
% 250.02/59.22 (13) ~ (e1 = e0)
% 250.02/59.22 (14) ~ (all_28_2 = e3)
% 250.02/59.22 (15) op(e4, e1) = e2
% 250.02/59.22 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.22 (17) all_252_3 = e1
% 250.02/59.22 (18) op(e2, e3) = all_10_2
% 250.02/59.22 (19) ~ (e3 = e2)
% 250.02/59.22 (20) op(e0, e0) = all_244_24
% 250.02/59.22 (21) ~ (e4 = e0)
% 250.02/59.22 (22) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.22 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.22 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.22 (23) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.22 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.22 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.22 (24) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.22 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.22 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.22 (25) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.02/59.22 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.02/59.22 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.02/59.22 (26) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.22 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.22 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.22 (27) ~ (all_36_2 = e2)
% 250.02/59.22 (28) op(e4, e2) = all_6_2
% 250.02/59.22 (29) op(e0, e3) = e0
% 250.02/59.22 (30) ~ (all_244_15 = e4)
% 250.02/59.22 (31) ~ (e2 = e1)
% 250.02/59.22 (32) all_252_13 = e2
% 250.02/59.22 (33) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.22 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.22 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.22 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.22 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.22 op(e0, e1) = e0)))
% 250.02/59.22 (34) op(e0, e2) = all_28_2
% 250.02/59.22 (35) ~ (e4 = e1)
% 250.02/59.22 (36) all_252_9 = e2
% 250.02/59.22 (37) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.22 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.22 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.22 (38) ~ (all_6_2 = e1)
% 250.02/59.22 (39) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.22 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.22 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.22 (40) all_80_2 = all_6_2
% 250.02/59.22 (41) op(all_34_2, e0) = e1
% 250.02/59.22 (42) op(e1, e4) = all_16_2
% 250.02/59.22 (43) op(e2, all_16_2) = e1
% 250.02/59.22 (44) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.22 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.22 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.22 (45) ~ (all_28_2 = all_20_2)
% 250.02/59.22 (46) op(e1, e3) = all_62_2
% 250.02/59.22 (47) ~ (e3 = e0)
% 250.02/59.22 (48) op(e2, e3) = e1
% 250.02/59.22 (49) ~ (all_30_2 = e2)
% 250.02/59.22 (50) ~ (all_22_2 = e4)
% 250.02/59.22 (51) ~ (e3 = e1)
% 250.02/59.22 (52) op(e3, e1) = all_36_2
% 250.02/59.22 (53) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.22 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.22 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.22 (54) ~ (all_16_2 = e2)
% 250.02/59.22 (55) all_252_11 = e4
% 250.02/59.22 (56) ~ (all_8_2 = e1)
% 250.02/59.22 (57) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.22 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.22 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.22 (58) ~ (all_22_2 = e1)
% 250.02/59.22 (59) all_252_21 = e0
% 250.02/59.22 (60) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.02/59.22 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.02/59.22 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.02/59.22 (61) op(e3, e1) = all_172_1
% 250.02/59.22 (62) ~ (all_8_2 = e0)
% 250.02/59.22 (63) all_74_2 = all_36_2
% 250.02/59.22 (64) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.22 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.22 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.22 (65) op(e1, e4) = all_242_1
% 250.02/59.22 (66) op(all_6_2, e0) = e2
% 250.02/59.22 (67) op(e0, e3) = all_22_2
% 250.02/59.22 (68) op(all_34_2, all_20_2) = e0
% 250.02/59.22 (69) all_252_20 = e2
% 250.02/59.22 (70) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.22 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.22 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.22 (71) ~ (e4 = e3)
% 250.02/59.22 (72) op(e1, e1) = all_244_15
% 250.02/59.22 (73) op(e0, e1) = all_20_2
% 250.02/59.22 (74) op(e2, e4) = e0
% 250.02/59.22 (75) all_82_2 = all_28_2
% 250.02/59.22 (76) ~ (all_244_24 = e2)
% 250.02/59.22 (77) op(e1, e2) = all_4_2
% 250.02/59.22 (78) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.02/59.22 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.02/59.22 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.02/59.22 (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.02/59.22 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.02/59.22 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.02/59.22 (80) ~ (all_244_15 = e2)
% 250.02/59.22 (81) ~ (e4 = e2)
% 250.02/59.22 (82) all_252_1 = e4
% 250.02/59.22 (83) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.22 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.22 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.22 (84) op(e3, e2) = all_8_2
% 250.02/59.22 (85) op(all_36_2, e1) = e3
% 250.02/59.22 (86) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.02/59.22 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.02/59.22 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.02/59.22 (87) ~ (all_20_2 = e4)
% 250.02/59.22 (88) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.02/59.22 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.02/59.22 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.02/59.22 (89) op(e2, e0) = all_40_2
% 250.02/59.22 (90) all_78_2 = e1
% 250.02/59.22 (91) ~ (all_20_2 = e3)
% 250.02/59.22 (92) ~ (all_16_2 = e3)
% 250.02/59.22 (93) ~ (all_10_2 = e0)
% 250.02/59.22 (94) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.02/59.22 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.02/59.22 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.02/59.22 (95) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.02/59.22 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.02/59.22 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.02/59.22 (96) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.02/59.22 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.02/59.22 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.02/59.22 (97) ~ (all_62_2 = e4)
% 250.02/59.22 (98) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.02/59.22 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.02/59.22 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.02/59.22 (99) ~ (all_4_2 = e2)
% 250.02/59.22 (100) ~ (all_16_2 = e0)
% 250.02/59.22 (101) ~ (all_20_2 = e2)
% 250.02/59.22 (102) all_250_23 = all_20_2
% 250.02/59.22
% 250.02/59.22 Begin of proof
% 250.02/59.22 |
% 250.02/59.22 | BETA: splitting (78) gives:
% 250.02/59.22 |
% 250.02/59.22 | Case 1:
% 250.02/59.22 | |
% 250.02/59.22 | | (103) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 250.02/59.22 | | e3)
% 250.02/59.22 | |
% 250.02/59.22 | | BETA: splitting (103) gives:
% 250.02/59.22 | |
% 250.02/59.22 | | Case 1:
% 250.02/59.22 | | |
% 250.02/59.22 | | | (104) all_252_1 = e3 & op(e4, e3) = e3
% 250.02/59.22 | | |
% 250.02/59.22 | | | REF_CLOSE: (71), (82), (104) are inconsistent by sub-proof #946.
% 250.02/59.22 | | |
% 250.02/59.22 | | Case 2:
% 250.02/59.22 | | |
% 250.02/59.22 | | | (105) all_252_3 = e3 & op(e3, e3) = e3
% 250.02/59.22 | | |
% 250.02/59.22 | | | REF_CLOSE: (17), (51), (105) are inconsistent by sub-proof #775.
% 250.02/59.22 | | |
% 250.02/59.22 | | End of split
% 250.02/59.22 | |
% 250.02/59.22 | Case 2:
% 250.02/59.22 | |
% 250.02/59.22 | | (106) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3)
% 250.02/59.22 | | = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.02/59.22 | |
% 250.02/59.22 | | BETA: splitting (106) gives:
% 250.02/59.22 | |
% 250.02/59.22 | | Case 1:
% 250.02/59.22 | | |
% 250.02/59.22 | | | (107) all_252_7 = e3 & op(e2, e3) = e3
% 250.02/59.22 | | |
% 250.02/59.22 | | | ALPHA: (107) implies:
% 250.02/59.22 | | | (108) all_252_7 = e3
% 250.02/59.22 | | |
% 250.02/59.22 | | | BETA: splitting (44) gives:
% 250.02/59.22 | | |
% 250.02/59.22 | | | Case 1:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | (109) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0,
% 250.02/59.22 | | | | e3) = e3)
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | REF_CLOSE: (19), (47), (59), (69), (109) are inconsistent by sub-proof
% 250.02/59.22 | | | | #208.
% 250.02/59.22 | | | |
% 250.02/59.22 | | | Case 2:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | (110) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.22 | | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | BETA: splitting (110) gives:
% 250.02/59.22 | | | |
% 250.02/59.22 | | | | Case 1:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (111) all_252_22 = e3 & op(e0, e2) = e3
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | ALPHA: (111) implies:
% 250.02/59.22 | | | | | (112) op(e0, e2) = e3
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | REF_CLOSE: (14), (16), (34), (112) are inconsistent by sub-proof #975.
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | Case 2:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | (113) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 250.02/59.22 | | | | | op(e0, e0) = e3)
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | BETA: splitting (113) gives:
% 250.02/59.22 | | | | |
% 250.02/59.22 | | | | | Case 1:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | (114) all_252_23 = e3 & op(e0, e1) = e3
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | ALPHA: (114) implies:
% 250.02/59.22 | | | | | | (115) op(e0, e1) = e3
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | REF_CLOSE: (16), (73), (91), (115) are inconsistent by sub-proof
% 250.02/59.22 | | | | | | #974.
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | Case 2:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | (116) all_252_24 = e3 & op(e0, e0) = e3
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | ALPHA: (116) implies:
% 250.02/59.22 | | | | | | (117) all_252_24 = e3
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | BETA: splitting (5) gives:
% 250.02/59.22 | | | | | |
% 250.02/59.22 | | | | | | Case 1:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | (118) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 250.02/59.22 | | | | | | | op(e0, e3) = e4)
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | BETA: splitting (118) gives:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | (119) all_252_20 = e4 & op(e0, e4) = e4
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | REF_CLOSE: (69), (81), (119) are inconsistent by sub-proof #543.
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | Case 2:
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | (120) all_252_21 = e4 & op(e0, e3) = e4
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | REF_CLOSE: (16), (50), (67), (120) are inconsistent by sub-proof
% 250.02/59.22 | | | | | | | | #805.
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | End of split
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | Case 2:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | (121) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 250.02/59.22 | | | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | BETA: splitting (121) gives:
% 250.02/59.22 | | | | | | |
% 250.02/59.22 | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | (122) all_252_22 = e4 & op(e0, e2) = e4
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | ALPHA: (122) implies:
% 250.02/59.22 | | | | | | | | (123) all_252_22 = e4
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | BETA: splitting (24) gives:
% 250.02/59.22 | | | | | | | |
% 250.02/59.22 | | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | | (124) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1
% 250.02/59.22 | | | | | | | | | & op(e3, e2) = e1)
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | | REF_CLOSE: (16), (28), (38), (56), (84), (124) are
% 250.02/59.22 | | | | | | | | | inconsistent by sub-proof #928.
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | Case 2:
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | | (125) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1
% 250.02/59.22 | | | | | | | | | & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2)
% 250.02/59.22 | | | | | | | | | = e1)
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | | BETA: splitting (125) gives:
% 250.02/59.22 | | | | | | | | |
% 250.02/59.22 | | | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | (126) all_252_8 = e1 & op(e2, e2) = e1
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | ALPHA: (126) implies:
% 250.02/59.22 | | | | | | | | | | (127) all_252_8 = e1
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | REF_CLOSE: (10), (12), (16), (18), (19), (23), (31), (47),
% 250.02/59.22 | | | | | | | | | | (48), (51), (55), (64), (71), (81), (108), (126),
% 250.02/59.22 | | | | | | | | | | (127) are inconsistent by sub-proof #205.
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | Case 2:
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | (128) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 =
% 250.02/59.22 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | BETA: splitting (128) gives:
% 250.02/59.22 | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | (129) all_252_14 = e1 & op(e1, e2) = e1
% 250.02/59.22 | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | ALPHA: (129) implies:
% 250.02/59.22 | | | | | | | | | | | (130) all_252_14 = e1
% 250.02/59.22 | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | BETA: splitting (39) gives:
% 250.02/59.22 | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | Case 1:
% 250.02/59.22 | | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | | (131) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 250.02/59.22 | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 250.02/59.22 | | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | | BETA: splitting (131) gives:
% 250.02/59.22 | | | | | | | | | | | |
% 250.02/59.22 | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | (132) all_252_4 = e0 & op(e4, e2) = e0
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | ALPHA: (132) implies:
% 250.02/59.23 | | | | | | | | | | | | | (133) all_252_4 = e0
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | BETA: splitting (57) gives:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | (134) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 250.02/59.23 | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (29), (31), (69), (134) are
% 250.02/59.23 | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | (135) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 250.02/59.23 | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 250.02/59.23 | | | | | | | | | | | | | | op(e0, e0) = e1)
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | (136) all_252_22 = e1 & op(e0, e2) = e1
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | (137) all_252_22 = e1
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | REF_CLOSE: (35), (123), (137) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | #530.
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | (138) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 250.02/59.23 | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | (139) all_252_23 = e1 & op(e0, e1) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | (140) all_252_23 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | (141) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (13), (14), (15), (16), (18), (19), (20), (21),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (22), (23), (24), (26), (28), (30), (31), (32),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (33), (34), (35), (38), (39), (40), (41), (42),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (50), (51), (52),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (61), (62), (63),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (64), (66), (67), (68), (69), (70), (71), (72),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (73), (74), (75), (76), (77), (81), (84), (85),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (87), (89), (90), (91), (92), (97), (101), (102),
% 250.02/59.23 | | | | | | | | | | | | | | | | | (141) are inconsistent by sub-proof #191.
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | (142) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | op(e2, e0) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | (143) all_252_8 = e1 & op(e2, e2) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | (144) all_252_8 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (145) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (146) all_252_4 = e3 & op(e4, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (133), (146) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | #689.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (147) all_252_5 = e3 & op(e3, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (148) all_252_5 = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (149) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (150) all_252_2 = e2 & op(e3, e4) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (151) all_252_2 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (152) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (153) all_252_0 = e3 & op(e4, e4) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_0 = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_0 = e1 & op(e4, e4) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (154), (156) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | #546.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_2 = e1 & op(e3, e4) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (151), (157) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | #778.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | (158) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_6 = e1 & op(e2, e4) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (159) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | #556.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (160) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_12 = e1 & op(e1, e4) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_12 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e4) = e4)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_0 = e4 & op(e4, e4) = e4
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (154), (164) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #547.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_252_2 = e4 & op(e3, e4) = e4
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_2 = e4
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (166) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) e4 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (167) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) $false
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e4)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_6 = e4 & op(e2, e4) = e4
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (21), (170) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e4) = e4)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (69), (81), (162), (171) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #190.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_20 = e1 & op(e0, e4) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (69), (172) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | #532.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_2 = e3 & op(e3, e4) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_2 = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (174) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (175) e3 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (175) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (176) e3 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (176) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | (177) $false
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (178) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (19), (42), (47), (69), (92), (178)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #189.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (179) all_252_3 = e2 & op(e3, e3) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (180) all_252_3 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (16), (18), (19), (21), (30),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (31), (35), (42), (43), (46), (47), (51), (54),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (58), (60), (65), (67), (70), (71), (72), (74),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (77), (78), (80), (81), (82), (93), (94), (96),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (97), (99), (180) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | #210.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (181) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (182) all_252_5 = e2 & op(e3, e2) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (148), (182) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | #862.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | (183) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (184) all_252_10 = e2 & op(e3, e1) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (185) op(e3, e1) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (27), (52), (185) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_17 = e2 & op(e3, e0) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_17 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (10), (12), (13), (15), (16),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (17), (19), (21), (30), (31), (32), (33), (35),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (36), (37), (42), (43), (46), (47), (51), (52),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (58), (62), (67), (69), (70), (71),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (77), (81), (83), (84), (86),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (87), (88), (92), (97), (98), (100), (117), (130),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | | (140), (187) are inconsistent by sub-proof #179.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (188) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (189) all_252_8 = e3 & op(e2, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (190) all_252_8 = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (190) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (191) e3 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (191) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (192) all_252_7 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (16), (18), (19), (23), (31), (47),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (48), (51), (55), (64), (71), (81), (144), (192)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (193) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (194) all_252_14 = e3 & op(e1, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (195) all_252_14 = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (195) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (196) e3 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (197) e3 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (197) imply:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (198) all_252_7 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (16), (18), (19), (23), (31), (47),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (48), (51), (55), (64), (71), (81), (144), (198)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (199) all_252_22 = e3 & op(e0, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (200) op(e0, e2) = e3
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (34), (200) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | sub-proof #975.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | (201) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 250.02/59.23 | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (202) all_252_11 = e1 & op(e2, e1) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (203) all_252_11 = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (55), (203) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | #188.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (204) all_252_18 = e1 & op(e2, e0) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | (205) op(e2, e0) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (206) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (207) all_252_16 = e2 & op(e4, e0) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (208) op(e4, e0) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (49), (208) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | sub-proof #830.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (209) all_252_17 = e2 & op(e3, e0) = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (210) all_252_17 = e2
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (10), (12), (13), (15), (16),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (17), (19), (21), (30), (31), (32), (33), (35),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (36), (37), (42), (43), (46), (47), (51), (52),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (55), (57), (58), (62), (67), (69), (70), (71),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (77), (81), (83), (84), (86),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (87), (88), (92), (97), (98), (100), (117), (130),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | | (140), (210) are inconsistent by sub-proof #179.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (211) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (16), (20), (30), (31), (42), (43),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (46), (70), (72), (74), (76), (77), (81), (89),
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | (97), (205), (211) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | | #178.
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | (212) all_252_24 = e1 & op(e0, e0) = e1
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12),
% 250.02/59.23 | | | | | | | | | | | | | | | | (13), (14), (15), (16), (18), (19), (20), (21),
% 250.02/59.23 | | | | | | | | | | | | | | | | (22), (23), (24), (26), (28), (30), (31), (32),
% 250.02/59.23 | | | | | | | | | | | | | | | | (33), (34), (35), (38), (39), (40), (41), (42),
% 250.02/59.23 | | | | | | | | | | | | | | | | (43), (44), (45), (46), (47), (48), (50), (51),
% 250.02/59.23 | | | | | | | | | | | | | | | | (52), (53), (55), (56), (57), (58), (61), (62),
% 250.02/59.23 | | | | | | | | | | | | | | | | (63), (64), (66), (67), (68), (69), (70), (71),
% 250.02/59.23 | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (77), (81), (84),
% 250.02/59.23 | | | | | | | | | | | | | | | | (85), (87), (89), (90), (91), (92), (97), (101),
% 250.02/59.23 | | | | | | | | | | | | | | | | (102), (108), (117), (212) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | | | | sub-proof #177.
% 250.02/59.23 | | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | (213) all_252_5 = e0 & op(e3, e2) = e0
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | REF_CLOSE: (16), (62), (84), (213) are inconsistent by
% 250.02/59.23 | | | | | | | | | | | | | sub-proof #874.
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | (214) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 250.02/59.23 | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 250.02/59.23 | | | | | | | | | | | | op(e0, e2) = e0)
% 250.02/59.23 | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | BETA: splitting (214) gives:
% 250.02/59.23 | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | (215) all_252_8 = e0 & op(e2, e2) = e0
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | ALPHA: (215) implies:
% 250.02/59.23 | | | | | | | | | | | | | (216) all_252_8 = e0
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | REF_CLOSE: (10), (12), (13), (16), (18), (19), (22), (23),
% 250.02/59.23 | | | | | | | | | | | | | (31), (35), (47), (48), (51), (55), (64), (71),
% 250.02/59.23 | | | | | | | | | | | | | (81), (89), (216) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | #200.
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | (217) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 250.02/59.23 | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | BETA: splitting (217) gives:
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | (218) all_252_14 = e0 & op(e1, e2) = e0
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | REF_CLOSE: (13), (130), (218) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | #521.
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | (219) all_252_22 = e0 & op(e0, e2) = e0
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | ALPHA: (219) implies:
% 250.02/59.23 | | | | | | | | | | | | | | (220) all_252_22 = e0
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | | REF_CLOSE: (21), (123), (220) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | | | | #528.
% 250.02/59.23 | | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | (221) all_252_22 = e1 & op(e0, e2) = e1
% 250.02/59.23 | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | | REF_CLOSE: (35), (123), (221) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | | | #446.
% 250.02/59.23 | | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | | |
% 250.02/59.23 | | | | | | | | | End of split
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | End of split
% 250.02/59.23 | | | | | | | |
% 250.02/59.23 | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | |
% 250.02/59.23 | | | | | | | | (222) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4
% 250.02/59.23 | | | | | | | | & op(e0, e0) = e4)
% 250.02/59.23 | | | | | | | |
% 250.02/59.23 | | | | | | | | BETA: splitting (222) gives:
% 250.02/59.23 | | | | | | | |
% 250.02/59.23 | | | | | | | | Case 1:
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | | (223) all_252_23 = e4 & op(e0, e1) = e4
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | | REF_CLOSE: (16), (73), (87), (223) are inconsistent by
% 250.02/59.23 | | | | | | | | | sub-proof #912.
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | Case 2:
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | | (224) all_252_24 = e4 & op(e0, e0) = e4
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | | REF_CLOSE: (71), (117), (224) are inconsistent by sub-proof
% 250.02/59.23 | | | | | | | | | #525.
% 250.02/59.23 | | | | | | | | |
% 250.02/59.23 | | | | | | | | End of split
% 250.02/59.23 | | | | | | | |
% 250.02/59.23 | | | | | | | End of split
% 250.02/59.23 | | | | | | |
% 250.02/59.23 | | | | | | End of split
% 250.02/59.23 | | | | | |
% 250.02/59.23 | | | | | End of split
% 250.02/59.23 | | | | |
% 250.02/59.23 | | | | End of split
% 250.02/59.23 | | | |
% 250.02/59.23 | | | End of split
% 250.02/59.23 | | |
% 250.02/59.23 | | Case 2:
% 250.02/59.23 | | |
% 250.02/59.23 | | | (225) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0,
% 250.02/59.23 | | | e3) = e3)
% 250.02/59.23 | | |
% 250.02/59.23 | | | REF_CLOSE: (19), (32), (47), (59), (225) are inconsistent by sub-proof
% 250.02/59.23 | | | #211.
% 250.02/59.23 | | |
% 250.02/59.23 | | End of split
% 250.02/59.23 | |
% 250.02/59.23 | End of split
% 250.02/59.23 |
% 250.02/59.23 End of proof
% 250.02/59.23
% 250.02/59.23 Sub-proof #177 shows that the following formulas are inconsistent:
% 250.02/59.23 ----------------------------------------------------------------
% 250.02/59.23 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.23 all_250_23 = e0
% 250.02/59.23 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.23 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.23 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.23 (3) ~ (all_4_2 = e4)
% 250.02/59.23 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.23 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.23 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.23 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.23 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.23 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.23 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.02/59.23 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.23 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.23 (7) all_252_6 = e0
% 250.02/59.23 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 250.02/59.23 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 250.02/59.23 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.23 (9) ~ (e2 = e0)
% 250.02/59.23 (10) ~ (e1 = e0)
% 250.02/59.23 (11) ~ (all_28_2 = e3)
% 250.02/59.23 (12) op(e4, e1) = e2
% 250.02/59.23 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.23 (14) op(e2, e3) = all_10_2
% 250.02/59.23 (15) ~ (e3 = e2)
% 250.02/59.23 (16) op(e0, e0) = all_244_24
% 250.02/59.23 (17) ~ (e4 = e0)
% 250.02/59.23 (18) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.23 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.23 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.23 (19) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.23 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.23 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.23 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.23 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.23 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.23 (21) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.23 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.23 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.23 (22) op(e4, e2) = all_6_2
% 250.02/59.23 (23) ~ (all_244_15 = e4)
% 250.02/59.23 (24) ~ (e2 = e1)
% 250.02/59.23 (25) all_252_13 = e2
% 250.02/59.23 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.23 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.23 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.23 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.23 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.23 op(e0, e1) = e0)))
% 250.02/59.23 (27) op(e0, e2) = all_28_2
% 250.02/59.23 (28) ~ (e4 = e1)
% 250.02/59.23 (29) ~ (all_6_2 = e1)
% 250.02/59.23 (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.23 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.23 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.23 (31) all_80_2 = all_6_2
% 250.02/59.23 (32) op(all_34_2, e0) = e1
% 250.02/59.23 (33) op(e1, e4) = all_16_2
% 250.02/59.23 (34) op(e2, all_16_2) = e1
% 250.02/59.23 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.23 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.23 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.23 (36) ~ (all_28_2 = all_20_2)
% 250.02/59.23 (37) op(e1, e3) = all_62_2
% 250.02/59.23 (38) ~ (e3 = e0)
% 250.02/59.23 (39) op(e2, e3) = e1
% 250.02/59.23 (40) ~ (all_22_2 = e4)
% 250.02/59.23 (41) ~ (e3 = e1)
% 250.02/59.23 (42) op(e3, e1) = all_36_2
% 250.02/59.23 (43) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.23 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.23 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.23 (44) all_252_11 = e4
% 250.02/59.23 (45) ~ (all_8_2 = e1)
% 250.02/59.24 (46) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.24 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.24 (47) ~ (all_22_2 = e1)
% 250.02/59.24 (48) all_252_24 = e3
% 250.02/59.24 (49) op(e3, e1) = all_172_1
% 250.02/59.24 (50) ~ (all_8_2 = e0)
% 250.02/59.24 (51) all_74_2 = all_36_2
% 250.02/59.24 (52) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.24 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.24 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.24 (53) all_252_7 = e3
% 250.02/59.24 (54) op(all_6_2, e0) = e2
% 250.02/59.24 (55) op(e0, e3) = all_22_2
% 250.02/59.24 (56) op(all_34_2, all_20_2) = e0
% 250.02/59.24 (57) all_252_20 = e2
% 250.02/59.24 (58) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.24 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.24 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.24 (59) all_252_24 = e1 & op(e0, e0) = e1
% 250.02/59.24 (60) ~ (e4 = e3)
% 250.02/59.24 (61) op(e1, e1) = all_244_15
% 250.02/59.24 (62) op(e0, e1) = all_20_2
% 250.02/59.24 (63) op(e2, e4) = e0
% 250.02/59.24 (64) all_82_2 = all_28_2
% 250.02/59.24 (65) ~ (all_244_24 = e2)
% 250.02/59.24 (66) op(e1, e2) = all_4_2
% 250.02/59.24 (67) ~ (e4 = e2)
% 250.02/59.24 (68) op(e3, e2) = all_8_2
% 250.02/59.24 (69) op(all_36_2, e1) = e3
% 250.02/59.24 (70) ~ (all_20_2 = e4)
% 250.02/59.24 (71) op(e2, e0) = all_40_2
% 250.02/59.24 (72) all_78_2 = e1
% 250.02/59.24 (73) ~ (all_20_2 = e3)
% 250.02/59.24 (74) ~ (all_16_2 = e3)
% 250.02/59.24 (75) ~ (all_62_2 = e4)
% 250.02/59.24 (76) ~ (all_20_2 = e2)
% 250.02/59.24 (77) all_250_23 = all_20_2
% 250.02/59.24
% 250.02/59.24 Begin of proof
% 250.02/59.24 |
% 250.02/59.24 | ALPHA: (59) implies:
% 250.02/59.24 | (78) all_252_24 = e1
% 250.02/59.24 |
% 250.02/59.24 | COMBINE_EQS: (48), (78) imply:
% 250.02/59.24 | (79) e3 = e1
% 250.02/59.24 |
% 250.02/59.24 | SIMP: (79) implies:
% 250.02/59.24 | (80) e3 = e1
% 250.02/59.24 |
% 250.02/59.24 | COMBINE_EQS: (53), (80) imply:
% 250.02/59.24 | (81) all_252_7 = e1
% 250.02/59.24 |
% 250.02/59.24 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.02/59.24 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.02/59.24 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.02/59.24 | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 250.02/59.24 | (46), (47), (49), (50), (51), (52), (54), (55), (56), (57), (58),
% 250.02/59.24 | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 250.02/59.24 | (71), (72), (73), (74), (75), (76), (77), (81) are inconsistent by
% 250.02/59.24 | sub-proof #192.
% 250.02/59.24 |
% 250.02/59.24 End of proof
% 250.02/59.24
% 250.02/59.24 Sub-proof #178 shows that the following formulas are inconsistent:
% 250.02/59.24 ----------------------------------------------------------------
% 250.02/59.24 (1) ~ (all_4_2 = e4)
% 250.02/59.24 (2) ~ (e1 = e0)
% 250.02/59.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.24 (4) op(e0, e0) = all_244_24
% 250.02/59.24 (5) ~ (all_244_15 = e4)
% 250.02/59.24 (6) op(e2, e0) = e1
% 250.02/59.24 (7) ~ (e2 = e1)
% 250.02/59.24 (8) op(e1, e4) = all_16_2
% 250.02/59.24 (9) op(e2, all_16_2) = e1
% 250.02/59.24 (10) op(e1, e3) = all_62_2
% 250.02/59.24 (11) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1, e0) =
% 250.02/59.24 e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.02/59.24 (12) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.24 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.24 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.24 (13) op(e1, e1) = all_244_15
% 250.02/59.24 (14) op(e2, e4) = e0
% 250.02/59.24 (15) ~ (all_244_24 = e2)
% 250.02/59.24 (16) op(e1, e2) = all_4_2
% 250.02/59.24 (17) ~ (e4 = e2)
% 250.02/59.24 (18) op(e2, e0) = all_40_2
% 250.02/59.24 (19) ~ (all_62_2 = e4)
% 250.02/59.24
% 250.02/59.24 Begin of proof
% 250.02/59.24 |
% 250.02/59.24 | BETA: splitting (11) gives:
% 250.02/59.24 |
% 250.02/59.24 | Case 1:
% 250.02/59.24 | |
% 250.02/59.24 | | (20) all_252_18 = e2 & op(e2, e0) = e2
% 250.02/59.24 | |
% 250.02/59.24 | | ALPHA: (20) implies:
% 250.02/59.24 | | (21) op(e2, e0) = e2
% 250.02/59.24 | |
% 250.02/59.24 | | REF_CLOSE: (3), (6), (7), (18), (21) are inconsistent by sub-proof #415.
% 250.02/59.24 | |
% 250.02/59.24 | Case 2:
% 250.02/59.24 | |
% 250.02/59.24 | | (22) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0)
% 250.02/59.24 | | = e2)
% 250.02/59.24 | |
% 250.02/59.24 | | BETA: splitting (22) gives:
% 250.02/59.24 | |
% 250.02/59.24 | | Case 1:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (23) all_252_19 = e2 & op(e1, e0) = e2
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (12), (13), (14), (16),
% 250.02/59.24 | | | (17), (19), (23) are inconsistent by sub-proof #213.
% 250.02/59.24 | | |
% 250.02/59.24 | | Case 2:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (24) all_252_24 = e2 & op(e0, e0) = e2
% 250.02/59.24 | | |
% 250.02/59.24 | | | ALPHA: (24) implies:
% 250.02/59.24 | | | (25) op(e0, e0) = e2
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (3), (4), (15), (25) are inconsistent by sub-proof #978.
% 250.02/59.24 | | |
% 250.02/59.24 | | End of split
% 250.02/59.24 | |
% 250.02/59.24 | End of split
% 250.02/59.24 |
% 250.02/59.24 End of proof
% 250.02/59.24
% 250.02/59.24 Sub-proof #179 shows that the following formulas are inconsistent:
% 250.02/59.24 ----------------------------------------------------------------
% 250.02/59.24 (1) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.02/59.24 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.24 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.24 (2) ~ (all_4_2 = e4)
% 250.02/59.24 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.24 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.24 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.24 (4) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.02/59.24 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.24 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.02/59.24 (5) all_252_17 = e2
% 250.02/59.24 (6) all_252_6 = e0
% 250.02/59.24 (7) ~ (e2 = e0)
% 250.02/59.24 (8) ~ (e1 = e0)
% 250.02/59.24 (9) op(e4, e1) = e2
% 250.02/59.24 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.24 (11) all_252_3 = e1
% 250.02/59.24 (12) ~ (e3 = e2)
% 250.02/59.24 (13) ~ (e4 = e0)
% 250.02/59.24 (14) ~ (all_244_15 = e4)
% 250.02/59.24 (15) ~ (e2 = e1)
% 250.02/59.24 (16) all_252_13 = e2
% 250.02/59.24 (17) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.24 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.24 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.24 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.24 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.24 op(e0, e1) = e0)))
% 250.02/59.24 (18) ~ (e4 = e1)
% 250.02/59.24 (19) all_252_9 = e2
% 250.02/59.24 (20) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.24 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.24 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.24 (21) op(e1, e4) = all_16_2
% 250.02/59.24 (22) op(e2, all_16_2) = e1
% 250.02/59.24 (23) op(e1, e3) = all_62_2
% 250.02/59.24 (24) ~ (e3 = e0)
% 250.02/59.24 (25) all_252_23 = e1
% 250.02/59.24 (26) ~ (e3 = e1)
% 250.02/59.24 (27) op(e3, e1) = all_36_2
% 250.02/59.24 (28) all_252_11 = e4
% 250.02/59.24 (29) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.24 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.24 (30) ~ (all_22_2 = e1)
% 250.02/59.24 (31) all_252_24 = e3
% 250.02/59.24 (32) ~ (all_8_2 = e0)
% 250.02/59.24 (33) op(e0, e3) = all_22_2
% 250.02/59.24 (34) all_252_20 = e2
% 250.02/59.24 (35) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.24 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.24 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.24 (36) ~ (e4 = e3)
% 250.02/59.24 (37) all_252_14 = e1
% 250.02/59.24 (38) op(e1, e1) = all_244_15
% 250.02/59.24 (39) op(e0, e1) = all_20_2
% 250.02/59.24 (40) op(e2, e4) = e0
% 250.02/59.24 (41) op(e1, e2) = all_4_2
% 250.02/59.24 (42) ~ (e4 = e2)
% 250.02/59.24 (43) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.24 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.24 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.24 (44) op(e3, e2) = all_8_2
% 250.02/59.24 (45) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.02/59.24 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.02/59.24 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.02/59.24 (46) ~ (all_20_2 = e4)
% 250.02/59.24 (47) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.02/59.24 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.02/59.24 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.02/59.24 (48) ~ (all_16_2 = e3)
% 250.02/59.24 (49) ~ (all_62_2 = e4)
% 250.02/59.24 (50) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.02/59.24 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.02/59.24 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.02/59.24 (51) ~ (all_16_2 = e0)
% 250.02/59.24
% 250.02/59.24 Begin of proof
% 250.02/59.24 |
% 250.02/59.24 | BETA: splitting (4) gives:
% 250.02/59.24 |
% 250.02/59.24 | Case 1:
% 250.02/59.24 | |
% 250.02/59.24 | | (52) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 250.02/59.24 | | e0)
% 250.02/59.24 | |
% 250.02/59.24 | | BETA: splitting (52) gives:
% 250.02/59.24 | |
% 250.02/59.24 | | Case 1:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (53) all_252_2 = e0 & op(e3, e4) = e0
% 250.02/59.24 | | |
% 250.02/59.24 | | | ALPHA: (53) implies:
% 250.02/59.24 | | | (54) all_252_2 = e0
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (6), (8), (10), (12), (13), (15), (18), (21), (24), (26), (34),
% 250.02/59.24 | | | (36), (42), (45), (47), (48), (50), (54) are inconsistent by
% 250.02/59.24 | | | sub-proof #538.
% 250.02/59.24 | | |
% 250.02/59.24 | | Case 2:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (55) all_252_3 = e0 & op(e3, e3) = e0
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (8), (11), (55) are inconsistent by sub-proof #777.
% 250.02/59.24 | | |
% 250.02/59.24 | | End of split
% 250.02/59.24 | |
% 250.02/59.24 | Case 2:
% 250.02/59.24 | |
% 250.02/59.24 | | (56) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 250.02/59.24 | | e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.02/59.24 | |
% 250.02/59.24 | | BETA: splitting (56) gives:
% 250.02/59.24 | |
% 250.02/59.24 | | Case 1:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (57) all_252_5 = e0 & op(e3, e2) = e0
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (10), (32), (44), (57) are inconsistent by sub-proof #874.
% 250.02/59.24 | | |
% 250.02/59.24 | | Case 2:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (58) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 = e0 & op(e3,
% 250.02/59.24 | | | e0) = e0)
% 250.02/59.24 | | |
% 250.02/59.24 | | | BETA: splitting (58) gives:
% 250.02/59.24 | | |
% 250.02/59.24 | | | Case 1:
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | (59) all_252_10 = e0 & op(e3, e1) = e0
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | ALPHA: (59) implies:
% 250.02/59.24 | | | | (60) op(e3, e1) = e0
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (12), (13), (14), (15),
% 250.02/59.24 | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 250.02/59.24 | | | | (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 250.02/59.24 | | | | (37), (38), (39), (40), (41), (42), (43), (46), (49), (51),
% 250.02/59.24 | | | | (60) are inconsistent by sub-proof #181.
% 250.02/59.24 | | | |
% 250.02/59.24 | | | Case 2:
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | (61) all_252_17 = e0 & op(e3, e0) = e0
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | REF_CLOSE: (5), (7), (61) are inconsistent by sub-proof #180.
% 250.02/59.24 | | | |
% 250.02/59.24 | | | End of split
% 250.02/59.24 | | |
% 250.02/59.24 | | End of split
% 250.02/59.24 | |
% 250.02/59.24 | End of split
% 250.02/59.24 |
% 250.02/59.24 End of proof
% 250.02/59.24
% 250.02/59.24 Sub-proof #180 shows that the following formulas are inconsistent:
% 250.02/59.24 ----------------------------------------------------------------
% 250.02/59.24 (1) all_252_17 = e0 & op(e3, e0) = e0
% 250.02/59.24 (2) all_252_17 = e2
% 250.02/59.24 (3) ~ (e2 = e0)
% 250.02/59.24
% 250.02/59.24 Begin of proof
% 250.02/59.24 |
% 250.02/59.24 | ALPHA: (1) implies:
% 250.02/59.24 | (4) all_252_17 = e0
% 250.02/59.24 |
% 250.02/59.24 | COMBINE_EQS: (2), (4) imply:
% 250.02/59.24 | (5) e2 = e0
% 250.02/59.24 |
% 250.02/59.24 | REDUCE: (3), (5) imply:
% 250.02/59.24 | (6) $false
% 250.02/59.24 |
% 250.02/59.24 | CLOSE: (6) is inconsistent.
% 250.02/59.24 |
% 250.02/59.24 End of proof
% 250.02/59.24
% 250.02/59.24 Sub-proof #181 shows that the following formulas are inconsistent:
% 250.02/59.24 ----------------------------------------------------------------
% 250.02/59.24 (1) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.02/59.24 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.24 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.24 (2) ~ (all_4_2 = e4)
% 250.02/59.24 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.24 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.24 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.24 (4) ~ (e2 = e0)
% 250.02/59.24 (5) ~ (e1 = e0)
% 250.02/59.24 (6) op(e4, e1) = e2
% 250.02/59.24 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.24 (8) ~ (e3 = e2)
% 250.02/59.24 (9) ~ (e4 = e0)
% 250.02/59.24 (10) ~ (all_244_15 = e4)
% 250.02/59.24 (11) ~ (e2 = e1)
% 250.02/59.24 (12) all_252_13 = e2
% 250.02/59.24 (13) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.24 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.24 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.24 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.24 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.24 op(e0, e1) = e0)))
% 250.02/59.24 (14) ~ (e4 = e1)
% 250.02/59.24 (15) all_252_9 = e2
% 250.02/59.24 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.24 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.24 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.24 (17) op(e1, e4) = all_16_2
% 250.02/59.24 (18) op(e2, all_16_2) = e1
% 250.02/59.24 (19) op(e1, e3) = all_62_2
% 250.02/59.24 (20) ~ (e3 = e0)
% 250.02/59.24 (21) all_252_23 = e1
% 250.02/59.24 (22) ~ (e3 = e1)
% 250.02/59.24 (23) op(e3, e1) = all_36_2
% 250.02/59.24 (24) all_252_11 = e4
% 250.02/59.24 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.24 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.24 (26) ~ (all_22_2 = e1)
% 250.02/59.24 (27) all_252_24 = e3
% 250.02/59.24 (28) op(e0, e3) = all_22_2
% 250.02/59.24 (29) all_252_20 = e2
% 250.02/59.24 (30) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.24 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.24 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.24 (31) ~ (e4 = e3)
% 250.02/59.24 (32) all_252_14 = e1
% 250.02/59.24 (33) op(e1, e1) = all_244_15
% 250.02/59.24 (34) op(e0, e1) = all_20_2
% 250.02/59.24 (35) op(e2, e4) = e0
% 250.02/59.24 (36) op(e1, e2) = all_4_2
% 250.02/59.24 (37) op(e3, e1) = e0
% 250.02/59.24 (38) ~ (e4 = e2)
% 250.02/59.24 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.24 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.24 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.24 (40) ~ (all_20_2 = e4)
% 250.02/59.24 (41) ~ (all_62_2 = e4)
% 250.02/59.24 (42) ~ (all_16_2 = e0)
% 250.02/59.24
% 250.02/59.24 Begin of proof
% 250.02/59.24 |
% 250.02/59.24 | BETA: splitting (16) gives:
% 250.02/59.24 |
% 250.02/59.24 | Case 1:
% 250.02/59.24 | |
% 250.02/59.24 | | (43) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.02/59.24 | | e3)
% 250.02/59.24 | |
% 250.02/59.24 | | BETA: splitting (43) gives:
% 250.02/59.24 | |
% 250.02/59.24 | | Case 1:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (44) all_252_9 = e3 & op(e4, e1) = e3
% 250.02/59.24 | | |
% 250.02/59.24 | | | ALPHA: (44) implies:
% 250.02/59.24 | | | (45) all_252_9 = e3
% 250.02/59.24 | | |
% 250.02/59.24 | | | COMBINE_EQS: (15), (45) imply:
% 250.02/59.24 | | | (46) e3 = e2
% 250.02/59.24 | | |
% 250.02/59.24 | | | REDUCE: (8), (46) imply:
% 250.02/59.24 | | | (47) $false
% 250.02/59.24 | | |
% 250.02/59.24 | | | CLOSE: (47) is inconsistent.
% 250.02/59.24 | | |
% 250.02/59.24 | | Case 2:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (48) all_252_10 = e3 & op(e3, e1) = e3
% 250.02/59.24 | | |
% 250.02/59.24 | | | ALPHA: (48) implies:
% 250.02/59.24 | | | (49) op(e3, e1) = e3
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (7), (20), (23), (37), (49) are inconsistent by sub-proof #748.
% 250.02/59.24 | | |
% 250.02/59.24 | | End of split
% 250.02/59.24 | |
% 250.02/59.24 | Case 2:
% 250.02/59.24 | |
% 250.02/59.24 | | (50) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1)
% 250.02/59.24 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.24 | |
% 250.02/59.24 | | BETA: splitting (50) gives:
% 250.02/59.24 | |
% 250.02/59.24 | | Case 1:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (51) all_252_11 = e3 & op(e2, e1) = e3
% 250.02/59.24 | | |
% 250.02/59.24 | | | REF_CLOSE: (24), (31), (51) are inconsistent by sub-proof #791.
% 250.02/59.24 | | |
% 250.02/59.24 | | Case 2:
% 250.02/59.24 | | |
% 250.02/59.24 | | | (52) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.24 | | | e1) = e3)
% 250.02/59.24 | | |
% 250.02/59.24 | | | BETA: splitting (52) gives:
% 250.02/59.24 | | |
% 250.02/59.24 | | | Case 1:
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | (53) all_252_15 = e3 & op(e1, e1) = e3
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | ALPHA: (53) implies:
% 250.02/59.24 | | | | (54) all_252_15 = e3
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | BETA: splitting (1) gives:
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | Case 1:
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | (55) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 &
% 250.02/59.24 | | | | | op(e1, e3) = e0)
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | BETA: splitting (55) gives:
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | Case 1:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | (56) all_252_12 = e0 & op(e1, e4) = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | ALPHA: (56) implies:
% 250.02/59.24 | | | | | | (57) op(e1, e4) = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | REF_CLOSE: (7), (17), (42), (57) are inconsistent by sub-proof #278.
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | Case 2:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | (58) all_252_13 = e0 & op(e1, e3) = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | ALPHA: (58) implies:
% 250.02/59.24 | | | | | | (59) all_252_13 = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | COMBINE_EQS: (12), (59) imply:
% 250.02/59.24 | | | | | | (60) e2 = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | REDUCE: (4), (60) imply:
% 250.02/59.24 | | | | | | (61) $false
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | CLOSE: (61) is inconsistent.
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | End of split
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | Case 2:
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | (62) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 &
% 250.02/59.24 | | | | | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | BETA: splitting (62) gives:
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | | Case 1:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | (63) all_252_14 = e0 & op(e1, e2) = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | ALPHA: (63) implies:
% 250.02/59.24 | | | | | | (64) all_252_14 = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | COMBINE_EQS: (32), (64) imply:
% 250.02/59.24 | | | | | | (65) e1 = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | COMBINE_EQS: (21), (65) imply:
% 250.02/59.24 | | | | | | (66) all_252_23 = e0
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | BETA: splitting (39) gives:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | Case 1:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | (67) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 &
% 250.02/59.24 | | | | | | | op(e3, e1) = e1)
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | BETA: splitting (67) gives:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (68) all_252_9 = e1 & op(e4, e1) = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | ALPHA: (68) implies:
% 250.02/59.24 | | | | | | | | (69) op(e4, e1) = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | REF_CLOSE: (6), (7), (11), (69) are inconsistent by sub-proof
% 250.02/59.24 | | | | | | | | #785.
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (70) all_252_10 = e1 & op(e3, e1) = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | ALPHA: (70) implies:
% 250.02/59.24 | | | | | | | | (71) op(e3, e1) = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | REF_CLOSE: (5), (7), (23), (37), (71) are inconsistent by
% 250.02/59.24 | | | | | | | | sub-proof #922.
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | End of split
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | Case 2:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | (72) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 &
% 250.02/59.24 | | | | | | | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | BETA: splitting (72) gives:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (73) all_252_11 = e1 & op(e2, e1) = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | ALPHA: (73) implies:
% 250.02/59.24 | | | | | | | | (74) all_252_11 = e1
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | REF_CLOSE: (14), (24), (74) are inconsistent by sub-proof #188.
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (75) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 250.02/59.24 | | | | | | | | op(e0, e1) = e1)
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | BETA: splitting (75) gives:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | (76) all_252_15 = e1 & op(e1, e1) = e1
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | REF_CLOSE: (22), (54), (76) are inconsistent by sub-proof
% 250.02/59.24 | | | | | | | | | #358.
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | (77) all_252_23 = e1 & op(e0, e1) = e1
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | REF_CLOSE: (5), (66), (77) are inconsistent by sub-proof #187.
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | End of split
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | End of split
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | End of split
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | Case 2:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | (78) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 = e0 &
% 250.02/59.24 | | | | | | op(e1, e0) = e0)
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | BETA: splitting (78) gives:
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | | Case 1:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | (79) all_252_15 = e0 & op(e1, e1) = e0
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | ALPHA: (79) implies:
% 250.02/59.24 | | | | | | | (80) all_252_15 = e0
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | REF_CLOSE: (20), (54), (80) are inconsistent by sub-proof #196.
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | Case 2:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | (81) all_252_19 = e0 & op(e1, e0) = e0
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | ALPHA: (81) implies:
% 250.02/59.24 | | | | | | | (82) all_252_19 = e0
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | BETA: splitting (30) gives:
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (83) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 &
% 250.02/59.24 | | | | | | | | op(e1, e3) = e4)
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | REF_CLOSE: (5), (7), (17), (18), (19), (35), (41), (83) are
% 250.02/59.24 | | | | | | | | inconsistent by sub-proof #195.
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | (84) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 250.02/59.24 | | | | | | | | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | BETA: splitting (84) gives:
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | (85) all_252_14 = e4 & op(e1, e2) = e4
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | ALPHA: (85) implies:
% 250.02/59.24 | | | | | | | | | (86) op(e1, e2) = e4
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | REF_CLOSE: (2), (7), (36), (86) are inconsistent by sub-proof
% 250.02/59.24 | | | | | | | | | #831.
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | (87) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4
% 250.02/59.24 | | | | | | | | | & op(e1, e0) = e4)
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | BETA: splitting (87) gives:
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | | Case 1:
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | (88) all_252_15 = e4 & op(e1, e1) = e4
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | ALPHA: (88) implies:
% 250.02/59.24 | | | | | | | | | | (89) op(e1, e1) = e4
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | REF_CLOSE: (7), (10), (33), (89) are inconsistent by
% 250.02/59.24 | | | | | | | | | | sub-proof #756.
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | Case 2:
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | (90) all_252_19 = e4 & op(e1, e0) = e4
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | ALPHA: (90) implies:
% 250.02/59.24 | | | | | | | | | | (91) all_252_19 = e4
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | | REF_CLOSE: (9), (82), (91) are inconsistent by sub-proof
% 250.02/59.24 | | | | | | | | | | #618.
% 250.02/59.24 | | | | | | | | | |
% 250.02/59.24 | | | | | | | | | End of split
% 250.02/59.24 | | | | | | | | |
% 250.02/59.24 | | | | | | | | End of split
% 250.02/59.24 | | | | | | | |
% 250.02/59.24 | | | | | | | End of split
% 250.02/59.24 | | | | | | |
% 250.02/59.24 | | | | | | End of split
% 250.02/59.24 | | | | | |
% 250.02/59.24 | | | | | End of split
% 250.02/59.24 | | | | |
% 250.02/59.24 | | | | End of split
% 250.02/59.24 | | | |
% 250.02/59.24 | | | Case 2:
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | (92) all_252_23 = e3 & op(e0, e1) = e3
% 250.02/59.24 | | | |
% 250.02/59.24 | | | | ALPHA: (92) implies:
% 250.02/59.24 | | | | (93) op(e0, e1) = e3
% 250.02/59.24 | | | |
% 250.02/59.25 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 250.02/59.25 | | | | (16), (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 250.02/59.25 | | | | (31), (34), (37), (38), (39), (40), (93) are inconsistent by
% 250.02/59.25 | | | | sub-proof #182.
% 250.02/59.25 | | | |
% 250.02/59.25 | | | End of split
% 250.02/59.25 | | |
% 250.02/59.25 | | End of split
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #182 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.25 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.25 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.25 (2) ~ (e2 = e0)
% 250.02/59.25 (3) ~ (e1 = e0)
% 250.02/59.25 (4) op(e4, e1) = e2
% 250.02/59.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.25 (6) ~ (e3 = e2)
% 250.02/59.25 (7) ~ (e4 = e0)
% 250.02/59.25 (8) ~ (e2 = e1)
% 250.02/59.25 (9) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.25 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.25 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.25 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.25 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.25 op(e0, e1) = e0)))
% 250.02/59.25 (10) ~ (e4 = e1)
% 250.02/59.25 (11) all_252_9 = e2
% 250.02/59.25 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.02/59.25 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.25 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.25 (13) ~ (e3 = e0)
% 250.02/59.25 (14) ~ (e3 = e1)
% 250.02/59.25 (15) op(e3, e1) = all_36_2
% 250.02/59.25 (16) all_252_11 = e4
% 250.02/59.25 (17) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.25 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.25 (18) ~ (all_22_2 = e1)
% 250.02/59.25 (19) all_252_24 = e3
% 250.02/59.25 (20) op(e0, e1) = e3
% 250.02/59.25 (21) op(e0, e3) = all_22_2
% 250.02/59.25 (22) all_252_20 = e2
% 250.02/59.25 (23) ~ (e4 = e3)
% 250.02/59.25 (24) op(e0, e1) = all_20_2
% 250.02/59.25 (25) op(e3, e1) = e0
% 250.02/59.25 (26) ~ (e4 = e2)
% 250.02/59.25 (27) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.02/59.25 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.02/59.25 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.02/59.25 (28) ~ (all_20_2 = e4)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | BETA: splitting (12) gives:
% 250.02/59.25 |
% 250.02/59.25 | Case 1:
% 250.02/59.25 | |
% 250.02/59.25 | | (29) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.02/59.25 | | e3)
% 250.02/59.25 | |
% 250.02/59.25 | | BETA: splitting (29) gives:
% 250.02/59.25 | |
% 250.02/59.25 | | Case 1:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (30) all_252_9 = e3 & op(e4, e1) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | ALPHA: (30) implies:
% 250.02/59.25 | | | (31) all_252_9 = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | REF_CLOSE: (6), (11), (31) are inconsistent by sub-proof #186.
% 250.02/59.25 | | |
% 250.02/59.25 | | Case 2:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (32) all_252_10 = e3 & op(e3, e1) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | ALPHA: (32) implies:
% 250.02/59.25 | | | (33) op(e3, e1) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | REF_CLOSE: (5), (13), (15), (25), (33) are inconsistent by sub-proof #748.
% 250.02/59.25 | | |
% 250.02/59.25 | | End of split
% 250.02/59.25 | |
% 250.02/59.25 | Case 2:
% 250.02/59.25 | |
% 250.02/59.25 | | (34) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1)
% 250.02/59.25 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.02/59.25 | |
% 250.02/59.25 | | BETA: splitting (34) gives:
% 250.02/59.25 | |
% 250.02/59.25 | | Case 1:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (35) all_252_11 = e3 & op(e2, e1) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | REF_CLOSE: (16), (23), (35) are inconsistent by sub-proof #768.
% 250.02/59.25 | | |
% 250.02/59.25 | | Case 2:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (36) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.25 | | | e1) = e3)
% 250.02/59.25 | | |
% 250.02/59.25 | | | BETA: splitting (36) gives:
% 250.02/59.25 | | |
% 250.02/59.25 | | | Case 1:
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | (37) all_252_15 = e3 & op(e1, e1) = e3
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | REF_CLOSE: (3), (4), (5), (8), (10), (14), (15), (16), (20), (25), (27),
% 250.02/59.25 | | | | (37) are inconsistent by sub-proof #746.
% 250.02/59.25 | | | |
% 250.02/59.25 | | | Case 2:
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | (38) all_252_23 = e3 & op(e0, e1) = e3
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | ALPHA: (38) implies:
% 250.02/59.25 | | | | (39) all_252_23 = e3
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | BETA: splitting (17) gives:
% 250.02/59.25 | | | |
% 250.02/59.25 | | | | Case 1:
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | | (40) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 &
% 250.02/59.25 | | | | | op(e0, e3) = e1)
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | | REF_CLOSE: (5), (8), (18), (21), (22), (40) are inconsistent by
% 250.02/59.25 | | | | | sub-proof #199.
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | Case 2:
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | | (41) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 &
% 250.02/59.25 | | | | | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | | BETA: splitting (41) gives:
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | | Case 1:
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | (42) all_252_22 = e1 & op(e0, e2) = e1
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | ALPHA: (42) implies:
% 250.02/59.25 | | | | | | (43) all_252_22 = e1
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | BETA: splitting (1) gives:
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | Case 1:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | (44) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 250.02/59.25 | | | | | | | op(e0, e3) = e4)
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | BETA: splitting (44) gives:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | (45) all_252_20 = e4 & op(e0, e4) = e4
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | REF_CLOSE: (22), (26), (45) are inconsistent by sub-proof #543.
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | (46) all_252_21 = e4 & op(e0, e3) = e4
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | ALPHA: (46) implies:
% 250.02/59.25 | | | | | | | | (47) all_252_21 = e4
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | BETA: splitting (9) gives:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | (48) all_252_24 = e0 & op(e0, e0) = e0
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | REF_CLOSE: (13), (19), (48) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | | | #533.
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | (49) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.02/59.25 | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.02/59.25 | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0))
% 250.02/59.25 | | | | | | | | | & ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 =
% 250.02/59.25 | | | | | | | | | e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.02/59.25 | | | | | | | | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | ALPHA: (49) implies:
% 250.02/59.25 | | | | | | | | | (50) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 250.02/59.25 | | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) =
% 250.02/59.25 | | | | | | | | | e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | BETA: splitting (50) gives:
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | (51) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 =
% 250.02/59.25 | | | | | | | | | | e0 & op(e0, e3) = e0)
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | REF_CLOSE: (2), (7), (22), (47), (51) are inconsistent by
% 250.02/59.25 | | | | | | | | | | sub-proof #184.
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | (52) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 =
% 250.02/59.25 | | | | | | | | | | e0 & op(e0, e1) = e0)
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | BETA: splitting (52) gives:
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | (53) all_252_22 = e0 & op(e0, e2) = e0
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | ALPHA: (53) implies:
% 250.02/59.25 | | | | | | | | | | | (54) all_252_22 = e0
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | REF_CLOSE: (3), (43), (54) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | | | | | #198.
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | (55) all_252_23 = e0 & op(e0, e1) = e0
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | ALPHA: (55) implies:
% 250.02/59.25 | | | | | | | | | | | (56) all_252_23 = e0
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | | REF_CLOSE: (13), (39), (56) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | | | | | #183.
% 250.02/59.25 | | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | | End of split
% 250.02/59.25 | | | | | | | | | |
% 250.02/59.25 | | | | | | | | | End of split
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | End of split
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | End of split
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | Case 2:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | (57) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 250.02/59.25 | | | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | BETA: splitting (57) gives:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | (58) all_252_22 = e4 & op(e0, e2) = e4
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | ALPHA: (58) implies:
% 250.02/59.25 | | | | | | | | (59) all_252_22 = e4
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | COMBINE_EQS: (43), (59) imply:
% 250.02/59.25 | | | | | | | | (60) e4 = e1
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | REDUCE: (10), (60) imply:
% 250.02/59.25 | | | | | | | | (61) $false
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | CLOSE: (61) is inconsistent.
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | (62) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.02/59.25 | | | | | | | | op(e0, e0) = e4)
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | BETA: splitting (62) gives:
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | | Case 1:
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | (63) all_252_23 = e4 & op(e0, e1) = e4
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | REF_CLOSE: (5), (24), (28), (63) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | | | #912.
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | Case 2:
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | (64) all_252_24 = e4 & op(e0, e0) = e4
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | | REF_CLOSE: (19), (23), (64) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | | | #525.
% 250.02/59.25 | | | | | | | | |
% 250.02/59.25 | | | | | | | | End of split
% 250.02/59.25 | | | | | | | |
% 250.02/59.25 | | | | | | | End of split
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | End of split
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | Case 2:
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | (65) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 250.02/59.25 | | | | | | op(e0, e0) = e1)
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | BETA: splitting (65) gives:
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | | Case 1:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | (66) all_252_23 = e1 & op(e0, e1) = e1
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | ALPHA: (66) implies:
% 250.02/59.25 | | | | | | | (67) op(e0, e1) = e1
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | REF_CLOSE: (5), (14), (20), (67) are inconsistent by sub-proof
% 250.02/59.25 | | | | | | | #915.
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | Case 2:
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | (68) all_252_24 = e1 & op(e0, e0) = e1
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | ALPHA: (68) implies:
% 250.02/59.25 | | | | | | | (69) all_252_24 = e1
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | | REF_CLOSE: (14), (19), (69) are inconsistent by sub-proof #621.
% 250.02/59.25 | | | | | | |
% 250.02/59.25 | | | | | | End of split
% 250.02/59.25 | | | | | |
% 250.02/59.25 | | | | | End of split
% 250.02/59.25 | | | | |
% 250.02/59.25 | | | | End of split
% 250.02/59.25 | | | |
% 250.02/59.25 | | | End of split
% 250.02/59.25 | | |
% 250.02/59.25 | | End of split
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #183 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_23 = e3
% 250.02/59.25 (2) all_252_23 = e0
% 250.02/59.25 (3) ~ (e3 = e0)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | COMBINE_EQS: (1), (2) imply:
% 250.02/59.25 | (4) e3 = e0
% 250.02/59.25 |
% 250.02/59.25 | SIMP: (4) implies:
% 250.02/59.25 | (5) e3 = e0
% 250.02/59.25 |
% 250.02/59.25 | REDUCE: (3), (5) imply:
% 250.02/59.25 | (6) $false
% 250.02/59.25 |
% 250.02/59.25 | CLOSE: (6) is inconsistent.
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #184 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) ~ (e2 = e0)
% 250.02/59.25 (2) ~ (e4 = e0)
% 250.02/59.25 (3) all_252_21 = e4
% 250.02/59.25 (4) all_252_20 = e2
% 250.02/59.25 (5) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | BETA: splitting (5) gives:
% 250.02/59.25 |
% 250.02/59.25 | Case 1:
% 250.02/59.25 | |
% 250.02/59.25 | | (6) all_252_20 = e0 & op(e0, e4) = e0
% 250.02/59.25 | |
% 250.02/59.25 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #185.
% 250.02/59.25 | |
% 250.02/59.25 | Case 2:
% 250.02/59.25 | |
% 250.02/59.25 | | (7) all_252_21 = e0 & op(e0, e3) = e0
% 250.02/59.25 | |
% 250.02/59.25 | | ALPHA: (7) implies:
% 250.02/59.25 | | (8) all_252_21 = e0
% 250.02/59.25 | |
% 250.02/59.25 | | COMBINE_EQS: (3), (8) imply:
% 250.02/59.25 | | (9) e4 = e0
% 250.02/59.25 | |
% 250.02/59.25 | | REDUCE: (2), (9) imply:
% 250.02/59.25 | | (10) $false
% 250.02/59.25 | |
% 250.02/59.25 | | CLOSE: (10) is inconsistent.
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #185 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_20 = e0 & op(e0, e4) = e0
% 250.02/59.25 (2) all_252_20 = e2
% 250.02/59.25 (3) ~ (e2 = e0)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | ALPHA: (1) implies:
% 250.02/59.25 | (4) all_252_20 = e0
% 250.02/59.25 |
% 250.02/59.25 | COMBINE_EQS: (2), (4) imply:
% 250.02/59.25 | (5) e2 = e0
% 250.02/59.25 |
% 250.02/59.25 | REDUCE: (3), (5) imply:
% 250.02/59.25 | (6) $false
% 250.02/59.25 |
% 250.02/59.25 | CLOSE: (6) is inconsistent.
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #186 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_9 = e3
% 250.02/59.25 (2) all_252_9 = e2
% 250.02/59.25 (3) ~ (e3 = e2)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | COMBINE_EQS: (1), (2) imply:
% 250.02/59.25 | (4) e3 = e2
% 250.02/59.25 |
% 250.02/59.25 | SIMP: (4) implies:
% 250.02/59.25 | (5) e3 = e2
% 250.02/59.25 |
% 250.02/59.25 | REDUCE: (3), (5) imply:
% 250.02/59.25 | (6) $false
% 250.02/59.25 |
% 250.02/59.25 | CLOSE: (6) is inconsistent.
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #187 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_23 = e1 & op(e0, e1) = e1
% 250.02/59.25 (2) all_252_23 = e0
% 250.02/59.25 (3) ~ (e1 = e0)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | ALPHA: (1) implies:
% 250.02/59.25 | (4) all_252_23 = e1
% 250.02/59.25 |
% 250.02/59.25 | COMBINE_EQS: (2), (4) imply:
% 250.02/59.25 | (5) e1 = e0
% 250.02/59.25 |
% 250.02/59.25 | REDUCE: (3), (5) imply:
% 250.02/59.25 | (6) $false
% 250.02/59.25 |
% 250.02/59.25 | CLOSE: (6) is inconsistent.
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #188 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_11 = e4
% 250.02/59.25 (2) all_252_11 = e1
% 250.02/59.25 (3) ~ (e4 = e1)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | COMBINE_EQS: (1), (2) imply:
% 250.02/59.25 | (4) e4 = e1
% 250.02/59.25 |
% 250.02/59.25 | SIMP: (4) implies:
% 250.02/59.25 | (5) e4 = e1
% 250.02/59.25 |
% 250.02/59.25 | REDUCE: (3), (5) imply:
% 250.02/59.25 | (6) $false
% 250.02/59.25 |
% 250.02/59.25 | CLOSE: (6) is inconsistent.
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #189 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_252_6 = e0
% 250.02/59.25 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.25 (3) ~ (e3 = e2)
% 250.02/59.25 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3)
% 250.02/59.25 | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.02/59.25 (5) op(e1, e4) = all_16_2
% 250.02/59.25 (6) ~ (e3 = e0)
% 250.02/59.25 (7) all_252_20 = e2
% 250.02/59.25 (8) ~ (all_16_2 = e3)
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | BETA: splitting (4) gives:
% 250.02/59.25 |
% 250.02/59.25 | Case 1:
% 250.02/59.25 | |
% 250.02/59.25 | | (9) all_252_6 = e3 & op(e2, e4) = e3
% 250.02/59.25 | |
% 250.02/59.25 | | ALPHA: (9) implies:
% 250.02/59.25 | | (10) all_252_6 = e3
% 250.02/59.25 | |
% 250.02/59.25 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #691.
% 250.02/59.25 | |
% 250.02/59.25 | Case 2:
% 250.02/59.25 | |
% 250.02/59.25 | | (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4)
% 250.02/59.25 | | = e3)
% 250.02/59.25 | |
% 250.02/59.25 | | BETA: splitting (11) gives:
% 250.02/59.25 | |
% 250.02/59.25 | | Case 1:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (12) all_252_12 = e3 & op(e1, e4) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | REF_CLOSE: (2), (5), (8), (12) are inconsistent by sub-proof #895.
% 250.02/59.25 | | |
% 250.02/59.25 | | Case 2:
% 250.02/59.25 | | |
% 250.02/59.25 | | | (13) all_252_20 = e3 & op(e0, e4) = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | ALPHA: (13) implies:
% 250.02/59.25 | | | (14) all_252_20 = e3
% 250.02/59.25 | | |
% 250.02/59.25 | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #520.
% 250.02/59.25 | | |
% 250.02/59.25 | | End of split
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #190 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) ~ (e4 = e1)
% 250.02/59.25 (2) all_252_20 = e2
% 250.02/59.25 (3) ~ (e4 = e2)
% 250.02/59.25 (4) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.02/59.25 (5) all_252_12 = e1
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | BETA: splitting (4) gives:
% 250.02/59.25 |
% 250.02/59.25 | Case 1:
% 250.02/59.25 | |
% 250.02/59.25 | | (6) all_252_12 = e4 & op(e1, e4) = e4
% 250.02/59.25 | |
% 250.02/59.25 | | ALPHA: (6) implies:
% 250.02/59.25 | | (7) all_252_12 = e4
% 250.02/59.25 | |
% 250.02/59.25 | | COMBINE_EQS: (5), (7) imply:
% 250.02/59.25 | | (8) e4 = e1
% 250.02/59.25 | |
% 250.02/59.25 | | REDUCE: (1), (8) imply:
% 250.02/59.25 | | (9) $false
% 250.02/59.25 | |
% 250.02/59.25 | | CLOSE: (9) is inconsistent.
% 250.02/59.25 | |
% 250.02/59.25 | Case 2:
% 250.02/59.25 | |
% 250.02/59.25 | | (10) all_252_20 = e4 & op(e0, e4) = e4
% 250.02/59.25 | |
% 250.02/59.25 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #543.
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #191 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.25 all_250_23 = e0
% 250.02/59.25 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.25 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.25 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.25 (3) ~ (all_4_2 = e4)
% 250.02/59.25 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.25 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.25 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.25 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.25 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.25 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.25 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.02/59.25 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.25 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.25 (7) all_252_6 = e0
% 250.02/59.25 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 250.02/59.25 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 250.02/59.25 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.25 (9) ~ (e2 = e0)
% 250.02/59.25 (10) ~ (e1 = e0)
% 250.02/59.25 (11) ~ (all_28_2 = e3)
% 250.02/59.25 (12) op(e4, e1) = e2
% 250.02/59.25 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.25 (14) op(e2, e3) = all_10_2
% 250.02/59.25 (15) ~ (e3 = e2)
% 250.02/59.25 (16) op(e0, e0) = all_244_24
% 250.02/59.25 (17) ~ (e4 = e0)
% 250.02/59.25 (18) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.25 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.25 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.25 (19) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.25 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.25 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.25 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.25 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.25 (21) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.25 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.25 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.25 (22) op(e4, e2) = all_6_2
% 250.02/59.25 (23) ~ (all_244_15 = e4)
% 250.02/59.25 (24) ~ (e2 = e1)
% 250.02/59.25 (25) all_252_13 = e2
% 250.02/59.25 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.25 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.25 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.25 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.25 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.25 op(e0, e1) = e0)))
% 250.02/59.25 (27) op(e0, e2) = all_28_2
% 250.02/59.25 (28) ~ (e4 = e1)
% 250.02/59.25 (29) ~ (all_6_2 = e1)
% 250.02/59.25 (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.25 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.25 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.25 (31) all_80_2 = all_6_2
% 250.02/59.25 (32) op(all_34_2, e0) = e1
% 250.02/59.25 (33) op(e1, e4) = all_16_2
% 250.02/59.25 (34) op(e2, all_16_2) = e1
% 250.02/59.25 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.25 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.25 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.25 (36) ~ (all_28_2 = all_20_2)
% 250.02/59.25 (37) op(e1, e3) = all_62_2
% 250.02/59.25 (38) ~ (e3 = e0)
% 250.02/59.25 (39) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.25 (40) ~ (all_22_2 = e4)
% 250.02/59.25 (41) ~ (e3 = e1)
% 250.02/59.25 (42) op(e3, e1) = all_36_2
% 250.02/59.25 (43) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.25 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.25 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.25 (44) all_252_11 = e4
% 250.02/59.25 (45) ~ (all_8_2 = e1)
% 250.02/59.25 (46) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.25 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.25 (47) ~ (all_22_2 = e1)
% 250.02/59.25 (48) op(e3, e1) = all_172_1
% 250.02/59.25 (49) ~ (all_8_2 = e0)
% 250.02/59.25 (50) all_74_2 = all_36_2
% 250.02/59.25 (51) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.25 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.25 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.25 (52) op(all_6_2, e0) = e2
% 250.02/59.25 (53) op(e0, e3) = all_22_2
% 250.02/59.25 (54) op(all_34_2, all_20_2) = e0
% 250.02/59.25 (55) all_252_20 = e2
% 250.02/59.25 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.25 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.25 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.25 (57) ~ (e4 = e3)
% 250.02/59.25 (58) op(e1, e1) = all_244_15
% 250.02/59.25 (59) op(e0, e1) = all_20_2
% 250.02/59.25 (60) op(e2, e4) = e0
% 250.02/59.25 (61) all_82_2 = all_28_2
% 250.02/59.25 (62) ~ (all_244_24 = e2)
% 250.02/59.25 (63) op(e1, e2) = all_4_2
% 250.02/59.25 (64) ~ (e4 = e2)
% 250.02/59.25 (65) op(e3, e2) = all_8_2
% 250.02/59.25 (66) op(all_36_2, e1) = e3
% 250.02/59.25 (67) ~ (all_20_2 = e4)
% 250.02/59.25 (68) op(e2, e0) = all_40_2
% 250.02/59.25 (69) all_78_2 = e1
% 250.02/59.25 (70) ~ (all_20_2 = e3)
% 250.02/59.25 (71) ~ (all_16_2 = e3)
% 250.02/59.25 (72) ~ (all_62_2 = e4)
% 250.02/59.25 (73) ~ (all_20_2 = e2)
% 250.02/59.25 (74) all_250_23 = all_20_2
% 250.02/59.25
% 250.02/59.25 Begin of proof
% 250.02/59.25 |
% 250.02/59.25 | BETA: splitting (39) gives:
% 250.02/59.25 |
% 250.02/59.25 | Case 1:
% 250.02/59.25 | |
% 250.02/59.25 | | (75) all_252_6 = e1 & op(e2, e4) = e1
% 250.02/59.25 | |
% 250.02/59.25 | | REF_CLOSE: (7), (10), (75) are inconsistent by sub-proof #545.
% 250.02/59.25 | |
% 250.02/59.25 | Case 2:
% 250.02/59.25 | |
% 250.02/59.25 | | (76) all_252_7 = e1 & op(e2, e3) = e1
% 250.02/59.25 | |
% 250.02/59.25 | | ALPHA: (76) implies:
% 250.02/59.25 | | (77) all_252_7 = e1
% 250.02/59.25 | | (78) op(e2, e3) = e1
% 250.02/59.25 | |
% 250.02/59.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.02/59.25 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.02/59.25 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.02/59.25 | | (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (46),
% 250.02/59.25 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.02/59.25 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 250.02/59.25 | | (69), (70), (71), (72), (73), (74), (77), (78) are inconsistent
% 250.02/59.25 | | by sub-proof #192.
% 250.02/59.25 | |
% 250.02/59.25 | End of split
% 250.02/59.25 |
% 250.02/59.25 End of proof
% 250.02/59.25
% 250.02/59.25 Sub-proof #192 shows that the following formulas are inconsistent:
% 250.02/59.25 ----------------------------------------------------------------
% 250.02/59.25 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.25 all_250_23 = e0
% 250.02/59.25 (2) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 250.02/59.25 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 250.02/59.25 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 250.02/59.25 (3) ~ (all_4_2 = e4)
% 250.02/59.26 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.26 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.26 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.26 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.26 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.26 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.26 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.02/59.26 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.26 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.26 (7) all_252_6 = e0
% 250.02/59.26 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 250.02/59.26 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 250.02/59.26 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.26 (9) ~ (e2 = e0)
% 250.02/59.26 (10) ~ (e1 = e0)
% 250.02/59.26 (11) ~ (all_28_2 = e3)
% 250.02/59.26 (12) op(e4, e1) = e2
% 250.02/59.26 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.26 (14) op(e2, e3) = all_10_2
% 250.02/59.26 (15) ~ (e3 = e2)
% 250.02/59.26 (16) op(e0, e0) = all_244_24
% 250.02/59.26 (17) ~ (e4 = e0)
% 250.02/59.26 (18) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.26 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.26 (19) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.26 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.26 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.26 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.26 (21) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.26 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.26 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.26 (22) op(e4, e2) = all_6_2
% 250.02/59.26 (23) ~ (all_244_15 = e4)
% 250.02/59.26 (24) ~ (e2 = e1)
% 250.02/59.26 (25) all_252_13 = e2
% 250.02/59.26 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.26 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.26 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.26 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.26 op(e0, e1) = e0)))
% 250.02/59.26 (27) op(e0, e2) = all_28_2
% 250.02/59.26 (28) ~ (e4 = e1)
% 250.02/59.26 (29) ~ (all_6_2 = e1)
% 250.02/59.26 (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.26 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.26 (31) all_80_2 = all_6_2
% 250.02/59.26 (32) op(all_34_2, e0) = e1
% 250.02/59.26 (33) op(e1, e4) = all_16_2
% 250.02/59.26 (34) op(e2, all_16_2) = e1
% 250.02/59.26 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.26 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.26 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.26 (36) ~ (all_28_2 = all_20_2)
% 250.02/59.26 (37) op(e1, e3) = all_62_2
% 250.02/59.26 (38) ~ (e3 = e0)
% 250.02/59.26 (39) op(e2, e3) = e1
% 250.02/59.26 (40) ~ (all_22_2 = e4)
% 250.02/59.26 (41) ~ (e3 = e1)
% 250.02/59.26 (42) op(e3, e1) = all_36_2
% 250.02/59.26 (43) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.02/59.26 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.02/59.26 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.26 (44) all_252_11 = e4
% 250.02/59.26 (45) ~ (all_8_2 = e1)
% 250.02/59.26 (46) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.26 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.26 (47) ~ (all_22_2 = e1)
% 250.02/59.26 (48) op(e3, e1) = all_172_1
% 250.02/59.26 (49) ~ (all_8_2 = e0)
% 250.02/59.26 (50) all_74_2 = all_36_2
% 250.02/59.26 (51) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.26 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.26 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.26 (52) op(all_6_2, e0) = e2
% 250.02/59.26 (53) op(e0, e3) = all_22_2
% 250.02/59.26 (54) op(all_34_2, all_20_2) = e0
% 250.02/59.26 (55) all_252_20 = e2
% 250.02/59.26 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.26 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.26 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.26 (57) ~ (e4 = e3)
% 250.02/59.26 (58) op(e1, e1) = all_244_15
% 250.02/59.26 (59) op(e0, e1) = all_20_2
% 250.02/59.26 (60) op(e2, e4) = e0
% 250.02/59.26 (61) all_82_2 = all_28_2
% 250.02/59.26 (62) ~ (all_244_24 = e2)
% 250.02/59.26 (63) op(e1, e2) = all_4_2
% 250.02/59.26 (64) all_252_7 = e1
% 250.02/59.26 (65) ~ (e4 = e2)
% 250.02/59.26 (66) op(e3, e2) = all_8_2
% 250.02/59.26 (67) op(all_36_2, e1) = e3
% 250.02/59.26 (68) ~ (all_20_2 = e4)
% 250.02/59.26 (69) op(e2, e0) = all_40_2
% 250.02/59.26 (70) all_78_2 = e1
% 250.02/59.26 (71) ~ (all_20_2 = e3)
% 250.02/59.26 (72) ~ (all_16_2 = e3)
% 250.02/59.26 (73) ~ (all_62_2 = e4)
% 250.02/59.26 (74) ~ (all_20_2 = e2)
% 250.02/59.26 (75) all_250_23 = all_20_2
% 250.02/59.26
% 250.02/59.26 Begin of proof
% 250.02/59.26 |
% 250.02/59.26 | GROUND_INST: instantiating (13) with all_36_2, all_172_1, e1, e3, simplifying
% 250.02/59.26 | with (42), (48) gives:
% 250.02/59.26 | (76) all_172_1 = all_36_2
% 250.02/59.26 |
% 250.02/59.26 | BETA: splitting (2) gives:
% 250.02/59.26 |
% 250.02/59.26 | Case 1:
% 250.02/59.26 | |
% 250.02/59.26 | | (77) ~ (all_74_2 = e0)
% 250.02/59.26 | |
% 250.02/59.26 | | REDUCE: (50), (77) imply:
% 250.02/59.26 | | (78) ~ (all_36_2 = e0)
% 250.02/59.26 | |
% 250.02/59.26 | | BETA: splitting (43) gives:
% 250.02/59.26 | |
% 250.02/59.26 | | Case 1:
% 250.02/59.26 | | |
% 250.02/59.26 | | | (79) ~ (all_78_2 = e1)
% 250.02/59.26 | | |
% 250.02/59.26 | | | REDUCE: (70), (79) imply:
% 250.02/59.26 | | | (80) $false
% 250.02/59.26 | | |
% 250.02/59.26 | | | CLOSE: (80) is inconsistent.
% 250.02/59.26 | | |
% 250.02/59.26 | | Case 2:
% 250.02/59.26 | | |
% 250.02/59.26 | | | (81) ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 & op(e1, all_78_1) =
% 250.02/59.26 | | | all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~ (all_78_1 = e0) &
% 250.02/59.26 | | | op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.02/59.26 | | |
% 250.02/59.26 | | | BETA: splitting (81) gives:
% 250.02/59.26 | | |
% 250.02/59.26 | | | Case 1:
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | (82) ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 & op(e1, all_78_1) =
% 250.02/59.26 | | | | all_78_0 & $i(all_78_0) & $i(all_78_1)
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | ALPHA: (82) implies:
% 250.02/59.26 | | | | (83) op(e3, e1) = all_78_1
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.02/59.26 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.02/59.26 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 250.02/59.26 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 250.02/59.26 | | | | (44), (45), (46), (47), (49), (51), (52), (53), (54), (55),
% 250.02/59.26 | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 250.02/59.26 | | | | (66), (68), (69), (71), (72), (73), (74), (75), (78), (83)
% 250.02/59.26 | | | | are inconsistent by sub-proof #193.
% 250.02/59.26 | | | |
% 250.02/59.26 | | | Case 2:
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | (84) ~ (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1)
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | ALPHA: (84) implies:
% 250.02/59.26 | | | | (85) op(e3, e1) = all_78_1
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.02/59.26 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.02/59.26 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 250.02/59.26 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 250.02/59.26 | | | | (44), (45), (46), (47), (49), (51), (52), (53), (54), (55),
% 250.02/59.26 | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 250.02/59.26 | | | | (66), (68), (69), (71), (72), (73), (74), (75), (78), (85)
% 250.02/59.26 | | | | are inconsistent by sub-proof #193.
% 250.02/59.26 | | | |
% 250.02/59.26 | | | End of split
% 250.02/59.26 | | |
% 250.02/59.26 | | End of split
% 250.02/59.26 | |
% 250.02/59.26 | Case 2:
% 250.02/59.26 | |
% 250.02/59.26 | | (86) all_74_2 = e0
% 250.02/59.26 | |
% 250.02/59.26 | | COMBINE_EQS: (50), (86) imply:
% 250.02/59.26 | | (87) all_36_2 = e0
% 250.02/59.26 | |
% 250.02/59.26 | | REDUCE: (67), (87) imply:
% 250.02/59.26 | | (88) op(e0, e1) = e3
% 250.02/59.26 | |
% 250.02/59.26 | | REF_CLOSE: (13), (59), (71), (88) are inconsistent by sub-proof #974.
% 250.02/59.26 | |
% 250.02/59.26 | End of split
% 250.02/59.26 |
% 250.02/59.26 End of proof
% 250.02/59.26
% 250.02/59.26 Sub-proof #193 shows that the following formulas are inconsistent:
% 250.02/59.26 ----------------------------------------------------------------
% 250.02/59.26 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.02/59.26 all_250_23 = e0
% 250.02/59.26 (2) ~ (all_4_2 = e4)
% 250.02/59.26 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.02/59.26 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.02/59.26 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.02/59.26 (4) op(e3, e1) = all_78_1
% 250.02/59.26 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.02/59.26 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.02/59.26 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.02/59.26 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.02/59.26 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.02/59.26 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.02/59.26 (7) all_252_6 = e0
% 250.02/59.26 (8) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 250.02/59.26 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 250.02/59.26 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.02/59.26 (9) ~ (e2 = e0)
% 250.02/59.26 (10) ~ (e1 = e0)
% 250.02/59.26 (11) ~ (all_28_2 = e3)
% 250.02/59.26 (12) op(e4, e1) = e2
% 250.02/59.26 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.02/59.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.02/59.26 (14) op(e2, e3) = all_10_2
% 250.02/59.26 (15) ~ (e3 = e2)
% 250.02/59.26 (16) op(e0, e0) = all_244_24
% 250.02/59.26 (17) ~ (e4 = e0)
% 250.02/59.26 (18) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.02/59.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.02/59.26 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.02/59.26 (19) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.02/59.26 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.02/59.26 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.02/59.26 (20) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.02/59.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.02/59.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.26 (21) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.02/59.26 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.02/59.26 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.02/59.26 (22) op(e4, e2) = all_6_2
% 250.02/59.26 (23) ~ (all_244_15 = e4)
% 250.02/59.26 (24) ~ (e2 = e1)
% 250.02/59.26 (25) all_252_13 = e2
% 250.02/59.26 (26) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.02/59.26 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.02/59.26 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.02/59.26 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.02/59.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.02/59.26 op(e0, e1) = e0)))
% 250.02/59.26 (27) op(e0, e2) = all_28_2
% 250.02/59.26 (28) ~ (e4 = e1)
% 250.02/59.26 (29) ~ (all_6_2 = e1)
% 250.02/59.26 (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.02/59.26 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.02/59.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.26 (31) all_80_2 = all_6_2
% 250.02/59.26 (32) op(all_34_2, e0) = e1
% 250.02/59.26 (33) op(e1, e4) = all_16_2
% 250.02/59.26 (34) op(e2, all_16_2) = e1
% 250.02/59.26 (35) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.02/59.26 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.02/59.26 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.02/59.26 (36) ~ (all_28_2 = all_20_2)
% 250.02/59.26 (37) op(e1, e3) = all_62_2
% 250.02/59.26 (38) ~ (e3 = e0)
% 250.02/59.26 (39) op(e2, e3) = e1
% 250.02/59.26 (40) ~ (all_22_2 = e4)
% 250.02/59.26 (41) ~ (e3 = e1)
% 250.02/59.26 (42) op(e3, e1) = all_36_2
% 250.02/59.26 (43) all_252_11 = e4
% 250.02/59.26 (44) ~ (all_8_2 = e1)
% 250.02/59.26 (45) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.02/59.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.02/59.26 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.02/59.26 (46) ~ (all_22_2 = e1)
% 250.02/59.26 (47) ~ (all_8_2 = e0)
% 250.02/59.26 (48) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.02/59.26 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.02/59.26 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.02/59.26 (49) op(all_6_2, e0) = e2
% 250.02/59.26 (50) op(e0, e3) = all_22_2
% 250.02/59.26 (51) op(all_34_2, all_20_2) = e0
% 250.02/59.26 (52) all_252_20 = e2
% 250.02/59.26 (53) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.02/59.26 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.02/59.26 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.02/59.26 (54) ~ (all_36_2 = e0)
% 250.02/59.26 (55) ~ (e4 = e3)
% 250.02/59.26 (56) op(e1, e1) = all_244_15
% 250.02/59.26 (57) op(e0, e1) = all_20_2
% 250.02/59.26 (58) op(e2, e4) = e0
% 250.02/59.26 (59) all_82_2 = all_28_2
% 250.02/59.26 (60) ~ (all_244_24 = e2)
% 250.02/59.26 (61) op(e1, e2) = all_4_2
% 250.02/59.26 (62) all_252_7 = e1
% 250.02/59.26 (63) ~ (e4 = e2)
% 250.02/59.26 (64) op(e3, e2) = all_8_2
% 250.02/59.26 (65) ~ (all_20_2 = e4)
% 250.02/59.26 (66) op(e2, e0) = all_40_2
% 250.02/59.26 (67) ~ (all_20_2 = e3)
% 250.02/59.26 (68) ~ (all_16_2 = e3)
% 250.02/59.26 (69) ~ (all_62_2 = e4)
% 250.02/59.26 (70) ~ (all_20_2 = e2)
% 250.02/59.26 (71) all_250_23 = all_20_2
% 250.02/59.26
% 250.02/59.26 Begin of proof
% 250.02/59.26 |
% 250.02/59.26 | GROUND_INST: instantiating (13) with all_36_2, all_78_1, e1, e3, simplifying
% 250.02/59.26 | with (4), (42) gives:
% 250.02/59.26 | (72) all_78_1 = all_36_2
% 250.02/59.26 |
% 250.02/59.26 | BETA: splitting (21) gives:
% 250.02/59.26 |
% 250.02/59.26 | Case 1:
% 250.02/59.26 | |
% 250.02/59.26 | | (73) ~ (all_80_2 = e0)
% 250.02/59.26 | |
% 250.02/59.26 | | REDUCE: (31), (73) imply:
% 250.02/59.26 | | (74) ~ (all_6_2 = e0)
% 250.02/59.26 | |
% 250.02/59.26 | | BETA: splitting (8) gives:
% 250.02/59.26 | |
% 250.02/59.26 | | Case 1:
% 250.02/59.26 | | |
% 250.02/59.26 | | | (75) ~ (all_82_2 = e1)
% 250.02/59.26 | | |
% 250.02/59.26 | | | REDUCE: (59), (75) imply:
% 250.02/59.26 | | | (76) ~ (all_28_2 = e1)
% 250.02/59.26 | | |
% 250.02/59.26 | | | BETA: splitting (20) gives:
% 250.02/59.26 | | |
% 250.02/59.26 | | | Case 1:
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | (77) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 250.02/59.26 | | | | e2) = e1)
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | REF_CLOSE: (13), (22), (29), (44), (64), (77) are inconsistent by
% 250.02/59.26 | | | | sub-proof #928.
% 250.02/59.26 | | | |
% 250.02/59.26 | | | Case 2:
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | (78) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1,
% 250.02/59.26 | | | | e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | BETA: splitting (78) gives:
% 250.02/59.26 | | | |
% 250.02/59.26 | | | | Case 1:
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | (79) all_252_8 = e1 & op(e2, e2) = e1
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | ALPHA: (79) implies:
% 250.02/59.26 | | | | | (80) all_252_8 = e1
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | REF_CLOSE: (7), (9), (13), (14), (15), (19), (24), (38), (39), (41),
% 250.02/59.26 | | | | | (43), (48), (55), (62), (63), (80) are inconsistent by
% 250.02/59.26 | | | | | sub-proof #202.
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | Case 2:
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | (81) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.02/59.26 | | | | | op(e0, e2) = e1)
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | BETA: splitting (81) gives:
% 250.02/59.26 | | | | |
% 250.02/59.26 | | | | | Case 1:
% 250.02/59.26 | | | | | |
% 250.02/59.26 | | | | | | (82) all_252_14 = e1 & op(e1, e2) = e1
% 250.02/59.26 | | | | | |
% 250.02/59.26 | | | | | | ALPHA: (82) implies:
% 250.02/59.26 | | | | | | (83) all_252_14 = e1
% 250.02/59.26 | | | | | |
% 250.02/59.26 | | | | | | BETA: splitting (30) gives:
% 250.02/59.26 | | | | | |
% 250.02/59.26 | | | | | | Case 1:
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | (84) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 &
% 250.02/59.26 | | | | | | | op(e3, e2) = e0)
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | BETA: splitting (84) gives:
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | (85) all_252_4 = e0 & op(e4, e2) = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | ALPHA: (85) implies:
% 250.02/59.26 | | | | | | | | (86) op(e4, e2) = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | GROUND_INST: instantiating (13) with all_6_2, e0, e2, e4,
% 250.02/59.26 | | | | | | | | simplifying with (22), (86) gives:
% 250.02/59.26 | | | | | | | | (87) all_6_2 = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | REDUCE: (74), (87) imply:
% 250.02/59.26 | | | | | | | | (88) $false
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | CLOSE: (88) is inconsistent.
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | Case 2:
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | (89) all_252_5 = e0 & op(e3, e2) = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | REF_CLOSE: (13), (47), (64), (89) are inconsistent by sub-proof
% 250.02/59.26 | | | | | | | | #874.
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | End of split
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | Case 2:
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | (90) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 &
% 250.02/59.26 | | | | | | | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | BETA: splitting (90) gives:
% 250.02/59.26 | | | | | | |
% 250.02/59.26 | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | (91) all_252_8 = e0 & op(e2, e2) = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | ALPHA: (91) implies:
% 250.02/59.26 | | | | | | | | (92) all_252_8 = e0
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | REF_CLOSE: (7), (9), (10), (13), (14), (15), (18), (19), (24),
% 250.02/59.26 | | | | | | | | (28), (38), (39), (41), (43), (48), (55), (63), (66),
% 250.02/59.26 | | | | | | | | (92) are inconsistent by sub-proof #200.
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | Case 2:
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | (93) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 250.02/59.26 | | | | | | | | op(e0, e2) = e0)
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | BETA: splitting (93) gives:
% 250.02/59.26 | | | | | | | |
% 250.02/59.26 | | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | (94) all_252_14 = e0 & op(e1, e2) = e0
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | REF_CLOSE: (10), (83), (94) are inconsistent by sub-proof
% 250.02/59.26 | | | | | | | | | #521.
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | Case 2:
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | (95) all_252_22 = e0 & op(e0, e2) = e0
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | ALPHA: (95) implies:
% 250.02/59.26 | | | | | | | | | (96) all_252_22 = e0
% 250.02/59.26 | | | | | | | | | (97) op(e0, e2) = e0
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | BETA: splitting (3) gives:
% 250.02/59.26 | | | | | | | | |
% 250.02/59.26 | | | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | (98) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 =
% 250.02/59.26 | | | | | | | | | | e4 & op(e0, e3) = e4)
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | BETA: splitting (98) gives:
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | (99) all_252_20 = e4 & op(e0, e4) = e4
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | REF_CLOSE: (52), (63), (99) are inconsistent by sub-proof
% 250.02/59.26 | | | | | | | | | | | #543.
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | Case 2:
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | (100) all_252_21 = e4 & op(e0, e3) = e4
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | REF_CLOSE: (13), (40), (50), (100) are inconsistent by
% 250.02/59.26 | | | | | | | | | | | sub-proof #805.
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | End of split
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | Case 2:
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | (101) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 =
% 250.02/59.26 | | | | | | | | | | e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 250.02/59.26 | | | | | | | | | | e0) = e4)
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | BETA: splitting (101) gives:
% 250.02/59.26 | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | Case 1:
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | (102) all_252_22 = e4 & op(e0, e2) = e4
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | ALPHA: (102) implies:
% 250.02/59.26 | | | | | | | | | | | (103) all_252_22 = e4
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | | REF_CLOSE: (17), (96), (103) are inconsistent by sub-proof
% 250.02/59.26 | | | | | | | | | | | #528.
% 250.02/59.26 | | | | | | | | | | |
% 250.02/59.26 | | | | | | | | | | Case 2:
% 250.32/59.26 | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | (104) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 250.32/59.26 | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.32/59.26 | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | BETA: splitting (104) gives:
% 250.32/59.26 | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | (105) all_252_23 = e4 & op(e0, e1) = e4
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | REF_CLOSE: (13), (57), (65), (105) are inconsistent by
% 250.32/59.26 | | | | | | | | | | | | sub-proof #912.
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | Case 2:
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | (106) all_252_24 = e4 & op(e0, e0) = e4
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | ALPHA: (106) implies:
% 250.32/59.26 | | | | | | | | | | | | (107) all_252_24 = e4
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | BETA: splitting (45) gives:
% 250.32/59.26 | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | (108) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 250.32/59.26 | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | REF_CLOSE: (13), (24), (46), (50), (52), (108) are
% 250.32/59.26 | | | | | | | | | | | | | inconsistent by sub-proof #199.
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | Case 2:
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | (109) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 250.32/59.26 | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 250.32/59.26 | | | | | | | | | | | | | op(e0, e0) = e1)
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | BETA: splitting (109) gives:
% 250.32/59.26 | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | (110) all_252_22 = e1 & op(e0, e2) = e1
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | ALPHA: (110) implies:
% 250.32/59.26 | | | | | | | | | | | | | | (111) all_252_22 = e1
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | REF_CLOSE: (10), (96), (111) are inconsistent by sub-proof
% 250.32/59.26 | | | | | | | | | | | | | | #198.
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | Case 2:
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | (112) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 250.32/59.26 | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 250.32/59.26 | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | (113) all_252_23 = e1 & op(e0, e1) = e1
% 250.32/59.26 | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 250.32/59.26 | | | | | | | | | | | | | | | (114) all_252_23 = e1
% 250.32/59.26 | | | | | | | | | | | | | | | (115) op(e0, e1) = e1
% 250.32/59.26 | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 250.32/59.26 | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | (116) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 250.32/59.26 | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 250.32/59.26 | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 250.32/59.26 | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | (117) all_252_20 = e3 & op(e0, e4) = e3
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 250.32/59.26 | | | | | | | | | | | | | | | | | (118) all_252_20 = e3
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (52), (118) are inconsistent by sub-proof
% 250.32/59.26 | | | | | | | | | | | | | | | | | #520.
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | (119) all_252_21 = e3 & op(e0, e3) = e3
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 250.32/59.26 | | | | | | | | | | | | | | | | | (120) all_252_21 = e3
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 250.32/59.26 | | | | | | | | | | | | | | | | |
% 250.32/59.26 | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.26 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | (121) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 250.32/59.27 | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | (122) all_252_9 = e0 & op(e4, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | (123) op(e4, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (123) are inconsistent by
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | sub-proof #767.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | (124) all_252_10 = e0 & op(e3, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (42), (54), (124) are inconsistent by
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | sub-proof #726.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | (125) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15
% 250.32/59.27 | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 250.32/59.27 | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | (126) all_252_11 = e0 & op(e2, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (126) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | #197.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | (127) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | (128) all_252_15 = e0 & op(e1, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | (129) all_252_15 = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | (130) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (131) all_252_12 = e3 & op(e1, e4) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (33), (68), (131) are inconsistent by
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | sub-proof #895.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (132) all_252_13 = e3 & op(e1, e3) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (133) all_252_13 = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (133) imply:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (134) e3 = e2
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (134) imply:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (135) all_252_21 = e2
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (10), (11), (13), (15), (17), (24),
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (26), (27), (28), (35), (38), (40), (41), (45),
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (46), (50), (52), (55), (57), (63), (65), (67),
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (135) are inconsistent by sub-proof #524.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | (136) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (137) all_252_14 = e3 & op(e1, e2) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (83), (137) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | #334.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | (138) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | (139) all_252_15 = e3 & op(e1, e1) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | (140) all_252_15 = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (129), (140) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | #196.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | (141) all_252_19 = e3 & op(e1, e0) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | (142) all_252_19 = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | (143) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (33), (34), (37), (58), (69), (143)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #195.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | (144) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (23), (55), (56), (61), (142), (144)
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #430.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | (145) all_252_23 = e0 & op(e0, e1) = e0
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (114), (145) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | | #527.
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | (146) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 250.32/59.27 | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 250.32/59.27 | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 250.32/59.27 | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | (147) all_252_22 = e3 & op(e0, e2) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | (148) op(e0, e2) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (27), (38), (97), (148) are inconsistent by
% 250.32/59.27 | | | | | | | | | | | | | | | | | sub-proof #473.
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | (149) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 250.32/59.27 | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | (150) all_252_23 = e3 & op(e0, e1) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 250.32/59.27 | | | | | | | | | | | | | | | | | | (151) op(e0, e1) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (41), (115), (151) are inconsistent by
% 250.32/59.27 | | | | | | | | | | | | | | | | | | sub-proof #915.
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | (152) all_252_24 = e3 & op(e0, e0) = e3
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (107), (152) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | | | | #194.
% 250.32/59.27 | | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | (153) all_252_24 = e1 & op(e0, e0) = e1
% 250.32/59.27 | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | | REF_CLOSE: (28), (107), (153) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | | | | | | | #499.
% 250.32/59.27 | | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | | |
% 250.32/59.27 | | | | | | | | | End of split
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | End of split
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | End of split
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | End of split
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | Case 2:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | (154) all_252_22 = e1 & op(e0, e2) = e1
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | ALPHA: (154) implies:
% 250.32/59.27 | | | | | | (155) op(e0, e2) = e1
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | REF_CLOSE: (13), (27), (76), (155) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | #907.
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | End of split
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | End of split
% 250.32/59.27 | | | |
% 250.32/59.27 | | | End of split
% 250.32/59.27 | | |
% 250.32/59.27 | | Case 2:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (156) all_82_2 = e1
% 250.32/59.27 | | |
% 250.32/59.27 | | | REF_CLOSE: (1), (13), (32), (36), (51), (59), (65), (67), (70), (71),
% 250.32/59.27 | | | (156) are inconsistent by sub-proof #779.
% 250.32/59.27 | | |
% 250.32/59.27 | | End of split
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (157) all_80_2 = e0
% 250.32/59.27 | |
% 250.32/59.27 | | COMBINE_EQS: (31), (157) imply:
% 250.32/59.27 | | (158) all_6_2 = e0
% 250.32/59.27 | |
% 250.32/59.27 | | SIMP: (158) implies:
% 250.32/59.27 | | (159) all_6_2 = e0
% 250.32/59.27 | |
% 250.32/59.27 | | REDUCE: (49), (159) imply:
% 250.32/59.27 | | (160) op(e0, e0) = e2
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (13), (16), (60), (160) are inconsistent by sub-proof #978.
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #194 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_24 = e3 & op(e0, e0) = e3
% 250.32/59.27 (2) all_252_24 = e4
% 250.32/59.27 (3) ~ (e4 = e3)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | ALPHA: (1) implies:
% 250.32/59.27 | (4) all_252_24 = e3
% 250.32/59.27 |
% 250.32/59.27 | COMBINE_EQS: (2), (4) imply:
% 250.32/59.27 | (5) e4 = e3
% 250.32/59.27 |
% 250.32/59.27 | REDUCE: (3), (5) imply:
% 250.32/59.27 | (6) $false
% 250.32/59.27 |
% 250.32/59.27 | CLOSE: (6) is inconsistent.
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #195 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) ~ (e1 = e0)
% 250.32/59.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (3) op(e1, e4) = all_16_2
% 250.32/59.27 (4) op(e2, all_16_2) = e1
% 250.32/59.27 (5) op(e1, e3) = all_62_2
% 250.32/59.27 (6) op(e2, e4) = e0
% 250.32/59.27 (7) ~ (all_62_2 = e4)
% 250.32/59.27 (8) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (8) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (9) all_252_12 = e4 & op(e1, e4) = e4
% 250.32/59.27 | |
% 250.32/59.27 | | ALPHA: (9) implies:
% 250.32/59.27 | | (10) op(e1, e4) = e4
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (2), (3), (4), (6), (10) are inconsistent by sub-proof #214.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (11) all_252_13 = e4 & op(e1, e3) = e4
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (2), (5), (7), (11) are inconsistent by sub-proof #952.
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #196 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_15 = e3
% 250.32/59.27 (2) all_252_15 = e0
% 250.32/59.27 (3) ~ (e3 = e0)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | COMBINE_EQS: (1), (2) imply:
% 250.32/59.27 | (4) e3 = e0
% 250.32/59.27 |
% 250.32/59.27 | SIMP: (4) implies:
% 250.32/59.27 | (5) e3 = e0
% 250.32/59.27 |
% 250.32/59.27 | REDUCE: (3), (5) imply:
% 250.32/59.27 | (6) $false
% 250.32/59.27 |
% 250.32/59.27 | CLOSE: (6) is inconsistent.
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #197 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_11 = e0 & op(e2, e1) = e0
% 250.32/59.27 (2) all_252_11 = e4
% 250.32/59.27 (3) ~ (e4 = e0)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | ALPHA: (1) implies:
% 250.32/59.27 | (4) all_252_11 = e0
% 250.32/59.27 |
% 250.32/59.27 | COMBINE_EQS: (2), (4) imply:
% 250.32/59.27 | (5) e4 = e0
% 250.32/59.27 |
% 250.32/59.27 | REDUCE: (3), (5) imply:
% 250.32/59.27 | (6) $false
% 250.32/59.27 |
% 250.32/59.27 | CLOSE: (6) is inconsistent.
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #198 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_22 = e1
% 250.32/59.27 (2) all_252_22 = e0
% 250.32/59.27 (3) ~ (e1 = e0)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | COMBINE_EQS: (1), (2) imply:
% 250.32/59.27 | (4) e1 = e0
% 250.32/59.27 |
% 250.32/59.27 | SIMP: (4) implies:
% 250.32/59.27 | (5) e1 = e0
% 250.32/59.27 |
% 250.32/59.27 | REDUCE: (3), (5) imply:
% 250.32/59.27 | (6) $false
% 250.32/59.27 |
% 250.32/59.27 | CLOSE: (6) is inconsistent.
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #199 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (2) ~ (e2 = e1)
% 250.32/59.27 (3) ~ (all_22_2 = e1)
% 250.32/59.27 (4) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.32/59.27 (5) op(e0, e3) = all_22_2
% 250.32/59.27 (6) all_252_20 = e2
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (4) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (7) all_252_20 = e1 & op(e0, e4) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #544.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (8) all_252_21 = e1 & op(e0, e3) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | ALPHA: (8) implies:
% 250.32/59.27 | | (9) op(e0, e3) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #714.
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #200 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_6 = e0
% 250.32/59.27 (2) ~ (e2 = e0)
% 250.32/59.27 (3) ~ (e1 = e0)
% 250.32/59.27 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (5) op(e2, e3) = all_10_2
% 250.32/59.27 (6) ~ (e3 = e2)
% 250.32/59.27 (7) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) |
% 250.32/59.27 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = e1)
% 250.32/59.27 | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.32/59.27 (8) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.32/59.27 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.32/59.27 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.27 (9) ~ (e2 = e1)
% 250.32/59.27 (10) ~ (e4 = e1)
% 250.32/59.27 (11) ~ (e3 = e0)
% 250.32/59.27 (12) op(e2, e3) = e1
% 250.32/59.27 (13) ~ (e3 = e1)
% 250.32/59.27 (14) all_252_11 = e4
% 250.32/59.27 (15) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.32/59.27 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.27 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.27 (16) ~ (e4 = e3)
% 250.32/59.27 (17) ~ (e4 = e2)
% 250.32/59.27 (18) op(e2, e0) = all_40_2
% 250.32/59.27 (19) all_252_8 = e0
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (15) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (20) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 250.32/59.27 | | e2)
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (2), (4), (5), (9), (12), (20) are inconsistent by sub-proof
% 250.32/59.27 | | #203.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (21) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.27 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.27 | |
% 250.32/59.27 | | BETA: splitting (21) gives:
% 250.32/59.27 | |
% 250.32/59.27 | | Case 1:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (22) all_252_8 = e2 & op(e2, e2) = e2
% 250.32/59.27 | | |
% 250.32/59.27 | | | REF_CLOSE: (2), (19), (22) are inconsistent by sub-proof #201.
% 250.32/59.27 | | |
% 250.32/59.27 | | Case 2:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (23) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 250.32/59.27 | | | e0) = e2)
% 250.32/59.27 | | |
% 250.32/59.27 | | | BETA: splitting (23) gives:
% 250.32/59.27 | | |
% 250.32/59.27 | | | Case 1:
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | (24) all_252_11 = e2 & op(e2, e1) = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | REF_CLOSE: (14), (17), (24) are inconsistent by sub-proof #787.
% 250.32/59.27 | | | |
% 250.32/59.27 | | | Case 2:
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | (25) all_252_18 = e2 & op(e2, e0) = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | ALPHA: (25) implies:
% 250.32/59.27 | | | | (26) all_252_18 = e2
% 250.32/59.27 | | | | (27) op(e2, e0) = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | BETA: splitting (8) gives:
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | Case 1:
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | (28) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 250.32/59.27 | | | | | e3) = e3)
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | BETA: splitting (28) gives:
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | Case 1:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | (29) all_252_6 = e3 & op(e2, e4) = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | ALPHA: (29) implies:
% 250.32/59.27 | | | | | | (30) all_252_6 = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | REF_CLOSE: (1), (11), (30) are inconsistent by sub-proof #691.
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | Case 2:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | (31) all_252_7 = e3 & op(e2, e3) = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | ALPHA: (31) implies:
% 250.32/59.27 | | | | | | (32) all_252_7 = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | BETA: splitting (7) gives:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | Case 1:
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | (33) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 &
% 250.32/59.27 | | | | | | | op(e2, e3) = e1)
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | BETA: splitting (33) gives:
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | (34) all_252_6 = e1 & op(e2, e4) = e1
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | REF_CLOSE: (1), (3), (34) are inconsistent by sub-proof #556.
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | (35) all_252_7 = e1 & op(e2, e3) = e1
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | ALPHA: (35) implies:
% 250.32/59.27 | | | | | | | | (36) all_252_7 = e1
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | REF_CLOSE: (13), (32), (36) are inconsistent by sub-proof #212.
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | End of split
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | Case 2:
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | (37) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 &
% 250.32/59.27 | | | | | | | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | BETA: splitting (37) gives:
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | (38) all_252_8 = e1 & op(e2, e2) = e1
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | ALPHA: (38) implies:
% 250.32/59.27 | | | | | | | | (39) all_252_8 = e1
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | REF_CLOSE: (3), (19), (39) are inconsistent by sub-proof #249.
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | (40) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 250.32/59.27 | | | | | | | | op(e2, e0) = e1)
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | BETA: splitting (40) gives:
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | | Case 1:
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | | (41) all_252_11 = e1 & op(e2, e1) = e1
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | | REF_CLOSE: (10), (14), (41) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | | | | #747.
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | Case 2:
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | | (42) all_252_18 = e1 & op(e2, e0) = e1
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | | ALPHA: (42) implies:
% 250.32/59.27 | | | | | | | | | (43) op(e2, e0) = e1
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | | REF_CLOSE: (4), (9), (18), (27), (43) are inconsistent by
% 250.32/59.27 | | | | | | | | | sub-proof #415.
% 250.32/59.27 | | | | | | | | |
% 250.32/59.27 | | | | | | | | End of split
% 250.32/59.27 | | | | | | | |
% 250.32/59.27 | | | | | | | End of split
% 250.32/59.27 | | | | | | |
% 250.32/59.27 | | | | | | End of split
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | End of split
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | Case 2:
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | (44) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2,
% 250.32/59.27 | | | | | e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | BETA: splitting (44) gives:
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | | Case 1:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | (45) all_252_8 = e3 & op(e2, e2) = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | ALPHA: (45) implies:
% 250.32/59.27 | | | | | | (46) all_252_8 = e3
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | REF_CLOSE: (11), (19), (46) are inconsistent by sub-proof #905.
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | Case 2:
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | (47) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.32/59.27 | | | | | | op(e2, e0) = e3)
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | | REF_CLOSE: (6), (14), (16), (26), (47) are inconsistent by sub-proof
% 250.32/59.27 | | | | | | #207.
% 250.32/59.27 | | | | | |
% 250.32/59.27 | | | | | End of split
% 250.32/59.27 | | | | |
% 250.32/59.27 | | | | End of split
% 250.32/59.27 | | | |
% 250.32/59.27 | | | End of split
% 250.32/59.27 | | |
% 250.32/59.27 | | End of split
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #201 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_8 = e2 & op(e2, e2) = e2
% 250.32/59.27 (2) all_252_8 = e0
% 250.32/59.27 (3) ~ (e2 = e0)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | ALPHA: (1) implies:
% 250.32/59.27 | (4) all_252_8 = e2
% 250.32/59.27 |
% 250.32/59.27 | COMBINE_EQS: (2), (4) imply:
% 250.32/59.27 | (5) e2 = e0
% 250.32/59.27 |
% 250.32/59.27 | SIMP: (5) implies:
% 250.32/59.27 | (6) e2 = e0
% 250.32/59.27 |
% 250.32/59.27 | REDUCE: (3), (6) imply:
% 250.32/59.27 | (7) $false
% 250.32/59.27 |
% 250.32/59.27 | CLOSE: (7) is inconsistent.
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #202 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_6 = e0
% 250.32/59.27 (2) ~ (e2 = e0)
% 250.32/59.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (4) op(e2, e3) = all_10_2
% 250.32/59.27 (5) ~ (e3 = e2)
% 250.32/59.27 (6) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.32/59.27 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.32/59.27 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.27 (7) ~ (e2 = e1)
% 250.32/59.27 (8) ~ (e3 = e0)
% 250.32/59.27 (9) op(e2, e3) = e1
% 250.32/59.27 (10) ~ (e3 = e1)
% 250.32/59.27 (11) all_252_11 = e4
% 250.32/59.27 (12) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.32/59.27 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.27 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.27 (13) ~ (e4 = e3)
% 250.32/59.27 (14) all_252_7 = e1
% 250.32/59.27 (15) ~ (e4 = e2)
% 250.32/59.27 (16) all_252_8 = e1
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (12) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (17) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 250.32/59.27 | | e2)
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (17) are inconsistent by sub-proof
% 250.32/59.27 | | #203.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (18) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.27 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.27 | |
% 250.32/59.27 | | BETA: splitting (18) gives:
% 250.32/59.27 | |
% 250.32/59.27 | | Case 1:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (19) all_252_8 = e2 & op(e2, e2) = e2
% 250.32/59.27 | | |
% 250.32/59.27 | | | REF_CLOSE: (7), (16), (19) are inconsistent by sub-proof #788.
% 250.32/59.27 | | |
% 250.32/59.27 | | Case 2:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (20) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 250.32/59.27 | | | e0) = e2)
% 250.32/59.27 | | |
% 250.32/59.27 | | | BETA: splitting (20) gives:
% 250.32/59.27 | | |
% 250.32/59.27 | | | Case 1:
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | (21) all_252_11 = e2 & op(e2, e1) = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | REF_CLOSE: (11), (15), (21) are inconsistent by sub-proof #787.
% 250.32/59.27 | | | |
% 250.32/59.27 | | | Case 2:
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | (22) all_252_18 = e2 & op(e2, e0) = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | ALPHA: (22) implies:
% 250.32/59.27 | | | | (23) all_252_18 = e2
% 250.32/59.27 | | | |
% 250.32/59.27 | | | | REF_CLOSE: (1), (5), (6), (8), (10), (11), (13), (14), (16), (23) are
% 250.32/59.27 | | | | inconsistent by sub-proof #206.
% 250.32/59.27 | | | |
% 250.32/59.27 | | | End of split
% 250.32/59.27 | | |
% 250.32/59.27 | | End of split
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #203 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_6 = e0
% 250.32/59.27 (2) ~ (e2 = e0)
% 250.32/59.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (4) op(e2, e3) = all_10_2
% 250.32/59.27 (5) ~ (e2 = e1)
% 250.32/59.27 (6) op(e2, e3) = e1
% 250.32/59.27 (7) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (7) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (8) all_252_6 = e2 & op(e2, e4) = e2
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #892.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (9) all_252_7 = e2 & op(e2, e3) = e2
% 250.32/59.27 | |
% 250.32/59.27 | | ALPHA: (9) implies:
% 250.32/59.27 | | (10) op(e2, e3) = e2
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #902.
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #204 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) ~ (e1 = e0)
% 250.32/59.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (3) op(e0, e3) = e0
% 250.32/59.27 (4) ~ (e2 = e1)
% 250.32/59.27 (5) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.32/59.27 (6) all_252_20 = e2
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (5) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (7) all_252_20 = e1 & op(e0, e4) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #544.
% 250.32/59.27 | |
% 250.32/59.27 | Case 2:
% 250.32/59.27 | |
% 250.32/59.27 | | (8) all_252_21 = e1 & op(e0, e3) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | ALPHA: (8) implies:
% 250.32/59.27 | | (9) op(e0, e3) = e1
% 250.32/59.27 | |
% 250.32/59.27 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #320.
% 250.32/59.27 | |
% 250.32/59.27 | End of split
% 250.32/59.27 |
% 250.32/59.27 End of proof
% 250.32/59.27
% 250.32/59.27 Sub-proof #205 shows that the following formulas are inconsistent:
% 250.32/59.27 ----------------------------------------------------------------
% 250.32/59.27 (1) all_252_6 = e0
% 250.32/59.27 (2) ~ (e2 = e0)
% 250.32/59.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.27 (4) op(e2, e3) = all_10_2
% 250.32/59.27 (5) ~ (e3 = e2)
% 250.32/59.27 (6) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.32/59.27 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.32/59.27 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.27 (7) ~ (e2 = e1)
% 250.32/59.27 (8) ~ (e3 = e0)
% 250.32/59.27 (9) op(e2, e3) = e1
% 250.32/59.27 (10) all_252_8 = e1 & op(e2, e2) = e1
% 250.32/59.27 (11) ~ (e3 = e1)
% 250.32/59.27 (12) all_252_11 = e4
% 250.32/59.27 (13) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.32/59.27 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.27 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.27 (14) all_252_7 = e3
% 250.32/59.27 (15) ~ (e4 = e3)
% 250.32/59.27 (16) ~ (e4 = e2)
% 250.32/59.27 (17) all_252_8 = e1
% 250.32/59.27
% 250.32/59.27 Begin of proof
% 250.32/59.27 |
% 250.32/59.27 | BETA: splitting (13) gives:
% 250.32/59.27 |
% 250.32/59.27 | Case 1:
% 250.32/59.27 | |
% 250.32/59.27 | | (18) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 250.32/59.27 | | e2)
% 250.32/59.27 | |
% 250.32/59.27 | | BETA: splitting (18) gives:
% 250.32/59.27 | |
% 250.32/59.27 | | Case 1:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (19) all_252_6 = e2 & op(e2, e4) = e2
% 250.32/59.27 | | |
% 250.32/59.27 | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #548.
% 250.32/59.27 | | |
% 250.32/59.27 | | Case 2:
% 250.32/59.27 | | |
% 250.32/59.27 | | | (20) all_252_7 = e2 & op(e2, e3) = e2
% 250.32/59.27 | | |
% 250.32/59.27 | | | ALPHA: (20) implies:
% 250.32/59.27 | | | (21) op(e2, e3) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (3), (4), (7), (9), (21) are inconsistent by sub-proof #902.
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (22) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.32/59.28 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (22) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (23) all_252_8 = e2 & op(e2, e2) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (7), (17), (23) are inconsistent by sub-proof #788.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (24) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 250.32/59.28 | | | e0) = e2)
% 250.32/59.28 | | |
% 250.32/59.28 | | | BETA: splitting (24) gives:
% 250.32/59.28 | | |
% 250.32/59.28 | | | Case 1:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (25) all_252_11 = e2 & op(e2, e1) = e2
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | REF_CLOSE: (12), (16), (25) are inconsistent by sub-proof #302.
% 250.32/59.28 | | | |
% 250.32/59.28 | | | Case 2:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (26) all_252_18 = e2 & op(e2, e0) = e2
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | ALPHA: (26) implies:
% 250.32/59.28 | | | | (27) all_252_18 = e2
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | BETA: splitting (6) gives:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | Case 1:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (28) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 250.32/59.28 | | | | | e3) = e3)
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | BETA: splitting (28) gives:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | Case 1:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (29) all_252_6 = e3 & op(e2, e4) = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | ALPHA: (29) implies:
% 250.32/59.28 | | | | | | (30) all_252_6 = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | REF_CLOSE: (1), (8), (30) are inconsistent by sub-proof #691.
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | Case 2:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (31) all_252_7 = e3 & op(e2, e3) = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | ALPHA: (31) implies:
% 250.32/59.28 | | | | | | (32) op(e2, e3) = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | GROUND_INST: instantiating (3) with e1, e3, e3, e2, simplifying with
% 250.32/59.28 | | | | | | (9), (32) gives:
% 250.32/59.28 | | | | | | (33) e3 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | COMBINE_EQS: (14), (33) imply:
% 250.32/59.28 | | | | | | (34) all_252_7 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | REF_CLOSE: (1), (5), (6), (8), (11), (12), (15), (17), (27), (34)
% 250.32/59.28 | | | | | | are inconsistent by sub-proof #206.
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | End of split
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | Case 2:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (35) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2,
% 250.32/59.28 | | | | | e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | BETA: splitting (35) gives:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | Case 1:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (36) all_252_8 = e3 & op(e2, e2) = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | ALPHA: (36) implies:
% 250.32/59.28 | | | | | | (37) all_252_8 = e3
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | COMBINE_EQS: (17), (37) imply:
% 250.32/59.28 | | | | | | (38) e3 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | COMBINE_EQS: (14), (38) imply:
% 250.32/59.28 | | | | | | (39) all_252_7 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | REF_CLOSE: (1), (5), (6), (8), (11), (12), (15), (17), (27), (39)
% 250.32/59.28 | | | | | | are inconsistent by sub-proof #206.
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | Case 2:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (40) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.32/59.28 | | | | | | op(e2, e0) = e3)
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | BETA: splitting (40) gives:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | Case 1:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (41) all_252_11 = e3 & op(e2, e1) = e3
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | REF_CLOSE: (12), (15), (41) are inconsistent by sub-proof #791.
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | Case 2:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (42) all_252_18 = e3 & op(e2, e0) = e3
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | ALPHA: (42) implies:
% 250.32/59.28 | | | | | | | (43) all_252_18 = e3
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | COMBINE_EQS: (27), (43) imply:
% 250.32/59.28 | | | | | | | (44) e3 = e2
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | REDUCE: (5), (44) imply:
% 250.32/59.28 | | | | | | | (45) $false
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | CLOSE: (45) is inconsistent.
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | End of split
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | End of split
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | End of split
% 250.32/59.28 | | | |
% 250.32/59.28 | | | End of split
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #206 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) all_252_6 = e0
% 250.32/59.28 (2) ~ (e3 = e2)
% 250.32/59.28 (3) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.32/59.28 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.32/59.28 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.28 (4) ~ (e3 = e0)
% 250.32/59.28 (5) ~ (e3 = e1)
% 250.32/59.28 (6) all_252_11 = e4
% 250.32/59.28 (7) all_252_18 = e2
% 250.32/59.28 (8) ~ (e4 = e3)
% 250.32/59.28 (9) all_252_7 = e1
% 250.32/59.28 (10) all_252_8 = e1
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (3) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (11) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 250.32/59.28 | | e3)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (11) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (12) all_252_6 = e3 & op(e2, e4) = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (12) implies:
% 250.32/59.28 | | | (13) all_252_6 = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #691.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (14) all_252_7 = e3 & op(e2, e3) = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (14) implies:
% 250.32/59.28 | | | (15) all_252_7 = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #212.
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (16) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.32/59.28 | | e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (16) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (17) all_252_8 = e3 & op(e2, e2) = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (17) implies:
% 250.32/59.28 | | | (18) all_252_8 = e3
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (5), (10), (18) are inconsistent by sub-proof #927.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (19) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2,
% 250.32/59.28 | | | e0) = e3)
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (2), (6), (7), (8), (19) are inconsistent by sub-proof #207.
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #207 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.32/59.28 (2) ~ (e3 = e2)
% 250.32/59.28 (3) all_252_11 = e4
% 250.32/59.28 (4) all_252_18 = e2
% 250.32/59.28 (5) ~ (e4 = e3)
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (1) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (6) all_252_11 = e3 & op(e2, e1) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #791.
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (7) all_252_18 = e3 & op(e2, e0) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | ALPHA: (7) implies:
% 250.32/59.28 | | (8) all_252_18 = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #786.
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #208 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) ~ (e3 = e2)
% 250.32/59.28 (2) ~ (e3 = e0)
% 250.32/59.28 (3) all_252_21 = e0
% 250.32/59.28 (4) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.32/59.28 (5) all_252_20 = e2
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (4) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (6) all_252_20 = e3 & op(e0, e4) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | ALPHA: (6) implies:
% 250.32/59.28 | | (7) all_252_20 = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #520.
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (8) all_252_21 = e3 & op(e0, e3) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | ALPHA: (8) implies:
% 250.32/59.28 | | (9) all_252_21 = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #773.
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #209 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) ~ (all_4_2 = e4)
% 250.32/59.28 (2) ~ (all_10_2 = e4)
% 250.32/59.28 (3) all_252_3 = e2
% 250.32/59.28 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.32/59.28 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.32/59.28 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.32/59.28 (5) ~ (e2 = e0)
% 250.32/59.28 (6) ~ (e1 = e0)
% 250.32/59.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.28 (8) op(e2, e3) = all_10_2
% 250.32/59.28 (9) ~ (e3 = e2)
% 250.32/59.28 (10) ~ (e4 = e0)
% 250.32/59.28 (11) ~ (all_244_15 = e4)
% 250.32/59.28 (12) ~ (e2 = e1)
% 250.32/59.28 (13) ~ (e4 = e1)
% 250.32/59.28 (14) op(e1, e4) = all_16_2
% 250.32/59.28 (15) op(e2, all_16_2) = e1
% 250.32/59.28 (16) op(e1, e3) = all_62_2
% 250.32/59.28 (17) ~ (e3 = e0)
% 250.32/59.28 (18) ~ (all_22_2 = e4)
% 250.32/59.28 (19) ~ (e3 = e1)
% 250.32/59.28 (20) ~ (all_16_2 = e2)
% 250.32/59.28 (21) ~ (all_22_2 = e1)
% 250.32/59.28 (22) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.32/59.28 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.32/59.28 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.32/59.28 (23) op(e1, e4) = all_242_1
% 250.32/59.28 (24) op(e0, e3) = all_22_2
% 250.32/59.28 (25) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.28 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.28 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.28 (26) ~ (e4 = e3)
% 250.32/59.28 (27) op(e1, e1) = all_244_15
% 250.32/59.28 (28) op(e2, e4) = e0
% 250.32/59.28 (29) op(e1, e2) = all_4_2
% 250.32/59.28 (30) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.32/59.28 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.32/59.28 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.32/59.28 (31) ~ (all_244_15 = e2)
% 250.32/59.28 (32) ~ (e4 = e2)
% 250.32/59.28 (33) ~ (all_10_2 = e0)
% 250.32/59.28 (34) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.32/59.28 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.32/59.28 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.32/59.28 (35) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.32/59.28 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.32/59.28 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.32/59.28 (36) ~ (all_62_2 = e4)
% 250.32/59.28 (37) ~ (all_4_2 = e2)
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (4) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (38) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.32/59.28 | | e4)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (38) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (39) all_252_1 = e4 & op(e4, e3) = e4
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (39) implies:
% 250.32/59.28 | | | (40) all_252_1 = e4
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.32/59.28 | | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 250.32/59.28 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.32/59.28 | | | (35), (36), (37), (40) are inconsistent by sub-proof #210.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (41) all_252_3 = e4 & op(e3, e3) = e4
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (41) implies:
% 250.32/59.28 | | | (42) all_252_3 = e4
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (3), (32), (42) are inconsistent by sub-proof #954.
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (43) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.28 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (2), (7), (8), (16), (18), (24), (36), (43) are inconsistent by
% 250.32/59.28 | | sub-proof #771.
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #210 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) ~ (all_4_2 = e4)
% 250.32/59.28 (2) all_252_3 = e2
% 250.32/59.28 (3) ~ (e2 = e0)
% 250.32/59.28 (4) ~ (e1 = e0)
% 250.32/59.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.28 (6) op(e2, e3) = all_10_2
% 250.32/59.28 (7) ~ (e3 = e2)
% 250.32/59.28 (8) ~ (e4 = e0)
% 250.32/59.28 (9) ~ (all_244_15 = e4)
% 250.32/59.28 (10) ~ (e2 = e1)
% 250.32/59.28 (11) ~ (e4 = e1)
% 250.32/59.28 (12) op(e1, e4) = all_16_2
% 250.32/59.28 (13) op(e2, all_16_2) = e1
% 250.32/59.28 (14) op(e1, e3) = all_62_2
% 250.32/59.28 (15) ~ (e3 = e0)
% 250.32/59.28 (16) ~ (e3 = e1)
% 250.32/59.28 (17) ~ (all_16_2 = e2)
% 250.32/59.28 (18) ~ (all_22_2 = e1)
% 250.32/59.28 (19) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.32/59.28 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.32/59.28 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.32/59.28 (20) op(e1, e4) = all_242_1
% 250.32/59.28 (21) op(e0, e3) = all_22_2
% 250.32/59.28 (22) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.28 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.28 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.28 (23) ~ (e4 = e3)
% 250.32/59.28 (24) op(e1, e1) = all_244_15
% 250.32/59.28 (25) op(e2, e4) = e0
% 250.32/59.28 (26) op(e1, e2) = all_4_2
% 250.32/59.28 (27) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.32/59.28 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.32/59.28 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.32/59.28 (28) ~ (all_244_15 = e2)
% 250.32/59.28 (29) ~ (e4 = e2)
% 250.32/59.28 (30) all_252_1 = e4
% 250.32/59.28 (31) ~ (all_10_2 = e0)
% 250.32/59.28 (32) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.32/59.28 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.32/59.28 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.32/59.28 (33) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.32/59.28 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.32/59.28 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.32/59.28 (34) ~ (all_62_2 = e4)
% 250.32/59.28 (35) ~ (all_4_2 = e2)
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (32) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (36) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 250.32/59.28 | | = e2)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (36) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (37) all_252_12 = e2 & op(e1, e4) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (37) implies:
% 250.32/59.28 | | | (38) op(e1, e4) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (5), (12), (17), (20), (38) are inconsistent by sub-proof #600.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (39) all_252_13 = e2 & op(e1, e3) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | ALPHA: (39) implies:
% 250.32/59.28 | | | (40) all_252_13 = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | BETA: splitting (33) gives:
% 250.32/59.28 | | |
% 250.32/59.28 | | | Case 1:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (41) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3,
% 250.32/59.28 | | | | e3) = e1)
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | BETA: splitting (41) gives:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | Case 1:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (42) all_252_1 = e1 & op(e4, e3) = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | ALPHA: (42) implies:
% 250.32/59.28 | | | | | (43) all_252_1 = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | COMBINE_EQS: (30), (43) imply:
% 250.32/59.28 | | | | | (44) e4 = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | REDUCE: (11), (44) imply:
% 250.32/59.28 | | | | | (45) $false
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | CLOSE: (45) is inconsistent.
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | Case 2:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (46) all_252_3 = e1 & op(e3, e3) = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | REF_CLOSE: (2), (10), (46) are inconsistent by sub-proof #949.
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | End of split
% 250.32/59.28 | | | |
% 250.32/59.28 | | | Case 2:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (47) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1,
% 250.32/59.28 | | | | e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | BETA: splitting (47) gives:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | Case 1:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (48) all_252_7 = e1 & op(e2, e3) = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | ALPHA: (48) implies:
% 250.32/59.28 | | | | | (49) all_252_7 = e1
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | BETA: splitting (19) gives:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | Case 1:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (50) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 &
% 250.32/59.28 | | | | | | op(e3, e3) = e0)
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | BETA: splitting (50) gives:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | Case 1:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (51) all_252_1 = e0 & op(e4, e3) = e0
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | REF_CLOSE: (8), (30), (51) are inconsistent by sub-proof #947.
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | Case 2:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (52) all_252_3 = e0 & op(e3, e3) = e0
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | ALPHA: (52) implies:
% 250.32/59.28 | | | | | | | (53) all_252_3 = e0
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | COMBINE_EQS: (2), (53) imply:
% 250.32/59.28 | | | | | | | (54) e2 = e0
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | REDUCE: (3), (54) imply:
% 250.32/59.28 | | | | | | | (55) $false
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | CLOSE: (55) is inconsistent.
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | End of split
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | Case 2:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (56) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 250.32/59.28 | | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | BETA: splitting (56) gives:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | Case 1:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (57) all_252_7 = e0 & op(e2, e3) = e0
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | REF_CLOSE: (5), (6), (31), (57) are inconsistent by sub-proof
% 250.32/59.28 | | | | | | | #816.
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | Case 2:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | (58) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 250.32/59.28 | | | | | | | op(e0, e3) = e0)
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | BETA: splitting (58) gives:
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | | Case 1:
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | (59) all_252_13 = e0 & op(e1, e3) = e0
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | ALPHA: (59) implies:
% 250.32/59.28 | | | | | | | | (60) all_252_13 = e0
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | REF_CLOSE: (3), (40), (60) are inconsistent by sub-proof #418.
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | Case 2:
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | (61) all_252_21 = e0 & op(e0, e3) = e0
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | ALPHA: (61) implies:
% 250.32/59.28 | | | | | | | | (62) all_252_21 = e0
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | BETA: splitting (27) gives:
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | | Case 1:
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | (63) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 250.32/59.28 | | | | | | | | | op(e3, e3) = e3)
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | BETA: splitting (63) gives:
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | Case 1:
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | (64) all_252_1 = e3 & op(e4, e3) = e3
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | REF_CLOSE: (23), (30), (64) are inconsistent by sub-proof
% 250.32/59.28 | | | | | | | | | | #946.
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | Case 2:
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | (65) all_252_3 = e3 & op(e3, e3) = e3
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | REF_CLOSE: (2), (7), (65) are inconsistent by sub-proof #257.
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | End of split
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | Case 2:
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | (66) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3
% 250.32/59.28 | | | | | | | | | & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.32/59.28 | | | | | | | | | e3)
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | BETA: splitting (66) gives:
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | | Case 1:
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | (67) all_252_7 = e3 & op(e2, e3) = e3
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | ALPHA: (67) implies:
% 250.32/59.28 | | | | | | | | | | (68) all_252_7 = e3
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | REF_CLOSE: (16), (49), (68) are inconsistent by sub-proof
% 250.32/59.28 | | | | | | | | | | #212.
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | Case 2:
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | (69) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 =
% 250.32/59.28 | | | | | | | | | | e3 & op(e0, e3) = e3)
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | | REF_CLOSE: (7), (15), (40), (62), (69) are inconsistent by
% 250.32/59.28 | | | | | | | | | | sub-proof #211.
% 250.32/59.28 | | | | | | | | | |
% 250.32/59.28 | | | | | | | | | End of split
% 250.32/59.28 | | | | | | | | |
% 250.32/59.28 | | | | | | | | End of split
% 250.32/59.28 | | | | | | | |
% 250.32/59.28 | | | | | | | End of split
% 250.32/59.28 | | | | | | |
% 250.32/59.28 | | | | | | End of split
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | End of split
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | Case 2:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | (70) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 250.32/59.28 | | | | | op(e0, e3) = e1)
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | BETA: splitting (70) gives:
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | | Case 1:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (71) all_252_13 = e1 & op(e1, e3) = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | ALPHA: (71) implies:
% 250.32/59.28 | | | | | | (72) all_252_13 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | COMBINE_EQS: (40), (72) imply:
% 250.32/59.28 | | | | | | (73) e2 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | SIMP: (73) implies:
% 250.32/59.28 | | | | | | (74) e2 = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | REDUCE: (10), (74) imply:
% 250.32/59.28 | | | | | | (75) $false
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | CLOSE: (75) is inconsistent.
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | Case 2:
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | (76) all_252_21 = e1 & op(e0, e3) = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | ALPHA: (76) implies:
% 250.32/59.28 | | | | | | (77) op(e0, e3) = e1
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | | REF_CLOSE: (5), (18), (21), (77) are inconsistent by sub-proof #714.
% 250.32/59.28 | | | | | |
% 250.32/59.28 | | | | | End of split
% 250.32/59.28 | | | | |
% 250.32/59.28 | | | | End of split
% 250.32/59.28 | | | |
% 250.32/59.28 | | | End of split
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (78) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 250.32/59.28 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.32/59.28 | |
% 250.32/59.28 | | BETA: splitting (78) gives:
% 250.32/59.28 | |
% 250.32/59.28 | | Case 1:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (79) all_252_14 = e2 & op(e1, e2) = e2
% 250.32/59.28 | | |
% 250.32/59.28 | | | REF_CLOSE: (5), (26), (35), (79) are inconsistent by sub-proof #820.
% 250.32/59.28 | | |
% 250.32/59.28 | | Case 2:
% 250.32/59.28 | | |
% 250.32/59.28 | | | (80) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 250.32/59.28 | | | e0) = e2)
% 250.32/59.28 | | |
% 250.32/59.28 | | | BETA: splitting (80) gives:
% 250.32/59.28 | | |
% 250.32/59.28 | | | Case 1:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (81) all_252_15 = e2 & op(e1, e1) = e2
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | REF_CLOSE: (5), (24), (28), (81) are inconsistent by sub-proof #966.
% 250.32/59.28 | | | |
% 250.32/59.28 | | | Case 2:
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | (82) all_252_19 = e2 & op(e1, e0) = e2
% 250.32/59.28 | | | |
% 250.32/59.28 | | | | REF_CLOSE: (1), (4), (5), (9), (12), (13), (14), (22), (24), (25), (26),
% 250.32/59.28 | | | | (29), (34), (82) are inconsistent by sub-proof #213.
% 250.32/59.28 | | | |
% 250.32/59.28 | | | End of split
% 250.32/59.28 | | |
% 250.32/59.28 | | End of split
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #211 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) ~ (e3 = e2)
% 250.32/59.28 (2) all_252_13 = e2
% 250.32/59.28 (3) ~ (e3 = e0)
% 250.32/59.28 (4) all_252_21 = e0
% 250.32/59.28 (5) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | BETA: splitting (5) gives:
% 250.32/59.28 |
% 250.32/59.28 | Case 1:
% 250.32/59.28 | |
% 250.32/59.28 | | (6) all_252_13 = e3 & op(e1, e3) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #684.
% 250.32/59.28 | |
% 250.32/59.28 | Case 2:
% 250.32/59.28 | |
% 250.32/59.28 | | (7) all_252_21 = e3 & op(e0, e3) = e3
% 250.32/59.28 | |
% 250.32/59.28 | | ALPHA: (7) implies:
% 250.32/59.28 | | (8) all_252_21 = e3
% 250.32/59.28 | |
% 250.32/59.28 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #773.
% 250.32/59.28 | |
% 250.32/59.28 | End of split
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #212 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) all_252_7 = e3
% 250.32/59.28 (2) all_252_7 = e1
% 250.32/59.28 (3) ~ (e3 = e1)
% 250.32/59.28
% 250.32/59.28 Begin of proof
% 250.32/59.28 |
% 250.32/59.28 | COMBINE_EQS: (1), (2) imply:
% 250.32/59.28 | (4) e3 = e1
% 250.32/59.28 |
% 250.32/59.28 | SIMP: (4) implies:
% 250.32/59.28 | (5) e3 = e1
% 250.32/59.28 |
% 250.32/59.28 | REDUCE: (3), (5) imply:
% 250.32/59.28 | (6) $false
% 250.32/59.28 |
% 250.32/59.28 | CLOSE: (6) is inconsistent.
% 250.32/59.28 |
% 250.32/59.28 End of proof
% 250.32/59.28
% 250.32/59.28 Sub-proof #213 shows that the following formulas are inconsistent:
% 250.32/59.28 ----------------------------------------------------------------
% 250.32/59.28 (1) ~ (all_4_2 = e4)
% 250.32/59.28 (2) ~ (e1 = e0)
% 250.32/59.28 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.28 (4) ~ (all_244_15 = e4)
% 250.32/59.28 (5) op(e1, e4) = all_16_2
% 250.32/59.29 (6) op(e2, all_16_2) = e1
% 250.32/59.29 (7) op(e1, e3) = all_62_2
% 250.32/59.29 (8) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.32/59.29 | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.29 e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.29 (9) op(e1, e1) = all_244_15
% 250.32/59.29 (10) op(e2, e4) = e0
% 250.32/59.29 (11) op(e1, e2) = all_4_2
% 250.32/59.29 (12) ~ (e4 = e2)
% 250.32/59.29 (13) all_252_19 = e2 & op(e1, e0) = e2
% 250.32/59.29 (14) ~ (all_62_2 = e4)
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | ALPHA: (13) implies:
% 250.32/59.29 | (15) op(e1, e0) = e2
% 250.32/59.29 |
% 250.32/59.29 | BETA: splitting (8) gives:
% 250.32/59.29 |
% 250.32/59.29 | Case 1:
% 250.32/59.29 | |
% 250.32/59.29 | | (16) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 250.32/59.29 | | = e4)
% 250.32/59.29 | |
% 250.32/59.29 | | BETA: splitting (16) gives:
% 250.32/59.29 | |
% 250.32/59.29 | | Case 1:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (17) all_252_12 = e4 & op(e1, e4) = e4
% 250.32/59.29 | | |
% 250.32/59.29 | | | ALPHA: (17) implies:
% 250.32/59.29 | | | (18) op(e1, e4) = e4
% 250.32/59.29 | | |
% 250.32/59.29 | | | REF_CLOSE: (2), (3), (5), (6), (10), (18) are inconsistent by sub-proof
% 250.32/59.29 | | | #214.
% 250.32/59.29 | | |
% 250.32/59.29 | | Case 2:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (19) all_252_13 = e4 & op(e1, e3) = e4
% 250.32/59.29 | | |
% 250.32/59.29 | | | REF_CLOSE: (3), (7), (14), (19) are inconsistent by sub-proof #952.
% 250.32/59.29 | | |
% 250.32/59.29 | | End of split
% 250.32/59.29 | |
% 250.32/59.29 | Case 2:
% 250.32/59.29 | |
% 250.32/59.29 | | (20) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1)
% 250.32/59.29 | | = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.29 | |
% 250.32/59.29 | | REF_CLOSE: (1), (3), (4), (9), (11), (12), (15), (20) are inconsistent by
% 250.32/59.29 | | sub-proof #730.
% 250.32/59.29 | |
% 250.32/59.29 | End of split
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #214 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) ~ (e1 = e0)
% 250.32/59.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.29 (3) op(e1, e4) = all_16_2
% 250.32/59.29 (4) op(e2, all_16_2) = e1
% 250.32/59.29 (5) op(e2, e4) = e0
% 250.32/59.29 (6) op(e1, e4) = e4
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | GROUND_INST: instantiating (2) with all_16_2, e4, e4, e1, simplifying with
% 250.32/59.29 | (3), (6) gives:
% 250.32/59.29 | (7) all_16_2 = e4
% 250.32/59.29 |
% 250.32/59.29 | REDUCE: (4), (7) imply:
% 250.32/59.29 | (8) op(e2, e4) = e1
% 250.32/59.29 |
% 250.32/59.29 | GROUND_INST: instantiating (2) with e0, e1, e4, e2, simplifying with (5), (8)
% 250.32/59.29 | gives:
% 250.32/59.29 | (9) e1 = e0
% 250.32/59.29 |
% 250.32/59.29 | REDUCE: (1), (9) imply:
% 250.32/59.29 | (10) $false
% 250.32/59.29 |
% 250.32/59.29 | CLOSE: (10) is inconsistent.
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #215 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) all_252_6 = e0
% 250.32/59.29 (2) ~ (e1 = e0)
% 250.32/59.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.29 (4) ~ (e3 = e2)
% 250.32/59.29 (5) ~ (e4 = e0)
% 250.32/59.29 (6) ~ (e2 = e1)
% 250.32/59.29 (7) ~ (e4 = e1)
% 250.32/59.29 (8) ~ (e3 = e0)
% 250.32/59.29 (9) ~ (e3 = e1)
% 250.32/59.29 (10) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2)
% 250.32/59.29 (11) all_252_20 = e2
% 250.32/59.29 (12) ~ (e4 = e3)
% 250.32/59.29 (13) op(e4, e3) = all_84_2
% 250.32/59.29 (14) ~ (e4 = e2)
% 250.32/59.29 (15) ~ (all_84_2 = e2)
% 250.32/59.29 (16) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.32/59.29 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.32/59.29 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.32/59.29 (17) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.32/59.29 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.32/59.29 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.32/59.29 (18) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.32/59.29 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.32/59.29 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | BETA: splitting (10) gives:
% 250.32/59.29 |
% 250.32/59.29 | Case 1:
% 250.32/59.29 | |
% 250.32/59.29 | | (19) all_252_0 = e2 & op(e4, e4) = e2
% 250.32/59.29 | |
% 250.32/59.29 | | ALPHA: (19) implies:
% 250.32/59.29 | | (20) all_252_0 = e2
% 250.32/59.29 | |
% 250.32/59.29 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (14), (16),
% 250.32/59.29 | | (17), (18), (20) are inconsistent by sub-proof #384.
% 250.32/59.29 | |
% 250.32/59.29 | Case 2:
% 250.32/59.29 | |
% 250.32/59.29 | | (21) all_252_1 = e2 & op(e4, e3) = e2
% 250.32/59.29 | |
% 250.32/59.29 | | REF_CLOSE: (3), (13), (15), (21) are inconsistent by sub-proof #956.
% 250.32/59.29 | |
% 250.32/59.29 | End of split
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #216 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) ~ (all_10_2 = e4)
% 250.32/59.29 (2) op(e4, e0) = all_30_2
% 250.32/59.29 (3) all_252_6 = e0
% 250.32/59.29 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.29 (5) op(e2, e3) = all_10_2
% 250.32/59.29 (6) ~ (e4 = e0)
% 250.32/59.29 (7) op(all_244_8, all_244_8) = e2
% 250.32/59.29 (8) op(e2, e2) = all_244_8
% 250.32/59.29 (9) op(e2, e1) = all_38_2
% 250.32/59.29 (10) ~ (all_244_0 = e2)
% 250.32/59.29 (11) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.32/59.29 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.32/59.29 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.32/59.29 (12) ~ (all_30_2 = e2)
% 250.32/59.29 (13) op(all_40_2, e0) = e2
% 250.32/59.29 (14) ~ (all_38_2 = e4)
% 250.32/59.29 (15) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.32/59.29 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.32/59.29 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.32/59.29 (16) op(e4, e4) = all_244_0
% 250.32/59.29 (17) op(e2, e0) = all_40_2
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | BETA: splitting (11) gives:
% 250.32/59.29 |
% 250.32/59.29 | Case 1:
% 250.32/59.29 | |
% 250.32/59.29 | | (18) ~ (all_40_2 = e4)
% 250.32/59.29 | |
% 250.32/59.29 | | BETA: splitting (15) gives:
% 250.32/59.29 | |
% 250.32/59.29 | | Case 1:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (19) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3)
% 250.32/59.29 | | | = e4)
% 250.32/59.29 | | |
% 250.32/59.29 | | | REF_CLOSE: (1), (3), (4), (5), (6), (19) are inconsistent by sub-proof
% 250.32/59.29 | | | #937.
% 250.32/59.29 | | |
% 250.32/59.29 | | Case 2:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (20) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1)
% 250.32/59.29 | | | = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.32/59.29 | | |
% 250.32/59.29 | | | BETA: splitting (20) gives:
% 250.32/59.29 | | |
% 250.32/59.29 | | | Case 1:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (21) all_252_8 = e4 & op(e2, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | ALPHA: (21) implies:
% 250.32/59.29 | | | | (22) op(e2, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REF_CLOSE: (4), (7), (8), (10), (16), (22) are inconsistent by sub-proof
% 250.32/59.29 | | | | #626.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | Case 2:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (23) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 250.32/59.29 | | | | e0) = e4)
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REF_CLOSE: (4), (9), (14), (17), (18), (23) are inconsistent by
% 250.32/59.29 | | | | sub-proof #933.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | End of split
% 250.32/59.29 | | |
% 250.32/59.29 | | End of split
% 250.32/59.29 | |
% 250.32/59.29 | Case 2:
% 250.32/59.29 | |
% 250.32/59.29 | | (24) all_40_2 = e4
% 250.32/59.29 | |
% 250.32/59.29 | | REDUCE: (13), (24) imply:
% 250.32/59.29 | | (25) op(e4, e0) = e2
% 250.32/59.29 | |
% 250.32/59.29 | | REF_CLOSE: (2), (4), (12), (25) are inconsistent by sub-proof #830.
% 250.32/59.29 | |
% 250.32/59.29 | End of split
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #217 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 | all_250_0 = e0
% 250.32/59.29 (2) all_250_0 = all_244_0
% 250.32/59.29 (3) ~ (all_244_0 = e2)
% 250.32/59.29 (4) ~ (all_244_0 = e1)
% 250.32/59.29 (5) ~ (all_244_0 = e0)
% 250.32/59.29 (6) ~ (all_244_0 = e3)
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | BETA: splitting (1) gives:
% 250.32/59.29 |
% 250.32/59.29 | Case 1:
% 250.32/59.29 | |
% 250.32/59.29 | | (7) all_250_0 = e3
% 250.32/59.29 | |
% 250.32/59.29 | | COMBINE_EQS: (2), (7) imply:
% 250.32/59.29 | | (8) all_244_0 = e3
% 250.32/59.29 | |
% 250.32/59.29 | | SIMP: (8) implies:
% 250.32/59.29 | | (9) all_244_0 = e3
% 250.32/59.29 | |
% 250.32/59.29 | | REDUCE: (6), (9) imply:
% 250.32/59.29 | | (10) $false
% 250.32/59.29 | |
% 250.32/59.29 | | CLOSE: (10) is inconsistent.
% 250.32/59.29 | |
% 250.32/59.29 | Case 2:
% 250.32/59.29 | |
% 250.32/59.29 | | (11) all_250_0 = e2 | all_250_0 = e1 | all_250_0 = e0
% 250.32/59.29 | |
% 250.32/59.29 | | BETA: splitting (11) gives:
% 250.32/59.29 | |
% 250.32/59.29 | | Case 1:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (12) all_250_0 = e2
% 250.32/59.29 | | |
% 250.32/59.29 | | | COMBINE_EQS: (2), (12) imply:
% 250.32/59.29 | | | (13) all_244_0 = e2
% 250.32/59.29 | | |
% 250.32/59.29 | | | SIMP: (13) implies:
% 250.32/59.29 | | | (14) all_244_0 = e2
% 250.32/59.29 | | |
% 250.32/59.29 | | | REDUCE: (3), (14) imply:
% 250.32/59.29 | | | (15) $false
% 250.32/59.29 | | |
% 250.32/59.29 | | | CLOSE: (15) is inconsistent.
% 250.32/59.29 | | |
% 250.32/59.29 | | Case 2:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (16) all_250_0 = e1 | all_250_0 = e0
% 250.32/59.29 | | |
% 250.32/59.29 | | | BETA: splitting (16) gives:
% 250.32/59.29 | | |
% 250.32/59.29 | | | Case 1:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (17) all_250_0 = e1
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | COMBINE_EQS: (2), (17) imply:
% 250.32/59.29 | | | | (18) all_244_0 = e1
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | SIMP: (18) implies:
% 250.32/59.29 | | | | (19) all_244_0 = e1
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REDUCE: (4), (19) imply:
% 250.32/59.29 | | | | (20) $false
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | CLOSE: (20) is inconsistent.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | Case 2:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (21) all_250_0 = e0
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | COMBINE_EQS: (2), (21) imply:
% 250.32/59.29 | | | | (22) all_244_0 = e0
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | SIMP: (22) implies:
% 250.32/59.29 | | | | (23) all_244_0 = e0
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REDUCE: (5), (23) imply:
% 250.32/59.29 | | | | (24) $false
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | CLOSE: (24) is inconsistent.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | End of split
% 250.32/59.29 | | |
% 250.32/59.29 | | End of split
% 250.32/59.29 | |
% 250.32/59.29 | End of split
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #218 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) op(e4, e2) = all_16_1
% 250.32/59.29 (2) ~ (all_4_2 = e4)
% 250.32/59.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.29 (4) op(all_244_8, all_244_8) = e2
% 250.32/59.29 (5) op(e2, e2) = all_244_8
% 250.32/59.29 (6) op(e4, e2) = all_6_2
% 250.32/59.29 (7) ~ (e4 = e1)
% 250.32/59.29 (8) ~ (all_244_0 = e2)
% 250.32/59.29 (9) ~ (all_156_2 = e4) | ( ~ (all_156_0 = e0) & op(e4, all_156_1) =
% 250.32/59.29 all_156_0 & op(e2, e4) = all_156_1 & $i(all_156_0) & $i(all_156_1)) | (
% 250.32/59.29 ~ (all_156_1 = e1) & op(e2, e4) = all_156_1 & $i(all_156_1))
% 250.32/59.29 (10) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 250.32/59.29 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 250.32/59.29 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 250.32/59.29 (11) op(e4, e2) = all_20_0
% 250.32/59.29 (12) all_156_2 = all_8_2
% 250.32/59.29 (13) op(e0, e2) = e1
% 250.32/59.29 (14) ~ (all_20_0 = e3)
% 250.32/59.29 (15) op(e4, e4) = all_244_0
% 250.32/59.29 (16) ~ (all_6_2 = e4)
% 250.32/59.29 (17) op(e1, e2) = all_4_2
% 250.32/59.29 (18) op(e3, e2) = all_8_2
% 250.32/59.29 (19) op(all_8_2, e2) = e3
% 250.32/59.29
% 250.32/59.29 Begin of proof
% 250.32/59.29 |
% 250.32/59.29 | BETA: splitting (9) gives:
% 250.32/59.29 |
% 250.32/59.29 | Case 1:
% 250.32/59.29 | |
% 250.32/59.29 | | (20) ~ (all_156_2 = e4)
% 250.32/59.29 | |
% 250.32/59.29 | | REDUCE: (12), (20) imply:
% 250.32/59.29 | | (21) ~ (all_8_2 = e4)
% 250.32/59.29 | |
% 250.32/59.29 | | BETA: splitting (10) gives:
% 250.32/59.29 | |
% 250.32/59.29 | | Case 1:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (22) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2)
% 250.32/59.29 | | | = e4)
% 250.32/59.29 | | |
% 250.32/59.29 | | | BETA: splitting (22) gives:
% 250.32/59.29 | | |
% 250.32/59.29 | | | Case 1:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (23) all_252_4 = e4 & op(e4, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | ALPHA: (23) implies:
% 250.32/59.29 | | | | (24) op(e4, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | GROUND_INST: instantiating (3) with e4, all_16_1, e2, e4, simplifying
% 250.32/59.29 | | | | with (1), (24) gives:
% 250.32/59.29 | | | | (25) all_16_1 = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | GROUND_INST: instantiating (3) with all_6_2, all_20_0, e2, e4,
% 250.32/59.29 | | | | simplifying with (6), (11) gives:
% 250.32/59.29 | | | | (26) all_20_0 = all_6_2
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | GROUND_INST: instantiating (3) with all_16_1, all_20_0, e2, e4,
% 250.32/59.29 | | | | simplifying with (1), (11) gives:
% 250.32/59.29 | | | | (27) all_20_0 = all_16_1
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | COMBINE_EQS: (26), (27) imply:
% 250.32/59.29 | | | | (28) all_16_1 = all_6_2
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | SIMP: (28) implies:
% 250.32/59.29 | | | | (29) all_16_1 = all_6_2
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | COMBINE_EQS: (25), (29) imply:
% 250.32/59.29 | | | | (30) all_6_2 = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | SIMP: (30) implies:
% 250.32/59.29 | | | | (31) all_6_2 = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REDUCE: (16), (31) imply:
% 250.32/59.29 | | | | (32) $false
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | CLOSE: (32) is inconsistent.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | Case 2:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (33) all_252_5 = e4 & op(e3, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | ALPHA: (33) implies:
% 250.32/59.29 | | | | (34) op(e3, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REF_CLOSE: (3), (18), (21), (34) are inconsistent by sub-proof #502.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | End of split
% 250.32/59.29 | | |
% 250.32/59.29 | | Case 2:
% 250.32/59.29 | | |
% 250.32/59.29 | | | (35) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2)
% 250.32/59.29 | | | = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 250.32/59.29 | | |
% 250.32/59.29 | | | BETA: splitting (35) gives:
% 250.32/59.29 | | |
% 250.32/59.29 | | | Case 1:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (36) all_252_8 = e4 & op(e2, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | ALPHA: (36) implies:
% 250.32/59.29 | | | | (37) op(e2, e2) = e4
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | REF_CLOSE: (3), (4), (5), (8), (15), (37) are inconsistent by sub-proof
% 250.32/59.29 | | | | #626.
% 250.32/59.29 | | | |
% 250.32/59.29 | | | Case 2:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | (38) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 = e4 & op(e0,
% 250.32/59.29 | | | | e2) = e4)
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | BETA: splitting (38) gives:
% 250.32/59.29 | | | |
% 250.32/59.29 | | | | Case 1:
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | (39) all_252_14 = e4 & op(e1, e2) = e4
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | ALPHA: (39) implies:
% 250.32/59.29 | | | | | (40) op(e1, e2) = e4
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | REF_CLOSE: (2), (3), (17), (40) are inconsistent by sub-proof #831.
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | Case 2:
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | (41) all_252_22 = e4 & op(e0, e2) = e4
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | ALPHA: (41) implies:
% 250.32/59.29 | | | | | (42) op(e0, e2) = e4
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | | REF_CLOSE: (3), (7), (13), (42) are inconsistent by sub-proof #859.
% 250.32/59.29 | | | | |
% 250.32/59.29 | | | | End of split
% 250.32/59.29 | | | |
% 250.32/59.29 | | | End of split
% 250.32/59.29 | | |
% 250.32/59.29 | | End of split
% 250.32/59.29 | |
% 250.32/59.29 | Case 2:
% 250.32/59.29 | |
% 250.32/59.29 | | (43) all_156_2 = e4
% 250.32/59.29 | |
% 250.32/59.29 | | COMBINE_EQS: (12), (43) imply:
% 250.32/59.29 | | (44) all_8_2 = e4
% 250.32/59.29 | |
% 250.32/59.29 | | SIMP: (44) implies:
% 250.32/59.29 | | (45) all_8_2 = e4
% 250.32/59.29 | |
% 250.32/59.29 | | REDUCE: (19), (45) imply:
% 250.32/59.29 | | (46) op(e4, e2) = e3
% 250.32/59.29 | |
% 250.32/59.29 | | GROUND_INST: instantiating (3) with all_16_1, all_20_0, e2, e4, simplifying
% 250.32/59.29 | | with (1), (11) gives:
% 250.32/59.29 | | (47) all_20_0 = all_16_1
% 250.32/59.29 | |
% 250.32/59.29 | | GROUND_INST: instantiating (3) with e3, all_20_0, e2, e4, simplifying with
% 250.32/59.29 | | (11), (46) gives:
% 250.32/59.29 | | (48) all_20_0 = e3
% 250.32/59.29 | |
% 250.32/59.29 | | COMBINE_EQS: (47), (48) imply:
% 250.32/59.29 | | (49) all_16_1 = e3
% 250.32/59.29 | |
% 250.32/59.29 | | REDUCE: (14), (48) imply:
% 250.32/59.29 | | (50) $false
% 250.32/59.29 | |
% 250.32/59.29 | | CLOSE: (50) is inconsistent.
% 250.32/59.29 | |
% 250.32/59.29 | End of split
% 250.32/59.29 |
% 250.32/59.29 End of proof
% 250.32/59.29
% 250.32/59.29 Sub-proof #219 shows that the following formulas are inconsistent:
% 250.32/59.29 ----------------------------------------------------------------
% 250.32/59.29 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.32/59.29 all_250_23 = e0
% 250.32/59.29 (2) all_32_2 = all_20_2
% 250.32/59.29 (3) ~ (all_26_2 = e2)
% 250.32/59.29 (4) ~ (all_4_2 = e4)
% 250.32/59.29 (5) all_120_2 = e1
% 250.32/59.29 (6) op(all_4_2, e2) = e1
% 250.32/59.29 (7) ~ (all_244_24 = all_34_2)
% 250.32/59.29 (8) ~ (all_76_2 = e4) | ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 &
% 250.32/59.29 op(e0, e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~ (all_76_1 =
% 250.32/59.29 e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 250.32/59.29 (9) ~ (all_38_2 = e1)
% 250.32/59.29 (10) ~ (all_244_24 = all_40_2)
% 250.32/59.29 (11) ~ (all_40_2 = all_38_2)
% 250.32/59.29 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.32/59.29 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.32/59.29 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.29 (13) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.29 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.29 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.29 (14) op(e2, e0) = e4
% 250.32/59.29 (15) op(e2, all_26_2) = e4
% 250.32/59.29 (16) op(all_38_2, e1) = e2
% 250.32/59.29 (17) op(all_38_2, all_4_2) = e1
% 250.32/59.29 (18) all_252_12 = e2
% 250.32/59.29 (19) ~ (all_244_24 = all_20_2)
% 250.32/59.29 (20) ~ (all_100_2 = e1)
% 250.32/59.29 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.29 (22) op(e2, e3) = all_10_2
% 250.32/59.29 (23) ~ (e3 = e2)
% 250.32/59.29 (24) op(e0, e0) = all_244_24
% 250.32/59.29 (25) op(e2, e2) = all_244_8
% 250.32/59.29 (26) all_252_6 = e1
% 250.32/59.29 (27) op(e2, e1) = all_38_2
% 250.32/59.29 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.32/59.29 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.32/59.29 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.32/59.29 (29) ~ (all_36_2 = all_20_2)
% 250.32/59.29 (30) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 250.32/59.29 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 250.32/59.29 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.29 (31) ~ (all_84_2 = all_62_2)
% 250.32/59.29 (32) ~ (all_48_2 = all_40_2)
% 250.32/59.29 (33) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 250.32/59.29 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 250.32/59.29 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.29 (34) op(e1, e0) = all_34_2
% 250.32/59.29 (35) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.29 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.29 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.29 (36) op(e4, e2) = all_6_2
% 250.32/59.29 (37) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.32/59.29 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.32/59.29 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.32/59.29 (38) ~ (all_20_2 = all_12_2)
% 250.32/59.29 (39) ~ (e2 = e1)
% 250.32/59.29 (40) ~ (all_100_2 = all_36_2)
% 250.32/59.29 (41) op(e0, e2) = all_28_2
% 250.32/59.29 (42) all_250_24 = all_244_24
% 250.32/59.29 (43) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.29 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.29 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.29 (44) ~ (all_6_2 = e1)
% 250.32/59.29 (45) all_252_16 = e2
% 250.32/59.29 (46) ~ (all_244_8 = all_38_2)
% 250.32/59.29 (47) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.32/59.29 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.32/59.29 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.32/59.29 (48) op(all_244_15, all_244_15) = e1
% 250.32/59.29 (49) ~ (all_244_3 = all_36_2)
% 250.32/59.29 (50) ~ (all_28_2 = all_20_2)
% 250.32/59.29 (51) op(e1, e3) = all_62_2
% 250.32/59.29 (52) op(all_16_2, all_26_2) = e4
% 250.32/59.29 (53) ~ (e3 = e0)
% 250.32/59.29 (54) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.32/59.29 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.32/59.29 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.32/59.29 (55) op(e0, e2) = all_54_1
% 250.32/59.29 (56) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.32/59.29 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.32/59.29 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.32/59.29 (57) op(all_20_2, e1) = e0
% 250.32/59.29 (58) ~ (all_48_2 = all_36_2)
% 250.32/59.29 (59) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.32/59.29 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.32/59.29 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.32/59.29 (60) ~ (all_36_2 = all_8_2)
% 250.32/59.29 (61) ~ (e3 = e1)
% 250.32/59.29 (62) op(e3, e1) = all_36_2
% 250.32/59.29 (63) ~ (all_8_2 = e1)
% 250.32/59.29 (64) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.32/59.29 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.32/59.29 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.32/59.29 (65) ~ (all_40_2 = all_34_2)
% 250.32/59.29 (66) ~ (all_244_15 = all_38_2)
% 250.32/59.29 (67) ~ (all_48_2 = all_8_2)
% 250.32/59.29 (68) ~ (all_36_2 = all_26_2)
% 250.32/59.29 (69) all_190_2 = all_38_2
% 250.32/59.29 (70) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.32/59.29 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.32/59.29 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.32/59.29 (71) op(e0, e3) = all_22_2
% 250.32/59.29 (72) ~ (all_40_2 = e1)
% 250.32/59.29 (73) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.29 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.29 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.29 (74) op(all_62_2, e3) = e1
% 250.32/59.30 (75) op(e4, e1) = all_26_2
% 250.32/59.30 (76) ~ (all_40_2 = e2)
% 250.32/59.30 (77) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.32/59.30 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.32/59.30 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.32/59.30 (78) ~ (all_244_15 = all_62_2)
% 250.32/59.30 (79) op(e3, e4) = all_100_2
% 250.32/59.30 (80) ~ (all_244_8 = e1)
% 250.32/59.30 (81) all_230_2 = all_20_2
% 250.32/59.30 (82) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.32/59.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.32/59.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.32/59.30 (83) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 |
% 250.32/59.30 all_250_24 = e0
% 250.32/59.30 (84) ~ (e4 = e3)
% 250.32/59.30 (85) op(e1, e1) = all_244_15
% 250.32/59.30 (86) op(e0, e1) = all_20_2
% 250.32/59.30 (87) op(e3, e0) = all_48_2
% 250.32/59.30 (88) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.30 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.30 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.30 (89) op(all_48_2, e0) = e3
% 250.32/59.30 (90) ~ (all_26_2 = e3)
% 250.32/59.30 (91) ~ (all_244_24 = e2)
% 250.32/59.30 (92) op(e1, e2) = all_4_2
% 250.32/59.30 (93) op(all_4_2, all_38_2) = e2
% 250.32/59.30 (94) op(e4, e3) = all_84_2
% 250.32/59.30 (95) op(all_244_3, all_244_3) = e3
% 250.32/59.30 (96) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.30 (97) ~ (all_22_2 = all_20_2)
% 250.32/59.30 (98) op(e3, e2) = all_8_2
% 250.32/59.30 (99) op(all_36_2, e1) = e3
% 250.32/59.30 (100) ~ (all_38_2 = all_20_2)
% 250.32/59.30 (101) ~ (all_38_2 = all_10_2)
% 250.32/59.30 (102) ~ (all_244_24 = all_48_2)
% 250.32/59.30 (103) ~ (all_20_2 = e4)
% 250.32/59.30 (104) op(all_16_2, e4) = e1
% 250.32/59.30 (105) op(e2, e0) = all_40_2
% 250.32/59.30 (106) op(e3, e3) = all_244_3
% 250.32/59.30 (107) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.32/59.30 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.32/59.30 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.32/59.30 (108) all_46_2 = all_36_2
% 250.32/59.30 (109) ~ (all_4_2 = e2)
% 250.32/59.30 (110) op(e0, e4) = all_12_2
% 250.32/59.30 (111) all_250_23 = all_20_2
% 250.32/59.30 (112) all_76_2 = all_40_2
% 250.32/59.30
% 250.32/59.30 Begin of proof
% 250.32/59.30 |
% 250.32/59.30 | GROUND_INST: instantiating (21) with all_28_2, all_54_1, e2, e0, simplifying
% 250.32/59.30 | with (41), (55) gives:
% 250.32/59.30 | (113) all_54_1 = all_28_2
% 250.32/59.30 |
% 250.32/59.30 | GROUND_INST: instantiating (21) with all_40_2, e4, e0, e2, simplifying with
% 250.32/59.30 | (14), (105) gives:
% 250.32/59.30 | (114) all_40_2 = e4
% 250.32/59.30 |
% 250.32/59.30 | COMBINE_EQS: (112), (114) imply:
% 250.32/59.30 | (115) all_76_2 = e4
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (10), (114) imply:
% 250.32/59.30 | (116) ~ (all_244_24 = e4)
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (32), (114) imply:
% 250.32/59.30 | (117) ~ (all_48_2 = e4)
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (11), (114) imply:
% 250.32/59.30 | (118) ~ (all_38_2 = e4)
% 250.32/59.30 |
% 250.32/59.30 | SIMP: (118) implies:
% 250.32/59.30 | (119) ~ (all_38_2 = e4)
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (65), (114) imply:
% 250.32/59.30 | (120) ~ (all_34_2 = e4)
% 250.32/59.30 |
% 250.32/59.30 | SIMP: (120) implies:
% 250.32/59.30 | (121) ~ (all_34_2 = e4)
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (76), (114) imply:
% 250.32/59.30 | (122) ~ (e4 = e2)
% 250.32/59.30 |
% 250.32/59.30 | REDUCE: (72), (114) imply:
% 250.32/59.30 | (123) ~ (e4 = e1)
% 250.32/59.30 |
% 250.32/59.30 | BETA: splitting (47) gives:
% 250.32/59.30 |
% 250.32/59.30 | Case 1:
% 250.32/59.30 | |
% 250.32/59.30 | | (124) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0)
% 250.32/59.30 | | = e4)
% 250.32/59.30 | |
% 250.32/59.30 | | REF_CLOSE: (21), (45), (87), (117), (122), (124) are inconsistent by
% 250.32/59.30 | | sub-proof #705.
% 250.32/59.30 | |
% 250.32/59.30 | Case 2:
% 250.32/59.30 | |
% 250.32/59.30 | | (125) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1, e0)
% 250.32/59.30 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.32/59.30 | |
% 250.32/59.30 | | BETA: splitting (125) gives:
% 250.32/59.30 | |
% 250.32/59.30 | | Case 1:
% 250.32/59.30 | | |
% 250.32/59.30 | | | (126) all_252_18 = e4 & op(e2, e0) = e4
% 250.32/59.30 | | |
% 250.32/59.30 | | | ALPHA: (126) implies:
% 250.32/59.30 | | | (127) all_252_18 = e4
% 250.32/59.30 | | |
% 250.32/59.30 | | | BETA: splitting (59) gives:
% 250.32/59.30 | | |
% 250.32/59.30 | | | Case 1:
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | (128) ~ (all_40_2 = e4)
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | REF_CLOSE: (14), (21), (105), (128) are inconsistent by sub-proof #707.
% 250.32/59.30 | | | |
% 250.32/59.30 | | | Case 2:
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | (129) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4)
% 250.32/59.30 | | | | = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.32/59.30 | | | | e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | BETA: splitting (8) gives:
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | Case 1:
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | (130) ~ (all_76_2 = e4)
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | REDUCE: (115), (130) imply:
% 250.32/59.30 | | | | | (131) $false
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | CLOSE: (131) is inconsistent.
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | Case 2:
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | (132) ( ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0,
% 250.32/59.30 | | | | | e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)) | ( ~
% 250.32/59.30 | | | | | (all_76_1 = e1) & op(e0, e4) = all_76_1 & $i(all_76_1))
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | BETA: splitting (132) gives:
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | | Case 1:
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | (133) ~ (all_76_0 = e3) & op(e4, all_76_1) = all_76_0 & op(e0,
% 250.32/59.30 | | | | | | e4) = all_76_1 & $i(all_76_0) & $i(all_76_1)
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | ALPHA: (133) implies:
% 250.32/59.30 | | | | | | (134) op(e0, e4) = all_76_1
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (15),
% 250.32/59.30 | | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.32/59.30 | | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 250.32/59.30 | | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 250.32/59.30 | | | | | | (44), (46), (48), (49), (50), (51), (52), (53), (54),
% 250.32/59.30 | | | | | | (56), (57), (58), (60), (61), (62), (63), (64), (66),
% 250.32/59.30 | | | | | | (67), (68), (69), (70), (71), (73), (74), (75), (77),
% 250.32/59.30 | | | | | | (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 250.32/59.30 | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 250.32/59.30 | | | | | | (96), (97), (98), (99), (100), (101), (102), (103),
% 250.32/59.30 | | | | | | (104), (106), (107), (108), (109), (110), (111), (116),
% 250.32/59.30 | | | | | | (119), (121), (123), (127), (129), (134) are inconsistent
% 250.32/59.30 | | | | | | by sub-proof #220.
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | Case 2:
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | (135) ~ (all_76_1 = e1) & op(e0, e4) = all_76_1 & $i(all_76_1)
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | ALPHA: (135) implies:
% 250.32/59.30 | | | | | | (136) op(e0, e4) = all_76_1
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (15),
% 250.32/59.30 | | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.32/59.30 | | | | | | (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 250.32/59.30 | | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 250.32/59.30 | | | | | | (44), (46), (48), (49), (50), (51), (52), (53), (54),
% 250.32/59.30 | | | | | | (56), (57), (58), (60), (61), (62), (63), (64), (66),
% 250.32/59.30 | | | | | | (67), (68), (69), (70), (71), (73), (74), (75), (77),
% 250.32/59.30 | | | | | | (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 250.32/59.30 | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 250.32/59.30 | | | | | | (96), (97), (98), (99), (100), (101), (102), (103),
% 250.32/59.30 | | | | | | (104), (106), (107), (108), (109), (110), (111), (116),
% 250.32/59.30 | | | | | | (119), (121), (123), (127), (129), (136) are inconsistent
% 250.32/59.30 | | | | | | by sub-proof #220.
% 250.32/59.30 | | | | | |
% 250.32/59.30 | | | | | End of split
% 250.32/59.30 | | | | |
% 250.32/59.30 | | | | End of split
% 250.32/59.30 | | | |
% 250.32/59.30 | | | End of split
% 250.32/59.30 | | |
% 250.32/59.30 | | Case 2:
% 250.32/59.30 | | |
% 250.32/59.30 | | | (137) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.32/59.30 | | | e0) = e4)
% 250.32/59.30 | | |
% 250.32/59.30 | | | BETA: splitting (137) gives:
% 250.32/59.30 | | |
% 250.32/59.30 | | | Case 1:
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | (138) all_252_19 = e4 & op(e1, e0) = e4
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | REF_CLOSE: (21), (34), (121), (138) are inconsistent by sub-proof #677.
% 250.32/59.30 | | | |
% 250.32/59.30 | | | Case 2:
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | (139) all_252_24 = e4 & op(e0, e0) = e4
% 250.32/59.30 | | | |
% 250.32/59.30 | | | | REF_CLOSE: (21), (24), (116), (139) are inconsistent by sub-proof #679.
% 250.32/59.30 | | | |
% 250.32/59.30 | | | End of split
% 250.32/59.30 | | |
% 250.32/59.30 | | End of split
% 250.32/59.30 | |
% 250.32/59.30 | End of split
% 250.32/59.30 |
% 250.32/59.30 End of proof
% 250.32/59.30
% 250.32/59.30 Sub-proof #220 shows that the following formulas are inconsistent:
% 250.32/59.30 ----------------------------------------------------------------
% 250.32/59.30 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.32/59.30 all_250_23 = e0
% 250.32/59.30 (2) all_32_2 = all_20_2
% 250.32/59.30 (3) ~ (all_26_2 = e2)
% 250.32/59.30 (4) ~ (all_4_2 = e4)
% 250.32/59.30 (5) all_120_2 = e1
% 250.32/59.30 (6) op(all_4_2, e2) = e1
% 250.32/59.30 (7) ~ (all_244_24 = all_34_2)
% 250.32/59.30 (8) ~ (all_38_2 = e1)
% 250.32/59.30 (9) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 250.32/59.30 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 250.32/59.30 | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.30 (10) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.30 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.30 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.30 (11) op(e2, all_26_2) = e4
% 250.32/59.30 (12) op(all_38_2, e1) = e2
% 250.32/59.30 (13) op(all_38_2, all_4_2) = e1
% 250.32/59.30 (14) all_252_12 = e2
% 250.32/59.30 (15) ~ (all_244_24 = all_20_2)
% 250.32/59.30 (16) all_252_18 = e4
% 250.32/59.30 (17) ~ (all_100_2 = e1)
% 250.32/59.30 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.30 (19) op(e2, e3) = all_10_2
% 250.32/59.30 (20) ~ (e3 = e2)
% 250.32/59.30 (21) op(e0, e0) = all_244_24
% 250.32/59.30 (22) op(e2, e2) = all_244_8
% 250.32/59.30 (23) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 250.32/59.30 all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0,
% 250.32/59.30 e4) = all_40_1 & $i(all_40_1))
% 250.32/59.30 (24) all_252_6 = e1
% 250.32/59.30 (25) op(e2, e1) = all_38_2
% 250.32/59.30 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.32/59.30 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.32/59.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.32/59.30 (27) ~ (all_36_2 = all_20_2)
% 250.32/59.30 (28) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 250.32/59.30 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 250.32/59.30 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.30 (29) ~ (all_84_2 = all_62_2)
% 250.32/59.30 (30) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 250.32/59.30 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 250.32/59.30 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.30 (31) op(e1, e0) = all_34_2
% 250.32/59.30 (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.30 (33) op(e4, e2) = all_6_2
% 250.32/59.30 (34) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.32/59.30 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.32/59.30 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.32/59.30 (35) ~ (all_20_2 = all_12_2)
% 250.32/59.30 (36) ~ (e2 = e1)
% 250.32/59.30 (37) ~ (all_100_2 = all_36_2)
% 250.32/59.30 (38) ~ (all_34_2 = e4)
% 250.32/59.30 (39) op(e0, e2) = all_28_2
% 250.32/59.30 (40) ~ (e4 = e1)
% 250.32/59.30 (41) all_250_24 = all_244_24
% 250.32/59.30 (42) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.30 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.30 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.30 (43) ~ (all_6_2 = e1)
% 250.32/59.30 (44) ~ (all_244_8 = all_38_2)
% 250.32/59.30 (45) op(all_244_15, all_244_15) = e1
% 250.32/59.30 (46) ~ (all_244_3 = all_36_2)
% 250.32/59.30 (47) ~ (all_28_2 = all_20_2)
% 250.32/59.30 (48) op(e1, e3) = all_62_2
% 250.32/59.30 (49) op(all_16_2, all_26_2) = e4
% 250.32/59.30 (50) ~ (e3 = e0)
% 250.32/59.30 (51) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.32/59.30 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.32/59.30 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.32/59.30 (52) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.32/59.30 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.32/59.30 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.32/59.30 (53) op(all_20_2, e1) = e0
% 250.32/59.30 (54) ~ (all_48_2 = all_36_2)
% 250.32/59.30 (55) ~ (all_36_2 = all_8_2)
% 250.32/59.30 (56) ~ (e3 = e1)
% 250.32/59.30 (57) op(e3, e1) = all_36_2
% 250.32/59.30 (58) op(e0, e4) = all_76_1
% 250.32/59.30 (59) ~ (all_8_2 = e1)
% 250.32/59.30 (60) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.32/59.30 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.32/59.30 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.32/59.30 (61) ~ (all_244_15 = all_38_2)
% 250.32/59.30 (62) ~ (all_48_2 = all_8_2)
% 250.32/59.30 (63) ~ (all_36_2 = all_26_2)
% 250.32/59.30 (64) ~ (all_38_2 = e4)
% 250.32/59.30 (65) all_190_2 = all_38_2
% 250.32/59.30 (66) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.32/59.30 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.32/59.30 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.32/59.30 (67) op(e0, e3) = all_22_2
% 250.32/59.30 (68) ~ (all_244_24 = e4)
% 250.32/59.30 (69) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.30 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.30 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.30 (70) op(all_62_2, e3) = e1
% 250.32/59.30 (71) op(e4, e1) = all_26_2
% 250.32/59.30 (72) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.32/59.30 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.32/59.30 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.32/59.30 (73) ~ (all_244_15 = all_62_2)
% 250.32/59.30 (74) op(e3, e4) = all_100_2
% 250.32/59.30 (75) ~ (all_244_8 = e1)
% 250.32/59.30 (76) all_230_2 = all_20_2
% 250.32/59.30 (77) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.32/59.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.32/59.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.32/59.30 (78) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 |
% 250.32/59.30 all_250_24 = e0
% 250.32/59.30 (79) ~ (e4 = e3)
% 250.32/59.30 (80) op(e1, e1) = all_244_15
% 250.32/59.30 (81) op(e0, e1) = all_20_2
% 250.32/59.30 (82) op(e3, e0) = all_48_2
% 250.32/59.30 (83) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.30 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.30 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.30 (84) op(all_48_2, e0) = e3
% 250.32/59.30 (85) ~ (all_26_2 = e3)
% 250.32/59.30 (86) ~ (all_244_24 = e2)
% 250.32/59.30 (87) op(e1, e2) = all_4_2
% 250.32/59.30 (88) op(all_4_2, all_38_2) = e2
% 250.32/59.30 (89) op(e4, e3) = all_84_2
% 250.32/59.30 (90) op(all_244_3, all_244_3) = e3
% 250.32/59.30 (91) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.30 (92) ~ (all_22_2 = all_20_2)
% 250.32/59.30 (93) op(e3, e2) = all_8_2
% 250.32/59.30 (94) op(all_36_2, e1) = e3
% 250.32/59.30 (95) ~ (all_38_2 = all_20_2)
% 250.32/59.30 (96) ~ (all_38_2 = all_10_2)
% 250.32/59.30 (97) ~ (all_244_24 = all_48_2)
% 250.32/59.30 (98) ~ (all_20_2 = e4)
% 250.32/59.30 (99) op(all_16_2, e4) = e1
% 250.32/59.30 (100) op(e3, e3) = all_244_3
% 250.32/59.30 (101) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.32/59.30 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.32/59.30 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.32/59.30 (102) all_46_2 = all_36_2
% 250.32/59.30 (103) ~ (all_4_2 = e2)
% 250.32/59.30 (104) op(e0, e4) = all_12_2
% 250.32/59.30 (105) all_250_23 = all_20_2
% 250.32/59.30
% 250.32/59.30 Begin of proof
% 250.32/59.30 |
% 250.32/59.30 | GROUND_INST: instantiating (18) with all_12_2, all_76_1, e4, e0, simplifying
% 250.32/59.30 | with (58), (104) gives:
% 250.32/59.30 | (106) all_76_1 = all_12_2
% 250.32/59.30 |
% 250.32/59.30 | BETA: splitting (23) gives:
% 250.32/59.30 |
% 250.32/59.30 | Case 1:
% 250.32/59.30 | |
% 250.32/59.30 | | (107) ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 250.32/59.30 | | all_40_1 & $i(all_40_0) & $i(all_40_1)
% 250.32/59.30 | |
% 250.32/59.30 | | ALPHA: (107) implies:
% 250.32/59.30 | | (108) op(e0, e4) = all_40_1
% 250.32/59.30 | |
% 250.32/59.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.32/59.30 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 250.32/59.30 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.32/59.30 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 250.32/59.30 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.32/59.30 | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 250.32/59.30 | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 250.32/59.30 | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 250.32/59.30 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 250.32/59.30 | | (102), (103), (104), (105), (108) are inconsistent by sub-proof
% 250.32/59.30 | | #221.
% 250.32/59.30 | |
% 250.32/59.30 | Case 2:
% 250.32/59.30 | |
% 250.32/59.30 | | (109) ~ (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1)
% 250.32/59.30 | |
% 250.32/59.30 | | ALPHA: (109) implies:
% 250.32/59.30 | | (110) op(e0, e4) = all_40_1
% 250.32/59.30 | |
% 250.32/59.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.32/59.30 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 250.32/59.30 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.32/59.30 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 250.32/59.30 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.32/59.30 | | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 250.32/59.30 | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 250.32/59.30 | | (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 250.32/59.30 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 250.32/59.30 | | (102), (103), (104), (105), (110) are inconsistent by sub-proof
% 250.32/59.30 | | #221.
% 250.32/59.30 | |
% 250.32/59.30 | End of split
% 250.32/59.30 |
% 250.32/59.30 End of proof
% 250.32/59.30
% 250.32/59.30 Sub-proof #221 shows that the following formulas are inconsistent:
% 250.32/59.30 ----------------------------------------------------------------
% 250.32/59.30 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.32/59.30 all_250_23 = e0
% 250.32/59.30 (2) all_32_2 = all_20_2
% 250.32/59.30 (3) ~ (all_26_2 = e2)
% 250.32/59.30 (4) ~ (all_4_2 = e4)
% 250.32/59.30 (5) all_120_2 = e1
% 250.32/59.30 (6) op(all_4_2, e2) = e1
% 250.32/59.30 (7) ~ (all_244_24 = all_34_2)
% 250.32/59.30 (8) ~ (all_38_2 = e1)
% 250.32/59.30 (9) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 250.32/59.30 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 250.32/59.30 | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.30 (10) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.30 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.30 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.30 (11) op(e2, all_26_2) = e4
% 250.32/59.30 (12) op(all_38_2, e1) = e2
% 250.32/59.30 (13) op(all_38_2, all_4_2) = e1
% 250.32/59.30 (14) all_252_12 = e2
% 250.32/59.30 (15) ~ (all_244_24 = all_20_2)
% 250.32/59.30 (16) all_252_18 = e4
% 250.32/59.30 (17) ~ (all_100_2 = e1)
% 250.32/59.30 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.30 (19) op(e2, e3) = all_10_2
% 250.32/59.30 (20) ~ (e3 = e2)
% 250.32/59.30 (21) op(e0, e0) = all_244_24
% 250.32/59.30 (22) op(e2, e2) = all_244_8
% 250.32/59.30 (23) all_252_6 = e1
% 250.32/59.30 (24) op(e2, e1) = all_38_2
% 250.32/59.30 (25) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.32/59.30 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.32/59.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.32/59.30 (26) ~ (all_36_2 = all_20_2)
% 250.32/59.30 (27) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 250.32/59.30 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 250.32/59.30 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.30 (28) ~ (all_84_2 = all_62_2)
% 250.32/59.30 (29) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 250.32/59.30 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 250.32/59.30 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.30 (30) op(e1, e0) = all_34_2
% 250.32/59.30 (31) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.30 (32) op(e4, e2) = all_6_2
% 250.32/59.30 (33) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.32/59.30 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.32/59.30 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.32/59.30 (34) ~ (all_20_2 = all_12_2)
% 250.32/59.30 (35) ~ (e2 = e1)
% 250.32/59.30 (36) ~ (all_100_2 = all_36_2)
% 250.32/59.30 (37) ~ (all_34_2 = e4)
% 250.32/59.30 (38) op(e0, e2) = all_28_2
% 250.32/59.30 (39) ~ (e4 = e1)
% 250.32/59.30 (40) all_250_24 = all_244_24
% 250.32/59.31 (41) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.31 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.31 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.31 (42) ~ (all_6_2 = e1)
% 250.32/59.31 (43) ~ (all_244_8 = all_38_2)
% 250.32/59.31 (44) op(all_244_15, all_244_15) = e1
% 250.32/59.31 (45) ~ (all_244_3 = all_36_2)
% 250.32/59.31 (46) ~ (all_28_2 = all_20_2)
% 250.32/59.31 (47) op(e1, e3) = all_62_2
% 250.32/59.31 (48) op(all_16_2, all_26_2) = e4
% 250.32/59.31 (49) ~ (e3 = e0)
% 250.32/59.31 (50) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.32/59.31 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.32/59.31 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.32/59.31 (51) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.32/59.31 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.32/59.31 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.32/59.31 (52) op(all_20_2, e1) = e0
% 250.32/59.31 (53) ~ (all_48_2 = all_36_2)
% 250.32/59.31 (54) ~ (all_36_2 = all_8_2)
% 250.32/59.31 (55) ~ (e3 = e1)
% 250.32/59.31 (56) op(e3, e1) = all_36_2
% 250.32/59.31 (57) ~ (all_8_2 = e1)
% 250.32/59.31 (58) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.32/59.31 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.32/59.31 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.32/59.31 (59) ~ (all_244_15 = all_38_2)
% 250.32/59.31 (60) ~ (all_48_2 = all_8_2)
% 250.32/59.31 (61) ~ (all_36_2 = all_26_2)
% 250.32/59.31 (62) ~ (all_38_2 = e4)
% 250.32/59.31 (63) all_190_2 = all_38_2
% 250.32/59.31 (64) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.32/59.31 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.32/59.31 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.32/59.31 (65) op(e0, e3) = all_22_2
% 250.32/59.31 (66) ~ (all_244_24 = e4)
% 250.32/59.31 (67) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.31 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.31 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.31 (68) op(all_62_2, e3) = e1
% 250.32/59.31 (69) op(e4, e1) = all_26_2
% 250.32/59.31 (70) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.32/59.31 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.32/59.31 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.32/59.31 (71) ~ (all_244_15 = all_62_2)
% 250.32/59.31 (72) op(e3, e4) = all_100_2
% 250.32/59.31 (73) ~ (all_244_8 = e1)
% 250.32/59.31 (74) all_230_2 = all_20_2
% 250.32/59.31 (75) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.32/59.31 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.32/59.31 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.32/59.31 (76) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 |
% 250.32/59.31 all_250_24 = e0
% 250.32/59.31 (77) ~ (e4 = e3)
% 250.32/59.31 (78) op(e1, e1) = all_244_15
% 250.32/59.31 (79) op(e0, e1) = all_20_2
% 250.32/59.31 (80) op(e3, e0) = all_48_2
% 250.32/59.31 (81) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.31 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.31 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.31 (82) op(all_48_2, e0) = e3
% 250.32/59.31 (83) ~ (all_26_2 = e3)
% 250.32/59.31 (84) ~ (all_244_24 = e2)
% 250.32/59.31 (85) op(e1, e2) = all_4_2
% 250.32/59.31 (86) op(all_4_2, all_38_2) = e2
% 250.32/59.31 (87) op(e4, e3) = all_84_2
% 250.32/59.31 (88) op(all_244_3, all_244_3) = e3
% 250.32/59.31 (89) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.31 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.31 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.31 (90) ~ (all_22_2 = all_20_2)
% 250.32/59.31 (91) op(e3, e2) = all_8_2
% 250.32/59.31 (92) op(all_36_2, e1) = e3
% 250.32/59.31 (93) ~ (all_38_2 = all_20_2)
% 250.32/59.31 (94) ~ (all_38_2 = all_10_2)
% 250.32/59.31 (95) ~ (all_244_24 = all_48_2)
% 250.32/59.31 (96) ~ (all_20_2 = e4)
% 250.32/59.31 (97) op(all_16_2, e4) = e1
% 250.32/59.31 (98) op(e0, e4) = all_40_1
% 250.32/59.31 (99) op(e3, e3) = all_244_3
% 250.32/59.31 (100) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.32/59.31 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.32/59.31 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.32/59.31 (101) all_46_2 = all_36_2
% 250.32/59.31 (102) ~ (all_4_2 = e2)
% 250.32/59.31 (103) op(e0, e4) = all_12_2
% 250.32/59.31 (104) all_250_23 = all_20_2
% 250.32/59.31
% 250.32/59.31 Begin of proof
% 250.32/59.31 |
% 250.32/59.31 | GROUND_INST: instantiating (18) with all_12_2, all_40_1, e4, e0, simplifying
% 250.32/59.31 | with (98), (103) gives:
% 250.32/59.31 | (105) all_40_1 = all_12_2
% 250.32/59.31 |
% 250.32/59.31 | BETA: splitting (50) gives:
% 250.32/59.31 |
% 250.32/59.31 | Case 1:
% 250.32/59.31 | |
% 250.32/59.31 | | (106) ~ (all_32_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (2), (106) imply:
% 250.32/59.31 | | (107) ~ (all_20_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | BETA: splitting (58) gives:
% 250.32/59.31 | |
% 250.32/59.31 | | Case 1:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (108) ~ (all_46_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REF_CLOSE: (3), (6), (8), (18), (22), (24), (44), (56), (69), (73), (75),
% 250.32/59.31 | | | (78), (79), (86), (101), (107), (108) are inconsistent by
% 250.32/59.31 | | | sub-proof #598.
% 250.32/59.31 | | |
% 250.32/59.31 | | Case 2:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (109) all_46_2 = e2
% 250.32/59.31 | | | (110) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 250.32/59.31 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 250.32/59.31 | | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.32/59.31 | | |
% 250.32/59.31 | | | COMBINE_EQS: (101), (109) imply:
% 250.32/59.31 | | | (111) all_36_2 = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | SIMP: (111) implies:
% 250.32/59.31 | | | (112) all_36_2 = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (45), (112) imply:
% 250.32/59.31 | | | (113) ~ (all_244_3 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (36), (112) imply:
% 250.32/59.31 | | | (114) ~ (all_100_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (53), (112) imply:
% 250.32/59.31 | | | (115) ~ (all_48_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (61), (112) imply:
% 250.32/59.31 | | | (116) ~ (all_26_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (26), (112) imply:
% 250.32/59.31 | | | (117) ~ (all_20_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (54), (112) imply:
% 250.32/59.31 | | | (118) ~ (all_8_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | SIMP: (118) implies:
% 250.32/59.31 | | | (119) ~ (all_8_2 = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | REDUCE: (92), (112) imply:
% 250.32/59.31 | | | (120) op(e2, e1) = e3
% 250.32/59.31 | | |
% 250.32/59.31 | | | BETA: splitting (110) gives:
% 250.32/59.31 | | |
% 250.32/59.31 | | | Case 1:
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | (121) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 250.32/59.31 | | | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | ALPHA: (121) implies:
% 250.32/59.31 | | | | (122) op(e1, e2) = all_46_1
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | BETA: splitting (100) gives:
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | Case 1:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | (123) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3,
% 250.32/59.31 | | | | | e3) = e2)
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | REF_CLOSE: (18), (72), (99), (113), (114), (123) are inconsistent by
% 250.32/59.31 | | | | | sub-proof #232.
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | Case 2:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | (124) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 &
% 250.32/59.31 | | | | | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | BETA: splitting (124) gives:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | Case 1:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | (125) all_252_5 = e2 & op(e3, e2) = e2
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REF_CLOSE: (18), (91), (119), (125) are inconsistent by sub-proof
% 250.32/59.31 | | | | | | #256.
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | Case 2:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | (126) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 250.32/59.31 | | | | | | op(e3, e0) = e2)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | BETA: splitting (126) gives:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | Case 1:
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | GROUND_INST: instantiating (18) with all_4_2, all_46_1, e2, e1,
% 250.32/59.31 | | | | | | | simplifying with (85), (122) gives:
% 250.32/59.31 | | | | | | | (127) all_46_1 = all_4_2
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | REF_CLOSE: (1), (3), (6), (7), (8), (12), (13), (15), (17), (18),
% 250.32/59.31 | | | | | | | (22), (24), (25), (30), (32), (33), (35), (38), (40),
% 250.32/59.31 | | | | | | | (42), (44), (46), (57), (59), (60), (64), (66), (69),
% 250.32/59.31 | | | | | | | (72), (73), (75), (76), (78), (79), (80), (82), (84),
% 250.32/59.31 | | | | | | | (86), (88), (91), (93), (95), (96), (99), (102), (104),
% 250.32/59.31 | | | | | | | (107), (120), (122), (127) are inconsistent by
% 250.32/59.31 | | | | | | | sub-proof #227.
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | Case 2:
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | (128) all_252_17 = e2 & op(e3, e0) = e2
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | REF_CLOSE: (18), (80), (115), (128) are inconsistent by sub-proof
% 250.32/59.31 | | | | | | | #653.
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | End of split
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | End of split
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | End of split
% 250.32/59.31 | | | |
% 250.32/59.31 | | | Case 2:
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | (129) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1)
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | ALPHA: (129) implies:
% 250.32/59.31 | | | | (130) op(e1, e2) = all_46_1
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | GROUND_INST: instantiating (18) with all_4_2, all_46_1, e2, e1,
% 250.32/59.31 | | | | simplifying with (85), (130) gives:
% 250.32/59.31 | | | | (131) all_46_1 = all_4_2
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | REF_CLOSE: (1), (3), (6), (7), (8), (12), (13), (15), (17), (18), (22),
% 250.32/59.31 | | | | (24), (25), (30), (32), (33), (35), (38), (40), (42), (44),
% 250.32/59.31 | | | | (46), (57), (59), (60), (64), (66), (69), (72), (73), (75),
% 250.32/59.31 | | | | (76), (78), (79), (80), (82), (84), (86), (88), (91), (93),
% 250.32/59.31 | | | | (95), (96), (99), (102), (104), (107), (120), (130), (131)
% 250.32/59.31 | | | | are inconsistent by sub-proof #227.
% 250.32/59.31 | | | |
% 250.32/59.31 | | | End of split
% 250.32/59.31 | | |
% 250.32/59.31 | | End of split
% 250.32/59.31 | |
% 250.32/59.31 | Case 2:
% 250.32/59.31 | |
% 250.32/59.31 | | (132) all_32_2 = e2
% 250.32/59.31 | |
% 250.32/59.31 | | COMBINE_EQS: (2), (132) imply:
% 250.32/59.31 | | (133) all_20_2 = e2
% 250.32/59.31 | |
% 250.32/59.31 | | SIMP: (133) implies:
% 250.32/59.31 | | (134) all_20_2 = e2
% 250.32/59.31 | |
% 250.32/59.31 | | COMBINE_EQS: (74), (134) imply:
% 250.32/59.31 | | (135) all_230_2 = e2
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (46), (134) imply:
% 250.32/59.31 | | (136) ~ (all_28_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (90), (134) imply:
% 250.32/59.31 | | (137) ~ (all_22_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (34), (134) imply:
% 250.32/59.31 | | (138) ~ (all_12_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | SIMP: (138) implies:
% 250.32/59.31 | | (139) ~ (all_12_2 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (96), (134) imply:
% 250.32/59.31 | | (140) ~ (e4 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | SIMP: (140) implies:
% 250.32/59.31 | | (141) ~ (e4 = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | REDUCE: (52), (134) imply:
% 250.32/59.31 | | (142) op(e2, e1) = e0
% 250.32/59.31 | |
% 250.32/59.31 | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18), (19), (20),
% 250.32/59.31 | | (21), (22), (23), (24), (27), (28), (29), (30), (31), (35), (37),
% 250.32/59.31 | | (38), (39), (41), (43), (47), (48), (49), (51), (55), (56), (62),
% 250.32/59.31 | | (63), (65), (67), (68), (69), (70), (71), (77), (78), (79), (81),
% 250.32/59.31 | | (83), (84), (85), (87), (89), (92), (94), (96), (97), (98),
% 250.32/59.31 | | (103), (135), (136), (137), (139), (141), (142) are inconsistent
% 250.32/59.31 | | by sub-proof #222.
% 250.32/59.31 | |
% 250.32/59.31 | End of split
% 250.32/59.31 |
% 250.32/59.31 End of proof
% 250.32/59.31
% 250.32/59.31 Sub-proof #222 shows that the following formulas are inconsistent:
% 250.32/59.31 ----------------------------------------------------------------
% 250.32/59.31 (1) ~ (all_4_2 = e4)
% 250.32/59.31 (2) all_120_2 = e1
% 250.32/59.31 (3) ~ (all_38_2 = e1)
% 250.32/59.31 (4) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 250.32/59.31 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 250.32/59.31 | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.31 (5) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.31 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.31 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.31 (6) ~ (all_22_2 = e2)
% 250.32/59.31 (7) op(e2, all_26_2) = e4
% 250.32/59.31 (8) all_252_12 = e2
% 250.32/59.31 (9) all_252_18 = e4
% 250.32/59.31 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.31 (11) all_230_2 = e2
% 250.32/59.31 (12) op(e2, e3) = all_10_2
% 250.32/59.31 (13) ~ (e3 = e2)
% 250.32/59.31 (14) op(e0, e0) = all_244_24
% 250.32/59.31 (15) op(e2, e2) = all_244_8
% 250.32/59.31 (16) all_252_6 = e1
% 250.32/59.31 (17) op(e2, e1) = all_38_2
% 250.32/59.31 (18) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 250.32/59.31 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 250.32/59.31 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.31 (19) ~ (all_84_2 = all_62_2)
% 250.32/59.31 (20) ~ (all_120_2 = e1) | ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 &
% 250.32/59.31 op(e1, all_120_1) = all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~
% 250.32/59.31 (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.31 (21) op(e1, e0) = all_34_2
% 250.32/59.31 (22) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.31 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.31 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.31 (23) ~ (e2 = e1)
% 250.32/59.31 (24) ~ (all_34_2 = e4)
% 250.32/59.31 (25) op(e0, e2) = all_28_2
% 250.32/59.31 (26) ~ (e4 = e1)
% 250.32/59.31 (27) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.31 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.31 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.31 (28) ~ (all_244_8 = all_38_2)
% 250.32/59.31 (29) op(e1, e3) = all_62_2
% 250.32/59.31 (30) op(all_16_2, all_26_2) = e4
% 250.32/59.31 (31) ~ (e3 = e0)
% 250.32/59.31 (32) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.32/59.31 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.32/59.31 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.32/59.31 (33) ~ (e3 = e1)
% 250.32/59.31 (34) ~ (all_12_2 = e2)
% 250.32/59.31 (35) op(e3, e1) = all_36_2
% 250.32/59.31 (36) ~ (all_38_2 = e4)
% 250.32/59.31 (37) all_190_2 = all_38_2
% 250.32/59.31 (38) ~ (all_28_2 = e2)
% 250.32/59.31 (39) op(e0, e3) = all_22_2
% 250.32/59.31 (40) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.31 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.31 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.31 (41) op(all_62_2, e3) = e1
% 250.32/59.31 (42) op(e4, e1) = all_26_2
% 250.32/59.31 (43) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.32/59.31 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.32/59.31 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.32/59.31 (44) ~ (all_244_15 = all_62_2)
% 250.32/59.31 (45) ~ (e4 = e3)
% 250.32/59.31 (46) op(e1, e1) = all_244_15
% 250.32/59.31 (47) op(e0, e1) = all_20_2
% 250.32/59.31 (48) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.31 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.31 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.31 (49) ~ (all_26_2 = e3)
% 250.32/59.31 (50) ~ (all_244_24 = e2)
% 250.32/59.31 (51) op(e1, e2) = all_4_2
% 250.32/59.31 (52) op(e4, e3) = all_84_2
% 250.32/59.31 (53) ~ (e4 = e2)
% 250.32/59.31 (54) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.31 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.31 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.31 (55) op(all_36_2, e1) = e3
% 250.32/59.31 (56) ~ (all_38_2 = all_10_2)
% 250.32/59.31 (57) ~ (all_20_2 = e4)
% 250.32/59.31 (58) op(all_16_2, e4) = e1
% 250.32/59.31 (59) op(e0, e4) = all_40_1
% 250.32/59.31 (60) op(e2, e1) = e0
% 250.32/59.31 (61) op(e0, e4) = all_12_2
% 250.32/59.31
% 250.32/59.31 Begin of proof
% 250.32/59.31 |
% 250.32/59.31 | BETA: splitting (43) gives:
% 250.32/59.31 |
% 250.32/59.31 | Case 1:
% 250.32/59.31 | |
% 250.32/59.31 | | (62) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3)
% 250.32/59.31 | | = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | BETA: splitting (62) gives:
% 250.32/59.31 | |
% 250.32/59.31 | | Case 1:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (63) all_252_20 = e2 & op(e0, e4) = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | REF_CLOSE: (10), (34), (59), (61), (63) are inconsistent by sub-proof
% 250.32/59.31 | | | #698.
% 250.32/59.31 | | |
% 250.32/59.31 | | Case 2:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (64) all_252_21 = e2 & op(e0, e3) = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | ALPHA: (64) implies:
% 250.32/59.31 | | | (65) op(e0, e3) = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | REF_CLOSE: (6), (10), (39), (65) are inconsistent by sub-proof #987.
% 250.32/59.31 | | |
% 250.32/59.31 | | End of split
% 250.32/59.31 | |
% 250.32/59.31 | Case 2:
% 250.32/59.31 | |
% 250.32/59.31 | | (66) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1)
% 250.32/59.31 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.32/59.31 | |
% 250.32/59.31 | | BETA: splitting (66) gives:
% 250.32/59.31 | |
% 250.32/59.31 | | Case 1:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (67) all_252_22 = e2 & op(e0, e2) = e2
% 250.32/59.31 | | |
% 250.32/59.31 | | | REF_CLOSE: (10), (25), (38), (67) are inconsistent by sub-proof #979.
% 250.32/59.31 | | |
% 250.32/59.31 | | Case 2:
% 250.32/59.31 | | |
% 250.32/59.31 | | | (68) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 250.32/59.31 | | | e0) = e2)
% 250.32/59.31 | | |
% 250.32/59.31 | | | BETA: splitting (68) gives:
% 250.32/59.31 | | |
% 250.32/59.31 | | | Case 1:
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | (69) all_252_23 = e2 & op(e0, e1) = e2
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | ALPHA: (69) implies:
% 250.32/59.31 | | | | (70) all_252_23 = e2
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | BETA: splitting (32) gives:
% 250.32/59.31 | | | |
% 250.32/59.31 | | | | Case 1:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | (71) ~ (all_230_2 = e2)
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | REDUCE: (11), (71) imply:
% 250.32/59.31 | | | | | (72) $false
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | CLOSE: (72) is inconsistent.
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | Case 2:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | (73) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1,
% 250.32/59.31 | | | | | e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) | ( ~
% 250.32/59.31 | | | | | (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | BETA: splitting (73) gives:
% 250.32/59.31 | | | | |
% 250.32/59.31 | | | | | Case 1:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | (74) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1,
% 250.32/59.31 | | | | | | e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | ALPHA: (74) implies:
% 250.32/59.31 | | | | | | (75) op(e1, e2) = all_230_1
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | GROUND_INST: instantiating (10) with all_4_2, all_230_1, e2, e1,
% 250.32/59.31 | | | | | | simplifying with (51), (75) gives:
% 250.32/59.31 | | | | | | (76) all_230_1 = all_4_2
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | GROUND_INST: instantiating (10) with all_38_2, e0, e1, e2,
% 250.32/59.31 | | | | | | simplifying with (17), (60) gives:
% 250.32/59.31 | | | | | | (77) all_38_2 = e0
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | COMBINE_EQS: (37), (77) imply:
% 250.32/59.31 | | | | | | (78) all_190_2 = e0
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (28), (77) imply:
% 250.32/59.31 | | | | | | (79) ~ (all_244_8 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (56), (77) imply:
% 250.32/59.31 | | | | | | (80) ~ (all_10_2 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (80) implies:
% 250.32/59.31 | | | | | | (81) ~ (all_10_2 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (36), (77) imply:
% 250.32/59.31 | | | | | | (82) ~ (e4 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (82) implies:
% 250.32/59.31 | | | | | | (83) ~ (e4 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (3), (77) imply:
% 250.32/59.31 | | | | | | (84) ~ (e1 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (84) implies:
% 250.32/59.31 | | | | | | (85) ~ (e1 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | BETA: splitting (20) gives:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | Case 1:
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | (86) ~ (all_120_2 = e1)
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | REDUCE: (2), (86) imply:
% 250.32/59.31 | | | | | | | (87) $false
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | CLOSE: (87) is inconsistent.
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | Case 2:
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | (88) ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1,
% 250.32/59.31 | | | | | | | all_120_1) = all_120_0 & $i(all_120_0) &
% 250.32/59.31 | | | | | | | $i(all_120_1)) | ( ~ (all_120_1 = e0) & op(e4, e1) =
% 250.32/59.31 | | | | | | | all_120_1 & $i(all_120_1))
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13),
% 250.32/59.31 | | | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 250.32/59.31 | | | | | | | (26), (27), (29), (30), (31), (33), (35), (36), (40),
% 250.32/59.31 | | | | | | | (41), (42), (44), (45), (46), (47), (48), (49), (51),
% 250.32/59.31 | | | | | | | (52), (53), (54), (55), (57), (58), (70), (78), (79),
% 250.32/59.31 | | | | | | | (81), (83), (85), (88) are inconsistent by sub-proof
% 250.32/59.31 | | | | | | | #223.
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | End of split
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | Case 2:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | (89) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | ALPHA: (89) implies:
% 250.32/59.31 | | | | | | (90) ~ (all_230_1 = e4)
% 250.32/59.31 | | | | | | (91) op(e1, e2) = all_230_1
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | GROUND_INST: instantiating (10) with all_4_2, all_230_1, e2, e1,
% 250.32/59.31 | | | | | | simplifying with (51), (91) gives:
% 250.32/59.31 | | | | | | (92) all_230_1 = all_4_2
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | GROUND_INST: instantiating (10) with all_38_2, e0, e1, e2,
% 250.32/59.31 | | | | | | simplifying with (17), (60) gives:
% 250.32/59.31 | | | | | | (93) all_38_2 = e0
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | COMBINE_EQS: (37), (93) imply:
% 250.32/59.31 | | | | | | (94) all_190_2 = e0
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (28), (93) imply:
% 250.32/59.31 | | | | | | (95) ~ (all_244_8 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (56), (93) imply:
% 250.32/59.31 | | | | | | (96) ~ (all_10_2 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (96) implies:
% 250.32/59.31 | | | | | | (97) ~ (all_10_2 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (36), (93) imply:
% 250.32/59.31 | | | | | | (98) ~ (e4 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (98) implies:
% 250.32/59.31 | | | | | | (99) ~ (e4 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | REDUCE: (3), (93) imply:
% 250.32/59.31 | | | | | | (100) ~ (e1 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | SIMP: (100) implies:
% 250.32/59.31 | | | | | | (101) ~ (e1 = e0)
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | BETA: splitting (20) gives:
% 250.32/59.31 | | | | | |
% 250.32/59.31 | | | | | | Case 1:
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | (102) ~ (all_120_2 = e1)
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | REDUCE: (2), (102) imply:
% 250.32/59.31 | | | | | | | (103) $false
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | | CLOSE: (103) is inconsistent.
% 250.32/59.31 | | | | | | |
% 250.32/59.31 | | | | | | Case 2:
% 250.32/59.31 | | | | | | |
% 250.32/59.32 | | | | | | | (104) ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1,
% 250.32/59.32 | | | | | | | all_120_1) = all_120_0 & $i(all_120_0) &
% 250.32/59.32 | | | | | | | $i(all_120_1)) | ( ~ (all_120_1 = e0) & op(e4, e1) =
% 250.32/59.32 | | | | | | | all_120_1 & $i(all_120_1))
% 250.32/59.32 | | | | | | |
% 250.32/59.32 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13),
% 250.32/59.32 | | | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 250.32/59.32 | | | | | | | (26), (27), (29), (30), (31), (33), (35), (36), (40),
% 250.32/59.32 | | | | | | | (41), (42), (44), (45), (46), (47), (48), (49), (51),
% 250.32/59.32 | | | | | | | (52), (53), (54), (55), (57), (58), (70), (94), (95),
% 250.32/59.32 | | | | | | | (97), (99), (101), (104) are inconsistent by sub-proof
% 250.32/59.32 | | | | | | | #223.
% 250.32/59.32 | | | | | | |
% 250.32/59.32 | | | | | | End of split
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | End of split
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | End of split
% 250.32/59.32 | | | |
% 250.32/59.32 | | | Case 2:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | (105) all_252_24 = e2 & op(e0, e0) = e2
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | ALPHA: (105) implies:
% 250.32/59.32 | | | | (106) op(e0, e0) = e2
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | REF_CLOSE: (10), (14), (50), (106) are inconsistent by sub-proof #978.
% 250.32/59.32 | | | |
% 250.32/59.32 | | | End of split
% 250.32/59.32 | | |
% 250.32/59.32 | | End of split
% 250.32/59.32 | |
% 250.32/59.32 | End of split
% 250.32/59.32 |
% 250.32/59.32 End of proof
% 250.32/59.32
% 250.32/59.32 Sub-proof #223 shows that the following formulas are inconsistent:
% 250.32/59.32 ----------------------------------------------------------------
% 250.32/59.32 (1) ~ (all_4_2 = e4)
% 250.32/59.32 (2) ~ (all_38_2 = e1)
% 250.32/59.32 (3) ~ (all_244_8 = e0)
% 250.32/59.32 (4) ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1, all_120_1) =
% 250.32/59.32 all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~ (all_120_1 = e0) &
% 250.32/59.32 op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.32 (5) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 250.32/59.32 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 250.32/59.32 | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.32 (6) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.32 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.32 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.32 (7) op(e2, all_26_2) = e4
% 250.32/59.32 (8) all_252_12 = e2
% 250.32/59.32 (9) ~ (e1 = e0)
% 250.32/59.32 (10) all_252_18 = e4
% 250.32/59.32 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.32 (12) op(e2, e3) = all_10_2
% 250.32/59.32 (13) ~ (e3 = e2)
% 250.32/59.32 (14) ~ (e4 = e0)
% 250.32/59.32 (15) op(e2, e2) = all_244_8
% 250.32/59.32 (16) all_252_6 = e1
% 250.32/59.32 (17) op(e2, e1) = all_38_2
% 250.32/59.32 (18) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 250.32/59.32 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 250.32/59.32 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.32 (19) ~ (all_84_2 = all_62_2)
% 250.32/59.32 (20) op(e1, e0) = all_34_2
% 250.32/59.32 (21) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.32 (22) ~ (e2 = e1)
% 250.32/59.32 (23) ~ (all_34_2 = e4)
% 250.32/59.32 (24) ~ (e4 = e1)
% 250.32/59.32 (25) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.32 (26) op(e1, e3) = all_62_2
% 250.32/59.32 (27) op(all_16_2, all_26_2) = e4
% 250.32/59.32 (28) ~ (e3 = e0)
% 250.32/59.32 (29) ~ (e3 = e1)
% 250.32/59.32 (30) op(e3, e1) = all_36_2
% 250.32/59.32 (31) ~ (all_38_2 = e4)
% 250.32/59.32 (32) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.32 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.32 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.32 (33) op(all_62_2, e3) = e1
% 250.32/59.32 (34) op(e4, e1) = all_26_2
% 250.32/59.32 (35) ~ (all_244_15 = all_62_2)
% 250.32/59.32 (36) ~ (e4 = e3)
% 250.32/59.32 (37) op(e1, e1) = all_244_15
% 250.32/59.32 (38) all_252_23 = e2
% 250.32/59.32 (39) op(e0, e1) = all_20_2
% 250.32/59.32 (40) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.32 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.32 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.32 (41) ~ (all_26_2 = e3)
% 250.32/59.32 (42) op(e1, e2) = all_4_2
% 250.32/59.32 (43) op(e4, e3) = all_84_2
% 250.32/59.32 (44) ~ (e4 = e2)
% 250.32/59.32 (45) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.32 (46) op(all_36_2, e1) = e3
% 250.32/59.32 (47) ~ (all_20_2 = e4)
% 250.32/59.32 (48) op(all_16_2, e4) = e1
% 250.32/59.32 (49) all_190_2 = e0
% 250.32/59.32 (50) ~ (all_10_2 = e0)
% 250.32/59.32
% 250.32/59.32 Begin of proof
% 250.32/59.32 |
% 250.32/59.32 | BETA: splitting (5) gives:
% 250.32/59.32 |
% 250.32/59.32 | Case 1:
% 250.32/59.32 | |
% 250.32/59.32 | | (51) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 250.32/59.32 | | e0)
% 250.32/59.32 | |
% 250.32/59.32 | | BETA: splitting (51) gives:
% 250.32/59.32 | |
% 250.32/59.32 | | Case 1:
% 250.32/59.32 | | |
% 250.32/59.32 | | | (52) all_252_6 = e0 & op(e2, e4) = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | ALPHA: (52) implies:
% 250.32/59.32 | | | (53) all_252_6 = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | COMBINE_EQS: (16), (53) imply:
% 250.32/59.32 | | | (54) e1 = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | REDUCE: (9), (54) imply:
% 250.32/59.32 | | | (55) $false
% 250.32/59.32 | | |
% 250.32/59.32 | | | CLOSE: (55) is inconsistent.
% 250.32/59.32 | | |
% 250.32/59.32 | | Case 2:
% 250.32/59.32 | | |
% 250.32/59.32 | | | (56) all_252_7 = e0 & op(e2, e3) = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | REF_CLOSE: (11), (12), (50), (56) are inconsistent by sub-proof #816.
% 250.32/59.32 | | |
% 250.32/59.32 | | End of split
% 250.32/59.32 | |
% 250.32/59.32 | Case 2:
% 250.32/59.32 | |
% 250.32/59.32 | | (57) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.32/59.32 | | e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.32/59.32 | |
% 250.32/59.32 | | BETA: splitting (57) gives:
% 250.32/59.32 | |
% 250.32/59.32 | | Case 1:
% 250.32/59.32 | | |
% 250.32/59.32 | | | (58) all_252_8 = e0 & op(e2, e2) = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | ALPHA: (58) implies:
% 250.32/59.32 | | | (59) op(e2, e2) = e0
% 250.32/59.32 | | |
% 250.32/59.32 | | | REF_CLOSE: (3), (11), (15), (59) are inconsistent by sub-proof #880.
% 250.32/59.32 | | |
% 250.32/59.32 | | Case 2:
% 250.32/59.32 | | |
% 250.32/59.32 | | | (60) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0 & op(e2,
% 250.32/59.32 | | | e0) = e0)
% 250.32/59.32 | | |
% 250.32/59.32 | | | BETA: splitting (60) gives:
% 250.32/59.32 | | |
% 250.32/59.32 | | | Case 1:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | (61) all_252_11 = e0 & op(e2, e1) = e0
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | ALPHA: (61) implies:
% 250.32/59.32 | | | | (62) all_252_11 = e0
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | BETA: splitting (18) gives:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | Case 1:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (63) ~ (all_190_2 = e0)
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | REDUCE: (49), (63) imply:
% 250.32/59.32 | | | | | (64) $false
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | CLOSE: (64) is inconsistent.
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | Case 2:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (65) ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 250.32/59.32 | | | | | all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) |
% 250.32/59.32 | | | | | ( ~ (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | BETA: splitting (65) gives:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | Case 1:
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | (66) ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 250.32/59.32 | | | | | | all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | ALPHA: (66) implies:
% 250.32/59.32 | | | | | | (67) op(e1, e0) = all_190_1
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (13), (14), (17),
% 250.32/59.32 | | | | | | (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 250.32/59.32 | | | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 250.32/59.32 | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 250.32/59.32 | | | | | | (46), (47), (48), (62), (67) are inconsistent by
% 250.32/59.32 | | | | | | sub-proof #224.
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | Case 2:
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | (68) ~ (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1)
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | ALPHA: (68) implies:
% 250.32/59.32 | | | | | | (69) op(e1, e0) = all_190_1
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (13), (14), (17),
% 250.32/59.32 | | | | | | (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 250.32/59.32 | | | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 250.32/59.32 | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 250.32/59.32 | | | | | | (46), (47), (48), (62), (69) are inconsistent by
% 250.32/59.32 | | | | | | sub-proof #224.
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | End of split
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | End of split
% 250.32/59.32 | | | |
% 250.32/59.32 | | | Case 2:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | (70) all_252_18 = e0 & op(e2, e0) = e0
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | REF_CLOSE: (10), (14), (70) are inconsistent by sub-proof #619.
% 250.32/59.32 | | | |
% 250.32/59.32 | | | End of split
% 250.32/59.32 | | |
% 250.32/59.32 | | End of split
% 250.32/59.32 | |
% 250.32/59.32 | End of split
% 250.32/59.32 |
% 250.32/59.32 End of proof
% 250.32/59.32
% 250.32/59.32 Sub-proof #224 shows that the following formulas are inconsistent:
% 250.32/59.32 ----------------------------------------------------------------
% 250.32/59.32 (1) ~ (all_4_2 = e4)
% 250.32/59.32 (2) ~ (all_38_2 = e1)
% 250.32/59.32 (3) ( ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1, all_120_1) =
% 250.32/59.32 all_120_0 & $i(all_120_0) & $i(all_120_1)) | ( ~ (all_120_1 = e0) &
% 250.32/59.32 op(e4, e1) = all_120_1 & $i(all_120_1))
% 250.32/59.32 (4) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.32 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.32 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.32 (5) op(e2, all_26_2) = e4
% 250.32/59.32 (6) all_252_12 = e2
% 250.32/59.32 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.32 (8) ~ (e3 = e2)
% 250.32/59.32 (9) ~ (e4 = e0)
% 250.32/59.32 (10) op(e2, e1) = all_38_2
% 250.32/59.32 (11) ~ (all_84_2 = all_62_2)
% 250.32/59.32 (12) op(e1, e0) = all_34_2
% 250.32/59.32 (13) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.32 (14) ~ (e2 = e1)
% 250.32/59.32 (15) ~ (all_34_2 = e4)
% 250.32/59.32 (16) ~ (e4 = e1)
% 250.32/59.32 (17) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.32 (18) op(e1, e3) = all_62_2
% 250.32/59.32 (19) op(all_16_2, all_26_2) = e4
% 250.32/59.32 (20) ~ (e3 = e0)
% 250.32/59.32 (21) ~ (e3 = e1)
% 250.32/59.32 (22) op(e3, e1) = all_36_2
% 250.32/59.32 (23) op(e1, e0) = all_190_1
% 250.32/59.32 (24) ~ (all_38_2 = e4)
% 250.32/59.32 (25) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.32 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.32 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.32 (26) op(all_62_2, e3) = e1
% 250.32/59.32 (27) op(e4, e1) = all_26_2
% 250.32/59.32 (28) ~ (all_244_15 = all_62_2)
% 250.32/59.32 (29) ~ (e4 = e3)
% 250.32/59.32 (30) op(e1, e1) = all_244_15
% 250.32/59.32 (31) all_252_23 = e2
% 250.32/59.32 (32) op(e0, e1) = all_20_2
% 250.32/59.32 (33) all_252_11 = e0
% 250.32/59.32 (34) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.32 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.32 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.32 (35) ~ (all_26_2 = e3)
% 250.32/59.32 (36) op(e1, e2) = all_4_2
% 250.32/59.32 (37) op(e4, e3) = all_84_2
% 250.32/59.32 (38) ~ (e4 = e2)
% 250.32/59.32 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.32 (40) op(all_36_2, e1) = e3
% 250.32/59.32 (41) ~ (all_20_2 = e4)
% 250.32/59.32 (42) op(all_16_2, e4) = e1
% 250.32/59.32
% 250.32/59.32 Begin of proof
% 250.32/59.32 |
% 250.32/59.32 | BETA: splitting (3) gives:
% 250.32/59.32 |
% 250.32/59.32 | Case 1:
% 250.32/59.32 | |
% 250.32/59.32 | | (43) ~ (all_120_0 = e3) & op(e4, e1) = all_120_1 & op(e1, all_120_1) =
% 250.32/59.32 | | all_120_0 & $i(all_120_0) & $i(all_120_1)
% 250.32/59.32 | |
% 250.32/59.32 | | ALPHA: (43) implies:
% 250.32/59.32 | | (44) op(e4, e1) = all_120_1
% 250.32/59.32 | |
% 250.32/59.32 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.32/59.32 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.32/59.32 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.32/59.32 | | (36), (37), (38), (39), (40), (41), (42), (44) are inconsistent
% 250.32/59.32 | | by sub-proof #225.
% 250.32/59.32 | |
% 250.32/59.32 | Case 2:
% 250.32/59.32 | |
% 250.32/59.32 | | (45) ~ (all_120_1 = e0) & op(e4, e1) = all_120_1 & $i(all_120_1)
% 250.32/59.32 | |
% 250.32/59.32 | | ALPHA: (45) implies:
% 250.32/59.32 | | (46) op(e4, e1) = all_120_1
% 250.32/59.32 | |
% 250.32/59.32 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.32/59.32 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.32/59.32 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.32/59.32 | | (36), (37), (38), (39), (40), (41), (42), (46) are inconsistent
% 250.32/59.32 | | by sub-proof #225.
% 250.32/59.32 | |
% 250.32/59.32 | End of split
% 250.32/59.32 |
% 250.32/59.32 End of proof
% 250.32/59.32
% 250.32/59.32 Sub-proof #225 shows that the following formulas are inconsistent:
% 250.32/59.32 ----------------------------------------------------------------
% 250.32/59.32 (1) ~ (all_4_2 = e4)
% 250.32/59.32 (2) ~ (all_38_2 = e1)
% 250.32/59.32 (3) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.32/59.32 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.32/59.32 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.32/59.32 (4) op(e2, all_26_2) = e4
% 250.32/59.32 (5) all_252_12 = e2
% 250.32/59.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.32/59.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.32/59.32 (7) ~ (e3 = e2)
% 250.32/59.32 (8) ~ (e4 = e0)
% 250.32/59.32 (9) op(e2, e1) = all_38_2
% 250.32/59.32 (10) ~ (all_84_2 = all_62_2)
% 250.32/59.32 (11) op(e1, e0) = all_34_2
% 250.32/59.32 (12) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.32/59.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.32/59.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.32/59.32 (13) op(e4, e1) = all_120_1
% 250.32/59.32 (14) ~ (e2 = e1)
% 250.32/59.32 (15) ~ (all_34_2 = e4)
% 250.32/59.32 (16) ~ (e4 = e1)
% 250.32/59.32 (17) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.32/59.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.32/59.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.32/59.32 (18) op(e1, e3) = all_62_2
% 250.32/59.32 (19) op(all_16_2, all_26_2) = e4
% 250.32/59.32 (20) ~ (e3 = e0)
% 250.32/59.32 (21) ~ (e3 = e1)
% 250.32/59.32 (22) op(e3, e1) = all_36_2
% 250.32/59.32 (23) op(e1, e0) = all_190_1
% 250.32/59.32 (24) ~ (all_38_2 = e4)
% 250.32/59.32 (25) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.32/59.32 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.32 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.32 (26) op(all_62_2, e3) = e1
% 250.32/59.32 (27) op(e4, e1) = all_26_2
% 250.32/59.32 (28) ~ (all_244_15 = all_62_2)
% 250.32/59.32 (29) ~ (e4 = e3)
% 250.32/59.32 (30) op(e1, e1) = all_244_15
% 250.32/59.32 (31) all_252_23 = e2
% 250.32/59.32 (32) op(e0, e1) = all_20_2
% 250.32/59.32 (33) all_252_11 = e0
% 250.32/59.32 (34) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.32/59.32 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.32/59.32 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.32/59.32 (35) ~ (all_26_2 = e3)
% 250.32/59.32 (36) op(e1, e2) = all_4_2
% 250.32/59.32 (37) op(e4, e3) = all_84_2
% 250.32/59.32 (38) ~ (e4 = e2)
% 250.32/59.32 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.32/59.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.32/59.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.32/59.32 (40) op(all_36_2, e1) = e3
% 250.32/59.32 (41) ~ (all_20_2 = e4)
% 250.32/59.32 (42) op(all_16_2, e4) = e1
% 250.32/59.32
% 250.32/59.32 Begin of proof
% 250.32/59.32 |
% 250.32/59.32 | GROUND_INST: instantiating (6) with all_34_2, all_190_1, e0, e1, simplifying
% 250.32/59.32 | with (11), (23) gives:
% 250.32/59.32 | (43) all_190_1 = all_34_2
% 250.32/59.32 |
% 250.32/59.32 | GROUND_INST: instantiating (6) with all_26_2, all_120_1, e1, e4, simplifying
% 250.32/59.32 | with (13), (27) gives:
% 250.32/59.32 | (44) all_120_1 = all_26_2
% 250.32/59.32 |
% 250.32/59.32 | BETA: splitting (3) gives:
% 250.32/59.32 |
% 250.32/59.32 | Case 1:
% 250.32/59.32 | |
% 250.32/59.32 | | (45) ~ (all_36_2 = e4)
% 250.32/59.32 | |
% 250.32/59.32 | | BETA: splitting (34) gives:
% 250.32/59.32 | |
% 250.32/59.32 | | Case 1:
% 250.32/59.32 | | |
% 250.32/59.32 | | | (46) ~ (all_62_2 = e4)
% 250.32/59.32 | | |
% 250.32/59.32 | | | BETA: splitting (25) gives:
% 250.32/59.32 | | |
% 250.32/59.32 | | | Case 1:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | (47) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 250.32/59.32 | | | | e3) = e4)
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | BETA: splitting (47) gives:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | Case 1:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (48) all_252_12 = e4 & op(e1, e4) = e4
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | REF_CLOSE: (5), (38), (48) are inconsistent by sub-proof #561.
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | Case 2:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (49) all_252_13 = e4 & op(e1, e3) = e4
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | REF_CLOSE: (6), (18), (46), (49) are inconsistent by sub-proof #952.
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | End of split
% 250.32/59.32 | | | |
% 250.32/59.32 | | | Case 2:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | (50) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.32/59.32 | | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | BETA: splitting (50) gives:
% 250.32/59.32 | | | |
% 250.32/59.32 | | | | Case 1:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (51) all_252_14 = e4 & op(e1, e2) = e4
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | ALPHA: (51) implies:
% 250.32/59.32 | | | | | (52) op(e1, e2) = e4
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | REF_CLOSE: (1), (6), (36), (52) are inconsistent by sub-proof #831.
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | Case 2:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | (53) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.32/59.32 | | | | | op(e1, e0) = e4)
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | BETA: splitting (53) gives:
% 250.32/59.32 | | | | |
% 250.32/59.32 | | | | | Case 1:
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | (54) all_252_15 = e4 & op(e1, e1) = e4
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | ALPHA: (54) implies:
% 250.32/59.32 | | | | | | (55) all_252_15 = e4
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | BETA: splitting (17) gives:
% 250.32/59.32 | | | | | |
% 250.32/59.32 | | | | | | Case 1:
% 250.32/59.32 | | | | | | |
% 250.32/59.32 | | | | | | | (56) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 &
% 250.32/59.32 | | | | | | | op(e3, e1) = e3)
% 250.32/59.32 | | | | | | |
% 250.32/59.32 | | | | | | | BETA: splitting (56) gives:
% 250.32/59.32 | | | | | | |
% 250.32/59.32 | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | (57) all_252_9 = e3 & op(e4, e1) = e3
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | ALPHA: (57) implies:
% 250.32/59.32 | | | | | | | | (58) op(e4, e1) = e3
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | REF_CLOSE: (6), (27), (35), (58) are inconsistent by sub-proof
% 250.32/59.32 | | | | | | | | #834.
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | Case 2:
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | (59) all_252_10 = e3 & op(e3, e1) = e3
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | ALPHA: (59) implies:
% 250.32/59.32 | | | | | | | | (60) all_252_10 = e3
% 250.32/59.32 | | | | | | | | (61) op(e3, e1) = e3
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | BETA: splitting (39) gives:
% 250.32/59.32 | | | | | | | |
% 250.32/59.32 | | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | | |
% 250.32/59.32 | | | | | | | | | (62) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1
% 250.32/59.32 | | | | | | | | | & op(e3, e1) = e1)
% 250.32/59.32 | | | | | | | | |
% 250.32/59.32 | | | | | | | | | BETA: splitting (62) gives:
% 250.32/59.32 | | | | | | | | |
% 250.32/59.32 | | | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | (63) all_252_9 = e1 & op(e4, e1) = e1
% 250.32/59.32 | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | ALPHA: (63) implies:
% 250.32/59.32 | | | | | | | | | | (64) all_252_9 = e1
% 250.32/59.32 | | | | | | | | | | (65) op(e4, e1) = e1
% 250.32/59.32 | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | BETA: splitting (12) gives:
% 250.32/59.32 | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | (66) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 250.32/59.32 | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | BETA: splitting (66) gives:
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | (67) all_252_9 = e4 & op(e4, e1) = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | ALPHA: (67) implies:
% 250.32/59.32 | | | | | | | | | | | | (68) all_252_9 = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | REF_CLOSE: (16), (64), (68) are inconsistent by sub-proof
% 250.32/59.32 | | | | | | | | | | | | #842.
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | Case 2:
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | (69) all_252_10 = e4 & op(e3, e1) = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | ALPHA: (69) implies:
% 250.32/59.32 | | | | | | | | | | | | (70) op(e3, e1) = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | REF_CLOSE: (6), (22), (29), (61), (70) are inconsistent by
% 250.32/59.32 | | | | | | | | | | | | sub-proof #614.
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | End of split
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | Case 2:
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | (71) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 250.32/59.32 | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 250.32/59.32 | | | | | | | | | | | op(e0, e1) = e4)
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | BETA: splitting (71) gives:
% 250.32/59.32 | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | Case 1:
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | (72) all_252_11 = e4 & op(e2, e1) = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | ALPHA: (72) implies:
% 250.32/59.32 | | | | | | | | | | | | (73) op(e2, e1) = e4
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | | REF_CLOSE: (6), (9), (24), (73) are inconsistent by sub-proof
% 250.32/59.32 | | | | | | | | | | | | #935.
% 250.32/59.32 | | | | | | | | | | | |
% 250.32/59.32 | | | | | | | | | | | Case 2:
% 250.32/59.32 | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | (74) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 250.44/59.32 | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 250.44/59.32 | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | BETA: splitting (74) gives:
% 250.44/59.32 | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | Case 1:
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_26_2, e1, e1, e4,
% 250.44/59.32 | | | | | | | | | | | | | simplifying with (27), (65) gives:
% 250.44/59.32 | | | | | | | | | | | | | (75) all_26_2 = e1
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | | REDUCE: (4), (75) imply:
% 250.44/59.32 | | | | | | | | | | | | | (76) op(e2, e1) = e4
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (24), (76) are inconsistent by sub-proof
% 250.44/59.32 | | | | | | | | | | | | | #935.
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | Case 2:
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | | (77) all_252_23 = e4 & op(e0, e1) = e4
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | | REF_CLOSE: (6), (32), (41), (77) are inconsistent by
% 250.44/59.32 | | | | | | | | | | | | | sub-proof #912.
% 250.44/59.32 | | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | | End of split
% 250.44/59.32 | | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | End of split
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | End of split
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | Case 2:
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | (78) all_252_10 = e1 & op(e3, e1) = e1
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | REF_CLOSE: (21), (60), (78) are inconsistent by sub-proof
% 250.44/59.32 | | | | | | | | | | #472.
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | End of split
% 250.44/59.32 | | | | | | | | |
% 250.44/59.32 | | | | | | | | Case 2:
% 250.44/59.32 | | | | | | | | |
% 250.44/59.32 | | | | | | | | | (79) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1
% 250.44/59.32 | | | | | | | | | & op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) =
% 250.44/59.32 | | | | | | | | | e1)
% 250.44/59.32 | | | | | | | | |
% 250.44/59.32 | | | | | | | | | BETA: splitting (79) gives:
% 250.44/59.32 | | | | | | | | |
% 250.44/59.32 | | | | | | | | | Case 1:
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | (80) all_252_11 = e1 & op(e2, e1) = e1
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | REF_CLOSE: (2), (6), (9), (80) are inconsistent by sub-proof
% 250.44/59.32 | | | | | | | | | | #226.
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | Case 2:
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | (81) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 =
% 250.44/59.32 | | | | | | | | | | e1 & op(e0, e1) = e1)
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | BETA: splitting (81) gives:
% 250.44/59.32 | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | Case 1:
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | (82) all_252_15 = e1 & op(e1, e1) = e1
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | ALPHA: (82) implies:
% 250.44/59.32 | | | | | | | | | | | (83) all_252_15 = e1
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | COMBINE_EQS: (55), (83) imply:
% 250.44/59.32 | | | | | | | | | | | (84) e4 = e1
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | REDUCE: (16), (84) imply:
% 250.44/59.32 | | | | | | | | | | | (85) $false
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | | CLOSE: (85) is inconsistent.
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.32 | | | | | | | | | | Case 2:
% 250.44/59.32 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | | (86) all_252_23 = e1 & op(e0, e1) = e1
% 250.44/59.33 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | | ALPHA: (86) implies:
% 250.44/59.33 | | | | | | | | | | | (87) all_252_23 = e1
% 250.44/59.33 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | | COMBINE_EQS: (31), (87) imply:
% 250.44/59.33 | | | | | | | | | | | (88) e2 = e1
% 250.44/59.33 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | | REDUCE: (14), (88) imply:
% 250.44/59.33 | | | | | | | | | | | (89) $false
% 250.44/59.33 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | | CLOSE: (89) is inconsistent.
% 250.44/59.33 | | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | End of split
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | End of split
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | End of split
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | End of split
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | Case 2:
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | (90) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 &
% 250.44/59.33 | | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | BETA: splitting (90) gives:
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | Case 1:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | (91) all_252_11 = e3 & op(e2, e1) = e3
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | REF_CLOSE: (20), (33), (91) are inconsistent by sub-proof #701.
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | Case 2:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | (92) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 250.44/59.33 | | | | | | | | op(e0, e1) = e3)
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | BETA: splitting (92) gives:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | Case 1:
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | (93) all_252_15 = e3 & op(e1, e1) = e3
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | REF_CLOSE: (29), (55), (93) are inconsistent by sub-proof
% 250.44/59.33 | | | | | | | | | #486.
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | Case 2:
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | (94) all_252_23 = e3 & op(e0, e1) = e3
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | REF_CLOSE: (7), (31), (94) are inconsistent by sub-proof #687.
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | End of split
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | End of split
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | End of split
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | Case 2:
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | (95) all_252_19 = e4 & op(e1, e0) = e4
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | REF_CLOSE: (6), (11), (15), (95) are inconsistent by sub-proof #677.
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | End of split
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | End of split
% 250.44/59.33 | | | |
% 250.44/59.33 | | | End of split
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (96) all_62_2 = e4
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (6), (8), (10), (12), (19), (22), (26), (27), (28), (30), (32),
% 250.44/59.33 | | | (33), (37), (41), (42), (45), (96) are inconsistent by
% 250.44/59.33 | | | sub-proof #715.
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (97) all_36_2 = e4
% 250.44/59.33 | |
% 250.44/59.33 | | REDUCE: (40), (97) imply:
% 250.44/59.33 | | (98) op(e4, e1) = e3
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (6), (27), (35), (98) are inconsistent by sub-proof #834.
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #226 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) all_252_11 = e1 & op(e2, e1) = e1
% 250.44/59.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (3) op(e2, e1) = all_38_2
% 250.44/59.33 (4) ~ (all_38_2 = e1)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | ALPHA: (1) implies:
% 250.44/59.33 | (5) op(e2, e1) = e1
% 250.44/59.33 |
% 250.44/59.33 | GROUND_INST: instantiating (2) with all_38_2, e1, e1, e2, simplifying with
% 250.44/59.33 | (3), (5) gives:
% 250.44/59.33 | (6) all_38_2 = e1
% 250.44/59.33 |
% 250.44/59.33 | REDUCE: (4), (6) imply:
% 250.44/59.33 | (7) $false
% 250.44/59.33 |
% 250.44/59.33 | CLOSE: (7) is inconsistent.
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #227 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.44/59.33 all_250_23 = e0
% 250.44/59.33 (2) ~ (all_26_2 = e2)
% 250.44/59.33 (3) op(all_4_2, e2) = e1
% 250.44/59.33 (4) ~ (all_244_24 = all_34_2)
% 250.44/59.33 (5) ~ (all_38_2 = e1)
% 250.44/59.33 (6) op(all_38_2, e1) = e2
% 250.44/59.33 (7) op(all_38_2, all_4_2) = e1
% 250.44/59.33 (8) ~ (all_244_24 = all_20_2)
% 250.44/59.33 (9) ~ (all_100_2 = e1)
% 250.44/59.33 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (11) op(e2, e2) = all_244_8
% 250.44/59.33 (12) all_46_1 = all_4_2
% 250.44/59.33 (13) op(e2, e1) = all_38_2
% 250.44/59.33 (14) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.44/59.33 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.44/59.33 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.44/59.33 (15) op(e1, e0) = all_34_2
% 250.44/59.33 (16) op(e4, e2) = all_6_2
% 250.44/59.33 (17) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.44/59.33 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.33 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.44/59.33 (18) ~ (e2 = e1)
% 250.44/59.33 (19) op(e0, e2) = all_28_2
% 250.44/59.33 (20) all_250_24 = all_244_24
% 250.44/59.33 (21) ~ (all_6_2 = e1)
% 250.44/59.33 (22) op(all_244_15, all_244_15) = e1
% 250.44/59.33 (23) ~ (all_28_2 = all_20_2)
% 250.44/59.33 (24) op(e2, e1) = e3
% 250.44/59.33 (25) ~ (all_8_2 = e1)
% 250.44/59.33 (26) ~ (all_244_15 = all_38_2)
% 250.44/59.33 (27) ~ (all_48_2 = all_8_2)
% 250.44/59.33 (28) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.44/59.33 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.44/59.33 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.44/59.33 (29) ~ (all_244_24 = e4)
% 250.44/59.33 (30) op(e4, e1) = all_26_2
% 250.44/59.33 (31) op(e3, e4) = all_100_2
% 250.44/59.33 (32) ~ (all_244_8 = e1)
% 250.44/59.33 (33) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.44/59.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.44/59.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.33 (34) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 |
% 250.44/59.33 all_250_24 = e0
% 250.44/59.33 (35) op(e1, e1) = all_244_15
% 250.44/59.33 (36) op(e0, e1) = all_20_2
% 250.44/59.33 (37) op(e3, e0) = all_48_2
% 250.44/59.33 (38) op(e1, e2) = all_46_1
% 250.44/59.33 (39) op(all_48_2, e0) = e3
% 250.44/59.33 (40) ~ (all_244_24 = e2)
% 250.44/59.33 (41) op(all_4_2, all_38_2) = e2
% 250.44/59.33 (42) op(all_244_3, all_244_3) = e3
% 250.44/59.33 (43) op(e3, e2) = all_8_2
% 250.44/59.33 (44) ~ (all_38_2 = all_20_2)
% 250.44/59.33 (45) ~ (all_244_24 = all_48_2)
% 250.44/59.33 (46) ~ (all_20_2 = e4)
% 250.44/59.33 (47) op(e3, e3) = all_244_3
% 250.44/59.33 (48) ~ (all_4_2 = e2)
% 250.44/59.33 (49) ~ (all_20_2 = e2)
% 250.44/59.33 (50) all_250_23 = all_20_2
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | GROUND_INST: instantiating (10) with all_38_2, e3, e1, e2, simplifying with
% 250.44/59.33 | (13), (24) gives:
% 250.44/59.33 | (51) all_38_2 = e3
% 250.44/59.33 |
% 250.44/59.33 | REDUCE: (26), (51) imply:
% 250.44/59.33 | (52) ~ (all_244_15 = e3)
% 250.44/59.33 |
% 250.44/59.33 | REDUCE: (44), (51) imply:
% 250.44/59.33 | (53) ~ (all_20_2 = e3)
% 250.44/59.33 |
% 250.44/59.33 | SIMP: (53) implies:
% 250.44/59.33 | (54) ~ (all_20_2 = e3)
% 250.44/59.33 |
% 250.44/59.33 | REDUCE: (12), (38) imply:
% 250.44/59.33 | (55) op(e1, e2) = all_4_2
% 250.44/59.33 |
% 250.44/59.33 | BETA: splitting (28) gives:
% 250.44/59.33 |
% 250.44/59.33 | Case 1:
% 250.44/59.33 | |
% 250.44/59.33 | | (56) ~ (all_48_2 = e1)
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (2), (3), (5), (9), (10), (11), (13), (17), (18), (22), (25),
% 250.44/59.33 | | (30), (31), (32), (33), (35), (36), (37), (41), (42), (43), (47),
% 250.44/59.33 | | (49), (52), (56) are inconsistent by sub-proof #230.
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (57) all_48_2 = e1
% 250.44/59.33 | |
% 250.44/59.33 | | REDUCE: (45), (57) imply:
% 250.44/59.33 | | (58) ~ (all_244_24 = e1)
% 250.44/59.33 | |
% 250.44/59.33 | | REDUCE: (27), (57) imply:
% 250.44/59.33 | | (59) ~ (all_8_2 = e1)
% 250.44/59.33 | |
% 250.44/59.33 | | REDUCE: (39), (57) imply:
% 250.44/59.33 | | (60) op(e1, e0) = e3
% 250.44/59.33 | |
% 250.44/59.33 | | GROUND_INST: instantiating (10) with all_34_2, e3, e0, e1, simplifying with
% 250.44/59.33 | | (15), (60) gives:
% 250.44/59.33 | | (61) all_34_2 = e3
% 250.44/59.33 | |
% 250.44/59.33 | | REDUCE: (4), (61) imply:
% 250.44/59.33 | | (62) ~ (all_244_24 = e3)
% 250.44/59.33 | |
% 250.44/59.33 | | BETA: splitting (34) gives:
% 250.44/59.33 | |
% 250.44/59.33 | | Case 1:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (63) all_250_24 = e4
% 250.44/59.33 | | |
% 250.44/59.33 | | | COMBINE_EQS: (20), (63) imply:
% 250.44/59.33 | | | (64) all_244_24 = e4
% 250.44/59.33 | | |
% 250.44/59.33 | | | SIMP: (64) implies:
% 250.44/59.33 | | | (65) all_244_24 = e4
% 250.44/59.33 | | |
% 250.44/59.33 | | | REDUCE: (29), (65) imply:
% 250.44/59.33 | | | (66) $false
% 250.44/59.33 | | |
% 250.44/59.33 | | | CLOSE: (66) is inconsistent.
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (67) all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 | all_250_24 =
% 250.44/59.33 | | | e0
% 250.44/59.33 | | |
% 250.44/59.33 | | | BETA: splitting (67) gives:
% 250.44/59.33 | | |
% 250.44/59.33 | | | Case 1:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (68) all_250_24 = e3
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | COMBINE_EQS: (20), (68) imply:
% 250.44/59.33 | | | | (69) all_244_24 = e3
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | SIMP: (69) implies:
% 250.44/59.33 | | | | (70) all_244_24 = e3
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | REDUCE: (62), (70) imply:
% 250.44/59.33 | | | | (71) $false
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | CLOSE: (71) is inconsistent.
% 250.44/59.33 | | | |
% 250.44/59.33 | | | Case 2:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (72) all_250_24 = e2 | all_250_24 = e1 | all_250_24 = e0
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | BETA: splitting (72) gives:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | Case 1:
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | (73) all_250_24 = e2
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | COMBINE_EQS: (20), (73) imply:
% 250.44/59.33 | | | | | (74) all_244_24 = e2
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | SIMP: (74) implies:
% 250.44/59.33 | | | | | (75) all_244_24 = e2
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | REDUCE: (40), (75) imply:
% 250.44/59.33 | | | | | (76) $false
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | CLOSE: (76) is inconsistent.
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | Case 2:
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | (77) all_250_24 = e1 | all_250_24 = e0
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | BETA: splitting (77) gives:
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | | Case 1:
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | (78) all_250_24 = e1
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | COMBINE_EQS: (20), (78) imply:
% 250.44/59.33 | | | | | | (79) all_244_24 = e1
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | SIMP: (79) implies:
% 250.44/59.33 | | | | | | (80) all_244_24 = e1
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | REDUCE: (58), (80) imply:
% 250.44/59.33 | | | | | | (81) $false
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | CLOSE: (81) is inconsistent.
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | Case 2:
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | (82) all_250_24 = e0
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | COMBINE_EQS: (20), (82) imply:
% 250.44/59.33 | | | | | | (83) all_244_24 = e0
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | SIMP: (83) implies:
% 250.44/59.33 | | | | | | (84) all_244_24 = e0
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | REDUCE: (8), (84) imply:
% 250.44/59.33 | | | | | | (85) ~ (all_20_2 = e0)
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | SIMP: (85) implies:
% 250.44/59.33 | | | | | | (86) ~ (all_20_2 = e0)
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | BETA: splitting (1) gives:
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | | Case 1:
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | (87) all_250_23 = e4
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | REF_CLOSE: (46), (50), (87) are inconsistent by sub-proof #784.
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | Case 2:
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | (88) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.44/59.33 | | | | | | | all_250_23 = e0
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | BETA: splitting (88) gives:
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | | Case 1:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | (89) all_250_23 = e3
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | REF_CLOSE: (50), (54), (89) are inconsistent by sub-proof #783.
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | Case 2:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | (90) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | BETA: splitting (90) gives:
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | | Case 1:
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | (91) all_250_23 = e2
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | REF_CLOSE: (49), (50), (91) are inconsistent by sub-proof
% 250.44/59.33 | | | | | | | | | #782.
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | Case 2:
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | (92) all_250_23 = e1 | all_250_23 = e0
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | BETA: splitting (92) gives:
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | | Case 1:
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | (93) all_250_23 = e1
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | COMBINE_EQS: (50), (93) imply:
% 250.44/59.33 | | | | | | | | | | (94) all_20_2 = e1
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | SIMP: (94) implies:
% 250.44/59.33 | | | | | | | | | | (95) all_20_2 = e1
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | REDUCE: (23), (95) imply:
% 250.44/59.33 | | | | | | | | | | (96) ~ (all_28_2 = e1)
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | REF_CLOSE: (6), (7), (10), (11), (14), (16), (19), (21),
% 250.44/59.33 | | | | | | | | | | (25), (32), (43), (48), (55), (96) are
% 250.44/59.33 | | | | | | | | | | inconsistent by sub-proof #228.
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | Case 2:
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | (97) all_250_23 = e0
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | COMBINE_EQS: (50), (97) imply:
% 250.44/59.33 | | | | | | | | | | (98) all_20_2 = e0
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | SIMP: (98) implies:
% 250.44/59.33 | | | | | | | | | | (99) all_20_2 = e0
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | REDUCE: (86), (99) imply:
% 250.44/59.33 | | | | | | | | | | (100) $false
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | | CLOSE: (100) is inconsistent.
% 250.44/59.33 | | | | | | | | | |
% 250.44/59.33 | | | | | | | | | End of split
% 250.44/59.33 | | | | | | | | |
% 250.44/59.33 | | | | | | | | End of split
% 250.44/59.33 | | | | | | | |
% 250.44/59.33 | | | | | | | End of split
% 250.44/59.33 | | | | | | |
% 250.44/59.33 | | | | | | End of split
% 250.44/59.33 | | | | | |
% 250.44/59.33 | | | | | End of split
% 250.44/59.33 | | | | |
% 250.44/59.33 | | | | End of split
% 250.44/59.33 | | | |
% 250.44/59.33 | | | End of split
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #228 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) op(all_38_2, e1) = e2
% 250.44/59.33 (2) op(all_38_2, all_4_2) = e1
% 250.44/59.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (4) op(e2, e2) = all_244_8
% 250.44/59.33 (5) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 250.44/59.33 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 250.44/59.33 | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.44/59.33 (6) op(e4, e2) = all_6_2
% 250.44/59.33 (7) op(e0, e2) = all_28_2
% 250.44/59.33 (8) ~ (all_28_2 = e1)
% 250.44/59.33 (9) ~ (all_6_2 = e1)
% 250.44/59.33 (10) ~ (all_8_2 = e1)
% 250.44/59.33 (11) ~ (all_244_8 = e1)
% 250.44/59.33 (12) op(e1, e2) = all_4_2
% 250.44/59.33 (13) op(e3, e2) = all_8_2
% 250.44/59.33 (14) ~ (all_4_2 = e2)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | BETA: splitting (5) gives:
% 250.44/59.33 |
% 250.44/59.33 | Case 1:
% 250.44/59.33 | |
% 250.44/59.33 | | (15) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 250.44/59.33 | | e1)
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (3), (6), (9), (10), (13), (15) are inconsistent by sub-proof
% 250.44/59.33 | | #928.
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (16) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.44/59.33 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.44/59.33 | |
% 250.44/59.33 | | BETA: splitting (16) gives:
% 250.44/59.33 | |
% 250.44/59.33 | | Case 1:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (17) all_252_8 = e1 & op(e2, e2) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | ALPHA: (17) implies:
% 250.44/59.33 | | | (18) op(e2, e2) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (3), (4), (11), (18) are inconsistent by sub-proof #690.
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (19) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 250.44/59.33 | | | e2) = e1)
% 250.44/59.33 | | |
% 250.44/59.33 | | | BETA: splitting (19) gives:
% 250.44/59.33 | | |
% 250.44/59.33 | | | Case 1:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (20) all_252_14 = e1 & op(e1, e2) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | REF_CLOSE: (1), (2), (3), (12), (14), (20) are inconsistent by sub-proof
% 250.44/59.33 | | | | #229.
% 250.44/59.33 | | | |
% 250.44/59.33 | | | Case 2:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (21) all_252_22 = e1 & op(e0, e2) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | ALPHA: (21) implies:
% 250.44/59.33 | | | | (22) op(e0, e2) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | REF_CLOSE: (3), (7), (8), (22) are inconsistent by sub-proof #907.
% 250.44/59.33 | | | |
% 250.44/59.33 | | | End of split
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #229 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) op(all_38_2, e1) = e2
% 250.44/59.33 (2) op(all_38_2, all_4_2) = e1
% 250.44/59.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (4) all_252_14 = e1 & op(e1, e2) = e1
% 250.44/59.33 (5) op(e1, e2) = all_4_2
% 250.44/59.33 (6) ~ (all_4_2 = e2)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | ALPHA: (4) implies:
% 250.44/59.33 | (7) op(e1, e2) = e1
% 250.44/59.33 |
% 250.44/59.33 | GROUND_INST: instantiating (3) with all_4_2, e1, e2, e1, simplifying with (5),
% 250.44/59.33 | (7) gives:
% 250.44/59.33 | (8) all_4_2 = e1
% 250.44/59.33 |
% 250.44/59.33 | REDUCE: (6), (8) imply:
% 250.44/59.33 | (9) ~ (e2 = e1)
% 250.44/59.33 |
% 250.44/59.33 | SIMP: (9) implies:
% 250.44/59.33 | (10) ~ (e2 = e1)
% 250.44/59.33 |
% 250.44/59.33 | REF_CLOSE: (1), (2), (3), (8), (10) are inconsistent by sub-proof #640.
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #230 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) ~ (all_26_2 = e2)
% 250.44/59.33 (2) op(all_4_2, e2) = e1
% 250.44/59.33 (3) ~ (all_38_2 = e1)
% 250.44/59.33 (4) ~ (all_100_2 = e1)
% 250.44/59.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (6) op(e2, e2) = all_244_8
% 250.44/59.33 (7) op(e2, e1) = all_38_2
% 250.44/59.33 (8) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 250.44/59.33 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.44/59.33 | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.44/59.33 (9) ~ (e2 = e1)
% 250.44/59.33 (10) op(all_244_15, all_244_15) = e1
% 250.44/59.33 (11) ~ (all_8_2 = e1)
% 250.44/59.33 (12) op(e4, e1) = all_26_2
% 250.44/59.33 (13) ~ (all_244_15 = e3)
% 250.44/59.33 (14) op(e3, e4) = all_100_2
% 250.44/59.33 (15) ~ (all_244_8 = e1)
% 250.44/59.33 (16) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.44/59.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.44/59.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.33 (17) op(e1, e1) = all_244_15
% 250.44/59.33 (18) op(e0, e1) = all_20_2
% 250.44/59.33 (19) op(e3, e0) = all_48_2
% 250.44/59.33 (20) op(all_4_2, all_38_2) = e2
% 250.44/59.33 (21) ~ (all_48_2 = e1)
% 250.44/59.33 (22) op(all_244_3, all_244_3) = e3
% 250.44/59.33 (23) op(e3, e2) = all_8_2
% 250.44/59.33 (24) op(e3, e3) = all_244_3
% 250.44/59.33 (25) ~ (all_20_2 = e2)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | BETA: splitting (8) gives:
% 250.44/59.33 |
% 250.44/59.33 | Case 1:
% 250.44/59.33 | |
% 250.44/59.33 | | (26) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 250.44/59.33 | | e1)
% 250.44/59.33 | |
% 250.44/59.33 | | BETA: splitting (26) gives:
% 250.44/59.33 | |
% 250.44/59.33 | | Case 1:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (27) all_252_2 = e1 & op(e3, e4) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | ALPHA: (27) implies:
% 250.44/59.33 | | | (28) op(e3, e4) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (4), (5), (14), (28) are inconsistent by sub-proof #628.
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (29) all_252_3 = e1 & op(e3, e3) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (5), (13), (17), (22), (24), (29) are inconsistent by sub-proof
% 250.44/59.33 | | | #632.
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (30) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.33 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.44/59.33 | |
% 250.44/59.33 | | BETA: splitting (30) gives:
% 250.44/59.33 | |
% 250.44/59.33 | | Case 1:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (31) all_252_5 = e1 & op(e3, e2) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | ALPHA: (31) implies:
% 250.44/59.33 | | | (32) op(e3, e2) = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (5), (11), (23), (32) are inconsistent by sub-proof #929.
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (33) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 250.44/59.33 | | | e0) = e1)
% 250.44/59.33 | | |
% 250.44/59.33 | | | BETA: splitting (33) gives:
% 250.44/59.33 | | |
% 250.44/59.33 | | | Case 1:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (34) all_252_10 = e1 & op(e3, e1) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | ALPHA: (34) implies:
% 250.44/59.33 | | | | (35) all_252_10 = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12), (15), (16),
% 250.44/59.33 | | | | (17), (18), (20), (25), (35) are inconsistent by sub-proof
% 250.44/59.33 | | | | #231.
% 250.44/59.33 | | | |
% 250.44/59.33 | | | Case 2:
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | (36) all_252_17 = e1 & op(e3, e0) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | ALPHA: (36) implies:
% 250.44/59.33 | | | | (37) op(e3, e0) = e1
% 250.44/59.33 | | | |
% 250.44/59.33 | | | | REF_CLOSE: (5), (19), (21), (37) are inconsistent by sub-proof #889.
% 250.44/59.33 | | | |
% 250.44/59.33 | | | End of split
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #231 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) ~ (all_26_2 = e2)
% 250.44/59.33 (2) op(all_4_2, e2) = e1
% 250.44/59.33 (3) ~ (all_38_2 = e1)
% 250.44/59.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (5) op(e2, e2) = all_244_8
% 250.44/59.33 (6) op(e2, e1) = all_38_2
% 250.44/59.33 (7) ~ (e2 = e1)
% 250.44/59.33 (8) op(all_244_15, all_244_15) = e1
% 250.44/59.33 (9) op(e4, e1) = all_26_2
% 250.44/59.33 (10) ~ (all_244_8 = e1)
% 250.44/59.33 (11) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.44/59.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.44/59.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.33 (12) op(e1, e1) = all_244_15
% 250.44/59.33 (13) op(e0, e1) = all_20_2
% 250.44/59.33 (14) all_252_10 = e1
% 250.44/59.33 (15) op(all_4_2, all_38_2) = e2
% 250.44/59.33 (16) ~ (all_20_2 = e2)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | BETA: splitting (11) gives:
% 250.44/59.33 |
% 250.44/59.33 | Case 1:
% 250.44/59.33 | |
% 250.44/59.33 | | (17) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.44/59.33 | | e2)
% 250.44/59.33 | |
% 250.44/59.33 | | BETA: splitting (17) gives:
% 250.44/59.33 | |
% 250.44/59.33 | | Case 1:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (18) all_252_9 = e2 & op(e4, e1) = e2
% 250.44/59.33 | | |
% 250.44/59.33 | | | REF_CLOSE: (1), (4), (9), (18) are inconsistent by sub-proof #970.
% 250.44/59.33 | | |
% 250.44/59.33 | | Case 2:
% 250.44/59.33 | | |
% 250.44/59.33 | | | (19) all_252_10 = e2 & op(e3, e1) = e2
% 250.44/59.33 | | |
% 250.44/59.33 | | | ALPHA: (19) implies:
% 250.44/59.33 | | | (20) all_252_10 = e2
% 250.44/59.33 | | |
% 250.44/59.33 | | | COMBINE_EQS: (14), (20) imply:
% 250.44/59.33 | | | (21) e2 = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | SIMP: (21) implies:
% 250.44/59.33 | | | (22) e2 = e1
% 250.44/59.33 | | |
% 250.44/59.33 | | | REDUCE: (7), (22) imply:
% 250.44/59.33 | | | (23) $false
% 250.44/59.33 | | |
% 250.44/59.33 | | | CLOSE: (23) is inconsistent.
% 250.44/59.33 | | |
% 250.44/59.33 | | End of split
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (24) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 250.44/59.33 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (12), (13), (15), (16), (24)
% 250.44/59.33 | | are inconsistent by sub-proof #737.
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #232 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) ~ (all_244_3 = e2)
% 250.44/59.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (3) op(e3, e4) = all_100_2
% 250.44/59.33 (4) ~ (all_100_2 = e2)
% 250.44/59.33 (5) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.44/59.33 (6) op(e3, e3) = all_244_3
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.33 | BETA: splitting (5) gives:
% 250.44/59.33 |
% 250.44/59.33 | Case 1:
% 250.44/59.33 | |
% 250.44/59.33 | | (7) all_252_2 = e2 & op(e3, e4) = e2
% 250.44/59.33 | |
% 250.44/59.33 | | ALPHA: (7) implies:
% 250.44/59.33 | | (8) op(e3, e4) = e2
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #233.
% 250.44/59.33 | |
% 250.44/59.33 | Case 2:
% 250.44/59.33 | |
% 250.44/59.33 | | (9) all_252_3 = e2 & op(e3, e3) = e2
% 250.44/59.33 | |
% 250.44/59.33 | | ALPHA: (9) implies:
% 250.44/59.33 | | (10) op(e3, e3) = e2
% 250.44/59.33 | |
% 250.44/59.33 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #694.
% 250.44/59.33 | |
% 250.44/59.33 | End of split
% 250.44/59.33 |
% 250.44/59.33 End of proof
% 250.44/59.33
% 250.44/59.33 Sub-proof #233 shows that the following formulas are inconsistent:
% 250.44/59.33 ----------------------------------------------------------------
% 250.44/59.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.33 (2) op(e3, e4) = all_100_2
% 250.44/59.33 (3) op(e3, e4) = e2
% 250.44/59.33 (4) ~ (all_100_2 = e2)
% 250.44/59.33
% 250.44/59.33 Begin of proof
% 250.44/59.33 |
% 250.44/59.34 | GROUND_INST: instantiating (1) with all_100_2, e2, e4, e3, simplifying with
% 250.44/59.34 | (2), (3) gives:
% 250.44/59.34 | (5) all_100_2 = e2
% 250.44/59.34 |
% 250.44/59.34 | REDUCE: (4), (5) imply:
% 250.44/59.34 | (6) $false
% 250.44/59.34 |
% 250.44/59.34 | CLOSE: (6) is inconsistent.
% 250.44/59.34 |
% 250.44/59.34 End of proof
% 250.44/59.34
% 250.44/59.34 Sub-proof #234 shows that the following formulas are inconsistent:
% 250.44/59.34 ----------------------------------------------------------------
% 250.44/59.34 (1) ~ (all_10_2 = e4)
% 250.44/59.34 (2) op(e4, e0) = all_30_2
% 250.44/59.34 (3) op(e2, all_26_2) = e4
% 250.44/59.34 (4) op(all_38_2, e1) = e2
% 250.44/59.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.34 (6) op(e2, e3) = all_10_2
% 250.44/59.34 (7) op(all_244_8, all_244_8) = e2
% 250.44/59.34 (8) op(e2, e2) = all_244_8
% 250.44/59.34 (9) all_252_6 = e1
% 250.44/59.34 (10) op(e2, e1) = all_38_2
% 250.44/59.34 (11) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 250.44/59.34 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 250.44/59.34 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 250.44/59.34 (12) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.44/59.34 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.44/59.34 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.44/59.34 (13) ~ (e4 = e1)
% 250.44/59.34 (14) ~ (all_244_0 = e2)
% 250.44/59.34 (15) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.44/59.34 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.44/59.34 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.44/59.34 (16) ~ (all_30_2 = e2)
% 250.44/59.34 (17) op(e3, e1) = all_36_2
% 250.44/59.34 (18) op(all_40_2, e0) = e2
% 250.44/59.34 (19) ~ (all_244_15 = all_38_2)
% 250.44/59.34 (20) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.44/59.34 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.44/59.34 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.44/59.34 (21) op(e4, e1) = all_26_2
% 250.44/59.34 (22) op(e4, e4) = all_244_0
% 250.44/59.34 (23) op(e1, e1) = all_244_15
% 250.44/59.34 (24) op(e0, e1) = all_20_2
% 250.44/59.34 (25) ~ (all_38_2 = all_36_2)
% 250.44/59.34 (26) ~ (e4 = e2)
% 250.44/59.34 (27) ~ (all_38_2 = all_20_2)
% 250.44/59.34 (28) op(e2, e0) = all_40_2
% 250.44/59.34
% 250.44/59.34 Begin of proof
% 250.44/59.34 |
% 250.44/59.34 | BETA: splitting (11) gives:
% 250.44/59.34 |
% 250.44/59.34 | Case 1:
% 250.44/59.34 | |
% 250.44/59.34 | | (29) ~ (all_38_2 = e4)
% 250.44/59.34 | |
% 250.44/59.34 | | BETA: splitting (15) gives:
% 250.44/59.34 | |
% 250.44/59.34 | | Case 1:
% 250.44/59.34 | | |
% 250.44/59.34 | | | (30) ~ (all_40_2 = e4)
% 250.44/59.34 | | |
% 250.44/59.34 | | | BETA: splitting (20) gives:
% 250.44/59.34 | | |
% 250.44/59.34 | | | Case 1:
% 250.44/59.34 | | | |
% 250.44/59.34 | | | | (31) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 250.44/59.34 | | | | e3) = e4)
% 250.44/59.34 | | | |
% 250.44/59.34 | | | | REF_CLOSE: (1), (5), (6), (9), (13), (31) are inconsistent by sub-proof
% 250.44/59.34 | | | | #236.
% 250.44/59.34 | | | |
% 250.44/59.34 | | | Case 2:
% 250.44/59.34 | | | |
% 250.44/59.34 | | | | (32) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2,
% 250.44/59.34 | | | | e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.44/59.34 | | | |
% 250.44/59.34 | | | | BETA: splitting (32) gives:
% 250.44/59.34 | | | |
% 250.44/59.34 | | | | Case 1:
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | | (33) all_252_8 = e4 & op(e2, e2) = e4
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | | ALPHA: (33) implies:
% 250.44/59.34 | | | | | (34) op(e2, e2) = e4
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | | REF_CLOSE: (5), (7), (8), (14), (22), (34) are inconsistent by
% 250.44/59.34 | | | | | sub-proof #626.
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | Case 2:
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | | (35) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 250.44/59.34 | | | | | op(e2, e0) = e4)
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | | REF_CLOSE: (5), (10), (28), (29), (30), (35) are inconsistent by
% 250.44/59.34 | | | | | sub-proof #933.
% 250.44/59.34 | | | | |
% 250.44/59.34 | | | | End of split
% 250.44/59.34 | | | |
% 250.44/59.34 | | | End of split
% 250.44/59.34 | | |
% 250.44/59.34 | | Case 2:
% 250.44/59.34 | | |
% 250.44/59.34 | | | (36) all_40_2 = e4
% 250.44/59.34 | | |
% 250.44/59.34 | | | REDUCE: (18), (36) imply:
% 250.44/59.34 | | | (37) op(e4, e0) = e2
% 250.44/59.34 | | |
% 250.44/59.34 | | | REF_CLOSE: (2), (5), (16), (37) are inconsistent by sub-proof #830.
% 250.44/59.34 | | |
% 250.44/59.34 | | End of split
% 250.44/59.34 | |
% 250.44/59.34 | Case 2:
% 250.44/59.34 | |
% 250.44/59.34 | | (38) all_38_2 = e4
% 250.44/59.34 | |
% 250.44/59.34 | | REF_CLOSE: (3), (4), (5), (7), (8), (12), (14), (17), (19), (21), (22),
% 250.44/59.34 | | (23), (24), (25), (26), (27), (38) are inconsistent by sub-proof
% 250.44/59.34 | | #235.
% 250.44/59.34 | |
% 250.44/59.34 | End of split
% 250.44/59.34 |
% 250.44/59.34 End of proof
% 250.44/59.34
% 250.44/59.34 Sub-proof #235 shows that the following formulas are inconsistent:
% 250.44/59.34 ----------------------------------------------------------------
% 250.44/59.34 (1) op(e2, all_26_2) = e4
% 250.44/59.34 (2) op(all_38_2, e1) = e2
% 250.44/59.34 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.34 (4) op(all_244_8, all_244_8) = e2
% 250.44/59.34 (5) op(e2, e2) = all_244_8
% 250.44/59.34 (6) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.44/59.34 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.44/59.34 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.44/59.34 (7) ~ (all_244_0 = e2)
% 250.44/59.34 (8) op(e3, e1) = all_36_2
% 250.44/59.34 (9) ~ (all_244_15 = all_38_2)
% 250.44/59.34 (10) all_38_2 = e4
% 250.44/59.34 (11) op(e4, e1) = all_26_2
% 250.44/59.34 (12) op(e4, e4) = all_244_0
% 250.44/59.34 (13) op(e1, e1) = all_244_15
% 250.44/59.34 (14) op(e0, e1) = all_20_2
% 250.44/59.34 (15) ~ (all_38_2 = all_36_2)
% 250.44/59.34 (16) ~ (e4 = e2)
% 250.44/59.34 (17) ~ (all_38_2 = all_20_2)
% 250.44/59.34
% 250.44/59.34 Begin of proof
% 250.44/59.34 |
% 250.44/59.34 | REDUCE: (9), (10) imply:
% 250.44/59.34 | (18) ~ (all_244_15 = e4)
% 250.44/59.34 |
% 250.44/59.34 | REDUCE: (10), (15) imply:
% 250.44/59.34 | (19) ~ (all_36_2 = e4)
% 250.44/59.34 |
% 250.44/59.34 | SIMP: (19) implies:
% 250.44/59.34 | (20) ~ (all_36_2 = e4)
% 250.44/59.34 |
% 250.44/59.34 | REDUCE: (10), (17) imply:
% 250.44/59.34 | (21) ~ (all_20_2 = e4)
% 250.44/59.34 |
% 250.44/59.34 | SIMP: (21) implies:
% 250.44/59.34 | (22) ~ (all_20_2 = e4)
% 250.44/59.34 |
% 250.44/59.34 | REDUCE: (2), (10) imply:
% 250.44/59.34 | (23) op(e4, e1) = e2
% 250.44/59.34 |
% 250.44/59.34 | BETA: splitting (6) gives:
% 250.44/59.34 |
% 250.44/59.34 | Case 1:
% 250.44/59.34 | |
% 250.44/59.34 | | (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.44/59.34 | | e4)
% 250.44/59.34 | |
% 250.44/59.34 | | REF_CLOSE: (3), (8), (11), (16), (20), (23), (24) are inconsistent by
% 250.44/59.34 | | sub-proof #795.
% 250.44/59.34 | |
% 250.44/59.34 | Case 2:
% 250.44/59.34 | |
% 250.44/59.34 | | (25) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 250.44/59.34 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.44/59.34 | |
% 250.44/59.34 | | BETA: splitting (25) gives:
% 250.44/59.34 | |
% 250.44/59.34 | | Case 1:
% 250.44/59.34 | | |
% 250.44/59.34 | | |
% 250.44/59.34 | | | GROUND_INST: instantiating (3) with all_26_2, e2, e1, e4, simplifying with
% 250.44/59.34 | | | (11), (23) gives:
% 250.44/59.34 | | | (26) all_26_2 = e2
% 250.44/59.34 | | |
% 250.44/59.34 | | | REDUCE: (1), (26) imply:
% 250.44/59.34 | | | (27) op(e2, e2) = e4
% 250.44/59.34 | | |
% 250.44/59.34 | | | REF_CLOSE: (3), (4), (5), (7), (12), (27) are inconsistent by sub-proof
% 250.44/59.34 | | | #626.
% 250.44/59.34 | | |
% 250.44/59.34 | | Case 2:
% 250.44/59.34 | | |
% 250.44/59.34 | | | (28) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0,
% 250.44/59.34 | | | e1) = e4)
% 250.44/59.34 | | |
% 250.44/59.34 | | | REF_CLOSE: (3), (13), (14), (18), (22), (28) are inconsistent by sub-proof
% 250.44/59.34 | | | #750.
% 250.44/59.34 | | |
% 250.44/59.34 | | End of split
% 250.44/59.34 | |
% 250.44/59.34 | End of split
% 250.44/59.34 |
% 250.44/59.34 End of proof
% 250.44/59.34
% 250.44/59.34 Sub-proof #236 shows that the following formulas are inconsistent:
% 250.44/59.34 ----------------------------------------------------------------
% 250.44/59.34 (1) ~ (all_10_2 = e4)
% 250.44/59.34 (2) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.44/59.34 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.34 (4) op(e2, e3) = all_10_2
% 250.44/59.34 (5) all_252_6 = e1
% 250.44/59.34 (6) ~ (e4 = e1)
% 250.44/59.34
% 250.44/59.34 Begin of proof
% 250.44/59.34 |
% 250.44/59.34 | BETA: splitting (2) gives:
% 250.44/59.34 |
% 250.44/59.34 | Case 1:
% 250.44/59.34 | |
% 250.44/59.34 | | (7) all_252_6 = e4 & op(e2, e4) = e4
% 250.44/59.34 | |
% 250.44/59.34 | | ALPHA: (7) implies:
% 250.44/59.34 | | (8) all_252_6 = e4
% 250.44/59.34 | |
% 250.44/59.34 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #844.
% 250.44/59.34 | |
% 250.44/59.34 | Case 2:
% 250.44/59.34 | |
% 250.44/59.34 | | (9) all_252_7 = e4 & op(e2, e3) = e4
% 250.44/59.34 | |
% 250.44/59.34 | | ALPHA: (9) implies:
% 250.44/59.34 | | (10) op(e2, e3) = e4
% 250.44/59.34 | |
% 250.44/59.34 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #953.
% 250.44/59.34 | |
% 250.44/59.34 | End of split
% 250.44/59.34 |
% 250.44/59.34 End of proof
% 250.44/59.34
% 250.44/59.34 Sub-proof #237 shows that the following formulas are inconsistent:
% 250.44/59.34 ----------------------------------------------------------------
% 250.44/59.34 (1) ~ (all_244_8 = all_4_2)
% 250.44/59.34 (2) ~ (all_30_2 = all_26_2)
% 250.44/59.34 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.44/59.34 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.44/59.34 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.44/59.34 (4) ~ (all_4_2 = e4)
% 250.44/59.34 (5) ~ (all_10_2 = e4)
% 250.44/59.34 (6) ~ (all_244_0 = all_30_2)
% 250.44/59.34 (7) op(all_4_2, e2) = e1
% 250.44/59.34 (8) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.44/59.34 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.44/59.34 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.44/59.34 (9) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.44/59.34 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.44/59.34 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.44/59.34 (10) op(e4, e1) = e0
% 250.44/59.34 (11) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.44/59.34 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.44/59.34 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.44/59.34 (12) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.44/59.34 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.44/59.34 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.44/59.34 (13) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.44/59.34 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.44/59.34 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.44/59.34 (14) op(e4, e0) = all_30_2
% 250.44/59.34 (15) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.44/59.34 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.44/59.34 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.44/59.34 (16) all_250_8 = all_36_2
% 250.44/59.34 (17) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.44/59.34 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.44/59.34 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.44/59.34 (18) op(all_62_2, all_36_2) = e3
% 250.44/59.34 (19) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 250.44/59.34 all_250_15 = e0
% 250.44/59.34 (20) ~ (all_28_2 = all_6_2)
% 250.44/59.34 (21) ~ (e2 = e0)
% 250.44/59.34 (22) op(all_38_2, all_4_2) = e1
% 250.44/59.34 (23) ~ (e1 = e0)
% 250.44/59.34 (24) ~ (all_22_2 = e3)
% 250.44/59.34 (25) ~ (all_28_2 = e3)
% 250.44/59.34 (26) ~ (all_62_2 = all_22_2)
% 250.44/59.34 (27) op(e3, e4) = e0
% 250.44/59.34 (28) op(e4, all_34_2) = e1
% 250.44/59.34 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.34 (30) op(e2, e3) = all_10_2
% 250.44/59.34 (31) ~ (e3 = e2)
% 250.44/59.34 (32) op(e0, e0) = all_244_24
% 250.44/59.34 (33) ~ (all_30_2 = all_6_2)
% 250.44/59.34 (34) op(e2, e2) = all_244_8
% 250.44/59.34 (35) all_72_2 = all_22_2
% 250.44/59.34 (36) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.44/59.34 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.44/59.34 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.44/59.34 (37) all_146_2 = e0
% 250.44/59.34 (38) op(e2, e1) = all_38_2
% 250.44/59.34 (39) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.44/59.34 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.44/59.34 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.44/59.34 (40) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 250.44/59.34 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 250.44/59.34 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 250.44/59.34 (41) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.44/59.34 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.44/59.34 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.44/59.34 (42) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.44/59.34 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.44/59.34 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.44/59.34 (43) ~ (all_244_15 = all_26_2)
% 250.44/59.34 (44) all_216_2 = all_26_2
% 250.44/59.34 (45) op(e1, e0) = all_34_2
% 250.44/59.34 (46) op(all_28_2, e2) = e0
% 250.44/59.34 (47) op(e4, e2) = all_6_2
% 250.44/59.34 (48) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.44/59.34 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.34 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.44/59.34 (49) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 250.44/59.34 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 250.44/59.34 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.44/59.34 (50) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.44/59.34 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.44/59.34 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.44/59.34 (51) all_78_2 = all_10_2
% 250.44/59.34 (52) ~ (all_8_2 = all_4_2)
% 250.44/59.34 (53) ~ (all_244_15 = e4)
% 250.44/59.34 (54) ~ (e2 = e1)
% 250.44/59.34 (55) op(all_26_2, e1) = e4
% 250.44/59.34 (56) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.44/59.34 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.44/59.34 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.44/59.34 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.44/59.34 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.44/59.34 op(e0, e1) = e0)))
% 250.44/59.34 (57) op(e0, e2) = all_28_2
% 250.44/59.34 (58) ~ (e4 = e1)
% 250.44/59.34 (59) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.44/59.34 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.44/59.34 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.44/59.34 (60) ~ (all_6_2 = e1)
% 250.44/59.34 (61) op(e1, e4) = all_20_1
% 250.44/59.34 (62) ~ (all_244_8 = all_38_2)
% 250.44/59.34 (63) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.44/59.34 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.44/59.34 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.44/59.34 (64) op(all_244_15, all_244_15) = e1
% 250.44/59.34 (65) all_250_21 = all_22_2
% 250.44/59.34 (66) all_50_2 = all_4_2
% 250.44/59.34 (67) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.44/59.34 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.44/59.34 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.44/59.34 (68) op(e1, e4) = all_16_2
% 250.44/59.34 (69) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 250.44/59.34 all_250_2 = e0
% 250.44/59.34 (70) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.44/59.34 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.44/59.34 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.44/59.34 (71) op(e1, e3) = all_62_2
% 250.44/59.34 (72) ~ (e3 = e0)
% 250.44/59.34 (73) ~ (all_48_2 = all_36_2)
% 250.44/59.34 (74) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.44/59.34 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.44/59.34 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.44/59.34 (75) all_252_2 = e0
% 250.44/59.34 (76) ~ (all_36_2 = e4)
% 250.44/59.34 (77) ~ (all_22_2 = e4)
% 250.44/59.34 (78) all_70_2 = all_62_2
% 250.44/59.34 (79) ~ (all_36_2 = all_8_2)
% 250.44/59.34 (80) ~ (e3 = e1)
% 250.44/59.34 (81) op(all_48_2, all_22_2) = e0
% 250.44/59.34 (82) op(e3, e1) = all_36_2
% 250.44/59.34 (83) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.44/59.34 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.44/59.34 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.44/59.34 (84) ~ (all_16_2 = e2)
% 250.44/59.34 (85) ~ (all_8_2 = e1)
% 250.44/59.34 (86) op(all_40_2, e0) = e2
% 250.44/59.34 (87) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.44/59.34 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.44/59.34 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.44/59.34 (88) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 250.44/59.34 all_250_8 = e0
% 250.44/59.34 (89) ~ (all_28_2 = all_4_2)
% 250.44/59.34 (90) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.44/59.34 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.44/59.34 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.44/59.34 (91) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.44/59.34 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.44/59.34 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.44/59.34 (92) ~ (all_72_2 = e1) | ( ~ (all_72_0 = e4) & op(e3, e1) = all_72_1 &
% 250.44/59.34 op(e1, all_72_1) = all_72_0 & $i(all_72_0) & $i(all_72_1)) | ( ~
% 250.44/59.34 (all_72_1 = e2) & op(e3, e1) = all_72_1 & $i(all_72_1))
% 250.44/59.34 (93) ~ (all_244_15 = all_38_2)
% 250.44/59.34 (94) ~ (all_48_2 = all_8_2)
% 250.44/59.34 (95) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.44/59.34 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.44/59.34 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.44/59.34 (96) ~ (all_36_2 = all_26_2)
% 250.44/59.34 (97) ~ (all_8_2 = e0)
% 250.44/59.34 (98) all_60_2 = e4
% 250.44/59.34 (99) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.44/59.34 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.44/59.34 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.44/59.34 (100) ~ (all_38_2 = e4)
% 250.44/59.34 (101) ~ (all_28_2 = e4)
% 250.44/59.34 (102) ~ (all_26_2 = all_6_2)
% 250.44/59.34 (103) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 250.44/59.34 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 250.44/59.34 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.44/59.34 (104) op(all_22_2, e3) = e0
% 250.44/59.34 (105) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0
% 250.44/59.34 & op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~
% 250.44/59.34 (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 250.44/59.34 (106) op(e0, e3) = all_22_2
% 250.44/59.34 (107) ~ (all_26_2 = e4)
% 250.44/59.34 (108) ~ (all_28_2 = all_22_2)
% 250.44/59.34 (109) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.44/59.34 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.44/59.34 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.44/59.34 (110) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.44/59.34 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.44/59.34 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.44/59.34 (111) op(all_62_2, e3) = e1
% 250.44/59.34 (112) op(e4, e1) = all_26_2
% 250.44/59.34 (113) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.44/59.34 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.44/59.34 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.44/59.34 (114) op(all_10_2, e3) = e2
% 250.44/59.34 (115) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 250.44/59.34 all_250_21 = e0
% 250.44/59.34 (116) ~ (all_62_2 = all_16_2)
% 250.44/59.34 (117) ~ (all_8_2 = all_6_2)
% 250.44/59.34 (118) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 250.44/59.34 op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~
% 250.44/59.34 (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 250.44/59.34 (119) all_250_15 = all_16_2
% 250.44/59.34 (120) op(e4, e4) = all_244_0
% 250.44/59.34 (121) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.44/59.34 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 250.44/59.34 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.34 (122) ~ (e4 = e3)
% 250.44/59.34 (123) op(e1, e1) = all_244_15
% 250.44/59.34 (124) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.44/59.34 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.44/59.34 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.44/59.34 (125) op(e0, e1) = all_20_2
% 250.44/59.34 (126) op(e3, e0) = all_48_2
% 250.44/59.34 (127) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 250.44/59.34 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 250.44/59.34 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.44/59.34 (128) op(all_48_2, e0) = e3
% 250.44/59.34 (129) ~ (all_38_2 = all_36_2)
% 250.44/59.34 (130) all_82_2 = all_28_2
% 250.44/59.34 (131) op(e1, e2) = all_4_2
% 250.44/59.34 (132) op(e3, all_30_2) = e4
% 250.44/59.34 (133) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.44/59.34 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.44/59.34 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.44/59.34 (134) ~ (all_28_2 = all_8_2)
% 250.44/59.34 (135) ~ (all_48_2 = e0)
% 250.44/59.34 (136) op(e4, e3) = all_84_2
% 250.44/59.34 (137) op(all_244_3, all_244_3) = e3
% 250.44/59.34 (138) ~ (all_62_2 = all_10_2)
% 250.44/59.34 (139) op(e2, e4) = all_64_2
% 250.44/59.34 (140) ~ (all_38_2 = all_26_2)
% 250.44/59.34 (141) ~ (all_6_2 = all_4_2)
% 250.44/59.34 (142) ~ (e4 = e2)
% 250.44/59.34 (143) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.34 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 250.44/59.34 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.44/59.34 (144) op(e3, e2) = all_8_2
% 250.44/59.34 (145) op(all_36_2, e1) = e3
% 250.44/59.34 (146) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.44/59.34 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.44/59.34 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.44/59.34 (147) ~ (all_244_15 = all_36_2)
% 250.44/59.34 (148) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.44/59.34 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.44/59.34 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.44/59.34 (149) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.44/59.34 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.44/59.34 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.44/59.34 (150) ~ (all_244_3 = e0)
% 250.44/59.34 (151) op(e2, e0) = all_40_2
% 250.44/59.34 (152) ~ (all_20_2 = e3)
% 250.44/59.34 (153) ~ (all_16_2 = e3)
% 250.44/59.34 (154) ~ (all_244_8 = all_28_2)
% 250.44/59.34 (155) all_252_23 = e4
% 250.44/59.34 (156) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.44/59.34 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.44/59.34 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.44/59.34 (157) op(e3, e3) = all_244_3
% 250.44/59.34 (158) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.44/59.34 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.44/59.34 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.44/59.34 (159) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.44/59.34 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.44/59.34 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.44/59.34 (160) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.44/59.34 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.44/59.34 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.44/59.34 (161) op(all_26_2, all_16_2) = e1
% 250.44/59.34 (162) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.44/59.34 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.44/59.34 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.44/59.34 (163) all_250_2 = all_6_2
% 250.44/59.34 (164) all_46_2 = all_36_2
% 250.44/59.34 (165) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 250.44/59.34 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 250.44/59.34 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 250.44/59.34 (166) ~ (all_146_2 = e0) | ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 250.44/59.34 op(e0, all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)) | ( ~
% 250.44/59.34 (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1))
% 250.44/59.34 (167) op(all_244_24, all_244_24) = e0
% 250.44/59.34 (168) ~ (all_16_2 = e0)
% 250.44/59.35 (169) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 250.44/59.35 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 250.44/59.35 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 250.44/59.35 (170) op(all_64_2, all_6_2) = e4
% 250.44/59.35 (171) all_252_20 = e3
% 250.44/59.35
% 250.44/59.35 Begin of proof
% 250.44/59.35 |
% 250.44/59.35 | BETA: splitting (105) gives:
% 250.44/59.35 |
% 250.44/59.35 | Case 1:
% 250.44/59.35 | |
% 250.44/59.35 | | (172) ~ (all_60_2 = e4)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (98), (172) imply:
% 250.44/59.35 | | (173) $false
% 250.44/59.35 | |
% 250.44/59.35 | | CLOSE: (173) is inconsistent.
% 250.44/59.35 | |
% 250.44/59.35 | Case 2:
% 250.44/59.35 | |
% 250.44/59.35 | | (174) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 250.44/59.35 | | all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 = e3) &
% 250.44/59.35 | | op(e1, e4) = all_60_1 & $i(all_60_1))
% 250.44/59.35 | |
% 250.44/59.35 | | GROUND_INST: instantiating (29) with all_16_2, all_20_1, e4, e1, simplifying
% 250.44/59.35 | | with (61), (68) gives:
% 250.44/59.35 | | (175) all_20_1 = all_16_2
% 250.44/59.35 | |
% 250.44/59.35 | | GROUND_INST: instantiating (29) with all_26_2, e0, e1, e4, simplifying with
% 250.44/59.35 | | (10), (112) gives:
% 250.44/59.35 | | (176) all_26_2 = e0
% 250.44/59.35 | |
% 250.44/59.35 | | COMBINE_EQS: (44), (176) imply:
% 250.44/59.35 | | (177) all_216_2 = e0
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (43), (176) imply:
% 250.44/59.35 | | (178) ~ (all_244_15 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (140), (176) imply:
% 250.44/59.35 | | (179) ~ (all_38_2 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (96), (176) imply:
% 250.44/59.35 | | (180) ~ (all_36_2 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (2), (176) imply:
% 250.44/59.35 | | (181) ~ (all_30_2 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (102), (176) imply:
% 250.44/59.35 | | (182) ~ (all_6_2 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | SIMP: (182) implies:
% 250.44/59.35 | | (183) ~ (all_6_2 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | REDUCE: (107), (176) imply:
% 250.44/59.35 | | (184) ~ (e4 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | SIMP: (184) implies:
% 250.44/59.35 | | (185) ~ (e4 = e0)
% 250.44/59.35 | |
% 250.44/59.35 | | BETA: splitting (11) gives:
% 250.44/59.35 | |
% 250.44/59.35 | | Case 1:
% 250.44/59.35 | | |
% 250.44/59.35 | | | (186) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3,
% 250.44/59.35 | | | e1) = e0)
% 250.44/59.35 | | |
% 250.44/59.35 | | | BETA: splitting (186) gives:
% 250.44/59.35 | | |
% 250.44/59.35 | | | Case 1:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (187) all_252_9 = e0 & op(e4, e1) = e0
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | ALPHA: (187) implies:
% 250.44/59.35 | | | | (188) all_252_9 = e0
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | BETA: splitting (174) gives:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | Case 1:
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | (189) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4)
% 250.44/59.35 | | | | | = all_60_1 & $i(all_60_0) & $i(all_60_1)
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | ALPHA: (189) implies:
% 250.44/59.35 | | | | | (190) op(e1, e4) = all_60_1
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 250.44/59.35 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.44/59.35 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 250.44/59.35 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (45),
% 250.44/59.35 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 250.44/59.35 | | | | | (56), (57), (58), (59), (60), (62), (63), (64), (65), (66),
% 250.44/59.35 | | | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 250.44/59.35 | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 250.44/59.35 | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95), (97),
% 250.44/59.35 | | | | | (99), (100), (101), (103), (104), (106), (108), (109),
% 250.44/59.35 | | | | | (110), (111), (113), (114), (115), (116), (117), (118),
% 250.44/59.35 | | | | | (119), (120), (121), (122), (123), (124), (125), (126),
% 250.44/59.35 | | | | | (127), (128), (129), (130), (131), (132), (133), (134),
% 250.44/59.35 | | | | | (135), (136), (137), (138), (139), (141), (142), (143),
% 250.44/59.35 | | | | | (144), (145), (146), (147), (148), (149), (150), (151),
% 250.44/59.35 | | | | | (152), (153), (154), (155), (156), (157), (158), (159),
% 250.44/59.35 | | | | | (160), (161), (162), (163), (164), (165), (166), (167),
% 250.44/59.35 | | | | | (168), (169), (170), (171), (177), (178), (180), (181),
% 250.44/59.35 | | | | | (183), (185), (188), (190) are inconsistent by sub-proof
% 250.44/59.35 | | | | | #238.
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | Case 2:
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | (191) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1)
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | ALPHA: (191) implies:
% 250.44/59.35 | | | | | (192) op(e1, e4) = all_60_1
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 250.44/59.35 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.44/59.35 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 250.44/59.35 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (45),
% 250.44/59.35 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 250.44/59.35 | | | | | (56), (57), (58), (59), (60), (62), (63), (64), (65), (66),
% 250.44/59.35 | | | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 250.44/59.35 | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 250.44/59.35 | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95), (97),
% 250.44/59.35 | | | | | (99), (100), (101), (103), (104), (106), (108), (109),
% 250.44/59.35 | | | | | (110), (111), (113), (114), (115), (116), (117), (118),
% 250.44/59.35 | | | | | (119), (120), (121), (122), (123), (124), (125), (126),
% 250.44/59.35 | | | | | (127), (128), (129), (130), (131), (132), (133), (134),
% 250.44/59.35 | | | | | (135), (136), (137), (138), (139), (141), (142), (143),
% 250.44/59.35 | | | | | (144), (145), (146), (147), (148), (149), (150), (151),
% 250.44/59.35 | | | | | (152), (153), (154), (155), (156), (157), (158), (159),
% 250.44/59.35 | | | | | (160), (161), (162), (163), (164), (165), (166), (167),
% 250.44/59.35 | | | | | (168), (169), (170), (171), (177), (178), (180), (181),
% 250.44/59.35 | | | | | (183), (185), (188), (192) are inconsistent by sub-proof
% 250.44/59.35 | | | | | #238.
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | End of split
% 250.44/59.35 | | | |
% 250.44/59.35 | | | Case 2:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (193) all_252_10 = e0 & op(e3, e1) = e0
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | REF_CLOSE: (29), (82), (180), (193) are inconsistent by sub-proof #726.
% 250.44/59.35 | | | |
% 250.44/59.35 | | | End of split
% 250.44/59.35 | | |
% 250.44/59.35 | | Case 2:
% 250.44/59.35 | | |
% 250.44/59.35 | | | (194) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1,
% 250.44/59.35 | | | e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.44/59.35 | | |
% 250.44/59.35 | | | BETA: splitting (194) gives:
% 250.44/59.35 | | |
% 250.44/59.35 | | | Case 1:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (195) all_252_11 = e0 & op(e2, e1) = e0
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | REF_CLOSE: (29), (38), (179), (195) are inconsistent by sub-proof #904.
% 250.44/59.35 | | | |
% 250.44/59.35 | | | Case 2:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (196) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0,
% 250.44/59.35 | | | | e1) = e0)
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | BETA: splitting (196) gives:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | Case 1:
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | (197) all_252_15 = e0 & op(e1, e1) = e0
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | ALPHA: (197) implies:
% 250.44/59.35 | | | | | (198) op(e1, e1) = e0
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | REF_CLOSE: (29), (123), (178), (198) are inconsistent by sub-proof
% 250.44/59.35 | | | | | #712.
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | Case 2:
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | (199) all_252_23 = e0 & op(e0, e1) = e0
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | REF_CLOSE: (155), (185), (199) are inconsistent by sub-proof #317.
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | End of split
% 250.44/59.35 | | | |
% 250.44/59.35 | | | End of split
% 250.44/59.35 | | |
% 250.44/59.35 | | End of split
% 250.44/59.35 | |
% 250.44/59.35 | End of split
% 250.44/59.35 |
% 250.44/59.35 End of proof
% 250.44/59.35
% 250.44/59.35 Sub-proof #238 shows that the following formulas are inconsistent:
% 250.44/59.35 ----------------------------------------------------------------
% 250.44/59.35 (1) ~ (all_244_8 = all_4_2)
% 250.44/59.35 (2) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.44/59.35 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.44/59.35 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.44/59.35 (3) ~ (all_4_2 = e4)
% 250.44/59.35 (4) ~ (all_10_2 = e4)
% 250.44/59.35 (5) ~ (all_244_0 = all_30_2)
% 250.44/59.35 (6) op(all_4_2, e2) = e1
% 250.44/59.35 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.44/59.35 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.44/59.35 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.44/59.35 (8) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.44/59.35 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.44/59.35 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.44/59.35 (9) op(e4, e1) = e0
% 250.44/59.35 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.44/59.35 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.44/59.35 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.44/59.35 (11) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.44/59.35 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.44/59.35 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.44/59.35 (12) op(e4, e0) = all_30_2
% 250.44/59.35 (13) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.44/59.35 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.44/59.35 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.44/59.35 (14) all_250_8 = all_36_2
% 250.44/59.35 (15) ~ (all_30_2 = e0)
% 250.44/59.35 (16) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.44/59.35 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.44/59.35 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.44/59.35 (17) op(all_62_2, all_36_2) = e3
% 250.44/59.35 (18) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 250.44/59.35 all_250_15 = e0
% 250.44/59.35 (19) ~ (all_28_2 = all_6_2)
% 250.44/59.35 (20) all_216_2 = e0
% 250.44/59.35 (21) ~ (e2 = e0)
% 250.44/59.35 (22) op(all_38_2, all_4_2) = e1
% 250.44/59.35 (23) ~ (e1 = e0)
% 250.44/59.35 (24) ~ (all_22_2 = e3)
% 250.44/59.35 (25) ~ (all_28_2 = e3)
% 250.44/59.35 (26) ~ (all_62_2 = all_22_2)
% 250.44/59.35 (27) op(e3, e4) = e0
% 250.44/59.35 (28) op(e4, all_34_2) = e1
% 250.44/59.35 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.44/59.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.44/59.35 (30) op(e2, e3) = all_10_2
% 250.44/59.35 (31) ~ (e3 = e2)
% 250.44/59.35 (32) op(e0, e0) = all_244_24
% 250.44/59.35 (33) ~ (e4 = e0)
% 250.44/59.35 (34) ~ (all_30_2 = all_6_2)
% 250.44/59.35 (35) op(e2, e2) = all_244_8
% 250.44/59.35 (36) all_72_2 = all_22_2
% 250.44/59.35 (37) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.44/59.35 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.44/59.35 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.44/59.35 (38) all_146_2 = e0
% 250.44/59.35 (39) op(e2, e1) = all_38_2
% 250.44/59.35 (40) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.44/59.35 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.44/59.35 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.44/59.35 (41) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 250.44/59.35 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 250.44/59.35 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 250.44/59.35 (42) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.44/59.35 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.44/59.35 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.44/59.35 (43) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.44/59.35 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.44/59.35 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.44/59.35 (44) op(e1, e0) = all_34_2
% 250.44/59.35 (45) op(all_28_2, e2) = e0
% 250.44/59.35 (46) op(e4, e2) = all_6_2
% 250.44/59.35 (47) ~ (all_244_15 = e0)
% 250.44/59.35 (48) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.44/59.35 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.35 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.44/59.35 (49) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 250.44/59.35 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 250.44/59.35 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.44/59.35 (50) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.44/59.35 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.44/59.35 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.44/59.35 (51) all_78_2 = all_10_2
% 250.44/59.35 (52) ~ (all_8_2 = all_4_2)
% 250.44/59.35 (53) ~ (all_244_15 = e4)
% 250.44/59.35 (54) ~ (e2 = e1)
% 250.44/59.35 (55) op(all_26_2, e1) = e4
% 250.44/59.35 (56) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.44/59.35 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.44/59.35 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.44/59.35 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.44/59.35 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.44/59.35 op(e0, e1) = e0)))
% 250.44/59.35 (57) op(e0, e2) = all_28_2
% 250.44/59.35 (58) ~ (e4 = e1)
% 250.44/59.35 (59) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.44/59.35 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.44/59.35 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.44/59.35 (60) ~ (all_6_2 = e1)
% 250.44/59.35 (61) ~ (all_244_8 = all_38_2)
% 250.44/59.35 (62) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.44/59.35 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.44/59.35 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.44/59.35 (63) op(all_244_15, all_244_15) = e1
% 250.44/59.35 (64) all_250_21 = all_22_2
% 250.44/59.35 (65) all_50_2 = all_4_2
% 250.44/59.35 (66) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.44/59.35 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.44/59.35 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.44/59.35 (67) op(e1, e4) = all_16_2
% 250.44/59.35 (68) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 250.44/59.35 all_250_2 = e0
% 250.44/59.35 (69) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.44/59.35 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.44/59.35 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.44/59.35 (70) op(e1, e3) = all_62_2
% 250.44/59.35 (71) ~ (e3 = e0)
% 250.44/59.35 (72) ~ (all_48_2 = all_36_2)
% 250.44/59.35 (73) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.44/59.35 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.44/59.35 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.44/59.35 (74) all_252_2 = e0
% 250.44/59.35 (75) ~ (all_36_2 = e4)
% 250.44/59.35 (76) ~ (all_22_2 = e4)
% 250.44/59.35 (77) all_70_2 = all_62_2
% 250.44/59.35 (78) ~ (all_36_2 = all_8_2)
% 250.44/59.35 (79) ~ (e3 = e1)
% 250.44/59.35 (80) op(all_48_2, all_22_2) = e0
% 250.44/59.35 (81) op(e3, e1) = all_36_2
% 250.44/59.35 (82) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.44/59.35 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.44/59.35 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.44/59.35 (83) ~ (all_16_2 = e2)
% 250.44/59.35 (84) ~ (all_8_2 = e1)
% 250.44/59.35 (85) op(all_40_2, e0) = e2
% 250.44/59.35 (86) all_252_9 = e0
% 250.44/59.35 (87) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.44/59.35 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.44/59.35 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.44/59.35 (88) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 250.44/59.35 all_250_8 = e0
% 250.44/59.35 (89) ~ (all_28_2 = all_4_2)
% 250.44/59.35 (90) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.44/59.35 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.44/59.35 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.44/59.35 (91) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.44/59.35 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.44/59.35 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.44/59.35 (92) ~ (all_72_2 = e1) | ( ~ (all_72_0 = e4) & op(e3, e1) = all_72_1 &
% 250.44/59.35 op(e1, all_72_1) = all_72_0 & $i(all_72_0) & $i(all_72_1)) | ( ~
% 250.44/59.35 (all_72_1 = e2) & op(e3, e1) = all_72_1 & $i(all_72_1))
% 250.44/59.35 (93) ~ (all_244_15 = all_38_2)
% 250.44/59.35 (94) ~ (all_48_2 = all_8_2)
% 250.44/59.35 (95) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.44/59.35 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.44/59.35 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.44/59.35 (96) ~ (all_8_2 = e0)
% 250.44/59.35 (97) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.44/59.35 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.44/59.35 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.44/59.35 (98) ~ (all_38_2 = e4)
% 250.44/59.35 (99) op(e1, e4) = all_60_1
% 250.44/59.35 (100) ~ (all_28_2 = e4)
% 250.44/59.35 (101) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 250.44/59.35 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 250.44/59.35 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.44/59.35 (102) op(all_22_2, e3) = e0
% 250.44/59.35 (103) op(e0, e3) = all_22_2
% 250.44/59.35 (104) ~ (all_28_2 = all_22_2)
% 250.44/59.35 (105) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.44/59.35 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.44/59.35 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.44/59.35 (106) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.44/59.35 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.44/59.35 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.44/59.35 (107) op(all_62_2, e3) = e1
% 250.44/59.35 (108) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.44/59.35 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.44/59.35 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.44/59.35 (109) op(all_10_2, e3) = e2
% 250.44/59.35 (110) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 250.44/59.35 all_250_21 = e0
% 250.44/59.35 (111) ~ (all_62_2 = all_16_2)
% 250.44/59.35 (112) ~ (all_8_2 = all_6_2)
% 250.44/59.35 (113) ~ (all_36_2 = e0)
% 250.44/59.35 (114) ~ (all_216_2 = e0) | ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 &
% 250.44/59.35 op(e0, all_216_1) = all_216_0 & $i(all_216_0) & $i(all_216_1)) | ( ~
% 250.44/59.35 (all_216_1 = e2) & op(e1, e0) = all_216_1 & $i(all_216_1))
% 250.44/59.35 (115) all_250_15 = all_16_2
% 250.44/59.35 (116) op(e4, e4) = all_244_0
% 250.44/59.35 (117) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.44/59.35 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 250.44/59.35 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.44/59.35 (118) ~ (e4 = e3)
% 250.44/59.35 (119) op(e1, e1) = all_244_15
% 250.44/59.35 (120) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.44/59.35 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.44/59.35 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.44/59.35 (121) op(e0, e1) = all_20_2
% 250.44/59.35 (122) op(e3, e0) = all_48_2
% 250.44/59.35 (123) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 250.44/59.35 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 250.44/59.35 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.44/59.35 (124) op(all_48_2, e0) = e3
% 250.44/59.35 (125) ~ (all_38_2 = all_36_2)
% 250.44/59.35 (126) all_82_2 = all_28_2
% 250.44/59.35 (127) op(e1, e2) = all_4_2
% 250.44/59.35 (128) op(e3, all_30_2) = e4
% 250.44/59.35 (129) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.44/59.35 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.44/59.35 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.44/59.35 (130) ~ (all_28_2 = all_8_2)
% 250.44/59.35 (131) ~ (all_48_2 = e0)
% 250.44/59.35 (132) op(e4, e3) = all_84_2
% 250.44/59.35 (133) op(all_244_3, all_244_3) = e3
% 250.44/59.35 (134) ~ (all_62_2 = all_10_2)
% 250.44/59.35 (135) op(e2, e4) = all_64_2
% 250.44/59.35 (136) ~ (all_6_2 = all_4_2)
% 250.44/59.35 (137) ~ (e4 = e2)
% 250.44/59.35 (138) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.44/59.35 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 250.44/59.35 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.44/59.35 (139) ~ (all_6_2 = e0)
% 250.44/59.35 (140) op(e3, e2) = all_8_2
% 250.44/59.35 (141) op(all_36_2, e1) = e3
% 250.44/59.35 (142) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.44/59.35 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.44/59.35 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.44/59.35 (143) ~ (all_244_15 = all_36_2)
% 250.44/59.35 (144) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.44/59.35 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.44/59.35 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.44/59.35 (145) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.44/59.35 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.44/59.35 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.44/59.35 (146) ~ (all_244_3 = e0)
% 250.44/59.35 (147) op(e2, e0) = all_40_2
% 250.44/59.35 (148) ~ (all_20_2 = e3)
% 250.44/59.35 (149) ~ (all_16_2 = e3)
% 250.44/59.35 (150) ~ (all_244_8 = all_28_2)
% 250.44/59.35 (151) all_252_23 = e4
% 250.44/59.35 (152) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.44/59.35 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.44/59.35 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.44/59.35 (153) op(e3, e3) = all_244_3
% 250.44/59.35 (154) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.44/59.35 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.44/59.35 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.44/59.35 (155) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.44/59.35 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.44/59.35 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.44/59.35 (156) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.44/59.35 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.44/59.35 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.44/59.35 (157) op(all_26_2, all_16_2) = e1
% 250.44/59.35 (158) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.44/59.35 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.44/59.35 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.44/59.35 (159) all_250_2 = all_6_2
% 250.44/59.35 (160) all_46_2 = all_36_2
% 250.44/59.35 (161) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 250.44/59.35 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 250.44/59.35 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 250.44/59.35 (162) ~ (all_146_2 = e0) | ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 250.44/59.35 op(e0, all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)) | ( ~
% 250.44/59.35 (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1))
% 250.44/59.35 (163) op(all_244_24, all_244_24) = e0
% 250.44/59.35 (164) ~ (all_16_2 = e0)
% 250.44/59.35 (165) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 250.44/59.35 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 250.44/59.35 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 250.44/59.35 (166) op(all_64_2, all_6_2) = e4
% 250.44/59.35 (167) all_252_20 = e3
% 250.44/59.35
% 250.44/59.35 Begin of proof
% 250.44/59.35 |
% 250.44/59.35 | GROUND_INST: instantiating (29) with all_16_2, all_60_1, e4, e1, simplifying
% 250.44/59.35 | with (67), (99) gives:
% 250.44/59.35 | (168) all_60_1 = all_16_2
% 250.44/59.35 |
% 250.44/59.35 | BETA: splitting (161) gives:
% 250.44/59.35 |
% 250.44/59.35 | Case 1:
% 250.44/59.35 | |
% 250.44/59.35 | | (169) ~ (all_22_2 = e1)
% 250.44/59.35 | |
% 250.44/59.35 | | BETA: splitting (41) gives:
% 250.44/59.35 | |
% 250.44/59.35 | | Case 1:
% 250.44/59.35 | | |
% 250.44/59.35 | | | (170) ~ (all_30_2 = e2)
% 250.44/59.35 | | |
% 250.44/59.35 | | | BETA: splitting (162) gives:
% 250.44/59.35 | | |
% 250.44/59.35 | | | Case 1:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (171) ~ (all_146_2 = e0)
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | REDUCE: (38), (171) imply:
% 250.44/59.35 | | | | (172) $false
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | CLOSE: (172) is inconsistent.
% 250.44/59.35 | | | |
% 250.44/59.35 | | | Case 2:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | (173) ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 & op(e0,
% 250.44/59.35 | | | | all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)) | (
% 250.44/59.35 | | | | ~ (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1))
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | BETA: splitting (173) gives:
% 250.44/59.35 | | | |
% 250.44/59.35 | | | | Case 1:
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | (174) ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 & op(e0,
% 250.44/59.35 | | | | | all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)
% 250.44/59.35 | | | | |
% 250.44/59.35 | | | | | ALPHA: (174) implies:
% 250.44/59.36 | | | | | (175) op(e4, e0) = all_146_1
% 250.44/59.36 | | | | |
% 250.44/59.36 | | | | | GROUND_INST: instantiating (29) with all_30_2, all_146_1, e0, e4,
% 250.44/59.36 | | | | | simplifying with (12), (175) gives:
% 250.44/59.36 | | | | | (176) all_146_1 = all_30_2
% 250.44/59.36 | | | | |
% 250.44/59.36 | | | | | BETA: splitting (49) gives:
% 250.44/59.36 | | | | |
% 250.44/59.36 | | | | | Case 1:
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | (177) ~ (all_34_2 = e2)
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | BETA: splitting (114) gives:
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | Case 1:
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | (178) ~ (all_216_2 = e0)
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | REDUCE: (20), (178) imply:
% 250.44/59.36 | | | | | | | (179) $false
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | CLOSE: (179) is inconsistent.
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | Case 2:
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | (180) ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 250.44/59.36 | | | | | | | all_216_1) = all_216_0 & $i(all_216_0) &
% 250.44/59.36 | | | | | | | $i(all_216_1)) | ( ~ (all_216_1 = e2) & op(e1, e0) =
% 250.44/59.36 | | | | | | | all_216_1 & $i(all_216_1))
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | BETA: splitting (180) gives:
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | | Case 1:
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | (181) ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 250.44/59.36 | | | | | | | | all_216_1) = all_216_0 & $i(all_216_0) &
% 250.44/59.36 | | | | | | | | $i(all_216_1)
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | ALPHA: (181) implies:
% 250.44/59.36 | | | | | | | | (182) op(e1, e0) = all_216_1
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13),
% 250.44/59.36 | | | | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 250.44/59.36 | | | | | | | | (25), (26), (27), (29), (30), (31), (32), (33), (35),
% 250.44/59.36 | | | | | | | | (37), (39), (40), (42), (43), (44), (45), (46), (47),
% 250.44/59.36 | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.44/59.36 | | | | | | | | (58), (61), (62), (63), (64), (65), (66), (67), (70),
% 250.44/59.36 | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 250.44/59.36 | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87), (89),
% 250.44/59.36 | | | | | | | | (90), (91), (93), (94), (95), (96), (97), (98),
% 250.44/59.36 | | | | | | | | (100), (101), (103), (104), (105), (106), (108),
% 250.44/59.36 | | | | | | | | (109), (110), (111), (113), (115), (117), (118),
% 250.44/59.36 | | | | | | | | (119), (120), (122), (123), (124), (125), (126),
% 250.44/59.36 | | | | | | | | (127), (129), (130), (131), (133), (136), (137),
% 250.44/59.36 | | | | | | | | (139), (140), (141), (142), (143), (144), (145),
% 250.44/59.36 | | | | | | | | (146), (147), (149), (150), (151), (152), (153),
% 250.44/59.36 | | | | | | | | (154), (155), (156), (157), (158), (160), (163),
% 250.44/59.36 | | | | | | | | (164), (165), (167), (169), (170), (177), (182) are
% 250.44/59.36 | | | | | | | | inconsistent by sub-proof #254.
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | Case 2:
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | (183) ~ (all_216_1 = e2) & op(e1, e0) = all_216_1 &
% 250.44/59.36 | | | | | | | | $i(all_216_1)
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | ALPHA: (183) implies:
% 250.44/59.36 | | | | | | | | (184) op(e1, e0) = all_216_1
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13),
% 250.44/59.36 | | | | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 250.44/59.36 | | | | | | | | (25), (26), (27), (29), (30), (31), (32), (33), (35),
% 250.44/59.36 | | | | | | | | (37), (39), (40), (42), (43), (44), (45), (46), (47),
% 250.44/59.36 | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.44/59.36 | | | | | | | | (58), (61), (62), (63), (64), (65), (66), (67), (70),
% 250.44/59.36 | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 250.44/59.36 | | | | | | | | (80), (81), (82), (83), (84), (85), (86), (87), (89),
% 250.44/59.36 | | | | | | | | (90), (91), (93), (94), (95), (96), (97), (98),
% 250.44/59.36 | | | | | | | | (100), (101), (103), (104), (105), (106), (108),
% 250.44/59.36 | | | | | | | | (109), (110), (111), (113), (115), (117), (118),
% 250.44/59.36 | | | | | | | | (119), (120), (122), (123), (124), (125), (126),
% 250.44/59.36 | | | | | | | | (127), (129), (130), (131), (133), (136), (137),
% 250.44/59.36 | | | | | | | | (139), (140), (141), (142), (143), (144), (145),
% 250.44/59.36 | | | | | | | | (146), (147), (149), (150), (151), (152), (153),
% 250.44/59.36 | | | | | | | | (154), (155), (156), (157), (158), (160), (163),
% 250.44/59.36 | | | | | | | | (164), (165), (167), (169), (170), (177), (184) are
% 250.44/59.36 | | | | | | | | inconsistent by sub-proof #254.
% 250.44/59.36 | | | | | | | |
% 250.44/59.36 | | | | | | | End of split
% 250.44/59.36 | | | | | | |
% 250.44/59.36 | | | | | | End of split
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | Case 2:
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | (185) all_34_2 = e2
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | REDUCE: (28), (185) imply:
% 250.44/59.36 | | | | | | (186) op(e4, e2) = e1
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | | REF_CLOSE: (29), (46), (60), (186) are inconsistent by sub-proof
% 250.44/59.36 | | | | | | #930.
% 250.44/59.36 | | | | | |
% 250.44/59.36 | | | | | End of split
% 250.44/59.36 | | | | |
% 250.44/59.36 | | | | Case 2:
% 250.44/59.36 | | | | |
% 250.44/59.36 | | | | | (187) ~ (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1)
% 250.44/59.36 | | | | |
% 250.47/59.36 | | | | | ALPHA: (187) implies:
% 250.47/59.36 | | | | | (188) ~ (all_146_1 = e2)
% 250.47/59.36 | | | | | (189) op(e4, e0) = all_146_1
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | GROUND_INST: instantiating (29) with all_30_2, all_146_1, e0, e4,
% 250.47/59.36 | | | | | simplifying with (12), (189) gives:
% 250.47/59.36 | | | | | (190) all_146_1 = all_30_2
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | BETA: splitting (49) gives:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | Case 1:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (191) ~ (all_34_2 = e2)
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | BETA: splitting (114) gives:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | Case 1:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (192) ~ (all_216_2 = e0)
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | REDUCE: (20), (192) imply:
% 250.47/59.36 | | | | | | | (193) $false
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | CLOSE: (193) is inconsistent.
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | Case 2:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (194) ( ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 250.47/59.36 | | | | | | | all_216_1) = all_216_0 & $i(all_216_0) &
% 250.47/59.36 | | | | | | | $i(all_216_1)) | ( ~ (all_216_1 = e2) & op(e1, e0) =
% 250.47/59.36 | | | | | | | all_216_1 & $i(all_216_1))
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | BETA: splitting (194) gives:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (195) ~ (all_216_0 = e3) & op(e1, e0) = all_216_1 & op(e0,
% 250.47/59.36 | | | | | | | | all_216_1) = all_216_0 & $i(all_216_0) &
% 250.47/59.36 | | | | | | | | $i(all_216_1)
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | ALPHA: (195) implies:
% 250.47/59.36 | | | | | | | | (196) op(e1, e0) = all_216_1
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | GROUND_INST: instantiating (29) with all_34_2, all_216_1, e0,
% 250.47/59.36 | | | | | | | | e1, simplifying with (44), (196) gives:
% 250.47/59.36 | | | | | | | | (197) all_216_1 = all_34_2
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12),
% 250.47/59.36 | | | | | | | | (13), (15), (16), (17), (18), (19), (21), (22), (23),
% 250.47/59.36 | | | | | | | | (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 250.47/59.36 | | | | | | | | (35), (37), (39), (40), (42), (43), (45), (46), (47),
% 250.47/59.36 | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.47/59.36 | | | | | | | | (58), (59), (61), (62), (63), (64), (65), (66), (67),
% 250.47/59.36 | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 250.47/59.36 | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 250.47/59.36 | | | | | | | | (89), (90), (91), (93), (94), (95), (96), (97), (98),
% 250.47/59.36 | | | | | | | | (100), (101), (103), (104), (105), (106), (108),
% 250.47/59.36 | | | | | | | | (109), (110), (111), (113), (115), (117), (118),
% 250.47/59.36 | | | | | | | | (119), (120), (121), (122), (123), (124), (125),
% 250.47/59.36 | | | | | | | | (126), (127), (129), (130), (131), (133), (136),
% 250.47/59.36 | | | | | | | | (137), (138), (139), (140), (141), (142), (143),
% 250.47/59.36 | | | | | | | | (144), (145), (146), (147), (148), (149), (150),
% 250.47/59.36 | | | | | | | | (151), (152), (153), (154), (155), (156), (157),
% 250.47/59.36 | | | | | | | | (158), (160), (163), (164), (165), (167), (169),
% 250.47/59.36 | | | | | | | | (188), (189), (191), (196), (197) are inconsistent by
% 250.47/59.36 | | | | | | | | sub-proof #244.
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (198) ~ (all_216_1 = e2) & op(e1, e0) = all_216_1 &
% 250.47/59.36 | | | | | | | | $i(all_216_1)
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | ALPHA: (198) implies:
% 250.47/59.36 | | | | | | | | (199) ~ (all_216_1 = e2)
% 250.47/59.36 | | | | | | | | (200) op(e1, e0) = all_216_1
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | GROUND_INST: instantiating (29) with all_34_2, all_216_1, e0,
% 250.47/59.36 | | | | | | | | e1, simplifying with (44), (200) gives:
% 250.47/59.36 | | | | | | | | (201) all_216_1 = all_34_2
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12),
% 250.47/59.36 | | | | | | | | (13), (15), (16), (17), (18), (19), (21), (22), (23),
% 250.47/59.36 | | | | | | | | (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 250.47/59.36 | | | | | | | | (35), (37), (39), (40), (42), (43), (45), (46), (47),
% 250.47/59.36 | | | | | | | | (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 250.47/59.36 | | | | | | | | (58), (59), (61), (62), (63), (64), (65), (66), (67),
% 250.47/59.36 | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 250.47/59.36 | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 250.47/59.36 | | | | | | | | (89), (90), (91), (93), (94), (95), (96), (97), (98),
% 250.47/59.36 | | | | | | | | (100), (101), (103), (104), (105), (106), (108),
% 250.47/59.36 | | | | | | | | (109), (110), (111), (113), (115), (117), (118),
% 250.47/59.36 | | | | | | | | (119), (120), (121), (122), (123), (124), (125),
% 250.47/59.36 | | | | | | | | (126), (127), (129), (130), (131), (133), (136),
% 250.47/59.36 | | | | | | | | (137), (138), (139), (140), (141), (142), (143),
% 250.47/59.36 | | | | | | | | (144), (145), (146), (147), (148), (149), (150),
% 250.47/59.36 | | | | | | | | (151), (152), (153), (154), (155), (156), (157),
% 250.47/59.36 | | | | | | | | (158), (160), (163), (164), (165), (167), (169),
% 250.47/59.36 | | | | | | | | (188), (189), (191), (200), (201) are inconsistent by
% 250.47/59.36 | | | | | | | | sub-proof #244.
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | End of split
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | End of split
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | Case 2:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (202) all_34_2 = e2
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | REDUCE: (28), (202) imply:
% 250.47/59.36 | | | | | | (203) op(e4, e2) = e1
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | REF_CLOSE: (29), (46), (60), (203) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | #930.
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | End of split
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | End of split
% 250.47/59.36 | | | |
% 250.47/59.36 | | | End of split
% 250.47/59.36 | | |
% 250.47/59.36 | | Case 2:
% 250.47/59.36 | | |
% 250.47/59.36 | | | (204) all_30_2 = e2
% 250.47/59.36 | | |
% 250.47/59.36 | | | REDUCE: (5), (204) imply:
% 250.47/59.36 | | | (205) ~ (all_244_0 = e2)
% 250.47/59.36 | | |
% 250.47/59.36 | | | REDUCE: (34), (204) imply:
% 250.47/59.36 | | | (206) ~ (all_6_2 = e2)
% 250.47/59.36 | | |
% 250.47/59.36 | | | SIMP: (206) implies:
% 250.47/59.36 | | | (207) ~ (all_6_2 = e2)
% 250.47/59.36 | | |
% 250.47/59.36 | | | REDUCE: (128), (204) imply:
% 250.47/59.36 | | | (208) op(e3, e2) = e4
% 250.47/59.36 | | |
% 250.47/59.36 | | | BETA: splitting (142) gives:
% 250.47/59.36 | | |
% 250.47/59.36 | | | Case 1:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | (209) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3,
% 250.47/59.36 | | | | e4) = e2)
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | REF_CLOSE: (8), (21), (29), (81), (96), (113), (116), (122), (131),
% 250.47/59.36 | | | | (140), (146), (153), (205), (209) are inconsistent by
% 250.47/59.36 | | | | sub-proof #459.
% 250.47/59.36 | | | |
% 250.47/59.36 | | | Case 2:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | (210) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 250.47/59.36 | | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | BETA: splitting (210) gives:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | Case 1:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | (211) all_252_6 = e2 & op(e2, e4) = e2
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | ALPHA: (211) implies:
% 250.47/59.36 | | | | | (212) op(e2, e4) = e2
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | GROUND_INST: instantiating (29) with all_64_2, e2, e4, e2, simplifying
% 250.47/59.36 | | | | | with (135), (212) gives:
% 250.47/59.36 | | | | | (213) all_64_2 = e2
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | GROUND_INST: instantiating (29) with all_8_2, e4, e2, e3, simplifying
% 250.47/59.36 | | | | | with (140), (208) gives:
% 250.47/59.36 | | | | | (214) all_8_2 = e4
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | REDUCE: (112), (214) imply:
% 250.47/59.36 | | | | | (215) ~ (all_6_2 = e4)
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | SIMP: (215) implies:
% 250.47/59.36 | | | | | (216) ~ (all_6_2 = e4)
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | REDUCE: (166), (213) imply:
% 250.47/59.36 | | | | | (217) op(e2, all_6_2) = e4
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | BETA: splitting (68) gives:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | Case 1:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (218) all_250_2 = e4
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | COMBINE_EQS: (159), (218) imply:
% 250.47/59.36 | | | | | | (219) all_6_2 = e4
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | REDUCE: (216), (219) imply:
% 250.47/59.36 | | | | | | (220) $false
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | CLOSE: (220) is inconsistent.
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | Case 2:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (221) all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 |
% 250.47/59.36 | | | | | | all_250_2 = e0
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | BETA: splitting (221) gives:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | Case 1:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (222) all_250_2 = e3
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | COMBINE_EQS: (159), (222) imply:
% 250.47/59.36 | | | | | | | (223) all_6_2 = e3
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | REDUCE: (217), (223) imply:
% 250.47/59.36 | | | | | | | (224) op(e2, e3) = e4
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | REF_CLOSE: (4), (29), (30), (224) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | #953.
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | Case 2:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (225) all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | REF_CLOSE: (60), (139), (159), (207), (225) are inconsistent by
% 250.47/59.36 | | | | | | | sub-proof #243.
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | End of split
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | End of split
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | Case 2:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | (226) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.47/59.36 | | | | | op(e0, e4) = e2)
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | BETA: splitting (226) gives:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | Case 1:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (227) all_252_12 = e2 & op(e1, e4) = e2
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | REF_CLOSE: (29), (67), (83), (227) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | #926.
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | Case 2:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (228) all_252_20 = e2 & op(e0, e4) = e2
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | REF_CLOSE: (31), (167), (228) are inconsistent by sub-proof #560.
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | End of split
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | End of split
% 250.47/59.36 | | | |
% 250.47/59.36 | | | End of split
% 250.47/59.36 | | |
% 250.47/59.36 | | End of split
% 250.47/59.36 | |
% 250.47/59.36 | Case 2:
% 250.47/59.36 | |
% 250.47/59.36 | | (229) all_22_2 = e1
% 250.47/59.36 | |
% 250.47/59.36 | | COMBINE_EQS: (36), (229) imply:
% 250.47/59.36 | | (230) all_72_2 = e1
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (26), (229) imply:
% 250.47/59.36 | | (231) ~ (all_62_2 = e1)
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (104), (229) imply:
% 250.47/59.36 | | (232) ~ (all_28_2 = e1)
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (76), (229) imply:
% 250.47/59.36 | | (233) ~ (e4 = e1)
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (24), (229) imply:
% 250.47/59.36 | | (234) ~ (e3 = e1)
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (102), (229) imply:
% 250.47/59.36 | | (235) op(e1, e3) = e0
% 250.47/59.36 | |
% 250.47/59.36 | | REDUCE: (103), (229) imply:
% 250.47/59.36 | | (236) op(e0, e3) = e1
% 250.47/59.36 | |
% 250.47/59.36 | | BETA: splitting (87) gives:
% 250.47/59.36 | |
% 250.47/59.36 | | Case 1:
% 250.47/59.36 | | |
% 250.47/59.36 | | | (237) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0,
% 250.47/59.36 | | | e3) = e1)
% 250.47/59.36 | | |
% 250.47/59.36 | | | BETA: splitting (237) gives:
% 250.47/59.36 | | |
% 250.47/59.36 | | | Case 1:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | (238) all_252_20 = e1 & op(e0, e4) = e1
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | REF_CLOSE: (79), (167), (238) are inconsistent by sub-proof #509.
% 250.47/59.36 | | | |
% 250.47/59.36 | | | Case 2:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | (239) all_252_21 = e1 & op(e0, e3) = e1
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | ALPHA: (239) implies:
% 250.47/59.36 | | | | (240) all_252_21 = e1
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | GROUND_INST: instantiating (29) with all_62_2, e0, e3, e1, simplifying
% 250.47/59.36 | | | | with (70), (235) gives:
% 250.47/59.36 | | | | (241) all_62_2 = e0
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | REDUCE: (134), (241) imply:
% 250.47/59.36 | | | | (242) ~ (all_10_2 = e0)
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | SIMP: (242) implies:
% 250.47/59.36 | | | | (243) ~ (all_10_2 = e0)
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | REDUCE: (231), (241) imply:
% 250.47/59.36 | | | | (244) ~ (e1 = e0)
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | REDUCE: (17), (241) imply:
% 250.47/59.36 | | | | (245) op(e0, all_36_2) = e3
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | BETA: splitting (90) gives:
% 250.47/59.36 | | | |
% 250.47/59.36 | | | | Case 1:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | (246) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 250.47/59.36 | | | | | e3) = e0)
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | BETA: splitting (246) gives:
% 250.47/59.36 | | | | |
% 250.47/59.36 | | | | | Case 1:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (247) all_252_1 = e0 & op(e4, e3) = e0
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | ALPHA: (247) implies:
% 250.47/59.36 | | | | | | (248) all_252_1 = e0
% 250.47/59.36 | | | | | | (249) op(e4, e3) = e0
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | BETA: splitting (10) gives:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | Case 1:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (250) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 250.47/59.36 | | | | | | | op(e3, e3) = e4)
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | BETA: splitting (250) gives:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (251) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | REF_CLOSE: (33), (248), (251) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | #898.
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (252) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | ALPHA: (252) implies:
% 250.47/59.36 | | | | | | | | (253) all_252_3 = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | BETA: splitting (129) gives:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (254) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3
% 250.47/59.36 | | | | | | | | | & op(e3, e3) = e3)
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | BETA: splitting (254) gives:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (255) all_252_1 = e3 & op(e4, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | REF_CLOSE: (71), (248), (255) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | #840.
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (256) all_252_3 = e3 & op(e3, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | REF_CLOSE: (118), (253), (256) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | #482.
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (257) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3
% 250.47/59.36 | | | | | | | | | & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.47/59.36 | | | | | | | | | = e3)
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | BETA: splitting (257) gives:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (258) all_252_7 = e3 & op(e2, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | ALPHA: (258) implies:
% 250.47/59.36 | | | | | | | | | | (259) all_252_7 = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | BETA: splitting (11) gives:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (260) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.47/59.36 | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | BETA: splitting (260) gives:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | (261) all_252_1 = e2 & op(e4, e3) = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | ALPHA: (261) implies:
% 250.47/59.36 | | | | | | | | | | | | (262) op(e4, e3) = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | REF_CLOSE: (21), (29), (132), (249), (262) are inconsistent
% 250.47/59.36 | | | | | | | | | | | | by sub-proof #850.
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | (263) all_252_3 = e2 & op(e3, e3) = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | ALPHA: (263) implies:
% 250.47/59.36 | | | | | | | | | | | | (264) all_252_3 = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | REF_CLOSE: (137), (253), (264) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | | | #954.
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (265) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.47/59.36 | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.47/59.36 | | | | | | | | | | | op(e0, e3) = e2)
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | BETA: splitting (265) gives:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | (266) all_252_7 = e2 & op(e2, e3) = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | REF_CLOSE: (31), (259), (266) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | | | #666.
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | (267) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 250.47/59.36 | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | BETA: splitting (267) gives:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | (268) all_252_13 = e2 & op(e1, e3) = e2
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | ALPHA: (268) implies:
% 250.47/59.36 | | | | | | | | | | | | | (269) op(e1, e3) = e2
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | REF_CLOSE: (21), (29), (235), (269) are inconsistent by
% 250.47/59.36 | | | | | | | | | | | | | sub-proof #776.
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | (270) all_252_21 = e2 & op(e0, e3) = e2
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | ALPHA: (270) implies:
% 250.47/59.36 | | | | | | | | | | | | | (271) op(e0, e3) = e2
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | | REF_CLOSE: (29), (54), (236), (271) are inconsistent by
% 250.47/59.36 | | | | | | | | | | | | | sub-proof #941.
% 250.47/59.36 | | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (272) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 =
% 250.47/59.36 | | | | | | | | | | e3 & op(e0, e3) = e3)
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | BETA: splitting (272) gives:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (273) all_252_13 = e3 & op(e1, e3) = e3
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | ALPHA: (273) implies:
% 250.47/59.36 | | | | | | | | | | | (274) op(e1, e3) = e3
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | REF_CLOSE: (29), (71), (235), (274) are inconsistent by
% 250.47/59.36 | | | | | | | | | | | sub-proof #592.
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (275) all_252_21 = e3 & op(e0, e3) = e3
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | REF_CLOSE: (24), (29), (103), (275) are inconsistent by
% 250.47/59.36 | | | | | | | | | | | sub-proof #959.
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | End of split
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | End of split
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | Case 2:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (276) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 250.47/59.36 | | | | | | | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | BETA: splitting (276) gives:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (277) all_252_7 = e4 & op(e2, e3) = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | ALPHA: (277) implies:
% 250.47/59.36 | | | | | | | | (278) op(e2, e3) = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | REF_CLOSE: (4), (29), (30), (278) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | #953.
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (279) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4
% 250.47/59.36 | | | | | | | | & op(e0, e3) = e4)
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | BETA: splitting (279) gives:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (280) all_252_13 = e4 & op(e1, e3) = e4
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | ALPHA: (280) implies:
% 250.47/59.36 | | | | | | | | | (281) op(e1, e3) = e4
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | REF_CLOSE: (29), (33), (235), (281) are inconsistent by
% 250.47/59.36 | | | | | | | | | sub-proof #886.
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (282) all_252_21 = e4 & op(e0, e3) = e4
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | ALPHA: (282) implies:
% 250.47/59.36 | | | | | | | | | (283) op(e0, e3) = e4
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | REF_CLOSE: (29), (58), (236), (283) are inconsistent by
% 250.47/59.36 | | | | | | | | | sub-proof #828.
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | End of split
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | End of split
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | End of split
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | Case 2:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | (284) all_252_3 = e0 & op(e3, e3) = e0
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | ALPHA: (284) implies:
% 250.47/59.36 | | | | | | (285) all_252_3 = e0
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | BETA: splitting (10) gives:
% 250.47/59.36 | | | | | |
% 250.47/59.36 | | | | | | Case 1:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | (286) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 250.47/59.36 | | | | | | | op(e3, e3) = e4)
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | BETA: splitting (286) gives:
% 250.47/59.36 | | | | | | |
% 250.47/59.36 | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | (287) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | ALPHA: (287) implies:
% 250.47/59.36 | | | | | | | | (288) all_252_1 = e4
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | BETA: splitting (129) gives:
% 250.47/59.36 | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (289) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3
% 250.47/59.36 | | | | | | | | | & op(e3, e3) = e3)
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | BETA: splitting (289) gives:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (290) all_252_1 = e3 & op(e4, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | REF_CLOSE: (118), (288), (290) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | #946.
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (291) all_252_3 = e3 & op(e3, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | REF_CLOSE: (71), (285), (291) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | #380.
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | End of split
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | (292) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3
% 250.47/59.36 | | | | | | | | | & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.47/59.36 | | | | | | | | | = e3)
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | BETA: splitting (292) gives:
% 250.47/59.36 | | | | | | | | |
% 250.47/59.36 | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | (293) all_252_7 = e3 & op(e2, e3) = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | ALPHA: (293) implies:
% 250.47/59.36 | | | | | | | | | | (294) all_252_7 = e3
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | BETA: splitting (11) gives:
% 250.47/59.36 | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (295) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.47/59.36 | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | REF_CLOSE: (21), (137), (285), (288), (295) are inconsistent
% 250.47/59.36 | | | | | | | | | | | by sub-proof #381.
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | (296) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.47/59.36 | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.47/59.36 | | | | | | | | | | | op(e0, e3) = e2)
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | BETA: splitting (296) gives:
% 250.47/59.36 | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 1:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | (297) all_252_7 = e2 & op(e2, e3) = e2
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | | REF_CLOSE: (31), (294), (297) are inconsistent by sub-proof
% 250.47/59.36 | | | | | | | | | | | | #666.
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.36 | | | | | | | | | | | Case 2:
% 250.47/59.36 | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | (298) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 250.47/59.37 | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.47/59.37 | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | BETA: splitting (298) gives:
% 250.47/59.37 | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | (299) all_252_13 = e2 & op(e1, e3) = e2
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | ALPHA: (299) implies:
% 250.47/59.37 | | | | | | | | | | | | | (300) all_252_13 = e2
% 250.47/59.37 | | | | | | | | | | | | | (301) op(e1, e3) = e2
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | GROUND_INST: instantiating (29) with e0, e2, e3, e1,
% 250.47/59.37 | | | | | | | | | | | | | simplifying with (235), (301) gives:
% 250.47/59.37 | | | | | | | | | | | | | (302) e2 = e0
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | COMBINE_EQS: (300), (302) imply:
% 250.47/59.37 | | | | | | | | | | | | | (303) all_252_13 = e0
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | REF_CLOSE: (10), (11), (21), (29), (31), (33), (54), (71),
% 250.47/59.37 | | | | | | | | | | | | | (76), (79), (103), (118), (129), (137), (236),
% 250.47/59.37 | | | | | | | | | | | | | (240), (285), (303) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | | | | | | #242.
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | (304) all_252_21 = e2 & op(e0, e3) = e2
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | | REF_CLOSE: (54), (240), (304) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | | | | | | #375.
% 250.47/59.37 | | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | (305) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 =
% 250.47/59.37 | | | | | | | | | | e3 & op(e0, e3) = e3)
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | BETA: splitting (305) gives:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | (306) all_252_13 = e3 & op(e1, e3) = e3
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | ALPHA: (306) implies:
% 250.47/59.37 | | | | | | | | | | | (307) all_252_13 = e3
% 250.47/59.37 | | | | | | | | | | | (308) op(e1, e3) = e3
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | REF_CLOSE: (11), (21), (29), (31), (54), (71), (79), (118),
% 250.47/59.37 | | | | | | | | | | | (129), (137), (235), (236), (240), (285), (288),
% 250.47/59.37 | | | | | | | | | | | (307), (308) are inconsistent by sub-proof #289.
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | (309) all_252_21 = e3 & op(e0, e3) = e3
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | ALPHA: (309) implies:
% 250.47/59.37 | | | | | | | | | | | (310) op(e0, e3) = e3
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | | REF_CLOSE: (29), (79), (236), (310) are inconsistent by
% 250.47/59.37 | | | | | | | | | | | sub-proof #590.
% 250.47/59.37 | | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | End of split
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (311) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (33), (285), (311) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #373.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | End of split
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | Case 2:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (312) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 250.47/59.37 | | | | | | | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | BETA: splitting (312) gives:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (313) all_252_7 = e4 & op(e2, e3) = e4
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | ALPHA: (313) implies:
% 250.47/59.37 | | | | | | | | (314) op(e2, e3) = e4
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (4), (29), (30), (314) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #953.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (315) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4
% 250.47/59.37 | | | | | | | | & op(e0, e3) = e4)
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | BETA: splitting (315) gives:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (316) all_252_13 = e4 & op(e1, e3) = e4
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | ALPHA: (316) implies:
% 250.47/59.37 | | | | | | | | | (317) all_252_13 = e4
% 250.47/59.37 | | | | | | | | | (318) op(e1, e3) = e4
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | GROUND_INST: instantiating (29) with e0, e4, e3, e1,
% 250.47/59.37 | | | | | | | | | simplifying with (235), (318) gives:
% 250.47/59.37 | | | | | | | | | (319) e4 = e0
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | COMBINE_EQS: (317), (319) imply:
% 250.47/59.37 | | | | | | | | | (320) all_252_13 = e0
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | REF_CLOSE: (10), (11), (21), (29), (31), (33), (54), (71),
% 250.47/59.37 | | | | | | | | | (76), (79), (103), (118), (129), (137), (236),
% 250.47/59.37 | | | | | | | | | (240), (285), (320) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | | #242.
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (321) all_252_21 = e4 & op(e0, e3) = e4
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | REF_CLOSE: (29), (76), (103), (321) are inconsistent by
% 250.47/59.37 | | | | | | | | | sub-proof #805.
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | End of split
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | End of split
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | End of split
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | End of split
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | Case 2:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | (322) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 250.47/59.37 | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | BETA: splitting (322) gives:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | Case 1:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (323) all_252_7 = e0 & op(e2, e3) = e0
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | REF_CLOSE: (29), (30), (243), (323) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | #816.
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | Case 2:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (324) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 250.47/59.37 | | | | | | op(e0, e3) = e0)
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | BETA: splitting (324) gives:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | Case 1:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (325) all_252_13 = e0 & op(e1, e3) = e0
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | ALPHA: (325) implies:
% 250.47/59.37 | | | | | | | (326) all_252_13 = e0
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | BETA: splitting (91) gives:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (327) ~ (all_46_2 = e2)
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REDUCE: (160), (327) imply:
% 250.47/59.37 | | | | | | | | (328) ~ (all_36_2 = e2)
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | BETA: splitting (92) gives:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (329) ~ (all_72_2 = e1)
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | REDUCE: (230), (329) imply:
% 250.47/59.37 | | | | | | | | | (330) $false
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | CLOSE: (330) is inconsistent.
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (331) ( ~ (all_72_0 = e4) & op(e3, e1) = all_72_1 & op(e1,
% 250.47/59.37 | | | | | | | | | all_72_1) = all_72_0 & $i(all_72_0) &
% 250.47/59.37 | | | | | | | | | $i(all_72_1)) | ( ~ (all_72_1 = e2) & op(e3, e1) =
% 250.47/59.37 | | | | | | | | | all_72_1 & $i(all_72_1))
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | BETA: splitting (331) gives:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | (332) ~ (all_72_0 = e4) & op(e3, e1) = all_72_1 & op(e1,
% 250.47/59.37 | | | | | | | | | | all_72_1) = all_72_0 & $i(all_72_0) &
% 250.47/59.37 | | | | | | | | | | $i(all_72_1)
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | ALPHA: (332) implies:
% 250.47/59.37 | | | | | | | | | | (333) op(e3, e1) = all_72_1
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | REF_CLOSE: (4), (10), (11), (14), (17), (21), (23), (27),
% 250.47/59.37 | | | | | | | | | | (29), (30), (31), (33), (48), (54), (58), (71),
% 250.47/59.37 | | | | | | | | | | (72), (75), (79), (81), (84), (88), (101), (107),
% 250.47/59.37 | | | | | | | | | | (113), (118), (121), (122), (129), (137), (140),
% 250.47/59.37 | | | | | | | | | | (148), (236), (240), (245), (326), (328), (333)
% 250.47/59.37 | | | | | | | | | | are inconsistent by sub-proof #241.
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | (334) ~ (all_72_1 = e2) & op(e3, e1) = all_72_1 &
% 250.47/59.37 | | | | | | | | | | $i(all_72_1)
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | ALPHA: (334) implies:
% 250.47/59.37 | | | | | | | | | | (335) op(e3, e1) = all_72_1
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | REF_CLOSE: (4), (10), (11), (14), (17), (21), (23), (27),
% 250.47/59.37 | | | | | | | | | | (29), (30), (31), (33), (48), (54), (58), (71),
% 250.47/59.37 | | | | | | | | | | (72), (75), (79), (81), (84), (88), (101), (107),
% 250.47/59.37 | | | | | | | | | | (113), (118), (121), (122), (129), (137), (140),
% 250.47/59.37 | | | | | | | | | | (148), (236), (240), (245), (326), (328), (335)
% 250.47/59.37 | | | | | | | | | | are inconsistent by sub-proof #241.
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | End of split
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (336) all_46_2 = e2
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | COMBINE_EQS: (160), (336) imply:
% 250.47/59.37 | | | | | | | | (337) all_36_2 = e2
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REDUCE: (245), (337) imply:
% 250.47/59.37 | | | | | | | | (338) op(e0, e2) = e3
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (25), (29), (57), (338) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #975.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | End of split
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | Case 2:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (339) all_252_21 = e0 & op(e0, e3) = e0
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | ALPHA: (339) implies:
% 250.47/59.37 | | | | | | | (340) op(e0, e3) = e0
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | REF_CLOSE: (23), (29), (236), (340) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | #320.
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | End of split
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | End of split
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | End of split
% 250.47/59.37 | | | |
% 250.47/59.37 | | | End of split
% 250.47/59.37 | | |
% 250.47/59.37 | | Case 2:
% 250.47/59.37 | | |
% 250.47/59.37 | | | (341) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.47/59.37 | | | e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.47/59.37 | | |
% 250.47/59.37 | | | BETA: splitting (341) gives:
% 250.47/59.37 | | |
% 250.47/59.37 | | | Case 1:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (342) all_252_22 = e1 & op(e0, e2) = e1
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | ALPHA: (342) implies:
% 250.47/59.37 | | | | (343) op(e0, e2) = e1
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | REF_CLOSE: (29), (57), (232), (343) are inconsistent by sub-proof #907.
% 250.47/59.37 | | | |
% 250.47/59.37 | | | Case 2:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (344) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 250.47/59.37 | | | | e0) = e1)
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | BETA: splitting (344) gives:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | Case 1:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | (345) all_252_23 = e1 & op(e0, e1) = e1
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | REF_CLOSE: (58), (151), (345) are inconsistent by sub-proof #284.
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | Case 2:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | (346) all_252_24 = e1 & op(e0, e0) = e1
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | ALPHA: (346) implies:
% 250.47/59.37 | | | | | (347) all_252_24 = e1
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | BETA: splitting (108) gives:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | Case 1:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (348) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 250.47/59.37 | | | | | | op(e0, e3) = e2)
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | BETA: splitting (348) gives:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | Case 1:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (349) all_252_20 = e2 & op(e0, e4) = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | ALPHA: (349) implies:
% 250.47/59.37 | | | | | | | (350) all_252_20 = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | REF_CLOSE: (21), (23), (29), (31), (33), (56), (69), (71), (79),
% 250.47/59.37 | | | | | | | (118), (151), (236), (347), (350) are inconsistent by
% 250.47/59.37 | | | | | | | sub-proof #239.
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | Case 2:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (351) all_252_21 = e2 & op(e0, e3) = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | ALPHA: (351) implies:
% 250.47/59.37 | | | | | | | (352) op(e0, e3) = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | REF_CLOSE: (29), (54), (236), (352) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | #941.
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | End of split
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | Case 2:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (353) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 250.47/59.37 | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | BETA: splitting (353) gives:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | Case 1:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (354) all_252_22 = e2 & op(e0, e2) = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | ALPHA: (354) implies:
% 250.47/59.37 | | | | | | | (355) all_252_22 = e2
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | BETA: splitting (56) gives:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (356) all_252_24 = e0 & op(e0, e0) = e0
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | ALPHA: (356) implies:
% 250.47/59.37 | | | | | | | | (357) all_252_24 = e0
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (23), (347), (357) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #623.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (358) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0
% 250.47/59.37 | | | | | | | | & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0)
% 250.47/59.37 | | | | | | | | = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.47/59.37 | | | | | | | | ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 250.47/59.37 | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2)
% 250.47/59.37 | | | | | | | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | ALPHA: (358) implies:
% 250.47/59.37 | | | | | | | | (359) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 250.47/59.37 | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) =
% 250.47/59.37 | | | | | | | | e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | BETA: splitting (359) gives:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (360) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 =
% 250.47/59.37 | | | | | | | | | e0 & op(e0, e3) = e0)
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | REF_CLOSE: (23), (29), (71), (167), (236), (360) are
% 250.47/59.37 | | | | | | | | | inconsistent by sub-proof #312.
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | (361) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 =
% 250.47/59.37 | | | | | | | | | e0 & op(e0, e1) = e0)
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | BETA: splitting (361) gives:
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | (362) all_252_22 = e0 & op(e0, e2) = e0
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | ALPHA: (362) implies:
% 250.47/59.37 | | | | | | | | | | (363) all_252_22 = e0
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | COMBINE_EQS: (355), (363) imply:
% 250.47/59.37 | | | | | | | | | | (364) e2 = e0
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | REDUCE: (21), (364) imply:
% 250.47/59.37 | | | | | | | | | | (365) $false
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | CLOSE: (365) is inconsistent.
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | (366) all_252_23 = e0 & op(e0, e1) = e0
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | | REF_CLOSE: (33), (151), (366) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | | | #259.
% 250.47/59.37 | | | | | | | | | |
% 250.47/59.37 | | | | | | | | | End of split
% 250.47/59.37 | | | | | | | | |
% 250.47/59.37 | | | | | | | | End of split
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | End of split
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | Case 2:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (367) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.47/59.37 | | | | | | | op(e0, e0) = e2)
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | BETA: splitting (367) gives:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | Case 1:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (368) all_252_23 = e2 & op(e0, e1) = e2
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (137), (151), (368) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #579.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | Case 2:
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | (369) all_252_24 = e2 & op(e0, e0) = e2
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | | REF_CLOSE: (54), (347), (369) are inconsistent by sub-proof
% 250.47/59.37 | | | | | | | | #260.
% 250.47/59.37 | | | | | | | |
% 250.47/59.37 | | | | | | | End of split
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | End of split
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | End of split
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | End of split
% 250.47/59.37 | | | |
% 250.47/59.37 | | | End of split
% 250.47/59.37 | | |
% 250.47/59.37 | | End of split
% 250.47/59.37 | |
% 250.47/59.37 | End of split
% 250.47/59.37 |
% 250.47/59.37 End of proof
% 250.47/59.37
% 250.47/59.37 Sub-proof #239 shows that the following formulas are inconsistent:
% 250.47/59.37 ----------------------------------------------------------------
% 250.47/59.37 (1) op(e0, e3) = e1
% 250.47/59.37 (2) ~ (e2 = e0)
% 250.47/59.37 (3) ~ (e1 = e0)
% 250.47/59.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.37 (5) ~ (e3 = e2)
% 250.47/59.37 (6) ~ (e4 = e0)
% 250.47/59.37 (7) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.47/59.37 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.37 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.47/59.37 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.47/59.37 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.37 op(e0, e1) = e0)))
% 250.47/59.37 (8) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.47/59.37 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 250.47/59.37 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.47/59.37 (9) ~ (e3 = e0)
% 250.47/59.37 (10) ~ (e3 = e1)
% 250.47/59.37 (11) all_252_20 = e2
% 250.47/59.37 (12) ~ (e4 = e3)
% 250.47/59.37 (13) all_252_24 = e1
% 250.47/59.37 (14) all_252_23 = e4
% 250.47/59.37
% 250.47/59.37 Begin of proof
% 250.47/59.37 |
% 250.47/59.37 | BETA: splitting (7) gives:
% 250.47/59.37 |
% 250.47/59.37 | Case 1:
% 250.47/59.37 | |
% 250.47/59.37 | | (15) all_252_24 = e0 & op(e0, e0) = e0
% 250.47/59.37 | |
% 250.47/59.37 | | REF_CLOSE: (3), (13), (15) are inconsistent by sub-proof #297.
% 250.47/59.37 | |
% 250.47/59.37 | Case 2:
% 250.47/59.37 | |
% 250.47/59.37 | | (16) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.47/59.37 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.47/59.37 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.47/59.37 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.47/59.37 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.47/59.37 | |
% 250.47/59.37 | | ALPHA: (16) implies:
% 250.47/59.37 | | (17) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 250.47/59.37 | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.37 | | op(e0, e1) = e0)
% 250.47/59.37 | |
% 250.47/59.37 | | BETA: splitting (17) gives:
% 250.47/59.37 | |
% 250.47/59.37 | | Case 1:
% 250.47/59.37 | | |
% 250.47/59.37 | | | (18) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0,
% 250.47/59.37 | | | e3) = e0)
% 250.47/59.37 | | |
% 250.47/59.37 | | | REF_CLOSE: (1), (2), (3), (4), (11), (18) are inconsistent by sub-proof
% 250.47/59.37 | | | #319.
% 250.47/59.37 | | |
% 250.47/59.37 | | Case 2:
% 250.47/59.37 | | |
% 250.47/59.37 | | | (19) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0,
% 250.47/59.37 | | | e1) = e0)
% 250.47/59.37 | | |
% 250.47/59.37 | | | BETA: splitting (19) gives:
% 250.47/59.37 | | |
% 250.47/59.37 | | | Case 1:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (20) all_252_22 = e0 & op(e0, e2) = e0
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | ALPHA: (20) implies:
% 250.47/59.37 | | | | (21) all_252_22 = e0
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | BETA: splitting (8) gives:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | Case 1:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | (22) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 250.47/59.37 | | | | | op(e0, e3) = e3)
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | BETA: splitting (22) gives:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | Case 1:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (23) all_252_20 = e3 & op(e0, e4) = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | ALPHA: (23) implies:
% 250.47/59.37 | | | | | | (24) all_252_20 = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | REF_CLOSE: (5), (11), (24) are inconsistent by sub-proof #520.
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | Case 2:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (25) all_252_21 = e3 & op(e0, e3) = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | ALPHA: (25) implies:
% 250.47/59.37 | | | | | | (26) op(e0, e3) = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | GROUND_INST: instantiating (4) with e1, e3, e3, e0, simplifying with
% 250.47/59.37 | | | | | | (1), (26) gives:
% 250.47/59.37 | | | | | | (27) e3 = e1
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | REDUCE: (10), (27) imply:
% 250.47/59.37 | | | | | | (28) $false
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | CLOSE: (28) is inconsistent.
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | End of split
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | Case 2:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | (29) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 250.47/59.37 | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | BETA: splitting (29) gives:
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | | Case 1:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (30) all_252_22 = e3 & op(e0, e2) = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | ALPHA: (30) implies:
% 250.47/59.37 | | | | | | (31) all_252_22 = e3
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | REF_CLOSE: (9), (21), (31) are inconsistent by sub-proof #318.
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | Case 2:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | (32) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 250.47/59.37 | | | | | | op(e0, e0) = e3)
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | BETA: splitting (32) gives:
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | | Case 1:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (33) all_252_23 = e3 & op(e0, e1) = e3
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | REF_CLOSE: (12), (14), (33) are inconsistent by sub-proof #240.
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | Case 2:
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | (34) all_252_24 = e3 & op(e0, e0) = e3
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | | REF_CLOSE: (10), (13), (34) are inconsistent by sub-proof #266.
% 250.47/59.37 | | | | | | |
% 250.47/59.37 | | | | | | End of split
% 250.47/59.37 | | | | | |
% 250.47/59.37 | | | | | End of split
% 250.47/59.37 | | | | |
% 250.47/59.37 | | | | End of split
% 250.47/59.37 | | | |
% 250.47/59.37 | | | Case 2:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (35) all_252_23 = e0 & op(e0, e1) = e0
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | REF_CLOSE: (6), (14), (35) are inconsistent by sub-proof #317.
% 250.47/59.37 | | | |
% 250.47/59.37 | | | End of split
% 250.47/59.37 | | |
% 250.47/59.37 | | End of split
% 250.47/59.37 | |
% 250.47/59.37 | End of split
% 250.47/59.37 |
% 250.47/59.37 End of proof
% 250.47/59.37
% 250.47/59.37 Sub-proof #240 shows that the following formulas are inconsistent:
% 250.47/59.37 ----------------------------------------------------------------
% 250.47/59.37 (1) all_252_23 = e3 & op(e0, e1) = e3
% 250.47/59.37 (2) all_252_23 = e4
% 250.47/59.37 (3) ~ (e4 = e3)
% 250.47/59.37
% 250.47/59.37 Begin of proof
% 250.47/59.37 |
% 250.47/59.37 | ALPHA: (1) implies:
% 250.47/59.37 | (4) all_252_23 = e3
% 250.47/59.37 |
% 250.47/59.37 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.37 | (5) e4 = e3
% 250.47/59.37 |
% 250.47/59.37 | SIMP: (5) implies:
% 250.47/59.37 | (6) e4 = e3
% 250.47/59.37 |
% 250.47/59.37 | REDUCE: (3), (6) imply:
% 250.47/59.37 | (7) $false
% 250.47/59.37 |
% 250.47/59.37 | CLOSE: (7) is inconsistent.
% 250.47/59.37 |
% 250.47/59.37 End of proof
% 250.47/59.37
% 250.47/59.37 Sub-proof #241 shows that the following formulas are inconsistent:
% 250.47/59.37 ----------------------------------------------------------------
% 250.47/59.37 (1) op(e0, e3) = e1
% 250.47/59.37 (2) ~ (all_10_2 = e4)
% 250.47/59.37 (3) all_252_21 = e1
% 250.47/59.37 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.47/59.37 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.47/59.37 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.37 (5) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.47/59.37 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.47/59.37 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.47/59.37 (6) all_250_8 = all_36_2
% 250.47/59.37 (7) op(e0, all_36_2) = e3
% 250.47/59.37 (8) op(all_62_2, all_36_2) = e3
% 250.47/59.37 (9) ~ (e2 = e0)
% 250.47/59.37 (10) ~ (e1 = e0)
% 250.47/59.37 (11) all_252_13 = e0
% 250.47/59.37 (12) op(e3, e4) = e0
% 250.47/59.37 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.37 (14) op(e2, e3) = all_10_2
% 250.47/59.37 (15) ~ (e3 = e2)
% 250.47/59.37 (16) ~ (e4 = e0)
% 250.47/59.37 (17) ~ (all_36_2 = e2)
% 250.47/59.37 (18) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.37 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.47/59.37 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.47/59.37 (19) ~ (e2 = e1)
% 250.47/59.37 (20) ~ (e4 = e1)
% 250.47/59.37 (21) ~ (e3 = e0)
% 250.47/59.37 (22) ~ (all_48_2 = all_36_2)
% 250.47/59.37 (23) ~ (all_36_2 = e4)
% 250.47/59.37 (24) ~ (e3 = e1)
% 250.47/59.37 (25) op(e3, e1) = all_36_2
% 250.47/59.37 (26) ~ (all_8_2 = e1)
% 250.47/59.37 (27) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 250.47/59.37 all_250_8 = e0
% 250.47/59.37 (28) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.47/59.37 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.47/59.37 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.47/59.37 (29) op(e3, e1) = all_72_1
% 250.47/59.37 (30) op(all_62_2, e3) = e1
% 250.47/59.37 (31) ~ (all_36_2 = e0)
% 250.47/59.37 (32) ~ (e4 = e3)
% 250.47/59.37 (33) op(e0, e1) = all_20_2
% 250.47/59.37 (34) op(e3, e0) = all_48_2
% 250.47/59.37 (35) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.37 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.37 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.47/59.37 (36) ~ (e4 = e2)
% 250.47/59.37 (37) op(e3, e2) = all_8_2
% 250.47/59.37 (38) ~ (all_20_2 = e3)
% 250.47/59.37
% 250.47/59.37 Begin of proof
% 250.47/59.37 |
% 250.47/59.37 | GROUND_INST: instantiating (13) with all_36_2, all_72_1, e1, e3, simplifying
% 250.47/59.37 | with (25), (29) gives:
% 250.47/59.37 | (39) all_72_1 = all_36_2
% 250.47/59.37 |
% 250.47/59.37 | BETA: splitting (28) gives:
% 250.47/59.37 |
% 250.47/59.37 | Case 1:
% 250.47/59.37 | |
% 250.47/59.37 | | (40) ~ (all_48_2 = e1)
% 250.47/59.37 | |
% 250.47/59.37 | | BETA: splitting (18) gives:
% 250.47/59.37 | |
% 250.47/59.37 | | Case 1:
% 250.47/59.37 | | |
% 250.47/59.37 | | | (41) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3)
% 250.47/59.37 | | | = e1)
% 250.47/59.37 | | |
% 250.47/59.37 | | | BETA: splitting (41) gives:
% 250.47/59.37 | | |
% 250.47/59.37 | | | Case 1:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (42) all_252_2 = e1 & op(e3, e4) = e1
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | ALPHA: (42) implies:
% 250.47/59.37 | | | | (43) op(e3, e4) = e1
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | REF_CLOSE: (10), (12), (13), (43) are inconsistent by sub-proof #607.
% 250.47/59.37 | | | |
% 250.47/59.37 | | | Case 2:
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | (44) all_252_3 = e1 & op(e3, e3) = e1
% 250.47/59.37 | | | |
% 250.47/59.37 | | | | ALPHA: (44) implies:
% 250.47/59.37 | | | | (45) all_252_3 = e1
% 250.47/59.37 | | | |
% 250.47/59.38 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (11), (13), (14), (15), (16),
% 250.47/59.38 | | | | (19), (20), (21), (24), (32), (35), (36), (45) are
% 250.47/59.38 | | | | inconsistent by sub-proof #363.
% 250.47/59.38 | | | |
% 250.47/59.38 | | | End of split
% 250.47/59.38 | | |
% 250.47/59.38 | | Case 2:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (46) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1)
% 250.47/59.38 | | | = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.47/59.38 | | |
% 250.47/59.38 | | | BETA: splitting (46) gives:
% 250.47/59.38 | | |
% 250.47/59.38 | | | Case 1:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | (47) all_252_5 = e1 & op(e3, e2) = e1
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | ALPHA: (47) implies:
% 250.47/59.38 | | | | (48) op(e3, e2) = e1
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | REF_CLOSE: (13), (26), (37), (48) are inconsistent by sub-proof #929.
% 250.47/59.38 | | | |
% 250.47/59.38 | | | Case 2:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | (49) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 250.47/59.38 | | | | e0) = e1)
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | BETA: splitting (49) gives:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | Case 1:
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | (50) all_252_10 = e1 & op(e3, e1) = e1
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | ALPHA: (50) implies:
% 250.47/59.38 | | | | | (51) op(e3, e1) = e1
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | GROUND_INST: instantiating (13) with all_36_2, e1, e1, e3, simplifying
% 250.47/59.38 | | | | | with (25), (51) gives:
% 250.47/59.38 | | | | | (52) all_36_2 = e1
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | REDUCE: (7), (52) imply:
% 250.47/59.38 | | | | | (53) op(e0, e1) = e3
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | REF_CLOSE: (13), (33), (38), (53) are inconsistent by sub-proof #974.
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | Case 2:
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | (54) all_252_17 = e1 & op(e3, e0) = e1
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | ALPHA: (54) implies:
% 250.47/59.38 | | | | | (55) op(e3, e0) = e1
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | REF_CLOSE: (13), (34), (40), (55) are inconsistent by sub-proof #889.
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | End of split
% 250.47/59.38 | | | |
% 250.47/59.38 | | | End of split
% 250.47/59.38 | | |
% 250.47/59.38 | | End of split
% 250.47/59.38 | |
% 250.47/59.38 | Case 2:
% 250.47/59.38 | |
% 250.47/59.38 | | (56) all_48_2 = e1
% 250.47/59.38 | |
% 250.47/59.38 | | REDUCE: (22), (56) imply:
% 250.47/59.38 | | (57) ~ (all_36_2 = e1)
% 250.47/59.38 | |
% 250.47/59.38 | | SIMP: (57) implies:
% 250.47/59.38 | | (58) ~ (all_36_2 = e1)
% 250.47/59.38 | |
% 250.47/59.38 | | REF_CLOSE: (6), (8), (13), (17), (23), (27), (30), (31), (58) are
% 250.47/59.38 | | inconsistent by sub-proof #658.
% 250.47/59.38 | |
% 250.47/59.38 | End of split
% 250.47/59.38 |
% 250.47/59.38 End of proof
% 250.47/59.38
% 250.47/59.38 Sub-proof #242 shows that the following formulas are inconsistent:
% 250.47/59.38 ----------------------------------------------------------------
% 250.47/59.38 (1) op(e0, e3) = e1
% 250.47/59.38 (2) all_252_21 = e1
% 250.47/59.38 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.47/59.38 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.47/59.38 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.38 (4) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.47/59.38 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.47/59.38 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.47/59.38 (5) ~ (e2 = e0)
% 250.47/59.38 (6) all_252_13 = e0
% 250.47/59.38 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.38 (8) ~ (e3 = e2)
% 250.47/59.38 (9) ~ (e4 = e0)
% 250.47/59.38 (10) ~ (e2 = e1)
% 250.47/59.38 (11) ~ (e3 = e0)
% 250.47/59.38 (12) ~ (all_22_2 = e4)
% 250.47/59.38 (13) ~ (e3 = e1)
% 250.47/59.38 (14) op(e0, e3) = all_22_2
% 250.47/59.38 (15) ~ (e4 = e3)
% 250.47/59.38 (16) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.38 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.38 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.47/59.38 (17) ~ (e4 = e2)
% 250.47/59.38 (18) all_252_3 = e0
% 250.47/59.38
% 250.47/59.38 Begin of proof
% 250.47/59.38 |
% 250.47/59.38 | BETA: splitting (3) gives:
% 250.47/59.38 |
% 250.47/59.38 | Case 1:
% 250.47/59.38 | |
% 250.47/59.38 | | (19) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.47/59.38 | | e4)
% 250.47/59.38 | |
% 250.47/59.38 | | BETA: splitting (19) gives:
% 250.47/59.38 | |
% 250.47/59.38 | | Case 1:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (20) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.38 | | |
% 250.47/59.38 | | | ALPHA: (20) implies:
% 250.47/59.38 | | | (21) all_252_1 = e4
% 250.47/59.38 | | |
% 250.47/59.38 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (13), (15),
% 250.47/59.38 | | | (16), (17), (18), (21) are inconsistent by sub-proof #374.
% 250.47/59.38 | | |
% 250.47/59.38 | | Case 2:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (22) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.38 | | |
% 250.47/59.38 | | | REF_CLOSE: (9), (18), (22) are inconsistent by sub-proof #373.
% 250.47/59.38 | | |
% 250.47/59.38 | | End of split
% 250.47/59.38 | |
% 250.47/59.38 | Case 2:
% 250.47/59.38 | |
% 250.47/59.38 | | (23) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.47/59.38 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.38 | |
% 250.47/59.38 | | BETA: splitting (23) gives:
% 250.47/59.38 | |
% 250.47/59.38 | | Case 1:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (24) all_252_7 = e4 & op(e2, e3) = e4
% 250.47/59.38 | | |
% 250.47/59.38 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (13), (15),
% 250.47/59.38 | | | (16), (17), (18), (24) are inconsistent by sub-proof #368.
% 250.47/59.38 | | |
% 250.47/59.38 | | Case 2:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (25) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 250.47/59.38 | | | e3) = e4)
% 250.47/59.38 | | |
% 250.47/59.38 | | | BETA: splitting (25) gives:
% 250.47/59.38 | | |
% 250.47/59.38 | | | Case 1:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | (26) all_252_13 = e4 & op(e1, e3) = e4
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | REF_CLOSE: (6), (9), (26) are inconsistent by sub-proof #413.
% 250.47/59.38 | | | |
% 250.47/59.38 | | | Case 2:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | (27) all_252_21 = e4 & op(e0, e3) = e4
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | REF_CLOSE: (7), (12), (14), (27) are inconsistent by sub-proof #805.
% 250.47/59.38 | | | |
% 250.47/59.38 | | | End of split
% 250.47/59.38 | | |
% 250.47/59.38 | | End of split
% 250.47/59.38 | |
% 250.47/59.38 | End of split
% 250.47/59.38 |
% 250.47/59.38 End of proof
% 250.47/59.38
% 250.47/59.38 Sub-proof #243 shows that the following formulas are inconsistent:
% 250.47/59.38 ----------------------------------------------------------------
% 250.47/59.38 (1) all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0
% 250.47/59.38 (2) ~ (all_6_2 = e1)
% 250.47/59.38 (3) ~ (all_6_2 = e2)
% 250.47/59.38 (4) ~ (all_6_2 = e0)
% 250.47/59.38 (5) all_250_2 = all_6_2
% 250.47/59.38
% 250.47/59.38 Begin of proof
% 250.47/59.38 |
% 250.47/59.38 | BETA: splitting (1) gives:
% 250.47/59.38 |
% 250.47/59.38 | Case 1:
% 250.47/59.38 | |
% 250.47/59.38 | | (6) all_250_2 = e2
% 250.47/59.38 | |
% 250.47/59.38 | | COMBINE_EQS: (5), (6) imply:
% 250.47/59.38 | | (7) all_6_2 = e2
% 250.47/59.38 | |
% 250.47/59.38 | | SIMP: (7) implies:
% 250.47/59.38 | | (8) all_6_2 = e2
% 250.47/59.38 | |
% 250.47/59.38 | | REDUCE: (3), (8) imply:
% 250.47/59.38 | | (9) $false
% 250.47/59.38 | |
% 250.47/59.38 | | CLOSE: (9) is inconsistent.
% 250.47/59.38 | |
% 250.47/59.38 | Case 2:
% 250.47/59.38 | |
% 250.47/59.38 | | (10) all_250_2 = e1 | all_250_2 = e0
% 250.47/59.38 | |
% 250.47/59.38 | | BETA: splitting (10) gives:
% 250.47/59.38 | |
% 250.47/59.38 | | Case 1:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (11) all_250_2 = e1
% 250.47/59.38 | | |
% 250.47/59.38 | | | COMBINE_EQS: (5), (11) imply:
% 250.47/59.38 | | | (12) all_6_2 = e1
% 250.47/59.38 | | |
% 250.47/59.38 | | | SIMP: (12) implies:
% 250.47/59.38 | | | (13) all_6_2 = e1
% 250.47/59.38 | | |
% 250.47/59.38 | | | REDUCE: (2), (13) imply:
% 250.47/59.38 | | | (14) $false
% 250.47/59.38 | | |
% 250.47/59.38 | | | CLOSE: (14) is inconsistent.
% 250.47/59.38 | | |
% 250.47/59.38 | | Case 2:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (15) all_250_2 = e0
% 250.47/59.38 | | |
% 250.47/59.38 | | | COMBINE_EQS: (5), (15) imply:
% 250.47/59.38 | | | (16) all_6_2 = e0
% 250.47/59.38 | | |
% 250.47/59.38 | | | SIMP: (16) implies:
% 250.47/59.38 | | | (17) all_6_2 = e0
% 250.47/59.38 | | |
% 250.47/59.38 | | | REDUCE: (4), (17) imply:
% 250.47/59.38 | | | (18) $false
% 250.47/59.38 | | |
% 250.47/59.38 | | | CLOSE: (18) is inconsistent.
% 250.47/59.38 | | |
% 250.47/59.38 | | End of split
% 250.47/59.38 | |
% 250.47/59.38 | End of split
% 250.47/59.38 |
% 250.47/59.38 End of proof
% 250.47/59.38
% 250.47/59.38 Sub-proof #244 shows that the following formulas are inconsistent:
% 250.47/59.38 ----------------------------------------------------------------
% 250.47/59.38 (1) ~ (all_244_8 = all_4_2)
% 250.47/59.38 (2) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.47/59.38 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.47/59.38 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.47/59.38 (3) ~ (all_4_2 = e4)
% 250.47/59.38 (4) ~ (all_10_2 = e4)
% 250.47/59.38 (5) op(all_4_2, e2) = e1
% 250.47/59.38 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.47/59.38 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.47/59.38 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.47/59.38 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.47/59.38 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.47/59.38 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.47/59.38 (8) op(e4, e1) = e0
% 250.47/59.38 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.47/59.38 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.47/59.38 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.38 (10) op(e4, e0) = all_30_2
% 250.47/59.38 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.38 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.47/59.38 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.47/59.38 (12) ~ (all_30_2 = e0)
% 250.47/59.38 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.47/59.38 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.47/59.38 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.47/59.38 (14) op(all_62_2, all_36_2) = e3
% 250.47/59.38 (15) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 250.47/59.38 all_250_15 = e0
% 250.47/59.38 (16) ~ (all_28_2 = all_6_2)
% 250.47/59.38 (17) ~ (e2 = e0)
% 250.47/59.38 (18) op(all_38_2, all_4_2) = e1
% 250.47/59.38 (19) ~ (e1 = e0)
% 250.47/59.38 (20) ~ (all_22_2 = e3)
% 250.47/59.38 (21) ~ (all_28_2 = e3)
% 250.47/59.38 (22) ~ (all_62_2 = all_22_2)
% 250.47/59.38 (23) op(e3, e4) = e0
% 250.47/59.38 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.38 (25) op(e2, e3) = all_10_2
% 250.47/59.38 (26) ~ (e3 = e2)
% 250.47/59.38 (27) op(e0, e0) = all_244_24
% 250.47/59.38 (28) ~ (e4 = e0)
% 250.47/59.38 (29) op(e2, e2) = all_244_8
% 250.47/59.38 (30) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.47/59.38 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.47/59.38 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.47/59.38 (31) op(e2, e1) = all_38_2
% 250.47/59.38 (32) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.47/59.38 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.47/59.38 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.47/59.38 (33) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.47/59.38 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.47/59.38 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.47/59.38 (34) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.47/59.38 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.47/59.38 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.38 (35) op(all_28_2, e2) = e0
% 250.47/59.38 (36) op(e4, e2) = all_6_2
% 250.47/59.38 (37) ~ (all_244_15 = e0)
% 250.47/59.38 (38) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.38 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.47/59.38 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.47/59.38 (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.47/59.38 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.47/59.38 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.47/59.38 (40) all_78_2 = all_10_2
% 250.47/59.38 (41) ~ (all_8_2 = all_4_2)
% 250.47/59.38 (42) ~ (all_244_15 = e4)
% 250.47/59.38 (43) ~ (all_34_2 = e2)
% 250.47/59.38 (44) ~ (e2 = e1)
% 250.47/59.38 (45) op(all_26_2, e1) = e4
% 250.47/59.38 (46) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.47/59.38 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.38 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.47/59.38 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.47/59.38 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.38 op(e0, e1) = e0)))
% 250.47/59.38 (47) op(e0, e2) = all_28_2
% 250.47/59.38 (48) ~ (e4 = e1)
% 250.47/59.38 (49) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.47/59.38 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.47/59.38 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.47/59.38 (50) ~ (all_244_8 = all_38_2)
% 250.47/59.38 (51) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.47/59.38 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.47/59.38 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.47/59.38 (52) op(all_244_15, all_244_15) = e1
% 250.47/59.38 (53) all_250_21 = all_22_2
% 250.47/59.38 (54) all_50_2 = all_4_2
% 250.47/59.38 (55) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.47/59.38 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.47/59.38 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.47/59.38 (56) op(e1, e4) = all_16_2
% 250.47/59.38 (57) op(e1, e3) = all_62_2
% 250.47/59.38 (58) ~ (e3 = e0)
% 250.47/59.38 (59) ~ (all_48_2 = all_36_2)
% 250.47/59.38 (60) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.47/59.38 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.47/59.38 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.47/59.38 (61) all_252_2 = e0
% 250.47/59.38 (62) ~ (all_36_2 = e4)
% 250.47/59.38 (63) ~ (all_22_2 = e4)
% 250.47/59.38 (64) all_70_2 = all_62_2
% 250.47/59.38 (65) ~ (all_36_2 = all_8_2)
% 250.47/59.38 (66) ~ (e3 = e1)
% 250.47/59.38 (67) op(all_48_2, all_22_2) = e0
% 250.47/59.38 (68) op(e3, e1) = all_36_2
% 250.47/59.38 (69) all_216_1 = all_34_2
% 250.47/59.38 (70) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.47/59.38 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.47/59.38 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.47/59.38 (71) ~ (all_16_2 = e2)
% 250.47/59.38 (72) ~ (all_8_2 = e1)
% 250.47/59.38 (73) op(all_40_2, e0) = e2
% 250.47/59.38 (74) all_252_9 = e0
% 250.47/59.38 (75) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.47/59.38 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.47/59.38 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.47/59.38 (76) ~ (all_22_2 = e1)
% 250.47/59.38 (77) ~ (all_28_2 = all_4_2)
% 250.47/59.38 (78) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.47/59.38 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.47/59.38 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.47/59.38 (79) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.47/59.38 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.47/59.38 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.47/59.38 (80) ~ (all_244_15 = all_38_2)
% 250.47/59.38 (81) ~ (all_48_2 = all_8_2)
% 250.47/59.38 (82) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.47/59.38 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.47/59.38 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.47/59.38 (83) ~ (all_8_2 = e0)
% 250.47/59.38 (84) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.47/59.38 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.47/59.38 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.47/59.38 (85) ~ (all_38_2 = e4)
% 250.47/59.38 (86) ~ (all_28_2 = e4)
% 250.47/59.38 (87) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.47/59.38 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.47/59.38 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.47/59.38 (88) op(e0, e3) = all_22_2
% 250.47/59.38 (89) ~ (all_28_2 = all_22_2)
% 250.47/59.38 (90) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.47/59.38 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.47/59.38 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.47/59.38 (91) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.47/59.38 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.47/59.38 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.47/59.38 (92) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.47/59.38 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.47/59.38 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.38 (93) op(all_10_2, e3) = e2
% 250.47/59.38 (94) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 250.47/59.38 all_250_21 = e0
% 250.47/59.38 (95) ~ (all_62_2 = all_16_2)
% 250.47/59.38 (96) ~ (all_36_2 = e0)
% 250.47/59.38 (97) all_250_15 = all_16_2
% 250.47/59.38 (98) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.47/59.38 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.47/59.38 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.47/59.38 (99) ~ (e4 = e3)
% 250.47/59.38 (100) op(e1, e1) = all_244_15
% 250.47/59.38 (101) op(e1, e0) = all_216_1
% 250.47/59.38 (102) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.47/59.38 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.47/59.38 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.47/59.38 (103) op(e0, e1) = all_20_2
% 250.47/59.38 (104) op(e3, e0) = all_48_2
% 250.47/59.38 (105) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 250.47/59.38 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 250.47/59.38 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.47/59.38 (106) op(all_48_2, e0) = e3
% 250.47/59.38 (107) ~ (all_38_2 = all_36_2)
% 250.47/59.38 (108) all_82_2 = all_28_2
% 250.47/59.38 (109) op(e1, e2) = all_4_2
% 250.47/59.38 (110) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.38 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.38 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.47/59.38 (111) ~ (all_28_2 = all_8_2)
% 250.47/59.38 (112) ~ (all_48_2 = e0)
% 250.47/59.38 (113) op(all_244_3, all_244_3) = e3
% 250.47/59.38 (114) ~ (all_6_2 = all_4_2)
% 250.47/59.38 (115) ~ (e4 = e2)
% 250.47/59.38 (116) ~ (all_146_1 = e2)
% 250.47/59.38 (117) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.47/59.38 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 250.47/59.38 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.47/59.38 (118) ~ (all_6_2 = e0)
% 250.47/59.38 (119) op(e3, e2) = all_8_2
% 250.47/59.38 (120) op(all_36_2, e1) = e3
% 250.47/59.38 (121) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.47/59.38 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.47/59.38 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.47/59.38 (122) ~ (all_244_15 = all_36_2)
% 250.47/59.38 (123) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.47/59.38 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.47/59.38 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.47/59.38 (124) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.38 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.47/59.38 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.47/59.38 (125) ~ (all_244_3 = e0)
% 250.47/59.38 (126) op(e2, e0) = all_40_2
% 250.47/59.38 (127) ~ (all_20_2 = e3)
% 250.47/59.38 (128) ~ (all_16_2 = e3)
% 250.47/59.38 (129) ~ (all_244_8 = all_28_2)
% 250.47/59.38 (130) all_252_23 = e4
% 250.47/59.38 (131) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.47/59.38 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.47/59.38 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.47/59.38 (132) op(e3, e3) = all_244_3
% 250.47/59.38 (133) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.47/59.38 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.47/59.38 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.47/59.38 (134) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.47/59.38 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.47/59.38 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.47/59.38 (135) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.38 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.47/59.38 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.47/59.38 (136) op(all_26_2, all_16_2) = e1
% 250.47/59.38 (137) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.47/59.38 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.47/59.38 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.47/59.38 (138) all_46_2 = all_36_2
% 250.47/59.38 (139) op(e4, e0) = all_146_1
% 250.47/59.38 (140) op(all_244_24, all_244_24) = e0
% 250.47/59.38 (141) ~ (all_16_2 = e0)
% 250.47/59.38 (142) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 250.47/59.38 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 250.47/59.38 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 250.47/59.38 (143) all_252_20 = e3
% 250.47/59.38
% 250.47/59.38 Begin of proof
% 250.47/59.38 |
% 250.47/59.38 | REDUCE: (69), (101) imply:
% 250.47/59.38 | (144) op(e1, e0) = all_34_2
% 250.47/59.38 |
% 250.47/59.38 | BETA: splitting (60) gives:
% 250.47/59.38 |
% 250.47/59.38 | Case 1:
% 250.47/59.38 | |
% 250.47/59.38 | | (145) ~ (all_40_2 = e4)
% 250.47/59.38 | |
% 250.47/59.38 | | BETA: splitting (79) gives:
% 250.47/59.38 | |
% 250.47/59.38 | | Case 1:
% 250.47/59.38 | | |
% 250.47/59.38 | | | (146) ~ (all_46_2 = e2)
% 250.47/59.38 | | |
% 250.47/59.38 | | | REDUCE: (138), (146) imply:
% 250.47/59.38 | | | (147) ~ (all_36_2 = e2)
% 250.47/59.38 | | |
% 250.47/59.38 | | | BETA: splitting (142) gives:
% 250.47/59.38 | | |
% 250.47/59.38 | | | Case 1:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | (148) ~ (all_50_2 = e3)
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | REDUCE: (54), (148) imply:
% 250.47/59.38 | | | | (149) ~ (all_4_2 = e3)
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | BETA: splitting (105) gives:
% 250.47/59.38 | | | |
% 250.47/59.38 | | | | Case 1:
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | (150) ~ (all_62_2 = e4)
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | BETA: splitting (82) gives:
% 250.47/59.38 | | | | |
% 250.47/59.38 | | | | | Case 1:
% 250.47/59.38 | | | | | |
% 250.47/59.38 | | | | | | (151) ~ (all_70_2 = e2)
% 250.47/59.38 | | | | | |
% 250.47/59.38 | | | | | | REDUCE: (64), (151) imply:
% 250.47/59.38 | | | | | | (152) ~ (all_62_2 = e2)
% 250.47/59.38 | | | | | |
% 250.47/59.38 | | | | | | BETA: splitting (70) gives:
% 250.47/59.38 | | | | | |
% 250.47/59.38 | | | | | | Case 1:
% 250.47/59.38 | | | | | | |
% 250.47/59.38 | | | | | | | (153) ~ (all_78_2 = e1)
% 250.47/59.38 | | | | | | |
% 250.47/59.38 | | | | | | | REDUCE: (40), (153) imply:
% 250.47/59.38 | | | | | | | (154) ~ (all_10_2 = e1)
% 250.47/59.38 | | | | | | |
% 250.47/59.38 | | | | | | | BETA: splitting (13) gives:
% 250.47/59.38 | | | | | | |
% 250.47/59.38 | | | | | | | Case 1:
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | (155) ~ (all_82_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (108), (155) imply:
% 250.47/59.38 | | | | | | | | (156) ~ (all_28_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REF_CLOSE: (24), (27), (37), (47), (48), (66), (75), (76), (88),
% 250.47/59.38 | | | | | | | | (100), (130), (140), (143), (156) are inconsistent by
% 250.47/59.38 | | | | | | | | sub-proof #283.
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | Case 2:
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | (157) all_82_2 = e1
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | COMBINE_EQS: (108), (157) imply:
% 250.47/59.38 | | | | | | | | (158) all_28_2 = e1
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | SIMP: (158) implies:
% 250.47/59.38 | | | | | | | | (159) all_28_2 = e1
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (129), (159) imply:
% 250.47/59.38 | | | | | | | | (160) ~ (all_244_8 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (89), (159) imply:
% 250.47/59.38 | | | | | | | | (161) ~ (all_22_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (111), (159) imply:
% 250.47/59.38 | | | | | | | | (162) ~ (all_8_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (16), (159) imply:
% 250.47/59.38 | | | | | | | | (163) ~ (all_6_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | SIMP: (163) implies:
% 250.47/59.38 | | | | | | | | (164) ~ (all_6_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (77), (159) imply:
% 250.47/59.38 | | | | | | | | (165) ~ (all_4_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | SIMP: (165) implies:
% 250.47/59.38 | | | | | | | | (166) ~ (all_4_2 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (86), (159) imply:
% 250.47/59.38 | | | | | | | | (167) ~ (e4 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (21), (159) imply:
% 250.47/59.38 | | | | | | | | (168) ~ (e3 = e1)
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (35), (159) imply:
% 250.47/59.38 | | | | | | | | (169) op(e1, e2) = e0
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | REDUCE: (47), (159) imply:
% 250.47/59.38 | | | | | | | | (170) op(e0, e2) = e1
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | BETA: splitting (75) gives:
% 250.47/59.38 | | | | | | | |
% 250.47/59.38 | | | | | | | | Case 1:
% 250.47/59.38 | | | | | | | | |
% 250.47/59.39 | | | | | | | | | (171) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 =
% 250.47/59.39 | | | | | | | | | e1 & op(e0, e3) = e1)
% 250.47/59.39 | | | | | | | | |
% 250.47/59.39 | | | | | | | | | REF_CLOSE: (24), (66), (76), (88), (143), (171) are
% 250.47/59.39 | | | | | | | | | inconsistent by sub-proof #285.
% 250.47/59.39 | | | | | | | | |
% 250.47/59.39 | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | |
% 250.47/59.39 | | | | | | | | | (172) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 =
% 250.47/59.39 | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 250.47/59.39 | | | | | | | | | e0) = e1)
% 250.47/59.39 | | | | | | | | |
% 250.47/59.39 | | | | | | | | | BETA: splitting (172) gives:
% 250.47/59.39 | | | | | | | | |
% 250.47/59.39 | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | (173) all_252_22 = e1 & op(e0, e2) = e1
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | ALPHA: (173) implies:
% 250.47/59.39 | | | | | | | | | | (174) all_252_22 = e1
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | REF_CLOSE: (1), (17), (24), (29), (36), (41), (43), (51),
% 250.47/59.39 | | | | | | | | | | (52), (56), (57), (71), (100), (109), (114),
% 250.47/59.39 | | | | | | | | | | (119), (131), (144), (152), (160), (166), (169),
% 250.47/59.39 | | | | | | | | | | (174) are inconsistent by sub-proof #868.
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | (175) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 =
% 250.47/59.39 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | BETA: splitting (175) gives:
% 250.47/59.39 | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | (176) all_252_23 = e1 & op(e0, e1) = e1
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | REF_CLOSE: (48), (130), (176) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | #284.
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | (177) all_252_24 = e1 & op(e0, e0) = e1
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | ALPHA: (177) implies:
% 250.47/59.39 | | | | | | | | | | | (178) all_252_24 = e1
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | BETA: splitting (32) gives:
% 250.47/59.39 | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | (179) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 250.47/59.39 | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | REF_CLOSE: (24), (36), (72), (119), (164), (179) are
% 250.47/59.39 | | | | | | | | | | | | inconsistent by sub-proof #928.
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | (180) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 250.47/59.39 | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.47/59.39 | | | | | | | | | | | | op(e0, e2) = e1)
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | BETA: splitting (180) gives:
% 250.47/59.39 | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | (181) all_252_8 = e1 & op(e2, e2) = e1
% 250.47/59.39 | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | ALPHA: (181) implies:
% 250.47/59.39 | | | | | | | | | | | | | (182) all_252_8 = e1
% 250.47/59.39 | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | BETA: splitting (91) gives:
% 250.47/59.39 | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | (183) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 250.47/59.39 | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 250.47/59.39 | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 250.47/59.39 | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | (184) all_252_6 = e4 & op(e2, e4) = e4
% 250.47/59.39 | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | (185) all_252_6 = e4
% 250.47/59.39 | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 250.47/59.39 | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | (186) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.47/59.39 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | (187) all_252_20 = e2 & op(e0, e4) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | (188) all_252_20 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (143), (188) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | #520.
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | (189) all_252_21 = e2 & op(e0, e3) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | (190) all_252_21 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | (191) op(e0, e3) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (192) all_252_24 = e0 & op(e0, e0) = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (193) all_252_24 = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (178), (193) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | #623.
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (194) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.47/59.39 | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | (195) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | = e0)
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | (196) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (197) all_252_0 = e2 & op(e4, e4) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (198) all_252_0 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | (199) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (19), (23), (24), (26), (44), (56),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | (68), (71), (83), (96), (104), (112), (115),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | (119), (121), (125), (132), (143), (185), (199)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #517.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | (200) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | (201) all_252_6 = e1 & op(e2, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | (202) all_252_6 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (185), (202) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | #844.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | (203) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | (204) all_252_12 = e1 & op(e1, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_12 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | (206) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (24), (44), (48), (57), (66), (137),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | (143), (150), (185), (198), (206) are inconsistent
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #282.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | (207) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_14 = e4 & op(e1, e2) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | (209) op(e1, e2) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (24), (109), (209) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | (210) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_252_15 = e4 & op(e1, e1) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (212) op(e1, e1) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (42), (100), (212) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #756.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_252_19 = e4 & op(e1, e0) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_19 = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (215) op(e1, e0) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_16 = e0 & op(e4, e0) = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (24), (217) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #469.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_17 = e0 & op(e3, e0) = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (104), (112), (218) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #573.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_18 = e0 & op(e2, e0) = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_18 = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_16 = e2 & op(e4, e0) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) op(e4, e0) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (116), (139), (224) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #253.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_17 = e2 & op(e3, e0) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_252_17 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) op(e3, e0) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_252_16 = e3 & op(e4, e0) = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_16 = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_252_0 = e1 & op(e4, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_0 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (24), (26), (44), (56), (68), (71),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (96), (104), (112), (115), (119), (121),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (132), (143), (185), (233) are inconsistent
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #518.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_1 = e1 & op(e4, e3) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_1 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (235), (237) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_252_3 = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_252_0 = e4 & op(e4, e4) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (198), (241) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #606.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (235), (242) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_252_4 = e4 & op(e4, e2) = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_4 = e4
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_252_2 = e1 & op(e3, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) op(e3, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (24), (248) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #607.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_252_3 = e1 & op(e3, e3) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_252_3 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (250) imply:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) e4 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (26), (28), (33), (48), (58), (66), (74),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (115), (198), (235), (245), (251) are
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #250.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_252_5 = e1 & op(e3, e2) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) op(e3, e2) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (72), (119), (254) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_252_10 = e1 & op(e3, e1) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_252_10 = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (23), (24), (28), (44), (48), (58),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (66), (68), (83), (96), (99), (104), (112),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (119), (123), (125), (132), (137), (143),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (198), (239), (258) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #281.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_252_5 = e3 & op(e3, e2) = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_252_5 = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (115), (245), (261), (262) are inconsistent
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_252_8 = e2 & op(e2, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (24), (26), (44), (56), (68), (71),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (96), (104), (112), (115), (119), (121),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (132), (143), (182), (185), (198), (264)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #477.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_252_14 = e2 & op(e1, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (17), (19), (20),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (28), (30), (31), (44),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (56), (57), (58), (63), (66), (68), (71),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (83), (84), (88), (96), (98), (99), (104),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (110), (112), (115), (119), (121), (123),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (128), (130), (131), (132), (135), (137),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (141), (143), (147), (149), (150), (154), (169),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (185), (190), (191), (198), (205), (214),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (221), (266) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_252_22 = e2 & op(e0, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_252_22 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) op(e0, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (17), (19), (23), (24), (25), (26), (28), (33),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (36), (38), (39), (42), (44), (46), (48),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (51), (55), (56), (57), (58), (63), (66),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (71), (72), (74), (83), (88), (90), (96),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (99), (100), (103), (104), (109), (112),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (116), (117), (118), (119), (121), (123),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (127), (128), (130), (131), (132), (137),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (141), (143), (149), (150), (152), (164),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (178), (182), (185), (268), (269) are
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #245.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_252_10 = e3 & op(e3, e1) = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (26), (39), (58), (66), (99), (178), (215),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221), (226), (230), (257), (271) are inconsistent
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #269.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_252_17 = e3 & op(e3, e0) = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (226), (272) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_252_17 = e1 & op(e3, e0) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) op(e3, e0) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (44), (227), (274) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #427.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (23), (24), (28), (44), (48), (66),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (74), (83), (96), (99), (104), (112), (115),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (119), (123), (125), (132), (137), (143), (185),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (205), (230), (275) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #268.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (11), (17), (24), (25), (26), (28),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (58), (63), (71), (88), (99), (109), (115),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (131), (141), (149), (214), (215), (276)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #277.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (24), (26), (36), (39), (58), (66), (74),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (99), (164), (178), (215), (221), (226), (277) are
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_252_17 = e3 & op(e3, e0) = e3
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (226), (278) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (58), (66), (99), (178), (215), (221), (279)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #265.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_18 = e2 & op(e2, e0) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (19), (24), (26), (28), (44), (48),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (66), (68), (83), (96), (99), (104), (112), (115),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (119), (121), (123), (125), (132), (137), (143),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (221), (281) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #275.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (24), (26), (44), (56), (68), (71),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (96), (104), (112), (115), (119), (121),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (132), (143), (178), (185), (198), (215),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) are inconsistent by sub-proof #264.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_252_19 = e0 & op(e1, e0) = e0
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24), (28), (48), (68), (83), (96), (99),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (112), (115), (119), (123), (125), (132),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (185), (198), (205), (214), (283) are
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #263.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | (284) all_252_20 = e1 & op(e0, e4) = e1
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (143), (284) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | | #509.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (285) all_252_2 = e2 & op(e3, e4) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (286) all_252_2 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (24), (68), (83), (96), (104), (112),
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (119), (125), (132), (286) are inconsistent by
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | sub-proof #571.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | (287) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (288) all_252_6 = e2 & op(e2, e4) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (185), (288) are inconsistent by sub-proof
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | #921.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | (289) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (26), (56), (71), (143), (289) are
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519.
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | End of split
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | Case 2:
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | (290) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.47/59.39 | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.47/59.39 | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 250.47/59.39 | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | (291) all_252_22 = e2 & op(e0, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.39 | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 250.47/59.39 | | | | | | | | | | | | | | | | | (292) all_252_22 = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | | (293) op(e0, e2) = e2
% 250.47/59.39 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (17), (19), (23), (24), (25), (26), (28), (33),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (34), (36), (38), (39), (42), (44), (46), (48),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (49), (51), (55), (56), (57), (58), (63), (66),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (68), (71), (72), (74), (83), (88), (90), (96),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (98), (99), (100), (103), (104), (109), (112),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (115), (116), (117), (118), (119), (121), (123),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (125), (127), (128), (130), (131), (132), (137),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (139), (141), (143), (149), (150), (152), (164),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (170), (178), (182), (185), (292), (293) are
% 250.47/59.40 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #245.
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | (294) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.47/59.40 | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | (295) all_252_23 = e2 & op(e0, e1) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (130), (295) are inconsistent by sub-proof
% 250.47/59.40 | | | | | | | | | | | | | | | | | | #274.
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | (296) all_252_24 = e2 & op(e0, e0) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (178), (296) are inconsistent by sub-proof
% 250.47/59.40 | | | | | | | | | | | | | | | | | | #260.
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | (297) all_252_7 = e4 & op(e2, e3) = e4
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | (298) op(e2, e3) = e4
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (25), (298) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | | | sub-proof #953.
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | (299) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 250.47/59.40 | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 250.47/59.40 | | | | | | | | | | | | | | op(e2, e0) = e4)
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | REF_CLOSE: (24), (31), (48), (85), (126), (145), (182), (299)
% 250.47/59.40 | | | | | | | | | | | | | | are inconsistent by sub-proof #262.
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | (300) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 250.47/59.40 | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | BETA: splitting (300) gives:
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | (301) all_252_14 = e1 & op(e1, e2) = e1
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | ALPHA: (301) implies:
% 250.47/59.40 | | | | | | | | | | | | | | (302) op(e1, e2) = e1
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | REF_CLOSE: (19), (24), (109), (169), (302) are inconsistent
% 250.47/59.40 | | | | | | | | | | | | | | by sub-proof #870.
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | (303) all_252_22 = e1 & op(e0, e2) = e1
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | ALPHA: (303) implies:
% 250.47/59.40 | | | | | | | | | | | | | | (304) all_252_22 = e1
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (28), (44), (46), (58), (92),
% 250.47/59.40 | | | | | | | | | | | | | | (115), (130), (143), (178), (304) are inconsistent
% 250.47/59.40 | | | | | | | | | | | | | | by sub-proof #258.
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | End of split
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | End of split
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | Case 2:
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | (305) all_78_2 = e1
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | REF_CLOSE: (24), (40), (57), (93), (152), (305) are inconsistent
% 250.47/59.40 | | | | | | | by sub-proof #971.
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | End of split
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | Case 2:
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | (306) all_70_2 = e2
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | COMBINE_EQS: (64), (306) imply:
% 250.47/59.40 | | | | | | (307) all_62_2 = e2
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | REF_CLOSE: (20), (22), (24), (53), (63), (67), (76), (94), (106),
% 250.47/59.40 | | | | | | (307) are inconsistent by sub-proof #852.
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | End of split
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | Case 2:
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | (308) all_62_2 = e4
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | REDUCE: (95), (308) imply:
% 250.47/59.40 | | | | | (309) ~ (all_16_2 = e4)
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | SIMP: (309) implies:
% 250.47/59.40 | | | | | (310) ~ (all_16_2 = e4)
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | REF_CLOSE: (15), (24), (45), (71), (97), (128), (136), (141), (310)
% 250.47/59.40 | | | | | are inconsistent by sub-proof #466.
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | End of split
% 250.47/59.40 | | | |
% 250.47/59.40 | | | Case 2:
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | (311) all_50_2 = e3
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | COMBINE_EQS: (54), (311) imply:
% 250.47/59.40 | | | | (312) all_4_2 = e3
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | REDUCE: (5), (312) imply:
% 250.47/59.40 | | | | (313) op(e3, e2) = e1
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | REF_CLOSE: (24), (72), (119), (313) are inconsistent by sub-proof #929.
% 250.47/59.40 | | | |
% 250.47/59.40 | | | End of split
% 250.47/59.40 | | |
% 250.47/59.40 | | Case 2:
% 250.47/59.40 | | |
% 250.47/59.40 | | | (314) all_46_2 = e2
% 250.47/59.40 | | | (315) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 250.47/59.40 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 250.47/59.40 | | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.47/59.40 | | |
% 250.47/59.40 | | | COMBINE_EQS: (138), (314) imply:
% 250.47/59.40 | | | (316) all_36_2 = e2
% 250.47/59.40 | | |
% 250.47/59.40 | | | SIMP: (316) implies:
% 250.47/59.40 | | | (317) all_36_2 = e2
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (122), (317) imply:
% 250.47/59.40 | | | (318) ~ (all_244_15 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (59), (317) imply:
% 250.47/59.40 | | | (319) ~ (all_48_2 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (107), (317) imply:
% 250.47/59.40 | | | (320) ~ (all_38_2 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (65), (317) imply:
% 250.47/59.40 | | | (321) ~ (all_8_2 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | SIMP: (321) implies:
% 250.47/59.40 | | | (322) ~ (all_8_2 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (62), (317) imply:
% 250.47/59.40 | | | (323) ~ (e4 = e2)
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (14), (317) imply:
% 250.47/59.40 | | | (324) op(all_62_2, e2) = e3
% 250.47/59.40 | | |
% 250.47/59.40 | | | REDUCE: (120), (317) imply:
% 250.47/59.40 | | | (325) op(e2, e1) = e3
% 250.47/59.40 | | |
% 250.47/59.40 | | | REF_CLOSE: (7), (8), (17), (18), (19), (23), (24), (26), (28), (29), (31),
% 250.47/59.40 | | | (38), (44), (48), (50), (56), (57), (58), (61), (62), (64),
% 250.47/59.40 | | | (66), (68), (71), (72), (80), (81), (82), (83), (87), (96),
% 250.47/59.40 | | | (98), (99), (100), (102), (104), (106), (109), (112), (113),
% 250.47/59.40 | | | (115), (119), (124), (125), (130), (131), (132), (134), (315),
% 250.47/59.40 | | | (318), (319), (320), (322), (324), (325) are inconsistent by
% 250.47/59.40 | | | sub-proof #255.
% 250.47/59.40 | | |
% 250.47/59.40 | | End of split
% 250.47/59.40 | |
% 250.47/59.40 | Case 2:
% 250.47/59.40 | |
% 250.47/59.40 | | (326) all_40_2 = e4
% 250.47/59.40 | |
% 250.47/59.40 | | REDUCE: (73), (326) imply:
% 250.47/59.40 | | (327) op(e4, e0) = e2
% 250.47/59.40 | |
% 250.47/59.40 | | REF_CLOSE: (24), (116), (139), (327) are inconsistent by sub-proof #253.
% 250.47/59.40 | |
% 250.47/59.40 | End of split
% 250.47/59.40 |
% 250.47/59.40 End of proof
% 250.47/59.40
% 250.47/59.40 Sub-proof #245 shows that the following formulas are inconsistent:
% 250.47/59.40 ----------------------------------------------------------------
% 250.47/59.40 (1) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.47/59.40 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.47/59.40 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.47/59.40 (2) ~ (all_4_2 = e4)
% 250.47/59.40 (3) ~ (all_10_2 = e4)
% 250.47/59.40 (4) all_252_6 = e4
% 250.47/59.40 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.47/59.40 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.47/59.40 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.47/59.40 (6) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.47/59.40 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.47/59.40 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.47/59.40 (7) op(e0, e2) = e2
% 250.47/59.40 (8) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.47/59.40 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.47/59.40 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.40 (9) op(e4, e0) = all_30_2
% 250.47/59.40 (10) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.40 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.47/59.40 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.47/59.40 (11) ~ (all_30_2 = e0)
% 250.47/59.40 (12) ~ (e2 = e0)
% 250.47/59.40 (13) ~ (e1 = e0)
% 250.47/59.40 (14) op(e3, e4) = e0
% 250.47/59.40 (15) ~ (all_62_2 = e2)
% 250.47/59.40 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.40 (17) op(e2, e3) = all_10_2
% 250.47/59.40 (18) ~ (e3 = e2)
% 250.47/59.40 (19) ~ (e4 = e0)
% 250.47/59.40 (20) all_252_22 = e2
% 250.47/59.40 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.47/59.40 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.47/59.40 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.47/59.40 (22) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.47/59.40 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.47/59.40 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.40 (23) op(e4, e2) = all_6_2
% 250.47/59.40 (24) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.40 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.47/59.40 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.47/59.40 (25) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.47/59.40 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.47/59.40 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.47/59.40 (26) ~ (all_244_15 = e4)
% 250.47/59.40 (27) ~ (e2 = e1)
% 250.47/59.40 (28) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.47/59.40 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.40 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.47/59.40 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.47/59.40 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.40 op(e0, e1) = e0)))
% 250.47/59.40 (29) ~ (e4 = e1)
% 250.47/59.40 (30) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.47/59.40 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.47/59.40 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.47/59.40 (31) ~ (all_6_2 = e1)
% 250.47/59.40 (32) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.47/59.40 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.47/59.40 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.47/59.40 (33) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.47/59.40 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.47/59.40 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.47/59.40 (34) op(e1, e4) = all_16_2
% 250.47/59.40 (35) op(e1, e3) = all_62_2
% 250.47/59.40 (36) ~ (e3 = e0)
% 250.47/59.40 (37) ~ (all_22_2 = e4)
% 250.47/59.40 (38) ~ (e3 = e1)
% 250.47/59.40 (39) op(e3, e1) = all_36_2
% 250.47/59.40 (40) ~ (all_16_2 = e2)
% 250.47/59.40 (41) ~ (all_8_2 = e1)
% 250.47/59.40 (42) all_252_9 = e0
% 250.47/59.40 (43) ~ (all_8_2 = e0)
% 250.47/59.40 (44) op(e0, e3) = all_22_2
% 250.47/59.40 (45) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.47/59.40 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.47/59.40 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.47/59.40 (46) op(e0, e2) = e1
% 250.47/59.40 (47) ~ (all_36_2 = e0)
% 250.47/59.40 (48) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.47/59.40 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.47/59.40 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.47/59.40 (49) ~ (e4 = e3)
% 250.47/59.40 (50) op(e1, e1) = all_244_15
% 250.47/59.40 (51) op(e0, e1) = all_20_2
% 250.47/59.40 (52) op(e3, e0) = all_48_2
% 250.47/59.40 (53) op(e1, e2) = all_4_2
% 250.47/59.40 (54) ~ (all_48_2 = e0)
% 250.47/59.40 (55) all_252_24 = e1
% 250.47/59.40 (56) ~ (e4 = e2)
% 250.47/59.40 (57) ~ (all_146_1 = e2)
% 250.47/59.40 (58) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.47/59.40 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.47/59.40 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 250.47/59.40 (59) ~ (all_6_2 = e0)
% 250.47/59.40 (60) op(e3, e2) = all_8_2
% 250.47/59.40 (61) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.47/59.40 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.47/59.40 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.47/59.40 (62) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.47/59.40 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.47/59.40 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.47/59.40 (63) ~ (all_244_3 = e0)
% 250.47/59.40 (64) ~ (all_20_2 = e3)
% 250.47/59.40 (65) ~ (all_16_2 = e3)
% 250.47/59.40 (66) all_252_8 = e1
% 250.47/59.40 (67) all_252_23 = e4
% 250.47/59.40 (68) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.47/59.40 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.47/59.40 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.47/59.40 (69) op(e3, e3) = all_244_3
% 250.47/59.40 (70) ~ (all_4_2 = e3)
% 250.47/59.40 (71) ~ (all_62_2 = e4)
% 250.47/59.40 (72) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.47/59.40 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.47/59.40 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.47/59.40 (73) op(e4, e0) = all_146_1
% 250.47/59.40 (74) ~ (all_16_2 = e0)
% 250.47/59.40 (75) all_252_20 = e3
% 250.47/59.40
% 250.47/59.40 Begin of proof
% 250.47/59.40 |
% 250.47/59.40 | BETA: splitting (32) gives:
% 250.47/59.40 |
% 250.47/59.40 | Case 1:
% 250.47/59.40 | |
% 250.47/59.40 | | (76) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 250.47/59.40 | | e0)
% 250.47/59.40 | |
% 250.47/59.40 | | BETA: splitting (76) gives:
% 250.47/59.40 | |
% 250.47/59.40 | | Case 1:
% 250.47/59.40 | | |
% 250.47/59.40 | | | (77) all_252_4 = e0 & op(e4, e2) = e0
% 250.47/59.40 | | |
% 250.47/59.40 | | | REF_CLOSE: (16), (23), (59), (77) are inconsistent by sub-proof #875.
% 250.47/59.40 | | |
% 250.47/59.40 | | Case 2:
% 250.47/59.40 | | |
% 250.47/59.40 | | | (78) all_252_5 = e0 & op(e3, e2) = e0
% 250.47/59.40 | | |
% 250.47/59.40 | | | REF_CLOSE: (16), (43), (60), (78) are inconsistent by sub-proof #874.
% 250.47/59.40 | | |
% 250.47/59.40 | | End of split
% 250.47/59.40 | |
% 250.47/59.40 | Case 2:
% 250.47/59.40 | |
% 250.47/59.40 | | (79) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.47/59.40 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.47/59.40 | |
% 250.47/59.40 | | BETA: splitting (79) gives:
% 250.47/59.40 | |
% 250.47/59.40 | | Case 1:
% 250.47/59.40 | | |
% 250.47/59.40 | | | (80) all_252_8 = e0 & op(e2, e2) = e0
% 250.47/59.40 | | |
% 250.47/59.40 | | | ALPHA: (80) implies:
% 250.47/59.40 | | | (81) all_252_8 = e0
% 250.47/59.40 | | |
% 250.47/59.40 | | | REF_CLOSE: (13), (66), (81) are inconsistent by sub-proof #249.
% 250.47/59.40 | | |
% 250.47/59.40 | | Case 2:
% 250.47/59.40 | | |
% 250.47/59.40 | | | (82) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 250.47/59.40 | | | e2) = e0)
% 250.47/59.40 | | |
% 250.47/59.40 | | | BETA: splitting (82) gives:
% 250.47/59.40 | | |
% 250.47/59.40 | | | Case 1:
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | (83) all_252_14 = e0 & op(e1, e2) = e0
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | ALPHA: (83) implies:
% 250.47/59.40 | | | | (84) all_252_14 = e0
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | BETA: splitting (28) gives:
% 250.47/59.40 | | | |
% 250.47/59.40 | | | | Case 1:
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | (85) all_252_24 = e0 & op(e0, e0) = e0
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | ALPHA: (85) implies:
% 250.47/59.40 | | | | | (86) all_252_24 = e0
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | REF_CLOSE: (13), (55), (86) are inconsistent by sub-proof #623.
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | Case 2:
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | (87) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.47/59.40 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.47/59.40 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.47/59.40 | | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.47/59.40 | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.40 | | | | | op(e0, e1) = e0))
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | ALPHA: (87) implies:
% 250.47/59.40 | | | | | (88) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.47/59.40 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.47/59.40 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | BETA: splitting (61) gives:
% 250.47/59.40 | | | | |
% 250.47/59.40 | | | | | Case 1:
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | (89) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 &
% 250.47/59.40 | | | | | | op(e3, e4) = e2)
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | BETA: splitting (89) gives:
% 250.47/59.40 | | | | | |
% 250.47/59.40 | | | | | | Case 1:
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | (90) all_252_0 = e2 & op(e4, e4) = e2
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | ALPHA: (90) implies:
% 250.47/59.40 | | | | | | | (91) all_252_0 = e2
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | BETA: splitting (72) gives:
% 250.47/59.40 | | | | | | |
% 250.47/59.40 | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | | (92) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 250.47/59.40 | | | | | | | | op(e3, e4) = e1)
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | | REF_CLOSE: (4), (6), (12), (13), (14), (16), (18), (27), (34),
% 250.47/59.40 | | | | | | | | (39), (40), (43), (47), (52), (54), (56), (60), (61),
% 250.47/59.40 | | | | | | | | (63), (69), (75), (92) are inconsistent by sub-proof
% 250.47/59.40 | | | | | | | | #517.
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | | (93) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 250.47/59.40 | | | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | | BETA: splitting (93) gives:
% 250.47/59.40 | | | | | | | |
% 250.47/59.40 | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | (94) all_252_6 = e1 & op(e2, e4) = e1
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | ALPHA: (94) implies:
% 250.47/59.40 | | | | | | | | | (95) all_252_6 = e1
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | REF_CLOSE: (4), (29), (95) are inconsistent by sub-proof #844.
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | (96) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1
% 250.47/59.40 | | | | | | | | | & op(e0, e4) = e1)
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | BETA: splitting (96) gives:
% 250.47/59.40 | | | | | | | | |
% 250.47/59.40 | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | (97) all_252_12 = e1 & op(e1, e4) = e1
% 250.47/59.40 | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | ALPHA: (97) implies:
% 250.47/59.40 | | | | | | | | | | (98) all_252_12 = e1
% 250.47/59.40 | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | BETA: splitting (45) gives:
% 250.47/59.40 | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | (99) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.47/59.40 | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | REF_CLOSE: (4), (13), (14), (16), (27), (29), (35), (38),
% 250.47/59.40 | | | | | | | | | | | (71), (72), (75), (91), (99) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | sub-proof #282.
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | (100) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.47/59.40 | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.47/59.40 | | | | | | | | | | | op(e1, e0) = e4)
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | BETA: splitting (100) gives:
% 250.47/59.40 | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | (101) all_252_14 = e4 & op(e1, e2) = e4
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | ALPHA: (101) implies:
% 250.47/59.40 | | | | | | | | | | | | (102) op(e1, e2) = e4
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | REF_CLOSE: (2), (16), (53), (102) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | sub-proof #831.
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | (103) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.47/59.40 | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | BETA: splitting (103) gives:
% 250.47/59.40 | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | (104) all_252_15 = e4 & op(e1, e1) = e4
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | ALPHA: (104) implies:
% 250.47/59.40 | | | | | | | | | | | | | (105) op(e1, e1) = e4
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | REF_CLOSE: (16), (26), (50), (105) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | sub-proof #756.
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | (106) all_252_19 = e4 & op(e1, e0) = e4
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | ALPHA: (106) implies:
% 250.47/59.40 | | | | | | | | | | | | | (107) all_252_19 = e4
% 250.47/59.40 | | | | | | | | | | | | | (108) op(e1, e0) = e4
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | BETA: splitting (88) gives:
% 250.47/59.40 | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | (109) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.40 | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | (110) all_252_16 = e0 & op(e4, e0) = e0
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (16), (110) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | | | sub-proof #469.
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | (111) all_252_17 = e0 & op(e3, e0) = e0
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | REF_CLOSE: (16), (52), (54), (111) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | | | sub-proof #573.
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | End of split
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | (112) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.47/59.40 | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 250.47/59.40 | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | (113) all_252_18 = e0 & op(e2, e0) = e0
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | (114) all_252_18 = e0
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 250.47/59.40 | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | (115) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 250.47/59.40 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (34), (35), (40), (115) are
% 250.47/59.40 | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | (116) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 250.47/59.40 | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 250.47/59.40 | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | (117) all_252_14 = e2 & op(e1, e2) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | (118) all_252_14 = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (118) imply:
% 250.47/59.40 | | | | | | | | | | | | | | | | | (119) e2 = e0
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (119) imply:
% 250.47/59.40 | | | | | | | | | | | | | | | | | (120) all_252_0 = e0
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (13), (16), (18), (19), (27), (29),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (38), (39), (43), (47), (49), (52), (54), (56),
% 250.47/59.40 | | | | | | | | | | | | | | | | | (60), (61), (62), (63), (69), (72), (75), (120)
% 250.47/59.40 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #559.
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | (121) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 250.47/59.40 | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | (122) all_252_15 = e2 & op(e1, e1) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | (123) all_252_15 = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | (124) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 250.47/59.40 | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | (125) all_252_16 = e2 & op(e4, e0) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | (126) op(e4, e0) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (57), (73), (126) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | sub-proof #253.
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | (127) all_252_17 = e2 & op(e3, e0) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | (128) all_252_17 = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | (129) op(e3, e0) = e2
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | (130) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | (131) all_252_16 = e3 & op(e4, e0) = e3
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | (132) all_252_16 = e3
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | (133) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (134) all_252_0 = e1 & op(e4, e4) = e1
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (135) all_252_0 = e1
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (16), (18), (27), (34), (39),
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (40), (43), (47), (52), (54), (56), (60), (61),
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (63), (69), (75), (135) are inconsistent by
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (136) all_252_1 = e1 & op(e4, e3) = e1
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | (137) all_252_1 = e1
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | (138) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (139) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (137), (139) are inconsistent by sub-proof
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (140) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (141) all_252_3 = e4
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (142) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (29), (141), (142) are
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (143) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144) all_252_5 = e1 & op(e3, e2) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145) op(e3, e2) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (41), (60), (145) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (147) all_252_10 = e1 & op(e3, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (148) all_252_10 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150) all_252_0 = e4 & op(e4, e4) = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (91), (150) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #606.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (151) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (137), (151) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (152) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153) all_252_4 = e4 & op(e4, e2) = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_4 = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_9 = e3 & op(e4, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (156) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_10 = e3 & op(e3, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (25), (36), (38), (49), (55), (108),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (128), (132), (148), (157) are inconsistent
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #269.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_11 = e3 & op(e2, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_11 = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_9 = e1 & op(e4, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (42), (162) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e1, e2, e2, e0,
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (7), (46) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) e2 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (163) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_0 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (16), (18), (27), (34), (39),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (40), (43), (47), (52), (54), (56), (60), (61),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (63), (69), (75), (164) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_11 = e1 & op(e2, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_11 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_252_9 = e3 & op(e4, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (169) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #251.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_10 = e3 & op(e3, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (148), (170) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (159), (167) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #449.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_15 = e3 & op(e1, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (123), (172) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #405.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_23 = e3 & op(e0, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_23 = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (174) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) e4 = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (175) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) $false
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_15 = e1 & op(e1, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_252_15 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_9 = e2 & op(e4, e1) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_9 = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (182) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) e2 = e0
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (183) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) $false
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_252_10 = e2 & op(e3, e1) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_10 = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (186) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) e2 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (187) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) $false
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_11 = e2 & op(e2, e1) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_11 = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (191) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) e3 = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (192) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) $false
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (122), (179) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #246.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_23 = e2 & op(e0, e1) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (67), (195) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #579.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_23 = e1 & op(e0, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_23 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (197) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e4 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) e4 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18), (19), (21), (29), (36), (38), (42),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (56), (91), (137), (154), (199) are
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #250.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_252_15 = e3 & op(e1, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (123), (201) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #405.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_23 = e3 & op(e0, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) op(e0, e1) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (64), (203) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_9 = e4 & op(e4, e1) = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (16), (19), (29), (39), (42), (43),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (49), (52), (54), (56), (60), (62), (63),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (75), (91), (98), (205) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #516.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_16 = e4 & op(e4, e0) = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_252_16 = e4
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (207) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) e4 = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (208) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_252_6 = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (16), (19), (27), (29), (38),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (43), (47), (49), (52), (54), (56), (60),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (63), (69), (72), (75), (91), (209) are
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_17 = e1 & op(e3, e0) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) op(e3, e0) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (27), (129), (211) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #427.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (10), (12), (16), (17), (18), (19),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (34), (36), (37), (40), (44), (49), (53), (56),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (65), (68), (70), (74), (107), (108), (212) are
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #277.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | (213) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_4 = e1 & op(e4, e2) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | (215) op(e4, e2) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (31), (215) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #930.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 =
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_9 = e1 & op(e4, e1) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (42), (217) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | #247.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_16 = e1 & op(e4, e0) = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_252_16 = e1
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (25), (36), (38), (49), (55), (108),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | (114), (128), (219) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | | #270.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | (220) all_252_17 = e3 & op(e3, e0) = e3
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (128), (220) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | | #272.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | (221) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (36), (38), (49), (55), (108), (114), (221)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #271.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | (222) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (223) all_252_18 = e2 & op(e2, e0) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (224) all_252_18 = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (224) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (225) e2 = e0
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (13), (16), (18), (19), (27), (29),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (38), (39), (43), (47), (49), (52), (54), (56),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (60), (61), (62), (63), (69), (72), (75), (91),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (225) are inconsistent by sub-proof #493.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (226) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (16), (18), (27), (34), (39),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (40), (43), (47), (52), (54), (55), (56), (60),
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | (61), (63), (69), (75), (91), (108), (226) are
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #264.
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | (227) all_252_19 = e2 & op(e1, e0) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | | | | (228) op(e1, e0) = e2
% 250.47/59.41 | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (108), (228) are inconsistent by
% 250.47/59.41 | | | | | | | | | | | | | | | | | | sub-proof #829.
% 250.47/59.41 | | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | (229) all_252_19 = e0 & op(e1, e0) = e0
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 250.47/59.41 | | | | | | | | | | | | | | | (230) all_252_19 = e0
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | COMBINE_EQS: (107), (230) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | (231) e4 = e0
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | COMBINE_EQS: (4), (231) imply:
% 250.47/59.41 | | | | | | | | | | | | | | | (232) all_252_6 = e0
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (19), (29), (39), (43), (47), (49),
% 250.47/59.41 | | | | | | | | | | | | | | | (52), (54), (56), (60), (62), (63), (69), (75),
% 250.47/59.41 | | | | | | | | | | | | | | | (91), (98), (232) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | | | | | | #551.
% 250.47/59.41 | | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | Case 2:
% 250.47/59.41 | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | (233) all_252_20 = e1 & op(e0, e4) = e1
% 250.47/59.41 | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | | REF_CLOSE: (38), (75), (233) are inconsistent by sub-proof
% 250.47/59.41 | | | | | | | | | | #509.
% 250.47/59.41 | | | | | | | | | |
% 250.47/59.41 | | | | | | | | | End of split
% 250.47/59.41 | | | | | | | | |
% 250.47/59.41 | | | | | | | | End of split
% 250.47/59.41 | | | | | | | |
% 250.47/59.41 | | | | | | | End of split
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | Case 2:
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | (234) all_252_2 = e2 & op(e3, e4) = e2
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | ALPHA: (234) implies:
% 250.47/59.41 | | | | | | | (235) all_252_2 = e2
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | REF_CLOSE: (6), (12), (16), (39), (43), (47), (52), (54), (60),
% 250.47/59.41 | | | | | | | (63), (69), (235) are inconsistent by sub-proof #571.
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | End of split
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | Case 2:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | (236) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 250.47/59.41 | | | | | | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | BETA: splitting (236) gives:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | Case 1:
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | (237) all_252_6 = e2 & op(e2, e4) = e2
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | REF_CLOSE: (4), (56), (237) are inconsistent by sub-proof #921.
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | Case 2:
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | (238) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.47/59.41 | | | | | | | op(e0, e4) = e2)
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | REF_CLOSE: (16), (18), (34), (40), (75), (238) are inconsistent by
% 250.47/59.41 | | | | | | | sub-proof #519.
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | End of split
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | End of split
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | End of split
% 250.47/59.41 | | | |
% 250.47/59.41 | | | Case 2:
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | (239) all_252_22 = e0 & op(e0, e2) = e0
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | REF_CLOSE: (12), (20), (239) are inconsistent by sub-proof #608.
% 250.47/59.41 | | | |
% 250.47/59.41 | | | End of split
% 250.47/59.41 | | |
% 250.47/59.41 | | End of split
% 250.47/59.41 | |
% 250.47/59.41 | End of split
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #246 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) all_252_15 = e2 & op(e1, e1) = e2
% 250.47/59.41 (2) all_252_15 = e1
% 250.47/59.41 (3) ~ (e2 = e1)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.41 | ALPHA: (1) implies:
% 250.47/59.41 | (4) all_252_15 = e2
% 250.47/59.41 |
% 250.47/59.41 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.41 | (5) e2 = e1
% 250.47/59.41 |
% 250.47/59.41 | REDUCE: (3), (5) imply:
% 250.47/59.41 | (6) $false
% 250.47/59.41 |
% 250.47/59.41 | CLOSE: (6) is inconsistent.
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #247 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) all_252_9 = e1 & op(e4, e1) = e1
% 250.47/59.41 (2) all_252_9 = e0
% 250.47/59.41 (3) ~ (e1 = e0)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.41 | ALPHA: (1) implies:
% 250.47/59.41 | (4) all_252_9 = e1
% 250.47/59.41 |
% 250.47/59.41 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.41 | (5) e1 = e0
% 250.47/59.41 |
% 250.47/59.41 | SIMP: (5) implies:
% 250.47/59.41 | (6) e1 = e0
% 250.47/59.41 |
% 250.47/59.41 | REDUCE: (3), (6) imply:
% 250.47/59.41 | (7) $false
% 250.47/59.41 |
% 250.47/59.41 | CLOSE: (7) is inconsistent.
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #248 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) all_252_9 = e3 & op(e4, e1) = e3
% 250.47/59.41 (2) all_252_9 = e0
% 250.47/59.41 (3) ~ (e3 = e0)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.41 | ALPHA: (1) implies:
% 250.47/59.41 | (4) all_252_9 = e3
% 250.47/59.41 |
% 250.47/59.41 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.41 | (5) e3 = e0
% 250.47/59.41 |
% 250.47/59.41 | SIMP: (5) implies:
% 250.47/59.41 | (6) e3 = e0
% 250.47/59.41 |
% 250.47/59.41 | REDUCE: (3), (6) imply:
% 250.47/59.41 | (7) $false
% 250.47/59.41 |
% 250.47/59.41 | CLOSE: (7) is inconsistent.
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #249 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) all_252_8 = e1
% 250.47/59.41 (2) all_252_8 = e0
% 250.47/59.41 (3) ~ (e1 = e0)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.41 | COMBINE_EQS: (1), (2) imply:
% 250.47/59.41 | (4) e1 = e0
% 250.47/59.41 |
% 250.47/59.41 | SIMP: (4) implies:
% 250.47/59.41 | (5) e1 = e0
% 250.47/59.41 |
% 250.47/59.41 | REDUCE: (3), (5) imply:
% 250.47/59.41 | (6) $false
% 250.47/59.41 |
% 250.47/59.41 | CLOSE: (6) is inconsistent.
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #250 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.47/59.41 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.47/59.41 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.47/59.41 (2) all_252_4 = e4
% 250.47/59.41 (3) ~ (e3 = e2)
% 250.47/59.41 (4) ~ (e4 = e0)
% 250.47/59.41 (5) all_252_0 = e2
% 250.47/59.41 (6) all_252_1 = e1
% 250.47/59.41 (7) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) |
% 250.47/59.41 (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = e4) |
% 250.47/59.41 (all_252_16 = e4 & op(e4, e0) = e4)
% 250.47/59.41 (8) ~ (e4 = e1)
% 250.47/59.41 (9) e4 = e1
% 250.47/59.41 (10) ~ (e3 = e0)
% 250.47/59.41 (11) ~ (e3 = e1)
% 250.47/59.41 (12) all_252_9 = e0
% 250.47/59.41 (13) ~ (e4 = e3)
% 250.47/59.41 (14) ~ (e4 = e2)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.41 | COMBINE_EQS: (2), (9) imply:
% 250.47/59.41 | (15) all_252_4 = e1
% 250.47/59.41 |
% 250.47/59.41 | BETA: splitting (1) gives:
% 250.47/59.41 |
% 250.47/59.41 | Case 1:
% 250.47/59.41 | |
% 250.47/59.41 | | (16) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) =
% 250.47/59.41 | | e3)
% 250.47/59.41 | |
% 250.47/59.41 | | BETA: splitting (16) gives:
% 250.47/59.41 | |
% 250.47/59.41 | | Case 1:
% 250.47/59.41 | | |
% 250.47/59.41 | | | (17) all_252_0 = e3 & op(e4, e4) = e3
% 250.47/59.41 | | |
% 250.47/59.41 | | | REF_CLOSE: (3), (5), (17) are inconsistent by sub-proof #897.
% 250.47/59.41 | | |
% 250.47/59.41 | | Case 2:
% 250.47/59.41 | | |
% 250.47/59.41 | | | (18) all_252_1 = e3 & op(e4, e3) = e3
% 250.47/59.41 | | |
% 250.47/59.41 | | | REF_CLOSE: (6), (11), (18) are inconsistent by sub-proof #686.
% 250.47/59.41 | | |
% 250.47/59.41 | | End of split
% 250.47/59.41 | |
% 250.47/59.41 | Case 2:
% 250.47/59.41 | |
% 250.47/59.41 | | (19) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) =
% 250.47/59.41 | | e3) | (all_252_16 = e3 & op(e4, e0) = e3)
% 250.47/59.41 | |
% 250.47/59.41 | | BETA: splitting (19) gives:
% 250.47/59.41 | |
% 250.47/59.41 | | Case 1:
% 250.47/59.41 | | |
% 250.47/59.41 | | | (20) all_252_4 = e3 & op(e4, e2) = e3
% 250.47/59.41 | | |
% 250.47/59.41 | | | REF_CLOSE: (11), (15), (20) are inconsistent by sub-proof #252.
% 250.47/59.41 | | |
% 250.47/59.41 | | Case 2:
% 250.47/59.41 | | |
% 250.47/59.41 | | | (21) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = e3 & op(e4, e0)
% 250.47/59.41 | | | = e3)
% 250.47/59.41 | | |
% 250.47/59.41 | | | BETA: splitting (21) gives:
% 250.47/59.41 | | |
% 250.47/59.41 | | | Case 1:
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | (22) all_252_9 = e3 & op(e4, e1) = e3
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | REF_CLOSE: (10), (12), (22) are inconsistent by sub-proof #251.
% 250.47/59.41 | | | |
% 250.47/59.41 | | | Case 2:
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | (23) all_252_16 = e3 & op(e4, e0) = e3
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | ALPHA: (23) implies:
% 250.47/59.41 | | | | (24) all_252_16 = e3
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | BETA: splitting (7) gives:
% 250.47/59.41 | | | |
% 250.47/59.41 | | | | Case 1:
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | (25) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4,
% 250.47/59.41 | | | | | e3) = e4)
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | BETA: splitting (25) gives:
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | Case 1:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | (26) all_252_0 = e4 & op(e4, e4) = e4
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | REF_CLOSE: (5), (14), (26) are inconsistent by sub-proof #606.
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | Case 2:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | (27) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | REF_CLOSE: (6), (8), (27) are inconsistent by sub-proof #955.
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | End of split
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | Case 2:
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | (28) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4,
% 250.47/59.41 | | | | | e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | BETA: splitting (28) gives:
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | | Case 1:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | (29) all_252_4 = e4 & op(e4, e2) = e4
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | COMBINE_EQS: (2), (15) imply:
% 250.47/59.41 | | | | | | (30) e4 = e1
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | REDUCE: (8), (9) imply:
% 250.47/59.41 | | | | | | (31) $false
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | CLOSE: (31) is inconsistent.
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | Case 2:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.47/59.41 | | | | | | op(e4, e0) = e4)
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | BETA: splitting (32) gives:
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | | Case 1:
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | (33) all_252_9 = e4 & op(e4, e1) = e4
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | REF_CLOSE: (4), (12), (33) are inconsistent by sub-proof #481.
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | Case 2:
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | (34) all_252_16 = e4 & op(e4, e0) = e4
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | | REF_CLOSE: (13), (24), (34) are inconsistent by sub-proof #483.
% 250.47/59.41 | | | | | | |
% 250.47/59.41 | | | | | | End of split
% 250.47/59.41 | | | | | |
% 250.47/59.41 | | | | | End of split
% 250.47/59.41 | | | | |
% 250.47/59.41 | | | | End of split
% 250.47/59.41 | | | |
% 250.47/59.41 | | | End of split
% 250.47/59.41 | | |
% 250.47/59.41 | | End of split
% 250.47/59.41 | |
% 250.47/59.41 | End of split
% 250.47/59.41 |
% 250.47/59.41 End of proof
% 250.47/59.41
% 250.47/59.41 Sub-proof #251 shows that the following formulas are inconsistent:
% 250.47/59.41 ----------------------------------------------------------------
% 250.47/59.41 (1) all_252_9 = e3 & op(e4, e1) = e3
% 250.47/59.41 (2) all_252_9 = e0
% 250.47/59.41 (3) ~ (e3 = e0)
% 250.47/59.41
% 250.47/59.41 Begin of proof
% 250.47/59.41 |
% 250.47/59.42 | ALPHA: (1) implies:
% 250.47/59.42 | (4) all_252_9 = e3
% 250.47/59.42 |
% 250.47/59.42 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.42 | (5) e3 = e0
% 250.47/59.42 |
% 250.47/59.42 | REDUCE: (3), (5) imply:
% 250.47/59.42 | (6) $false
% 250.47/59.42 |
% 250.47/59.42 | CLOSE: (6) is inconsistent.
% 250.47/59.42 |
% 250.47/59.42 End of proof
% 250.47/59.42
% 250.47/59.42 Sub-proof #252 shows that the following formulas are inconsistent:
% 250.47/59.42 ----------------------------------------------------------------
% 250.47/59.42 (1) all_252_4 = e3 & op(e4, e2) = e3
% 250.47/59.42 (2) all_252_4 = e1
% 250.47/59.42 (3) ~ (e3 = e1)
% 250.47/59.42
% 250.47/59.42 Begin of proof
% 250.47/59.42 |
% 250.47/59.42 | ALPHA: (1) implies:
% 250.47/59.42 | (4) all_252_4 = e3
% 250.47/59.42 |
% 250.47/59.42 | COMBINE_EQS: (2), (4) imply:
% 250.47/59.42 | (5) e3 = e1
% 250.47/59.42 |
% 250.47/59.42 | SIMP: (5) implies:
% 250.47/59.42 | (6) e3 = e1
% 250.47/59.42 |
% 250.47/59.42 | REDUCE: (3), (6) imply:
% 250.47/59.42 | (7) $false
% 250.47/59.42 |
% 250.47/59.42 | CLOSE: (7) is inconsistent.
% 250.47/59.42 |
% 250.47/59.42 End of proof
% 250.47/59.42
% 250.47/59.42 Sub-proof #253 shows that the following formulas are inconsistent:
% 250.47/59.42 ----------------------------------------------------------------
% 250.47/59.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.42 (2) op(e4, e0) = all_146_1
% 250.47/59.42 (3) op(e4, e0) = e2
% 250.47/59.42 (4) ~ (all_146_1 = e2)
% 250.47/59.42
% 250.47/59.42 Begin of proof
% 250.47/59.42 |
% 250.47/59.42 | GROUND_INST: instantiating (1) with e2, all_146_1, e0, e4, simplifying with
% 250.47/59.42 | (2), (3) gives:
% 250.47/59.42 | (5) all_146_1 = e2
% 250.47/59.42 |
% 250.47/59.42 | REDUCE: (4), (5) imply:
% 250.47/59.42 | (6) $false
% 250.47/59.42 |
% 250.47/59.42 | CLOSE: (6) is inconsistent.
% 250.47/59.42 |
% 250.47/59.42 End of proof
% 250.47/59.42
% 250.47/59.42 Sub-proof #254 shows that the following formulas are inconsistent:
% 250.47/59.42 ----------------------------------------------------------------
% 250.47/59.42 (1) ~ (all_244_8 = all_4_2)
% 250.47/59.42 (2) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.47/59.42 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.47/59.42 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.47/59.42 (3) ~ (all_4_2 = e4)
% 250.47/59.42 (4) ~ (all_10_2 = e4)
% 250.47/59.42 (5) op(all_4_2, e2) = e1
% 250.47/59.42 (6) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.47/59.42 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.47/59.42 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.47/59.42 (7) op(e4, e1) = e0
% 250.47/59.42 (8) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.47/59.42 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.47/59.42 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.47/59.42 (9) op(e4, e0) = all_30_2
% 250.47/59.42 (10) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.42 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.47/59.42 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.47/59.42 (11) ~ (all_30_2 = e0)
% 250.47/59.42 (12) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.47/59.42 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.47/59.42 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.47/59.42 (13) op(all_62_2, all_36_2) = e3
% 250.47/59.42 (14) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 250.47/59.42 all_250_15 = e0
% 250.47/59.42 (15) ~ (all_28_2 = all_6_2)
% 250.47/59.42 (16) ~ (e2 = e0)
% 250.47/59.42 (17) op(all_38_2, all_4_2) = e1
% 250.47/59.42 (18) ~ (e1 = e0)
% 250.47/59.42 (19) ~ (all_22_2 = e3)
% 250.47/59.42 (20) ~ (all_28_2 = e3)
% 250.47/59.42 (21) ~ (all_62_2 = all_22_2)
% 250.47/59.42 (22) op(e3, e4) = e0
% 250.47/59.42 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.47/59.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.47/59.42 (24) op(e2, e3) = all_10_2
% 250.47/59.42 (25) ~ (e3 = e2)
% 250.47/59.42 (26) op(e0, e0) = all_244_24
% 250.47/59.42 (27) ~ (e4 = e0)
% 250.47/59.42 (28) op(e2, e2) = all_244_8
% 250.47/59.42 (29) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.47/59.42 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.47/59.42 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.47/59.42 (30) op(e2, e1) = all_38_2
% 250.47/59.42 (31) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.47/59.42 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.47/59.42 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.47/59.42 (32) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.47/59.42 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.47/59.42 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.47/59.42 (33) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.47/59.42 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.47/59.42 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.42 (34) op(e1, e0) = all_34_2
% 250.47/59.42 (35) op(all_28_2, e2) = e0
% 250.47/59.42 (36) op(e4, e2) = all_6_2
% 250.47/59.42 (37) ~ (all_244_15 = e0)
% 250.47/59.42 (38) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.42 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.47/59.42 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.47/59.42 (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.47/59.42 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.47/59.42 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.47/59.42 (40) all_78_2 = all_10_2
% 250.47/59.42 (41) ~ (all_8_2 = all_4_2)
% 250.47/59.42 (42) ~ (all_244_15 = e4)
% 250.47/59.42 (43) ~ (all_34_2 = e2)
% 250.47/59.42 (44) ~ (e2 = e1)
% 250.47/59.42 (45) op(all_26_2, e1) = e4
% 250.47/59.42 (46) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.47/59.42 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.42 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.47/59.42 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.47/59.42 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.47/59.42 op(e0, e1) = e0)))
% 250.47/59.42 (47) op(e0, e2) = all_28_2
% 250.47/59.42 (48) ~ (e4 = e1)
% 250.47/59.42 (49) ~ (all_244_8 = all_38_2)
% 250.47/59.42 (50) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.47/59.42 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.47/59.42 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.47/59.42 (51) op(all_244_15, all_244_15) = e1
% 250.47/59.42 (52) all_250_21 = all_22_2
% 250.47/59.42 (53) all_50_2 = all_4_2
% 250.47/59.42 (54) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.47/59.42 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.47/59.42 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.47/59.42 (55) op(e1, e4) = all_16_2
% 250.47/59.42 (56) op(e1, e3) = all_62_2
% 250.47/59.42 (57) ~ (e3 = e0)
% 250.47/59.42 (58) ~ (all_48_2 = all_36_2)
% 250.47/59.42 (59) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.47/59.42 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.47/59.42 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.47/59.42 (60) all_252_2 = e0
% 250.47/59.42 (61) ~ (all_30_2 = e2)
% 250.47/59.42 (62) ~ (all_36_2 = e4)
% 250.47/59.42 (63) ~ (all_22_2 = e4)
% 250.47/59.42 (64) all_70_2 = all_62_2
% 250.47/59.42 (65) ~ (all_36_2 = all_8_2)
% 250.47/59.42 (66) ~ (e3 = e1)
% 250.47/59.42 (67) op(all_48_2, all_22_2) = e0
% 250.47/59.42 (68) op(e3, e1) = all_36_2
% 250.47/59.42 (69) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.47/59.42 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.47/59.42 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.47/59.42 (70) ~ (all_16_2 = e2)
% 250.47/59.42 (71) ~ (all_8_2 = e1)
% 250.47/59.42 (72) op(all_40_2, e0) = e2
% 250.47/59.42 (73) all_252_9 = e0
% 250.47/59.42 (74) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.47/59.42 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.47/59.42 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.47/59.42 (75) ~ (all_22_2 = e1)
% 250.47/59.42 (76) ~ (all_28_2 = all_4_2)
% 250.47/59.42 (77) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.47/59.42 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.47/59.42 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.47/59.42 (78) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 250.47/59.42 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 250.47/59.42 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.47/59.42 (79) ~ (all_244_15 = all_38_2)
% 250.47/59.42 (80) ~ (all_48_2 = all_8_2)
% 250.47/59.42 (81) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.47/59.42 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.47/59.42 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.47/59.42 (82) ~ (all_8_2 = e0)
% 250.47/59.42 (83) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.47/59.42 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.47/59.42 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.47/59.42 (84) ~ (all_38_2 = e4)
% 250.47/59.42 (85) ~ (all_28_2 = e4)
% 250.47/59.42 (86) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.47/59.42 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.47/59.42 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.47/59.42 (87) op(e0, e3) = all_22_2
% 250.47/59.42 (88) ~ (all_28_2 = all_22_2)
% 250.47/59.42 (89) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.47/59.42 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.47/59.42 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.47/59.42 (90) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.47/59.42 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.47/59.42 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.47/59.42 (91) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.47/59.42 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.47/59.42 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.47/59.42 (92) op(all_10_2, e3) = e2
% 250.47/59.42 (93) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 250.47/59.42 all_250_21 = e0
% 250.47/59.42 (94) ~ (all_62_2 = all_16_2)
% 250.47/59.42 (95) ~ (all_36_2 = e0)
% 250.47/59.42 (96) all_250_15 = all_16_2
% 250.47/59.42 (97) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.47/59.42 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.47/59.42 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.47/59.42 (98) ~ (e4 = e3)
% 250.47/59.42 (99) op(e1, e1) = all_244_15
% 250.47/59.42 (100) op(e1, e0) = all_216_1
% 250.47/59.42 (101) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.47/59.42 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.47/59.42 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.47/59.42 (102) op(e3, e0) = all_48_2
% 250.47/59.42 (103) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 250.47/59.42 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 250.47/59.42 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.47/59.42 (104) op(all_48_2, e0) = e3
% 250.47/59.42 (105) ~ (all_38_2 = all_36_2)
% 250.47/59.42 (106) all_82_2 = all_28_2
% 250.47/59.42 (107) op(e1, e2) = all_4_2
% 250.47/59.42 (108) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.42 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.47/59.42 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.47/59.42 (109) ~ (all_28_2 = all_8_2)
% 250.47/59.42 (110) ~ (all_48_2 = e0)
% 250.47/59.42 (111) op(all_244_3, all_244_3) = e3
% 250.47/59.42 (112) ~ (all_6_2 = all_4_2)
% 250.47/59.42 (113) ~ (e4 = e2)
% 250.47/59.42 (114) ~ (all_6_2 = e0)
% 250.47/59.42 (115) op(e3, e2) = all_8_2
% 250.47/59.42 (116) op(all_36_2, e1) = e3
% 250.47/59.42 (117) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.47/59.42 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.47/59.42 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.47/59.42 (118) ~ (all_244_15 = all_36_2)
% 250.47/59.42 (119) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.47/59.42 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.47/59.42 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.47/59.42 (120) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.47/59.42 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.47/59.42 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.47/59.42 (121) ~ (all_244_3 = e0)
% 250.47/59.42 (122) op(e2, e0) = all_40_2
% 250.47/59.42 (123) ~ (all_16_2 = e3)
% 250.47/59.42 (124) ~ (all_244_8 = all_28_2)
% 250.47/59.42 (125) all_252_23 = e4
% 250.47/59.42 (126) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.47/59.42 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.47/59.42 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.47/59.42 (127) op(e3, e3) = all_244_3
% 250.47/59.42 (128) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.47/59.42 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.47/59.42 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.47/59.42 (129) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.47/59.42 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.47/59.42 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.47/59.42 (130) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.47/59.42 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.47/59.42 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.47/59.42 (131) op(all_26_2, all_16_2) = e1
% 250.47/59.42 (132) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.47/59.42 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.47/59.42 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.47/59.42 (133) all_46_2 = all_36_2
% 250.47/59.42 (134) op(all_244_24, all_244_24) = e0
% 250.47/59.42 (135) ~ (all_16_2 = e0)
% 250.47/59.42 (136) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 250.47/59.42 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 250.47/59.42 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 250.47/59.42 (137) all_252_20 = e3
% 250.47/59.42
% 250.47/59.42 Begin of proof
% 250.47/59.42 |
% 250.47/59.42 | GROUND_INST: instantiating (23) with all_34_2, all_216_1, e0, e1, simplifying
% 250.47/59.42 | with (34), (100) gives:
% 250.47/59.42 | (138) all_216_1 = all_34_2
% 250.47/59.42 |
% 250.47/59.42 | BETA: splitting (59) gives:
% 250.47/59.42 |
% 250.47/59.42 | Case 1:
% 250.47/59.42 | |
% 250.47/59.42 | | (139) ~ (all_40_2 = e4)
% 250.47/59.42 | |
% 250.47/59.42 | | BETA: splitting (78) gives:
% 250.47/59.42 | |
% 250.47/59.42 | | Case 1:
% 250.47/59.42 | | |
% 250.47/59.42 | | | (140) ~ (all_46_2 = e2)
% 250.47/59.42 | | |
% 250.47/59.42 | | | REDUCE: (133), (140) imply:
% 250.47/59.42 | | | (141) ~ (all_36_2 = e2)
% 250.47/59.42 | | |
% 250.47/59.42 | | | BETA: splitting (136) gives:
% 250.47/59.42 | | |
% 250.47/59.42 | | | Case 1:
% 250.47/59.42 | | | |
% 250.47/59.42 | | | | (142) ~ (all_50_2 = e3)
% 250.47/59.42 | | | |
% 250.47/59.42 | | | | REDUCE: (53), (142) imply:
% 250.47/59.42 | | | | (143) ~ (all_4_2 = e3)
% 250.47/59.42 | | | |
% 250.47/59.42 | | | | BETA: splitting (103) gives:
% 250.47/59.42 | | | |
% 250.47/59.42 | | | | Case 1:
% 250.47/59.42 | | | | |
% 250.47/59.42 | | | | | (144) ~ (all_62_2 = e4)
% 250.47/59.42 | | | | |
% 250.47/59.42 | | | | | BETA: splitting (81) gives:
% 250.47/59.42 | | | | |
% 250.47/59.42 | | | | | Case 1:
% 250.47/59.42 | | | | | |
% 250.47/59.42 | | | | | | (145) ~ (all_70_2 = e2)
% 250.47/59.42 | | | | | |
% 250.47/59.42 | | | | | | REDUCE: (64), (145) imply:
% 250.47/59.42 | | | | | | (146) ~ (all_62_2 = e2)
% 250.47/59.42 | | | | | |
% 250.47/59.42 | | | | | | BETA: splitting (69) gives:
% 250.47/59.42 | | | | | |
% 250.47/59.42 | | | | | | Case 1:
% 250.47/59.42 | | | | | | |
% 250.47/59.42 | | | | | | | (147) ~ (all_78_2 = e1)
% 250.47/59.42 | | | | | | |
% 250.47/59.42 | | | | | | | REDUCE: (40), (147) imply:
% 250.47/59.42 | | | | | | | (148) ~ (all_10_2 = e1)
% 250.47/59.42 | | | | | | |
% 250.47/59.42 | | | | | | | BETA: splitting (12) gives:
% 250.47/59.42 | | | | | | |
% 250.47/59.42 | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | (149) ~ (all_82_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (106), (149) imply:
% 250.47/59.42 | | | | | | | | (150) ~ (all_28_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REF_CLOSE: (23), (26), (37), (47), (48), (66), (74), (75), (87),
% 250.47/59.42 | | | | | | | | (99), (125), (134), (137), (150) are inconsistent by
% 250.47/59.42 | | | | | | | | sub-proof #283.
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | (151) all_82_2 = e1
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | COMBINE_EQS: (106), (151) imply:
% 250.47/59.42 | | | | | | | | (152) all_28_2 = e1
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | SIMP: (152) implies:
% 250.47/59.42 | | | | | | | | (153) all_28_2 = e1
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (124), (153) imply:
% 250.47/59.42 | | | | | | | | (154) ~ (all_244_8 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (88), (153) imply:
% 250.47/59.42 | | | | | | | | (155) ~ (all_22_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (109), (153) imply:
% 250.47/59.42 | | | | | | | | (156) ~ (all_8_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (15), (153) imply:
% 250.47/59.42 | | | | | | | | (157) ~ (all_6_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | SIMP: (157) implies:
% 250.47/59.42 | | | | | | | | (158) ~ (all_6_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (76), (153) imply:
% 250.47/59.42 | | | | | | | | (159) ~ (all_4_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | SIMP: (159) implies:
% 250.47/59.42 | | | | | | | | (160) ~ (all_4_2 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (85), (153) imply:
% 250.47/59.42 | | | | | | | | (161) ~ (e4 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (20), (153) imply:
% 250.47/59.42 | | | | | | | | (162) ~ (e3 = e1)
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | REDUCE: (35), (153) imply:
% 250.47/59.42 | | | | | | | | (163) op(e1, e2) = e0
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | BETA: splitting (74) gives:
% 250.47/59.42 | | | | | | | |
% 250.47/59.42 | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | | (164) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 =
% 250.47/59.42 | | | | | | | | | e1 & op(e0, e3) = e1)
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | | REF_CLOSE: (23), (66), (75), (87), (137), (164) are
% 250.47/59.42 | | | | | | | | | inconsistent by sub-proof #285.
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | | (165) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 =
% 250.47/59.42 | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 250.47/59.42 | | | | | | | | | e0) = e1)
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | | BETA: splitting (165) gives:
% 250.47/59.42 | | | | | | | | |
% 250.47/59.42 | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | (166) all_252_22 = e1 & op(e0, e2) = e1
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | ALPHA: (166) implies:
% 250.47/59.42 | | | | | | | | | | (167) all_252_22 = e1
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | REF_CLOSE: (1), (16), (23), (28), (34), (36), (41), (43),
% 250.47/59.42 | | | | | | | | | | (50), (51), (55), (56), (70), (99), (107), (112),
% 250.47/59.42 | | | | | | | | | | (115), (126), (146), (154), (160), (163), (167)
% 250.47/59.42 | | | | | | | | | | are inconsistent by sub-proof #868.
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | (168) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 =
% 250.47/59.42 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | BETA: splitting (168) gives:
% 250.47/59.42 | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | (169) all_252_23 = e1 & op(e0, e1) = e1
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | REF_CLOSE: (48), (125), (169) are inconsistent by sub-proof
% 250.47/59.42 | | | | | | | | | | | #284.
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | (170) all_252_24 = e1 & op(e0, e0) = e1
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | ALPHA: (170) implies:
% 250.47/59.42 | | | | | | | | | | | (171) all_252_24 = e1
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | BETA: splitting (31) gives:
% 250.47/59.42 | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | (172) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 250.47/59.42 | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | REF_CLOSE: (23), (36), (71), (115), (158), (172) are
% 250.47/59.42 | | | | | | | | | | | | inconsistent by sub-proof #928.
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | (173) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 250.47/59.42 | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.47/59.42 | | | | | | | | | | | | op(e0, e2) = e1)
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | BETA: splitting (173) gives:
% 250.47/59.42 | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | (174) all_252_8 = e1 & op(e2, e2) = e1
% 250.47/59.42 | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | ALPHA: (174) implies:
% 250.47/59.42 | | | | | | | | | | | | | (175) all_252_8 = e1
% 250.47/59.42 | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | BETA: splitting (50) gives:
% 250.47/59.42 | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | (176) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 250.47/59.42 | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | (177) all_252_4 = e0 & op(e4, e2) = e0
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | REF_CLOSE: (23), (36), (114), (177) are inconsistent by
% 250.47/59.42 | | | | | | | | | | | | | | | sub-proof #875.
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | (178) all_252_5 = e0 & op(e3, e2) = e0
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | REF_CLOSE: (23), (82), (115), (178) are inconsistent by
% 250.47/59.42 | | | | | | | | | | | | | | | sub-proof #874.
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | End of split
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | (179) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 250.47/59.42 | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 250.47/59.42 | | | | | | | | | | | | | | op(e0, e2) = e0)
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 250.47/59.42 | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | (180) all_252_8 = e0 & op(e2, e2) = e0
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | REF_CLOSE: (18), (175), (180) are inconsistent by sub-proof
% 250.47/59.42 | | | | | | | | | | | | | | | #873.
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | (181) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 250.47/59.42 | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 250.47/59.42 | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | (182) all_252_14 = e0 & op(e1, e2) = e0
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (28), (34), (43), (51), (55), (56),
% 250.47/59.42 | | | | | | | | | | | | | | | | (70), (99), (126), (146), (154), (182) are
% 250.47/59.42 | | | | | | | | | | | | | | | | inconsistent by sub-proof #872.
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | (183) all_252_22 = e0 & op(e0, e2) = e0
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | (184) all_252_22 = e0
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | (185) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.47/59.42 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.47/59.42 | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | (186) all_252_20 = e2 & op(e0, e4) = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (137), (186) are inconsistent by sub-proof
% 250.47/59.42 | | | | | | | | | | | | | | | | | | #560.
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | (187) all_252_21 = e2 & op(e0, e3) = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | (188) all_252_21 = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | | (189) op(e0, e3) = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | (190) all_252_24 = e0 & op(e0, e0) = e0
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (171), (190) are inconsistent by sub-proof
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | #297.
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | (191) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | (192) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | = e0)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | (193) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | (194) all_252_6 = e4 & op(e2, e4) = e4
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | (195) all_252_6 = e4
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | (196) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_0 = e2 & op(e4, e4) = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | (198) all_252_0 = e2
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | (199) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (18), (22), (23), (25), (44), (55),
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | (68), (70), (82), (95), (102), (110), (113),
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | (115), (117), (121), (127), (137), (195), (199)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #517.
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | (200) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_252_6 = e1 & op(e2, e4) = e1
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_6 = e1
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (195), (202) are inconsistent by sub-proof
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | #844.
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | (203) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_252_12 = e1 & op(e1, e4) = e1
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_12 = e1
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (22), (23), (44), (48), (56), (66), (132),
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (144), (195), (198), (206) are inconsistent
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #282.
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_14 = e4 & op(e1, e2) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) op(e1, e2) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (23), (107), (209) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_252_15 = e4 & op(e1, e1) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) op(e1, e1) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (42), (99), (212) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #756.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_252_19 = e4 & op(e1, e0) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_19 = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) op(e1, e0) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_16 = e0 & op(e4, e0) = e0
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (23), (217) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #469.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_17 = e0 & op(e3, e0) = e0
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (102), (110), (218) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #573.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_18 = e0 & op(e2, e0) = e0
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_18 = e0
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_16 = e2 & op(e4, e0) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) op(e4, e0) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (23), (61), (224) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #830.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_17 = e2 & op(e3, e0) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_252_17 = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) op(e3, e0) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_252_16 = e3 & op(e4, e0) = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_16 = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_252_0 = e1 & op(e4, e4) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_0 = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (25), (44), (55), (68), (70),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (95), (102), (110), (113), (115), (117),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (127), (137), (195), (233) are inconsistent
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #518.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_1 = e1 & op(e4, e3) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_1 = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (235), (237) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_3 = e4 & op(e3, e3) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_252_3 = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (22), (23), (48), (239), (240) are
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_5 = e1 & op(e3, e2) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) op(e3, e2) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (71), (115), (243) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_10 = e1 & op(e3, e1) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_252_10 = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_0 = e4 & op(e4, e4) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (198), (248) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #606.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_252_1 = e4 & op(e4, e3) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (235), (249) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #955.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_252_4 = e4 & op(e4, e2) = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_252_4 = e4
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (22), (23), (27), (44), (48), (57),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (66), (68), (82), (95), (98), (102), (110),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (115), (119), (121), (127), (132), (137),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (198), (239), (253) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #281.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_252_5 = e3 & op(e3, e2) = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_252_5 = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (113), (252), (256), (257) are inconsistent
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_252_8 = e2 & op(e2, e2) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (25), (44), (55), (68), (70),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (95), (102), (110), (113), (115), (117),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (127), (137), (175), (195), (198), (259)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #477.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_252_14 = e2 & op(e1, e2) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (16), (18), (19),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (24), (25), (27), (29), (30), (44),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (55), (56), (57), (63), (66), (68), (70),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (77), (82), (83), (87), (95), (97), (98), (102),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (108), (110), (113), (115), (117), (119),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (123), (125), (126), (127), (130), (132),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (137), (141), (143), (144), (148), (163),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175), (188), (189), (195), (198), (205), (214),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (221), (261) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_252_22 = e2 & op(e0, e2) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_252_22 = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (263) imply:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) e2 = e0
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (18), (23), (25), (27), (44), (48),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (66), (68), (82), (95), (98), (102), (110), (113),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (117), (119), (121), (127), (132), (137),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (264) are inconsistent by sub-proof #493.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_252_10 = e3 & op(e3, e1) = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (25), (39), (57), (66), (98), (171), (215),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221), (226), (230), (246), (266) are inconsistent
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #269.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_252_17 = e3 & op(e3, e0) = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (226), (267) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (22), (23), (27), (44), (48), (66),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (73), (82), (95), (98), (102), (110), (113),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (119), (121), (127), (132), (137), (195),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (205), (230), (268) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #268.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_252_17 = e1 & op(e3, e0) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) op(e3, e0) = e1
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (44), (227), (270) are inconsistent by
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #427.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (10), (16), (23), (24), (25), (27),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (63), (70), (87), (98), (107), (113),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (126), (135), (143), (214), (215), (271)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #277.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (25), (36), (39), (57), (66), (73),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (158), (171), (215), (221), (226), (272) are
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #267.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_252_17 = e3 & op(e3, e0) = e3
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (226), (273) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (57), (66), (98), (171), (215), (221), (274)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #265.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_252_18 = e2 & op(e2, e0) = e2
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (18), (23), (25), (27), (44), (48),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (66), (68), (82), (95), (98), (102), (110), (113),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (117), (119), (121), (127), (132), (137),
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198), (221), (276) are inconsistent by sub-proof
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #275.
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.47/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (25), (44), (55), (68), (70),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (95), (102), (110), (113), (115), (117),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (127), (137), (171), (195), (198), (215),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) are inconsistent by sub-proof #264.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_252_19 = e0 & op(e1, e0) = e0
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (27), (48), (68), (82), (95), (98),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (102), (110), (113), (115), (119), (121), (127),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (195), (198), (205), (214), (278) are
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #263.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_252_20 = e1 & op(e0, e4) = e1
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (137), (279) are inconsistent by sub-proof
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | | #509.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | (280) all_252_2 = e2 & op(e3, e4) = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_2 = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (68), (82), (95), (102), (110),
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | (115), (121), (127), (281) are inconsistent by
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #571.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | (282) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | (283) all_252_6 = e2 & op(e2, e4) = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (195), (283) are inconsistent by sub-proof
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | #921.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | (284) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (25), (55), (70), (137), (284) are
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | (285) all_252_7 = e4 & op(e2, e3) = e4
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | (286) op(e2, e3) = e4
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (24), (286) are inconsistent by
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | (287) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (30), (48), (84), (122), (139), (175), (287)
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #262.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | (288) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.57/59.43 | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.57/59.43 | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.57/59.43 | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 250.57/59.43 | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | Case 1:
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | (289) all_252_22 = e2 & op(e0, e2) = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (184), (289) are inconsistent by sub-proof
% 250.57/59.43 | | | | | | | | | | | | | | | | | | #261.
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | (290) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.57/59.43 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | Case 1:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | (291) all_252_23 = e2 & op(e0, e1) = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (125), (291) are inconsistent by sub-proof
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | #274.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | (292) all_252_24 = e2 & op(e0, e0) = e2
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (171), (292) are inconsistent by sub-proof
% 250.57/59.43 | | | | | | | | | | | | | | | | | | | #260.
% 250.57/59.43 | | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | (293) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 250.57/59.43 | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 250.57/59.43 | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | BETA: splitting (293) gives:
% 250.57/59.43 | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | Case 1:
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | (294) all_252_14 = e1 & op(e1, e2) = e1
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | ALPHA: (294) implies:
% 250.57/59.43 | | | | | | | | | | | | | | (295) op(e1, e2) = e1
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (107), (163), (295) are inconsistent
% 250.57/59.43 | | | | | | | | | | | | | | by sub-proof #870.
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | Case 2:
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | (296) all_252_22 = e1 & op(e0, e2) = e1
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | ALPHA: (296) implies:
% 250.57/59.43 | | | | | | | | | | | | | | (297) all_252_22 = e1
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (25), (27), (44), (46), (57), (91),
% 250.57/59.43 | | | | | | | | | | | | | | (113), (125), (137), (171), (297) are inconsistent
% 250.57/59.43 | | | | | | | | | | | | | | by sub-proof #258.
% 250.57/59.43 | | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | | |
% 250.57/59.43 | | | | | | | | | End of split
% 250.57/59.43 | | | | | | | | |
% 250.57/59.43 | | | | | | | | End of split
% 250.57/59.43 | | | | | | | |
% 250.57/59.43 | | | | | | | End of split
% 250.57/59.43 | | | | | | |
% 250.57/59.43 | | | | | | Case 2:
% 250.57/59.43 | | | | | | |
% 250.57/59.43 | | | | | | | (298) all_78_2 = e1
% 250.57/59.43 | | | | | | |
% 250.57/59.43 | | | | | | | REF_CLOSE: (23), (40), (56), (92), (146), (298) are inconsistent
% 250.57/59.43 | | | | | | | by sub-proof #971.
% 250.57/59.43 | | | | | | |
% 250.57/59.43 | | | | | | End of split
% 250.57/59.43 | | | | | |
% 250.57/59.43 | | | | | Case 2:
% 250.57/59.43 | | | | | |
% 250.57/59.43 | | | | | | (299) all_70_2 = e2
% 250.57/59.43 | | | | | |
% 250.57/59.43 | | | | | | COMBINE_EQS: (64), (299) imply:
% 250.57/59.43 | | | | | | (300) all_62_2 = e2
% 250.57/59.43 | | | | | |
% 250.57/59.43 | | | | | | REF_CLOSE: (19), (21), (23), (52), (63), (67), (75), (93), (104),
% 250.57/59.43 | | | | | | (300) are inconsistent by sub-proof #852.
% 250.57/59.43 | | | | | |
% 250.57/59.43 | | | | | End of split
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | Case 2:
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | | (301) all_62_2 = e4
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | | REDUCE: (94), (301) imply:
% 250.57/59.43 | | | | | (302) ~ (all_16_2 = e4)
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | | SIMP: (302) implies:
% 250.57/59.43 | | | | | (303) ~ (all_16_2 = e4)
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | | REF_CLOSE: (14), (23), (45), (70), (96), (123), (131), (135), (303)
% 250.57/59.43 | | | | | are inconsistent by sub-proof #466.
% 250.57/59.43 | | | | |
% 250.57/59.43 | | | | End of split
% 250.57/59.43 | | | |
% 250.57/59.43 | | | Case 2:
% 250.57/59.43 | | | |
% 250.57/59.43 | | | | (304) all_50_2 = e3
% 250.57/59.43 | | | |
% 250.57/59.43 | | | | COMBINE_EQS: (53), (304) imply:
% 250.57/59.43 | | | | (305) all_4_2 = e3
% 250.57/59.43 | | | |
% 250.57/59.43 | | | | REDUCE: (5), (305) imply:
% 250.57/59.43 | | | | (306) op(e3, e2) = e1
% 250.57/59.43 | | | |
% 250.57/59.43 | | | | REF_CLOSE: (23), (71), (115), (306) are inconsistent by sub-proof #929.
% 250.57/59.43 | | | |
% 250.57/59.43 | | | End of split
% 250.57/59.43 | | |
% 250.57/59.43 | | Case 2:
% 250.57/59.43 | | |
% 250.57/59.43 | | | (307) all_46_2 = e2
% 250.57/59.43 | | | (308) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 250.57/59.43 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 250.57/59.43 | | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.57/59.43 | | |
% 250.57/59.43 | | | COMBINE_EQS: (133), (307) imply:
% 250.57/59.43 | | | (309) all_36_2 = e2
% 250.57/59.43 | | |
% 250.57/59.43 | | | SIMP: (309) implies:
% 250.57/59.43 | | | (310) all_36_2 = e2
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (118), (310) imply:
% 250.57/59.43 | | | (311) ~ (all_244_15 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (58), (310) imply:
% 250.57/59.43 | | | (312) ~ (all_48_2 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (105), (310) imply:
% 250.57/59.43 | | | (313) ~ (all_38_2 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (65), (310) imply:
% 250.57/59.43 | | | (314) ~ (all_8_2 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | SIMP: (314) implies:
% 250.57/59.43 | | | (315) ~ (all_8_2 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (62), (310) imply:
% 250.57/59.43 | | | (316) ~ (e4 = e2)
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (13), (310) imply:
% 250.57/59.43 | | | (317) op(all_62_2, e2) = e3
% 250.57/59.43 | | |
% 250.57/59.43 | | | REDUCE: (116), (310) imply:
% 250.57/59.43 | | | (318) op(e2, e1) = e3
% 250.57/59.43 | | |
% 250.57/59.43 | | | REF_CLOSE: (6), (7), (16), (17), (18), (22), (23), (25), (27), (28), (30),
% 250.57/59.43 | | | (38), (44), (48), (49), (55), (56), (57), (60), (62), (64),
% 250.57/59.43 | | | (66), (68), (70), (71), (79), (80), (81), (82), (86), (95),
% 250.57/59.43 | | | (97), (98), (99), (101), (102), (104), (107), (110), (111),
% 250.57/59.43 | | | (113), (115), (120), (121), (125), (126), (127), (129), (308),
% 250.57/59.43 | | | (311), (312), (313), (315), (317), (318) are inconsistent by
% 250.57/59.43 | | | sub-proof #255.
% 250.57/59.43 | | |
% 250.57/59.43 | | End of split
% 250.57/59.43 | |
% 250.57/59.43 | Case 2:
% 250.57/59.43 | |
% 250.57/59.43 | | (319) all_40_2 = e4
% 250.57/59.43 | |
% 250.57/59.43 | | REDUCE: (72), (319) imply:
% 250.57/59.43 | | (320) op(e4, e0) = e2
% 250.57/59.43 | |
% 250.57/59.43 | | REF_CLOSE: (9), (23), (61), (320) are inconsistent by sub-proof #830.
% 250.57/59.43 | |
% 250.57/59.43 | End of split
% 250.57/59.43 |
% 250.57/59.43 End of proof
% 250.57/59.43
% 250.57/59.43 Sub-proof #255 shows that the following formulas are inconsistent:
% 250.57/59.43 ----------------------------------------------------------------
% 250.57/59.43 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.43 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.43 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.43 (2) op(e4, e1) = e0
% 250.57/59.43 (3) ~ (all_48_2 = e2)
% 250.57/59.43 (4) ~ (e2 = e0)
% 250.57/59.43 (5) op(all_38_2, all_4_2) = e1
% 250.57/59.43 (6) ~ (e1 = e0)
% 250.57/59.43 (7) op(e3, e4) = e0
% 250.57/59.43 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.43 (9) ~ (e3 = e2)
% 250.57/59.43 (10) ~ (e4 = e0)
% 250.57/59.43 (11) op(e2, e2) = all_244_8
% 250.57/59.43 (12) op(e2, e1) = all_38_2
% 250.57/59.43 (13) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.57/59.43 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.57/59.43 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.57/59.43 (14) ~ (all_8_2 = e2)
% 250.57/59.43 (15) ~ (e2 = e1)
% 250.57/59.43 (16) ~ (e4 = e1)
% 250.57/59.43 (17) op(all_62_2, e2) = e3
% 250.57/59.43 (18) ~ (all_244_8 = all_38_2)
% 250.57/59.43 (19) op(e1, e4) = all_16_2
% 250.57/59.43 (20) op(e1, e3) = all_62_2
% 250.57/59.43 (21) ~ (e3 = e0)
% 250.57/59.43 (22) all_252_2 = e0
% 250.57/59.43 (23) ~ (all_36_2 = e4)
% 250.57/59.43 (24) all_70_2 = all_62_2
% 250.57/59.43 (25) ~ (e3 = e1)
% 250.57/59.43 (26) op(e3, e1) = all_36_2
% 250.57/59.43 (27) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 250.57/59.43 all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1,
% 250.57/59.43 e2) = all_46_1 & $i(all_46_1))
% 250.57/59.44 (28) op(e2, e1) = e3
% 250.57/59.44 (29) ~ (all_16_2 = e2)
% 250.57/59.44 (30) ~ (all_8_2 = e1)
% 250.57/59.44 (31) ~ (all_38_2 = e2)
% 250.57/59.44 (32) ~ (all_244_15 = all_38_2)
% 250.57/59.44 (33) ~ (all_48_2 = all_8_2)
% 250.57/59.44 (34) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.57/59.44 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.57/59.44 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.57/59.44 (35) ~ (all_8_2 = e0)
% 250.57/59.44 (36) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.57/59.44 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.57/59.44 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.57/59.44 (37) ~ (all_36_2 = e0)
% 250.57/59.44 (38) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.57/59.44 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.57/59.44 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.57/59.44 (39) ~ (e4 = e3)
% 250.57/59.44 (40) op(e1, e1) = all_244_15
% 250.57/59.44 (41) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.57/59.44 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.57/59.44 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.57/59.44 (42) op(e3, e0) = all_48_2
% 250.57/59.44 (43) op(all_48_2, e0) = e3
% 250.57/59.44 (44) op(e1, e2) = all_4_2
% 250.57/59.44 (45) ~ (all_48_2 = e0)
% 250.57/59.44 (46) op(all_244_3, all_244_3) = e3
% 250.57/59.44 (47) ~ (all_244_15 = e2)
% 250.57/59.44 (48) ~ (e4 = e2)
% 250.57/59.44 (49) op(e3, e2) = all_8_2
% 250.57/59.44 (50) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.57/59.44 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.57/59.44 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.57/59.44 (51) ~ (all_244_3 = e0)
% 250.57/59.44 (52) all_252_23 = e4
% 250.57/59.44 (53) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.57/59.44 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.57/59.44 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.57/59.44 (54) op(e3, e3) = all_244_3
% 250.57/59.44 (55) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.57/59.44 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.57/59.44 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | BETA: splitting (55) gives:
% 250.57/59.44 |
% 250.57/59.44 | Case 1:
% 250.57/59.44 | |
% 250.57/59.44 | | (56) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 250.57/59.44 | | e2)
% 250.57/59.44 | |
% 250.57/59.44 | | BETA: splitting (56) gives:
% 250.57/59.44 | |
% 250.57/59.44 | | Case 1:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (57) all_252_2 = e2 & op(e3, e4) = e2
% 250.57/59.44 | | |
% 250.57/59.44 | | | ALPHA: (57) implies:
% 250.57/59.44 | | | (58) all_252_2 = e2
% 250.57/59.44 | | |
% 250.57/59.44 | | | REF_CLOSE: (1), (4), (8), (26), (35), (37), (42), (45), (49), (51), (54),
% 250.57/59.44 | | | (58) are inconsistent by sub-proof #571.
% 250.57/59.44 | | |
% 250.57/59.44 | | Case 2:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (59) all_252_3 = e2 & op(e3, e3) = e2
% 250.57/59.44 | | |
% 250.57/59.44 | | | ALPHA: (59) implies:
% 250.57/59.44 | | | (60) all_252_3 = e2
% 250.57/59.44 | | |
% 250.57/59.44 | | | BETA: splitting (38) gives:
% 250.57/59.44 | | |
% 250.57/59.44 | | | Case 1:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (61) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3,
% 250.57/59.44 | | | | e1) = e2)
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | BETA: splitting (61) gives:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | Case 1:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (62) all_252_9 = e2 & op(e4, e1) = e2
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | ALPHA: (62) implies:
% 250.57/59.44 | | | | | (63) op(e4, e1) = e2
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | REF_CLOSE: (2), (4), (8), (63) are inconsistent by sub-proof #767.
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | Case 2:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (64) all_252_10 = e2 & op(e3, e1) = e2
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | ALPHA: (64) implies:
% 250.57/59.44 | | | | | (65) all_252_10 = e2
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | BETA: splitting (13) gives:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | Case 1:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (66) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 &
% 250.57/59.44 | | | | | | op(e3, e3) = e1)
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | BETA: splitting (66) gives:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | Case 1:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (67) all_252_2 = e1 & op(e3, e4) = e1
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | ALPHA: (67) implies:
% 250.57/59.44 | | | | | | | (68) op(e3, e4) = e1
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | REF_CLOSE: (6), (7), (8), (68) are inconsistent by sub-proof #607.
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | Case 2:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (69) all_252_3 = e1 & op(e3, e3) = e1
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | REF_CLOSE: (15), (60), (69) are inconsistent by sub-proof #949.
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | End of split
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | Case 2:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (70) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 &
% 250.57/59.44 | | | | | | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | BETA: splitting (70) gives:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | Case 1:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (71) all_252_5 = e1 & op(e3, e2) = e1
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | ALPHA: (71) implies:
% 250.57/59.44 | | | | | | | (72) op(e3, e2) = e1
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | REF_CLOSE: (8), (30), (49), (72) are inconsistent by sub-proof
% 250.57/59.44 | | | | | | | #929.
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | Case 2:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (73) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.57/59.44 | | | | | | | op(e3, e0) = e1)
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | BETA: splitting (73) gives:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | (74) all_252_10 = e1 & op(e3, e1) = e1
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | REF_CLOSE: (15), (65), (74) are inconsistent by sub-proof #464.
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | (75) all_252_17 = e1 & op(e3, e0) = e1
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | ALPHA: (75) implies:
% 250.57/59.44 | | | | | | | | (76) op(e3, e0) = e1
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | BETA: splitting (50) gives:
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | (77) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 &
% 250.57/59.44 | | | | | | | | | op(e3, e3) = e3)
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | BETA: splitting (77) gives:
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | (78) all_252_2 = e3 & op(e3, e4) = e3
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | REF_CLOSE: (21), (22), (78) are inconsistent by sub-proof
% 250.57/59.44 | | | | | | | | | | #541.
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | (79) all_252_3 = e3 & op(e3, e3) = e3
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | REF_CLOSE: (9), (60), (79) are inconsistent by sub-proof
% 250.57/59.44 | | | | | | | | | | #257.
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | (80) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3
% 250.57/59.44 | | | | | | | | | & op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.57/59.44 | | | | | | | | | e3)
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | BETA: splitting (80) gives:
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | (81) all_252_5 = e3 & op(e3, e2) = e3
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | ALPHA: (81) implies:
% 250.57/59.44 | | | | | | | | | | (82) all_252_5 = e3
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | BETA: splitting (41) gives:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | (83) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 250.57/59.44 | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | BETA: splitting (83) gives:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | (84) all_252_2 = e4 & op(e3, e4) = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | ALPHA: (84) implies:
% 250.57/59.44 | | | | | | | | | | | | (85) all_252_2 = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | REF_CLOSE: (1), (8), (10), (26), (35), (37), (42), (45),
% 250.57/59.44 | | | | | | | | | | | | (49), (51), (54), (85) are inconsistent by
% 250.57/59.44 | | | | | | | | | | | | sub-proof #569.
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | (86) all_252_3 = e4 & op(e3, e3) = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | ALPHA: (86) implies:
% 250.57/59.44 | | | | | | | | | | | | (87) all_252_3 = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | REF_CLOSE: (48), (60), (87) are inconsistent by sub-proof
% 250.57/59.44 | | | | | | | | | | | | #954.
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | (88) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 250.57/59.44 | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 250.57/59.44 | | | | | | | | | | | op(e3, e0) = e4)
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | BETA: splitting (88) gives:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | (89) all_252_5 = e4 & op(e3, e2) = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | ALPHA: (89) implies:
% 250.57/59.44 | | | | | | | | | | | | (90) all_252_5 = e4
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | COMBINE_EQS: (82), (90) imply:
% 250.57/59.44 | | | | | | | | | | | | (91) e4 = e3
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | REDUCE: (39), (91) imply:
% 250.57/59.44 | | | | | | | | | | | | (92) $false
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | CLOSE: (92) is inconsistent.
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | (93) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 250.57/59.44 | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | BETA: splitting (93) gives:
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | | (94) all_252_10 = e4 & op(e3, e1) = e4
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | | REF_CLOSE: (8), (23), (26), (94) are inconsistent by
% 250.57/59.44 | | | | | | | | | | | | | sub-proof #914.
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | | (95) all_252_17 = e4 & op(e3, e0) = e4
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | | ALPHA: (95) implies:
% 250.57/59.44 | | | | | | | | | | | | | (96) op(e3, e0) = e4
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | | REF_CLOSE: (8), (16), (76), (96) are inconsistent by
% 250.57/59.44 | | | | | | | | | | | | | sub-proof #441.
% 250.57/59.44 | | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | (97) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 =
% 250.57/59.44 | | | | | | | | | | e3 & op(e3, e0) = e3)
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | BETA: splitting (97) gives:
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | Case 1:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | (98) all_252_10 = e3 & op(e3, e1) = e3
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | ALPHA: (98) implies:
% 250.57/59.44 | | | | | | | | | | | (99) all_252_10 = e3
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | COMBINE_EQS: (65), (99) imply:
% 250.57/59.44 | | | | | | | | | | | (100) e3 = e2
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | SIMP: (100) implies:
% 250.57/59.44 | | | | | | | | | | | (101) e3 = e2
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | REDUCE: (9), (101) imply:
% 250.57/59.44 | | | | | | | | | | | (102) $false
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | CLOSE: (102) is inconsistent.
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | Case 2:
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | (103) all_252_17 = e3 & op(e3, e0) = e3
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | | REF_CLOSE: (8), (25), (76), (103) are inconsistent by
% 250.57/59.44 | | | | | | | | | | | sub-proof #436.
% 250.57/59.44 | | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | | |
% 250.57/59.44 | | | | | | | | | End of split
% 250.57/59.44 | | | | | | | | |
% 250.57/59.44 | | | | | | | | End of split
% 250.57/59.44 | | | | | | | |
% 250.57/59.44 | | | | | | | End of split
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | End of split
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | End of split
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | End of split
% 250.57/59.44 | | | |
% 250.57/59.44 | | | Case 2:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (104) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 250.57/59.44 | | | | e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | BETA: splitting (104) gives:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | Case 1:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (105) all_252_11 = e2 & op(e2, e1) = e2
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | REF_CLOSE: (8), (9), (12), (28), (105) are inconsistent by sub-proof
% 250.57/59.44 | | | | | #462.
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | Case 2:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (106) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 250.57/59.44 | | | | | op(e0, e1) = e2)
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | BETA: splitting (106) gives:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | Case 1:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (107) all_252_15 = e2 & op(e1, e1) = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | REF_CLOSE: (8), (40), (47), (107) are inconsistent by sub-proof
% 250.57/59.44 | | | | | | #966.
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | Case 2:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (108) all_252_23 = e2 & op(e0, e1) = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | REF_CLOSE: (48), (52), (108) are inconsistent by sub-proof #274.
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | End of split
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | End of split
% 250.57/59.44 | | | |
% 250.57/59.44 | | | End of split
% 250.57/59.44 | | |
% 250.57/59.44 | | End of split
% 250.57/59.44 | |
% 250.57/59.44 | Case 2:
% 250.57/59.44 | |
% 250.57/59.44 | | (109) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1)
% 250.57/59.44 | | = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.57/59.44 | |
% 250.57/59.44 | | BETA: splitting (109) gives:
% 250.57/59.44 | |
% 250.57/59.44 | | Case 1:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (110) all_252_5 = e2 & op(e3, e2) = e2
% 250.57/59.44 | | |
% 250.57/59.44 | | | REF_CLOSE: (8), (14), (49), (110) are inconsistent by sub-proof #256.
% 250.57/59.44 | | |
% 250.57/59.44 | | Case 2:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (111) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 = e2 & op(e3,
% 250.57/59.44 | | | e0) = e2)
% 250.57/59.44 | | |
% 250.57/59.44 | | | BETA: splitting (111) gives:
% 250.57/59.44 | | |
% 250.57/59.44 | | | Case 1:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (112) all_252_10 = e2 & op(e3, e1) = e2
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | ALPHA: (112) implies:
% 250.57/59.44 | | | | (113) all_252_10 = e2
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | BETA: splitting (27) gives:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | Case 1:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (114) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2)
% 250.57/59.44 | | | | | = all_46_1 & $i(all_46_0) & $i(all_46_1)
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | ALPHA: (114) implies:
% 250.57/59.44 | | | | | (115) op(e1, e2) = all_46_1
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | REF_CLOSE: (5), (6), (7), (8), (11), (12), (13), (15), (17), (18),
% 250.57/59.44 | | | | | (19), (20), (24), (28), (29), (30), (31), (32), (33), (34),
% 250.57/59.44 | | | | | (36), (40), (42), (43), (44), (46), (47), (49), (53), (54),
% 250.57/59.44 | | | | | (113), (115) are inconsistent by sub-proof #463.
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | Case 2:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (116) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1)
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | ALPHA: (116) implies:
% 250.57/59.44 | | | | | (117) op(e1, e2) = all_46_1
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | REF_CLOSE: (5), (6), (7), (8), (11), (12), (13), (15), (17), (18),
% 250.57/59.44 | | | | | (19), (20), (24), (28), (29), (30), (31), (32), (33), (34),
% 250.57/59.44 | | | | | (36), (40), (42), (43), (44), (46), (47), (49), (53), (54),
% 250.57/59.44 | | | | | (113), (117) are inconsistent by sub-proof #463.
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | End of split
% 250.57/59.44 | | | |
% 250.57/59.44 | | | Case 2:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (118) all_252_17 = e2 & op(e3, e0) = e2
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | REF_CLOSE: (3), (8), (42), (118) are inconsistent by sub-proof #653.
% 250.57/59.44 | | | |
% 250.57/59.44 | | | End of split
% 250.57/59.44 | | |
% 250.57/59.44 | | End of split
% 250.57/59.44 | |
% 250.57/59.44 | End of split
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #256 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_5 = e2 & op(e3, e2) = e2
% 250.57/59.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.44 (3) op(e3, e2) = all_8_2
% 250.57/59.44 (4) ~ (all_8_2 = e2)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (1) implies:
% 250.57/59.44 | (5) op(e3, e2) = e2
% 250.57/59.44 |
% 250.57/59.44 | GROUND_INST: instantiating (2) with all_8_2, e2, e2, e3, simplifying with (3),
% 250.57/59.44 | (5) gives:
% 250.57/59.44 | (6) all_8_2 = e2
% 250.57/59.44 |
% 250.57/59.44 | REDUCE: (4), (6) imply:
% 250.57/59.44 | (7) $false
% 250.57/59.44 |
% 250.57/59.44 | CLOSE: (7) is inconsistent.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #257 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_3 = e3 & op(e3, e3) = e3
% 250.57/59.44 (2) all_252_3 = e2
% 250.57/59.44 (3) ~ (e3 = e2)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (1) implies:
% 250.57/59.44 | (4) all_252_3 = e3
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.44 | (5) e3 = e2
% 250.57/59.44 |
% 250.57/59.44 | SIMP: (5) implies:
% 250.57/59.44 | (6) e3 = e2
% 250.57/59.44 |
% 250.57/59.44 | REDUCE: (3), (6) imply:
% 250.57/59.44 | (7) $false
% 250.57/59.44 |
% 250.57/59.44 | CLOSE: (7) is inconsistent.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #258 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) ~ (e2 = e0)
% 250.57/59.44 (2) ~ (e1 = e0)
% 250.57/59.44 (3) ~ (e3 = e2)
% 250.57/59.44 (4) ~ (e4 = e0)
% 250.57/59.44 (5) ~ (e2 = e1)
% 250.57/59.44 (6) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.57/59.44 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.57/59.44 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.57/59.44 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.57/59.44 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.57/59.44 op(e0, e1) = e0)))
% 250.57/59.44 (7) all_252_22 = e1
% 250.57/59.44 (8) ~ (e3 = e0)
% 250.57/59.44 (9) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.57/59.44 | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) =
% 250.57/59.44 e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.57/59.44 (10) all_252_24 = e1
% 250.57/59.44 (11) ~ (e4 = e2)
% 250.57/59.44 (12) all_252_23 = e4
% 250.57/59.44 (13) all_252_20 = e3
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | BETA: splitting (6) gives:
% 250.57/59.44 |
% 250.57/59.44 | Case 1:
% 250.57/59.44 | |
% 250.57/59.44 | | (14) all_252_24 = e0 & op(e0, e0) = e0
% 250.57/59.44 | |
% 250.57/59.44 | | ALPHA: (14) implies:
% 250.57/59.44 | | (15) all_252_24 = e0
% 250.57/59.44 | |
% 250.57/59.44 | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #623.
% 250.57/59.44 | |
% 250.57/59.44 | Case 2:
% 250.57/59.44 | |
% 250.57/59.44 | | (16) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.57/59.44 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.57/59.44 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.57/59.44 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.57/59.44 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.57/59.44 | |
% 250.57/59.44 | | ALPHA: (16) implies:
% 250.57/59.44 | | (17) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 250.57/59.44 | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.57/59.44 | | op(e0, e1) = e0)
% 250.57/59.44 | |
% 250.57/59.44 | | BETA: splitting (17) gives:
% 250.57/59.44 | |
% 250.57/59.44 | | Case 1:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (18) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0,
% 250.57/59.44 | | | e3) = e0)
% 250.57/59.44 | | |
% 250.57/59.44 | | | BETA: splitting (18) gives:
% 250.57/59.44 | | |
% 250.57/59.44 | | | Case 1:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (19) all_252_20 = e0 & op(e0, e4) = e0
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | REF_CLOSE: (8), (13), (19) are inconsistent by sub-proof #307.
% 250.57/59.44 | | | |
% 250.57/59.44 | | | Case 2:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (20) all_252_21 = e0 & op(e0, e3) = e0
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | ALPHA: (20) implies:
% 250.57/59.44 | | | | (21) all_252_21 = e0
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | BETA: splitting (9) gives:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | Case 1:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (22) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 250.57/59.44 | | | | | op(e0, e3) = e2)
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | BETA: splitting (22) gives:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | Case 1:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (23) all_252_20 = e2 & op(e0, e4) = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | ALPHA: (23) implies:
% 250.57/59.44 | | | | | | (24) all_252_20 = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | REF_CLOSE: (3), (13), (24) are inconsistent by sub-proof #520.
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | Case 2:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (25) all_252_21 = e2 & op(e0, e3) = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | ALPHA: (25) implies:
% 250.57/59.44 | | | | | | (26) all_252_21 = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | REF_CLOSE: (1), (21), (26) are inconsistent by sub-proof #942.
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | End of split
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | Case 2:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | (27) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 250.57/59.44 | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | BETA: splitting (27) gives:
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | | Case 1:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (28) all_252_22 = e2 & op(e0, e2) = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | ALPHA: (28) implies:
% 250.57/59.44 | | | | | | (29) all_252_22 = e2
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | COMBINE_EQS: (7), (29) imply:
% 250.57/59.44 | | | | | | (30) e2 = e1
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | REDUCE: (5), (30) imply:
% 250.57/59.44 | | | | | | (31) $false
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | CLOSE: (31) is inconsistent.
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | Case 2:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | (32) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.57/59.44 | | | | | | op(e0, e0) = e2)
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | BETA: splitting (32) gives:
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | | Case 1:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (33) all_252_23 = e2 & op(e0, e1) = e2
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | REF_CLOSE: (11), (12), (33) are inconsistent by sub-proof #274.
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | Case 2:
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | (34) all_252_24 = e2 & op(e0, e0) = e2
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | | REF_CLOSE: (5), (10), (34) are inconsistent by sub-proof #260.
% 250.57/59.44 | | | | | | |
% 250.57/59.44 | | | | | | End of split
% 250.57/59.44 | | | | | |
% 250.57/59.44 | | | | | End of split
% 250.57/59.44 | | | | |
% 250.57/59.44 | | | | End of split
% 250.57/59.44 | | | |
% 250.57/59.44 | | | End of split
% 250.57/59.44 | | |
% 250.57/59.44 | | Case 2:
% 250.57/59.44 | | |
% 250.57/59.44 | | | (35) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0,
% 250.57/59.44 | | | e1) = e0)
% 250.57/59.44 | | |
% 250.57/59.44 | | | BETA: splitting (35) gives:
% 250.57/59.44 | | |
% 250.57/59.44 | | | Case 1:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (36) all_252_22 = e0 & op(e0, e2) = e0
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | REF_CLOSE: (2), (7), (36) are inconsistent by sub-proof #869.
% 250.57/59.44 | | | |
% 250.57/59.44 | | | Case 2:
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | (37) all_252_23 = e0 & op(e0, e1) = e0
% 250.57/59.44 | | | |
% 250.57/59.44 | | | | REF_CLOSE: (4), (12), (37) are inconsistent by sub-proof #259.
% 250.57/59.44 | | | |
% 250.57/59.44 | | | End of split
% 250.57/59.44 | | |
% 250.57/59.44 | | End of split
% 250.57/59.44 | |
% 250.57/59.44 | End of split
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #259 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_23 = e0 & op(e0, e1) = e0
% 250.57/59.44 (2) all_252_23 = e4
% 250.57/59.44 (3) ~ (e4 = e0)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (1) implies:
% 250.57/59.44 | (4) all_252_23 = e0
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.44 | (5) e4 = e0
% 250.57/59.44 |
% 250.57/59.44 | SIMP: (5) implies:
% 250.57/59.44 | (6) e4 = e0
% 250.57/59.44 |
% 250.57/59.44 | REDUCE: (3), (6) imply:
% 250.57/59.44 | (7) $false
% 250.57/59.44 |
% 250.57/59.44 | CLOSE: (7) is inconsistent.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #260 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_24 = e2 & op(e0, e0) = e2
% 250.57/59.44 (2) all_252_24 = e1
% 250.57/59.44 (3) ~ (e2 = e1)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (1) implies:
% 250.57/59.44 | (4) all_252_24 = e2
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.44 | (5) e2 = e1
% 250.57/59.44 |
% 250.57/59.44 | REDUCE: (3), (5) imply:
% 250.57/59.44 | (6) $false
% 250.57/59.44 |
% 250.57/59.44 | CLOSE: (6) is inconsistent.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #261 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_22 = e2 & op(e0, e2) = e2
% 250.57/59.44 (2) all_252_22 = e0
% 250.57/59.44 (3) ~ (e2 = e0)
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (1) implies:
% 250.57/59.44 | (4) all_252_22 = e2
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.44 | (5) e2 = e0
% 250.57/59.44 |
% 250.57/59.44 | REDUCE: (3), (5) imply:
% 250.57/59.44 | (6) $false
% 250.57/59.44 |
% 250.57/59.44 | CLOSE: (6) is inconsistent.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #262 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.44 (2) op(e2, e1) = all_38_2
% 250.57/59.44 (3) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = e4)
% 250.57/59.44 | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.57/59.44 (4) ~ (all_40_2 = e4)
% 250.57/59.44 (5) ~ (e4 = e1)
% 250.57/59.44 (6) ~ (all_38_2 = e4)
% 250.57/59.44 (7) op(e2, e0) = all_40_2
% 250.57/59.44 (8) all_252_8 = e1
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | BETA: splitting (3) gives:
% 250.57/59.44 |
% 250.57/59.44 | Case 1:
% 250.57/59.44 | |
% 250.57/59.44 | | (9) all_252_8 = e4 & op(e2, e2) = e4
% 250.57/59.44 | |
% 250.57/59.44 | | ALPHA: (9) implies:
% 250.57/59.44 | | (10) all_252_8 = e4
% 250.57/59.44 | |
% 250.57/59.44 | | REF_CLOSE: (5), (8), (10) are inconsistent by sub-proof #864.
% 250.57/59.44 | |
% 250.57/59.44 | Case 2:
% 250.57/59.44 | |
% 250.57/59.44 | | (11) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0)
% 250.57/59.44 | | = e4)
% 250.57/59.44 | |
% 250.57/59.44 | | REF_CLOSE: (1), (2), (4), (6), (7), (11) are inconsistent by sub-proof #933.
% 250.57/59.44 | |
% 250.57/59.44 | End of split
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #263 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_6 = e4
% 250.57/59.44 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.44 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.44 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.44 (3) all_252_19 = e0 & op(e1, e0) = e0
% 250.57/59.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.44 (5) ~ (e4 = e0)
% 250.57/59.44 (6) all_252_0 = e2
% 250.57/59.44 (7) ~ (e4 = e1)
% 250.57/59.44 (8) op(e3, e1) = all_36_2
% 250.57/59.44 (9) ~ (all_8_2 = e0)
% 250.57/59.44 (10) ~ (all_36_2 = e0)
% 250.57/59.44 (11) ~ (e4 = e3)
% 250.57/59.44 (12) op(e3, e0) = all_48_2
% 250.57/59.44 (13) ~ (all_48_2 = e0)
% 250.57/59.44 (14) ~ (e4 = e2)
% 250.57/59.44 (15) op(e3, e2) = all_8_2
% 250.57/59.44 (16) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.57/59.44 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.57/59.44 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.57/59.44 (17) ~ (all_244_3 = e0)
% 250.57/59.44 (18) all_252_19 = e4
% 250.57/59.44 (19) op(e3, e3) = all_244_3
% 250.57/59.44 (20) all_252_12 = e1
% 250.57/59.44 (21) all_252_20 = e3
% 250.57/59.44
% 250.57/59.44 Begin of proof
% 250.57/59.44 |
% 250.57/59.44 | ALPHA: (3) implies:
% 250.57/59.44 | (22) all_252_19 = e0
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (18), (22) imply:
% 250.57/59.44 | (23) e4 = e0
% 250.57/59.44 |
% 250.57/59.44 | SIMP: (23) implies:
% 250.57/59.44 | (24) e4 = e0
% 250.57/59.44 |
% 250.57/59.44 | COMBINE_EQS: (1), (24) imply:
% 250.57/59.44 | (25) all_252_6 = e0
% 250.57/59.44 |
% 250.57/59.44 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 250.57/59.44 | (15), (16), (17), (19), (20), (21), (25) are inconsistent by
% 250.57/59.44 | sub-proof #551.
% 250.57/59.44 |
% 250.57/59.44 End of proof
% 250.57/59.44
% 250.57/59.44 Sub-proof #264 shows that the following formulas are inconsistent:
% 250.57/59.44 ----------------------------------------------------------------
% 250.57/59.44 (1) all_252_6 = e4
% 250.57/59.44 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.44 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.44 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.44 (3) op(e1, e0) = e4
% 250.57/59.44 (4) ~ (e2 = e0)
% 250.57/59.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (6) ~ (e3 = e2)
% 250.57/59.45 (7) all_252_0 = e2
% 250.57/59.45 (8) ~ (e2 = e1)
% 250.57/59.45 (9) op(e1, e4) = all_16_2
% 250.57/59.45 (10) op(e3, e1) = all_36_2
% 250.57/59.45 (11) ~ (all_16_2 = e2)
% 250.57/59.45 (12) ~ (all_8_2 = e0)
% 250.57/59.45 (13) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) =
% 250.57/59.45 e2)
% 250.57/59.45 (14) ~ (all_36_2 = e0)
% 250.57/59.45 (15) op(e3, e0) = all_48_2
% 250.57/59.45 (16) ~ (all_48_2 = e0)
% 250.57/59.45 (17) all_252_24 = e1
% 250.57/59.45 (18) ~ (e4 = e2)
% 250.57/59.45 (19) op(e3, e2) = all_8_2
% 250.57/59.45 (20) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.57/59.45 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.57/59.45 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.57/59.45 (21) ~ (all_244_3 = e0)
% 250.57/59.45 (22) op(e3, e3) = all_244_3
% 250.57/59.45 (23) all_252_20 = e3
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (13) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (24) all_252_19 = e2 & op(e1, e0) = e2
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (24) implies:
% 250.57/59.45 | | (25) op(e1, e0) = e2
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (3), (5), (18), (25) are inconsistent by sub-proof #829.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (26) all_252_24 = e2 & op(e0, e0) = e2
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (26) implies:
% 250.57/59.45 | | (27) all_252_24 = e2
% 250.57/59.45 | |
% 250.57/59.45 | | COMBINE_EQS: (17), (27) imply:
% 250.57/59.45 | | (28) e2 = e1
% 250.57/59.45 | |
% 250.57/59.45 | | COMBINE_EQS: (7), (28) imply:
% 250.57/59.45 | | (29) all_252_0 = e1
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 250.57/59.45 | | (16), (18), (19), (20), (21), (22), (23), (29) are inconsistent
% 250.57/59.45 | | by sub-proof #518.
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #265 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.45 | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 (2) op(e1, e0) = e4
% 250.57/59.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (4) all_252_18 = e0
% 250.57/59.45 (5) ~ (e3 = e0)
% 250.57/59.45 (6) ~ (e3 = e1)
% 250.57/59.45 (7) ~ (e4 = e3)
% 250.57/59.45 (8) all_252_24 = e1
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (1) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (9) all_252_18 = e3 & op(e2, e0) = e3
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (9) implies:
% 250.57/59.45 | | (10) all_252_18 = e3
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #422.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (11) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0)
% 250.57/59.45 | | = e3)
% 250.57/59.45 | |
% 250.57/59.45 | | BETA: splitting (11) gives:
% 250.57/59.45 | |
% 250.57/59.45 | | Case 1:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (12) all_252_19 = e3 & op(e1, e0) = e3
% 250.57/59.45 | | |
% 250.57/59.45 | | | ALPHA: (12) implies:
% 250.57/59.45 | | | (13) op(e1, e0) = e3
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (2), (3), (7), (13) are inconsistent by sub-proof #827.
% 250.57/59.45 | | |
% 250.57/59.45 | | Case 2:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (14) all_252_24 = e3 & op(e0, e0) = e3
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #266.
% 250.57/59.45 | | |
% 250.57/59.45 | | End of split
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #266 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_24 = e3 & op(e0, e0) = e3
% 250.57/59.45 (2) all_252_24 = e1
% 250.57/59.45 (3) ~ (e3 = e1)
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | ALPHA: (1) implies:
% 250.57/59.45 | (4) all_252_24 = e3
% 250.57/59.45 |
% 250.57/59.45 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.45 | (5) e3 = e1
% 250.57/59.45 |
% 250.57/59.45 | REDUCE: (3), (5) imply:
% 250.57/59.45 | (6) $false
% 250.57/59.45 |
% 250.57/59.45 | CLOSE: (6) is inconsistent.
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #267 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_17 = e2
% 250.57/59.45 (2) op(e1, e0) = e4
% 250.57/59.45 (3) ~ (e1 = e0)
% 250.57/59.45 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (5) ~ (e3 = e2)
% 250.57/59.45 (6) op(e4, e2) = all_6_2
% 250.57/59.45 (7) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.57/59.45 | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) =
% 250.57/59.45 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 (8) all_252_18 = e0
% 250.57/59.45 (9) ~ (all_6_2 = e1)
% 250.57/59.45 (10) ~ (e3 = e0)
% 250.57/59.45 (11) ~ (e3 = e1)
% 250.57/59.45 (12) all_252_9 = e0
% 250.57/59.45 (13) ~ (e4 = e3)
% 250.57/59.45 (14) all_252_24 = e1
% 250.57/59.45 (15) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1)
% 250.57/59.45 | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (15) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (16) all_252_4 = e1 & op(e4, e2) = e1
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (16) implies:
% 250.57/59.45 | | (17) op(e4, e2) = e1
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (4), (6), (9), (17) are inconsistent by sub-proof #930.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (18) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 = e1 & op(e4, e0) =
% 250.57/59.45 | | e1)
% 250.57/59.45 | |
% 250.57/59.45 | | BETA: splitting (18) gives:
% 250.57/59.45 | |
% 250.57/59.45 | | Case 1:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (19) all_252_9 = e1 & op(e4, e1) = e1
% 250.57/59.45 | | |
% 250.57/59.45 | | | ALPHA: (19) implies:
% 250.57/59.45 | | | (20) all_252_9 = e1
% 250.57/59.45 | | |
% 250.57/59.45 | | | COMBINE_EQS: (12), (20) imply:
% 250.57/59.45 | | | (21) e1 = e0
% 250.57/59.45 | | |
% 250.57/59.45 | | | REDUCE: (3), (21) imply:
% 250.57/59.45 | | | (22) $false
% 250.57/59.45 | | |
% 250.57/59.45 | | | CLOSE: (22) is inconsistent.
% 250.57/59.45 | | |
% 250.57/59.45 | | Case 2:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (23) all_252_16 = e1 & op(e4, e0) = e1
% 250.57/59.45 | | |
% 250.57/59.45 | | | ALPHA: (23) implies:
% 250.57/59.45 | | | (24) all_252_16 = e1
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (13), (14), (24) are
% 250.57/59.45 | | | inconsistent by sub-proof #270.
% 250.57/59.45 | | |
% 250.57/59.45 | | End of split
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #268 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_6 = e4
% 250.57/59.45 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.45 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.45 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.45 (3) ~ (e1 = e0)
% 250.57/59.45 (4) all_252_16 = e3
% 250.57/59.45 (5) op(e3, e4) = e0
% 250.57/59.45 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (7) ~ (e4 = e0)
% 250.57/59.45 (8) all_252_0 = e2
% 250.57/59.45 (9) ~ (e2 = e1)
% 250.57/59.45 (10) ~ (e4 = e1)
% 250.57/59.45 (11) ~ (e3 = e1)
% 250.57/59.45 (12) op(e3, e1) = all_36_2
% 250.57/59.45 (13) all_252_9 = e0
% 250.57/59.45 (14) ~ (all_8_2 = e0)
% 250.57/59.45 (15) ~ (all_36_2 = e0)
% 250.57/59.45 (16) ~ (e4 = e3)
% 250.57/59.45 (17) op(e3, e0) = all_48_2
% 250.57/59.45 (18) ~ (all_48_2 = e0)
% 250.57/59.45 (19) ~ (e4 = e2)
% 250.57/59.45 (20) op(e3, e2) = all_8_2
% 250.57/59.45 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.57/59.45 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.57/59.45 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.57/59.45 (22) ~ (all_244_3 = e0)
% 250.57/59.45 (23) op(e3, e3) = all_244_3
% 250.57/59.45 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.57/59.45 (25) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.57/59.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.57/59.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.45 (26) all_252_12 = e1
% 250.57/59.45 (27) all_252_20 = e3
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (24) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (28) all_252_9 = e4 & op(e4, e1) = e4
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (12), (13), (14), (15), (16),
% 250.57/59.45 | | (17), (18), (19), (20), (21), (22), (23), (26), (27), (28) are
% 250.57/59.45 | | inconsistent by sub-proof #516.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (29) all_252_16 = e4 & op(e4, e0) = e4
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (29) implies:
% 250.57/59.45 | | (30) all_252_16 = e4
% 250.57/59.45 | |
% 250.57/59.45 | | COMBINE_EQS: (4), (30) imply:
% 250.57/59.45 | | (31) e4 = e3
% 250.57/59.45 | |
% 250.57/59.45 | | SIMP: (31) implies:
% 250.57/59.45 | | (32) e4 = e3
% 250.57/59.45 | |
% 250.57/59.45 | | COMBINE_EQS: (1), (32) imply:
% 250.57/59.45 | | (33) all_252_6 = e3
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 250.57/59.45 | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (27), (33)
% 250.57/59.45 | | are inconsistent by sub-proof #536.
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #269 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_17 = e2
% 250.57/59.45 (2) op(e1, e0) = e4
% 250.57/59.45 (3) all_252_16 = e3
% 250.57/59.45 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (5) ~ (e3 = e2)
% 250.57/59.45 (6) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.57/59.45 | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) =
% 250.57/59.45 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 (7) all_252_18 = e0
% 250.57/59.45 (8) ~ (e3 = e0)
% 250.57/59.45 (9) ~ (e3 = e1)
% 250.57/59.45 (10) ~ (e4 = e3)
% 250.57/59.45 (11) all_252_10 = e1
% 250.57/59.45 (12) all_252_24 = e1
% 250.57/59.45 (13) all_252_10 = e3 & op(e3, e1) = e3
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | ALPHA: (13) implies:
% 250.57/59.45 | (14) all_252_10 = e3
% 250.57/59.45 |
% 250.57/59.45 | COMBINE_EQS: (11), (14) imply:
% 250.57/59.45 | (15) e3 = e1
% 250.57/59.45 |
% 250.57/59.45 | SIMP: (15) implies:
% 250.57/59.45 | (16) e3 = e1
% 250.57/59.45 |
% 250.57/59.45 | COMBINE_EQS: (3), (16) imply:
% 250.57/59.45 | (17) all_252_16 = e1
% 250.57/59.45 |
% 250.57/59.45 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (17) are
% 250.57/59.45 | inconsistent by sub-proof #270.
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #270 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_17 = e2
% 250.57/59.45 (2) op(e1, e0) = e4
% 250.57/59.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (4) ~ (e3 = e2)
% 250.57/59.45 (5) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.57/59.45 | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) =
% 250.57/59.45 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 (6) all_252_18 = e0
% 250.57/59.45 (7) ~ (e3 = e0)
% 250.57/59.45 (8) ~ (e3 = e1)
% 250.57/59.45 (9) all_252_16 = e1
% 250.57/59.45 (10) ~ (e4 = e3)
% 250.57/59.45 (11) all_252_24 = e1
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (5) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (12) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0)
% 250.57/59.45 | | = e3)
% 250.57/59.45 | |
% 250.57/59.45 | | BETA: splitting (12) gives:
% 250.57/59.45 | |
% 250.57/59.45 | | Case 1:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (13) all_252_16 = e3 & op(e4, e0) = e3
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #488.
% 250.57/59.45 | | |
% 250.57/59.45 | | Case 2:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (14) all_252_17 = e3 & op(e3, e0) = e3
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #272.
% 250.57/59.45 | | |
% 250.57/59.45 | | End of split
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (15) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0)
% 250.57/59.45 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (15) are inconsistent by
% 250.57/59.45 | | sub-proof #271.
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #271 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.45 | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.57/59.45 (2) op(e1, e0) = e4
% 250.57/59.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (4) all_252_18 = e0
% 250.57/59.45 (5) ~ (e3 = e0)
% 250.57/59.45 (6) ~ (e3 = e1)
% 250.57/59.45 (7) ~ (e4 = e3)
% 250.57/59.45 (8) all_252_24 = e1
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (1) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (9) all_252_18 = e3 & op(e2, e0) = e3
% 250.57/59.45 | |
% 250.57/59.45 | | ALPHA: (9) implies:
% 250.57/59.45 | | (10) all_252_18 = e3
% 250.57/59.45 | |
% 250.57/59.45 | | COMBINE_EQS: (4), (10) imply:
% 250.57/59.45 | | (11) e3 = e0
% 250.57/59.45 | |
% 250.57/59.45 | | REDUCE: (5), (11) imply:
% 250.57/59.45 | | (12) $false
% 250.57/59.45 | |
% 250.57/59.45 | | CLOSE: (12) is inconsistent.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (13) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0)
% 250.57/59.45 | | = e3)
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (2), (3), (6), (7), (8), (13) are inconsistent by sub-proof #620.
% 250.57/59.45 | |
% 250.57/59.45 | End of split
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #272 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) all_252_17 = e3 & op(e3, e0) = e3
% 250.57/59.45 (2) all_252_17 = e2
% 250.57/59.45 (3) ~ (e3 = e2)
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | ALPHA: (1) implies:
% 250.57/59.45 | (4) all_252_17 = e3
% 250.57/59.45 |
% 250.57/59.45 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.45 | (5) e3 = e2
% 250.57/59.45 |
% 250.57/59.45 | REDUCE: (3), (5) imply:
% 250.57/59.45 | (6) $false
% 250.57/59.45 |
% 250.57/59.45 | CLOSE: (6) is inconsistent.
% 250.57/59.45 |
% 250.57/59.45 End of proof
% 250.57/59.45
% 250.57/59.45 Sub-proof #273 shows that the following formulas are inconsistent:
% 250.57/59.45 ----------------------------------------------------------------
% 250.57/59.45 (1) op(e0, e3) = e2
% 250.57/59.45 (2) all_252_21 = e2
% 250.57/59.45 (3) ~ (all_10_2 = e1)
% 250.57/59.45 (4) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.57/59.45 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.57/59.45 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.57/59.45 (5) ~ (all_10_2 = e4)
% 250.57/59.45 (6) all_252_6 = e4
% 250.57/59.45 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.45 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.45 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.45 (8) op(e4, e1) = e0
% 250.57/59.45 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.57/59.45 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.57/59.45 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.57/59.45 (10) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.57/59.45 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.57/59.45 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.45 (11) op(e1, e0) = e4
% 250.57/59.45 (12) ~ (e2 = e0)
% 250.57/59.45 (13) ~ (e1 = e0)
% 250.57/59.45 (14) ~ (all_22_2 = e3)
% 250.57/59.45 (15) op(e3, e4) = e0
% 250.57/59.45 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.45 (17) op(e2, e3) = all_10_2
% 250.57/59.45 (18) ~ (e3 = e2)
% 250.57/59.45 (19) ~ (e4 = e0)
% 250.57/59.45 (20) all_252_0 = e2
% 250.57/59.45 (21) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.57/59.45 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.57/59.45 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.57/59.45 (22) op(e2, e1) = all_38_2
% 250.57/59.45 (23) ~ (all_36_2 = e2)
% 250.57/59.45 (24) all_252_18 = e0
% 250.57/59.45 (25) ~ (e2 = e1)
% 250.57/59.45 (26) ~ (e4 = e1)
% 250.57/59.45 (27) op(e1, e4) = all_16_2
% 250.57/59.45 (28) op(e1, e3) = all_62_2
% 250.57/59.45 (29) ~ (e3 = e0)
% 250.57/59.45 (30) ~ (all_22_2 = e4)
% 250.57/59.45 (31) ~ (e3 = e1)
% 250.57/59.45 (32) op(e3, e1) = all_36_2
% 250.57/59.45 (33) ~ (all_16_2 = e2)
% 250.57/59.45 (34) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.57/59.45 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.57/59.45 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.57/59.45 (35) ~ (all_8_2 = e0)
% 250.57/59.45 (36) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.57/59.45 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.57/59.45 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.57/59.45 (37) op(e0, e3) = all_22_2
% 250.57/59.45 (38) op(e1, e2) = e0
% 250.57/59.45 (39) ~ (all_36_2 = e0)
% 250.57/59.45 (40) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 250.57/59.45 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 250.57/59.45 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.57/59.45 (41) ~ (e4 = e3)
% 250.57/59.45 (42) op(e3, e0) = all_48_2
% 250.57/59.45 (43) op(e1, e2) = all_4_2
% 250.57/59.45 (44) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.57/59.45 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.57/59.45 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.57/59.45 (45) ~ (all_48_2 = e0)
% 250.57/59.45 (46) all_252_14 = e2 & op(e1, e2) = e2
% 250.57/59.45 (47) ~ (e4 = e2)
% 250.57/59.45 (48) op(e3, e2) = all_8_2
% 250.57/59.45 (49) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.57/59.45 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.57/59.45 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.57/59.45 (50) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.57/59.45 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.57/59.45 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.57/59.45 (51) ~ (all_244_3 = e0)
% 250.57/59.45 (52) all_252_19 = e4
% 250.57/59.45 (53) ~ (all_16_2 = e3)
% 250.57/59.45 (54) all_252_8 = e1
% 250.57/59.45 (55) all_252_23 = e4
% 250.57/59.45 (56) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.57/59.45 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.57/59.45 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.57/59.45 (57) op(e3, e3) = all_244_3
% 250.57/59.45 (58) ~ (all_4_2 = e3)
% 250.57/59.45 (59) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.57/59.45 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.57/59.45 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.57/59.45 (60) ~ (all_62_2 = e4)
% 250.57/59.45 (61) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.57/59.45 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.57/59.45 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.45 (62) ~ (all_16_2 = e0)
% 250.57/59.45 (63) all_252_12 = e1
% 250.57/59.45 (64) all_252_20 = e3
% 250.57/59.45
% 250.57/59.45 Begin of proof
% 250.57/59.45 |
% 250.57/59.45 | BETA: splitting (40) gives:
% 250.57/59.45 |
% 250.57/59.45 | Case 1:
% 250.57/59.45 | |
% 250.57/59.45 | | (65) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.57/59.45 | | e2)
% 250.57/59.45 | |
% 250.57/59.45 | | REF_CLOSE: (8), (12), (16), (23), (32), (65) are inconsistent by sub-proof
% 250.57/59.45 | | #580.
% 250.57/59.45 | |
% 250.57/59.45 | Case 2:
% 250.57/59.45 | |
% 250.57/59.45 | | (66) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 250.57/59.45 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.57/59.45 | |
% 250.57/59.45 | | BETA: splitting (66) gives:
% 250.57/59.45 | |
% 250.57/59.45 | | Case 1:
% 250.57/59.45 | | |
% 250.57/59.45 | | |
% 250.57/59.45 | | | ALPHA: (46) implies:
% 250.57/59.45 | | | (67) op(e1, e2) = e2
% 250.57/59.45 | | |
% 250.57/59.45 | | | GROUND_INST: instantiating (16) with all_4_2, e0, e2, e1, simplifying with
% 250.57/59.45 | | | (38), (43) gives:
% 250.57/59.45 | | | (68) all_4_2 = e0
% 250.57/59.45 | | |
% 250.57/59.45 | | | GROUND_INST: instantiating (16) with all_4_2, e2, e2, e1, simplifying with
% 250.57/59.45 | | | (43), (67) gives:
% 250.57/59.45 | | | (69) all_4_2 = e2
% 250.57/59.45 | | |
% 250.57/59.45 | | | COMBINE_EQS: (68), (69) imply:
% 250.57/59.45 | | | (70) e2 = e0
% 250.57/59.45 | | |
% 250.57/59.45 | | | COMBINE_EQS: (20), (70) imply:
% 250.57/59.45 | | | (71) all_252_0 = e0
% 250.57/59.45 | | |
% 250.57/59.45 | | | REF_CLOSE: (7), (12), (13), (16), (18), (19), (25), (26), (31), (32),
% 250.57/59.45 | | | (35), (39), (41), (42), (45), (47), (48), (49), (50), (51),
% 250.57/59.45 | | | (57), (61), (64), (71) are inconsistent by sub-proof #559.
% 250.57/59.45 | | |
% 250.57/59.45 | | Case 2:
% 250.57/59.45 | | |
% 250.57/59.45 | | | (72) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0,
% 250.57/59.45 | | | e1) = e2)
% 250.57/59.45 | | |
% 250.57/59.45 | | | BETA: splitting (72) gives:
% 250.57/59.45 | | |
% 250.57/59.45 | | | Case 1:
% 250.57/59.45 | | | |
% 250.57/59.45 | | | | (73) all_252_15 = e2 & op(e1, e1) = e2
% 250.57/59.45 | | | |
% 250.57/59.45 | | | | ALPHA: (73) implies:
% 250.57/59.45 | | | | (74) all_252_15 = e2
% 250.57/59.45 | | | |
% 250.57/59.45 | | | | BETA: splitting (10) gives:
% 250.57/59.45 | | | |
% 250.57/59.45 | | | | Case 1:
% 250.57/59.45 | | | | |
% 250.57/59.45 | | | | | (75) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 &
% 250.57/59.45 | | | | | op(e1, e3) = e3)
% 250.57/59.45 | | | | |
% 250.57/59.45 | | | | | BETA: splitting (75) gives:
% 250.57/59.45 | | | | |
% 250.57/59.45 | | | | | Case 1:
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | (76) all_252_12 = e3 & op(e1, e4) = e3
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | REF_CLOSE: (16), (27), (53), (76) are inconsistent by sub-proof
% 250.57/59.45 | | | | | | #895.
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | Case 2:
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | (77) all_252_13 = e3 & op(e1, e3) = e3
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | ALPHA: (77) implies:
% 250.57/59.45 | | | | | | (78) all_252_13 = e3
% 250.57/59.45 | | | | | | (79) op(e1, e3) = e3
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | BETA: splitting (34) gives:
% 250.57/59.45 | | | | | |
% 250.57/59.45 | | | | | | Case 1:
% 250.57/59.45 | | | | | | |
% 250.57/59.45 | | | | | | | (80) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 &
% 250.57/59.45 | | | | | | | op(e3, e3) = e0)
% 250.57/59.45 | | | | | | |
% 250.57/59.45 | | | | | | | BETA: splitting (80) gives:
% 250.57/59.45 | | | | | | |
% 250.57/59.45 | | | | | | | Case 1:
% 250.57/59.45 | | | | | | | |
% 250.57/59.45 | | | | | | | | (81) all_252_1 = e0 & op(e4, e3) = e0
% 250.57/59.45 | | | | | | | |
% 250.57/59.45 | | | | | | | | ALPHA: (81) implies:
% 250.57/59.45 | | | | | | | | (82) all_252_1 = e0
% 250.57/59.45 | | | | | | | |
% 250.57/59.45 | | | | | | | | BETA: splitting (9) gives:
% 250.57/59.45 | | | | | | | |
% 250.57/59.45 | | | | | | | | Case 1:
% 250.57/59.45 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (83) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 250.57/59.46 | | | | | | | | | op(e3, e3) = e4)
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | BETA: splitting (83) gives:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (84) all_252_1 = e4 & op(e4, e3) = e4
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | ALPHA: (84) implies:
% 250.57/59.46 | | | | | | | | | | (85) all_252_1 = e4
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | COMBINE_EQS: (82), (85) imply:
% 250.57/59.46 | | | | | | | | | | (86) e4 = e0
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | SIMP: (86) implies:
% 250.57/59.46 | | | | | | | | | | (87) e4 = e0
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | COMBINE_EQS: (6), (87) imply:
% 250.57/59.46 | | | | | | | | | | (88) all_252_6 = e0
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | REF_CLOSE: (7), (16), (19), (20), (26), (32), (35), (39),
% 250.57/59.46 | | | | | | | | | | (41), (42), (45), (47), (48), (50), (51), (57),
% 250.57/59.46 | | | | | | | | | | (63), (64), (88) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | #551.
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (89) all_252_3 = e4 & op(e3, e3) = e4
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | ALPHA: (89) implies:
% 250.57/59.46 | | | | | | | | | | (90) all_252_3 = e4
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | BETA: splitting (59) gives:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | (91) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 250.57/59.46 | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | BETA: splitting (91) gives:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (92) all_252_1 = e1 & op(e4, e3) = e1
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | REF_CLOSE: (13), (82), (92) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | | | #851.
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (93) all_252_3 = e1 & op(e3, e3) = e1
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | REF_CLOSE: (26), (90), (93) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | | | #890.
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | (94) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 250.57/59.46 | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 250.57/59.46 | | | | | | | | | | | op(e0, e3) = e1)
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | BETA: splitting (94) gives:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (95) all_252_7 = e1 & op(e2, e3) = e1
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | ALPHA: (95) implies:
% 250.57/59.46 | | | | | | | | | | | | (96) op(e2, e3) = e1
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | REF_CLOSE: (3), (16), (17), (96) are inconsistent by
% 250.57/59.46 | | | | | | | | | | | | sub-proof #948.
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (97) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 250.57/59.46 | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | BETA: splitting (97) gives:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (98) all_252_13 = e1 & op(e1, e3) = e1
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | REF_CLOSE: (31), (78), (98) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | | | | #823.
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (99) all_252_21 = e1 & op(e0, e3) = e1
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | ALPHA: (99) implies:
% 250.57/59.46 | | | | | | | | | | | | | (100) op(e0, e3) = e1
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | REF_CLOSE: (1), (16), (25), (100) are inconsistent by
% 250.57/59.46 | | | | | | | | | | | | | sub-proof #941.
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (101) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4
% 250.57/59.46 | | | | | | | | | & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 250.57/59.46 | | | | | | | | | = e4)
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | REF_CLOSE: (4), (5), (10), (11), (12), (16), (17), (18), (19),
% 250.57/59.46 | | | | | | | | | (27), (29), (30), (33), (37), (41), (43), (47),
% 250.57/59.46 | | | | | | | | | (52), (53), (56), (58), (62), (101) are
% 250.57/59.46 | | | | | | | | | inconsistent by sub-proof #277.
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | End of split
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | (102) all_252_3 = e0 & op(e3, e3) = e0
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | ALPHA: (102) implies:
% 250.57/59.46 | | | | | | | | (103) op(e3, e3) = e0
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | REF_CLOSE: (16), (51), (57), (103) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | #973.
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | End of split
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | Case 2:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (104) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 250.57/59.46 | | | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | BETA: splitting (104) gives:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | (105) all_252_7 = e0 & op(e2, e3) = e0
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | ALPHA: (105) implies:
% 250.57/59.46 | | | | | | | | (106) all_252_7 = e0
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | BETA: splitting (21) gives:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (107) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3
% 250.57/59.46 | | | | | | | | | & op(e2, e3) = e3)
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | BETA: splitting (107) gives:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (108) all_252_6 = e3 & op(e2, e4) = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | ALPHA: (108) implies:
% 250.57/59.46 | | | | | | | | | | (109) all_252_6 = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | REF_CLOSE: (7), (13), (15), (16), (19), (20), (25), (26),
% 250.57/59.46 | | | | | | | | | | (31), (32), (35), (39), (41), (42), (45), (47),
% 250.57/59.46 | | | | | | | | | | (48), (50), (51), (57), (61), (64), (109) are
% 250.57/59.46 | | | | | | | | | | inconsistent by sub-proof #536.
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (110) all_252_7 = e3 & op(e2, e3) = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | ALPHA: (110) implies:
% 250.57/59.46 | | | | | | | | | | (111) all_252_7 = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | COMBINE_EQS: (106), (111) imply:
% 250.57/59.46 | | | | | | | | | | (112) e3 = e0
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | SIMP: (112) implies:
% 250.57/59.46 | | | | | | | | | | (113) e3 = e0
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (13), (14), (16), (17), (25),
% 250.57/59.46 | | | | | | | | | | (26), (28), (29), (30), (31), (37), (41), (44),
% 250.57/59.46 | | | | | | | | | | (59), (60), (78), (106), (113) are inconsistent by
% 250.57/59.46 | | | | | | | | | | sub-proof #276.
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (114) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3
% 250.57/59.46 | | | | | | | | | & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0)
% 250.57/59.46 | | | | | | | | | = e3)
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | BETA: splitting (114) gives:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (115) all_252_8 = e3 & op(e2, e2) = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | ALPHA: (115) implies:
% 250.57/59.46 | | | | | | | | | | (116) all_252_8 = e3
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | REF_CLOSE: (31), (54), (116) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | #927.
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | (117) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 =
% 250.57/59.46 | | | | | | | | | | e3 & op(e2, e0) = e3)
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | BETA: splitting (117) gives:
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | (118) all_252_11 = e3 & op(e2, e1) = e3
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | ALPHA: (118) implies:
% 250.57/59.46 | | | | | | | | | | | (119) op(e2, e1) = e3
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | BETA: splitting (36) gives:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (120) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 250.57/59.46 | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | BETA: splitting (120) gives:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (121) all_252_6 = e2 & op(e2, e4) = e2
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | ALPHA: (121) implies:
% 250.57/59.46 | | | | | | | | | | | | | (122) all_252_6 = e2
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | REF_CLOSE: (6), (47), (122) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | | | | | | #833.
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (123) all_252_7 = e2 & op(e2, e3) = e2
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | ALPHA: (123) implies:
% 250.57/59.46 | | | | | | | | | | | | | (124) all_252_7 = e2
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | COMBINE_EQS: (106), (124) imply:
% 250.57/59.46 | | | | | | | | | | | | | (125) e2 = e0
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | REF_CLOSE: (7), (12), (13), (16), (18), (19), (20), (25),
% 250.57/59.46 | | | | | | | | | | | | | (26), (31), (32), (35), (39), (41), (42), (45),
% 250.57/59.46 | | | | | | | | | | | | | (47), (48), (49), (50), (51), (57), (61), (64),
% 250.57/59.46 | | | | | | | | | | | | | (125) are inconsistent by sub-proof #493.
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | (126) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 250.57/59.46 | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 250.57/59.46 | | | | | | | | | | | | op(e2, e0) = e2)
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | BETA: splitting (126) gives:
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (127) all_252_8 = e2 & op(e2, e2) = e2
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (12), (16), (18), (20), (25), (27),
% 250.57/59.46 | | | | | | | | | | | | | (32), (33), (35), (39), (42), (45), (47), (48),
% 250.57/59.46 | | | | | | | | | | | | | (49), (51), (54), (57), (64), (127) are
% 250.57/59.46 | | | | | | | | | | | | | inconsistent by sub-proof #477.
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | (128) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 250.57/59.46 | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | BETA: splitting (128) gives:
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | | (129) all_252_11 = e2 & op(e2, e1) = e2
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (22), (119), (129) are inconsistent by
% 250.57/59.46 | | | | | | | | | | | | | | sub-proof #462.
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | | (130) all_252_18 = e2 & op(e2, e0) = e2
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (13), (16), (18), (19), (20), (24),
% 250.57/59.46 | | | | | | | | | | | | | | (25), (26), (31), (32), (35), (39), (41), (42),
% 250.57/59.46 | | | | | | | | | | | | | | (45), (47), (48), (49), (50), (51), (57), (61),
% 250.57/59.46 | | | | | | | | | | | | | | (64), (130) are inconsistent by sub-proof #275.
% 250.57/59.46 | | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | (131) all_252_18 = e3 & op(e2, e0) = e3
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | ALPHA: (131) implies:
% 250.57/59.46 | | | | | | | | | | | (132) all_252_18 = e3
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | COMBINE_EQS: (24), (132) imply:
% 250.57/59.46 | | | | | | | | | | | (133) e3 = e0
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (13), (14), (16), (17), (25),
% 250.57/59.46 | | | | | | | | | | | (26), (28), (29), (30), (31), (37), (41), (44),
% 250.57/59.46 | | | | | | | | | | | (59), (60), (78), (106), (133) are inconsistent by
% 250.57/59.46 | | | | | | | | | | | sub-proof #276.
% 250.57/59.46 | | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | | |
% 250.57/59.46 | | | | | | | | | End of split
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | End of split
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | (134) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0
% 250.57/59.46 | | | | | | | | & op(e0, e3) = e0)
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | BETA: splitting (134) gives:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (135) all_252_13 = e0 & op(e1, e3) = e0
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | ALPHA: (135) implies:
% 250.57/59.46 | | | | | | | | | (136) op(e1, e3) = e0
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | REF_CLOSE: (16), (29), (79), (136) are inconsistent by
% 250.57/59.46 | | | | | | | | | sub-proof #592.
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | Case 2:
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | (137) all_252_21 = e0 & op(e0, e3) = e0
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | ALPHA: (137) implies:
% 250.57/59.46 | | | | | | | | | (138) all_252_21 = e0
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | COMBINE_EQS: (2), (138) imply:
% 250.57/59.46 | | | | | | | | | (139) e2 = e0
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | | REF_CLOSE: (7), (12), (13), (16), (18), (19), (20), (25),
% 250.57/59.46 | | | | | | | | | (26), (31), (32), (35), (39), (41), (42), (45),
% 250.57/59.46 | | | | | | | | | (47), (48), (49), (50), (51), (57), (61), (64),
% 250.57/59.46 | | | | | | | | | (139) are inconsistent by sub-proof #493.
% 250.57/59.46 | | | | | | | | |
% 250.57/59.46 | | | | | | | | End of split
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | End of split
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | End of split
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | End of split
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | Case 2:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (140) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 250.57/59.46 | | | | | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | BETA: splitting (140) gives:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | Case 1:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (141) all_252_14 = e3 & op(e1, e2) = e3
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | REF_CLOSE: (16), (43), (58), (141) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | #858.
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | Case 2:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (142) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.57/59.46 | | | | | | op(e1, e0) = e3)
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | BETA: splitting (142) gives:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | Case 1:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (143) all_252_15 = e3 & op(e1, e1) = e3
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | REF_CLOSE: (18), (74), (143) are inconsistent by sub-proof #501.
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | Case 2:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (144) all_252_19 = e3 & op(e1, e0) = e3
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | ALPHA: (144) implies:
% 250.57/59.46 | | | | | | | (145) op(e1, e0) = e3
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | REF_CLOSE: (11), (16), (41), (145) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | #827.
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | End of split
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | End of split
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | End of split
% 250.57/59.46 | | | |
% 250.57/59.46 | | | Case 2:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (146) all_252_23 = e2 & op(e0, e1) = e2
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (47), (55), (146) are inconsistent by sub-proof #274.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | End of split
% 250.57/59.46 | | |
% 250.57/59.46 | | End of split
% 250.57/59.46 | |
% 250.57/59.46 | End of split
% 250.57/59.46 |
% 250.57/59.46 End of proof
% 250.57/59.46
% 250.57/59.46 Sub-proof #274 shows that the following formulas are inconsistent:
% 250.57/59.46 ----------------------------------------------------------------
% 250.57/59.46 (1) all_252_23 = e2 & op(e0, e1) = e2
% 250.57/59.46 (2) all_252_23 = e4
% 250.57/59.46 (3) ~ (e4 = e2)
% 250.57/59.46
% 250.57/59.46 Begin of proof
% 250.57/59.46 |
% 250.57/59.46 | ALPHA: (1) implies:
% 250.57/59.46 | (4) all_252_23 = e2
% 250.57/59.46 |
% 250.57/59.46 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.46 | (5) e4 = e2
% 250.57/59.46 |
% 250.57/59.46 | SIMP: (5) implies:
% 250.57/59.46 | (6) e4 = e2
% 250.57/59.46 |
% 250.57/59.46 | REDUCE: (3), (6) imply:
% 250.57/59.46 | (7) $false
% 250.57/59.46 |
% 250.57/59.46 | CLOSE: (7) is inconsistent.
% 250.57/59.46 |
% 250.57/59.46 End of proof
% 250.57/59.46
% 250.57/59.46 Sub-proof #275 shows that the following formulas are inconsistent:
% 250.57/59.46 ----------------------------------------------------------------
% 250.57/59.46 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.46 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.46 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.46 (2) ~ (e2 = e0)
% 250.57/59.46 (3) ~ (e1 = e0)
% 250.57/59.46 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.46 (5) ~ (e3 = e2)
% 250.57/59.46 (6) ~ (e4 = e0)
% 250.57/59.46 (7) all_252_0 = e2
% 250.57/59.46 (8) all_252_18 = e0
% 250.57/59.46 (9) ~ (e2 = e1)
% 250.57/59.46 (10) ~ (e4 = e1)
% 250.57/59.46 (11) ~ (e3 = e1)
% 250.57/59.46 (12) op(e3, e1) = all_36_2
% 250.57/59.46 (13) ~ (all_8_2 = e0)
% 250.57/59.46 (14) ~ (all_36_2 = e0)
% 250.57/59.46 (15) ~ (e4 = e3)
% 250.57/59.46 (16) op(e3, e0) = all_48_2
% 250.57/59.46 (17) ~ (all_48_2 = e0)
% 250.57/59.46 (18) ~ (e4 = e2)
% 250.57/59.46 (19) op(e3, e2) = all_8_2
% 250.57/59.46 (20) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.57/59.46 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.57/59.46 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.57/59.46 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.57/59.46 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.57/59.46 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.57/59.46 (22) ~ (all_244_3 = e0)
% 250.57/59.46 (23) op(e3, e3) = all_244_3
% 250.57/59.46 (24) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.57/59.46 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.57/59.46 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.46 (25) all_252_18 = e2 & op(e2, e0) = e2
% 250.57/59.46 (26) all_252_20 = e3
% 250.57/59.46
% 250.57/59.46 Begin of proof
% 250.57/59.46 |
% 250.57/59.46 | ALPHA: (25) implies:
% 250.57/59.46 | (27) all_252_18 = e2
% 250.57/59.46 |
% 250.57/59.46 | COMBINE_EQS: (8), (27) imply:
% 250.57/59.46 | (28) e2 = e0
% 250.57/59.46 |
% 250.57/59.46 | COMBINE_EQS: (7), (28) imply:
% 250.57/59.46 | (29) all_252_0 = e0
% 250.57/59.46 |
% 250.57/59.46 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 250.57/59.46 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 250.57/59.46 | (29) are inconsistent by sub-proof #559.
% 250.57/59.46 |
% 250.57/59.46 End of proof
% 250.57/59.46
% 250.57/59.46 Sub-proof #276 shows that the following formulas are inconsistent:
% 250.57/59.46 ----------------------------------------------------------------
% 250.57/59.46 (1) op(e0, e3) = e2
% 250.57/59.46 (2) ~ (all_10_2 = e1)
% 250.57/59.46 (3) ~ (all_10_2 = e4)
% 250.57/59.46 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.57/59.46 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.57/59.46 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.57/59.46 (5) ~ (e1 = e0)
% 250.57/59.46 (6) ~ (all_22_2 = e3)
% 250.57/59.46 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.46 (8) op(e2, e3) = all_10_2
% 250.57/59.46 (9) ~ (e2 = e1)
% 250.57/59.46 (10) ~ (e4 = e1)
% 250.57/59.46 (11) all_252_7 = e0
% 250.57/59.46 (12) op(e1, e3) = all_62_2
% 250.57/59.46 (13) ~ (e3 = e0)
% 250.57/59.46 (14) e3 = e0
% 250.57/59.46 (15) ~ (all_22_2 = e4)
% 250.57/59.46 (16) ~ (e3 = e1)
% 250.57/59.46 (17) all_252_13 = e3
% 250.57/59.46 (18) op(e0, e3) = all_22_2
% 250.57/59.46 (19) ~ (e4 = e3)
% 250.57/59.46 (20) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.57/59.46 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.57/59.46 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.57/59.46 (21) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.57/59.46 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.57/59.46 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.57/59.46 (22) ~ (all_62_2 = e4)
% 250.57/59.46
% 250.57/59.46 Begin of proof
% 250.57/59.46 |
% 250.57/59.46 | COMBINE_EQS: (14), (17) imply:
% 250.57/59.46 | (23) all_252_13 = e0
% 250.57/59.46 |
% 250.57/59.46 | BETA: splitting (21) gives:
% 250.57/59.46 |
% 250.57/59.46 | Case 1:
% 250.57/59.46 | |
% 250.57/59.46 | | (24) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 250.57/59.46 | | e1)
% 250.57/59.46 | |
% 250.57/59.46 | | BETA: splitting (24) gives:
% 250.57/59.46 | |
% 250.57/59.46 | | Case 1:
% 250.57/59.46 | | |
% 250.57/59.46 | | | (25) all_252_1 = e1 & op(e4, e3) = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | ALPHA: (25) implies:
% 250.57/59.46 | | | (26) all_252_1 = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | BETA: splitting (4) gives:
% 250.57/59.46 | | |
% 250.57/59.46 | | | Case 1:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (27) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3,
% 250.57/59.46 | | | | e3) = e4)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | BETA: splitting (27) gives:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | Case 1:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (28) all_252_1 = e4 & op(e4, e3) = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | REF_CLOSE: (10), (26), (28) are inconsistent by sub-proof #955.
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | Case 2:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (29) all_252_3 = e4 & op(e3, e3) = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | ALPHA: (29) implies:
% 250.57/59.46 | | | | | (30) all_252_3 = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | BETA: splitting (20) gives:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | Case 1:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (31) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 250.57/59.46 | | | | | | op(e3, e3) = e3)
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | BETA: splitting (31) gives:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | Case 1:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (32) all_252_1 = e3 & op(e4, e3) = e3
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | REF_CLOSE: (16), (26), (32) are inconsistent by sub-proof #686.
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | Case 2:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (33) all_252_3 = e3 & op(e3, e3) = e3
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | REF_CLOSE: (19), (30), (33) are inconsistent by sub-proof #482.
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | End of split
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | Case 2:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (34) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 250.57/59.46 | | | | | | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | REF_CLOSE: (6), (7), (11), (13), (18), (23), (34) are inconsistent
% 250.57/59.46 | | | | | | by sub-proof #882.
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | End of split
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | End of split
% 250.57/59.46 | | | |
% 250.57/59.46 | | | Case 2:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (35) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1,
% 250.57/59.46 | | | | e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (3), (7), (8), (12), (15), (18), (22), (35) are inconsistent
% 250.57/59.46 | | | | by sub-proof #771.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | End of split
% 250.57/59.46 | | |
% 250.57/59.46 | | Case 2:
% 250.57/59.46 | | |
% 250.57/59.46 | | | (36) all_252_3 = e1 & op(e3, e3) = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | ALPHA: (36) implies:
% 250.57/59.46 | | | (37) all_252_3 = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | BETA: splitting (4) gives:
% 250.57/59.46 | | |
% 250.57/59.46 | | | Case 1:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (38) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3,
% 250.57/59.46 | | | | e3) = e4)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | BETA: splitting (38) gives:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | Case 1:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (39) all_252_1 = e4 & op(e4, e3) = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | ALPHA: (39) implies:
% 250.57/59.46 | | | | | (40) all_252_1 = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | BETA: splitting (20) gives:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | Case 1:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (41) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 250.57/59.46 | | | | | | op(e3, e3) = e3)
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | REF_CLOSE: (16), (19), (37), (40), (41) are inconsistent by
% 250.57/59.46 | | | | | | sub-proof #884.
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | Case 2:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (42) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 250.57/59.46 | | | | | | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | REF_CLOSE: (6), (7), (11), (13), (18), (23), (42) are inconsistent
% 250.57/59.46 | | | | | | by sub-proof #882.
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | End of split
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | Case 2:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (43) all_252_3 = e4 & op(e3, e3) = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | ALPHA: (43) implies:
% 250.57/59.46 | | | | | (44) all_252_3 = e4
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | REF_CLOSE: (10), (37), (44) are inconsistent by sub-proof #772.
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | End of split
% 250.57/59.46 | | | |
% 250.57/59.46 | | | Case 2:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (45) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1,
% 250.57/59.46 | | | | e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (3), (7), (8), (12), (15), (18), (22), (45) are inconsistent
% 250.57/59.46 | | | | by sub-proof #771.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | End of split
% 250.57/59.46 | | |
% 250.57/59.46 | | End of split
% 250.57/59.46 | |
% 250.57/59.46 | Case 2:
% 250.57/59.46 | |
% 250.57/59.46 | | (46) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.57/59.46 | | e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.57/59.46 | |
% 250.57/59.46 | | BETA: splitting (46) gives:
% 250.57/59.46 | |
% 250.57/59.46 | | Case 1:
% 250.57/59.46 | | |
% 250.57/59.46 | | | (47) all_252_7 = e1 & op(e2, e3) = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | ALPHA: (47) implies:
% 250.57/59.46 | | | (48) op(e2, e3) = e1
% 250.57/59.46 | | |
% 250.57/59.46 | | | REF_CLOSE: (2), (7), (8), (48) are inconsistent by sub-proof #948.
% 250.57/59.46 | | |
% 250.57/59.46 | | Case 2:
% 250.57/59.46 | | |
% 250.57/59.46 | | | (49) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0,
% 250.57/59.46 | | | e3) = e1)
% 250.57/59.46 | | |
% 250.57/59.46 | | | BETA: splitting (49) gives:
% 250.57/59.46 | | |
% 250.57/59.46 | | | Case 1:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (50) all_252_13 = e1 & op(e1, e3) = e1
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (5), (23), (50) are inconsistent by sub-proof #411.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | Case 2:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (51) all_252_21 = e1 & op(e0, e3) = e1
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | ALPHA: (51) implies:
% 250.57/59.46 | | | | (52) op(e0, e3) = e1
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (1), (7), (9), (52) are inconsistent by sub-proof #941.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | End of split
% 250.57/59.46 | | |
% 250.57/59.46 | | End of split
% 250.57/59.46 | |
% 250.57/59.46 | End of split
% 250.57/59.46 |
% 250.57/59.46 End of proof
% 250.57/59.46
% 250.57/59.46 Sub-proof #277 shows that the following formulas are inconsistent:
% 250.57/59.46 ----------------------------------------------------------------
% 250.57/59.46 (1) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 250.57/59.46 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.57/59.46 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.57/59.46 (2) ~ (all_10_2 = e4)
% 250.57/59.46 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.57/59.46 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.57/59.46 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.46 (4) op(e1, e0) = e4
% 250.57/59.46 (5) ~ (e2 = e0)
% 250.57/59.46 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.46 (7) op(e2, e3) = all_10_2
% 250.57/59.46 (8) ~ (e3 = e2)
% 250.57/59.46 (9) ~ (e4 = e0)
% 250.57/59.46 (10) op(e1, e4) = all_16_2
% 250.57/59.46 (11) ~ (e3 = e0)
% 250.57/59.46 (12) ~ (all_22_2 = e4)
% 250.57/59.46 (13) ~ (all_16_2 = e2)
% 250.57/59.46 (14) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.57/59.46 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.57/59.46 (15) op(e0, e3) = all_22_2
% 250.57/59.46 (16) ~ (e4 = e3)
% 250.57/59.46 (17) op(e1, e2) = all_4_2
% 250.57/59.46 (18) ~ (e4 = e2)
% 250.57/59.46 (19) all_252_19 = e4
% 250.57/59.46 (20) ~ (all_16_2 = e3)
% 250.57/59.46 (21) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.57/59.46 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.57/59.46 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.57/59.46 (22) ~ (all_4_2 = e3)
% 250.57/59.46 (23) ~ (all_16_2 = e0)
% 250.57/59.46
% 250.57/59.46 Begin of proof
% 250.57/59.46 |
% 250.57/59.46 | BETA: splitting (14) gives:
% 250.57/59.46 |
% 250.57/59.46 | Case 1:
% 250.57/59.46 | |
% 250.57/59.46 | | (24) all_252_7 = e4 & op(e2, e3) = e4
% 250.57/59.46 | |
% 250.57/59.46 | | ALPHA: (24) implies:
% 250.57/59.46 | | (25) op(e2, e3) = e4
% 250.57/59.46 | |
% 250.57/59.46 | | REF_CLOSE: (2), (6), (7), (25) are inconsistent by sub-proof #953.
% 250.57/59.46 | |
% 250.57/59.46 | Case 2:
% 250.57/59.46 | |
% 250.57/59.46 | | (26) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 250.57/59.46 | | = e4)
% 250.57/59.46 | |
% 250.57/59.46 | | BETA: splitting (26) gives:
% 250.57/59.46 | |
% 250.57/59.46 | | Case 1:
% 250.57/59.46 | | |
% 250.57/59.46 | | | (27) all_252_13 = e4 & op(e1, e3) = e4
% 250.57/59.46 | | |
% 250.57/59.46 | | | ALPHA: (27) implies:
% 250.57/59.46 | | | (28) all_252_13 = e4
% 250.57/59.46 | | |
% 250.57/59.46 | | | BETA: splitting (3) gives:
% 250.57/59.46 | | |
% 250.57/59.46 | | | Case 1:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (29) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1,
% 250.57/59.46 | | | | e3) = e3)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | REF_CLOSE: (6), (10), (16), (20), (28), (29) are inconsistent by
% 250.57/59.46 | | | | sub-proof #806.
% 250.57/59.46 | | | |
% 250.57/59.46 | | | Case 2:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | (30) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.57/59.46 | | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | BETA: splitting (30) gives:
% 250.57/59.46 | | | |
% 250.57/59.46 | | | | Case 1:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (31) all_252_14 = e3 & op(e1, e2) = e3
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | REF_CLOSE: (6), (17), (22), (31) are inconsistent by sub-proof #858.
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | Case 2:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | (32) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.57/59.46 | | | | | op(e1, e0) = e3)
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | BETA: splitting (32) gives:
% 250.57/59.46 | | | | |
% 250.57/59.46 | | | | | Case 1:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | (33) all_252_15 = e3 & op(e1, e1) = e3
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | ALPHA: (33) implies:
% 250.57/59.46 | | | | | | (34) all_252_15 = e3
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | BETA: splitting (21) gives:
% 250.57/59.46 | | | | | |
% 250.57/59.46 | | | | | | Case 1:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | (35) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 &
% 250.57/59.46 | | | | | | | op(e1, e3) = e2)
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | BETA: splitting (35) gives:
% 250.57/59.46 | | | | | | |
% 250.57/59.46 | | | | | | | Case 1:
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | (36) all_252_12 = e2 & op(e1, e4) = e2
% 250.57/59.46 | | | | | | | |
% 250.57/59.46 | | | | | | | | REF_CLOSE: (6), (10), (13), (36) are inconsistent by sub-proof
% 250.57/59.46 | | | | | | | | #926.
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | (37) all_252_13 = e2 & op(e1, e3) = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | ALPHA: (37) implies:
% 250.57/59.47 | | | | | | | | (38) all_252_13 = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | COMBINE_EQS: (28), (38) imply:
% 250.57/59.47 | | | | | | | | (39) e4 = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | SIMP: (39) implies:
% 250.57/59.47 | | | | | | | | (40) e4 = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | REDUCE: (18), (40) imply:
% 250.57/59.47 | | | | | | | | (41) $false
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | CLOSE: (41) is inconsistent.
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | End of split
% 250.57/59.47 | | | | | | |
% 250.57/59.47 | | | | | | Case 2:
% 250.57/59.47 | | | | | | |
% 250.57/59.47 | | | | | | | (42) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 250.57/59.47 | | | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.57/59.47 | | | | | | |
% 250.57/59.47 | | | | | | | BETA: splitting (42) gives:
% 250.57/59.47 | | | | | | |
% 250.57/59.47 | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | (43) all_252_14 = e2 & op(e1, e2) = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | ALPHA: (43) implies:
% 250.57/59.47 | | | | | | | | (44) all_252_14 = e2
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | BETA: splitting (1) gives:
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | (45) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0
% 250.57/59.47 | | | | | | | | | & op(e1, e3) = e0)
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | BETA: splitting (45) gives:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | (46) all_252_12 = e0 & op(e1, e4) = e0
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | ALPHA: (46) implies:
% 250.57/59.47 | | | | | | | | | | (47) op(e1, e4) = e0
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | REF_CLOSE: (6), (10), (23), (47) are inconsistent by
% 250.57/59.47 | | | | | | | | | | sub-proof #278.
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | (48) all_252_13 = e0 & op(e1, e3) = e0
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | ALPHA: (48) implies:
% 250.57/59.47 | | | | | | | | | | (49) all_252_13 = e0
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | REF_CLOSE: (9), (28), (49) are inconsistent by sub-proof
% 250.57/59.47 | | | | | | | | | | #407.
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | End of split
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | (50) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0
% 250.57/59.47 | | | | | | | | | & op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) =
% 250.57/59.47 | | | | | | | | | e0)
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | BETA: splitting (50) gives:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | (51) all_252_14 = e0 & op(e1, e2) = e0
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | REF_CLOSE: (5), (44), (51) are inconsistent by sub-proof
% 250.57/59.47 | | | | | | | | | | #751.
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | (52) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 =
% 250.57/59.47 | | | | | | | | | | e0 & op(e1, e0) = e0)
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | BETA: splitting (52) gives:
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | | (53) all_252_15 = e0 & op(e1, e1) = e0
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | | REF_CLOSE: (11), (34), (53) are inconsistent by sub-proof
% 250.57/59.47 | | | | | | | | | | | #763.
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | | (54) all_252_19 = e0 & op(e1, e0) = e0
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | | ALPHA: (54) implies:
% 250.57/59.47 | | | | | | | | | | | (55) all_252_19 = e0
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | | REF_CLOSE: (9), (19), (55) are inconsistent by sub-proof
% 250.57/59.47 | | | | | | | | | | | #618.
% 250.57/59.47 | | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | | End of split
% 250.57/59.47 | | | | | | | | | |
% 250.57/59.47 | | | | | | | | | End of split
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | End of split
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | (56) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 250.57/59.47 | | | | | | | | op(e1, e0) = e2)
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | BETA: splitting (56) gives:
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | | Case 1:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | (57) all_252_15 = e2 & op(e1, e1) = e2
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | ALPHA: (57) implies:
% 250.57/59.47 | | | | | | | | | (58) all_252_15 = e2
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | COMBINE_EQS: (34), (58) imply:
% 250.57/59.47 | | | | | | | | | (59) e3 = e2
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | REDUCE: (8), (59) imply:
% 250.57/59.47 | | | | | | | | | (60) $false
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | CLOSE: (60) is inconsistent.
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | Case 2:
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | (61) all_252_19 = e2 & op(e1, e0) = e2
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | ALPHA: (61) implies:
% 250.57/59.47 | | | | | | | | | (62) op(e1, e0) = e2
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | | REF_CLOSE: (4), (6), (18), (62) are inconsistent by sub-proof
% 250.57/59.47 | | | | | | | | | #829.
% 250.57/59.47 | | | | | | | | |
% 250.57/59.47 | | | | | | | | End of split
% 250.57/59.47 | | | | | | | |
% 250.57/59.47 | | | | | | | End of split
% 250.57/59.47 | | | | | | |
% 250.57/59.47 | | | | | | End of split
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | Case 2:
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | | (63) all_252_19 = e3 & op(e1, e0) = e3
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | | ALPHA: (63) implies:
% 250.57/59.47 | | | | | | (64) all_252_19 = e3
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | | COMBINE_EQS: (19), (64) imply:
% 250.57/59.47 | | | | | | (65) e4 = e3
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | | REDUCE: (16), (65) imply:
% 250.57/59.47 | | | | | | (66) $false
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | | CLOSE: (66) is inconsistent.
% 250.57/59.47 | | | | | |
% 250.57/59.47 | | | | | End of split
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | End of split
% 250.57/59.47 | | | |
% 250.57/59.47 | | | End of split
% 250.57/59.47 | | |
% 250.57/59.47 | | Case 2:
% 250.57/59.47 | | |
% 250.57/59.47 | | | (67) all_252_21 = e4 & op(e0, e3) = e4
% 250.57/59.47 | | |
% 250.57/59.47 | | | REF_CLOSE: (6), (12), (15), (67) are inconsistent by sub-proof #805.
% 250.57/59.47 | | |
% 250.57/59.47 | | End of split
% 250.57/59.47 | |
% 250.57/59.47 | End of split
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #278 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.47 (2) op(e1, e4) = all_16_2
% 250.57/59.47 (3) op(e1, e4) = e0
% 250.57/59.47 (4) ~ (all_16_2 = e0)
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | GROUND_INST: instantiating (1) with all_16_2, e0, e4, e1, simplifying with
% 250.57/59.47 | (2), (3) gives:
% 250.57/59.47 | (5) all_16_2 = e0
% 250.57/59.47 |
% 250.57/59.47 | REDUCE: (4), (5) imply:
% 250.57/59.47 | (6) $false
% 250.57/59.47 |
% 250.57/59.47 | CLOSE: (6) is inconsistent.
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #279 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) all_252_4 = e4
% 250.57/59.47 (2) ~ (e3 = e2)
% 250.57/59.47 (3) all_252_5 = e3
% 250.57/59.47 (4) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.57/59.47 (5) ~ (e4 = e2)
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | BETA: splitting (4) gives:
% 250.57/59.47 |
% 250.57/59.47 | Case 1:
% 250.57/59.47 | |
% 250.57/59.47 | | (6) all_252_4 = e2 & op(e4, e2) = e2
% 250.57/59.47 | |
% 250.57/59.47 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #280.
% 250.57/59.47 | |
% 250.57/59.47 | Case 2:
% 250.57/59.47 | |
% 250.57/59.47 | | (7) all_252_5 = e2 & op(e3, e2) = e2
% 250.57/59.47 | |
% 250.57/59.47 | | ALPHA: (7) implies:
% 250.57/59.47 | | (8) all_252_5 = e2
% 250.57/59.47 | |
% 250.57/59.47 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #507.
% 250.57/59.47 | |
% 250.57/59.47 | End of split
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #280 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) all_252_4 = e2 & op(e4, e2) = e2
% 250.57/59.47 (2) all_252_4 = e4
% 250.57/59.47 (3) ~ (e4 = e2)
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | ALPHA: (1) implies:
% 250.57/59.47 | (4) all_252_4 = e2
% 250.57/59.47 |
% 250.57/59.47 | COMBINE_EQS: (2), (4) imply:
% 250.57/59.47 | (5) e4 = e2
% 250.57/59.47 |
% 250.57/59.47 | REDUCE: (3), (5) imply:
% 250.57/59.47 | (6) $false
% 250.57/59.47 |
% 250.57/59.47 | CLOSE: (6) is inconsistent.
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #281 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) all_252_3 = e4
% 250.57/59.47 (2) all_252_6 = e4
% 250.57/59.47 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.57/59.47 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.57/59.47 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.57/59.47 (4) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.57/59.47 (5) ~ (e1 = e0)
% 250.57/59.47 (6) op(e3, e4) = e0
% 250.57/59.47 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.47 (8) ~ (e4 = e0)
% 250.57/59.47 (9) all_252_0 = e2
% 250.57/59.47 (10) ~ (e2 = e1)
% 250.57/59.47 (11) ~ (e4 = e1)
% 250.57/59.47 (12) ~ (e3 = e0)
% 250.57/59.47 (13) all_252_2 = e0
% 250.57/59.47 (14) ~ (e3 = e1)
% 250.57/59.47 (15) op(e3, e1) = all_36_2
% 250.57/59.47 (16) ~ (all_8_2 = e0)
% 250.57/59.47 (17) ~ (all_36_2 = e0)
% 250.57/59.47 (18) ~ (e4 = e3)
% 250.57/59.47 (19) op(e3, e0) = all_48_2
% 250.57/59.47 (20) ~ (all_48_2 = e0)
% 250.57/59.47 (21) ~ (e4 = e2)
% 250.57/59.47 (22) op(e3, e2) = all_8_2
% 250.57/59.47 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.57/59.47 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.57/59.47 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.57/59.47 (24) ~ (all_244_3 = e0)
% 250.57/59.47 (25) op(e3, e3) = all_244_3
% 250.57/59.47 (26) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.57/59.47 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.57/59.47 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.47 (27) all_252_20 = e3
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | BETA: splitting (4) gives:
% 250.57/59.47 |
% 250.57/59.47 | Case 1:
% 250.57/59.47 | |
% 250.57/59.47 | | (28) all_252_2 = e3 & op(e3, e4) = e3
% 250.57/59.47 | |
% 250.57/59.47 | | ALPHA: (28) implies:
% 250.57/59.47 | | (29) all_252_2 = e3
% 250.57/59.47 | |
% 250.57/59.47 | | COMBINE_EQS: (13), (29) imply:
% 250.57/59.47 | | (30) e3 = e0
% 250.57/59.47 | |
% 250.57/59.47 | | REDUCE: (12), (30) imply:
% 250.57/59.47 | | (31) $false
% 250.57/59.47 | |
% 250.57/59.47 | | CLOSE: (31) is inconsistent.
% 250.57/59.47 | |
% 250.57/59.47 | Case 2:
% 250.57/59.47 | |
% 250.57/59.47 | | (32) all_252_3 = e3 & op(e3, e3) = e3
% 250.57/59.47 | |
% 250.57/59.47 | | ALPHA: (32) implies:
% 250.57/59.47 | | (33) all_252_3 = e3
% 250.57/59.47 | |
% 250.57/59.47 | | COMBINE_EQS: (1), (33) imply:
% 250.57/59.47 | | (34) e4 = e3
% 250.57/59.47 | |
% 250.57/59.47 | | COMBINE_EQS: (2), (34) imply:
% 250.57/59.47 | | (35) all_252_6 = e3
% 250.57/59.47 | |
% 250.57/59.47 | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (14), (15), (16), (17),
% 250.57/59.47 | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (35)
% 250.57/59.47 | | are inconsistent by sub-proof #536.
% 250.57/59.47 | |
% 250.57/59.47 | End of split
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #282 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) all_252_6 = e4
% 250.57/59.47 (2) ~ (e1 = e0)
% 250.57/59.47 (3) op(e3, e4) = e0
% 250.57/59.47 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.47 (5) all_252_0 = e2
% 250.57/59.47 (6) ~ (e2 = e1)
% 250.57/59.47 (7) ~ (e4 = e1)
% 250.57/59.47 (8) op(e1, e3) = all_62_2
% 250.57/59.47 (9) ~ (e3 = e1)
% 250.57/59.47 (10) ~ (all_62_2 = e4)
% 250.57/59.47 (11) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.57/59.47 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.57/59.47 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.47 (12) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.57/59.47 e4)
% 250.57/59.47 (13) all_252_20 = e3
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | BETA: splitting (12) gives:
% 250.57/59.47 |
% 250.57/59.47 | Case 1:
% 250.57/59.47 | |
% 250.57/59.47 | | (14) all_252_12 = e4 & op(e1, e4) = e4
% 250.57/59.47 | |
% 250.57/59.47 | | ALPHA: (14) implies:
% 250.57/59.47 | | (15) all_252_12 = e4
% 250.57/59.47 | |
% 250.57/59.47 | | BETA: splitting (11) gives:
% 250.57/59.47 | |
% 250.57/59.47 | | Case 1:
% 250.57/59.47 | | |
% 250.57/59.47 | | | (16) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4)
% 250.57/59.47 | | | = e1)
% 250.57/59.47 | | |
% 250.57/59.47 | | | REF_CLOSE: (2), (3), (4), (5), (6), (16) are inconsistent by sub-proof
% 250.57/59.47 | | | #557.
% 250.57/59.47 | | |
% 250.57/59.47 | | Case 2:
% 250.57/59.47 | | |
% 250.57/59.47 | | | (17) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4)
% 250.57/59.47 | | | = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.57/59.47 | | |
% 250.57/59.47 | | | BETA: splitting (17) gives:
% 250.57/59.47 | | |
% 250.57/59.47 | | | Case 1:
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | (18) all_252_6 = e1 & op(e2, e4) = e1
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #903.
% 250.57/59.47 | | | |
% 250.57/59.47 | | | Case 2:
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | (19) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 250.57/59.47 | | | | e4) = e1)
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | BETA: splitting (19) gives:
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | Case 1:
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | | (20) all_252_12 = e1 & op(e1, e4) = e1
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | | REF_CLOSE: (7), (15), (20) are inconsistent by sub-proof #566.
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | Case 2:
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | | (21) all_252_20 = e1 & op(e0, e4) = e1
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | | REF_CLOSE: (9), (13), (21) are inconsistent by sub-proof #565.
% 250.57/59.47 | | | | |
% 250.57/59.47 | | | | End of split
% 250.57/59.47 | | | |
% 250.57/59.47 | | | End of split
% 250.57/59.47 | | |
% 250.57/59.47 | | End of split
% 250.57/59.47 | |
% 250.57/59.47 | Case 2:
% 250.57/59.47 | |
% 250.57/59.47 | | (22) all_252_13 = e4 & op(e1, e3) = e4
% 250.57/59.47 | |
% 250.57/59.47 | | REF_CLOSE: (4), (8), (10), (22) are inconsistent by sub-proof #952.
% 250.57/59.47 | |
% 250.57/59.47 | End of split
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #283 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.57/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.57/59.47 (2) op(e0, e0) = all_244_24
% 250.57/59.47 (3) ~ (all_244_15 = e0)
% 250.57/59.47 (4) op(e0, e2) = all_28_2
% 250.57/59.47 (5) ~ (e4 = e1)
% 250.57/59.47 (6) ~ (all_28_2 = e1)
% 250.57/59.47 (7) ~ (e3 = e1)
% 250.57/59.47 (8) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.57/59.47 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) =
% 250.57/59.47 e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.57/59.47 (9) ~ (all_22_2 = e1)
% 250.57/59.47 (10) op(e0, e3) = all_22_2
% 250.57/59.47 (11) op(e1, e1) = all_244_15
% 250.57/59.47 (12) all_252_23 = e4
% 250.57/59.47 (13) op(all_244_24, all_244_24) = e0
% 250.57/59.47 (14) all_252_20 = e3
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | BETA: splitting (8) gives:
% 250.57/59.47 |
% 250.57/59.47 | Case 1:
% 250.57/59.47 | |
% 250.57/59.47 | | (15) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3)
% 250.57/59.47 | | = e1)
% 250.57/59.47 | |
% 250.57/59.47 | | REF_CLOSE: (1), (7), (9), (10), (14), (15) are inconsistent by sub-proof
% 250.57/59.47 | | #285.
% 250.57/59.47 | |
% 250.57/59.47 | Case 2:
% 250.57/59.47 | |
% 250.57/59.47 | | (16) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1)
% 250.57/59.47 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.57/59.47 | |
% 250.57/59.47 | | BETA: splitting (16) gives:
% 250.57/59.47 | |
% 250.57/59.47 | | Case 1:
% 250.57/59.47 | | |
% 250.57/59.47 | | | (17) all_252_22 = e1 & op(e0, e2) = e1
% 250.57/59.47 | | |
% 250.57/59.47 | | | ALPHA: (17) implies:
% 250.57/59.47 | | | (18) op(e0, e2) = e1
% 250.57/59.47 | | |
% 250.57/59.47 | | | REF_CLOSE: (1), (4), (6), (18) are inconsistent by sub-proof #907.
% 250.57/59.47 | | |
% 250.57/59.47 | | Case 2:
% 250.57/59.47 | | |
% 250.57/59.47 | | | (19) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0,
% 250.57/59.47 | | | e0) = e1)
% 250.57/59.47 | | |
% 250.57/59.47 | | | BETA: splitting (19) gives:
% 250.57/59.47 | | |
% 250.57/59.47 | | | Case 1:
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | (20) all_252_23 = e1 & op(e0, e1) = e1
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | REF_CLOSE: (5), (12), (20) are inconsistent by sub-proof #284.
% 250.57/59.47 | | | |
% 250.57/59.47 | | | Case 2:
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | (21) all_252_24 = e1 & op(e0, e0) = e1
% 250.57/59.47 | | | |
% 250.57/59.47 | | | | REF_CLOSE: (1), (2), (3), (11), (13), (21) are inconsistent by sub-proof
% 250.57/59.47 | | | | #611.
% 250.57/59.47 | | | |
% 250.57/59.47 | | | End of split
% 250.57/59.47 | | |
% 250.57/59.47 | | End of split
% 250.57/59.47 | |
% 250.57/59.47 | End of split
% 250.57/59.47 |
% 250.57/59.47 End of proof
% 250.57/59.47
% 250.57/59.47 Sub-proof #284 shows that the following formulas are inconsistent:
% 250.57/59.47 ----------------------------------------------------------------
% 250.57/59.47 (1) all_252_23 = e1 & op(e0, e1) = e1
% 250.57/59.47 (2) all_252_23 = e4
% 250.57/59.47 (3) ~ (e4 = e1)
% 250.57/59.47
% 250.57/59.47 Begin of proof
% 250.57/59.47 |
% 250.57/59.47 | ALPHA: (1) implies:
% 250.66/59.47 | (4) all_252_23 = e1
% 250.66/59.47 |
% 250.66/59.47 | COMBINE_EQS: (2), (4) imply:
% 250.66/59.47 | (5) e4 = e1
% 250.66/59.47 |
% 250.66/59.47 | REDUCE: (3), (5) imply:
% 250.66/59.47 | (6) $false
% 250.66/59.47 |
% 250.66/59.47 | CLOSE: (6) is inconsistent.
% 250.66/59.47 |
% 250.66/59.47 End of proof
% 250.66/59.47
% 250.66/59.47 Sub-proof #285 shows that the following formulas are inconsistent:
% 250.66/59.47 ----------------------------------------------------------------
% 250.66/59.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.47 (2) ~ (e3 = e1)
% 250.66/59.47 (3) ~ (all_22_2 = e1)
% 250.66/59.47 (4) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.66/59.47 (5) op(e0, e3) = all_22_2
% 250.66/59.47 (6) all_252_20 = e3
% 250.66/59.47
% 250.66/59.47 Begin of proof
% 250.66/59.47 |
% 250.66/59.47 | BETA: splitting (4) gives:
% 250.66/59.47 |
% 250.66/59.47 | Case 1:
% 250.66/59.47 | |
% 250.66/59.47 | | (7) all_252_20 = e1 & op(e0, e4) = e1
% 250.66/59.47 | |
% 250.66/59.47 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #509.
% 250.66/59.47 | |
% 250.66/59.47 | Case 2:
% 250.66/59.47 | |
% 250.66/59.47 | | (8) all_252_21 = e1 & op(e0, e3) = e1
% 250.66/59.47 | |
% 250.66/59.47 | | ALPHA: (8) implies:
% 250.66/59.47 | | (9) op(e0, e3) = e1
% 250.66/59.47 | |
% 250.66/59.47 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #714.
% 250.66/59.47 | |
% 250.66/59.47 | End of split
% 250.66/59.47 |
% 250.66/59.47 End of proof
% 250.66/59.47
% 250.66/59.47 Sub-proof #286 shows that the following formulas are inconsistent:
% 250.66/59.47 ----------------------------------------------------------------
% 250.66/59.47 (1) op(e4, e1) = e0
% 250.66/59.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.47 (3) ~ (e4 = e0)
% 250.66/59.47 (4) op(e4, e1) = all_26_2
% 250.66/59.47 (5) op(e4, e1) = e4
% 250.66/59.47
% 250.66/59.47 Begin of proof
% 250.66/59.47 |
% 250.66/59.47 | GROUND_INST: instantiating (2) with all_26_2, e0, e1, e4, simplifying with
% 250.66/59.47 | (1), (4) gives:
% 250.66/59.47 | (6) all_26_2 = e0
% 250.66/59.47 |
% 250.66/59.47 | GROUND_INST: instantiating (2) with all_26_2, e4, e1, e4, simplifying with
% 250.66/59.47 | (4), (5) gives:
% 250.66/59.47 | (7) all_26_2 = e4
% 250.66/59.47 |
% 250.66/59.47 | COMBINE_EQS: (6), (7) imply:
% 250.66/59.47 | (8) e4 = e0
% 250.66/59.47 |
% 250.66/59.47 | SIMP: (8) implies:
% 250.66/59.47 | (9) e4 = e0
% 250.66/59.47 |
% 250.66/59.47 | REDUCE: (3), (9) imply:
% 250.66/59.47 | (10) $false
% 250.66/59.47 |
% 250.66/59.47 | CLOSE: (10) is inconsistent.
% 250.66/59.47 |
% 250.66/59.47 End of proof
% 250.66/59.47
% 250.66/59.47 Sub-proof #287 shows that the following formulas are inconsistent:
% 250.66/59.47 ----------------------------------------------------------------
% 250.66/59.47 (1) all_252_23 = e1 & op(e0, e1) = e1
% 250.66/59.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.47 (3) op(e0, e1) = all_20_2
% 250.66/59.47 (4) ~ (all_20_2 = e1)
% 250.66/59.47
% 250.66/59.47 Begin of proof
% 250.66/59.47 |
% 250.66/59.47 | ALPHA: (1) implies:
% 250.66/59.47 | (5) op(e0, e1) = e1
% 250.66/59.47 |
% 250.66/59.47 | GROUND_INST: instantiating (2) with all_20_2, e1, e1, e0, simplifying with
% 250.66/59.47 | (3), (5) gives:
% 250.66/59.47 | (6) all_20_2 = e1
% 250.66/59.47 |
% 250.66/59.47 | REDUCE: (4), (6) imply:
% 250.66/59.47 | (7) $false
% 250.66/59.47 |
% 250.66/59.47 | CLOSE: (7) is inconsistent.
% 250.66/59.47 |
% 250.66/59.47 End of proof
% 250.66/59.47
% 250.66/59.47 Sub-proof #288 shows that the following formulas are inconsistent:
% 250.66/59.47 ----------------------------------------------------------------
% 250.66/59.47 (1) op(e1, e3) = e0
% 250.66/59.47 (2) op(e0, e3) = e1
% 250.66/59.47 (3) ~ (all_10_2 = e4)
% 250.66/59.47 (4) all_252_21 = e1
% 250.66/59.47 (5) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.66/59.47 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.66/59.47 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.47 (6) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.66/59.47 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.66/59.47 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.47 (7) ~ (e2 = e0)
% 250.66/59.47 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.47 (9) op(e2, e3) = all_10_2
% 250.66/59.47 (10) ~ (e3 = e2)
% 250.66/59.47 (11) ~ (e4 = e0)
% 250.66/59.47 (12) ~ (e2 = e1)
% 250.66/59.47 (13) ~ (e4 = e1)
% 250.66/59.47 (14) ~ (e3 = e0)
% 250.66/59.47 (15) ~ (e3 = e1)
% 250.66/59.47 (16) ~ (e4 = e3)
% 250.66/59.47 (17) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.47 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.47 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.47 (18) ~ (e4 = e2)
% 250.66/59.47 (19) all_252_3 = e0
% 250.66/59.47
% 250.66/59.47 Begin of proof
% 250.66/59.47 |
% 250.66/59.47 | BETA: splitting (5) gives:
% 250.66/59.47 |
% 250.66/59.47 | Case 1:
% 250.66/59.47 | |
% 250.66/59.47 | | (20) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.66/59.47 | | e4)
% 250.66/59.47 | |
% 250.66/59.47 | | BETA: splitting (20) gives:
% 250.66/59.47 | |
% 250.66/59.47 | | Case 1:
% 250.66/59.47 | | |
% 250.66/59.47 | | | (21) all_252_1 = e4 & op(e4, e3) = e4
% 250.66/59.47 | | |
% 250.66/59.47 | | | ALPHA: (21) implies:
% 250.66/59.47 | | | (22) all_252_1 = e4
% 250.66/59.47 | | |
% 250.66/59.47 | | | BETA: splitting (6) gives:
% 250.66/59.47 | | |
% 250.66/59.47 | | | Case 1:
% 250.66/59.47 | | | |
% 250.66/59.47 | | | | (23) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3,
% 250.66/59.47 | | | | e3) = e2)
% 250.66/59.47 | | | |
% 250.66/59.47 | | | | REF_CLOSE: (7), (18), (19), (22), (23) are inconsistent by sub-proof
% 250.66/59.47 | | | | #381.
% 250.66/59.47 | | | |
% 250.66/59.47 | | | Case 2:
% 250.66/59.47 | | | |
% 250.66/59.47 | | | | (24) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1,
% 250.66/59.47 | | | | e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.47 | | | |
% 250.66/59.47 | | | | BETA: splitting (24) gives:
% 250.66/59.47 | | | |
% 250.66/59.47 | | | | Case 1:
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | (25) all_252_7 = e2 & op(e2, e3) = e2
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | ALPHA: (25) implies:
% 250.66/59.47 | | | | | (26) all_252_7 = e2
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | BETA: splitting (17) gives:
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | Case 1:
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | (27) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 250.66/59.47 | | | | | | op(e3, e3) = e3)
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | BETA: splitting (27) gives:
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | Case 1:
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | (28) all_252_1 = e3 & op(e4, e3) = e3
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | REF_CLOSE: (16), (22), (28) are inconsistent by sub-proof #946.
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | Case 2:
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | (29) all_252_3 = e3 & op(e3, e3) = e3
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | REF_CLOSE: (14), (19), (29) are inconsistent by sub-proof #380.
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | End of split
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | Case 2:
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | (30) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 250.66/59.47 | | | | | | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | BETA: splitting (30) gives:
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | Case 1:
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | (31) all_252_7 = e3 & op(e2, e3) = e3
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | ALPHA: (31) implies:
% 250.66/59.47 | | | | | | | (32) all_252_7 = e3
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | REF_CLOSE: (10), (26), (32) are inconsistent by sub-proof #939.
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | Case 2:
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | (33) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 250.66/59.47 | | | | | | | op(e0, e3) = e3)
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | BETA: splitting (33) gives:
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | | Case 1:
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | (34) all_252_13 = e3 & op(e1, e3) = e3
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | ALPHA: (34) implies:
% 250.66/59.47 | | | | | | | | (35) all_252_13 = e3
% 250.66/59.47 | | | | | | | | (36) op(e1, e3) = e3
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (12), (14), (15),
% 250.66/59.47 | | | | | | | | (16), (17), (18), (19), (22), (35), (36) are
% 250.66/59.47 | | | | | | | | inconsistent by sub-proof #289.
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | Case 2:
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | (37) all_252_21 = e3 & op(e0, e3) = e3
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | ALPHA: (37) implies:
% 250.66/59.47 | | | | | | | | (38) op(e0, e3) = e3
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | | REF_CLOSE: (2), (8), (15), (38) are inconsistent by sub-proof
% 250.66/59.47 | | | | | | | | #590.
% 250.66/59.47 | | | | | | | |
% 250.66/59.47 | | | | | | | End of split
% 250.66/59.47 | | | | | | |
% 250.66/59.47 | | | | | | End of split
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | End of split
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | Case 2:
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | (39) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.66/59.47 | | | | | op(e0, e3) = e2)
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | BETA: splitting (39) gives:
% 250.66/59.47 | | | | |
% 250.66/59.47 | | | | | Case 1:
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | (40) all_252_13 = e2 & op(e1, e3) = e2
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | ALPHA: (40) implies:
% 250.66/59.47 | | | | | | (41) all_252_13 = e2
% 250.66/59.47 | | | | | | (42) op(e1, e3) = e2
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | GROUND_INST: instantiating (8) with e0, e2, e3, e1, simplifying with
% 250.66/59.47 | | | | | | (1), (42) gives:
% 250.66/59.47 | | | | | | (43) e2 = e0
% 250.66/59.47 | | | | | |
% 250.66/59.47 | | | | | | COMBINE_EQS: (41), (43) imply:
% 250.66/59.47 | | | | | | (44) all_252_13 = e0
% 250.66/59.47 | | | | | |
% 250.66/59.48 | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (12), (14), (15), (16),
% 250.66/59.48 | | | | | | (17), (18), (19), (22), (44) are inconsistent by
% 250.66/59.48 | | | | | | sub-proof #374.
% 250.66/59.48 | | | | | |
% 250.66/59.48 | | | | | Case 2:
% 250.66/59.48 | | | | | |
% 250.66/59.48 | | | | | | (45) all_252_21 = e2 & op(e0, e3) = e2
% 250.66/59.48 | | | | | |
% 250.66/59.48 | | | | | | REF_CLOSE: (4), (12), (45) are inconsistent by sub-proof #375.
% 250.66/59.48 | | | | | |
% 250.66/59.48 | | | | | End of split
% 250.66/59.48 | | | | |
% 250.66/59.48 | | | | End of split
% 250.66/59.48 | | | |
% 250.66/59.48 | | | End of split
% 250.66/59.48 | | |
% 250.66/59.48 | | Case 2:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (46) all_252_3 = e4 & op(e3, e3) = e4
% 250.66/59.48 | | |
% 250.66/59.48 | | | REF_CLOSE: (11), (19), (46) are inconsistent by sub-proof #373.
% 250.66/59.48 | | |
% 250.66/59.48 | | End of split
% 250.66/59.48 | |
% 250.66/59.48 | Case 2:
% 250.66/59.48 | |
% 250.66/59.48 | | (47) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.48 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.48 | |
% 250.66/59.48 | | BETA: splitting (47) gives:
% 250.66/59.48 | |
% 250.66/59.48 | | Case 1:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (48) all_252_7 = e4 & op(e2, e3) = e4
% 250.66/59.48 | | |
% 250.66/59.48 | | | ALPHA: (48) implies:
% 250.66/59.48 | | | (49) op(e2, e3) = e4
% 250.66/59.48 | | |
% 250.66/59.48 | | | REF_CLOSE: (3), (8), (9), (49) are inconsistent by sub-proof #953.
% 250.66/59.48 | | |
% 250.66/59.48 | | Case 2:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (50) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 250.66/59.48 | | | e3) = e4)
% 250.66/59.48 | | |
% 250.66/59.48 | | | BETA: splitting (50) gives:
% 250.66/59.48 | | |
% 250.66/59.48 | | | Case 1:
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | (51) all_252_13 = e4 & op(e1, e3) = e4
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | ALPHA: (51) implies:
% 250.66/59.48 | | | | (52) all_252_13 = e4
% 250.66/59.48 | | | | (53) op(e1, e3) = e4
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | GROUND_INST: instantiating (8) with e0, e4, e3, e1, simplifying with
% 250.66/59.48 | | | | (1), (53) gives:
% 250.66/59.48 | | | | (54) e4 = e0
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | COMBINE_EQS: (52), (54) imply:
% 250.66/59.48 | | | | (55) all_252_13 = e0
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 250.66/59.48 | | | | (15), (16), (17), (18), (19), (55) are inconsistent by
% 250.66/59.48 | | | | sub-proof #365.
% 250.66/59.48 | | | |
% 250.66/59.48 | | | Case 2:
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | (56) all_252_21 = e4 & op(e0, e3) = e4
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | REF_CLOSE: (4), (13), (56) are inconsistent by sub-proof #367.
% 250.66/59.48 | | | |
% 250.66/59.48 | | | End of split
% 250.66/59.48 | | |
% 250.66/59.48 | | End of split
% 250.66/59.48 | |
% 250.66/59.48 | End of split
% 250.66/59.48 |
% 250.66/59.48 End of proof
% 250.66/59.48
% 250.66/59.48 Sub-proof #289 shows that the following formulas are inconsistent:
% 250.66/59.48 ----------------------------------------------------------------
% 250.66/59.48 (1) op(e1, e3) = e0
% 250.66/59.48 (2) op(e0, e3) = e1
% 250.66/59.48 (3) all_252_21 = e1
% 250.66/59.48 (4) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.66/59.48 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.66/59.48 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.48 (5) ~ (e2 = e0)
% 250.66/59.48 (6) op(e1, e3) = e3
% 250.66/59.48 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.48 (8) ~ (e3 = e2)
% 250.66/59.48 (9) ~ (e2 = e1)
% 250.66/59.48 (10) ~ (e3 = e0)
% 250.66/59.48 (11) ~ (e3 = e1)
% 250.66/59.48 (12) all_252_13 = e3
% 250.66/59.48 (13) ~ (e4 = e3)
% 250.66/59.48 (14) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.48 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.48 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.48 (15) ~ (e4 = e2)
% 250.66/59.48 (16) all_252_1 = e4
% 250.66/59.48 (17) all_252_3 = e0
% 250.66/59.48
% 250.66/59.48 Begin of proof
% 250.66/59.48 |
% 250.66/59.48 | BETA: splitting (4) gives:
% 250.66/59.48 |
% 250.66/59.48 | Case 1:
% 250.66/59.48 | |
% 250.66/59.48 | | (18) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 250.66/59.48 | | e2)
% 250.66/59.48 | |
% 250.66/59.48 | | REF_CLOSE: (5), (15), (16), (17), (18) are inconsistent by sub-proof #381.
% 250.66/59.48 | |
% 250.66/59.48 | Case 2:
% 250.66/59.48 | |
% 250.66/59.48 | | (19) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.48 | | e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.48 | |
% 250.66/59.48 | | BETA: splitting (19) gives:
% 250.66/59.48 | |
% 250.66/59.48 | | Case 1:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (20) all_252_7 = e2 & op(e2, e3) = e2
% 250.66/59.48 | | |
% 250.66/59.48 | | | ALPHA: (20) implies:
% 250.66/59.48 | | | (21) all_252_7 = e2
% 250.66/59.48 | | |
% 250.66/59.48 | | | GROUND_INST: instantiating (7) with e0, e3, e3, e1, simplifying with (1),
% 250.66/59.48 | | | (6) gives:
% 250.66/59.48 | | | (22) e3 = e0
% 250.66/59.48 | | |
% 250.66/59.48 | | | COMBINE_EQS: (12), (22) imply:
% 250.66/59.48 | | | (23) all_252_13 = e0
% 250.66/59.48 | | |
% 250.66/59.48 | | | REF_CLOSE: (2), (7), (8), (10), (11), (13), (14), (16), (17), (21), (23)
% 250.66/59.48 | | | are inconsistent by sub-proof #377.
% 250.66/59.48 | | |
% 250.66/59.48 | | Case 2:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (24) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0,
% 250.66/59.48 | | | e3) = e2)
% 250.66/59.48 | | |
% 250.66/59.48 | | | BETA: splitting (24) gives:
% 250.66/59.48 | | |
% 250.66/59.48 | | | Case 1:
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | (25) all_252_13 = e2 & op(e1, e3) = e2
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | ALPHA: (25) implies:
% 250.66/59.48 | | | | (26) all_252_13 = e2
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | COMBINE_EQS: (12), (26) imply:
% 250.66/59.48 | | | | (27) e3 = e2
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | REDUCE: (8), (27) imply:
% 250.66/59.48 | | | | (28) $false
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | CLOSE: (28) is inconsistent.
% 250.66/59.48 | | | |
% 250.66/59.48 | | | Case 2:
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | (29) all_252_21 = e2 & op(e0, e3) = e2
% 250.66/59.48 | | | |
% 250.66/59.48 | | | | REF_CLOSE: (3), (9), (29) are inconsistent by sub-proof #375.
% 250.66/59.48 | | | |
% 250.66/59.48 | | | End of split
% 250.66/59.48 | | |
% 250.66/59.48 | | End of split
% 250.66/59.48 | |
% 250.66/59.48 | End of split
% 250.66/59.48 |
% 250.66/59.48 End of proof
% 250.66/59.48
% 250.66/59.48 Sub-proof #290 shows that the following formulas are inconsistent:
% 250.66/59.48 ----------------------------------------------------------------
% 250.66/59.48 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.66/59.48 all_250_23 = e0
% 250.66/59.48 (2) all_32_2 = all_20_2
% 250.66/59.48 (3) op(e0, e3) = e1
% 250.66/59.48 (4) ~ (all_4_2 = e4)
% 250.66/59.48 (5) ~ (all_10_2 = e4)
% 250.66/59.48 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.48 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.66/59.48 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.48 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.66/59.48 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.66/59.48 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.66/59.48 (8) ~ (all_244_24 = all_34_2)
% 250.66/59.48 (9) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.66/59.48 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.66/59.48 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.66/59.48 (10) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.66/59.48 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 250.66/59.48 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.66/59.48 (11) all_252_21 = e1
% 250.66/59.48 (12) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.48 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.66/59.48 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.66/59.48 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.48 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.48 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.48 (14) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.66/59.48 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.48 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.48 (15) op(e4, e0) = all_30_2
% 250.66/59.48 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.48 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.66/59.48 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.66/59.48 (17) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.66/59.48 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.66/59.48 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.48 (18) all_174_2 = all_40_2
% 250.66/59.48 (19) all_114_2 = e0
% 250.66/59.48 (20) op(e0, all_36_2) = e3
% 250.66/59.48 (21) ~ (e2 = e0)
% 250.66/59.48 (22) op(all_38_2, all_4_2) = e1
% 250.66/59.48 (23) ~ (all_34_2 = e0)
% 250.66/59.48 (24) ~ (e1 = e0)
% 250.66/59.48 (25) ~ (all_22_2 = e3)
% 250.66/59.48 (26) all_252_13 = e0
% 250.66/59.48 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.48 (28) op(e2, e3) = all_10_2
% 250.66/59.48 (29) ~ (e3 = e2)
% 250.66/59.48 (30) op(e0, e0) = all_244_24
% 250.66/59.48 (31) ~ (e4 = e0)
% 250.66/59.48 (32) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.66/59.48 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.66/59.48 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.66/59.48 (33) op(e2, e2) = all_244_8
% 250.66/59.48 (34) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.66/59.48 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.66/59.48 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.66/59.48 (35) all_146_2 = e0
% 250.66/59.48 (36) op(e2, e1) = all_38_2
% 250.66/59.48 (37) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.66/59.48 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.66/59.48 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.48 (38) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.66/59.48 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.66/59.48 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.66/59.48 (39) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.66/59.48 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.66/59.48 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.48 (40) op(e1, e0) = all_34_2
% 250.66/59.48 (41) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.66/59.48 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.66/59.48 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.66/59.48 (42) op(e4, e2) = all_6_2
% 250.66/59.48 (43) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.66/59.48 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.48 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.48 (44) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 250.66/59.48 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 250.66/59.48 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.66/59.48 (45) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.66/59.48 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.66/59.48 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.48 (46) ~ (e2 = e1)
% 250.66/59.48 (47) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.66/59.48 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.48 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.48 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.66/59.48 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.66/59.48 op(e0, e1) = e0)))
% 250.66/59.48 (48) op(e0, e2) = all_28_2
% 250.66/59.48 (49) ~ (e4 = e1)
% 250.66/59.48 (50) ~ (all_28_2 = e1)
% 250.66/59.48 (51) ~ (all_6_2 = e1)
% 250.66/59.48 (52) ~ (all_20_2 = e1)
% 250.66/59.48 (53) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.66/59.48 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.66/59.48 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.66/59.48 (54) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.66/59.48 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.66/59.48 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.48 (55) op(all_34_2, e0) = e1
% 250.66/59.48 (56) op(e1, e4) = all_16_2
% 250.66/59.48 (57) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.66/59.48 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.66/59.48 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.48 (58) ~ (e3 = e0)
% 250.66/59.48 (59) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.66/59.48 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.66/59.48 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.66/59.48 (60) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.66/59.48 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.66/59.48 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.66/59.48 (61) ~ (all_40_2 = all_10_2)
% 250.66/59.48 (62) op(all_20_2, e1) = e0
% 250.66/59.48 (63) all_252_2 = e0
% 250.66/59.48 (64) ~ (e3 = e1)
% 250.66/59.48 (65) op(e3, e1) = all_36_2
% 250.66/59.48 (66) ~ (all_16_2 = e2)
% 250.66/59.48 (67) ~ (all_8_2 = e1)
% 250.66/59.48 (68) op(all_40_2, e0) = e2
% 250.66/59.48 (69) ~ (all_40_2 = all_34_2)
% 250.66/59.48 (70) ~ (all_48_2 = all_34_2)
% 250.66/59.48 (71) ~ (all_8_2 = e0)
% 250.66/59.48 (72) ~ (all_114_2 = e0) | ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 &
% 250.66/59.48 op(e0, all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1)) | ( ~
% 250.66/59.48 (all_114_1 = e2) & op(e3, e0) = all_114_1 & $i(all_114_1))
% 250.66/59.48 (73) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.66/59.48 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.66/59.48 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.66/59.48 (74) op(e0, e3) = all_22_2
% 250.66/59.48 (75) op(all_34_2, all_20_2) = e0
% 250.66/59.48 (76) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 250.66/59.48 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 250.66/59.48 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.66/59.48 (77) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.48 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.66/59.48 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.66/59.48 (78) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.66/59.48 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.66/59.48 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.66/59.48 (79) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.66/59.48 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.66/59.48 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.48 (80) ~ (all_36_2 = e0)
% 250.66/59.48 (81) op(e4, e4) = all_244_0
% 250.66/59.48 (82) all_230_2 = all_20_2
% 250.66/59.48 (83) ~ (e4 = e3)
% 250.66/59.48 (84) op(e1, e1) = all_244_15
% 250.66/59.48 (85) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.48 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.66/59.48 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.66/59.48 (86) ~ (all_34_2 = all_30_2)
% 250.66/59.48 (87) op(e0, e1) = all_20_2
% 250.66/59.48 (88) ~ (all_244_15 = all_20_2)
% 250.66/59.48 (89) op(e3, e0) = all_48_2
% 250.66/59.48 (90) op(e1, e2) = all_4_2
% 250.66/59.48 (91) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.48 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.48 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.48 (92) ~ (all_48_2 = e0)
% 250.66/59.48 (93) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.66/59.48 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.66/59.48 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.66/59.48 (94) ~ (e4 = e2)
% 250.66/59.48 (95) op(e3, e2) = all_8_2
% 250.66/59.48 (96) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.66/59.48 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.66/59.48 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.66/59.48 (97) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.66/59.48 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.66/59.48 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.66/59.48 (98) ~ (all_20_2 = e4)
% 250.66/59.48 (99) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.66/59.48 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.66/59.48 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.66/59.48 (100) ~ (all_244_3 = e0)
% 250.66/59.48 (101) op(e2, e0) = all_40_2
% 250.66/59.48 (102) ~ (all_20_2 = e3)
% 250.66/59.48 (103) ~ (all_16_2 = e3)
% 250.66/59.48 (104) ~ (all_244_8 = all_28_2)
% 250.66/59.48 (105) ~ (all_10_2 = e0)
% 250.66/59.48 (106) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.48 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.66/59.48 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.66/59.48 (107) ~ (all_244_0 = e3)
% 250.66/59.48 (108) op(e3, e3) = all_244_3
% 250.66/59.48 (109) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.66/59.48 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.66/59.48 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.66/59.48 (110) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 250.66/59.48 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 250.66/59.48 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 250.66/59.48 (111) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.66/59.48 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.66/59.48 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.66/59.48 (112) ~ (all_4_2 = e0)
% 250.66/59.48 (113) ~ (all_146_2 = e0) | ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 &
% 250.66/59.48 op(e0, all_146_1) = all_146_0 & $i(all_146_0) & $i(all_146_1)) | ( ~
% 250.66/59.48 (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1))
% 250.66/59.48 (114) all_250_23 = all_20_2
% 250.66/59.48 (115) all_252_20 = e3
% 250.66/59.48
% 250.66/59.48 Begin of proof
% 250.66/59.48 |
% 250.66/59.48 | BETA: splitting (113) gives:
% 250.66/59.48 |
% 250.66/59.48 | Case 1:
% 250.66/59.48 | |
% 250.66/59.48 | | (116) ~ (all_146_2 = e0)
% 250.66/59.48 | |
% 250.66/59.48 | | REDUCE: (35), (116) imply:
% 250.66/59.48 | | (117) $false
% 250.66/59.48 | |
% 250.66/59.48 | | CLOSE: (117) is inconsistent.
% 250.66/59.48 | |
% 250.66/59.48 | Case 2:
% 250.66/59.48 | |
% 250.66/59.48 | | (118) ( ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 & op(e0, all_146_1) =
% 250.66/59.48 | | all_146_0 & $i(all_146_0) & $i(all_146_1)) | ( ~ (all_146_1 = e2)
% 250.66/59.48 | | & op(e4, e0) = all_146_1 & $i(all_146_1))
% 250.66/59.48 | |
% 250.66/59.48 | | BETA: splitting (118) gives:
% 250.66/59.48 | |
% 250.66/59.48 | | Case 1:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (119) ~ (all_146_0 = e1) & op(e4, e0) = all_146_1 & op(e0, all_146_1)
% 250.66/59.48 | | | = all_146_0 & $i(all_146_0) & $i(all_146_1)
% 250.66/59.48 | | |
% 250.66/59.48 | | | ALPHA: (119) implies:
% 250.66/59.48 | | | (120) op(e4, e0) = all_146_1
% 250.66/59.48 | | |
% 250.66/59.48 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.66/59.48 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.66/59.48 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 250.66/59.48 | | | (33), (34), (36), (37), (38), (39), (40), (41), (42), (43),
% 250.66/59.48 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 250.66/59.48 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 250.66/59.48 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 250.66/59.48 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 250.66/59.48 | | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 250.66/59.48 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 250.66/59.48 | | | (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 250.66/59.48 | | | (114), (115), (120) are inconsistent by sub-proof #291.
% 250.66/59.48 | | |
% 250.66/59.48 | | Case 2:
% 250.66/59.48 | | |
% 250.66/59.48 | | | (121) ~ (all_146_1 = e2) & op(e4, e0) = all_146_1 & $i(all_146_1)
% 250.66/59.48 | | |
% 250.66/59.48 | | | ALPHA: (121) implies:
% 250.66/59.48 | | | (122) op(e4, e0) = all_146_1
% 250.66/59.48 | | |
% 250.66/59.48 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.66/59.48 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.66/59.48 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 250.66/59.48 | | | (33), (34), (36), (37), (38), (39), (40), (41), (42), (43),
% 250.66/59.48 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 250.66/59.48 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 250.66/59.48 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 250.66/59.48 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 250.66/59.48 | | | (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 250.66/59.48 | | | (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 250.66/59.48 | | | (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 250.66/59.48 | | | (114), (115), (122) are inconsistent by sub-proof #291.
% 250.66/59.48 | | |
% 250.66/59.48 | | End of split
% 250.66/59.48 | |
% 250.66/59.48 | End of split
% 250.66/59.48 |
% 250.66/59.48 End of proof
% 250.66/59.48
% 250.66/59.48 Sub-proof #291 shows that the following formulas are inconsistent:
% 250.66/59.48 ----------------------------------------------------------------
% 250.66/59.48 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.66/59.48 all_250_23 = e0
% 250.66/59.48 (2) all_32_2 = all_20_2
% 250.66/59.48 (3) op(e0, e3) = e1
% 250.66/59.48 (4) ~ (all_4_2 = e4)
% 250.66/59.48 (5) ~ (all_10_2 = e4)
% 250.66/59.48 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.48 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.66/59.48 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.48 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.66/59.48 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.66/59.48 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.66/59.48 (8) ~ (all_244_24 = all_34_2)
% 250.66/59.48 (9) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.66/59.48 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.66/59.48 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.66/59.48 (10) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.66/59.48 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 250.66/59.48 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.66/59.48 (11) all_252_21 = e1
% 250.66/59.48 (12) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.48 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.66/59.48 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.66/59.48 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.48 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.48 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.48 (14) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.66/59.48 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.48 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.48 (15) op(e4, e0) = all_30_2
% 250.66/59.48 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.48 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.66/59.48 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.66/59.48 (17) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.66/59.48 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.66/59.48 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.48 (18) all_174_2 = all_40_2
% 250.66/59.48 (19) all_114_2 = e0
% 250.66/59.48 (20) op(e0, all_36_2) = e3
% 250.66/59.48 (21) ~ (e2 = e0)
% 250.66/59.49 (22) op(all_38_2, all_4_2) = e1
% 250.66/59.49 (23) ~ (all_34_2 = e0)
% 250.66/59.49 (24) ~ (e1 = e0)
% 250.66/59.49 (25) ~ (all_22_2 = e3)
% 250.66/59.49 (26) all_252_13 = e0
% 250.66/59.49 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.49 (28) op(e2, e3) = all_10_2
% 250.66/59.49 (29) ~ (e3 = e2)
% 250.66/59.49 (30) op(e0, e0) = all_244_24
% 250.66/59.49 (31) ~ (e4 = e0)
% 250.66/59.49 (32) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.66/59.49 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.66/59.49 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.66/59.49 (33) op(e2, e2) = all_244_8
% 250.66/59.49 (34) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.66/59.49 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.66/59.49 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.66/59.49 (35) op(e2, e1) = all_38_2
% 250.66/59.49 (36) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.66/59.49 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.66/59.49 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.49 (37) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.66/59.49 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.66/59.49 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.66/59.49 (38) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.66/59.49 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.66/59.49 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.49 (39) op(e1, e0) = all_34_2
% 250.66/59.49 (40) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.66/59.49 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.66/59.49 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.66/59.49 (41) op(e4, e2) = all_6_2
% 250.66/59.49 (42) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.66/59.49 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.49 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.49 (43) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 250.66/59.49 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 250.66/59.49 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.66/59.49 (44) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.66/59.49 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.66/59.49 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.49 (45) ~ (e2 = e1)
% 250.66/59.49 (46) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.66/59.49 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.49 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.49 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.66/59.49 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.66/59.49 op(e0, e1) = e0)))
% 250.66/59.49 (47) op(e0, e2) = all_28_2
% 250.66/59.49 (48) ~ (e4 = e1)
% 250.66/59.49 (49) ~ (all_28_2 = e1)
% 250.66/59.49 (50) ~ (all_6_2 = e1)
% 250.66/59.49 (51) ~ (all_20_2 = e1)
% 250.66/59.49 (52) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.66/59.49 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.66/59.49 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.66/59.49 (53) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.66/59.49 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.66/59.49 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.49 (54) op(all_34_2, e0) = e1
% 250.66/59.49 (55) op(e1, e4) = all_16_2
% 250.66/59.49 (56) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.66/59.49 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.66/59.49 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.49 (57) ~ (e3 = e0)
% 250.66/59.49 (58) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.66/59.49 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.66/59.49 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.66/59.49 (59) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 250.66/59.49 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 250.66/59.49 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.66/59.49 (60) ~ (all_40_2 = all_10_2)
% 250.66/59.49 (61) op(all_20_2, e1) = e0
% 250.66/59.49 (62) all_252_2 = e0
% 250.66/59.49 (63) ~ (e3 = e1)
% 250.66/59.49 (64) op(e3, e1) = all_36_2
% 250.66/59.49 (65) ~ (all_16_2 = e2)
% 250.66/59.49 (66) ~ (all_8_2 = e1)
% 250.66/59.49 (67) op(all_40_2, e0) = e2
% 250.66/59.49 (68) ~ (all_40_2 = all_34_2)
% 250.66/59.49 (69) ~ (all_48_2 = all_34_2)
% 250.66/59.49 (70) ~ (all_8_2 = e0)
% 250.66/59.49 (71) ~ (all_114_2 = e0) | ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 &
% 250.66/59.49 op(e0, all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1)) | ( ~
% 250.66/59.49 (all_114_1 = e2) & op(e3, e0) = all_114_1 & $i(all_114_1))
% 250.66/59.49 (72) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.66/59.49 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.66/59.49 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.66/59.49 (73) op(e0, e3) = all_22_2
% 250.66/59.49 (74) op(all_34_2, all_20_2) = e0
% 250.66/59.49 (75) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 250.66/59.49 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 250.66/59.49 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.66/59.49 (76) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.49 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.66/59.49 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.66/59.49 (77) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.66/59.49 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.66/59.49 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.66/59.49 (78) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.66/59.49 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.66/59.49 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.49 (79) ~ (all_36_2 = e0)
% 250.66/59.49 (80) op(e4, e4) = all_244_0
% 250.66/59.49 (81) all_230_2 = all_20_2
% 250.66/59.49 (82) ~ (e4 = e3)
% 250.66/59.49 (83) op(e1, e1) = all_244_15
% 250.66/59.49 (84) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.49 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.66/59.49 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.66/59.49 (85) ~ (all_34_2 = all_30_2)
% 250.66/59.49 (86) op(e0, e1) = all_20_2
% 250.66/59.49 (87) ~ (all_244_15 = all_20_2)
% 250.66/59.49 (88) op(e3, e0) = all_48_2
% 250.66/59.49 (89) op(e1, e2) = all_4_2
% 250.66/59.49 (90) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.49 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.49 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.49 (91) ~ (all_48_2 = e0)
% 250.66/59.49 (92) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.66/59.49 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.66/59.49 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.66/59.49 (93) ~ (e4 = e2)
% 250.66/59.49 (94) op(e3, e2) = all_8_2
% 250.66/59.49 (95) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.66/59.49 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.66/59.49 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.66/59.49 (96) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.66/59.49 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.66/59.49 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.66/59.49 (97) ~ (all_20_2 = e4)
% 250.66/59.49 (98) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.66/59.49 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.66/59.49 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.66/59.49 (99) ~ (all_244_3 = e0)
% 250.66/59.49 (100) op(e2, e0) = all_40_2
% 250.66/59.49 (101) ~ (all_20_2 = e3)
% 250.66/59.49 (102) ~ (all_16_2 = e3)
% 250.66/59.49 (103) ~ (all_244_8 = all_28_2)
% 250.66/59.49 (104) ~ (all_10_2 = e0)
% 250.66/59.49 (105) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.49 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.66/59.49 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.66/59.49 (106) ~ (all_244_0 = e3)
% 250.66/59.49 (107) op(e3, e3) = all_244_3
% 250.66/59.49 (108) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.66/59.49 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.66/59.49 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.66/59.49 (109) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 250.66/59.49 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 250.66/59.49 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 250.66/59.49 (110) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.66/59.49 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.66/59.49 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.66/59.49 (111) ~ (all_4_2 = e0)
% 250.66/59.49 (112) op(e4, e0) = all_146_1
% 250.66/59.49 (113) all_250_23 = all_20_2
% 250.66/59.49 (114) all_252_20 = e3
% 250.66/59.49
% 250.66/59.49 Begin of proof
% 250.66/59.49 |
% 250.66/59.49 | GROUND_INST: instantiating (27) with all_30_2, all_146_1, e0, e4, simplifying
% 250.66/59.49 | with (15), (112) gives:
% 250.66/59.49 | (115) all_146_1 = all_30_2
% 250.66/59.49 |
% 250.66/59.49 | BETA: splitting (43) gives:
% 250.66/59.49 |
% 250.66/59.49 | Case 1:
% 250.66/59.49 | |
% 250.66/59.49 | | (116) ~ (all_34_2 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | BETA: splitting (58) gives:
% 250.66/59.49 | |
% 250.66/59.49 | | Case 1:
% 250.66/59.49 | | |
% 250.66/59.49 | | | (117) ~ (all_32_2 = e2)
% 250.66/59.49 | | |
% 250.66/59.49 | | | REDUCE: (2), (117) imply:
% 250.66/59.49 | | | (118) ~ (all_20_2 = e2)
% 250.66/59.49 | | |
% 250.66/59.49 | | | REF_CLOSE: (1), (27), (51), (54), (74), (97), (101), (113), (118) are
% 250.66/59.49 | | | inconsistent by sub-proof #780.
% 250.66/59.49 | | |
% 250.66/59.49 | | Case 2:
% 250.66/59.49 | | |
% 250.66/59.49 | | | (119) all_32_2 = e2
% 250.66/59.49 | | |
% 250.66/59.49 | | | COMBINE_EQS: (2), (119) imply:
% 250.66/59.49 | | | (120) all_20_2 = e2
% 250.66/59.49 | | |
% 250.66/59.49 | | | COMBINE_EQS: (81), (120) imply:
% 250.66/59.49 | | | (121) all_230_2 = e2
% 250.66/59.49 | | |
% 250.66/59.49 | | | REDUCE: (87), (120) imply:
% 250.66/59.49 | | | (122) ~ (all_244_15 = e2)
% 250.66/59.49 | | |
% 250.66/59.49 | | | REDUCE: (61), (120) imply:
% 250.66/59.49 | | | (123) op(e2, e1) = e0
% 250.66/59.49 | | |
% 250.66/59.49 | | | BETA: splitting (59) gives:
% 250.66/59.49 | | |
% 250.66/59.49 | | | Case 1:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (124) ~ (all_230_2 = e2)
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | REDUCE: (121), (124) imply:
% 250.66/59.49 | | | | (125) $false
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | CLOSE: (125) is inconsistent.
% 250.66/59.49 | | | |
% 250.66/59.49 | | | Case 2:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (126) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1,
% 250.66/59.49 | | | | e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) | ( ~
% 250.66/59.49 | | | | (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | BETA: splitting (126) gives:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | Case 1:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (127) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1,
% 250.66/59.49 | | | | | e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | ALPHA: (127) implies:
% 250.66/59.49 | | | | | (128) op(e1, e2) = all_230_1
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | REF_CLOSE: (21), (22), (26), (27), (33), (35), (36), (39), (41), (45),
% 250.66/59.49 | | | | | (47), (49), (50), (55), (65), (66), (83), (89), (94),
% 250.66/59.49 | | | | | (103), (105), (116), (122), (123), (128) are inconsistent
% 250.66/59.49 | | | | | by sub-proof #417.
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | Case 2:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (129) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1)
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | ALPHA: (129) implies:
% 250.66/59.49 | | | | | (130) op(e1, e2) = all_230_1
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | REF_CLOSE: (21), (22), (26), (27), (33), (35), (36), (39), (41), (45),
% 250.66/59.49 | | | | | (47), (49), (50), (55), (65), (66), (83), (89), (94),
% 250.66/59.49 | | | | | (103), (105), (116), (122), (123), (130) are inconsistent
% 250.66/59.49 | | | | | by sub-proof #417.
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | End of split
% 250.66/59.49 | | | |
% 250.66/59.49 | | | End of split
% 250.66/59.49 | | |
% 250.66/59.49 | | End of split
% 250.66/59.49 | |
% 250.66/59.49 | Case 2:
% 250.66/59.49 | |
% 250.66/59.49 | | (131) all_34_2 = e2
% 250.66/59.49 | | (132) ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0, e2) =
% 250.66/59.49 | | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e3) &
% 250.66/59.49 | | op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.66/59.49 | |
% 250.66/59.49 | | REDUCE: (8), (131) imply:
% 250.66/59.49 | | (133) ~ (all_244_24 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | REDUCE: (69), (131) imply:
% 250.66/59.49 | | (134) ~ (all_48_2 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | REDUCE: (68), (131) imply:
% 250.66/59.49 | | (135) ~ (all_40_2 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | REDUCE: (85), (131) imply:
% 250.66/59.49 | | (136) ~ (all_30_2 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | SIMP: (136) implies:
% 250.66/59.49 | | (137) ~ (all_30_2 = e2)
% 250.66/59.49 | |
% 250.66/59.49 | | REDUCE: (54), (131) imply:
% 250.66/59.49 | | (138) op(e2, e0) = e1
% 250.66/59.49 | |
% 250.66/59.49 | | BETA: splitting (38) gives:
% 250.66/59.49 | |
% 250.66/59.49 | | Case 1:
% 250.66/59.49 | | |
% 250.66/59.49 | | | (139) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3,
% 250.66/59.49 | | | e0) = e2)
% 250.66/59.49 | | |
% 250.66/59.49 | | | BETA: splitting (139) gives:
% 250.66/59.49 | | |
% 250.66/59.49 | | | Case 1:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (140) all_252_16 = e2 & op(e4, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | ALPHA: (140) implies:
% 250.66/59.49 | | | | (141) op(e4, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | REF_CLOSE: (15), (27), (137), (141) are inconsistent by sub-proof #830.
% 250.66/59.49 | | | |
% 250.66/59.49 | | | Case 2:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (142) all_252_17 = e2 & op(e3, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | ALPHA: (142) implies:
% 250.66/59.49 | | | | (143) op(e3, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | BETA: splitting (71) gives:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | Case 1:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (144) ~ (all_114_2 = e0)
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | REDUCE: (19), (144) imply:
% 250.66/59.49 | | | | | (145) $false
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | CLOSE: (145) is inconsistent.
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | Case 2:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (146) ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0,
% 250.66/59.49 | | | | | all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1)) |
% 250.66/59.49 | | | | | ( ~ (all_114_1 = e2) & op(e3, e0) = all_114_1 &
% 250.66/59.49 | | | | | $i(all_114_1))
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | BETA: splitting (146) gives:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | Case 1:
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | (147) ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0,
% 250.66/59.49 | | | | | | all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1)
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | ALPHA: (147) implies:
% 250.66/59.49 | | | | | | (148) op(e3, e0) = all_114_1
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | REF_CLOSE: (27), (88), (134), (143), (148) are inconsistent by
% 250.66/59.49 | | | | | | sub-proof #416.
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | Case 2:
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | (149) ~ (all_114_1 = e2) & op(e3, e0) = all_114_1 &
% 250.66/59.49 | | | | | | $i(all_114_1)
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | ALPHA: (149) implies:
% 250.66/59.49 | | | | | | (150) op(e3, e0) = all_114_1
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | REF_CLOSE: (27), (88), (134), (143), (150) are inconsistent by
% 250.66/59.49 | | | | | | sub-proof #416.
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | End of split
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | End of split
% 250.66/59.49 | | | |
% 250.66/59.49 | | | End of split
% 250.66/59.49 | | |
% 250.66/59.49 | | Case 2:
% 250.66/59.49 | | |
% 250.66/59.49 | | | (151) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.66/59.49 | | | e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.49 | | |
% 250.66/59.49 | | | BETA: splitting (151) gives:
% 250.66/59.49 | | |
% 250.66/59.49 | | | Case 1:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (152) all_252_18 = e2 & op(e2, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | ALPHA: (152) implies:
% 250.66/59.49 | | | | (153) op(e2, e0) = e2
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | REF_CLOSE: (27), (45), (100), (138), (153) are inconsistent by sub-proof
% 250.66/59.49 | | | | #415.
% 250.66/59.49 | | | |
% 250.66/59.49 | | | Case 2:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | (154) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0,
% 250.66/59.49 | | | | e0) = e2)
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | BETA: splitting (154) gives:
% 250.66/59.49 | | | |
% 250.66/59.49 | | | | Case 1:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (155) all_252_19 = e2 & op(e1, e0) = e2
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | ALPHA: (155) implies:
% 250.66/59.49 | | | | | (156) all_252_19 = e2
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | BETA: splitting (71) gives:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | Case 1:
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | (157) ~ (all_114_2 = e0)
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | REDUCE: (19), (157) imply:
% 250.66/59.49 | | | | | | (158) $false
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | CLOSE: (158) is inconsistent.
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | Case 2:
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | (159) ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0,
% 250.66/59.49 | | | | | | all_114_1) = all_114_0 & $i(all_114_0) & $i(all_114_1))
% 250.66/59.49 | | | | | | | ( ~ (all_114_1 = e2) & op(e3, e0) = all_114_1 &
% 250.66/59.49 | | | | | | $i(all_114_1))
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | BETA: splitting (132) gives:
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | | Case 1:
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | (160) ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 & op(e0,
% 250.66/59.49 | | | | | | | e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | ALPHA: (160) implies:
% 250.66/59.49 | | | | | | | (161) op(e0, e2) = all_34_1
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 250.66/59.49 | | | | | | | (14), (16), (17), (18), (20), (21), (24), (25), (26),
% 250.66/59.49 | | | | | | | (27), (28), (29), (30), (31), (32), (34), (36), (37),
% 250.66/59.49 | | | | | | | (40), (41), (42), (44), (46), (47), (48), (49), (50),
% 250.66/59.49 | | | | | | | (52), (53), (55), (56), (57), (60), (62), (63), (64),
% 250.66/59.49 | | | | | | | (66), (67), (70), (72), (73), (75), (76), (77), (78),
% 250.66/59.49 | | | | | | | (79), (80), (82), (83), (84), (86), (87), (88), (89),
% 250.66/59.49 | | | | | | | (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 250.66/59.49 | | | | | | | (99), (100), (102), (104), (106), (107), (108), (109),
% 250.66/59.49 | | | | | | | (110), (111), (114), (133), (135), (138), (156), (159),
% 250.66/59.49 | | | | | | | (161) are inconsistent by sub-proof #292.
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | Case 2:
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | (162) ~ (all_34_1 = e3) & op(e0, e2) = all_34_1 & $i(all_34_1)
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | ALPHA: (162) implies:
% 250.66/59.49 | | | | | | | (163) op(e0, e2) = all_34_1
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 250.66/59.49 | | | | | | | (14), (16), (17), (18), (20), (21), (24), (25), (26),
% 250.66/59.49 | | | | | | | (27), (28), (29), (30), (31), (32), (34), (36), (37),
% 250.66/59.49 | | | | | | | (40), (41), (42), (44), (46), (47), (48), (49), (50),
% 250.66/59.49 | | | | | | | (52), (53), (55), (56), (57), (60), (62), (63), (64),
% 250.66/59.49 | | | | | | | (66), (67), (70), (72), (73), (75), (76), (77), (78),
% 250.66/59.49 | | | | | | | (79), (80), (82), (83), (84), (86), (87), (88), (89),
% 250.66/59.49 | | | | | | | (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 250.66/59.49 | | | | | | | (99), (100), (102), (104), (106), (107), (108), (109),
% 250.66/59.49 | | | | | | | (110), (111), (114), (133), (135), (138), (156), (159),
% 250.66/59.49 | | | | | | | (163) are inconsistent by sub-proof #292.
% 250.66/59.49 | | | | | | |
% 250.66/59.49 | | | | | | End of split
% 250.66/59.49 | | | | | |
% 250.66/59.49 | | | | | End of split
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | Case 2:
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | (164) all_252_24 = e2 & op(e0, e0) = e2
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | ALPHA: (164) implies:
% 250.66/59.49 | | | | | (165) op(e0, e0) = e2
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | | REF_CLOSE: (27), (30), (133), (165) are inconsistent by sub-proof
% 250.66/59.49 | | | | | #978.
% 250.66/59.49 | | | | |
% 250.66/59.49 | | | | End of split
% 250.66/59.49 | | | |
% 250.66/59.49 | | | End of split
% 250.66/59.49 | | |
% 250.66/59.49 | | End of split
% 250.66/59.49 | |
% 250.66/59.49 | End of split
% 250.66/59.49 |
% 250.66/59.49 End of proof
% 250.66/59.49
% 250.66/59.49 Sub-proof #292 shows that the following formulas are inconsistent:
% 250.66/59.49 ----------------------------------------------------------------
% 250.66/59.49 (1) op(e0, e3) = e1
% 250.66/59.49 (2) ~ (all_4_2 = e4)
% 250.66/59.49 (3) ~ (all_10_2 = e4)
% 250.66/59.49 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.49 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.66/59.49 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.49 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.66/59.49 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.66/59.49 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.66/59.49 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.66/59.49 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.66/59.49 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.66/59.49 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.66/59.49 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.49 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.66/59.49 (8) all_252_21 = e1
% 250.66/59.49 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.49 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.66/59.49 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.66/59.49 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.49 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.49 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.49 (11) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.66/59.49 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.49 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.49 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.49 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.66/59.49 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.66/59.49 (13) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.66/59.49 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.66/59.49 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.49 (14) all_174_2 = all_40_2
% 250.66/59.49 (15) op(e0, all_36_2) = e3
% 250.66/59.49 (16) ~ (e2 = e0)
% 250.66/59.49 (17) all_252_19 = e2
% 250.66/59.49 (18) ~ (e1 = e0)
% 250.66/59.49 (19) ~ (all_22_2 = e3)
% 250.66/59.49 (20) all_252_13 = e0
% 250.66/59.49 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.49 (22) op(e2, e3) = all_10_2
% 250.66/59.49 (23) ~ (e3 = e2)
% 250.66/59.49 (24) op(e0, e0) = all_244_24
% 250.66/59.49 (25) ~ (e4 = e0)
% 250.66/59.49 (26) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.66/59.49 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.66/59.49 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.66/59.50 (27) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.66/59.50 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.66/59.50 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.66/59.50 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.66/59.50 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.66/59.50 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.50 (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.66/59.50 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.66/59.50 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.66/59.50 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.66/59.50 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.66/59.50 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.66/59.50 (31) op(e4, e2) = all_6_2
% 250.66/59.50 (32) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.66/59.50 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.50 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.50 (33) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.66/59.50 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.66/59.50 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.50 (34) op(e2, e0) = e1
% 250.66/59.50 (35) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.66/59.50 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.50 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.50 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.66/59.50 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.66/59.50 op(e0, e1) = e0)))
% 250.66/59.50 (36) op(e0, e2) = all_28_2
% 250.66/59.50 (37) ~ (e4 = e1)
% 250.66/59.50 (38) ~ (all_28_2 = e1)
% 250.66/59.50 (39) ~ (all_6_2 = e1)
% 250.66/59.50 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.66/59.50 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.66/59.50 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.66/59.50 (41) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.66/59.50 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.66/59.50 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.50 (42) op(e1, e4) = all_16_2
% 250.66/59.50 (43) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.66/59.50 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.66/59.50 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.50 (44) ~ (e3 = e0)
% 250.66/59.50 (45) ~ (all_40_2 = all_10_2)
% 250.66/59.50 (46) all_252_2 = e0
% 250.66/59.50 (47) ~ (e3 = e1)
% 250.66/59.50 (48) op(e3, e1) = all_36_2
% 250.66/59.50 (49) ~ (all_8_2 = e1)
% 250.66/59.50 (50) op(all_40_2, e0) = e2
% 250.66/59.50 (51) ~ (all_8_2 = e0)
% 250.66/59.50 (52) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.66/59.50 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.66/59.50 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.66/59.50 (53) op(e0, e2) = all_34_1
% 250.66/59.50 (54) op(e0, e3) = all_22_2
% 250.66/59.50 (55) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 250.66/59.50 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 250.66/59.50 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.66/59.50 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.50 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.66/59.50 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.66/59.50 (57) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.66/59.50 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.66/59.50 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.66/59.50 (58) ~ (all_40_2 = e2)
% 250.66/59.50 (59) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.66/59.50 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.66/59.50 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.50 (60) ~ (all_36_2 = e0)
% 250.66/59.50 (61) op(e4, e4) = all_244_0
% 250.66/59.50 (62) ~ (e4 = e3)
% 250.66/59.50 (63) op(e1, e1) = all_244_15
% 250.66/59.50 (64) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.50 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.66/59.50 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.66/59.50 (65) op(e0, e1) = all_20_2
% 250.66/59.50 (66) ~ (all_244_15 = all_20_2)
% 250.66/59.50 (67) op(e3, e0) = all_48_2
% 250.66/59.50 (68) ~ (all_244_24 = e2)
% 250.66/59.50 (69) op(e1, e2) = all_4_2
% 250.66/59.50 (70) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.50 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.50 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.50 (71) ~ (all_48_2 = e0)
% 250.66/59.50 (72) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.66/59.50 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.66/59.50 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.66/59.50 (73) ( ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0, all_114_1) =
% 250.66/59.50 all_114_0 & $i(all_114_0) & $i(all_114_1)) | ( ~ (all_114_1 = e2) &
% 250.66/59.50 op(e3, e0) = all_114_1 & $i(all_114_1))
% 250.66/59.50 (74) ~ (e4 = e2)
% 250.66/59.50 (75) op(e3, e2) = all_8_2
% 250.66/59.50 (76) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.66/59.50 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.66/59.50 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.66/59.50 (77) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.66/59.50 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.66/59.50 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.66/59.50 (78) ~ (all_20_2 = e4)
% 250.66/59.50 (79) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.66/59.50 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.66/59.50 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.66/59.50 (80) ~ (all_244_3 = e0)
% 250.66/59.50 (81) op(e2, e0) = all_40_2
% 250.66/59.50 (82) ~ (all_16_2 = e3)
% 250.66/59.50 (83) ~ (all_10_2 = e0)
% 250.66/59.50 (84) ~ (all_244_0 = e3)
% 250.66/59.50 (85) op(e3, e3) = all_244_3
% 250.66/59.50 (86) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.66/59.50 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.66/59.50 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.66/59.50 (87) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 250.66/59.50 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 250.66/59.50 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 250.66/59.50 (88) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.66/59.50 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.66/59.50 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.66/59.50 (89) ~ (all_4_2 = e0)
% 250.66/59.50 (90) all_252_20 = e3
% 250.66/59.50
% 250.66/59.50 Begin of proof
% 250.66/59.50 |
% 250.66/59.50 | BETA: splitting (73) gives:
% 250.66/59.50 |
% 250.66/59.50 | Case 1:
% 250.66/59.50 | |
% 250.66/59.50 | | (91) ~ (all_114_0 = e4) & op(e3, e0) = all_114_1 & op(e0, all_114_1) =
% 250.66/59.50 | | all_114_0 & $i(all_114_0) & $i(all_114_1)
% 250.66/59.50 | |
% 250.66/59.50 | | ALPHA: (91) implies:
% 250.66/59.50 | | (92) op(e3, e0) = all_114_1
% 250.66/59.50 | |
% 250.66/59.50 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.66/59.50 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.66/59.50 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.66/59.50 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 250.66/59.50 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 250.66/59.50 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 250.66/59.50 | | (68), (69), (70), (71), (72), (74), (75), (76), (77), (78), (79),
% 250.66/59.50 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 250.66/59.50 | | (92) are inconsistent by sub-proof #293.
% 250.66/59.50 | |
% 250.66/59.50 | Case 2:
% 250.66/59.50 | |
% 250.66/59.50 | | (93) ~ (all_114_1 = e2) & op(e3, e0) = all_114_1 & $i(all_114_1)
% 250.66/59.50 | |
% 250.66/59.50 | | ALPHA: (93) implies:
% 250.66/59.50 | | (94) op(e3, e0) = all_114_1
% 250.66/59.50 | |
% 250.66/59.50 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.66/59.50 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.66/59.50 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.66/59.50 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 250.66/59.50 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 250.66/59.50 | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 250.66/59.50 | | (68), (69), (70), (71), (72), (74), (75), (76), (77), (78), (79),
% 250.66/59.50 | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 250.66/59.50 | | (94) are inconsistent by sub-proof #293.
% 250.66/59.50 | |
% 250.66/59.50 | End of split
% 250.66/59.50 |
% 250.66/59.50 End of proof
% 250.66/59.50
% 250.66/59.50 Sub-proof #293 shows that the following formulas are inconsistent:
% 250.66/59.50 ----------------------------------------------------------------
% 250.66/59.50 (1) op(e0, e3) = e1
% 250.66/59.50 (2) ~ (all_4_2 = e4)
% 250.66/59.50 (3) ~ (all_10_2 = e4)
% 250.66/59.50 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.50 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.66/59.50 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.50 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.66/59.50 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.66/59.50 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.66/59.50 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.66/59.50 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.66/59.50 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.66/59.50 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.66/59.50 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.50 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.66/59.50 (8) all_252_21 = e1
% 250.66/59.50 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.50 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.66/59.50 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.66/59.50 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.50 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.50 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.50 (11) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.66/59.50 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.50 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.50 (12) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.50 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.66/59.50 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.66/59.50 (13) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.66/59.50 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.66/59.50 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.50 (14) all_174_2 = all_40_2
% 250.66/59.50 (15) op(e0, all_36_2) = e3
% 250.66/59.50 (16) ~ (e2 = e0)
% 250.66/59.50 (17) all_252_19 = e2
% 250.66/59.50 (18) ~ (e1 = e0)
% 250.66/59.50 (19) ~ (all_22_2 = e3)
% 250.66/59.50 (20) all_252_13 = e0
% 250.66/59.50 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.50 (22) op(e2, e3) = all_10_2
% 250.66/59.50 (23) ~ (e3 = e2)
% 250.66/59.50 (24) op(e0, e0) = all_244_24
% 250.66/59.50 (25) ~ (e4 = e0)
% 250.66/59.50 (26) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 250.66/59.50 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 250.66/59.50 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.66/59.50 (27) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.66/59.50 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.66/59.50 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.66/59.50 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.66/59.50 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.66/59.50 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.50 (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.66/59.50 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.66/59.50 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.66/59.50 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.66/59.50 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.66/59.50 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.66/59.50 (31) op(e4, e2) = all_6_2
% 250.66/59.50 (32) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.66/59.50 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.50 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.50 (33) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.66/59.50 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.66/59.50 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.50 (34) op(e2, e0) = e1
% 250.66/59.50 (35) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.66/59.50 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.50 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.50 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.66/59.50 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.66/59.50 op(e0, e1) = e0)))
% 250.66/59.50 (36) op(e0, e2) = all_28_2
% 250.66/59.50 (37) ~ (e4 = e1)
% 250.66/59.50 (38) ~ (all_28_2 = e1)
% 250.66/59.50 (39) ~ (all_6_2 = e1)
% 250.66/59.50 (40) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.66/59.50 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.66/59.50 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.66/59.50 (41) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.66/59.50 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.66/59.50 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.50 (42) op(e1, e4) = all_16_2
% 250.66/59.50 (43) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.66/59.50 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.66/59.50 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.50 (44) ~ (e3 = e0)
% 250.66/59.50 (45) ~ (all_40_2 = all_10_2)
% 250.66/59.50 (46) all_252_2 = e0
% 250.66/59.50 (47) ~ (e3 = e1)
% 250.66/59.50 (48) op(e3, e1) = all_36_2
% 250.66/59.50 (49) ~ (all_8_2 = e1)
% 250.66/59.50 (50) op(all_40_2, e0) = e2
% 250.66/59.50 (51) ~ (all_8_2 = e0)
% 250.66/59.50 (52) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.66/59.50 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.66/59.50 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.66/59.50 (53) op(e0, e2) = all_34_1
% 250.66/59.50 (54) op(e0, e3) = all_22_2
% 250.66/59.50 (55) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 250.66/59.50 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 250.66/59.50 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.66/59.50 (56) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.50 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.66/59.50 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.66/59.50 (57) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.66/59.50 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.66/59.50 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.66/59.50 (58) ~ (all_40_2 = e2)
% 250.66/59.50 (59) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.66/59.50 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.66/59.50 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.50 (60) op(e3, e0) = all_114_1
% 250.66/59.50 (61) ~ (all_36_2 = e0)
% 250.66/59.50 (62) op(e4, e4) = all_244_0
% 250.66/59.50 (63) ~ (e4 = e3)
% 250.66/59.50 (64) op(e1, e1) = all_244_15
% 250.66/59.50 (65) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.50 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.66/59.50 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.66/59.50 (66) op(e0, e1) = all_20_2
% 250.66/59.50 (67) ~ (all_244_15 = all_20_2)
% 250.66/59.50 (68) op(e3, e0) = all_48_2
% 250.66/59.50 (69) ~ (all_244_24 = e2)
% 250.66/59.50 (70) op(e1, e2) = all_4_2
% 250.66/59.50 (71) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.50 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.50 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.50 (72) ~ (all_48_2 = e0)
% 250.66/59.50 (73) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.66/59.50 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.66/59.50 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.66/59.50 (74) ~ (e4 = e2)
% 250.66/59.50 (75) op(e3, e2) = all_8_2
% 250.66/59.50 (76) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.66/59.50 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.66/59.50 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.66/59.50 (77) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.66/59.50 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.66/59.50 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.66/59.50 (78) ~ (all_20_2 = e4)
% 250.66/59.50 (79) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.66/59.50 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.66/59.50 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.66/59.50 (80) ~ (all_244_3 = e0)
% 250.66/59.50 (81) op(e2, e0) = all_40_2
% 250.66/59.50 (82) ~ (all_16_2 = e3)
% 250.66/59.50 (83) ~ (all_10_2 = e0)
% 250.66/59.50 (84) ~ (all_244_0 = e3)
% 250.66/59.50 (85) op(e3, e3) = all_244_3
% 250.66/59.50 (86) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.66/59.50 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.66/59.50 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.66/59.50 (87) ~ (all_174_2 = e1) | ( ~ (all_174_0 = e3) & op(e1, all_174_1) =
% 250.66/59.50 all_174_0 & op(e0, e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) |
% 250.66/59.50 ( ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 250.66/59.50 (88) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.66/59.50 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.66/59.50 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.66/59.50 (89) ~ (all_4_2 = e0)
% 250.66/59.50 (90) all_252_20 = e3
% 250.66/59.50
% 250.66/59.50 Begin of proof
% 250.66/59.50 |
% 250.66/59.50 | GROUND_INST: instantiating (21) with all_28_2, all_34_1, e2, e0, simplifying
% 250.66/59.50 | with (36), (53) gives:
% 250.66/59.50 | (91) all_34_1 = all_28_2
% 250.66/59.50 |
% 250.66/59.50 | GROUND_INST: instantiating (21) with all_40_2, e1, e0, e2, simplifying with
% 250.66/59.50 | (34), (81) gives:
% 250.66/59.50 | (92) all_40_2 = e1
% 250.66/59.50 |
% 250.66/59.50 | GROUND_INST: instantiating (21) with all_48_2, all_114_1, e0, e3, simplifying
% 250.66/59.50 | with (60), (68) gives:
% 250.66/59.50 | (93) all_114_1 = all_48_2
% 250.66/59.50 |
% 250.66/59.50 | COMBINE_EQS: (14), (92) imply:
% 250.66/59.50 | (94) all_174_2 = e1
% 250.66/59.50 |
% 250.66/59.50 | REDUCE: (45), (92) imply:
% 250.66/59.50 | (95) ~ (all_10_2 = e1)
% 250.66/59.50 |
% 250.66/59.50 | SIMP: (95) implies:
% 250.66/59.50 | (96) ~ (all_10_2 = e1)
% 250.66/59.50 |
% 250.66/59.50 | REDUCE: (58), (92) imply:
% 250.66/59.50 | (97) ~ (e2 = e1)
% 250.66/59.50 |
% 250.66/59.50 | SIMP: (97) implies:
% 250.66/59.50 | (98) ~ (e2 = e1)
% 250.66/59.50 |
% 250.66/59.50 | REDUCE: (50), (92) imply:
% 250.66/59.50 | (99) op(e1, e0) = e2
% 250.66/59.50 |
% 250.66/59.50 | BETA: splitting (55) gives:
% 250.66/59.50 |
% 250.66/59.50 | Case 1:
% 250.66/59.50 | |
% 250.66/59.50 | | (100) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0)
% 250.66/59.50 | | = e1)
% 250.66/59.50 | |
% 250.66/59.50 | | BETA: splitting (100) gives:
% 250.66/59.50 | |
% 250.66/59.50 | | Case 1:
% 250.66/59.50 | | |
% 250.66/59.50 | | | (101) all_252_16 = e1 & op(e4, e0) = e1
% 250.66/59.50 | | |
% 250.66/59.50 | | | ALPHA: (101) implies:
% 250.66/59.50 | | | (102) all_252_16 = e1
% 250.66/59.50 | | |
% 250.66/59.50 | | | BETA: splitting (26) gives:
% 250.66/59.50 | | |
% 250.66/59.50 | | | Case 1:
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | (103) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2,
% 250.66/59.50 | | | | e3) = e1)
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | BETA: splitting (103) gives:
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | Case 1:
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | (104) all_252_6 = e1 & op(e2, e4) = e1
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | ALPHA: (104) implies:
% 250.66/59.50 | | | | | (105) all_252_6 = e1
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | REF_CLOSE: (2), (6), (7), (12), (16), (17), (18), (20), (21), (23),
% 250.66/59.50 | | | | | (25), (33), (34), (35), (37), (41), (42), (44), (47), (48),
% 250.66/59.50 | | | | | (51), (56), (61), (63), (68), (70), (72), (74), (75), (77),
% 250.66/59.50 | | | | | (79), (80), (82), (85), (88), (90), (98), (99), (102),
% 250.66/59.50 | | | | | (105) are inconsistent by sub-proof #391.
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | Case 2:
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | (106) all_252_7 = e1 & op(e2, e3) = e1
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | ALPHA: (106) implies:
% 250.66/59.50 | | | | | (107) op(e2, e3) = e1
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | REF_CLOSE: (21), (22), (96), (107) are inconsistent by sub-proof #948.
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | End of split
% 250.66/59.50 | | | |
% 250.66/59.50 | | | Case 2:
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | (108) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2,
% 250.66/59.50 | | | | e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | BETA: splitting (108) gives:
% 250.66/59.50 | | | |
% 250.66/59.50 | | | | Case 1:
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | (109) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 250.66/59.50 | | | | | (13), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 250.66/59.50 | | | | | (27), (29), (30), (32), (33), (34), (35), (37), (40), (41),
% 250.66/59.50 | | | | | (42), (44), (46), (47), (48), (49), (51), (52), (54), (56),
% 250.66/59.50 | | | | | (57), (61), (62), (63), (65), (66), (68), (70), (71), (72),
% 250.66/59.50 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 250.66/59.50 | | | | | (83), (84), (85), (86), (88), (89), (90), (98), (99),
% 250.66/59.50 | | | | | (102), (109) are inconsistent by sub-proof #335.
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | Case 2:
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | (110) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 250.66/59.50 | | | | | op(e2, e0) = e1)
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | BETA: splitting (110) gives:
% 250.66/59.50 | | | | |
% 250.66/59.50 | | | | | Case 1:
% 250.66/59.50 | | | | | |
% 250.66/59.50 | | | | | | (111) all_252_11 = e1 & op(e2, e1) = e1
% 250.66/59.50 | | | | | |
% 250.66/59.50 | | | | | | ALPHA: (111) implies:
% 250.66/59.50 | | | | | | (112) all_252_11 = e1
% 250.66/59.50 | | | | | |
% 250.66/59.50 | | | | | | BETA: splitting (13) gives:
% 250.66/59.50 | | | | | |
% 250.66/59.50 | | | | | | Case 1:
% 250.66/59.50 | | | | | | |
% 250.66/59.50 | | | | | | | (113) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 &
% 250.66/59.50 | | | | | | | op(e2, e3) = e0)
% 250.66/59.50 | | | | | | |
% 250.66/59.50 | | | | | | | BETA: splitting (113) gives:
% 250.66/59.50 | | | | | | |
% 250.66/59.50 | | | | | | | Case 1:
% 250.66/59.50 | | | | | | | |
% 250.66/59.50 | | | | | | | | (114) all_252_6 = e0 & op(e2, e4) = e0
% 250.66/59.50 | | | | | | | |
% 250.66/59.50 | | | | | | | | ALPHA: (114) implies:
% 250.66/59.50 | | | | | | | | (115) all_252_6 = e0
% 250.66/59.50 | | | | | | | |
% 250.66/59.50 | | | | | | | | BETA: splitting (28) gives:
% 250.66/59.50 | | | | | | | |
% 250.66/59.50 | | | | | | | | Case 1:
% 250.66/59.50 | | | | | | | | |
% 250.66/59.50 | | | | | | | | | (116) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1
% 250.66/59.50 | | | | | | | | | & op(e3, e2) = e1)
% 250.66/59.50 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | REF_CLOSE: (21), (31), (39), (49), (75), (116) are
% 250.66/59.51 | | | | | | | | | inconsistent by sub-proof #928.
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | (117) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1
% 250.66/59.51 | | | | | | | | | & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2)
% 250.66/59.51 | | | | | | | | | = e1)
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | BETA: splitting (117) gives:
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | (118) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | ALPHA: (118) implies:
% 250.66/59.51 | | | | | | | | | | (119) all_252_8 = e1
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10),
% 250.66/59.51 | | | | | | | | | | (11), (12), (16), (17), (18), (20), (21), (22),
% 250.66/59.51 | | | | | | | | | | (23), (25), (29), (33), (34), (35), (37), (40),
% 250.66/59.51 | | | | | | | | | | (41), (42), (44), (46), (47), (48), (51), (56),
% 250.66/59.51 | | | | | | | | | | (61), (62), (63), (66), (68), (70), (71), (72),
% 250.66/59.51 | | | | | | | | | | (73), (74), (75), (76), (77), (78), (79), (80),
% 250.66/59.51 | | | | | | | | | | (82), (84), (85), (86), (88), (89), (90), (98),
% 250.66/59.51 | | | | | | | | | | (99), (102), (115), (119) are inconsistent by
% 250.66/59.51 | | | | | | | | | | sub-proof #350.
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | (120) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 =
% 250.66/59.51 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | BETA: splitting (120) gives:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | (121) all_252_14 = e1 & op(e1, e2) = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | ALPHA: (121) implies:
% 250.66/59.51 | | | | | | | | | | | (122) all_252_14 = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (16), (17), (18), (20), (21),
% 250.66/59.51 | | | | | | | | | | | (23), (25), (33), (34), (35), (37), (41), (42),
% 250.66/59.51 | | | | | | | | | | | (44), (46), (47), (48), (51), (56), (61), (63),
% 250.66/59.51 | | | | | | | | | | | (68), (70), (72), (74), (75), (76), (77), (79),
% 250.66/59.51 | | | | | | | | | | | (80), (82), (85), (88), (90), (98), (99), (102),
% 250.66/59.51 | | | | | | | | | | | (115), (122) are inconsistent by sub-proof #333.
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | (123) all_252_22 = e1 & op(e0, e2) = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | ALPHA: (123) implies:
% 250.66/59.51 | | | | | | | | | | | (124) op(e0, e2) = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | REF_CLOSE: (21), (36), (38), (124) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | sub-proof #907.
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | End of split
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | (125) all_252_7 = e0 & op(e2, e3) = e0
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | REF_CLOSE: (21), (22), (83), (125) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | #816.
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | End of split
% 250.66/59.51 | | | | | | |
% 250.66/59.51 | | | | | | Case 2:
% 250.66/59.51 | | | | | | |
% 250.66/59.51 | | | | | | | (126) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 250.66/59.51 | | | | | | | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.51 | | | | | | |
% 250.66/59.51 | | | | | | | BETA: splitting (126) gives:
% 250.66/59.51 | | | | | | |
% 250.66/59.51 | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | (127) all_252_8 = e0 & op(e2, e2) = e0
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | ALPHA: (127) implies:
% 250.66/59.51 | | | | | | | | (128) all_252_8 = e0
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | BETA: splitting (28) gives:
% 250.66/59.51 | | | | | | | |
% 250.66/59.51 | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | (129) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1
% 250.66/59.51 | | | | | | | | | & op(e3, e2) = e1)
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | REF_CLOSE: (21), (31), (39), (49), (75), (129) are
% 250.66/59.51 | | | | | | | | | inconsistent by sub-proof #928.
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | (130) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1
% 250.66/59.51 | | | | | | | | | & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2)
% 250.66/59.51 | | | | | | | | | = e1)
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | BETA: splitting (130) gives:
% 250.66/59.51 | | | | | | | | |
% 250.66/59.51 | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | (131) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10),
% 250.66/59.51 | | | | | | | | | | (11), (12), (13), (16), (17), (18), (19), (20),
% 250.66/59.51 | | | | | | | | | | (21), (22), (23), (25), (27), (29), (30), (32),
% 250.66/59.51 | | | | | | | | | | (33), (34), (35), (37), (40), (41), (42), (44),
% 250.66/59.51 | | | | | | | | | | (46), (47), (48), (49), (51), (52), (54), (56),
% 250.66/59.51 | | | | | | | | | | (57), (61), (62), (63), (65), (66), (68), (70),
% 250.66/59.51 | | | | | | | | | | (71), (72), (73), (74), (75), (76), (77), (78),
% 250.66/59.51 | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (86),
% 250.66/59.51 | | | | | | | | | | (88), (89), (90), (98), (99), (102), (131) are
% 250.66/59.51 | | | | | | | | | | inconsistent by sub-proof #335.
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | (132) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 =
% 250.66/59.51 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | BETA: splitting (132) gives:
% 250.66/59.51 | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | (133) all_252_14 = e1 & op(e1, e2) = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | ALPHA: (133) implies:
% 250.66/59.51 | | | | | | | | | | | (134) all_252_14 = e1
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | BETA: splitting (27) gives:
% 250.66/59.51 | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | (135) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 250.66/59.51 | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | BETA: splitting (135) gives:
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | (136) all_252_6 = e3 & op(e2, e4) = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | ALPHA: (136) implies:
% 250.66/59.51 | | | | | | | | | | | | | (137) all_252_6 = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (16), (17), (18), (20), (21),
% 250.66/59.51 | | | | | | | | | | | | | (23), (25), (33), (34), (35), (37), (41), (42),
% 250.66/59.51 | | | | | | | | | | | | | (44), (46), (47), (48), (51), (56), (61), (63),
% 250.66/59.51 | | | | | | | | | | | | | (68), (70), (72), (74), (75), (77), (79), (80),
% 250.66/59.51 | | | | | | | | | | | | | (82), (85), (88), (90), (98), (99), (102), (137)
% 250.66/59.51 | | | | | | | | | | | | | are inconsistent by sub-proof #347.
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | (138) all_252_7 = e3 & op(e2, e3) = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | ALPHA: (138) implies:
% 250.66/59.51 | | | | | | | | | | | | | (139) all_252_7 = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | BETA: splitting (12) gives:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | (140) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 250.66/59.51 | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (42), (44), (82), (140) are
% 250.66/59.51 | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | (141) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 250.66/59.51 | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.66/59.51 | | | | | | | | | | | | | | op(e1, e0) = e3)
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | (142) all_252_14 = e3 & op(e1, e2) = e3
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | REF_CLOSE: (47), (134), (142) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | #334.
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | (143) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 250.66/59.51 | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | (144) all_252_15 = e3 & op(e1, e1) = e3
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | (145) all_252_15 = e3
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | (146) all_252_24 = e0 & op(e0, e0) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | (147) all_252_24 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | (148) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (149) all_252_6 = e2 & op(e2, e4) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (150) all_252_6 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | (151) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (21), (37), (63), (90), (151) are
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #390.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | (152) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | (153) all_252_22 = e4 & op(e0, e2) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | (154) all_252_22 = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_12 = e4 & op(e1, e4) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_12 = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | (158) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (10), (11), (16), (18), (20), (21),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | (22), (23), (25), (37), (44), (46), (47), (63),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | (71), (74), (98), (158) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #346.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | (159) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_5 = e1 & op(e3, e2) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | (161) op(e3, e2) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (49), (75), (161) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | (162) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_10 = e1 & op(e3, e1) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_10 = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (165) op(e3, e1) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_20 = e2 & op(e0, e4) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_20 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (168) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) e3 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) e3 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (170) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_252_15 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (12), (18), (20), (21), (23), (25),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (42), (44), (47), (56), (70), (74), (82),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (99), (171) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #404.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_21 = e2 & op(e0, e3) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) op(e0, e3) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (21), (98), (173) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #941.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_22 = e2 & op(e0, e2) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (12), (18), (20), (21), (23), (25),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (42), (44), (47), (56), (63), (70), (74),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (98), (99), (154), (157), (175) are
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_23 = e2 & op(e0, e1) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_23 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_252_9 = e4 & op(e4, e1) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_9 = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_252_0 = e1 & op(e4, e4) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_252_0 = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_9 = e0 & op(e4, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (181), (186) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #505.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_10 = e0 & op(e3, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) op(e3, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (48), (165), (188) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #922.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_11 = e0 & op(e2, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_11 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (191) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) e1 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (192) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_0 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (37), (46), (47), (88), (90), (98), (150),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (193) are inconsistent by sub-proof #564.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_15 = e0 & op(e1, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (145), (195) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #763.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_23 = e0 & op(e0, e1) = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_23 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (197) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e2 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (198) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_252_6 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (16), (17), (18), (20), (21),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (25), (33), (34), (35), (37), (41), (42),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (46), (47), (48), (51), (56), (61), (63),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (68), (70), (72), (74), (75), (76), (77), (79),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (85), (88), (90), (98), (99), (102),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (134), (199) are inconsistent by sub-proof #333.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_2 = e1 & op(e3, e4) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (46), (200) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #568.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_6 = e1 & op(e2, e4) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_6 = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (16), (17), (18), (20), (21),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (25), (33), (34), (35), (37), (41), (42),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (47), (48), (51), (56), (61), (63), (68),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (72), (74), (75), (77), (79), (80), (82),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (88), (90), (98), (99), (102), (203) are
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_12 = e1 & op(e1, e4) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (157), (205) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #566.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_20 = e1 & op(e0, e4) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (90), (206) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #509.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_252_10 = e4 & op(e3, e1) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_10 = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (164), (208) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #434.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_11 = e4 & op(e2, e1) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_252_11 = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (211) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e4 = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (212) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) $false
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (63), (66), (78), (145), (214) are
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #674.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_24 = e2 & op(e0, e0) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) op(e0, e0) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (69), (216) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #978.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_17 = e1 & op(e3, e0) = e1
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (23), (33), (34), (44), (47), (99), (102),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | | (147), (217) are inconsistent by sub-proof #340.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_13 = e4 & op(e1, e3) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (218) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | | #413.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (21), (63), (70), (74), (99), (145), (219)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #357.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | (220) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | (221) all_252_23 = e4 & op(e0, e1) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (66), (78), (221) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | (222) all_252_24 = e4 & op(e0, e0) = e4
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (147), (222) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | | #331.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (223) all_252_7 = e2 & op(e2, e3) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (224) all_252_7 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (224) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (225) e3 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (225) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (226) all_252_15 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (12), (18), (20), (21), (23), (25),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (37), (42), (44), (47), (56), (70), (74), (82),
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (98), (99), (226) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | #404.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | (227) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 250.66/59.51 | | | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (228) all_252_8 = e2 & op(e2, e2) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (229) all_252_8 = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (229) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (230) e2 = e0
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (230) imply:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (231) $false
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | (232) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | (233) all_252_11 = e2 & op(e2, e1) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (112), (233) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | #330.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | (234) all_252_18 = e2 & op(e2, e0) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | (235) op(e2, e0) = e2
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (34), (81), (98), (235) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | | sub-proof #415.
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | (236) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.66/59.51 | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.66/59.51 | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.66/59.51 | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.66/59.51 | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.66/59.51 | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | | (237) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.66/59.51 | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.51 | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.66/59.51 | | | | | | | | | | | | | | | | | = e0)
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (21), (34), (68), (72), (102),
% 250.66/59.51 | | | | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #348.
% 250.66/59.51 | | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | (238) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 250.66/59.51 | | | | | | | | | | | | | | | | (239) op(e1, e0) = e3
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (23), (99), (239) are inconsistent by
% 250.66/59.51 | | | | | | | | | | | | | | | | sub-proof #736.
% 250.66/59.51 | | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | End of split
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | (240) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 250.66/59.51 | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.66/59.51 | | | | | | | | | | | | op(e2, e0) = e3)
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | BETA: splitting (240) gives:
% 250.66/59.51 | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | (241) all_252_8 = e3 & op(e2, e2) = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | ALPHA: (241) implies:
% 250.66/59.51 | | | | | | | | | | | | | (242) all_252_8 = e3
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | REF_CLOSE: (44), (128), (242) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | #905.
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | (243) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 250.66/59.51 | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | BETA: splitting (243) gives:
% 250.66/59.51 | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | Case 1:
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | (244) all_252_11 = e3 & op(e2, e1) = e3
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | REF_CLOSE: (47), (112), (244) are inconsistent by sub-proof
% 250.66/59.51 | | | | | | | | | | | | | | #329.
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | Case 2:
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | (245) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.51 | | | | | | | | | | | | | |
% 250.66/59.51 | | | | | | | | | | | | | | ALPHA: (245) implies:
% 250.66/59.52 | | | | | | | | | | | | | | (246) op(e2, e0) = e3
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | REF_CLOSE: (21), (34), (47), (246) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | | | | sub-proof #399.
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (247) all_252_22 = e1 & op(e0, e2) = e1
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | ALPHA: (247) implies:
% 250.66/59.52 | | | | | | | | | | | (248) op(e0, e2) = e1
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (21), (36), (38), (248) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | sub-proof #907.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (249) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0
% 250.66/59.52 | | | | | | | | & op(e2, e0) = e0)
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (249) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (250) all_252_11 = e0 & op(e2, e1) = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (250) implies:
% 250.66/59.52 | | | | | | | | | (251) all_252_11 = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | COMBINE_EQS: (112), (251) imply:
% 250.66/59.52 | | | | | | | | | (252) e1 = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REDUCE: (18), (252) imply:
% 250.66/59.52 | | | | | | | | | (253) $false
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | CLOSE: (253) is inconsistent.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (254) all_252_18 = e0 & op(e2, e0) = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (254) implies:
% 250.66/59.52 | | | | | | | | | (255) op(e2, e0) = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REF_CLOSE: (18), (21), (34), (255) are inconsistent by
% 250.66/59.52 | | | | | | | | | sub-proof #901.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | End of split
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | Case 2:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | (256) all_252_18 = e1 & op(e2, e0) = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | ALPHA: (256) implies:
% 250.66/59.52 | | | | | | (257) all_252_18 = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | BETA: splitting (33) gives:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | Case 1:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (258) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 &
% 250.66/59.52 | | | | | | | op(e3, e0) = e3)
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (258) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (259) all_252_16 = e3 & op(e4, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (47), (102), (259) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | #488.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (260) all_252_17 = e3 & op(e3, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (260) implies:
% 250.66/59.52 | | | | | | | | (261) all_252_17 = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (35) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (262) all_252_24 = e0 & op(e0, e0) = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (262) implies:
% 250.66/59.52 | | | | | | | | | (263) all_252_24 = e0
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (41) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (264) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | | e4 & op(e3, e0) = e4)
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | BETA: splitting (264) gives:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (265) all_252_16 = e4 & op(e4, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (37), (102), (265) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | #359.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (266) all_252_17 = e4 & op(e3, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (63), (261), (266) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | #837.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (267) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 =
% 250.66/59.52 | | | | | | | | | | e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.66/59.52 | | | | | | | | | | e0) = e4)
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | BETA: splitting (267) gives:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (268) all_252_18 = e4 & op(e2, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (37), (257), (268) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | #328.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (269) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24
% 250.66/59.52 | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (21), (25), (74), (99), (263), (269) are
% 250.66/59.52 | | | | | | | | | | | inconsistent by sub-proof #400.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (270) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.66/59.52 | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) =
% 250.66/59.52 | | | | | | | | | e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.66/59.52 | | | | | | | | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 =
% 250.66/59.52 | | | | | | | | | e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0,
% 250.66/59.52 | | | | | | | | | e1) = e0))
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (270) implies:
% 250.66/59.52 | | | | | | | | | (271) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.66/59.52 | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REF_CLOSE: (16), (17), (18), (21), (34), (68), (72), (102),
% 250.66/59.52 | | | | | | | | | (271) are inconsistent by sub-proof #348.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | Case 2:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (272) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 250.66/59.52 | | | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (272) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (273) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (273) implies:
% 250.66/59.52 | | | | | | | | (274) op(e2, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (21), (34), (47), (274) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | #399.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (275) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3
% 250.66/59.52 | | | | | | | | & op(e0, e0) = e3)
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (275) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (276) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (276) implies:
% 250.66/59.52 | | | | | | | | | (277) op(e1, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REF_CLOSE: (21), (23), (99), (277) are inconsistent by
% 250.66/59.52 | | | | | | | | | sub-proof #736.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (278) all_252_24 = e3 & op(e0, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (278) implies:
% 250.66/59.52 | | | | | | | | | (279) all_252_24 = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (35) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (280) all_252_24 = e0 & op(e0, e0) = e0
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (44), (279), (280) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | #533.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (281) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.66/59.52 | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.52 | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.66/59.52 | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) =
% 250.66/59.52 | | | | | | | | | | e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.66/59.52 | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 250.66/59.52 | | | | | | | | | | = e0 & op(e0, e1) = e0))
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | ALPHA: (281) implies:
% 250.66/59.52 | | | | | | | | | | (282) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.66/59.52 | | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (16), (17), (18), (21), (34), (68), (72), (102),
% 250.66/59.52 | | | | | | | | | | (282) are inconsistent by sub-proof #348.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | End of split
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | End of split
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | End of split
% 250.66/59.52 | | | |
% 250.66/59.52 | | | End of split
% 250.66/59.52 | | |
% 250.66/59.52 | | Case 2:
% 250.66/59.52 | | |
% 250.66/59.52 | | | (283) all_252_17 = e1 & op(e3, e0) = e1
% 250.66/59.52 | | |
% 250.66/59.52 | | | ALPHA: (283) implies:
% 250.66/59.52 | | | (284) all_252_17 = e1
% 250.66/59.52 | | |
% 250.66/59.52 | | | BETA: splitting (28) gives:
% 250.66/59.52 | | |
% 250.66/59.52 | | | Case 1:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | (285) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 250.66/59.52 | | | | e2) = e1)
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | REF_CLOSE: (21), (31), (39), (49), (75), (285) are inconsistent by
% 250.66/59.52 | | | | sub-proof #928.
% 250.66/59.52 | | | |
% 250.66/59.52 | | | Case 2:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | (286) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1,
% 250.66/59.52 | | | | e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | BETA: splitting (286) gives:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | Case 1:
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | (287) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | ALPHA: (287) implies:
% 250.66/59.52 | | | | | (288) all_252_8 = e1
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | BETA: splitting (33) gives:
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | Case 1:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | (289) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 &
% 250.66/59.52 | | | | | | op(e3, e0) = e3)
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | BETA: splitting (289) gives:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | Case 1:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (290) all_252_16 = e3 & op(e4, e0) = e3
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | ALPHA: (290) implies:
% 250.66/59.52 | | | | | | | (291) all_252_16 = e3
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (35) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (292) all_252_24 = e0 & op(e0, e0) = e0
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (292) implies:
% 250.66/59.52 | | | | | | | | (293) all_252_24 = e0
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (41) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (294) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | e4 & op(e3, e0) = e4)
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (294) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (295) all_252_16 = e4 & op(e4, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (63), (291), (295) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | #483.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (296) all_252_17 = e4 & op(e3, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | ALPHA: (296) implies:
% 250.66/59.52 | | | | | | | | | | (297) all_252_17 = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | COMBINE_EQS: (284), (297) imply:
% 250.66/59.52 | | | | | | | | | | (298) e4 = e1
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | SIMP: (298) implies:
% 250.66/59.52 | | | | | | | | | | (299) e4 = e1
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REDUCE: (37), (299) imply:
% 250.66/59.52 | | | | | | | | | | (300) $false
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | CLOSE: (300) is inconsistent.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (301) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 =
% 250.66/59.52 | | | | | | | | | e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.66/59.52 | | | | | | | | | e0) = e4)
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (301) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (302) all_252_18 = e4 & op(e2, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | BETA: splitting (4) gives:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (303) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 250.66/59.52 | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (1), (21), (37), (63), (90), (303) are
% 250.66/59.52 | | | | | | | | | | | inconsistent by sub-proof #390.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (304) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 250.66/59.52 | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.66/59.52 | | | | | | | | | | | op(e0, e0) = e4)
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | BETA: splitting (304) gives:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | (305) all_252_22 = e4 & op(e0, e2) = e4
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | ALPHA: (305) implies:
% 250.66/59.52 | | | | | | | | | | | | (306) all_252_22 = e4
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | BETA: splitting (40) gives:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | (307) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 250.66/59.52 | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | BETA: splitting (307) gives:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | (308) all_252_4 = e0 & op(e4, e2) = e0
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | ALPHA: (308) implies:
% 250.66/59.52 | | | | | | | | | | | | | | (309) all_252_4 = e0
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | (310) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 250.66/59.52 | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | (311) all_252_4 = e2 & op(e4, e2) = e2
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (309), (311) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | | | | #863.
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 250.66/59.52 | | | | | | | | | | | | | | | | (312) all_252_18 = e4
% 250.66/59.52 | | | | | | | | | | | | | | | | (313) op(e2, e0) = e4
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with e1, e4, e0, e2,
% 250.66/59.52 | | | | | | | | | | | | | | | | simplifying with (34), (313) gives:
% 250.66/59.52 | | | | | | | | | | | | | | | | (314) e4 = e1
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (314) imply:
% 250.66/59.52 | | | | | | | | | | | | | | | | (315) all_252_18 = e1
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | REF_CLOSE: (21), (25), (37), (41), (63), (74), (99), (284),
% 250.66/59.52 | | | | | | | | | | | | | | | | (291), (293), (315) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | | | | #325.
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | (316) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 250.66/59.52 | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 250.66/59.52 | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | (317) all_252_8 = e2 & op(e2, e2) = e2
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | REF_CLOSE: (98), (288), (317) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | | | | #788.
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | (318) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 250.66/59.52 | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (12), (18), (20), (21), (23), (25),
% 250.66/59.52 | | | | | | | | | | | | | | | | (37), (42), (44), (47), (56), (63), (70), (74),
% 250.66/59.52 | | | | | | | | | | | | | | | | (82), (98), (99), (306), (318) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | | | | | | sub-proof #354.
% 250.66/59.52 | | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | (319) all_252_5 = e0 & op(e3, e2) = e0
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | REF_CLOSE: (21), (51), (75), (319) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | | | | sub-proof #874.
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | (320) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 250.66/59.52 | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 250.66/59.52 | | | | | | | | | | | | | op(e0, e2) = e0)
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | BETA: splitting (320) gives:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | (321) all_252_8 = e0 & op(e2, e2) = e0
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | REF_CLOSE: (18), (288), (321) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | | #873.
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | (322) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 250.66/59.52 | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | (323) all_252_14 = e0 & op(e1, e2) = e0
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | REF_CLOSE: (21), (70), (89), (323) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | | | | | sub-proof #855.
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | (324) all_252_22 = e0 & op(e0, e2) = e0
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 250.66/59.52 | | | | | | | | | | | | | | | (325) all_252_22 = e0
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | | REF_CLOSE: (25), (306), (325) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | | | #528.
% 250.66/59.52 | | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | (326) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 250.66/59.52 | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | BETA: splitting (326) gives:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | (327) all_252_23 = e4 & op(e0, e1) = e4
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | REF_CLOSE: (21), (66), (78), (327) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | | | sub-proof #912.
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | (328) all_252_24 = e4 & op(e0, e0) = e4
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | | REF_CLOSE: (25), (293), (328) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | | #331.
% 250.66/59.52 | | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (329) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 =
% 250.66/59.52 | | | | | | | | | | e4 & op(e0, e0) = e4)
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (21), (25), (74), (99), (293), (329) are
% 250.66/59.52 | | | | | | | | | | inconsistent by sub-proof #326.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (330) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0
% 250.66/59.52 | | | | | | | | & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0)
% 250.66/59.52 | | | | | | | | = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.52 | | | | | | | | ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0
% 250.66/59.52 | | | | | | | | & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2)
% 250.66/59.52 | | | | | | | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (330) implies:
% 250.66/59.52 | | | | | | | | (331) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0
% 250.66/59.52 | | | | | | | | & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) =
% 250.66/59.52 | | | | | | | | e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (16), (17), (18), (21), (34), (44), (68), (72),
% 250.66/59.52 | | | | | | | | (291), (331) are inconsistent by sub-proof #324.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | Case 2:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (332) all_252_17 = e3 & op(e3, e0) = e3
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | REF_CLOSE: (47), (284), (332) are inconsistent by sub-proof #323.
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | End of split
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | Case 2:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | (333) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 250.66/59.52 | | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | BETA: splitting (333) gives:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | Case 1:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (334) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | ALPHA: (334) implies:
% 250.66/59.52 | | | | | | | (335) op(e2, e0) = e3
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | REF_CLOSE: (21), (34), (47), (335) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | #399.
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | Case 2:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (336) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.66/59.52 | | | | | | | op(e0, e0) = e3)
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (336) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (337) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (337) implies:
% 250.66/59.52 | | | | | | | | (338) op(e1, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (21), (23), (99), (338) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | #736.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (339) all_252_24 = e3 & op(e0, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (339) implies:
% 250.66/59.52 | | | | | | | | (340) all_252_24 = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (1), (4), (8), (16), (18), (21), (23), (24), (25),
% 250.66/59.52 | | | | | | | | (35), (37), (43), (44), (47), (59), (63), (66), (69),
% 250.66/59.52 | | | | | | | | (74), (78), (90), (98), (340) are inconsistent by
% 250.66/59.52 | | | | | | | | sub-proof #310.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | End of split
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | End of split
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | Case 2:
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | (341) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.66/59.52 | | | | | op(e0, e2) = e1)
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | BETA: splitting (341) gives:
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | | Case 1:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | (342) all_252_14 = e1 & op(e1, e2) = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | ALPHA: (342) implies:
% 250.66/59.52 | | | | | | (343) all_252_14 = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | BETA: splitting (33) gives:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | Case 1:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (344) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 &
% 250.66/59.52 | | | | | | | op(e3, e0) = e3)
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (344) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (345) all_252_16 = e3 & op(e4, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (345) implies:
% 250.66/59.52 | | | | | | | | (346) all_252_16 = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (41) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (347) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 =
% 250.66/59.52 | | | | | | | | | e4 & op(e3, e0) = e4)
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (347) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (348) all_252_16 = e4 & op(e4, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | ALPHA: (348) implies:
% 250.66/59.52 | | | | | | | | | | (349) all_252_16 = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | COMBINE_EQS: (346), (349) imply:
% 250.66/59.52 | | | | | | | | | | (350) e4 = e3
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | SIMP: (350) implies:
% 250.66/59.52 | | | | | | | | | | (351) e4 = e3
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REDUCE: (63), (351) imply:
% 250.66/59.52 | | | | | | | | | | (352) $false
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | CLOSE: (352) is inconsistent.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (353) all_252_17 = e4 & op(e3, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (37), (284), (353) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | #327.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (354) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 =
% 250.66/59.52 | | | | | | | | | e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.66/59.52 | | | | | | | | | e0) = e4)
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | BETA: splitting (354) gives:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (355) all_252_18 = e4 & op(e2, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | ALPHA: (355) implies:
% 250.66/59.52 | | | | | | | | | | (356) all_252_18 = e4
% 250.66/59.52 | | | | | | | | | | (357) op(e2, e0) = e4
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | GROUND_INST: instantiating (21) with e1, e4, e0, e2,
% 250.66/59.52 | | | | | | | | | | simplifying with (34), (357) gives:
% 250.66/59.52 | | | | | | | | | | (358) e4 = e1
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | COMBINE_EQS: (356), (358) imply:
% 250.66/59.52 | | | | | | | | | | (359) all_252_18 = e1
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (12), (16), (17), (18),
% 250.66/59.52 | | | | | | | | | | (20), (21), (23), (24), (25), (33), (34), (35),
% 250.66/59.52 | | | | | | | | | | (37), (41), (42), (44), (46), (47), (48), (51),
% 250.66/59.52 | | | | | | | | | | (56), (59), (61), (63), (66), (68), (69), (70),
% 250.66/59.52 | | | | | | | | | | (72), (74), (75), (76), (77), (78), (79), (80),
% 250.66/59.52 | | | | | | | | | | (82), (85), (88), (90), (98), (99), (284), (343),
% 250.66/59.52 | | | | | | | | | | (359) are inconsistent by sub-proof #304.
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | (360) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 =
% 250.66/59.52 | | | | | | | | | | e4 & op(e0, e0) = e4)
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | BETA: splitting (360) gives:
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (361) all_252_19 = e4 & op(e1, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | ALPHA: (361) implies:
% 250.66/59.52 | | | | | | | | | | | (362) op(e1, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | REF_CLOSE: (21), (74), (99), (362) are inconsistent by
% 250.66/59.52 | | | | | | | | | | | sub-proof #829.
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | (363) all_252_24 = e4 & op(e0, e0) = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | ALPHA: (363) implies:
% 250.66/59.52 | | | | | | | | | | | (364) all_252_24 = e4
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | BETA: splitting (35) gives:
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | (365) all_252_24 = e0 & op(e0, e0) = e0
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | ALPHA: (365) implies:
% 250.66/59.52 | | | | | | | | | | | | (366) all_252_24 = e0
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | REF_CLOSE: (25), (364), (366) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | | | | | #401.
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | (367) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.66/59.52 | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.52 | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.66/59.52 | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.66/59.52 | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.66/59.52 | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.66/59.52 | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | ALPHA: (367) implies:
% 250.66/59.52 | | | | | | | | | | | | (368) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.66/59.52 | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.52 | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.66/59.52 | | | | | | | | | | | | = e0)
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (21), (34), (44), (68), (72),
% 250.66/59.52 | | | | | | | | | | | | (346), (368) are inconsistent by sub-proof #324.
% 250.66/59.52 | | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | | |
% 250.66/59.52 | | | | | | | | | End of split
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (369) all_252_17 = e3 & op(e3, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (47), (284), (369) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | #341.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | Case 2:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | (370) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 250.66/59.52 | | | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | BETA: splitting (370) gives:
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (371) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | ALPHA: (371) implies:
% 250.66/59.52 | | | | | | | | (372) op(e2, e0) = e3
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | REF_CLOSE: (21), (34), (47), (372) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | | | #399.
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | (373) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3
% 250.66/59.52 | | | | | | | | & op(e0, e0) = e3)
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | BETA: splitting (373) gives:
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 1:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (374) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (374) implies:
% 250.66/59.52 | | | | | | | | | (375) op(e1, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REF_CLOSE: (21), (23), (99), (375) are inconsistent by
% 250.66/59.52 | | | | | | | | | sub-proof #736.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | Case 2:
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | (376) all_252_24 = e3 & op(e0, e0) = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | ALPHA: (376) implies:
% 250.66/59.52 | | | | | | | | | (377) all_252_24 = e3
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | | REF_CLOSE: (1), (4), (8), (16), (18), (21), (23), (24), (25),
% 250.66/59.52 | | | | | | | | | (35), (37), (43), (44), (47), (59), (63), (66),
% 250.66/59.52 | | | | | | | | | (69), (74), (78), (90), (98), (377) are
% 250.66/59.52 | | | | | | | | | inconsistent by sub-proof #310.
% 250.66/59.52 | | | | | | | | |
% 250.66/59.52 | | | | | | | | End of split
% 250.66/59.52 | | | | | | | |
% 250.66/59.52 | | | | | | | End of split
% 250.66/59.52 | | | | | | |
% 250.66/59.52 | | | | | | End of split
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | Case 2:
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | (378) all_252_22 = e1 & op(e0, e2) = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | ALPHA: (378) implies:
% 250.66/59.52 | | | | | | (379) op(e0, e2) = e1
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | | REF_CLOSE: (21), (36), (38), (379) are inconsistent by sub-proof
% 250.66/59.52 | | | | | | #907.
% 250.66/59.52 | | | | | |
% 250.66/59.52 | | | | | End of split
% 250.66/59.52 | | | | |
% 250.66/59.52 | | | | End of split
% 250.66/59.52 | | | |
% 250.66/59.52 | | | End of split
% 250.66/59.52 | | |
% 250.66/59.52 | | End of split
% 250.66/59.52 | |
% 250.66/59.52 | Case 2:
% 250.66/59.52 | |
% 250.66/59.52 | | (380) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0)
% 250.66/59.52 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.66/59.52 | |
% 250.66/59.52 | | BETA: splitting (380) gives:
% 250.66/59.52 | |
% 250.66/59.52 | | Case 1:
% 250.66/59.52 | | |
% 250.66/59.52 | | | (381) all_252_18 = e1 & op(e2, e0) = e1
% 250.66/59.52 | | |
% 250.66/59.52 | | | ALPHA: (381) implies:
% 250.66/59.52 | | | (382) all_252_18 = e1
% 250.66/59.52 | | |
% 250.66/59.52 | | | BETA: splitting (87) gives:
% 250.66/59.52 | | |
% 250.66/59.52 | | | Case 1:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | (383) ~ (all_174_2 = e1)
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | REDUCE: (94), (383) imply:
% 250.66/59.52 | | | | (384) $false
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | CLOSE: (384) is inconsistent.
% 250.66/59.52 | | | |
% 250.66/59.52 | | | Case 2:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | (385) ( ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0,
% 250.66/59.52 | | | | e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)) | ( ~
% 250.66/59.52 | | | | (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1))
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | BETA: splitting (385) gives:
% 250.66/59.52 | | | |
% 250.66/59.52 | | | | Case 1:
% 250.66/59.52 | | | | |
% 250.66/59.53 | | | | | (386) ~ (all_174_0 = e3) & op(e1, all_174_1) = all_174_0 & op(e0,
% 250.66/59.53 | | | | | e1) = all_174_1 & $i(all_174_0) & $i(all_174_1)
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | ALPHA: (386) implies:
% 250.66/59.53 | | | | | (387) op(e0, e1) = all_174_1
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 250.66/59.53 | | | | | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.66/59.53 | | | | | (24), (25), (27), (28), (30), (31), (32), (33), (34), (35),
% 250.66/59.53 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 250.66/59.53 | | | | | (47), (48), (49), (51), (52), (54), (56), (57), (59), (61),
% 250.66/59.53 | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 250.66/59.53 | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 250.66/59.53 | | | | | (82), (83), (84), (85), (86), (88), (89), (90), (98), (99),
% 250.66/59.53 | | | | | (382), (387) are inconsistent by sub-proof #294.
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | Case 2:
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | (388) ~ (all_174_1 = e4) & op(e0, e1) = all_174_1 & $i(all_174_1)
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | ALPHA: (388) implies:
% 250.66/59.53 | | | | | (389) op(e0, e1) = all_174_1
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 250.66/59.53 | | | | | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 250.66/59.53 | | | | | (24), (25), (27), (28), (30), (31), (32), (33), (34), (35),
% 250.66/59.53 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 250.66/59.53 | | | | | (47), (48), (49), (51), (52), (54), (56), (57), (59), (61),
% 250.66/59.53 | | | | | (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 250.66/59.53 | | | | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 250.66/59.53 | | | | | (82), (83), (84), (85), (86), (88), (89), (90), (98), (99),
% 250.66/59.53 | | | | | (382), (389) are inconsistent by sub-proof #294.
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | End of split
% 250.66/59.53 | | | |
% 250.66/59.53 | | | End of split
% 250.66/59.53 | | |
% 250.66/59.53 | | Case 2:
% 250.66/59.53 | | |
% 250.66/59.53 | | | (390) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0,
% 250.66/59.53 | | | e0) = e1)
% 250.66/59.53 | | |
% 250.66/59.53 | | | BETA: splitting (390) gives:
% 250.66/59.53 | | |
% 250.66/59.53 | | | Case 1:
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | (391) all_252_19 = e1 & op(e1, e0) = e1
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | REF_CLOSE: (21), (98), (99), (391) are inconsistent by sub-proof #408.
% 250.66/59.53 | | | |
% 250.66/59.53 | | | Case 2:
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | (392) all_252_24 = e1 & op(e0, e0) = e1
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | ALPHA: (392) implies:
% 250.66/59.53 | | | | (393) all_252_24 = e1
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | REF_CLOSE: (1), (4), (16), (18), (21), (23), (25), (35), (37), (43),
% 250.66/59.53 | | | | (44), (47), (59), (63), (66), (74), (78), (90), (98), (393)
% 250.66/59.53 | | | | are inconsistent by sub-proof #295.
% 250.66/59.53 | | | |
% 250.66/59.53 | | | End of split
% 250.66/59.53 | | |
% 250.66/59.53 | | End of split
% 250.66/59.53 | |
% 250.66/59.53 | End of split
% 250.66/59.53 |
% 250.66/59.53 End of proof
% 250.66/59.53
% 250.66/59.53 Sub-proof #294 shows that the following formulas are inconsistent:
% 250.66/59.53 ----------------------------------------------------------------
% 250.66/59.53 (1) op(e0, e3) = e1
% 250.66/59.53 (2) ~ (all_4_2 = e4)
% 250.66/59.53 (3) ~ (all_10_2 = e4)
% 250.66/59.53 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.53 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.66/59.53 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.53 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.66/59.53 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.66/59.53 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.66/59.53 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.66/59.53 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.66/59.53 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.66/59.53 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.66/59.53 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.66/59.53 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.66/59.53 (8) all_252_21 = e1
% 250.66/59.53 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.66/59.53 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.66/59.53 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.66/59.53 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.66/59.53 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.66/59.53 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.66/59.53 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.53 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.66/59.53 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.66/59.53 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.66/59.53 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.66/59.53 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.53 (13) op(e0, all_36_2) = e3
% 250.66/59.53 (14) op(e0, e1) = all_174_1
% 250.66/59.53 (15) ~ (e2 = e0)
% 250.66/59.53 (16) all_252_19 = e2
% 250.66/59.53 (17) ~ (e1 = e0)
% 250.66/59.53 (18) ~ (all_22_2 = e3)
% 250.66/59.53 (19) all_252_13 = e0
% 250.66/59.53 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.66/59.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.66/59.53 (21) op(e2, e3) = all_10_2
% 250.66/59.53 (22) ~ (e3 = e2)
% 250.66/59.53 (23) op(e0, e0) = all_244_24
% 250.66/59.53 (24) ~ (e4 = e0)
% 250.66/59.53 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.66/59.53 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.66/59.53 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.66/59.53 (26) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.66/59.53 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.66/59.53 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.53 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.66/59.53 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.66/59.53 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.66/59.53 (28) op(e4, e2) = all_6_2
% 250.66/59.53 (29) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.66/59.53 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.53 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.53 (30) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.66/59.53 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.66/59.53 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.53 (31) op(e2, e0) = e1
% 250.66/59.53 (32) ~ (e2 = e1)
% 250.66/59.53 (33) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.66/59.53 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.66/59.53 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.66/59.53 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.66/59.53 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.66/59.53 op(e0, e1) = e0)))
% 250.66/59.53 (34) op(e0, e2) = all_28_2
% 250.66/59.53 (35) ~ (e4 = e1)
% 250.66/59.53 (36) ~ (all_28_2 = e1)
% 250.66/59.53 (37) ~ (all_6_2 = e1)
% 250.66/59.53 (38) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.66/59.53 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.66/59.53 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.66/59.53 (39) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.66/59.53 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.66/59.53 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.66/59.53 (40) op(e1, e4) = all_16_2
% 250.66/59.53 (41) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.66/59.53 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.66/59.53 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.66/59.53 (42) ~ (e3 = e0)
% 250.66/59.53 (43) all_252_2 = e0
% 250.66/59.53 (44) ~ (e3 = e1)
% 250.66/59.53 (45) op(e3, e1) = all_36_2
% 250.66/59.53 (46) ~ (all_8_2 = e1)
% 250.66/59.53 (47) op(e1, e0) = e2
% 250.66/59.53 (48) ~ (all_8_2 = e0)
% 250.66/59.53 (49) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.66/59.53 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.66/59.53 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.66/59.53 (50) op(e0, e3) = all_22_2
% 250.66/59.53 (51) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.66/59.53 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.66/59.53 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.66/59.53 (52) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.66/59.53 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.66/59.53 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.66/59.53 (53) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.66/59.53 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.66/59.53 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.66/59.53 (54) ~ (all_36_2 = e0)
% 250.66/59.53 (55) op(e4, e4) = all_244_0
% 250.66/59.53 (56) ~ (e4 = e3)
% 250.66/59.53 (57) op(e1, e1) = all_244_15
% 250.66/59.53 (58) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.66/59.53 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.66/59.53 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.66/59.53 (59) op(e0, e1) = all_20_2
% 250.66/59.53 (60) all_252_18 = e1
% 250.66/59.53 (61) ~ (all_244_15 = all_20_2)
% 250.66/59.53 (62) op(e3, e0) = all_48_2
% 250.66/59.53 (63) ~ (all_244_24 = e2)
% 250.66/59.53 (64) op(e1, e2) = all_4_2
% 250.66/59.53 (65) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.66/59.53 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.66/59.53 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.66/59.53 (66) ~ (all_48_2 = e0)
% 250.66/59.53 (67) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.66/59.53 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.66/59.53 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.66/59.53 (68) ~ (e4 = e2)
% 250.66/59.53 (69) op(e3, e2) = all_8_2
% 250.66/59.53 (70) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.66/59.53 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.66/59.53 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.66/59.53 (71) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.66/59.53 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.66/59.53 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.66/59.53 (72) ~ (all_20_2 = e4)
% 250.66/59.53 (73) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.66/59.53 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.66/59.53 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.66/59.53 (74) ~ (all_244_3 = e0)
% 250.66/59.53 (75) op(e2, e0) = all_40_2
% 250.66/59.53 (76) ~ (all_16_2 = e3)
% 250.66/59.53 (77) ~ (all_10_2 = e0)
% 250.66/59.53 (78) ~ (all_244_0 = e3)
% 250.66/59.53 (79) op(e3, e3) = all_244_3
% 250.66/59.53 (80) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.66/59.53 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.66/59.53 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.66/59.53 (81) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.66/59.53 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.66/59.53 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.66/59.53 (82) ~ (all_4_2 = e0)
% 250.66/59.53 (83) all_252_20 = e3
% 250.66/59.53
% 250.66/59.53 Begin of proof
% 250.66/59.53 |
% 250.66/59.53 | BETA: splitting (29) gives:
% 250.66/59.53 |
% 250.66/59.53 | Case 1:
% 250.66/59.53 | |
% 250.66/59.53 | | (84) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 250.66/59.53 | | e1)
% 250.66/59.53 | |
% 250.66/59.53 | | REF_CLOSE: (1), (3), (8), (9), (10), (15), (17), (19), (20), (21), (22),
% 250.66/59.53 | | (24), (32), (35), (42), (43), (44), (56), (65), (68), (84) are
% 250.66/59.53 | | inconsistent by sub-proof #346.
% 250.66/59.53 | |
% 250.66/59.53 | Case 2:
% 250.66/59.53 | |
% 250.66/59.53 | | (85) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.66/59.53 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.66/59.53 | |
% 250.66/59.53 | | BETA: splitting (85) gives:
% 250.66/59.53 | |
% 250.66/59.53 | | Case 1:
% 250.66/59.53 | | |
% 250.66/59.53 | | | (86) all_252_5 = e1 & op(e3, e2) = e1
% 250.66/59.53 | | |
% 250.66/59.53 | | | ALPHA: (86) implies:
% 250.66/59.53 | | | (87) op(e3, e2) = e1
% 250.66/59.53 | | |
% 250.66/59.53 | | | REF_CLOSE: (20), (46), (69), (87) are inconsistent by sub-proof #929.
% 250.66/59.53 | | |
% 250.66/59.53 | | Case 2:
% 250.66/59.53 | | |
% 250.66/59.53 | | | (88) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 250.66/59.53 | | | e0) = e1)
% 250.66/59.53 | | |
% 250.66/59.53 | | | BETA: splitting (88) gives:
% 250.66/59.53 | | |
% 250.66/59.53 | | | Case 1:
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | (89) all_252_10 = e1 & op(e3, e1) = e1
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | ALPHA: (89) implies:
% 250.66/59.53 | | | | (90) op(e3, e1) = e1
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | BETA: splitting (26) gives:
% 250.66/59.53 | | | |
% 250.66/59.53 | | | | Case 1:
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | (91) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 250.66/59.53 | | | | | e2) = e1)
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | REF_CLOSE: (20), (28), (37), (46), (69), (91) are inconsistent by
% 250.66/59.53 | | | | | sub-proof #928.
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | Case 2:
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | (92) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1,
% 250.66/59.53 | | | | | e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | BETA: splitting (92) gives:
% 250.66/59.53 | | | | |
% 250.66/59.53 | | | | | Case 1:
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | (93) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | ALPHA: (93) implies:
% 250.66/59.53 | | | | | | (94) all_252_8 = e1
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | BETA: splitting (12) gives:
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | Case 1:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | (95) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 &
% 250.66/59.53 | | | | | | | op(e2, e3) = e0)
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | BETA: splitting (95) gives:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (96) all_252_6 = e0 & op(e2, e4) = e0
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | ALPHA: (96) implies:
% 250.66/59.53 | | | | | | | | (97) all_252_6 = e0
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | BETA: splitting (52) gives:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (98) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 250.66/59.53 | | | | | | | | | op(e2, e3) = e4)
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | BETA: splitting (98) gives:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (99) all_252_6 = e4 & op(e2, e4) = e4
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | REF_CLOSE: (24), (97), (99) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | #387.
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (100) all_252_7 = e4 & op(e2, e3) = e4
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | ALPHA: (100) implies:
% 250.66/59.53 | | | | | | | | | | (101) op(e2, e3) = e4
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | REF_CLOSE: (3), (20), (21), (101) are inconsistent by
% 250.66/59.53 | | | | | | | | | | sub-proof #953.
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (102) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4
% 250.66/59.53 | | | | | | | | | & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0)
% 250.66/59.53 | | | | | | | | | = e4)
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | BETA: splitting (102) gives:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (103) all_252_8 = e4 & op(e2, e2) = e4
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | ALPHA: (103) implies:
% 250.66/59.53 | | | | | | | | | | (104) all_252_8 = e4
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | REF_CLOSE: (35), (94), (104) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | #864.
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (105) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 =
% 250.66/59.53 | | | | | | | | | | e4 & op(e2, e0) = e4)
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | BETA: splitting (105) gives:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (106) all_252_11 = e4 & op(e2, e1) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | ALPHA: (106) implies:
% 250.66/59.53 | | | | | | | | | | | (107) all_252_11 = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | REF_CLOSE: (15), (22), (25), (32), (42), (44), (49), (56),
% 250.66/59.53 | | | | | | | | | | | (60), (68), (94), (97), (107) are inconsistent by
% 250.66/59.53 | | | | | | | | | | | sub-proof #301.
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (108) all_252_18 = e4 & op(e2, e0) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | REF_CLOSE: (35), (60), (108) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | #328.
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | End of split
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (109) all_252_7 = e0 & op(e2, e3) = e0
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | REF_CLOSE: (20), (21), (77), (109) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | #816.
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | End of split
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | Case 2:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | (110) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 250.66/59.53 | | | | | | | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | BETA: splitting (110) gives:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (111) all_252_8 = e0 & op(e2, e2) = e0
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | REF_CLOSE: (17), (94), (111) are inconsistent by sub-proof #873.
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (112) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0
% 250.66/59.53 | | | | | | | | & op(e2, e0) = e0)
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | BETA: splitting (112) gives:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (113) all_252_11 = e0 & op(e2, e1) = e0
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | ALPHA: (113) implies:
% 250.66/59.53 | | | | | | | | | (114) all_252_11 = e0
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | BETA: splitting (52) gives:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (115) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 250.66/59.53 | | | | | | | | | | e4 & op(e2, e3) = e4)
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | BETA: splitting (115) gives:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (116) all_252_6 = e4 & op(e2, e4) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | ALPHA: (116) implies:
% 250.66/59.53 | | | | | | | | | | | (117) all_252_6 = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | BETA: splitting (25) gives:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | (118) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 250.66/59.53 | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | BETA: splitting (118) gives:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | (119) all_252_6 = e3 & op(e2, e4) = e3
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | REF_CLOSE: (56), (117), (119) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | | | #629.
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | (120) all_252_7 = e3 & op(e2, e3) = e3
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | ALPHA: (120) implies:
% 250.66/59.53 | | | | | | | | | | | | | (121) all_252_7 = e3
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | REF_CLOSE: (15), (20), (22), (31), (32), (49), (68), (75),
% 250.66/59.53 | | | | | | | | | | | | | (94), (114), (117), (121) are inconsistent by
% 250.66/59.53 | | | | | | | | | | | | | sub-proof #300.
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | (122) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 250.66/59.53 | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.66/59.53 | | | | | | | | | | | | op(e2, e0) = e3)
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | BETA: splitting (122) gives:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | (123) all_252_8 = e3 & op(e2, e2) = e3
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | REF_CLOSE: (44), (94), (123) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | | | #474.
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | (124) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 250.66/59.53 | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | BETA: splitting (124) gives:
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | | (125) all_252_11 = e3 & op(e2, e1) = e3
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | | REF_CLOSE: (42), (114), (125) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | | | | #701.
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | | (126) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | | ALPHA: (126) implies:
% 250.66/59.53 | | | | | | | | | | | | | | (127) op(e2, e0) = e3
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | | REF_CLOSE: (20), (31), (44), (127) are inconsistent by
% 250.66/59.53 | | | | | | | | | | | | | | sub-proof #399.
% 250.66/59.53 | | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (128) all_252_7 = e4 & op(e2, e3) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | ALPHA: (128) implies:
% 250.66/59.53 | | | | | | | | | | | (129) op(e2, e3) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | REF_CLOSE: (3), (20), (21), (129) are inconsistent by
% 250.66/59.53 | | | | | | | | | | | sub-proof #953.
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (130) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 250.66/59.53 | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 250.66/59.53 | | | | | | | | | | e0) = e4)
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | BETA: splitting (130) gives:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (131) all_252_8 = e4 & op(e2, e2) = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | ALPHA: (131) implies:
% 250.66/59.53 | | | | | | | | | | | (132) all_252_8 = e4
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | REF_CLOSE: (35), (94), (132) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | #864.
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | (133) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 250.66/59.53 | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | BETA: splitting (133) gives:
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | (134) all_252_11 = e4 & op(e2, e1) = e4
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | ALPHA: (134) implies:
% 250.66/59.53 | | | | | | | | | | | | (135) all_252_11 = e4
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | REF_CLOSE: (24), (114), (135) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | | #766.
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | (136) all_252_18 = e4 & op(e2, e0) = e4
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | | REF_CLOSE: (35), (60), (136) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | | | | #328.
% 250.66/59.53 | | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | End of split
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (137) all_252_18 = e0 & op(e2, e0) = e0
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | ALPHA: (137) implies:
% 250.66/59.53 | | | | | | | | | (138) op(e2, e0) = e0
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | REF_CLOSE: (17), (20), (31), (138) are inconsistent by
% 250.66/59.53 | | | | | | | | | sub-proof #901.
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | End of split
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | End of split
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | End of split
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | Case 2:
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | (139) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.66/59.53 | | | | | | op(e0, e2) = e1)
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | BETA: splitting (139) gives:
% 250.66/59.53 | | | | | |
% 250.66/59.53 | | | | | | Case 1:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | (140) all_252_14 = e1 & op(e1, e2) = e1
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | ALPHA: (140) implies:
% 250.66/59.53 | | | | | | | (141) all_252_14 = e1
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | BETA: splitting (11) gives:
% 250.66/59.53 | | | | | | |
% 250.66/59.53 | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (142) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3
% 250.66/59.53 | | | | | | | | & op(e1, e3) = e3)
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | BETA: splitting (142) gives:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (143) all_252_12 = e3 & op(e1, e4) = e3
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | REF_CLOSE: (20), (40), (76), (143) are inconsistent by
% 250.66/59.53 | | | | | | | | | sub-proof #895.
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (144) all_252_13 = e3 & op(e1, e3) = e3
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | REF_CLOSE: (19), (42), (144) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | #883.
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | End of split
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | (145) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3
% 250.66/59.53 | | | | | | | | & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) =
% 250.66/59.53 | | | | | | | | e3)
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | BETA: splitting (145) gives:
% 250.66/59.53 | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (146) all_252_14 = e3 & op(e1, e2) = e3
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | REF_CLOSE: (44), (141), (146) are inconsistent by sub-proof
% 250.66/59.53 | | | | | | | | | #299.
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | Case 2:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | (147) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 =
% 250.66/59.53 | | | | | | | | | e3 & op(e1, e0) = e3)
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | BETA: splitting (147) gives:
% 250.66/59.53 | | | | | | | | |
% 250.66/59.53 | | | | | | | | | Case 1:
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | (148) all_252_15 = e3 & op(e1, e1) = e3
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | ALPHA: (148) implies:
% 250.66/59.53 | | | | | | | | | | (149) op(e1, e1) = e3
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | GROUND_INST: instantiating (20) with all_20_2, all_174_1, e1,
% 250.66/59.53 | | | | | | | | | | e0, simplifying with (14), (59) gives:
% 250.66/59.53 | | | | | | | | | | (150) all_174_1 = all_20_2
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | GROUND_INST: instantiating (20) with all_244_15, e3, e1, e1,
% 250.66/59.53 | | | | | | | | | | simplifying with (57), (149) gives:
% 250.66/59.53 | | | | | | | | | | (151) all_244_15 = e3
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | GROUND_INST: instantiating (20) with all_36_2, e1, e1, e3,
% 250.66/59.53 | | | | | | | | | | simplifying with (45), (90) gives:
% 250.66/59.53 | | | | | | | | | | (152) all_36_2 = e1
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | REDUCE: (61), (151) imply:
% 250.66/59.53 | | | | | | | | | | (153) ~ (all_20_2 = e3)
% 250.66/59.53 | | | | | | | | | |
% 250.66/59.53 | | | | | | | | | | SIMP: (153) implies:
% 250.66/59.54 | | | | | | | | | | (154) ~ (all_20_2 = e3)
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | REDUCE: (13), (152) imply:
% 250.66/59.54 | | | | | | | | | | (155) op(e0, e1) = e3
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | REF_CLOSE: (20), (59), (154), (155) are inconsistent by
% 250.66/59.54 | | | | | | | | | | sub-proof #974.
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | (156) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | ALPHA: (156) implies:
% 250.66/59.54 | | | | | | | | | | (157) op(e1, e0) = e3
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | REF_CLOSE: (20), (22), (47), (157) are inconsistent by
% 250.66/59.54 | | | | | | | | | | sub-proof #736.
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | |
% 250.66/59.54 | | | | | | | | End of split
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | End of split
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | Case 2:
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | (158) all_252_22 = e1 & op(e0, e2) = e1
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | ALPHA: (158) implies:
% 250.66/59.54 | | | | | | | (159) op(e0, e2) = e1
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | REF_CLOSE: (20), (34), (36), (159) are inconsistent by sub-proof
% 250.66/59.54 | | | | | | | #907.
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | End of split
% 250.66/59.54 | | | | | |
% 250.66/59.54 | | | | | End of split
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | End of split
% 250.66/59.54 | | | |
% 250.66/59.54 | | | Case 2:
% 250.66/59.54 | | | |
% 250.66/59.54 | | | | (160) all_252_17 = e1 & op(e3, e0) = e1
% 250.66/59.54 | | | |
% 250.66/59.54 | | | | ALPHA: (160) implies:
% 250.66/59.54 | | | | (161) all_252_17 = e1
% 250.66/59.54 | | | |
% 250.66/59.54 | | | | BETA: splitting (26) gives:
% 250.66/59.54 | | | |
% 250.66/59.54 | | | | Case 1:
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | | (162) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 250.66/59.54 | | | | | e2) = e1)
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | | REF_CLOSE: (20), (28), (37), (46), (69), (162) are inconsistent by
% 250.66/59.54 | | | | | sub-proof #928.
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | Case 2:
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | | (163) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 250.66/59.54 | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | | BETA: splitting (163) gives:
% 250.66/59.54 | | | | |
% 250.66/59.54 | | | | | Case 1:
% 250.66/59.54 | | | | | |
% 250.66/59.54 | | | | | | (164) all_252_8 = e1 & op(e2, e2) = e1
% 250.66/59.54 | | | | | |
% 250.66/59.54 | | | | | | ALPHA: (164) implies:
% 250.66/59.54 | | | | | | (165) all_252_8 = e1
% 250.66/59.54 | | | | | |
% 250.66/59.54 | | | | | | BETA: splitting (12) gives:
% 250.66/59.54 | | | | | |
% 250.66/59.54 | | | | | | Case 1:
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | (166) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 &
% 250.66/59.54 | | | | | | | op(e2, e3) = e0)
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | BETA: splitting (166) gives:
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | (167) all_252_6 = e0 & op(e2, e4) = e0
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | ALPHA: (167) implies:
% 250.66/59.54 | | | | | | | | (168) all_252_6 = e0
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | REF_CLOSE: (2), (6), (7), (11), (15), (16), (17), (19), (20),
% 250.66/59.54 | | | | | | | | (22), (24), (30), (31), (32), (33), (35), (39), (40),
% 250.66/59.54 | | | | | | | | (42), (43), (44), (45), (47), (48), (51), (54), (56),
% 250.66/59.54 | | | | | | | | (60), (62), (64), (66), (68), (69), (70), (71), (73),
% 250.66/59.54 | | | | | | | | (74), (76), (79), (81), (83), (161), (168) are
% 250.66/59.54 | | | | | | | | inconsistent by sub-proof #305.
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | (169) all_252_7 = e0 & op(e2, e3) = e0
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | REF_CLOSE: (20), (21), (77), (169) are inconsistent by sub-proof
% 250.66/59.54 | | | | | | | | #816.
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | End of split
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | Case 2:
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | (170) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 &
% 250.66/59.54 | | | | | | | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | BETA: splitting (170) gives:
% 250.66/59.54 | | | | | | |
% 250.66/59.54 | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | (171) all_252_8 = e0 & op(e2, e2) = e0
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | REF_CLOSE: (17), (165), (171) are inconsistent by sub-proof
% 250.66/59.54 | | | | | | | | #873.
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | (172) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0
% 250.66/59.54 | | | | | | | | & op(e2, e0) = e0)
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | BETA: splitting (172) gives:
% 250.66/59.54 | | | | | | | |
% 250.66/59.54 | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | |
% 250.66/59.54 | | | | | | | | | (173) all_252_11 = e0 & op(e2, e1) = e0
% 250.66/59.54 | | | | | | | | |
% 250.66/59.54 | | | | | | | | | ALPHA: (173) implies:
% 250.66/59.54 | | | | | | | | | (174) all_252_11 = e0
% 250.66/59.54 | | | | | | | | |
% 250.66/59.54 | | | | | | | | | BETA: splitting (30) gives:
% 250.66/59.54 | | | | | | | | |
% 250.66/59.54 | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | (175) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 =
% 250.66/59.54 | | | | | | | | | | e3 & op(e3, e0) = e3)
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | BETA: splitting (175) gives:
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | (176) all_252_16 = e3 & op(e4, e0) = e3
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | ALPHA: (176) implies:
% 250.66/59.54 | | | | | | | | | | | (177) all_252_16 = e3
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | BETA: splitting (25) gives:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | (178) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 250.66/59.54 | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | BETA: splitting (178) gives:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | (179) all_252_6 = e3 & op(e2, e4) = e3
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | ALPHA: (179) implies:
% 250.66/59.54 | | | | | | | | | | | | | (180) all_252_6 = e3
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | BETA: splitting (71) gives:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | (181) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 250.66/59.54 | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | (182) all_252_0 = e2 & op(e4, e4) = e2
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 250.66/59.54 | | | | | | | | | | | | | | | (183) all_252_0 = e2
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (16), (17), (20), (22), (24), (31),
% 250.66/59.54 | | | | | | | | | | | | | | | (32), (33), (35), (39), (42), (44), (45), (47),
% 250.66/59.54 | | | | | | | | | | | | | | | (48), (54), (56), (60), (62), (66), (68), (69),
% 250.66/59.54 | | | | | | | | | | | | | | | (71), (73), (74), (79), (81), (83), (161), (177),
% 250.66/59.54 | | | | | | | | | | | | | | | (183) are inconsistent by sub-proof #306.
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | (184) all_252_2 = e2 & op(e3, e4) = e2
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 250.66/59.54 | | | | | | | | | | | | | | | (185) all_252_2 = e2
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (20), (45), (48), (54), (62), (66),
% 250.66/59.54 | | | | | | | | | | | | | | | (69), (74), (79), (185) are inconsistent by
% 250.66/59.54 | | | | | | | | | | | | | | | sub-proof #571.
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | (186) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 250.66/59.54 | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.66/59.54 | | | | | | | | | | | | | | op(e0, e4) = e2)
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (17), (19), (20), (22), (24),
% 250.66/59.54 | | | | | | | | | | | | | | (32), (35), (40), (42), (44), (47), (51), (56),
% 250.66/59.54 | | | | | | | | | | | | | | (64), (68), (76), (83), (180), (186) are
% 250.66/59.54 | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | (187) all_252_7 = e3 & op(e2, e3) = e3
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | REF_CLOSE: (3), (15), (20), (21), (22), (24), (31), (32),
% 250.66/59.54 | | | | | | | | | | | | | (35), (49), (52), (60), (68), (75), (165), (174),
% 250.66/59.54 | | | | | | | | | | | | | (187) are inconsistent by sub-proof #298.
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | (188) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 250.66/59.54 | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.66/59.54 | | | | | | | | | | | | op(e2, e0) = e3)
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | BETA: splitting (188) gives:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | (189) all_252_8 = e3 & op(e2, e2) = e3
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | ALPHA: (189) implies:
% 250.66/59.54 | | | | | | | | | | | | | (190) all_252_8 = e3
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | COMBINE_EQS: (165), (190) imply:
% 250.66/59.54 | | | | | | | | | | | | | (191) e3 = e1
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | SIMP: (191) implies:
% 250.66/59.54 | | | | | | | | | | | | | (192) e3 = e1
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | COMBINE_EQS: (177), (192) imply:
% 250.66/59.54 | | | | | | | | | | | | | (193) all_252_16 = e1
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 250.66/59.54 | | | | | | | | | | | | | (11), (15), (16), (17), (18), (19), (20), (21),
% 250.66/59.54 | | | | | | | | | | | | | (22), (24), (25), (27), (29), (30), (31), (32),
% 250.66/59.54 | | | | | | | | | | | | | (33), (35), (38), (39), (40), (42), (43), (44),
% 250.66/59.54 | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52),
% 250.66/59.54 | | | | | | | | | | | | | (54), (55), (56), (58), (59), (62), (64), (65),
% 250.66/59.54 | | | | | | | | | | | | | (66), (67), (68), (69), (71), (72), (73), (74),
% 250.66/59.54 | | | | | | | | | | | | | (75), (76), (78), (79), (80), (81), (82), (83),
% 250.66/59.54 | | | | | | | | | | | | | (165), (174), (193) are inconsistent by sub-proof
% 250.66/59.54 | | | | | | | | | | | | | #336.
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | (194) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 250.66/59.54 | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | REF_CLOSE: (20), (31), (42), (44), (174), (194) are
% 250.66/59.54 | | | | | | | | | | | | | inconsistent by sub-proof #337.
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | (195) all_252_17 = e3 & op(e3, e0) = e3
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | REF_CLOSE: (44), (161), (195) are inconsistent by sub-proof
% 250.66/59.54 | | | | | | | | | | | #341.
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | End of split
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | (196) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 =
% 250.66/59.54 | | | | | | | | | | e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0,
% 250.66/59.54 | | | | | | | | | | e0) = e3)
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | BETA: splitting (196) gives:
% 250.66/59.54 | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | (197) all_252_18 = e3 & op(e2, e0) = e3
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | ALPHA: (197) implies:
% 250.66/59.54 | | | | | | | | | | | (198) op(e2, e0) = e3
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | REF_CLOSE: (20), (31), (44), (198) are inconsistent by
% 250.66/59.54 | | | | | | | | | | | sub-proof #399.
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | (199) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 250.66/59.54 | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | BETA: splitting (199) gives:
% 250.66/59.54 | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | (200) all_252_19 = e3 & op(e1, e0) = e3
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | ALPHA: (200) implies:
% 250.66/59.54 | | | | | | | | | | | | (201) op(e1, e0) = e3
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | REF_CLOSE: (20), (22), (47), (201) are inconsistent by
% 250.66/59.54 | | | | | | | | | | | | sub-proof #736.
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | Case 2:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | (202) all_252_24 = e3 & op(e0, e0) = e3
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | ALPHA: (202) implies:
% 250.66/59.54 | | | | | | | | | | | | (203) all_252_24 = e3
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | BETA: splitting (25) gives:
% 250.66/59.54 | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | (204) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 250.66/59.54 | | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 250.66/59.54 | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | (205) all_252_6 = e3 & op(e2, e4) = e3
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | ALPHA: (205) implies:
% 250.66/59.54 | | | | | | | | | | | | | | (206) all_252_6 = e3
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 250.66/59.54 | | | | | | | | | | | | | |
% 250.66/59.54 | | | | | | | | | | | | | | Case 1:
% 250.66/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | (207) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 250.84/59.54 | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | (208) all_252_0 = e2 & op(e4, e4) = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 250.84/59.54 | | | | | | | | | | | | | | | | (209) all_252_0 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (16), (17), (20), (22), (24), (31),
% 250.84/59.54 | | | | | | | | | | | | | | | | (32), (33), (35), (39), (42), (44), (45), (47),
% 250.84/59.54 | | | | | | | | | | | | | | | | (48), (54), (56), (60), (62), (66), (68), (69),
% 250.84/59.54 | | | | | | | | | | | | | | | | (71), (73), (74), (79), (81), (83), (161), (203),
% 250.84/59.54 | | | | | | | | | | | | | | | | (209) are inconsistent by sub-proof #308.
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | (210) all_252_2 = e2 & op(e3, e4) = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 250.84/59.54 | | | | | | | | | | | | | | | | (211) all_252_2 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (20), (45), (48), (54), (62), (66),
% 250.84/59.54 | | | | | | | | | | | | | | | | (69), (74), (79), (211) are inconsistent by
% 250.84/59.54 | | | | | | | | | | | | | | | | sub-proof #571.
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | (212) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 250.84/59.54 | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.84/59.54 | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | (213) all_252_6 = e2 & op(e2, e4) = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 250.84/59.54 | | | | | | | | | | | | | | | | (214) all_252_6 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (214) imply:
% 250.84/59.54 | | | | | | | | | | | | | | | | (215) e3 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (15), (17), (20), (22), (24), (33),
% 250.84/59.54 | | | | | | | | | | | | | | | | (35), (41), (42), (44), (56), (68), (83), (203),
% 250.84/59.54 | | | | | | | | | | | | | | | | (215) are inconsistent by sub-proof #314.
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | (216) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 250.84/59.54 | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | (217) all_252_12 = e2 & op(e1, e4) = e2
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 250.84/59.54 | | | | | | | | | | | | | | | | | (218) all_252_12 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (17), (19), (20), (22), (24),
% 250.84/59.54 | | | | | | | | | | | | | | | | | (32), (35), (40), (42), (44), (47), (51), (56),
% 250.84/59.54 | | | | | | | | | | | | | | | | | (64), (68), (76), (218) are inconsistent by
% 250.84/59.54 | | | | | | | | | | | | | | | | | sub-proof #392.
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | (219) all_252_20 = e2 & op(e0, e4) = e2
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 250.84/59.54 | | | | | | | | | | | | | | | | | (220) all_252_20 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (220) imply:
% 250.84/59.54 | | | | | | | | | | | | | | | | | (221) e3 = e2
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (15), (17), (20), (22), (24), (33),
% 250.84/59.54 | | | | | | | | | | | | | | | | | (35), (41), (42), (44), (56), (68), (83), (203),
% 250.84/59.54 | | | | | | | | | | | | | | | | | (221) are inconsistent by sub-proof #314.
% 250.84/59.54 | | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | (222) all_252_7 = e3 & op(e2, e3) = e3
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | REF_CLOSE: (3), (15), (20), (21), (22), (24), (31), (32),
% 250.84/59.54 | | | | | | | | | | | | | | (35), (49), (52), (60), (68), (75), (165), (174),
% 250.84/59.54 | | | | | | | | | | | | | | (222) are inconsistent by sub-proof #298.
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | (223) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 250.84/59.54 | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 250.84/59.54 | | | | | | | | | | | | | op(e2, e0) = e3)
% 250.84/59.54 | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | BETA: splitting (223) gives:
% 250.84/59.54 | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | (224) all_252_8 = e3 & op(e2, e2) = e3
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | ALPHA: (224) implies:
% 250.84/59.54 | | | | | | | | | | | | | | (225) all_252_8 = e3
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | COMBINE_EQS: (165), (225) imply:
% 250.84/59.54 | | | | | | | | | | | | | | (226) e3 = e1
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | SIMP: (226) implies:
% 250.84/59.54 | | | | | | | | | | | | | | (227) e3 = e1
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | COMBINE_EQS: (203), (227) imply:
% 250.84/59.54 | | | | | | | | | | | | | | (228) all_252_24 = e1
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (15), (17), (20), (22), (24), (32),
% 250.84/59.54 | | | | | | | | | | | | | | (33), (35), (41), (42), (44), (53), (56), (59),
% 250.84/59.54 | | | | | | | | | | | | | | (68), (72), (83), (228) are inconsistent by
% 250.84/59.54 | | | | | | | | | | | | | | sub-proof #295.
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | (229) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 250.84/59.54 | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | | REF_CLOSE: (20), (31), (42), (44), (174), (229) are
% 250.84/59.54 | | | | | | | | | | | | | | inconsistent by sub-proof #337.
% 250.84/59.54 | | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | | |
% 250.84/59.54 | | | | | | | | | End of split
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | (230) all_252_18 = e0 & op(e2, e0) = e0
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | ALPHA: (230) implies:
% 250.84/59.54 | | | | | | | | | (231) op(e2, e0) = e0
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | REF_CLOSE: (17), (20), (31), (231) are inconsistent by
% 250.84/59.54 | | | | | | | | | sub-proof #901.
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | End of split
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | End of split
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | End of split
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | Case 2:
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | (232) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.84/59.54 | | | | | | op(e0, e2) = e1)
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | BETA: splitting (232) gives:
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | Case 1:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | (233) all_252_14 = e1 & op(e1, e2) = e1
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | ALPHA: (233) implies:
% 250.84/59.54 | | | | | | | (234) all_252_14 = e1
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (11), (15), (16), (17), (19),
% 250.84/59.54 | | | | | | | (20), (22), (23), (24), (30), (31), (32), (33), (35),
% 250.84/59.54 | | | | | | | (39), (40), (42), (43), (44), (45), (47), (48), (51),
% 250.84/59.54 | | | | | | | (53), (54), (56), (59), (60), (62), (63), (64), (66),
% 250.84/59.54 | | | | | | | (68), (69), (70), (71), (72), (73), (74), (76), (79),
% 250.84/59.54 | | | | | | | (81), (83), (161), (234) are inconsistent by sub-proof
% 250.84/59.54 | | | | | | | #304.
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | Case 2:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | (235) all_252_22 = e1 & op(e0, e2) = e1
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | ALPHA: (235) implies:
% 250.84/59.54 | | | | | | | (236) op(e0, e2) = e1
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | REF_CLOSE: (20), (34), (36), (236) are inconsistent by sub-proof
% 250.84/59.54 | | | | | | | #907.
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | End of split
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | End of split
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | End of split
% 250.84/59.54 | | | |
% 250.84/59.54 | | | End of split
% 250.84/59.54 | | |
% 250.84/59.54 | | End of split
% 250.84/59.54 | |
% 250.84/59.54 | End of split
% 250.84/59.54 |
% 250.84/59.54 End of proof
% 250.84/59.54
% 250.84/59.54 Sub-proof #295 shows that the following formulas are inconsistent:
% 250.84/59.54 ----------------------------------------------------------------
% 250.84/59.54 (1) op(e0, e3) = e1
% 250.84/59.54 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.84/59.54 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.84/59.54 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.54 (3) ~ (e2 = e0)
% 250.84/59.54 (4) ~ (e1 = e0)
% 250.84/59.54 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.54 (6) ~ (e3 = e2)
% 250.84/59.54 (7) ~ (e4 = e0)
% 250.84/59.54 (8) ~ (e2 = e1)
% 250.84/59.54 (9) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.54 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.54 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.54 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.54 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.54 op(e0, e1) = e0)))
% 250.84/59.54 (10) ~ (e4 = e1)
% 250.84/59.54 (11) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.84/59.54 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.84/59.54 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.54 (12) ~ (e3 = e0)
% 250.84/59.54 (13) ~ (e3 = e1)
% 250.84/59.54 (14) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.84/59.54 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.84/59.54 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.84/59.54 (15) ~ (e4 = e3)
% 250.84/59.54 (16) op(e0, e1) = all_20_2
% 250.84/59.54 (17) all_252_24 = e1
% 250.84/59.54 (18) ~ (e4 = e2)
% 250.84/59.54 (19) ~ (all_20_2 = e4)
% 250.84/59.54 (20) all_252_20 = e3
% 250.84/59.54
% 250.84/59.54 Begin of proof
% 250.84/59.54 |
% 250.84/59.54 | BETA: splitting (2) gives:
% 250.84/59.54 |
% 250.84/59.54 | Case 1:
% 250.84/59.54 | |
% 250.84/59.54 | | (21) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3)
% 250.84/59.54 | | = e4)
% 250.84/59.54 | |
% 250.84/59.54 | | REF_CLOSE: (1), (5), (10), (15), (20), (21) are inconsistent by sub-proof
% 250.84/59.54 | | #390.
% 250.84/59.54 | |
% 250.84/59.54 | Case 2:
% 250.84/59.54 | |
% 250.84/59.54 | | (22) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1)
% 250.84/59.54 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.54 | |
% 250.84/59.54 | | BETA: splitting (22) gives:
% 250.84/59.54 | |
% 250.84/59.54 | | Case 1:
% 250.84/59.54 | | |
% 250.84/59.54 | | | (23) all_252_22 = e4 & op(e0, e2) = e4
% 250.84/59.54 | | |
% 250.84/59.54 | | | ALPHA: (23) implies:
% 250.84/59.54 | | | (24) all_252_22 = e4
% 250.84/59.54 | | |
% 250.84/59.54 | | | BETA: splitting (9) gives:
% 250.84/59.54 | | |
% 250.84/59.54 | | | Case 1:
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | (25) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | REF_CLOSE: (4), (17), (25) are inconsistent by sub-proof #297.
% 250.84/59.54 | | | |
% 250.84/59.54 | | | Case 2:
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | (26) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3,
% 250.84/59.54 | | | | e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.84/59.54 | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.84/59.54 | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.84/59.54 | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.54 | | | | op(e0, e1) = e0))
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | ALPHA: (26) implies:
% 250.84/59.54 | | | | (27) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0,
% 250.84/59.54 | | | | e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.84/59.54 | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | BETA: splitting (27) gives:
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | Case 1:
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | | (28) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 250.84/59.54 | | | | | op(e0, e3) = e0)
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | | REF_CLOSE: (1), (4), (5), (12), (20), (28) are inconsistent by
% 250.84/59.54 | | | | | sub-proof #312.
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | Case 2:
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | | (29) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.54 | | | | | op(e0, e1) = e0)
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | | BETA: splitting (29) gives:
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | | Case 1:
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | (30) all_252_22 = e0 & op(e0, e2) = e0
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | REF_CLOSE: (7), (24), (30) are inconsistent by sub-proof #444.
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | Case 2:
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | (31) all_252_23 = e0 & op(e0, e1) = e0
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | ALPHA: (31) implies:
% 250.84/59.54 | | | | | | (32) all_252_23 = e0
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | BETA: splitting (14) gives:
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | | Case 1:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | (33) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 250.84/59.54 | | | | | | | op(e0, e3) = e2)
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | BETA: splitting (33) gives:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | (34) all_252_20 = e2 & op(e0, e4) = e2
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | ALPHA: (34) implies:
% 250.84/59.54 | | | | | | | | (35) all_252_20 = e2
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (12), (13),
% 250.84/59.54 | | | | | | | | (15), (17), (24), (35) are inconsistent by sub-proof
% 250.84/59.54 | | | | | | | | #296.
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | (36) all_252_21 = e2 & op(e0, e3) = e2
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | ALPHA: (36) implies:
% 250.84/59.54 | | | | | | | | (37) op(e0, e3) = e2
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | GROUND_INST: instantiating (5) with e1, e2, e3, e0, simplifying
% 250.84/59.54 | | | | | | | | with (1), (37) gives:
% 250.84/59.54 | | | | | | | | (38) e2 = e1
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | REDUCE: (8), (38) imply:
% 250.84/59.54 | | | | | | | | (39) $false
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | CLOSE: (39) is inconsistent.
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | End of split
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | Case 2:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | (40) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 250.84/59.54 | | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | BETA: splitting (40) gives:
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | (41) all_252_22 = e2 & op(e0, e2) = e2
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | REF_CLOSE: (18), (24), (41) are inconsistent by sub-proof #445.
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | (42) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.84/59.54 | | | | | | | | op(e0, e0) = e2)
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | BETA: splitting (42) gives:
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | | Case 1:
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | (43) all_252_23 = e2 & op(e0, e1) = e2
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | ALPHA: (43) implies:
% 250.84/59.54 | | | | | | | | | (44) all_252_23 = e2
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | REF_CLOSE: (3), (32), (44) are inconsistent by sub-proof #311.
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | Case 2:
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | (45) all_252_24 = e2 & op(e0, e0) = e2
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | ALPHA: (45) implies:
% 250.84/59.54 | | | | | | | | | (46) all_252_24 = e2
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | | REF_CLOSE: (8), (17), (46) are inconsistent by sub-proof #825.
% 250.84/59.54 | | | | | | | | |
% 250.84/59.54 | | | | | | | | End of split
% 250.84/59.54 | | | | | | | |
% 250.84/59.54 | | | | | | | End of split
% 250.84/59.54 | | | | | | |
% 250.84/59.54 | | | | | | End of split
% 250.84/59.54 | | | | | |
% 250.84/59.54 | | | | | End of split
% 250.84/59.54 | | | | |
% 250.84/59.54 | | | | End of split
% 250.84/59.54 | | | |
% 250.84/59.54 | | | End of split
% 250.84/59.54 | | |
% 250.84/59.54 | | Case 2:
% 250.84/59.54 | | |
% 250.84/59.54 | | | (47) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 250.84/59.54 | | | e0) = e4)
% 250.84/59.54 | | |
% 250.84/59.54 | | | BETA: splitting (47) gives:
% 250.84/59.54 | | |
% 250.84/59.54 | | | Case 1:
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | (48) all_252_23 = e4 & op(e0, e1) = e4
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | REF_CLOSE: (5), (16), (19), (48) are inconsistent by sub-proof #912.
% 250.84/59.54 | | | |
% 250.84/59.54 | | | Case 2:
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | (49) all_252_24 = e4 & op(e0, e0) = e4
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | ALPHA: (49) implies:
% 250.84/59.54 | | | | (50) all_252_24 = e4
% 250.84/59.54 | | | |
% 250.84/59.54 | | | | REF_CLOSE: (10), (17), (50) are inconsistent by sub-proof #514.
% 250.84/59.54 | | | |
% 250.84/59.54 | | | End of split
% 250.84/59.54 | | |
% 250.84/59.54 | | End of split
% 250.84/59.54 | |
% 250.84/59.54 | End of split
% 250.84/59.54 |
% 250.84/59.54 End of proof
% 250.84/59.54
% 250.84/59.54 Sub-proof #296 shows that the following formulas are inconsistent:
% 250.84/59.54 ----------------------------------------------------------------
% 250.84/59.54 (1) op(e0, e3) = e1
% 250.84/59.54 (2) all_252_22 = e4
% 250.84/59.54 (3) ~ (e2 = e0)
% 250.84/59.54 (4) ~ (e1 = e0)
% 250.84/59.54 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.54 (6) ~ (e3 = e2)
% 250.84/59.54 (7) ~ (e4 = e0)
% 250.84/59.54 (8) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.54 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.54 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.54 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.54 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.54 op(e0, e1) = e0)))
% 250.84/59.55 (9) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.84/59.55 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 250.84/59.55 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.55 (10) ~ (e3 = e0)
% 250.84/59.55 (11) ~ (e3 = e1)
% 250.84/59.55 (12) all_252_20 = e2
% 250.84/59.55 (13) ~ (e4 = e3)
% 250.84/59.55 (14) all_252_24 = e1
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (9) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (15) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.84/59.55 | | = e3)
% 250.84/59.55 | |
% 250.84/59.55 | | REF_CLOSE: (1), (5), (6), (11), (12), (15) are inconsistent by sub-proof
% 250.84/59.55 | | #322.
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (16) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 250.84/59.55 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (16) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (17) all_252_22 = e3 & op(e0, e2) = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (17) implies:
% 250.84/59.55 | | | (18) all_252_22 = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | COMBINE_EQS: (2), (18) imply:
% 250.84/59.55 | | | (19) e4 = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | REDUCE: (13), (19) imply:
% 250.84/59.55 | | | (20) $false
% 250.84/59.55 | | |
% 250.84/59.55 | | | CLOSE: (20) is inconsistent.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (21) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 250.84/59.55 | | | e0) = e3)
% 250.84/59.55 | | |
% 250.84/59.55 | | | BETA: splitting (21) gives:
% 250.84/59.55 | | |
% 250.84/59.55 | | | Case 1:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (22) all_252_23 = e3 & op(e0, e1) = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (22) implies:
% 250.84/59.55 | | | | (23) all_252_23 = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | BETA: splitting (8) gives:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | Case 1:
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | (24) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | REF_CLOSE: (4), (14), (24) are inconsistent by sub-proof #297.
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | Case 2:
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | (25) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.84/59.55 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.84/59.55 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.84/59.55 | | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.84/59.55 | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.55 | | | | | op(e0, e1) = e0))
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (12), (23), (25) are
% 250.84/59.55 | | | | | inconsistent by sub-proof #315.
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | End of split
% 250.84/59.55 | | | |
% 250.84/59.55 | | | Case 2:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (26) all_252_24 = e3 & op(e0, e0) = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (26) implies:
% 250.84/59.55 | | | | (27) all_252_24 = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REF_CLOSE: (11), (14), (27) are inconsistent by sub-proof #621.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | End of split
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | End of split
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #297 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.55 (2) all_252_24 = e1
% 250.84/59.55 (3) ~ (e1 = e0)
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | ALPHA: (1) implies:
% 250.84/59.55 | (4) all_252_24 = e0
% 250.84/59.55 |
% 250.84/59.55 | COMBINE_EQS: (2), (4) imply:
% 250.84/59.55 | (5) e1 = e0
% 250.84/59.55 |
% 250.84/59.55 | REDUCE: (3), (5) imply:
% 250.84/59.55 | (6) $false
% 250.84/59.55 |
% 250.84/59.55 | CLOSE: (6) is inconsistent.
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #298 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) ~ (all_10_2 = e4)
% 250.84/59.55 (2) ~ (e2 = e0)
% 250.84/59.55 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.55 (4) op(e2, e3) = all_10_2
% 250.84/59.55 (5) ~ (e3 = e2)
% 250.84/59.55 (6) ~ (e4 = e0)
% 250.84/59.55 (7) op(e2, e0) = e1
% 250.84/59.55 (8) ~ (e2 = e1)
% 250.84/59.55 (9) ~ (e4 = e1)
% 250.84/59.55 (10) all_252_7 = e3 & op(e2, e3) = e3
% 250.84/59.55 (11) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.84/59.55 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.84/59.55 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.84/59.55 (12) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.84/59.55 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.84/59.55 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.84/59.55 (13) all_252_11 = e0
% 250.84/59.55 (14) all_252_18 = e1
% 250.84/59.55 (15) ~ (e4 = e2)
% 250.84/59.55 (16) op(e2, e0) = all_40_2
% 250.84/59.55 (17) all_252_8 = e1
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | ALPHA: (10) implies:
% 250.84/59.55 | (18) all_252_7 = e3
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (12) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (19) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 250.84/59.55 | | e4)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (19) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (20) all_252_6 = e4 & op(e2, e4) = e4
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (20) implies:
% 250.84/59.55 | | | (21) all_252_6 = e4
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (2), (3), (5), (7), (8), (11), (13), (15), (16), (17), (18),
% 250.84/59.55 | | | (21) are inconsistent by sub-proof #300.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (22) all_252_7 = e4 & op(e2, e3) = e4
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (22) implies:
% 250.84/59.55 | | | (23) op(e2, e3) = e4
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (1), (3), (4), (23) are inconsistent by sub-proof #953.
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (24) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.84/59.55 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (24) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (25) all_252_8 = e4 & op(e2, e2) = e4
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (9), (17), (25) are inconsistent by sub-proof #723.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (26) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 250.84/59.55 | | | e0) = e4)
% 250.84/59.55 | | |
% 250.84/59.55 | | | BETA: splitting (26) gives:
% 250.84/59.55 | | |
% 250.84/59.55 | | | Case 1:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (27) all_252_11 = e4 & op(e2, e1) = e4
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (27) implies:
% 250.84/59.55 | | | | (28) all_252_11 = e4
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REF_CLOSE: (6), (13), (28) are inconsistent by sub-proof #766.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | Case 2:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (29) all_252_18 = e4 & op(e2, e0) = e4
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (29) implies:
% 250.84/59.55 | | | | (30) all_252_18 = e4
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REF_CLOSE: (9), (14), (30) are inconsistent by sub-proof #448.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | End of split
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | End of split
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #299 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_14 = e3 & op(e1, e2) = e3
% 250.84/59.55 (2) all_252_14 = e1
% 250.84/59.55 (3) ~ (e3 = e1)
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | ALPHA: (1) implies:
% 250.84/59.55 | (4) all_252_14 = e3
% 250.84/59.55 |
% 250.84/59.55 | COMBINE_EQS: (2), (4) imply:
% 250.84/59.55 | (5) e3 = e1
% 250.84/59.55 |
% 250.84/59.55 | SIMP: (5) implies:
% 250.84/59.55 | (6) e3 = e1
% 250.84/59.55 |
% 250.84/59.55 | REDUCE: (3), (6) imply:
% 250.84/59.55 | (7) $false
% 250.84/59.55 |
% 250.84/59.55 | CLOSE: (7) is inconsistent.
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #300 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_6 = e4
% 250.84/59.55 (2) ~ (e2 = e0)
% 250.84/59.55 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.55 (4) ~ (e3 = e2)
% 250.84/59.55 (5) op(e2, e0) = e1
% 250.84/59.55 (6) ~ (e2 = e1)
% 250.84/59.55 (7) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) |
% 250.84/59.55 (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = e2)
% 250.84/59.55 | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.84/59.55 (8) all_252_7 = e3
% 250.84/59.55 (9) all_252_11 = e0
% 250.84/59.55 (10) ~ (e4 = e2)
% 250.84/59.55 (11) op(e2, e0) = all_40_2
% 250.84/59.55 (12) all_252_8 = e1
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (7) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (13) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 250.84/59.55 | | e2)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (13) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (14) all_252_6 = e2 & op(e2, e4) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #921.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (15) all_252_7 = e2 & op(e2, e3) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (15) implies:
% 250.84/59.55 | | | (16) all_252_7 = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #939.
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (17) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.84/59.55 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (17) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (18) all_252_8 = e2 & op(e2, e2) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (6), (12), (18) are inconsistent by sub-proof #788.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (19) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 250.84/59.55 | | | e0) = e2)
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (2), (3), (5), (6), (9), (11), (19) are inconsistent by
% 250.84/59.55 | | | sub-proof #338.
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | End of split
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #301 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_6 = e0
% 250.84/59.55 (2) ~ (e2 = e0)
% 250.84/59.55 (3) ~ (e3 = e2)
% 250.84/59.55 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.84/59.55 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.84/59.55 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.84/59.55 (5) ~ (e2 = e1)
% 250.84/59.55 (6) ~ (e3 = e0)
% 250.84/59.55 (7) ~ (e3 = e1)
% 250.84/59.55 (8) all_252_11 = e4
% 250.84/59.55 (9) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) |
% 250.84/59.55 (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = e2)
% 250.84/59.55 | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.84/59.55 (10) ~ (e4 = e3)
% 250.84/59.55 (11) all_252_18 = e1
% 250.84/59.55 (12) ~ (e4 = e2)
% 250.84/59.55 (13) all_252_8 = e1
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (9) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (14) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 250.84/59.55 | | e2)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (14) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (15) all_252_6 = e2 & op(e2, e4) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (1), (2), (15) are inconsistent by sub-proof #892.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (16) all_252_7 = e2 & op(e2, e3) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (16) implies:
% 250.84/59.55 | | | (17) all_252_7 = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (13), (17) are
% 250.84/59.55 | | | inconsistent by sub-proof #303.
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (18) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.84/59.55 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (18) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (19) all_252_8 = e2 & op(e2, e2) = e2
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (5), (13), (19) are inconsistent by sub-proof #788.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (20) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 250.84/59.55 | | | e0) = e2)
% 250.84/59.55 | | |
% 250.84/59.55 | | | BETA: splitting (20) gives:
% 250.84/59.55 | | |
% 250.84/59.55 | | | Case 1:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (21) all_252_11 = e2 & op(e2, e1) = e2
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REF_CLOSE: (8), (12), (21) are inconsistent by sub-proof #302.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | Case 2:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (22) all_252_18 = e2 & op(e2, e0) = e2
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (22) implies:
% 250.84/59.55 | | | | (23) all_252_18 = e2
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | COMBINE_EQS: (11), (23) imply:
% 250.84/59.55 | | | | (24) e2 = e1
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | SIMP: (24) implies:
% 250.84/59.55 | | | | (25) e2 = e1
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REDUCE: (5), (25) imply:
% 250.84/59.55 | | | | (26) $false
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | CLOSE: (26) is inconsistent.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | End of split
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | End of split
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #302 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_11 = e2 & op(e2, e1) = e2
% 250.84/59.55 (2) all_252_11 = e4
% 250.84/59.55 (3) ~ (e4 = e2)
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | ALPHA: (1) implies:
% 250.84/59.55 | (4) all_252_11 = e2
% 250.84/59.55 |
% 250.84/59.55 | COMBINE_EQS: (2), (4) imply:
% 250.84/59.55 | (5) e4 = e2
% 250.84/59.55 |
% 250.84/59.55 | SIMP: (5) implies:
% 250.84/59.55 | (6) e4 = e2
% 250.84/59.55 |
% 250.84/59.55 | REDUCE: (3), (6) imply:
% 250.84/59.55 | (7) $false
% 250.84/59.55 |
% 250.84/59.55 | CLOSE: (7) is inconsistent.
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #303 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) all_252_6 = e0
% 250.84/59.55 (2) ~ (e3 = e2)
% 250.84/59.55 (3) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 250.84/59.55 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 250.84/59.55 | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.84/59.55 (4) all_252_7 = e2
% 250.84/59.55 (5) ~ (e3 = e0)
% 250.84/59.55 (6) ~ (e3 = e1)
% 250.84/59.55 (7) all_252_11 = e4
% 250.84/59.55 (8) ~ (e4 = e3)
% 250.84/59.55 (9) all_252_18 = e1
% 250.84/59.55 (10) all_252_8 = e1
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (3) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (11) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 250.84/59.55 | | e3)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (11) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (12) all_252_6 = e3 & op(e2, e4) = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (12) implies:
% 250.84/59.55 | | | (13) all_252_6 = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #691.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (14) all_252_7 = e3 & op(e2, e3) = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | ALPHA: (14) implies:
% 250.84/59.55 | | | (15) all_252_7 = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #939.
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (16) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.84/59.55 | | e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (16) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (17) all_252_8 = e3 & op(e2, e2) = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #474.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (18) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2,
% 250.84/59.55 | | | e0) = e3)
% 250.84/59.55 | | |
% 250.84/59.55 | | | BETA: splitting (18) gives:
% 250.84/59.55 | | |
% 250.84/59.55 | | | Case 1:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (19) all_252_11 = e3 & op(e2, e1) = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #791.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | Case 2:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (20) all_252_18 = e3 & op(e2, e0) = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (20) implies:
% 250.84/59.55 | | | | (21) all_252_18 = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | COMBINE_EQS: (9), (21) imply:
% 250.84/59.55 | | | | (22) e3 = e1
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | REDUCE: (6), (22) imply:
% 250.84/59.55 | | | | (23) $false
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | CLOSE: (23) is inconsistent.
% 250.84/59.55 | | | |
% 250.84/59.55 | | | End of split
% 250.84/59.55 | | |
% 250.84/59.55 | | End of split
% 250.84/59.55 | |
% 250.84/59.55 | End of split
% 250.84/59.55 |
% 250.84/59.55 End of proof
% 250.84/59.55
% 250.84/59.55 Sub-proof #304 shows that the following formulas are inconsistent:
% 250.84/59.55 ----------------------------------------------------------------
% 250.84/59.55 (1) op(e0, e3) = e1
% 250.84/59.55 (2) ~ (all_4_2 = e4)
% 250.84/59.55 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.84/59.55 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.84/59.55 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.55 (4) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.84/59.55 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.84/59.55 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.84/59.55 (5) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.84/59.55 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.84/59.55 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.84/59.55 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.84/59.55 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.84/59.55 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.84/59.55 (7) ~ (e2 = e0)
% 250.84/59.55 (8) all_252_19 = e2
% 250.84/59.55 (9) ~ (e1 = e0)
% 250.84/59.55 (10) all_252_13 = e0
% 250.84/59.55 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.55 (12) ~ (e3 = e2)
% 250.84/59.55 (13) all_252_17 = e1
% 250.84/59.55 (14) op(e0, e0) = all_244_24
% 250.84/59.55 (15) ~ (e4 = e0)
% 250.84/59.55 (16) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.84/59.55 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.84/59.55 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.55 (17) op(e2, e0) = e1
% 250.84/59.55 (18) ~ (e2 = e1)
% 250.84/59.55 (19) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.55 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.55 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.55 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.55 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.55 op(e0, e1) = e0)))
% 250.84/59.55 (20) ~ (e4 = e1)
% 250.84/59.55 (21) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.84/59.55 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.84/59.55 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.55 (22) op(e1, e4) = all_16_2
% 250.84/59.55 (23) ~ (e3 = e0)
% 250.84/59.55 (24) all_252_2 = e0
% 250.84/59.55 (25) ~ (e3 = e1)
% 250.84/59.55 (26) op(e3, e1) = all_36_2
% 250.84/59.55 (27) op(e1, e0) = e2
% 250.84/59.55 (28) ~ (all_8_2 = e0)
% 250.84/59.55 (29) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.84/59.55 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.84/59.55 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.84/59.55 (30) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.84/59.55 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.84/59.55 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.84/59.55 (31) ~ (all_36_2 = e0)
% 250.84/59.55 (32) ~ (e4 = e3)
% 250.84/59.55 (33) all_252_14 = e1
% 250.84/59.55 (34) op(e0, e1) = all_20_2
% 250.84/59.55 (35) all_252_18 = e1
% 250.84/59.55 (36) op(e3, e0) = all_48_2
% 250.84/59.55 (37) ~ (all_244_24 = e2)
% 250.84/59.55 (38) op(e1, e2) = all_4_2
% 250.84/59.55 (39) ~ (all_48_2 = e0)
% 250.84/59.55 (40) ~ (e4 = e2)
% 250.84/59.55 (41) op(e3, e2) = all_8_2
% 250.84/59.55 (42) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.84/59.55 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.84/59.55 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.84/59.55 (43) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.84/59.55 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.84/59.55 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.84/59.55 (44) ~ (all_20_2 = e4)
% 250.84/59.55 (45) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.84/59.55 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.84/59.55 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.84/59.55 (46) ~ (all_244_3 = e0)
% 250.84/59.55 (47) ~ (all_16_2 = e3)
% 250.84/59.55 (48) op(e3, e3) = all_244_3
% 250.84/59.55 (49) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.84/59.55 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.84/59.55 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.84/59.55 (50) all_252_20 = e3
% 250.84/59.55
% 250.84/59.55 Begin of proof
% 250.84/59.55 |
% 250.84/59.55 | BETA: splitting (6) gives:
% 250.84/59.55 |
% 250.84/59.55 | Case 1:
% 250.84/59.55 | |
% 250.84/59.55 | | (51) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 250.84/59.55 | | = e3)
% 250.84/59.55 | |
% 250.84/59.55 | | REF_CLOSE: (10), (11), (22), (23), (47), (51) are inconsistent by sub-proof
% 250.84/59.55 | | #412.
% 250.84/59.55 | |
% 250.84/59.55 | Case 2:
% 250.84/59.55 | |
% 250.84/59.55 | | (52) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1)
% 250.84/59.55 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.84/59.55 | |
% 250.84/59.55 | | BETA: splitting (52) gives:
% 250.84/59.55 | |
% 250.84/59.55 | | Case 1:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (53) all_252_14 = e3 & op(e1, e2) = e3
% 250.84/59.55 | | |
% 250.84/59.55 | | | REF_CLOSE: (25), (33), (53) are inconsistent by sub-proof #334.
% 250.84/59.55 | | |
% 250.84/59.55 | | Case 2:
% 250.84/59.55 | | |
% 250.84/59.55 | | | (54) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1,
% 250.84/59.55 | | | e0) = e3)
% 250.84/59.55 | | |
% 250.84/59.55 | | | BETA: splitting (54) gives:
% 250.84/59.55 | | |
% 250.84/59.55 | | | Case 1:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | (55) all_252_15 = e3 & op(e1, e1) = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | ALPHA: (55) implies:
% 250.84/59.55 | | | | (56) all_252_15 = e3
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | BETA: splitting (29) gives:
% 250.84/59.55 | | | |
% 250.84/59.55 | | | | Case 1:
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | (57) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 &
% 250.84/59.55 | | | | | op(e1, e3) = e4)
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | BETA: splitting (57) gives:
% 250.84/59.55 | | | | |
% 250.84/59.55 | | | | | Case 1:
% 250.84/59.55 | | | | | |
% 250.84/59.55 | | | | | | (58) all_252_12 = e4 & op(e1, e4) = e4
% 250.84/59.55 | | | | | |
% 250.84/59.55 | | | | | | ALPHA: (58) implies:
% 250.84/59.55 | | | | | | (59) all_252_12 = e4
% 250.84/59.55 | | | | | |
% 250.84/59.55 | | | | | | BETA: splitting (16) gives:
% 250.84/59.55 | | | | | |
% 250.84/59.55 | | | | | | Case 1:
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | (60) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 &
% 250.84/59.55 | | | | | | | op(e3, e0) = e3)
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | BETA: splitting (60) gives:
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | (61) all_252_16 = e3 & op(e4, e0) = e3
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | ALPHA: (61) implies:
% 250.84/59.55 | | | | | | | | (62) all_252_16 = e3
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | BETA: splitting (19) gives:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | (63) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | ALPHA: (63) implies:
% 250.84/59.55 | | | | | | | | | (64) all_252_24 = e0
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | REF_CLOSE: (11), (13), (15), (20), (21), (27), (32), (35),
% 250.84/59.55 | | | | | | | | | (40), (62), (64) are inconsistent by sub-proof
% 250.84/59.55 | | | | | | | | | #325.
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | Case 2:
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | (65) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.84/59.55 | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.84/59.55 | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0))
% 250.84/59.55 | | | | | | | | | & ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 =
% 250.84/59.55 | | | | | | | | | e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.84/59.55 | | | | | | | | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | ALPHA: (65) implies:
% 250.84/59.55 | | | | | | | | | (66) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0
% 250.84/59.55 | | | | | | | | | & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) =
% 250.84/59.55 | | | | | | | | | e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | REF_CLOSE: (7), (8), (9), (11), (17), (23), (36), (39), (62),
% 250.84/59.55 | | | | | | | | | (66) are inconsistent by sub-proof #324.
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | End of split
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | Case 2:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | (67) all_252_17 = e3 & op(e3, e0) = e3
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | REF_CLOSE: (13), (25), (67) are inconsistent by sub-proof #323.
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | End of split
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | Case 2:
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | (68) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 250.84/59.55 | | | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | BETA: splitting (68) gives:
% 250.84/59.55 | | | | | | |
% 250.84/59.55 | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | (69) all_252_18 = e3 & op(e2, e0) = e3
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | ALPHA: (69) implies:
% 250.84/59.55 | | | | | | | | (70) op(e2, e0) = e3
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | REF_CLOSE: (11), (17), (25), (70) are inconsistent by sub-proof
% 250.84/59.55 | | | | | | | | #399.
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | Case 2:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | (71) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.84/59.55 | | | | | | | | op(e0, e0) = e3)
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | BETA: splitting (71) gives:
% 250.84/59.55 | | | | | | | |
% 250.84/59.55 | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | (72) all_252_19 = e3 & op(e1, e0) = e3
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | ALPHA: (72) implies:
% 250.84/59.55 | | | | | | | | | (73) op(e1, e0) = e3
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | REF_CLOSE: (11), (12), (27), (73) are inconsistent by
% 250.84/59.55 | | | | | | | | | sub-proof #736.
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | Case 2:
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | (74) all_252_24 = e3 & op(e0, e0) = e3
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | ALPHA: (74) implies:
% 250.84/59.55 | | | | | | | | | (75) all_252_24 = e3
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | BETA: splitting (3) gives:
% 250.84/59.55 | | | | | | | | |
% 250.84/59.55 | | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | (76) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 =
% 250.84/59.55 | | | | | | | | | | e4 & op(e0, e3) = e4)
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | REF_CLOSE: (1), (11), (20), (32), (50), (76) are inconsistent
% 250.84/59.55 | | | | | | | | | | by sub-proof #390.
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | Case 2:
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | (77) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 =
% 250.84/59.55 | | | | | | | | | | e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 250.84/59.55 | | | | | | | | | | e0) = e4)
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | BETA: splitting (77) gives:
% 250.84/59.55 | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | (78) all_252_22 = e4 & op(e0, e2) = e4
% 250.84/59.55 | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | ALPHA: (78) implies:
% 250.84/59.55 | | | | | | | | | | | (79) all_252_22 = e4
% 250.84/59.55 | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | BETA: splitting (30) gives:
% 250.84/59.55 | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | | (80) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.84/59.55 | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.84/59.55 | | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | | BETA: splitting (80) gives:
% 250.84/59.55 | | | | | | | | | | | |
% 250.84/59.55 | | | | | | | | | | | | Case 1:
% 250.84/59.55 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | (81) all_252_20 = e2 & op(e0, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (12), (15), (18),
% 250.84/59.56 | | | | | | | | | | | | | (20), (22), (23), (25), (27), (29), (38), (40),
% 250.84/59.56 | | | | | | | | | | | | | (47), (50), (56), (81) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | sub-proof #309.
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | (82) all_252_21 = e2 & op(e0, e3) = e2
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | ALPHA: (82) implies:
% 250.84/59.56 | | | | | | | | | | | | | (83) op(e0, e3) = e2
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | REF_CLOSE: (1), (11), (18), (83) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | sub-proof #941.
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | (84) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.84/59.56 | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.84/59.56 | | | | | | | | | | | | op(e0, e0) = e2)
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | BETA: splitting (84) gives:
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | (85) all_252_22 = e2 & op(e0, e2) = e2
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (12), (15), (18),
% 250.84/59.56 | | | | | | | | | | | | | (20), (22), (23), (25), (27), (29), (32), (38),
% 250.84/59.56 | | | | | | | | | | | | | (40), (47), (59), (79), (85) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | sub-proof #332.
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | (86) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.84/59.56 | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | BETA: splitting (86) gives:
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | (87) all_252_23 = e2 & op(e0, e1) = e2
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | ALPHA: (87) implies:
% 250.84/59.56 | | | | | | | | | | | | | | (88) all_252_23 = e2
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | (89) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 250.84/59.56 | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | (90) all_252_0 = e2 & op(e4, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | (91) all_252_0 = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (11), (12), (13), (15), (17),
% 250.84/59.56 | | | | | | | | | | | | | | | | (18), (19), (20), (21), (23), (25), (26), (27),
% 250.84/59.56 | | | | | | | | | | | | | | | | (28), (31), (32), (35), (36), (39), (40), (41),
% 250.84/59.56 | | | | | | | | | | | | | | | | (43), (45), (46), (48), (49), (50), (75), (91) are
% 250.84/59.56 | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | (92) all_252_2 = e2 & op(e3, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | (93) all_252_2 = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (26), (28), (31), (36), (39),
% 250.84/59.56 | | | | | | | | | | | | | | | | (41), (46), (48), (93) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | | | | sub-proof #571.
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | (94) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 250.84/59.56 | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 250.84/59.56 | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | (95) all_252_6 = e2 & op(e2, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | (96) all_252_6 = e2
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (97) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (75), (97) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | | | | | | | | | | | | #533.
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (98) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.84/59.56 | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.56 | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.84/59.56 | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.84/59.56 | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | (99) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21
% 250.84/59.56 | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 &
% 250.84/59.56 | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1)
% 250.84/59.56 | | | | | | | | | | | | | | | | | = e0)
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | (100) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21
% 250.84/59.56 | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (101) all_252_20 = e0 & op(e0, e4) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (50), (101) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | #307.
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (102) all_252_21 = e0 & op(e0, e3) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (103) op(e0, e3) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (11), (103) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | sub-proof #320.
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | (104) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 250.84/59.56 | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (105) all_252_22 = e0 & op(e0, e2) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (106) all_252_22 = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (79), (106) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | #528.
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (107) all_252_23 = e0 & op(e0, e1) = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (108) all_252_23 = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (108) imply:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (109) e2 = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | SIMP: (109) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (110) e2 = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (110) imply:
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (111) all_252_6 = e0
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (12), (13), (15), (16), (17), (18), (19), (20),
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (29), (31), (32), (35), (36), (38), (39), (40),
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (41), (42), (43), (45), (46), (47), (48), (49),
% 250.84/59.56 | | | | | | | | | | | | | | | | | | | (50), (111) are inconsistent by sub-proof #305.
% 250.84/59.56 | | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | (112) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 250.84/59.56 | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (113) all_252_12 = e2 & op(e1, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 250.84/59.56 | | | | | | | | | | | | | | | | | (114) all_252_12 = e2
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (12), (15), (18),
% 250.84/59.56 | | | | | | | | | | | | | | | | | (20), (22), (23), (25), (27), (29), (32), (38),
% 250.84/59.56 | | | | | | | | | | | | | | | | | (40), (47), (114) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | | | | | | | | | | | | #392.
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | (115) all_252_20 = e2 & op(e0, e4) = e2
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (11), (12), (15), (18),
% 250.84/59.56 | | | | | | | | | | | | | | | | | (20), (22), (23), (25), (27), (29), (38), (40),
% 250.84/59.56 | | | | | | | | | | | | | | | | | (47), (50), (56), (115) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | | | | | sub-proof #309.
% 250.84/59.56 | | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | (116) all_252_24 = e2 & op(e0, e0) = e2
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | ALPHA: (116) implies:
% 250.84/59.56 | | | | | | | | | | | | | | (117) op(e0, e0) = e2
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (37), (117) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | | | sub-proof #978.
% 250.84/59.56 | | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | (118) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 250.84/59.56 | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.84/59.56 | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | BETA: splitting (118) gives:
% 250.84/59.56 | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | Case 1:
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | (119) all_252_23 = e4 & op(e0, e1) = e4
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | REF_CLOSE: (11), (34), (44), (119) are inconsistent by
% 250.84/59.56 | | | | | | | | | | | | sub-proof #912.
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | Case 2:
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | (120) all_252_24 = e4 & op(e0, e0) = e4
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | | REF_CLOSE: (32), (75), (120) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | | | | | | | #525.
% 250.84/59.56 | | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | | |
% 250.84/59.56 | | | | | | | | | End of split
% 250.84/59.56 | | | | | | | | |
% 250.84/59.56 | | | | | | | | End of split
% 250.84/59.56 | | | | | | | |
% 250.84/59.56 | | | | | | | End of split
% 250.84/59.56 | | | | | | |
% 250.84/59.56 | | | | | | End of split
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | Case 2:
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | (121) all_252_13 = e4 & op(e1, e3) = e4
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | ALPHA: (121) implies:
% 250.84/59.56 | | | | | | (122) all_252_13 = e4
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | REF_CLOSE: (10), (15), (122) are inconsistent by sub-proof #407.
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | End of split
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | Case 2:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | (123) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 250.84/59.56 | | | | | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | REF_CLOSE: (2), (11), (27), (32), (38), (40), (56), (123) are
% 250.84/59.56 | | | | | inconsistent by sub-proof #357.
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | End of split
% 250.84/59.56 | | | |
% 250.84/59.56 | | | Case 2:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | (124) all_252_19 = e3 & op(e1, e0) = e3
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | ALPHA: (124) implies:
% 250.84/59.56 | | | | (125) op(e1, e0) = e3
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | REF_CLOSE: (11), (12), (27), (125) are inconsistent by sub-proof #736.
% 250.84/59.56 | | | |
% 250.84/59.56 | | | End of split
% 250.84/59.56 | | |
% 250.84/59.56 | | End of split
% 250.84/59.56 | |
% 250.84/59.56 | End of split
% 250.84/59.56 |
% 250.84/59.56 End of proof
% 250.84/59.56
% 250.84/59.56 Sub-proof #305 shows that the following formulas are inconsistent:
% 250.84/59.56 ----------------------------------------------------------------
% 250.84/59.56 (1) ~ (all_4_2 = e4)
% 250.84/59.56 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.84/59.56 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.84/59.56 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.84/59.56 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.84/59.56 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.84/59.56 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.84/59.56 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.84/59.56 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.84/59.56 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.84/59.56 (5) all_252_6 = e0
% 250.84/59.56 (6) ~ (e2 = e0)
% 250.84/59.56 (7) all_252_19 = e2
% 250.84/59.56 (8) ~ (e1 = e0)
% 250.84/59.56 (9) all_252_13 = e0
% 250.84/59.56 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.56 (11) ~ (e3 = e2)
% 250.84/59.56 (12) all_252_17 = e1
% 250.84/59.56 (13) ~ (e4 = e0)
% 250.84/59.56 (14) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.84/59.56 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.84/59.56 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.56 (15) op(e2, e0) = e1
% 250.84/59.56 (16) ~ (e2 = e1)
% 250.84/59.56 (17) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.56 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.56 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.56 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.56 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.56 op(e0, e1) = e0)))
% 250.84/59.56 (18) ~ (e4 = e1)
% 250.84/59.56 (19) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.84/59.56 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.84/59.56 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.56 (20) op(e1, e4) = all_16_2
% 250.84/59.56 (21) ~ (e3 = e0)
% 250.84/59.56 (22) all_252_2 = e0
% 250.84/59.56 (23) ~ (e3 = e1)
% 250.84/59.56 (24) op(e3, e1) = all_36_2
% 250.84/59.56 (25) op(e1, e0) = e2
% 250.84/59.56 (26) ~ (all_8_2 = e0)
% 250.84/59.56 (27) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.84/59.56 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.84/59.56 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.84/59.56 (28) ~ (all_36_2 = e0)
% 250.84/59.56 (29) ~ (e4 = e3)
% 250.84/59.56 (30) all_252_18 = e1
% 250.84/59.56 (31) op(e3, e0) = all_48_2
% 250.84/59.56 (32) op(e1, e2) = all_4_2
% 250.84/59.56 (33) ~ (all_48_2 = e0)
% 250.84/59.56 (34) ~ (e4 = e2)
% 250.84/59.56 (35) op(e3, e2) = all_8_2
% 250.84/59.56 (36) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.84/59.56 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.84/59.56 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.84/59.56 (37) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.84/59.56 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.84/59.56 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.84/59.56 (38) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.84/59.56 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.84/59.56 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.84/59.56 (39) ~ (all_244_3 = e0)
% 250.84/59.56 (40) ~ (all_16_2 = e3)
% 250.84/59.56 (41) op(e3, e3) = all_244_3
% 250.84/59.56 (42) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.84/59.56 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.84/59.56 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.84/59.56 (43) all_252_20 = e3
% 250.84/59.56
% 250.84/59.56 Begin of proof
% 250.84/59.56 |
% 250.84/59.56 | BETA: splitting (37) gives:
% 250.84/59.56 |
% 250.84/59.56 | Case 1:
% 250.84/59.56 | |
% 250.84/59.56 | | (44) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 250.84/59.56 | | e2)
% 250.84/59.56 | |
% 250.84/59.56 | | BETA: splitting (44) gives:
% 250.84/59.56 | |
% 250.84/59.56 | | Case 1:
% 250.84/59.56 | | |
% 250.84/59.56 | | | (45) all_252_0 = e2 & op(e4, e4) = e2
% 250.84/59.56 | | |
% 250.84/59.56 | | | ALPHA: (45) implies:
% 250.84/59.56 | | | (46) all_252_0 = e2
% 250.84/59.56 | | |
% 250.84/59.56 | | | BETA: splitting (14) gives:
% 250.84/59.56 | | |
% 250.84/59.56 | | | Case 1:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | (47) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3,
% 250.84/59.56 | | | | e0) = e3)
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | BETA: splitting (47) gives:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | Case 1:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | (48) all_252_16 = e3 & op(e4, e0) = e3
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | ALPHA: (48) implies:
% 250.84/59.56 | | | | | (49) all_252_16 = e3
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (11), (12), (13), (15), (16),
% 250.84/59.56 | | | | | (17), (18), (19), (21), (23), (24), (25), (26), (28), (29),
% 250.84/59.56 | | | | | (30), (31), (33), (34), (35), (37), (38), (39), (41), (42),
% 250.84/59.56 | | | | | (43), (46), (49) are inconsistent by sub-proof #306.
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | Case 2:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | (50) all_252_17 = e3 & op(e3, e0) = e3
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | REF_CLOSE: (12), (23), (50) are inconsistent by sub-proof #323.
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | End of split
% 250.84/59.56 | | | |
% 250.84/59.56 | | | Case 2:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | (51) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.84/59.56 | | | | e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | BETA: splitting (51) gives:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | Case 1:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | (52) all_252_18 = e3 & op(e2, e0) = e3
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | ALPHA: (52) implies:
% 250.84/59.56 | | | | | (53) op(e2, e0) = e3
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | REF_CLOSE: (10), (15), (23), (53) are inconsistent by sub-proof #399.
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | Case 2:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | (54) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.84/59.56 | | | | | op(e0, e0) = e3)
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | BETA: splitting (54) gives:
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | | Case 1:
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | (55) all_252_19 = e3 & op(e1, e0) = e3
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | ALPHA: (55) implies:
% 250.84/59.56 | | | | | | (56) op(e1, e0) = e3
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | REF_CLOSE: (10), (11), (25), (56) are inconsistent by sub-proof
% 250.84/59.56 | | | | | | #736.
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | Case 2:
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | (57) all_252_24 = e3 & op(e0, e0) = e3
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | ALPHA: (57) implies:
% 250.84/59.56 | | | | | | (58) all_252_24 = e3
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (11), (12), (13), (15), (16),
% 250.84/59.56 | | | | | | (17), (18), (19), (21), (23), (24), (25), (26), (28),
% 250.84/59.56 | | | | | | (29), (30), (31), (33), (34), (35), (37), (38), (39),
% 250.84/59.56 | | | | | | (41), (42), (43), (46), (58) are inconsistent by
% 250.84/59.56 | | | | | | sub-proof #308.
% 250.84/59.56 | | | | | |
% 250.84/59.56 | | | | | End of split
% 250.84/59.56 | | | | |
% 250.84/59.56 | | | | End of split
% 250.84/59.56 | | | |
% 250.84/59.56 | | | End of split
% 250.84/59.56 | | |
% 250.84/59.56 | | Case 2:
% 250.84/59.56 | | |
% 250.84/59.56 | | | (59) all_252_2 = e2 & op(e3, e4) = e2
% 250.84/59.56 | | |
% 250.84/59.56 | | | ALPHA: (59) implies:
% 250.84/59.56 | | | (60) all_252_2 = e2
% 250.84/59.56 | | |
% 250.84/59.56 | | | REF_CLOSE: (3), (6), (10), (24), (26), (28), (31), (33), (35), (39), (41),
% 250.84/59.56 | | | (60) are inconsistent by sub-proof #571.
% 250.84/59.56 | | |
% 250.84/59.56 | | End of split
% 250.84/59.56 | |
% 250.84/59.56 | Case 2:
% 250.84/59.56 | |
% 250.84/59.56 | | (61) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.84/59.56 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.84/59.56 | |
% 250.84/59.56 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (13), (16), (18),
% 250.84/59.56 | | (20), (21), (22), (23), (25), (27), (29), (32), (34), (36), (38),
% 250.84/59.56 | | (40), (42), (61) are inconsistent by sub-proof #351.
% 250.84/59.56 | |
% 250.84/59.56 | End of split
% 250.84/59.56 |
% 250.84/59.56 End of proof
% 250.84/59.56
% 250.84/59.56 Sub-proof #306 shows that the following formulas are inconsistent:
% 250.84/59.56 ----------------------------------------------------------------
% 250.84/59.56 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.84/59.56 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.84/59.56 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.84/59.56 (2) ~ (e2 = e0)
% 250.84/59.56 (3) all_252_19 = e2
% 250.84/59.56 (4) ~ (e1 = e0)
% 250.84/59.56 (5) all_252_16 = e3
% 250.84/59.56 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.56 (7) ~ (e3 = e2)
% 250.84/59.56 (8) all_252_17 = e1
% 250.84/59.56 (9) ~ (e4 = e0)
% 250.84/59.56 (10) all_252_0 = e2
% 250.84/59.56 (11) op(e2, e0) = e1
% 250.84/59.56 (12) ~ (e2 = e1)
% 250.84/59.56 (13) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.56 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.56 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.56 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.56 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.56 op(e0, e1) = e0)))
% 250.84/59.56 (14) ~ (e4 = e1)
% 250.84/59.56 (15) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.84/59.56 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.84/59.56 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.56 (16) ~ (e3 = e0)
% 250.84/59.56 (17) ~ (e3 = e1)
% 250.84/59.56 (18) op(e3, e1) = all_36_2
% 250.84/59.56 (19) op(e1, e0) = e2
% 250.84/59.56 (20) ~ (all_8_2 = e0)
% 250.84/59.56 (21) ~ (all_36_2 = e0)
% 250.84/59.56 (22) ~ (e4 = e3)
% 250.84/59.56 (23) all_252_18 = e1
% 250.84/59.56 (24) op(e3, e0) = all_48_2
% 250.84/59.56 (25) ~ (all_48_2 = e0)
% 250.84/59.56 (26) ~ (e4 = e2)
% 250.84/59.56 (27) op(e3, e2) = all_8_2
% 250.84/59.56 (28) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.84/59.56 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.84/59.56 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.84/59.56 (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.84/59.56 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.84/59.56 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.84/59.56 (30) ~ (all_244_3 = e0)
% 250.84/59.56 (31) op(e3, e3) = all_244_3
% 250.84/59.56 (32) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.84/59.56 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.84/59.56 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.84/59.56 (33) all_252_20 = e3
% 250.84/59.56
% 250.84/59.56 Begin of proof
% 250.84/59.56 |
% 250.84/59.56 | BETA: splitting (13) gives:
% 250.84/59.56 |
% 250.84/59.56 | Case 1:
% 250.84/59.56 | |
% 250.84/59.56 | | (34) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.56 | |
% 250.84/59.56 | | ALPHA: (34) implies:
% 250.84/59.56 | | (35) all_252_24 = e0
% 250.84/59.56 | |
% 250.84/59.56 | | REF_CLOSE: (5), (6), (8), (9), (14), (15), (19), (22), (23), (26), (35) are
% 250.84/59.56 | | inconsistent by sub-proof #325.
% 250.84/59.56 | |
% 250.84/59.56 | Case 2:
% 250.84/59.56 | |
% 250.84/59.56 | | (36) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.84/59.56 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.84/59.56 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.84/59.56 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.84/59.56 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.84/59.56 | |
% 250.84/59.56 | | ALPHA: (36) implies:
% 250.84/59.56 | | (37) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.84/59.56 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.84/59.56 | | op(e1, e0) = e0)
% 250.84/59.56 | |
% 250.84/59.56 | | BETA: splitting (37) gives:
% 250.84/59.56 | |
% 250.84/59.56 | | Case 1:
% 250.84/59.56 | | |
% 250.84/59.56 | | | (38) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3,
% 250.84/59.56 | | | e0) = e0)
% 250.84/59.56 | | |
% 250.84/59.56 | | | BETA: splitting (38) gives:
% 250.84/59.56 | | |
% 250.84/59.56 | | | Case 1:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | (39) all_252_16 = e0 & op(e4, e0) = e0
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | ALPHA: (39) implies:
% 250.84/59.56 | | | | (40) all_252_16 = e0
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | COMBINE_EQS: (5), (40) imply:
% 250.84/59.56 | | | | (41) e3 = e0
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | REDUCE: (16), (41) imply:
% 250.84/59.56 | | | | (42) $false
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | CLOSE: (42) is inconsistent.
% 250.84/59.56 | | | |
% 250.84/59.56 | | | Case 2:
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | (43) all_252_17 = e0 & op(e3, e0) = e0
% 250.84/59.56 | | | |
% 250.84/59.56 | | | | REF_CLOSE: (6), (24), (25), (43) are inconsistent by sub-proof #573.
% 250.84/59.56 | | | |
% 250.84/59.56 | | | End of split
% 250.84/59.56 | | |
% 250.84/59.56 | | Case 2:
% 250.84/59.56 | | |
% 250.84/59.56 | | | (44) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.84/59.56 | | | e0) = e0)
% 250.84/59.56 | | |
% 250.84/59.56 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (14),
% 250.84/59.56 | | | (17), (18), (20), (21), (22), (24), (25), (26), (27), (28),
% 250.84/59.56 | | | (29), (30), (31), (32), (33), (44) are inconsistent by
% 250.84/59.56 | | | sub-proof #396.
% 250.84/59.56 | | |
% 250.84/59.56 | | End of split
% 250.84/59.56 | |
% 250.84/59.56 | End of split
% 250.84/59.56 |
% 250.84/59.56 End of proof
% 250.84/59.56
% 250.84/59.56 Sub-proof #307 shows that the following formulas are inconsistent:
% 250.84/59.56 ----------------------------------------------------------------
% 250.84/59.56 (1) all_252_20 = e0 & op(e0, e4) = e0
% 250.84/59.56 (2) all_252_20 = e3
% 250.84/59.56 (3) ~ (e3 = e0)
% 250.84/59.56
% 250.84/59.56 Begin of proof
% 250.84/59.56 |
% 250.84/59.56 | ALPHA: (1) implies:
% 250.84/59.56 | (4) all_252_20 = e0
% 250.84/59.56 |
% 250.84/59.56 | COMBINE_EQS: (2), (4) imply:
% 250.84/59.56 | (5) e3 = e0
% 250.84/59.56 |
% 250.84/59.56 | SIMP: (5) implies:
% 250.84/59.56 | (6) e3 = e0
% 250.84/59.56 |
% 250.84/59.56 | REDUCE: (3), (6) imply:
% 250.84/59.56 | (7) $false
% 250.84/59.56 |
% 250.84/59.56 | CLOSE: (7) is inconsistent.
% 250.84/59.56 |
% 250.84/59.56 End of proof
% 250.84/59.56
% 250.84/59.56 Sub-proof #308 shows that the following formulas are inconsistent:
% 250.84/59.56 ----------------------------------------------------------------
% 250.84/59.56 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.84/59.56 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.84/59.56 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.84/59.56 (2) ~ (e2 = e0)
% 250.84/59.56 (3) all_252_19 = e2
% 250.84/59.56 (4) ~ (e1 = e0)
% 250.84/59.56 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.84/59.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.84/59.56 (6) ~ (e3 = e2)
% 250.84/59.56 (7) all_252_17 = e1
% 250.84/59.56 (8) ~ (e4 = e0)
% 250.84/59.56 (9) all_252_0 = e2
% 250.84/59.56 (10) op(e2, e0) = e1
% 250.84/59.56 (11) ~ (e2 = e1)
% 250.84/59.56 (12) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.84/59.56 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.84/59.56 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.84/59.56 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.84/59.56 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.84/59.56 op(e0, e1) = e0)))
% 250.84/59.56 (13) ~ (e4 = e1)
% 250.84/59.56 (14) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.84/59.56 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.84/59.56 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.84/59.56 (15) ~ (e3 = e0)
% 250.84/59.56 (16) ~ (e3 = e1)
% 250.84/59.56 (17) op(e3, e1) = all_36_2
% 250.84/59.56 (18) all_252_24 = e3
% 250.84/59.56 (19) op(e1, e0) = e2
% 250.84/59.56 (20) ~ (all_8_2 = e0)
% 250.84/59.56 (21) ~ (all_36_2 = e0)
% 250.84/59.56 (22) ~ (e4 = e3)
% 250.84/59.56 (23) all_252_18 = e1
% 250.84/59.56 (24) op(e3, e0) = all_48_2
% 250.84/59.56 (25) ~ (all_48_2 = e0)
% 250.84/59.56 (26) ~ (e4 = e2)
% 250.84/59.56 (27) op(e3, e2) = all_8_2
% 250.84/59.56 (28) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.84/59.56 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.84/59.56 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.84/59.56 (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.84/59.56 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.84/59.56 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.84/59.56 (30) ~ (all_244_3 = e0)
% 250.84/59.56 (31) op(e3, e3) = all_244_3
% 250.84/59.56 (32) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.84/59.56 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.84/59.56 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.84/59.56 (33) all_252_20 = e3
% 250.84/59.56
% 250.84/59.56 Begin of proof
% 250.84/59.56 |
% 250.84/59.56 | BETA: splitting (12) gives:
% 250.84/59.56 |
% 250.84/59.56 | Case 1:
% 250.84/59.56 | |
% 250.84/59.56 | | (34) all_252_24 = e0 & op(e0, e0) = e0
% 250.84/59.56 | |
% 250.84/59.56 | | ALPHA: (34) implies:
% 250.84/59.56 | | (35) all_252_24 = e0
% 250.84/59.56 | |
% 250.84/59.56 | | REF_CLOSE: (15), (18), (35) are inconsistent by sub-proof #343.
% 250.84/59.56 | |
% 250.84/59.56 | Case 2:
% 250.84/59.56 | |
% 250.84/59.56 | | (36) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.84/59.56 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.84/59.56 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.84/59.56 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.84/59.56 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.84/59.56 | |
% 250.84/59.56 | | ALPHA: (36) implies:
% 250.84/59.56 | | (37) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.84/59.56 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.84/59.56 | | op(e1, e0) = e0)
% 250.84/59.56 | |
% 250.84/59.56 | | BETA: splitting (14) gives:
% 250.84/59.56 | |
% 250.84/59.56 | | Case 1:
% 250.84/59.56 | | |
% 250.84/59.56 | | | (38) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3,
% 250.84/59.56 | | | e0) = e4)
% 250.84/59.56 | | |
% 250.84/59.56 | | | BETA: splitting (38) gives:
% 250.84/59.57 | | |
% 250.84/59.57 | | | Case 1:
% 250.84/59.57 | | | |
% 250.84/59.57 | | | | (39) all_252_16 = e4 & op(e4, e0) = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | ALPHA: (39) implies:
% 250.88/59.57 | | | | (40) all_252_16 = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (37) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (41) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.88/59.57 | | | | | op(e3, e0) = e0)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (41) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (42) all_252_16 = e0 & op(e4, e0) = e0
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (42) implies:
% 250.88/59.57 | | | | | | (43) all_252_16 = e0
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | COMBINE_EQS: (40), (43) imply:
% 250.88/59.57 | | | | | | (44) e4 = e0
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REDUCE: (8), (44) imply:
% 250.88/59.57 | | | | | | (45) $false
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | CLOSE: (45) is inconsistent.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (46) all_252_17 = e0 & op(e3, e0) = e0
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (5), (24), (25), (46) are inconsistent by sub-proof #573.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (47) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.88/59.57 | | | | | op(e1, e0) = e0)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13),
% 250.88/59.57 | | | | | (16), (17), (20), (21), (22), (24), (25), (26), (27), (28),
% 250.88/59.57 | | | | | (29), (30), (31), (32), (33), (47) are inconsistent by
% 250.88/59.57 | | | | | sub-proof #396.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (48) all_252_17 = e4 & op(e3, e0) = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REF_CLOSE: (7), (13), (48) are inconsistent by sub-proof #327.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | Case 2:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (49) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.57 | | | e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 | | |
% 250.88/59.57 | | | BETA: splitting (49) gives:
% 250.88/59.57 | | |
% 250.88/59.57 | | | Case 1:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (50) all_252_18 = e4 & op(e2, e0) = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | ALPHA: (50) implies:
% 250.88/59.57 | | | | (51) all_252_18 = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REF_CLOSE: (13), (23), (51) are inconsistent by sub-proof #448.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (52) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.88/59.57 | | | | e0) = e4)
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (52) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (53) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | ALPHA: (53) implies:
% 250.88/59.57 | | | | | (54) op(e1, e0) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (5), (19), (26), (54) are inconsistent by sub-proof #829.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (55) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (18), (22), (55) are inconsistent by sub-proof #525.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | End of split
% 250.88/59.57 | |
% 250.88/59.57 | End of split
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #309 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) ~ (all_4_2 = e4)
% 250.88/59.57 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.57 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.57 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.57 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.88/59.57 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.88/59.57 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.57 (4) ~ (e1 = e0)
% 250.88/59.57 (5) all_252_13 = e0
% 250.88/59.57 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.57 (7) ~ (e3 = e2)
% 250.88/59.57 (8) ~ (e4 = e0)
% 250.88/59.57 (9) ~ (e2 = e1)
% 250.88/59.57 (10) ~ (e4 = e1)
% 250.88/59.57 (11) op(e1, e4) = all_16_2
% 250.88/59.57 (12) ~ (e3 = e0)
% 250.88/59.57 (13) ~ (e3 = e1)
% 250.88/59.57 (14) op(e1, e0) = e2
% 250.88/59.57 (15) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.57 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.57 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.57 (16) all_252_20 = e2 & op(e0, e4) = e2
% 250.88/59.57 (17) op(e1, e2) = all_4_2
% 250.88/59.57 (18) all_252_15 = e3
% 250.88/59.57 (19) ~ (e4 = e2)
% 250.88/59.57 (20) ~ (all_16_2 = e3)
% 250.88/59.57 (21) all_252_20 = e3
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | ALPHA: (16) implies:
% 250.88/59.57 | (22) all_252_20 = e2
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (21), (22) imply:
% 250.88/59.57 | (23) e3 = e2
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (18), (23) imply:
% 250.88/59.57 | (24) all_252_15 = e2
% 250.88/59.57 |
% 250.88/59.57 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.88/59.57 | (13), (14), (15), (17), (19), (20), (24) are inconsistent by
% 250.88/59.57 | sub-proof #404.
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #310 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) op(e0, e3) = e1
% 250.88/59.57 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.57 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.88/59.57 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 (3) all_252_21 = e1
% 250.88/59.57 (4) ~ (e2 = e0)
% 250.88/59.57 (5) ~ (e1 = e0)
% 250.88/59.57 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.57 (7) ~ (e3 = e2)
% 250.88/59.57 (8) op(e0, e0) = all_244_24
% 250.88/59.57 (9) ~ (e4 = e0)
% 250.88/59.57 (10) ~ (e2 = e1)
% 250.88/59.57 (11) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.57 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.57 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.57 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.57 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 op(e0, e1) = e0)))
% 250.88/59.57 (12) ~ (e4 = e1)
% 250.88/59.57 (13) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.88/59.57 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.88/59.57 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.57 (14) ~ (e3 = e0)
% 250.88/59.57 (15) ~ (e3 = e1)
% 250.88/59.57 (16) all_252_24 = e3
% 250.88/59.57 (17) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.88/59.57 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.88/59.57 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.88/59.57 (18) ~ (e4 = e3)
% 250.88/59.57 (19) op(e0, e1) = all_20_2
% 250.88/59.57 (20) ~ (all_244_24 = e2)
% 250.88/59.57 (21) ~ (e4 = e2)
% 250.88/59.57 (22) ~ (all_20_2 = e4)
% 250.88/59.57 (23) all_252_20 = e3
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | BETA: splitting (2) gives:
% 250.88/59.57 |
% 250.88/59.57 | Case 1:
% 250.88/59.57 | |
% 250.88/59.57 | | (24) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3)
% 250.88/59.57 | | = e4)
% 250.88/59.57 | |
% 250.88/59.57 | | REF_CLOSE: (1), (6), (12), (18), (23), (24) are inconsistent by sub-proof
% 250.88/59.57 | | #390.
% 250.88/59.57 | |
% 250.88/59.57 | Case 2:
% 250.88/59.57 | |
% 250.88/59.57 | | (25) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1)
% 250.88/59.57 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 | |
% 250.88/59.57 | | BETA: splitting (25) gives:
% 250.88/59.57 | |
% 250.88/59.57 | | Case 1:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (26) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.57 | | |
% 250.88/59.57 | | | ALPHA: (26) implies:
% 250.88/59.57 | | | (27) all_252_22 = e4
% 250.88/59.57 | | |
% 250.88/59.57 | | | BETA: splitting (11) gives:
% 250.88/59.57 | | |
% 250.88/59.57 | | | Case 1:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (28) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | ALPHA: (28) implies:
% 250.88/59.57 | | | | (29) all_252_24 = e0
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REF_CLOSE: (14), (16), (29) are inconsistent by sub-proof #343.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (30) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3,
% 250.88/59.57 | | | | e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.88/59.57 | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.88/59.57 | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.88/59.57 | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 | | | | op(e0, e1) = e0))
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | ALPHA: (30) implies:
% 250.88/59.57 | | | | (31) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0,
% 250.88/59.57 | | | | e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.88/59.57 | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (17) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (32) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 &
% 250.88/59.57 | | | | | op(e0, e3) = e2)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (32) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (33) all_252_20 = e2 & op(e0, e4) = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (33) implies:
% 250.88/59.57 | | | | | | (34) all_252_20 = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | COMBINE_EQS: (23), (34) imply:
% 250.88/59.57 | | | | | | (35) e3 = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13),
% 250.88/59.57 | | | | | | (14), (15), (16), (18), (21), (23), (35) are inconsistent
% 250.88/59.57 | | | | | | by sub-proof #314.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (36) all_252_21 = e2 & op(e0, e3) = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (36) implies:
% 250.88/59.57 | | | | | | (37) op(e0, e3) = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (1), (6), (10), (37) are inconsistent by sub-proof #941.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (38) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 &
% 250.88/59.57 | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (38) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (39) all_252_22 = e2 & op(e0, e2) = e2
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (21), (27), (39) are inconsistent by sub-proof #355.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (40) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.88/59.57 | | | | | | op(e0, e0) = e2)
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | BETA: splitting (40) gives:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | Case 1:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (41) all_252_23 = e2 & op(e0, e1) = e2
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | ALPHA: (41) implies:
% 250.88/59.57 | | | | | | | (42) all_252_23 = e2
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | BETA: splitting (31) gives:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | Case 1:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | (43) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 250.88/59.57 | | | | | | | | op(e0, e3) = e0)
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | REF_CLOSE: (1), (5), (6), (14), (23), (43) are inconsistent by
% 250.88/59.57 | | | | | | | | sub-proof #312.
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | Case 2:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | (44) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 | | | | | | | | op(e0, e1) = e0)
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | BETA: splitting (44) gives:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | Case 1:
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | (45) all_252_22 = e0 & op(e0, e2) = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | ALPHA: (45) implies:
% 250.88/59.57 | | | | | | | | | (46) all_252_22 = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | REF_CLOSE: (9), (27), (46) are inconsistent by sub-proof #528.
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | Case 2:
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | (47) all_252_23 = e0 & op(e0, e1) = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | ALPHA: (47) implies:
% 250.88/59.57 | | | | | | | | | (48) all_252_23 = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | REF_CLOSE: (4), (42), (48) are inconsistent by sub-proof #311.
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | End of split
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | End of split
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | Case 2:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (49) all_252_24 = e2 & op(e0, e0) = e2
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | ALPHA: (49) implies:
% 250.88/59.57 | | | | | | | (50) op(e0, e0) = e2
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REF_CLOSE: (6), (8), (20), (50) are inconsistent by sub-proof
% 250.88/59.57 | | | | | | | #978.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | End of split
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | Case 2:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (51) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 250.88/59.57 | | | e0) = e4)
% 250.88/59.57 | | |
% 250.88/59.57 | | | BETA: splitting (51) gives:
% 250.88/59.57 | | |
% 250.88/59.57 | | | Case 1:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (52) all_252_23 = e4 & op(e0, e1) = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REF_CLOSE: (6), (19), (22), (52) are inconsistent by sub-proof #912.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (53) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REF_CLOSE: (16), (18), (53) are inconsistent by sub-proof #421.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | End of split
% 250.88/59.57 | |
% 250.88/59.57 | End of split
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #311 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) all_252_23 = e2
% 250.88/59.57 (2) all_252_23 = e0
% 250.88/59.57 (3) ~ (e2 = e0)
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (1), (2) imply:
% 250.88/59.57 | (4) e2 = e0
% 250.88/59.57 |
% 250.88/59.57 | SIMP: (4) implies:
% 250.88/59.57 | (5) e2 = e0
% 250.88/59.57 |
% 250.88/59.57 | REDUCE: (3), (5) imply:
% 250.88/59.57 | (6) $false
% 250.88/59.57 |
% 250.88/59.57 | CLOSE: (6) is inconsistent.
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #312 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) op(e0, e3) = e1
% 250.88/59.57 (2) ~ (e1 = e0)
% 250.88/59.57 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.57 (4) ~ (e3 = e0)
% 250.88/59.57 (5) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.88/59.57 (6) all_252_20 = e3
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | BETA: splitting (5) gives:
% 250.88/59.57 |
% 250.88/59.57 | Case 1:
% 250.88/59.57 | |
% 250.88/59.57 | | (7) all_252_20 = e0 & op(e0, e4) = e0
% 250.88/59.57 | |
% 250.88/59.57 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #313.
% 250.88/59.57 | |
% 250.88/59.57 | Case 2:
% 250.88/59.57 | |
% 250.88/59.57 | | (8) all_252_21 = e0 & op(e0, e3) = e0
% 250.88/59.57 | |
% 250.88/59.57 | | ALPHA: (8) implies:
% 250.88/59.57 | | (9) op(e0, e3) = e0
% 250.88/59.57 | |
% 250.88/59.57 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #320.
% 250.88/59.57 | |
% 250.88/59.57 | End of split
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #313 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) all_252_20 = e0 & op(e0, e4) = e0
% 250.88/59.57 (2) all_252_20 = e3
% 250.88/59.57 (3) ~ (e3 = e0)
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | ALPHA: (1) implies:
% 250.88/59.57 | (4) all_252_20 = e0
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.57 | (5) e3 = e0
% 250.88/59.57 |
% 250.88/59.57 | REDUCE: (3), (5) imply:
% 250.88/59.57 | (6) $false
% 250.88/59.57 |
% 250.88/59.57 | CLOSE: (6) is inconsistent.
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #314 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) op(e0, e3) = e1
% 250.88/59.57 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.57 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.88/59.57 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 (3) all_252_21 = e1
% 250.88/59.57 (4) ~ (e2 = e0)
% 250.88/59.57 (5) ~ (e1 = e0)
% 250.88/59.57 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.57 (7) ~ (e3 = e2)
% 250.88/59.57 (8) e3 = e2
% 250.88/59.57 (9) ~ (e4 = e0)
% 250.88/59.57 (10) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.57 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.57 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.57 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.57 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 op(e0, e1) = e0)))
% 250.88/59.57 (11) ~ (e4 = e1)
% 250.88/59.57 (12) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.88/59.57 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.88/59.57 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.57 (13) ~ (e3 = e0)
% 250.88/59.57 (14) ~ (e3 = e1)
% 250.88/59.57 (15) all_252_24 = e3
% 250.88/59.57 (16) ~ (e4 = e3)
% 250.88/59.57 (17) ~ (e4 = e2)
% 250.88/59.57 (18) all_252_20 = e3
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (8), (15) imply:
% 250.88/59.57 | (19) all_252_24 = e2
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (8), (18) imply:
% 250.88/59.57 | (20) all_252_20 = e2
% 250.88/59.57 |
% 250.88/59.57 | BETA: splitting (12) gives:
% 250.88/59.57 |
% 250.88/59.57 | Case 1:
% 250.88/59.57 | |
% 250.88/59.57 | | (21) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.88/59.57 | | = e3)
% 250.88/59.57 | |
% 250.88/59.57 | | REF_CLOSE: (1), (6), (7), (14), (20), (21) are inconsistent by sub-proof
% 250.88/59.57 | | #322.
% 250.88/59.57 | |
% 250.88/59.57 | Case 2:
% 250.88/59.57 | |
% 250.88/59.57 | | (22) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 250.88/59.57 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.57 | |
% 250.88/59.57 | | BETA: splitting (22) gives:
% 250.88/59.57 | |
% 250.88/59.57 | | Case 1:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (23) all_252_22 = e3 & op(e0, e2) = e3
% 250.88/59.57 | | |
% 250.88/59.57 | | | ALPHA: (23) implies:
% 250.88/59.57 | | | (24) all_252_22 = e3
% 250.88/59.57 | | |
% 250.88/59.57 | | | BETA: splitting (2) gives:
% 250.88/59.57 | | |
% 250.88/59.57 | | | Case 1:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (25) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0,
% 250.88/59.57 | | | | e3) = e4)
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (25) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (26) all_252_20 = e4 & op(e0, e4) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (17), (20), (26) are inconsistent by sub-proof #543.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (27) all_252_21 = e4 & op(e0, e3) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (3), (11), (27) are inconsistent by sub-proof #344.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (28) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0,
% 250.88/59.57 | | | | e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (28) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (29) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | REF_CLOSE: (16), (24), (29) are inconsistent by sub-proof #321.
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (30) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.88/59.57 | | | | | op(e0, e0) = e4)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (30) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (31) all_252_23 = e4 & op(e0, e1) = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (31) implies:
% 250.88/59.57 | | | | | | (32) all_252_23 = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | BETA: splitting (10) gives:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | Case 1:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (33) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REF_CLOSE: (4), (19), (33) are inconsistent by sub-proof #424.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | Case 2:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (34) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.88/59.57 | | | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.88/59.57 | | | | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 =
% 250.88/59.57 | | | | | | | e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 250.88/59.57 | | | | | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.88/59.57 | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | ALPHA: (34) implies:
% 250.88/59.57 | | | | | | | (35) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 250.88/59.57 | | | | | | | op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.88/59.57 | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | BETA: splitting (35) gives:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | Case 1:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | (36) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 250.88/59.57 | | | | | | | | op(e0, e3) = e0)
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (20), (36) are inconsistent by
% 250.88/59.57 | | | | | | | | sub-proof #319.
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | Case 2:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | (37) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 | | | | | | | | op(e0, e1) = e0)
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | BETA: splitting (37) gives:
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | | Case 1:
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | (38) all_252_22 = e0 & op(e0, e2) = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | ALPHA: (38) implies:
% 250.88/59.57 | | | | | | | | | (39) all_252_22 = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | REF_CLOSE: (13), (24), (39) are inconsistent by sub-proof
% 250.88/59.57 | | | | | | | | | #318.
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | Case 2:
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | (40) all_252_23 = e0 & op(e0, e1) = e0
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | | REF_CLOSE: (9), (32), (40) are inconsistent by sub-proof #317.
% 250.88/59.57 | | | | | | | | |
% 250.88/59.57 | | | | | | | | End of split
% 250.88/59.57 | | | | | | | |
% 250.88/59.57 | | | | | | | End of split
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | End of split
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (41) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (41) implies:
% 250.88/59.57 | | | | | | (42) all_252_24 = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (17), (19), (42) are inconsistent by sub-proof #492.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | Case 2:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (43) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 250.88/59.57 | | | e0) = e3)
% 250.88/59.57 | | |
% 250.88/59.57 | | | BETA: splitting (43) gives:
% 250.88/59.57 | | |
% 250.88/59.57 | | | Case 1:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (44) all_252_23 = e3 & op(e0, e1) = e3
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | ALPHA: (44) implies:
% 250.88/59.57 | | | | (45) all_252_23 = e3
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | BETA: splitting (2) gives:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | Case 1:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (46) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 250.88/59.57 | | | | | op(e0, e3) = e4)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (46) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (47) all_252_20 = e4 & op(e0, e4) = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (17), (20), (47) are inconsistent by sub-proof #543.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (48) all_252_21 = e4 & op(e0, e3) = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | REF_CLOSE: (3), (11), (48) are inconsistent by sub-proof #344.
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | Case 2:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | (49) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 250.88/59.57 | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | BETA: splitting (49) gives:
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | | Case 1:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (50) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | ALPHA: (50) implies:
% 250.88/59.57 | | | | | | (51) all_252_22 = e4
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | BETA: splitting (10) gives:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | Case 1:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (52) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REF_CLOSE: (4), (19), (52) are inconsistent by sub-proof #424.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | Case 2:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (53) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.88/59.57 | | | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.88/59.57 | | | | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 =
% 250.88/59.57 | | | | | | | e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 250.88/59.57 | | | | | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.88/59.57 | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REF_CLOSE: (1), (4), (5), (6), (9), (13), (20), (45), (51), (53)
% 250.88/59.57 | | | | | | | are inconsistent by sub-proof #315.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | End of split
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | Case 2:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | (54) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.88/59.57 | | | | | | op(e0, e0) = e4)
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | BETA: splitting (54) gives:
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | | Case 1:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (55) all_252_23 = e4 & op(e0, e1) = e4
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | ALPHA: (55) implies:
% 250.88/59.57 | | | | | | | (56) all_252_23 = e4
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | COMBINE_EQS: (45), (56) imply:
% 250.88/59.57 | | | | | | | (57) e4 = e3
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REDUCE: (16), (57) imply:
% 250.88/59.57 | | | | | | | (58) $false
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | CLOSE: (58) is inconsistent.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | Case 2:
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | (59) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | ALPHA: (59) implies:
% 250.88/59.57 | | | | | | | (60) all_252_24 = e4
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | | REF_CLOSE: (17), (19), (60) are inconsistent by sub-proof #492.
% 250.88/59.57 | | | | | | |
% 250.88/59.57 | | | | | | End of split
% 250.88/59.57 | | | | | |
% 250.88/59.57 | | | | | End of split
% 250.88/59.57 | | | | |
% 250.88/59.57 | | | | End of split
% 250.88/59.57 | | | |
% 250.88/59.57 | | | Case 2:
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | (61) all_252_24 = e3 & op(e0, e0) = e3
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | REDUCE: (7), (8) imply:
% 250.88/59.57 | | | | (62) $false
% 250.88/59.57 | | | |
% 250.88/59.57 | | | | CLOSE: (62) is inconsistent.
% 250.88/59.57 | | | |
% 250.88/59.57 | | | End of split
% 250.88/59.57 | | |
% 250.88/59.57 | | End of split
% 250.88/59.57 | |
% 250.88/59.57 | End of split
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #315 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) op(e0, e3) = e1
% 250.88/59.57 (2) all_252_22 = e4
% 250.88/59.57 (3) ~ (e2 = e0)
% 250.88/59.57 (4) ~ (e1 = e0)
% 250.88/59.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.57 (6) ~ (e4 = e0)
% 250.88/59.57 (7) all_252_23 = e3
% 250.88/59.57 (8) ~ (e3 = e0)
% 250.88/59.57 (9) all_252_20 = e2
% 250.88/59.57 (10) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) =
% 250.88/59.57 e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.88/59.57 op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.88/59.57 (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) =
% 250.88/59.57 e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | ALPHA: (10) implies:
% 250.88/59.57 | (11) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.57 | e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.57 | op(e0, e1) = e0)
% 250.88/59.57 |
% 250.88/59.57 | BETA: splitting (11) gives:
% 250.88/59.57 |
% 250.88/59.57 | Case 1:
% 250.88/59.57 | |
% 250.88/59.57 | | (12) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 250.88/59.57 | | = e0)
% 250.88/59.57 | |
% 250.88/59.57 | | REF_CLOSE: (1), (3), (4), (5), (9), (12) are inconsistent by sub-proof #319.
% 250.88/59.57 | |
% 250.88/59.57 | Case 2:
% 250.88/59.57 | |
% 250.88/59.57 | | (13) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1)
% 250.88/59.57 | | = e0)
% 250.88/59.57 | |
% 250.88/59.57 | | BETA: splitting (13) gives:
% 250.88/59.57 | |
% 250.88/59.57 | | Case 1:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (14) all_252_22 = e0 & op(e0, e2) = e0
% 250.88/59.57 | | |
% 250.88/59.57 | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #444.
% 250.88/59.57 | | |
% 250.88/59.57 | | Case 2:
% 250.88/59.57 | | |
% 250.88/59.57 | | | (15) all_252_23 = e0 & op(e0, e1) = e0
% 250.88/59.57 | | |
% 250.88/59.57 | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #316.
% 250.88/59.57 | | |
% 250.88/59.57 | | End of split
% 250.88/59.57 | |
% 250.88/59.57 | End of split
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #316 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) all_252_23 = e0 & op(e0, e1) = e0
% 250.88/59.57 (2) all_252_23 = e3
% 250.88/59.57 (3) ~ (e3 = e0)
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | ALPHA: (1) implies:
% 250.88/59.57 | (4) all_252_23 = e0
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.57 | (5) e3 = e0
% 250.88/59.57 |
% 250.88/59.57 | REDUCE: (3), (5) imply:
% 250.88/59.57 | (6) $false
% 250.88/59.57 |
% 250.88/59.57 | CLOSE: (6) is inconsistent.
% 250.88/59.57 |
% 250.88/59.57 End of proof
% 250.88/59.57
% 250.88/59.57 Sub-proof #317 shows that the following formulas are inconsistent:
% 250.88/59.57 ----------------------------------------------------------------
% 250.88/59.57 (1) all_252_23 = e0 & op(e0, e1) = e0
% 250.88/59.57 (2) all_252_23 = e4
% 250.88/59.57 (3) ~ (e4 = e0)
% 250.88/59.57
% 250.88/59.57 Begin of proof
% 250.88/59.57 |
% 250.88/59.57 | ALPHA: (1) implies:
% 250.88/59.57 | (4) all_252_23 = e0
% 250.88/59.57 |
% 250.88/59.57 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e4 = e0
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #318 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_22 = e3
% 250.88/59.58 (2) all_252_22 = e0
% 250.88/59.58 (3) ~ (e3 = e0)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (1), (2) imply:
% 250.88/59.58 | (4) e3 = e0
% 250.88/59.58 |
% 250.88/59.58 | SIMP: (4) implies:
% 250.88/59.58 | (5) e3 = e0
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #319 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) op(e0, e3) = e1
% 250.88/59.58 (2) ~ (e2 = e0)
% 250.88/59.58 (3) ~ (e1 = e0)
% 250.88/59.58 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (5) all_252_20 = e2
% 250.88/59.58 (6) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (6) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (7) all_252_20 = e0 & op(e0, e4) = e0
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #529.
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (8) all_252_21 = e0 & op(e0, e3) = e0
% 250.88/59.58 | |
% 250.88/59.58 | | ALPHA: (8) implies:
% 250.88/59.58 | | (9) op(e0, e3) = e0
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #320.
% 250.88/59.58 | |
% 250.88/59.58 | End of split
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #320 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (2) op(e0, e3) = e1
% 250.88/59.58 (3) op(e0, e3) = e0
% 250.88/59.58 (4) ~ (e1 = e0)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | GROUND_INST: instantiating (1) with e0, e1, e3, e0, simplifying with (2), (3)
% 250.88/59.58 | gives:
% 250.88/59.58 | (5) e1 = e0
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (4), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #321 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.58 (2) all_252_22 = e3
% 250.88/59.58 (3) ~ (e4 = e3)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_22 = e4
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e4 = e3
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #322 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) op(e0, e3) = e1
% 250.88/59.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (3) ~ (e3 = e2)
% 250.88/59.58 (4) ~ (e3 = e1)
% 250.88/59.58 (5) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.88/59.58 (6) all_252_20 = e2
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (5) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (7) all_252_20 = e3 & op(e0, e4) = e3
% 250.88/59.58 | |
% 250.88/59.58 | | ALPHA: (7) implies:
% 250.88/59.58 | | (8) all_252_20 = e3
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #520.
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (9) all_252_21 = e3 & op(e0, e3) = e3
% 250.88/59.58 | |
% 250.88/59.58 | | ALPHA: (9) implies:
% 250.88/59.58 | | (10) op(e0, e3) = e3
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #590.
% 250.88/59.58 | |
% 250.88/59.58 | End of split
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #323 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_17 = e3 & op(e3, e0) = e3
% 250.88/59.58 (2) all_252_17 = e1
% 250.88/59.58 (3) ~ (e3 = e1)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_17 = e3
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e3 = e1
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #324 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) ~ (e2 = e0)
% 250.88/59.58 (2) all_252_19 = e2
% 250.88/59.58 (3) ~ (e1 = e0)
% 250.88/59.58 (4) all_252_16 = e3
% 250.88/59.58 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (6) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.58 | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) =
% 250.88/59.58 e0)
% 250.88/59.58 (7) op(e2, e0) = e1
% 250.88/59.58 (8) ~ (e3 = e0)
% 250.88/59.58 (9) op(e3, e0) = all_48_2
% 250.88/59.58 (10) ~ (all_48_2 = e0)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (6) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (11) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.88/59.58 | | = e0)
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (4), (5), (8), (9), (10), (11) are inconsistent by sub-proof
% 250.88/59.58 | | #425.
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (12) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.88/59.58 | | = e0)
% 250.88/59.58 | |
% 250.88/59.58 | | BETA: splitting (12) gives:
% 250.88/59.58 | |
% 250.88/59.58 | | Case 1:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (13) all_252_18 = e0 & op(e2, e0) = e0
% 250.88/59.58 | | |
% 250.88/59.58 | | | ALPHA: (13) implies:
% 250.88/59.58 | | | (14) op(e2, e0) = e0
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (3), (5), (7), (14) are inconsistent by sub-proof #901.
% 250.88/59.58 | | |
% 250.88/59.58 | | Case 2:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (15) all_252_19 = e0 & op(e1, e0) = e0
% 250.88/59.58 | | |
% 250.88/59.58 | | | ALPHA: (15) implies:
% 250.88/59.58 | | | (16) all_252_19 = e0
% 250.88/59.58 | | |
% 250.88/59.58 | | | COMBINE_EQS: (2), (16) imply:
% 250.88/59.58 | | | (17) e2 = e0
% 250.88/59.58 | | |
% 250.88/59.58 | | | REDUCE: (1), (17) imply:
% 250.88/59.58 | | | (18) $false
% 250.88/59.58 | | |
% 250.88/59.58 | | | CLOSE: (18) is inconsistent.
% 250.88/59.58 | | |
% 250.88/59.58 | | End of split
% 250.88/59.58 | |
% 250.88/59.58 | End of split
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #325 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_16 = e3
% 250.88/59.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (3) all_252_17 = e1
% 250.88/59.58 (4) ~ (e4 = e0)
% 250.88/59.58 (5) ~ (e4 = e1)
% 250.88/59.58 (6) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.88/59.58 | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1, e0) =
% 250.88/59.58 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.58 (7) all_252_24 = e0
% 250.88/59.58 (8) op(e1, e0) = e2
% 250.88/59.58 (9) ~ (e4 = e3)
% 250.88/59.58 (10) all_252_18 = e1
% 250.88/59.58 (11) ~ (e4 = e2)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (6) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (12) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0)
% 250.88/59.58 | | = e4)
% 250.88/59.58 | |
% 250.88/59.58 | | BETA: splitting (12) gives:
% 250.88/59.58 | |
% 250.88/59.58 | | Case 1:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (13) all_252_16 = e4 & op(e4, e0) = e4
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #483.
% 250.88/59.58 | | |
% 250.88/59.58 | | Case 2:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (14) all_252_17 = e4 & op(e3, e0) = e4
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (3), (5), (14) are inconsistent by sub-proof #327.
% 250.88/59.58 | | |
% 250.88/59.58 | | End of split
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (15) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1, e0)
% 250.88/59.58 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.58 | |
% 250.88/59.58 | | BETA: splitting (15) gives:
% 250.88/59.58 | |
% 250.88/59.58 | | Case 1:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (16) all_252_18 = e4 & op(e2, e0) = e4
% 250.88/59.58 | | |
% 250.88/59.58 | | | ALPHA: (16) implies:
% 250.88/59.58 | | | (17) all_252_18 = e4
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (5), (10), (17) are inconsistent by sub-proof #448.
% 250.88/59.58 | | |
% 250.88/59.58 | | Case 2:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (18) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 250.88/59.58 | | | e0) = e4)
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (2), (4), (7), (8), (11), (18) are inconsistent by sub-proof
% 250.88/59.58 | | | #326.
% 250.88/59.58 | | |
% 250.88/59.58 | | End of split
% 250.88/59.58 | |
% 250.88/59.58 | End of split
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #326 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (2) ~ (e4 = e0)
% 250.88/59.58 (3) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.58 (4) all_252_24 = e0
% 250.88/59.58 (5) op(e1, e0) = e2
% 250.88/59.58 (6) ~ (e4 = e2)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (3) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (7) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.58 | |
% 250.88/59.58 | | ALPHA: (7) implies:
% 250.88/59.58 | | (8) op(e1, e0) = e4
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #829.
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (9) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.58 | |
% 250.88/59.58 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #331.
% 250.88/59.58 | |
% 250.88/59.58 | End of split
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #327 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_17 = e4 & op(e3, e0) = e4
% 250.88/59.58 (2) all_252_17 = e1
% 250.88/59.58 (3) ~ (e4 = e1)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_17 = e4
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e4 = e1
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #328 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_18 = e4 & op(e2, e0) = e4
% 250.88/59.58 (2) all_252_18 = e1
% 250.88/59.58 (3) ~ (e4 = e1)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_18 = e4
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e4 = e1
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #329 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_11 = e3 & op(e2, e1) = e3
% 250.88/59.58 (2) all_252_11 = e1
% 250.88/59.58 (3) ~ (e3 = e1)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_11 = e3
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e3 = e1
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #330 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_11 = e2 & op(e2, e1) = e2
% 250.88/59.58 (2) all_252_11 = e1
% 250.88/59.58 (3) ~ (e2 = e1)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_11 = e2
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e2 = e1
% 250.88/59.58 |
% 250.88/59.58 | SIMP: (5) implies:
% 250.88/59.58 | (6) e2 = e1
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (6) imply:
% 250.88/59.58 | (7) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (7) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #331 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) all_252_24 = e4 & op(e0, e0) = e4
% 250.88/59.58 (2) all_252_24 = e0
% 250.88/59.58 (3) ~ (e4 = e0)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (1) implies:
% 250.88/59.58 | (4) all_252_24 = e4
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.58 | (5) e4 = e0
% 250.88/59.58 |
% 250.88/59.58 | REDUCE: (3), (5) imply:
% 250.88/59.58 | (6) $false
% 250.88/59.58 |
% 250.88/59.58 | CLOSE: (6) is inconsistent.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #332 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) ~ (all_4_2 = e4)
% 250.88/59.58 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.58 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.58 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.58 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.88/59.58 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.88/59.58 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.58 (4) all_252_22 = e4
% 250.88/59.58 (5) ~ (e1 = e0)
% 250.88/59.58 (6) all_252_13 = e0
% 250.88/59.58 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (8) ~ (e3 = e2)
% 250.88/59.58 (9) ~ (e4 = e0)
% 250.88/59.58 (10) all_252_12 = e4
% 250.88/59.58 (11) all_252_22 = e2 & op(e0, e2) = e2
% 250.88/59.58 (12) ~ (e2 = e1)
% 250.88/59.58 (13) ~ (e4 = e1)
% 250.88/59.58 (14) op(e1, e4) = all_16_2
% 250.88/59.58 (15) ~ (e3 = e0)
% 250.88/59.58 (16) ~ (e3 = e1)
% 250.88/59.58 (17) op(e1, e0) = e2
% 250.88/59.58 (18) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.58 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.58 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.58 (19) ~ (e4 = e3)
% 250.88/59.58 (20) op(e1, e2) = all_4_2
% 250.88/59.58 (21) ~ (e4 = e2)
% 250.88/59.58 (22) ~ (all_16_2 = e3)
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | ALPHA: (11) implies:
% 250.88/59.58 | (23) all_252_22 = e2
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (4), (23) imply:
% 250.88/59.58 | (24) e4 = e2
% 250.88/59.58 |
% 250.88/59.58 | SIMP: (24) implies:
% 250.88/59.58 | (25) e4 = e2
% 250.88/59.58 |
% 250.88/59.58 | COMBINE_EQS: (10), (25) imply:
% 250.88/59.58 | (26) all_252_12 = e2
% 250.88/59.58 |
% 250.88/59.58 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 250.88/59.58 | (16), (17), (18), (19), (20), (21), (22), (26) are inconsistent by
% 250.88/59.58 | sub-proof #392.
% 250.88/59.58 |
% 250.88/59.58 End of proof
% 250.88/59.58
% 250.88/59.58 Sub-proof #333 shows that the following formulas are inconsistent:
% 250.88/59.58 ----------------------------------------------------------------
% 250.88/59.58 (1) ~ (all_4_2 = e4)
% 250.88/59.58 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.58 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.58 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.58 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.88/59.58 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.88/59.58 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.58 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.88/59.58 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.88/59.58 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.58 (5) all_252_6 = e0
% 250.88/59.58 (6) ~ (e2 = e0)
% 250.88/59.58 (7) all_252_19 = e2
% 250.88/59.58 (8) ~ (e1 = e0)
% 250.88/59.58 (9) all_252_13 = e0
% 250.88/59.58 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.58 (11) ~ (e3 = e2)
% 250.88/59.58 (12) ~ (e4 = e0)
% 250.88/59.58 (13) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.88/59.58 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.88/59.58 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.58 (14) op(e2, e0) = e1
% 250.88/59.58 (15) ~ (e2 = e1)
% 250.88/59.58 (16) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.58 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.58 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.58 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.58 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.58 op(e0, e1) = e0)))
% 250.88/59.58 (17) ~ (e4 = e1)
% 250.88/59.58 (18) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.88/59.58 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.58 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.58 (19) op(e1, e4) = all_16_2
% 250.88/59.58 (20) ~ (e3 = e0)
% 250.88/59.58 (21) all_252_2 = e0
% 250.88/59.58 (22) ~ (e3 = e1)
% 250.88/59.58 (23) all_252_16 = e1
% 250.88/59.58 (24) op(e3, e1) = all_36_2
% 250.88/59.58 (25) op(e1, e0) = e2
% 250.88/59.58 (26) ~ (all_8_2 = e0)
% 250.88/59.58 (27) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.58 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.58 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.58 (28) ~ (all_36_2 = e0)
% 250.88/59.58 (29) ~ (e4 = e3)
% 250.88/59.58 (30) all_252_14 = e1
% 250.88/59.58 (31) op(e3, e0) = all_48_2
% 250.88/59.58 (32) op(e1, e2) = all_4_2
% 250.88/59.58 (33) ~ (all_48_2 = e0)
% 250.88/59.58 (34) ~ (e4 = e2)
% 250.88/59.58 (35) op(e3, e2) = all_8_2
% 250.88/59.58 (36) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.88/59.58 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.88/59.58 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.88/59.58 (37) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.88/59.58 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.58 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.58 (38) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.88/59.58 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.88/59.58 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.58 (39) ~ (all_244_3 = e0)
% 250.88/59.58 (40) ~ (all_16_2 = e3)
% 250.88/59.58 (41) op(e3, e3) = all_244_3
% 250.88/59.58 (42) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.88/59.58 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.88/59.58 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.58 (43) all_252_20 = e3
% 250.88/59.58
% 250.88/59.58 Begin of proof
% 250.88/59.58 |
% 250.88/59.58 | BETA: splitting (37) gives:
% 250.88/59.58 |
% 250.88/59.58 | Case 1:
% 250.88/59.58 | |
% 250.88/59.58 | | (44) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 250.88/59.58 | | e2)
% 250.88/59.58 | |
% 250.88/59.58 | | BETA: splitting (44) gives:
% 250.88/59.58 | |
% 250.88/59.58 | | Case 1:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (45) all_252_0 = e2 & op(e4, e4) = e2
% 250.88/59.58 | | |
% 250.88/59.58 | | | ALPHA: (45) implies:
% 250.88/59.58 | | | (46) all_252_0 = e2
% 250.88/59.58 | | |
% 250.88/59.58 | | | BETA: splitting (4) gives:
% 250.88/59.58 | | |
% 250.88/59.58 | | | Case 1:
% 250.88/59.58 | | | |
% 250.88/59.58 | | | | (47) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1,
% 250.88/59.58 | | | | e3) = e3)
% 250.88/59.58 | | | |
% 250.88/59.58 | | | | REF_CLOSE: (9), (10), (19), (20), (40), (47) are inconsistent by
% 250.88/59.58 | | | | sub-proof #412.
% 250.88/59.58 | | | |
% 250.88/59.58 | | | Case 2:
% 250.88/59.58 | | | |
% 250.88/59.58 | | | | (48) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.88/59.58 | | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.58 | | | |
% 250.88/59.58 | | | | BETA: splitting (48) gives:
% 250.88/59.58 | | | |
% 250.88/59.58 | | | | Case 1:
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | | (49) all_252_14 = e3 & op(e1, e2) = e3
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | | REF_CLOSE: (22), (30), (49) are inconsistent by sub-proof #334.
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | Case 2:
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | | (50) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.88/59.58 | | | | | op(e1, e0) = e3)
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | | BETA: splitting (50) gives:
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | | Case 1:
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | (51) all_252_15 = e3 & op(e1, e1) = e3
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | ALPHA: (51) implies:
% 250.88/59.58 | | | | | | (52) all_252_15 = e3
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | BETA: splitting (27) gives:
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | Case 1:
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | (53) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 &
% 250.88/59.58 | | | | | | | op(e1, e3) = e4)
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | BETA: splitting (53) gives:
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | (54) all_252_12 = e4 & op(e1, e4) = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | ALPHA: (54) implies:
% 250.88/59.58 | | | | | | | | (55) all_252_12 = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | BETA: splitting (42) gives:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | (56) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 250.88/59.58 | | | | | | | | | op(e3, e4) = e1)
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | BETA: splitting (56) gives:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | (57) all_252_0 = e1 & op(e4, e4) = e1
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | REF_CLOSE: (15), (46), (57) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | | | #558.
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | (58) all_252_2 = e1 & op(e3, e4) = e1
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | REF_CLOSE: (8), (21), (58) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | | | #568.
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | End of split
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | (59) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1
% 250.88/59.58 | | | | | | | | | & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) =
% 250.88/59.58 | | | | | | | | | e1)
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | BETA: splitting (59) gives:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | (60) all_252_6 = e1 & op(e2, e4) = e1
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | ALPHA: (60) implies:
% 250.88/59.58 | | | | | | | | | | (61) all_252_6 = e1
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 250.88/59.58 | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18),
% 250.88/59.58 | | | | | | | | | | (19), (20), (22), (23), (24), (25), (26), (27),
% 250.88/59.58 | | | | | | | | | | (28), (29), (31), (32), (33), (34), (35), (37),
% 250.88/59.58 | | | | | | | | | | (38), (39), (40), (41), (42), (43), (46), (61) are
% 250.88/59.58 | | | | | | | | | | inconsistent by sub-proof #394.
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | (62) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 =
% 250.88/59.58 | | | | | | | | | | e1 & op(e0, e4) = e1)
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | BETA: splitting (62) gives:
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | | (63) all_252_12 = e1 & op(e1, e4) = e1
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | | REF_CLOSE: (17), (55), (63) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | | | | #566.
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | | (64) all_252_20 = e1 & op(e0, e4) = e1
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | | REF_CLOSE: (22), (43), (64) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | | | | #565.
% 250.88/59.58 | | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | | End of split
% 250.88/59.58 | | | | | | | | | |
% 250.88/59.58 | | | | | | | | | End of split
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | End of split
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | (65) all_252_13 = e4 & op(e1, e3) = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | ALPHA: (65) implies:
% 250.88/59.58 | | | | | | | | (66) all_252_13 = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | REF_CLOSE: (9), (12), (66) are inconsistent by sub-proof #407.
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | End of split
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | Case 2:
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | (67) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 250.88/59.58 | | | | | | | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | BETA: splitting (67) gives:
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | (68) all_252_14 = e4 & op(e1, e2) = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | ALPHA: (68) implies:
% 250.88/59.58 | | | | | | | | (69) op(e1, e2) = e4
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | REF_CLOSE: (1), (10), (32), (69) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | #831.
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | (70) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.88/59.58 | | | | | | | | op(e1, e0) = e4)
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | BETA: splitting (70) gives:
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | | Case 1:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | (71) all_252_15 = e4 & op(e1, e1) = e4
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | REF_CLOSE: (29), (52), (71) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | | | | #678.
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | Case 2:
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | (72) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | ALPHA: (72) implies:
% 250.88/59.58 | | | | | | | | | (73) op(e1, e0) = e4
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | | REF_CLOSE: (10), (25), (34), (73) are inconsistent by
% 250.88/59.58 | | | | | | | | | sub-proof #829.
% 250.88/59.58 | | | | | | | | |
% 250.88/59.58 | | | | | | | | End of split
% 250.88/59.58 | | | | | | | |
% 250.88/59.58 | | | | | | | End of split
% 250.88/59.58 | | | | | | |
% 250.88/59.58 | | | | | | End of split
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | Case 2:
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | (74) all_252_19 = e3 & op(e1, e0) = e3
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | ALPHA: (74) implies:
% 250.88/59.58 | | | | | | (75) op(e1, e0) = e3
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | | REF_CLOSE: (10), (11), (25), (75) are inconsistent by sub-proof
% 250.88/59.58 | | | | | | #736.
% 250.88/59.58 | | | | | |
% 250.88/59.58 | | | | | End of split
% 250.88/59.58 | | | | |
% 250.88/59.58 | | | | End of split
% 250.88/59.58 | | | |
% 250.88/59.58 | | | End of split
% 250.88/59.58 | | |
% 250.88/59.58 | | Case 2:
% 250.88/59.58 | | |
% 250.88/59.58 | | | (76) all_252_2 = e2 & op(e3, e4) = e2
% 250.88/59.58 | | |
% 250.88/59.58 | | | ALPHA: (76) implies:
% 250.88/59.58 | | | (77) all_252_2 = e2
% 250.88/59.58 | | |
% 250.88/59.58 | | | REF_CLOSE: (3), (6), (10), (24), (26), (28), (31), (33), (35), (39), (41),
% 250.88/59.58 | | | (77) are inconsistent by sub-proof #571.
% 250.88/59.58 | | |
% 250.88/59.58 | | End of split
% 250.88/59.58 | |
% 250.88/59.58 | Case 2:
% 250.88/59.58 | |
% 250.88/59.58 | | (78) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.58 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.58 | |
% 250.88/59.59 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (15), (17),
% 250.88/59.59 | | (19), (20), (21), (22), (25), (27), (29), (32), (34), (36), (38),
% 250.88/59.59 | | (40), (42), (78) are inconsistent by sub-proof #351.
% 250.88/59.59 | |
% 250.88/59.59 | End of split
% 250.88/59.59 |
% 250.88/59.59 End of proof
% 250.88/59.59
% 250.88/59.59 Sub-proof #334 shows that the following formulas are inconsistent:
% 250.88/59.59 ----------------------------------------------------------------
% 250.88/59.59 (1) all_252_14 = e3 & op(e1, e2) = e3
% 250.88/59.59 (2) all_252_14 = e1
% 250.88/59.59 (3) ~ (e3 = e1)
% 250.88/59.59
% 250.88/59.59 Begin of proof
% 250.88/59.59 |
% 250.88/59.59 | ALPHA: (1) implies:
% 250.88/59.59 | (4) all_252_14 = e3
% 250.88/59.59 |
% 250.88/59.59 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.59 | (5) e3 = e1
% 250.88/59.59 |
% 250.88/59.59 | REDUCE: (3), (5) imply:
% 250.88/59.59 | (6) $false
% 250.88/59.59 |
% 250.88/59.59 | CLOSE: (6) is inconsistent.
% 250.88/59.59 |
% 250.88/59.59 End of proof
% 250.88/59.59
% 250.88/59.59 Sub-proof #335 shows that the following formulas are inconsistent:
% 250.88/59.59 ----------------------------------------------------------------
% 250.88/59.59 (1) op(e0, e3) = e1
% 250.88/59.59 (2) ~ (all_4_2 = e4)
% 250.88/59.59 (3) ~ (all_10_2 = e4)
% 250.88/59.59 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.59 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.88/59.59 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.59 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.88/59.59 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.88/59.59 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.88/59.59 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.59 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.59 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.59 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.88/59.59 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.88/59.59 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.59 (8) all_252_21 = e1
% 250.88/59.59 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.88/59.59 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.88/59.59 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.59 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.88/59.59 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.88/59.59 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.88/59.59 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.59 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.88/59.59 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.59 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.88/59.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.88/59.59 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.88/59.59 (13) ~ (e2 = e0)
% 250.88/59.59 (14) all_252_19 = e2
% 250.88/59.59 (15) ~ (e1 = e0)
% 250.88/59.59 (16) ~ (all_22_2 = e3)
% 250.88/59.59 (17) all_252_13 = e0
% 250.88/59.59 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.59 (19) op(e2, e3) = all_10_2
% 250.88/59.59 (20) ~ (e3 = e2)
% 250.88/59.59 (21) ~ (e4 = e0)
% 250.88/59.59 (22) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.88/59.59 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.88/59.59 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.88/59.59 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.88/59.59 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.88/59.59 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.88/59.59 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.88/59.59 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.88/59.59 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.88/59.59 (25) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.88/59.59 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.88/59.59 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.88/59.59 (26) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.88/59.59 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.88/59.59 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.59 (27) op(e2, e0) = e1
% 250.88/59.59 (28) ~ (e2 = e1)
% 250.88/59.59 (29) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.59 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.59 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.59 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.59 op(e0, e1) = e0)))
% 250.88/59.59 (30) ~ (e4 = e1)
% 250.88/59.59 (31) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.88/59.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.88/59.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.88/59.59 (32) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.88/59.59 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.59 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.59 (33) op(e1, e4) = all_16_2
% 250.88/59.59 (34) ~ (e3 = e0)
% 250.88/59.59 (35) all_252_2 = e0
% 250.88/59.59 (36) all_252_8 = e1 & op(e2, e2) = e1
% 250.88/59.59 (37) ~ (e3 = e1)
% 250.88/59.59 (38) all_252_16 = e1
% 250.88/59.59 (39) op(e3, e1) = all_36_2
% 250.88/59.59 (40) ~ (all_8_2 = e1)
% 250.88/59.59 (41) op(e1, e0) = e2
% 250.88/59.59 (42) ~ (all_8_2 = e0)
% 250.88/59.59 (43) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.88/59.59 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.88/59.59 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.88/59.59 (44) op(e0, e3) = all_22_2
% 250.88/59.59 (45) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.59 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.59 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.59 (46) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.88/59.59 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.88/59.59 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.88/59.59 (47) ~ (all_36_2 = e0)
% 250.88/59.59 (48) op(e4, e4) = all_244_0
% 250.88/59.59 (49) ~ (e4 = e3)
% 250.88/59.59 (50) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.88/59.59 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.88/59.59 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.88/59.59 (51) op(e0, e1) = all_20_2
% 250.88/59.59 (52) op(e3, e0) = all_48_2
% 250.88/59.59 (53) op(e1, e2) = all_4_2
% 250.88/59.59 (54) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.88/59.59 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.59 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.88/59.59 (55) ~ (all_48_2 = e0)
% 250.88/59.59 (56) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.88/59.59 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.88/59.59 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.88/59.59 (57) ~ (e4 = e2)
% 250.88/59.59 (58) op(e3, e2) = all_8_2
% 250.88/59.59 (59) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.88/59.59 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.88/59.59 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.88/59.59 (60) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.88/59.59 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.59 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.59 (61) ~ (all_20_2 = e4)
% 250.88/59.59 (62) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.88/59.59 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.88/59.59 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.59 (63) ~ (all_244_3 = e0)
% 250.88/59.59 (64) op(e2, e0) = all_40_2
% 250.88/59.59 (65) ~ (all_16_2 = e3)
% 250.88/59.59 (66) ~ (all_10_2 = e0)
% 250.88/59.59 (67) ~ (all_244_0 = e3)
% 250.88/59.59 (68) op(e3, e3) = all_244_3
% 250.88/59.59 (69) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.88/59.59 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.88/59.59 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.88/59.59 (70) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.88/59.59 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.88/59.59 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.59 (71) ~ (all_4_2 = e0)
% 250.88/59.59 (72) all_252_20 = e3
% 250.88/59.59
% 250.88/59.59 Begin of proof
% 250.88/59.59 |
% 250.88/59.59 | ALPHA: (36) implies:
% 250.88/59.59 | (73) all_252_8 = e1
% 250.88/59.59 |
% 250.88/59.59 | BETA: splitting (12) gives:
% 250.88/59.59 |
% 250.88/59.59 | Case 1:
% 250.88/59.59 | |
% 250.88/59.59 | | (74) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 250.88/59.59 | | e0)
% 250.88/59.59 | |
% 250.88/59.59 | | BETA: splitting (74) gives:
% 250.88/59.59 | |
% 250.88/59.59 | | Case 1:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (75) all_252_6 = e0 & op(e2, e4) = e0
% 250.88/59.59 | | |
% 250.88/59.59 | | | ALPHA: (75) implies:
% 250.88/59.59 | | | (76) all_252_6 = e0
% 250.88/59.59 | | |
% 250.88/59.59 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 250.88/59.59 | | | (14), (15), (17), (18), (19), (20), (21), (23), (26), (27),
% 250.88/59.59 | | | (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 250.88/59.59 | | | (39), (41), (42), (45), (47), (48), (49), (51), (52), (53),
% 250.88/59.59 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 250.88/59.59 | | | (65), (67), (68), (69), (70), (71), (72), (73), (76) are
% 250.88/59.59 | | | inconsistent by sub-proof #350.
% 250.88/59.59 | | |
% 250.88/59.59 | | Case 2:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (77) all_252_7 = e0 & op(e2, e3) = e0
% 250.88/59.59 | | |
% 250.88/59.59 | | | REF_CLOSE: (18), (19), (66), (77) are inconsistent by sub-proof #816.
% 250.88/59.59 | | |
% 250.88/59.59 | | End of split
% 250.88/59.59 | |
% 250.88/59.59 | Case 2:
% 250.88/59.59 | |
% 250.88/59.59 | | (78) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.88/59.59 | | e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.88/59.59 | |
% 250.88/59.59 | | BETA: splitting (78) gives:
% 250.88/59.59 | |
% 250.88/59.59 | | Case 1:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (79) all_252_8 = e0 & op(e2, e2) = e0
% 250.88/59.59 | | |
% 250.88/59.59 | | | REF_CLOSE: (15), (73), (79) are inconsistent by sub-proof #873.
% 250.88/59.59 | | |
% 250.88/59.59 | | Case 2:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (80) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0 & op(e2,
% 250.88/59.59 | | | e0) = e0)
% 250.88/59.59 | | |
% 250.88/59.59 | | | BETA: splitting (80) gives:
% 250.88/59.59 | | |
% 250.88/59.59 | | | Case 1:
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | (81) all_252_11 = e0 & op(e2, e1) = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | ALPHA: (81) implies:
% 250.88/59.59 | | | | (82) all_252_11 = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 250.88/59.59 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.88/59.59 | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 250.88/59.59 | | | | (34), (35), (37), (38), (39), (40), (41), (42), (43), (44),
% 250.88/59.59 | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 250.88/59.59 | | | | (55), (56), (57), (58), (60), (61), (62), (63), (64), (65),
% 250.88/59.59 | | | | (67), (68), (69), (70), (71), (72), (73), (82) are
% 250.88/59.59 | | | | inconsistent by sub-proof #336.
% 250.88/59.59 | | | |
% 250.88/59.59 | | | Case 2:
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | (83) all_252_18 = e0 & op(e2, e0) = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | ALPHA: (83) implies:
% 250.88/59.59 | | | | (84) op(e2, e0) = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | REF_CLOSE: (15), (18), (27), (84) are inconsistent by sub-proof #901.
% 250.88/59.59 | | | |
% 250.88/59.59 | | | End of split
% 250.88/59.59 | | |
% 250.88/59.59 | | End of split
% 250.88/59.59 | |
% 250.88/59.59 | End of split
% 250.88/59.59 |
% 250.88/59.59 End of proof
% 250.88/59.59
% 250.88/59.59 Sub-proof #336 shows that the following formulas are inconsistent:
% 250.88/59.59 ----------------------------------------------------------------
% 250.88/59.59 (1) op(e0, e3) = e1
% 250.88/59.59 (2) ~ (all_4_2 = e4)
% 250.88/59.59 (3) ~ (all_10_2 = e4)
% 250.88/59.59 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.59 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.88/59.59 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.59 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.88/59.59 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.88/59.59 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.88/59.59 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.59 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.59 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.59 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.88/59.59 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.88/59.59 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.59 (8) all_252_21 = e1
% 250.88/59.59 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.88/59.59 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.88/59.59 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.59 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.88/59.59 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.88/59.59 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.88/59.59 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.59 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.88/59.59 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.59 (12) ~ (e2 = e0)
% 250.88/59.59 (13) all_252_19 = e2
% 250.88/59.59 (14) ~ (e1 = e0)
% 250.88/59.59 (15) ~ (all_22_2 = e3)
% 250.88/59.59 (16) all_252_13 = e0
% 250.88/59.59 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.59 (18) op(e2, e3) = all_10_2
% 250.88/59.59 (19) ~ (e3 = e2)
% 250.88/59.59 (20) ~ (e4 = e0)
% 250.88/59.59 (21) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.88/59.59 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.88/59.59 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.88/59.59 (22) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.88/59.59 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.88/59.59 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.88/59.59 (23) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.88/59.59 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.88/59.59 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.88/59.59 (24) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.88/59.59 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.88/59.59 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.59 (25) op(e2, e0) = e1
% 250.88/59.59 (26) ~ (e2 = e1)
% 250.88/59.59 (27) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.59 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.59 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.59 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.59 op(e0, e1) = e0)))
% 250.88/59.59 (28) ~ (e4 = e1)
% 250.88/59.59 (29) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.88/59.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.88/59.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.88/59.59 (30) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.88/59.59 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.59 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.59 (31) op(e1, e4) = all_16_2
% 250.88/59.59 (32) ~ (e3 = e0)
% 250.88/59.59 (33) all_252_2 = e0
% 250.88/59.59 (34) ~ (e3 = e1)
% 250.88/59.59 (35) all_252_16 = e1
% 250.88/59.59 (36) op(e3, e1) = all_36_2
% 250.88/59.59 (37) ~ (all_8_2 = e1)
% 250.88/59.59 (38) op(e1, e0) = e2
% 250.88/59.59 (39) ~ (all_8_2 = e0)
% 250.88/59.59 (40) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 250.88/59.59 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 250.88/59.59 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.88/59.59 (41) op(e0, e3) = all_22_2
% 250.88/59.59 (42) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.59 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.59 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.59 (43) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.88/59.59 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.88/59.59 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.88/59.59 (44) ~ (all_36_2 = e0)
% 250.88/59.59 (45) op(e4, e4) = all_244_0
% 250.88/59.59 (46) ~ (e4 = e3)
% 250.88/59.59 (47) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.88/59.59 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.88/59.59 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.88/59.59 (48) op(e0, e1) = all_20_2
% 250.88/59.59 (49) all_252_11 = e0
% 250.88/59.59 (50) op(e3, e0) = all_48_2
% 250.88/59.59 (51) op(e1, e2) = all_4_2
% 250.88/59.59 (52) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.88/59.59 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.59 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.88/59.59 (53) ~ (all_48_2 = e0)
% 250.88/59.59 (54) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.88/59.59 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.88/59.59 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.88/59.59 (55) ~ (e4 = e2)
% 250.88/59.59 (56) op(e3, e2) = all_8_2
% 250.88/59.59 (57) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.88/59.59 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.59 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.59 (58) ~ (all_20_2 = e4)
% 250.88/59.59 (59) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.88/59.59 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.88/59.59 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.59 (60) ~ (all_244_3 = e0)
% 250.88/59.59 (61) op(e2, e0) = all_40_2
% 250.88/59.59 (62) ~ (all_16_2 = e3)
% 250.88/59.59 (63) all_252_8 = e1
% 250.88/59.59 (64) ~ (all_244_0 = e3)
% 250.88/59.59 (65) op(e3, e3) = all_244_3
% 250.88/59.59 (66) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.88/59.59 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.88/59.59 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.88/59.59 (67) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.88/59.59 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.88/59.59 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.59 (68) ~ (all_4_2 = e0)
% 250.88/59.59 (69) all_252_20 = e3
% 250.88/59.59
% 250.88/59.59 Begin of proof
% 250.88/59.59 |
% 250.88/59.59 | BETA: splitting (21) gives:
% 250.88/59.59 |
% 250.88/59.59 | Case 1:
% 250.88/59.59 | |
% 250.88/59.59 | | (70) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 250.88/59.59 | | e3)
% 250.88/59.59 | |
% 250.88/59.59 | | BETA: splitting (70) gives:
% 250.88/59.59 | |
% 250.88/59.59 | | Case 1:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (71) all_252_6 = e3 & op(e2, e4) = e3
% 250.88/59.59 | | |
% 250.88/59.59 | | | ALPHA: (71) implies:
% 250.88/59.59 | | | (72) all_252_6 = e3
% 250.88/59.59 | | |
% 250.88/59.59 | | | REF_CLOSE: (2), (6), (7), (11), (12), (13), (14), (16), (17), (19), (20),
% 250.88/59.59 | | | (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 250.88/59.59 | | | (35), (36), (38), (39), (42), (44), (46), (50), (51), (53),
% 250.88/59.59 | | | (55), (56), (57), (59), (60), (62), (65), (67), (69), (72) are
% 250.88/59.59 | | | inconsistent by sub-proof #347.
% 250.88/59.59 | | |
% 250.88/59.59 | | Case 2:
% 250.88/59.59 | | |
% 250.88/59.59 | | | (73) all_252_7 = e3 & op(e2, e3) = e3
% 250.88/59.59 | | |
% 250.88/59.59 | | | ALPHA: (73) implies:
% 250.88/59.59 | | | (74) all_252_7 = e3
% 250.88/59.59 | | |
% 250.88/59.59 | | | BETA: splitting (27) gives:
% 250.88/59.59 | | |
% 250.88/59.59 | | | Case 1:
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | (75) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | ALPHA: (75) implies:
% 250.88/59.59 | | | | (76) all_252_24 = e0
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | BETA: splitting (4) gives:
% 250.88/59.59 | | | |
% 250.88/59.59 | | | | Case 1:
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | | (77) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 250.88/59.59 | | | | | op(e0, e3) = e4)
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | | REF_CLOSE: (1), (17), (28), (46), (69), (77) are inconsistent by
% 250.88/59.59 | | | | | sub-proof #390.
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | Case 2:
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | | (78) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 250.88/59.59 | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | | BETA: splitting (78) gives:
% 250.88/59.59 | | | | |
% 250.88/59.59 | | | | | Case 1:
% 250.88/59.59 | | | | | |
% 250.88/59.59 | | | | | | (79) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.59 | | | | | |
% 250.88/59.59 | | | | | | ALPHA: (79) implies:
% 250.88/59.59 | | | | | | (80) all_252_22 = e4
% 250.88/59.59 | | | | | | (81) op(e0, e2) = e4
% 250.88/59.59 | | | | | |
% 250.88/59.59 | | | | | | BETA: splitting (40) gives:
% 250.88/59.59 | | | | | |
% 250.88/59.59 | | | | | | Case 1:
% 250.88/59.59 | | | | | | |
% 250.88/59.59 | | | | | | | (82) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 &
% 250.88/59.59 | | | | | | | op(e2, e3) = e2)
% 250.88/59.59 | | | | | | |
% 250.88/59.59 | | | | | | | BETA: splitting (82) gives:
% 250.88/59.59 | | | | | | |
% 250.88/59.59 | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | |
% 250.88/59.59 | | | | | | | | (83) all_252_6 = e2 & op(e2, e4) = e2
% 250.88/59.59 | | | | | | | |
% 250.88/59.59 | | | | | | | | ALPHA: (83) implies:
% 250.88/59.59 | | | | | | | | (84) all_252_6 = e2
% 250.88/59.59 | | | | | | | |
% 250.88/59.59 | | | | | | | | BETA: splitting (29) gives:
% 250.88/59.59 | | | | | | | |
% 250.88/59.59 | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | |
% 250.88/59.59 | | | | | | | | | (85) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 &
% 250.88/59.59 | | | | | | | | | op(e3, e2) = e0)
% 250.88/59.59 | | | | | | | | |
% 250.88/59.59 | | | | | | | | | BETA: splitting (85) gives:
% 250.88/59.59 | | | | | | | | |
% 250.88/59.59 | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | (86) all_252_4 = e0 & op(e4, e2) = e0
% 250.88/59.59 | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | ALPHA: (86) implies:
% 250.88/59.59 | | | | | | | | | | (87) all_252_4 = e0
% 250.88/59.59 | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | BETA: splitting (66) gives:
% 250.88/59.59 | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | (88) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 250.88/59.59 | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 250.88/59.59 | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | BETA: splitting (88) gives:
% 250.88/59.59 | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | (89) all_252_4 = e2 & op(e4, e2) = e2
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | REF_CLOSE: (12), (87), (89) are inconsistent by sub-proof
% 250.88/59.59 | | | | | | | | | | | | #863.
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | (90) all_252_5 = e2 & op(e3, e2) = e2
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | ALPHA: (90) implies:
% 250.88/59.59 | | | | | | | | | | | | (91) all_252_5 = e2
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | BETA: splitting (23) gives:
% 250.88/59.59 | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | (92) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 250.88/59.59 | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (9), (10), (12), (14), (16), (17),
% 250.88/59.59 | | | | | | | | | | | | | (18), (19), (20), (26), (28), (32), (33), (34),
% 250.88/59.59 | | | | | | | | | | | | | (46), (52), (55), (92) are inconsistent by
% 250.88/59.59 | | | | | | | | | | | | | sub-proof #346.
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | (93) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 250.88/59.59 | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.88/59.59 | | | | | | | | | | | | | op(e3, e0) = e1)
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 250.88/59.59 | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | (94) all_252_5 = e1 & op(e3, e2) = e1
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | ALPHA: (94) implies:
% 250.88/59.59 | | | | | | | | | | | | | | (95) op(e3, e2) = e1
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | REF_CLOSE: (17), (37), (56), (95) are inconsistent by
% 250.88/59.59 | | | | | | | | | | | | | | sub-proof #929.
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | (96) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 250.88/59.59 | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 250.88/59.59 | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | (97) all_252_10 = e1 & op(e3, e1) = e1
% 250.88/59.59 | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | (98) all_252_10 = e1
% 250.88/59.59 | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 250.88/59.59 | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | (99) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 250.88/59.59 | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 250.88/59.59 | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | (100) all_252_0 = e3 & op(e4, e4) = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | | | (101) op(e4, e4) = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (45), (64), (101) are inconsistent by
% 250.88/59.59 | | | | | | | | | | | | | | | | | sub-proof #813.
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | (102) all_252_1 = e3 & op(e4, e3) = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | | | (103) all_252_1 = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | (104) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 250.88/59.59 | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (32), (87), (91), (104) are inconsistent by
% 250.88/59.59 | | | | | | | | | | | | | | | | | | sub-proof #345.
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | (105) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 250.88/59.59 | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 250.88/59.59 | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | (106) all_252_8 = e3 & op(e2, e2) = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | (107) all_252_8 = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (63), (107) are inconsistent by sub-proof
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | #927.
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | (108) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | (109) all_252_14 = e3 & op(e1, e2) = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | (110) all_252_14 = e3
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | (111) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | | (112) all_252_1 = e2 & op(e4, e3) = e2
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | | (113) all_252_1 = e2
% 250.88/59.59 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (113) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (114) e3 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (114) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (115) all_252_14 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (14), (16), (17), (19), (20),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (26), (28), (31), (32), (34), (38), (42), (46),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (51), (55), (62), (115) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #356.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (116) all_252_3 = e2 & op(e3, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (117) all_252_3 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (118) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (119) all_252_1 = e4 & op(e4, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (120) all_252_1 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (120) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (121) e4 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (121) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (122) e4 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (122) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (123) $false
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (124) all_252_3 = e4 & op(e3, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (125) all_252_3 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (117), (125) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | #954.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (126) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (127) all_252_7 = e4 & op(e2, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (128) op(e2, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (18), (128) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (129) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (130) all_252_13 = e4 & op(e1, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (131) all_252_13 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (131) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | #407.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (132) all_252_21 = e4 & op(e0, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (132) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | #344.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | (133) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (134) all_252_7 = e2 & op(e2, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (135) all_252_7 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (135) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (136) e3 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (136) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (137) e3 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (137) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (138) all_252_14 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (14), (16), (17), (19), (20),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (26), (28), (31), (32), (34), (38), (42), (46),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (51), (55), (62), (138) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #356.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (139) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (140) all_252_13 = e2 & op(e1, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (140) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | #376.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (141) all_252_21 = e2 & op(e0, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (142) op(e0, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (26), (142) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #941.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | (143) all_252_22 = e3 & op(e0, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | (144) op(e0, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (46), (81), (144) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | sub-proof #857.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | (145) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 250.88/59.60 | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 250.88/59.60 | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | (146) all_252_4 = e3 & op(e4, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (87), (146) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | #865.
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | (147) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | (148) all_252_9 = e3 & op(e4, e1) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | (149) all_252_9 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | (150) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | (151) all_252_16 = e3 & op(e4, e0) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (35), (151) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | #488.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | (152) all_252_17 = e3 & op(e3, e0) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | (153) all_252_17 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | (154) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (32), (87), (91), (154) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | sub-proof #345.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | (155) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (156) all_252_8 = e3 & op(e2, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (157) all_252_8 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (63), (157) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | #927.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | (158) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_14 = e3 & op(e1, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_14 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (161) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_9 = e4 & op(e4, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (149), (162) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | #360.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_10 = e4 & op(e3, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_10 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (98), (164) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | #434.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_11 = e4 & op(e2, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_11 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (49), (167) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | #766.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_252_15 = e4 & op(e1, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_15 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_2 = e4 & op(e3, e4) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_2 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (20), (36), (39), (44), (50), (53),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (60), (65), (173) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #569.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_3 = e4 & op(e3, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_3 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_6 = e4 & op(e2, e4) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_6 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (178) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) e4 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) e4 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (180) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_15 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (14), (16), (17), (20), (26), (28),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (38), (42), (51), (55), (160), (181) are
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #406.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_7 = e4 & op(e2, e3) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_252_7 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_252_1 = e3 & op(e4, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_1 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_252_1 = e2 & op(e4, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (186), (188) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_252_3 = e2 & op(e3, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (175), (189) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #496.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (16), (26), (55), (183), (190) are
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #370.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_3 = e3 & op(e3, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (175), (191) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (32), (34), (46), (183), (192)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #369.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_8 = e4 & op(e2, e2) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_8 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (195) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) e4 = e1
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (196) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_3 = e1
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (9), (10), (12), (16), (17), (18),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (26), (28), (32), (34), (46), (52),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (197) are inconsistent by sub-proof #363.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_252_11 = e4 & op(e2, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_11 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (200) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) e4 = e0
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (201) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) e4 = e0
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (202) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_3 = e0
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (9), (10), (12), (16), (17), (19), (20),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (26), (28), (32), (34), (46), (52), (55), (203)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #365.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_252_18 = e4 & op(e2, e0) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_1 = e3 & op(e4, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_252_1 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_252_1 = e2 & op(e4, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (207), (209) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_3 = e2 & op(e3, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (175), (210) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #496.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_252_7 = e2 & op(e2, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (74), (212) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #666.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_13 = e2 & op(e1, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_13 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (215) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_252_21 = e2 & op(e0, e3) = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (216) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #375.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_3 = e3 & op(e3, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (175), (217) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) op(e2, e0) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e1, e4, e0, e2,
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (25), (219) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) e4 = e1
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (220) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_3 = e1
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (9), (10), (12), (16), (17), (18),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (26), (28), (32), (34), (46), (52),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (221) are inconsistent by sub-proof #363.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_13 = e3 & op(e1, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (32), (223) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #883.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_252_21 = e3 & op(e0, e3) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (41), (224) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #959.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_252_5 = e4 & op(e3, e2) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_5 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (227) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) e4 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) e4 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (229) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_15 = e2
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (14), (16), (17), (20), (26), (28),
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (34), (38), (42), (51), (55), (160), (230) are
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #406.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_252_10 = e4 & op(e3, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_10 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (98), (233) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #434.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_17 = e4 & op(e3, e0) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_17 = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (235) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) e4 = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (236) imply:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) $false
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (237) is inconsistent.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_23 = e4 & op(e0, e1) = e4
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (48), (58), (238) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (239) all_252_22 = e3 & op(e0, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | (240) op(e0, e2) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (46), (81), (240) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #857.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | (241) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (25), (32), (34), (38), (76), (241)
% 250.88/59.60 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #342.
% 250.88/59.60 | | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | (242) all_252_16 = e3 & op(e4, e0) = e3
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (35), (242) are inconsistent by sub-proof
% 250.88/59.60 | | | | | | | | | | | | | | | | | | #488.
% 250.88/59.60 | | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | (243) all_252_17 = e1 & op(e3, e0) = e1
% 250.88/59.60 | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (24), (25), (32), (34), (35), (38),
% 250.88/59.60 | | | | | | | | | | | | | | | (76), (243) are inconsistent by sub-proof #340.
% 250.88/59.60 | | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | (244) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 250.88/59.60 | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 250.88/59.60 | | | | | | | | | | | op(e0, e2) = e2)
% 250.88/59.60 | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | BETA: splitting (244) gives:
% 250.88/59.60 | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | (245) all_252_8 = e2 & op(e2, e2) = e2
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | ALPHA: (245) implies:
% 250.88/59.60 | | | | | | | | | | | | (246) all_252_8 = e2
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | COMBINE_EQS: (63), (246) imply:
% 250.88/59.60 | | | | | | | | | | | | (247) e2 = e1
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | SIMP: (247) implies:
% 250.88/59.60 | | | | | | | | | | | | (248) e2 = e1
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | COMBINE_EQS: (84), (248) imply:
% 250.88/59.60 | | | | | | | | | | | | (249) all_252_6 = e1
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (11), (12), (13), (14), (16), (17),
% 250.88/59.60 | | | | | | | | | | | | (19), (20), (24), (25), (26), (27), (28), (30),
% 250.88/59.60 | | | | | | | | | | | | (31), (32), (34), (35), (36), (38), (39), (42),
% 250.88/59.60 | | | | | | | | | | | | (44), (46), (50), (51), (53), (55), (56), (57),
% 250.88/59.60 | | | | | | | | | | | | (59), (60), (62), (65), (67), (69), (249) are
% 250.88/59.60 | | | | | | | | | | | | inconsistent by sub-proof #391.
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | (250) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 250.88/59.60 | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (14), (16), (17), (19), (20),
% 250.88/59.60 | | | | | | | | | | | | (26), (28), (31), (32), (34), (38), (42), (46),
% 250.88/59.60 | | | | | | | | | | | | (51), (55), (62), (80), (250) are inconsistent by
% 250.88/59.60 | | | | | | | | | | | | sub-proof #354.
% 250.88/59.60 | | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | (251) all_252_5 = e0 & op(e3, e2) = e0
% 250.88/59.60 | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | | REF_CLOSE: (17), (39), (56), (251) are inconsistent by
% 250.88/59.60 | | | | | | | | | | sub-proof #874.
% 250.88/59.60 | | | | | | | | | |
% 250.88/59.60 | | | | | | | | | End of split
% 250.88/59.60 | | | | | | | | |
% 250.88/59.60 | | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | | |
% 250.88/59.60 | | | | | | | | | (252) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0
% 250.88/59.60 | | | | | | | | | & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2)
% 250.88/59.60 | | | | | | | | | = e0)
% 250.88/59.60 | | | | | | | | |
% 250.88/59.60 | | | | | | | | | REF_CLOSE: (14), (17), (20), (51), (63), (68), (80), (252) are
% 250.88/59.60 | | | | | | | | | inconsistent by sub-proof #353.
% 250.88/59.60 | | | | | | | | |
% 250.88/59.60 | | | | | | | | End of split
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | (253) all_252_7 = e2 & op(e2, e3) = e2
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | REF_CLOSE: (19), (74), (253) are inconsistent by sub-proof #666.
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | End of split
% 250.88/59.60 | | | | | | |
% 250.88/59.60 | | | | | | Case 2:
% 250.88/59.60 | | | | | | |
% 250.88/59.60 | | | | | | | (254) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 &
% 250.88/59.60 | | | | | | | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.88/59.60 | | | | | | |
% 250.88/59.60 | | | | | | | BETA: splitting (254) gives:
% 250.88/59.60 | | | | | | |
% 250.88/59.60 | | | | | | | Case 1:
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | (255) all_252_8 = e2 & op(e2, e2) = e2
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | REF_CLOSE: (26), (63), (255) are inconsistent by sub-proof #339.
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | Case 2:
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | (256) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2
% 250.88/59.60 | | | | | | | | & op(e2, e0) = e2)
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | | REF_CLOSE: (12), (17), (25), (26), (49), (61), (256) are
% 250.88/59.60 | | | | | | | | inconsistent by sub-proof #338.
% 250.88/59.60 | | | | | | | |
% 250.88/59.60 | | | | | | | End of split
% 250.88/59.60 | | | | | | |
% 250.88/59.60 | | | | | | End of split
% 250.88/59.60 | | | | | |
% 250.88/59.60 | | | | | Case 2:
% 250.88/59.60 | | | | | |
% 250.88/59.60 | | | | | | (257) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.88/59.60 | | | | | | op(e0, e0) = e4)
% 250.88/59.60 | | | | | |
% 250.88/59.60 | | | | | | REF_CLOSE: (17), (20), (48), (58), (76), (257) are inconsistent by
% 250.88/59.60 | | | | | | sub-proof #352.
% 250.88/59.60 | | | | | |
% 250.88/59.60 | | | | | End of split
% 250.88/59.60 | | | | |
% 250.88/59.60 | | | | End of split
% 250.88/59.60 | | | |
% 250.88/59.60 | | | Case 2:
% 250.88/59.60 | | | |
% 250.88/59.60 | | | | (258) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.88/59.60 | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.88/59.60 | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.88/59.60 | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.88/59.60 | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.60 | | | | op(e0, e1) = e0))
% 250.88/59.60 | | | |
% 250.88/59.60 | | | | ALPHA: (258) implies:
% 250.88/59.60 | | | | (259) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3,
% 250.88/59.60 | | | | e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.88/59.60 | | | | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.88/59.60 | | | |
% 250.88/59.60 | | | | REF_CLOSE: (12), (13), (14), (17), (25), (35), (50), (53), (259) are
% 250.88/59.60 | | | | inconsistent by sub-proof #348.
% 250.88/59.60 | | | |
% 250.88/59.60 | | | End of split
% 250.88/59.60 | | |
% 250.88/59.60 | | End of split
% 250.88/59.60 | |
% 250.88/59.60 | Case 2:
% 250.88/59.60 | |
% 250.88/59.60 | | (260) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1)
% 250.88/59.60 | | = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.88/59.60 | |
% 250.88/59.60 | | BETA: splitting (260) gives:
% 250.88/59.60 | |
% 250.88/59.60 | | Case 1:
% 250.88/59.60 | | |
% 250.88/59.60 | | | (261) all_252_8 = e3 & op(e2, e2) = e3
% 250.88/59.60 | | |
% 250.88/59.60 | | | ALPHA: (261) implies:
% 250.88/59.60 | | | (262) all_252_8 = e3
% 250.88/59.60 | | |
% 250.88/59.60 | | | REF_CLOSE: (34), (63), (262) are inconsistent by sub-proof #927.
% 250.88/59.60 | | |
% 250.88/59.60 | | Case 2:
% 250.88/59.60 | | |
% 250.88/59.60 | | | (263) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2,
% 250.88/59.60 | | | e0) = e3)
% 250.88/59.60 | | |
% 250.88/59.60 | | | REF_CLOSE: (17), (25), (32), (34), (49), (263) are inconsistent by
% 250.88/59.60 | | | sub-proof #337.
% 250.88/59.60 | | |
% 250.88/59.60 | | End of split
% 250.88/59.60 | |
% 250.88/59.60 | End of split
% 250.88/59.60 |
% 250.88/59.60 End of proof
% 250.88/59.60
% 250.88/59.60 Sub-proof #337 shows that the following formulas are inconsistent:
% 250.88/59.60 ----------------------------------------------------------------
% 250.88/59.60 (1) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.88/59.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.60 (3) op(e2, e0) = e1
% 250.88/59.60 (4) ~ (e3 = e0)
% 250.88/59.60 (5) ~ (e3 = e1)
% 250.88/59.60 (6) all_252_11 = e0
% 250.88/59.60
% 250.88/59.60 Begin of proof
% 250.88/59.60 |
% 250.88/59.60 | BETA: splitting (1) gives:
% 250.88/59.60 |
% 250.88/59.60 | Case 1:
% 250.88/59.60 | |
% 250.88/59.60 | | (7) all_252_11 = e3 & op(e2, e1) = e3
% 250.88/59.60 | |
% 250.88/59.60 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #725.
% 250.88/59.60 | |
% 250.88/59.60 | Case 2:
% 250.88/59.60 | |
% 250.88/59.60 | | (8) all_252_18 = e3 & op(e2, e0) = e3
% 250.88/59.60 | |
% 250.88/59.60 | | ALPHA: (8) implies:
% 250.88/59.60 | | (9) op(e2, e0) = e3
% 250.88/59.60 | |
% 250.88/59.60 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #399.
% 250.88/59.60 | |
% 250.88/59.60 | End of split
% 250.88/59.60 |
% 250.88/59.60 End of proof
% 250.88/59.60
% 250.88/59.60 Sub-proof #338 shows that the following formulas are inconsistent:
% 250.88/59.60 ----------------------------------------------------------------
% 250.88/59.60 (1) ~ (e2 = e0)
% 250.88/59.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.60 (3) op(e2, e0) = e1
% 250.88/59.60 (4) ~ (e2 = e1)
% 250.88/59.60 (5) all_252_11 = e0
% 250.88/59.60 (6) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 250.88/59.60 (7) op(e2, e0) = all_40_2
% 250.88/59.60
% 250.88/59.60 Begin of proof
% 250.88/59.60 |
% 250.88/59.60 | BETA: splitting (6) gives:
% 250.88/59.60 |
% 250.88/59.60 | Case 1:
% 250.88/59.60 | |
% 250.88/59.61 | | (8) all_252_11 = e2 & op(e2, e1) = e2
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (8) implies:
% 250.88/59.61 | | (9) all_252_11 = e2
% 250.88/59.61 | |
% 250.88/59.61 | | COMBINE_EQS: (5), (9) imply:
% 250.88/59.61 | | (10) e2 = e0
% 250.88/59.61 | |
% 250.88/59.61 | | SIMP: (10) implies:
% 250.88/59.61 | | (11) e2 = e0
% 250.88/59.61 | |
% 250.88/59.61 | | REDUCE: (1), (11) imply:
% 250.88/59.61 | | (12) $false
% 250.88/59.61 | |
% 250.88/59.61 | | CLOSE: (12) is inconsistent.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (13) all_252_18 = e2 & op(e2, e0) = e2
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (13) implies:
% 250.88/59.61 | | (14) op(e2, e0) = e2
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (2), (3), (4), (7), (14) are inconsistent by sub-proof #415.
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #339 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) all_252_8 = e2 & op(e2, e2) = e2
% 250.88/59.61 (2) all_252_8 = e1
% 250.88/59.61 (3) ~ (e2 = e1)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | ALPHA: (1) implies:
% 250.88/59.61 | (4) all_252_8 = e2
% 250.88/59.61 |
% 250.88/59.61 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.61 | (5) e2 = e1
% 250.88/59.61 |
% 250.88/59.61 | REDUCE: (3), (5) imply:
% 250.88/59.61 | (6) $false
% 250.88/59.61 |
% 250.88/59.61 | CLOSE: (6) is inconsistent.
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #340 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (2) ~ (e3 = e2)
% 250.88/59.61 (3) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.88/59.61 | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) =
% 250.88/59.61 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.61 (4) op(e2, e0) = e1
% 250.88/59.61 (5) ~ (e3 = e0)
% 250.88/59.61 (6) ~ (e3 = e1)
% 250.88/59.61 (7) all_252_16 = e1
% 250.88/59.61 (8) all_252_24 = e0
% 250.88/59.61 (9) op(e1, e0) = e2
% 250.88/59.61 (10) all_252_17 = e1 & op(e3, e0) = e1
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | ALPHA: (10) implies:
% 250.88/59.61 | (11) all_252_17 = e1
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (3) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (12) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0)
% 250.88/59.61 | | = e3)
% 250.88/59.61 | |
% 250.88/59.61 | | BETA: splitting (12) gives:
% 250.88/59.61 | |
% 250.88/59.61 | | Case 1:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (13) all_252_16 = e3 & op(e4, e0) = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #488.
% 250.88/59.61 | | |
% 250.88/59.61 | | Case 2:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (14) all_252_17 = e3 & op(e3, e0) = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (6), (11), (14) are inconsistent by sub-proof #341.
% 250.88/59.61 | | |
% 250.88/59.61 | | End of split
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (15) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0)
% 250.88/59.61 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (15) are inconsistent by
% 250.88/59.61 | | sub-proof #342.
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #341 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) all_252_17 = e3 & op(e3, e0) = e3
% 250.88/59.61 (2) all_252_17 = e1
% 250.88/59.61 (3) ~ (e3 = e1)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | ALPHA: (1) implies:
% 250.88/59.61 | (4) all_252_17 = e3
% 250.88/59.61 |
% 250.88/59.61 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.61 | (5) e3 = e1
% 250.88/59.61 |
% 250.88/59.61 | SIMP: (5) implies:
% 250.88/59.61 | (6) e3 = e1
% 250.88/59.61 |
% 250.88/59.61 | REDUCE: (3), (6) imply:
% 250.88/59.61 | (7) $false
% 250.88/59.61 |
% 250.88/59.61 | CLOSE: (7) is inconsistent.
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #342 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.61 | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.61 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (3) ~ (e3 = e2)
% 250.88/59.61 (4) op(e2, e0) = e1
% 250.88/59.61 (5) ~ (e3 = e0)
% 250.88/59.61 (6) ~ (e3 = e1)
% 250.88/59.61 (7) all_252_24 = e0
% 250.88/59.61 (8) op(e1, e0) = e2
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (1) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (9) all_252_18 = e3 & op(e2, e0) = e3
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (9) implies:
% 250.88/59.61 | | (10) op(e2, e0) = e3
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #399.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (11) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0)
% 250.88/59.61 | | = e3)
% 250.88/59.61 | |
% 250.88/59.61 | | BETA: splitting (11) gives:
% 250.88/59.61 | |
% 250.88/59.61 | | Case 1:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (12) all_252_19 = e3 & op(e1, e0) = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | ALPHA: (12) implies:
% 250.88/59.61 | | | (13) op(e1, e0) = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (2), (3), (8), (13) are inconsistent by sub-proof #736.
% 250.88/59.61 | | |
% 250.88/59.61 | | Case 2:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (14) all_252_24 = e3 & op(e0, e0) = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | ALPHA: (14) implies:
% 250.88/59.61 | | | (15) all_252_24 = e3
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #343.
% 250.88/59.61 | | |
% 250.88/59.61 | | End of split
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #343 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) all_252_24 = e3
% 250.88/59.61 (2) all_252_24 = e0
% 250.88/59.61 (3) ~ (e3 = e0)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | COMBINE_EQS: (1), (2) imply:
% 250.88/59.61 | (4) e3 = e0
% 250.88/59.61 |
% 250.88/59.61 | SIMP: (4) implies:
% 250.88/59.61 | (5) e3 = e0
% 250.88/59.61 |
% 250.88/59.61 | REDUCE: (3), (5) imply:
% 250.88/59.61 | (6) $false
% 250.88/59.61 |
% 250.88/59.61 | CLOSE: (6) is inconsistent.
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #344 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) all_252_21 = e4 & op(e0, e3) = e4
% 250.88/59.61 (2) all_252_21 = e1
% 250.88/59.61 (3) ~ (e4 = e1)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | ALPHA: (1) implies:
% 250.88/59.61 | (4) all_252_21 = e4
% 250.88/59.61 |
% 250.88/59.61 | COMBINE_EQS: (2), (4) imply:
% 250.88/59.61 | (5) e4 = e1
% 250.88/59.61 |
% 250.88/59.61 | REDUCE: (3), (5) imply:
% 250.88/59.61 | (6) $false
% 250.88/59.61 |
% 250.88/59.61 | CLOSE: (6) is inconsistent.
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #345 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) all_252_4 = e0
% 250.88/59.61 (2) ~ (e3 = e2)
% 250.88/59.61 (3) all_252_5 = e2
% 250.88/59.61 (4) ~ (e3 = e0)
% 250.88/59.61 (5) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (5) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (6) all_252_4 = e3 & op(e4, e2) = e3
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #865.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (7) all_252_5 = e3 & op(e3, e2) = e3
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (7) implies:
% 250.88/59.61 | | (8) all_252_5 = e3
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #507.
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #346 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) op(e0, e3) = e1
% 250.88/59.61 (2) ~ (all_10_2 = e4)
% 250.88/59.61 (3) all_252_21 = e1
% 250.88/59.61 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.88/59.61 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.88/59.61 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.61 (5) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.88/59.61 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.88/59.61 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.88/59.61 (6) ~ (e2 = e0)
% 250.88/59.61 (7) ~ (e1 = e0)
% 250.88/59.61 (8) all_252_13 = e0
% 250.88/59.61 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (10) op(e2, e3) = all_10_2
% 250.88/59.61 (11) ~ (e3 = e2)
% 250.88/59.61 (12) ~ (e4 = e0)
% 250.88/59.61 (13) ~ (e2 = e1)
% 250.88/59.61 (14) ~ (e4 = e1)
% 250.88/59.61 (15) ~ (e3 = e0)
% 250.88/59.61 (16) all_252_2 = e0
% 250.88/59.61 (17) ~ (e3 = e1)
% 250.88/59.61 (18) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.88/59.61 (19) ~ (e4 = e3)
% 250.88/59.61 (20) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.88/59.61 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.61 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.88/59.61 (21) ~ (e4 = e2)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (18) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (22) all_252_2 = e1 & op(e3, e4) = e1
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (7), (16), (22) are inconsistent by sub-proof #568.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (23) all_252_3 = e1 & op(e3, e3) = e1
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (23) implies:
% 250.88/59.61 | | (24) all_252_3 = e1
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 250.88/59.61 | | (14), (15), (17), (19), (20), (21), (24) are inconsistent by
% 250.88/59.61 | | sub-proof #363.
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #347 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) ~ (all_4_2 = e4)
% 250.88/59.61 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.61 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.61 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.61 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.88/59.61 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.88/59.61 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.61 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.88/59.61 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.88/59.61 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.61 (5) ~ (e2 = e0)
% 250.88/59.61 (6) all_252_19 = e2
% 250.88/59.61 (7) ~ (e1 = e0)
% 250.88/59.61 (8) all_252_13 = e0
% 250.88/59.61 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (10) ~ (e3 = e2)
% 250.88/59.61 (11) ~ (e4 = e0)
% 250.88/59.61 (12) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.88/59.61 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.88/59.61 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.61 (13) op(e2, e0) = e1
% 250.88/59.61 (14) ~ (e2 = e1)
% 250.88/59.61 (15) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.61 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.61 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.61 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.61 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.61 op(e0, e1) = e0)))
% 250.88/59.61 (16) ~ (e4 = e1)
% 250.88/59.61 (17) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.88/59.61 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.61 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.61 (18) op(e1, e4) = all_16_2
% 250.88/59.61 (19) ~ (e3 = e0)
% 250.88/59.61 (20) all_252_2 = e0
% 250.88/59.61 (21) ~ (e3 = e1)
% 250.88/59.61 (22) all_252_16 = e1
% 250.88/59.61 (23) op(e3, e1) = all_36_2
% 250.88/59.61 (24) op(e1, e0) = e2
% 250.88/59.61 (25) ~ (all_8_2 = e0)
% 250.88/59.61 (26) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.61 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.61 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.61 (27) ~ (all_36_2 = e0)
% 250.88/59.61 (28) ~ (e4 = e3)
% 250.88/59.61 (29) op(e3, e0) = all_48_2
% 250.88/59.61 (30) op(e1, e2) = all_4_2
% 250.88/59.61 (31) ~ (all_48_2 = e0)
% 250.88/59.61 (32) ~ (e4 = e2)
% 250.88/59.61 (33) op(e3, e2) = all_8_2
% 250.88/59.61 (34) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.88/59.61 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.61 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.61 (35) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.88/59.61 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.88/59.61 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.61 (36) ~ (all_244_3 = e0)
% 250.88/59.61 (37) ~ (all_16_2 = e3)
% 250.88/59.61 (38) all_252_6 = e3
% 250.88/59.61 (39) op(e3, e3) = all_244_3
% 250.88/59.61 (40) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.88/59.61 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.88/59.61 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.61 (41) all_252_20 = e3
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (15) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (42) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (42) implies:
% 250.88/59.61 | | (43) all_252_24 = e0
% 250.88/59.61 | |
% 250.88/59.61 | | BETA: splitting (34) gives:
% 250.88/59.61 | |
% 250.88/59.61 | | Case 1:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (44) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4)
% 250.88/59.61 | | | = e2)
% 250.88/59.61 | | |
% 250.88/59.61 | | | BETA: splitting (44) gives:
% 250.88/59.61 | | |
% 250.88/59.61 | | | Case 1:
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | (45) all_252_0 = e2 & op(e4, e4) = e2
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | ALPHA: (45) implies:
% 250.88/59.61 | | | | (46) all_252_0 = e2
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | BETA: splitting (35) gives:
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | Case 1:
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | | (47) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 250.88/59.61 | | | | | e4) = e4)
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | | REF_CLOSE: (3), (9), (11), (23), (25), (27), (29), (31), (32), (33),
% 250.88/59.61 | | | | | (36), (39), (46), (47) are inconsistent by sub-proof #555.
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | Case 2:
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | | (48) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 250.88/59.61 | | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | | BETA: splitting (48) gives:
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | | Case 1:
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | (49) all_252_6 = e4 & op(e2, e4) = e4
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | ALPHA: (49) implies:
% 250.88/59.61 | | | | | | (50) all_252_6 = e4
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | COMBINE_EQS: (38), (50) imply:
% 250.88/59.61 | | | | | | (51) e4 = e3
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | REDUCE: (28), (51) imply:
% 250.88/59.61 | | | | | | (52) $false
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | CLOSE: (52) is inconsistent.
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | Case 2:
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | (53) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.88/59.61 | | | | | | op(e0, e4) = e4)
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | BETA: splitting (53) gives:
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | | Case 1:
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | (54) all_252_12 = e4 & op(e1, e4) = e4
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | ALPHA: (54) implies:
% 250.88/59.61 | | | | | | | (55) all_252_12 = e4
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | BETA: splitting (40) gives:
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | Case 1:
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | (56) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 250.88/59.61 | | | | | | | | op(e3, e4) = e1)
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | BETA: splitting (56) gives:
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | Case 1:
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | (57) all_252_0 = e1 & op(e4, e4) = e1
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | REF_CLOSE: (14), (46), (57) are inconsistent by sub-proof
% 250.88/59.61 | | | | | | | | | #558.
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | Case 2:
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | (58) all_252_2 = e1 & op(e3, e4) = e1
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | REF_CLOSE: (7), (20), (58) are inconsistent by sub-proof #568.
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | End of split
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | Case 2:
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | (59) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 &
% 250.88/59.61 | | | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | BETA: splitting (59) gives:
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | | Case 1:
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | (60) all_252_6 = e1 & op(e2, e4) = e1
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | ALPHA: (60) implies:
% 250.88/59.61 | | | | | | | | | (61) all_252_6 = e1
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11),
% 250.88/59.61 | | | | | | | | | (12), (13), (14), (16), (17), (18), (19), (21),
% 250.88/59.61 | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 250.88/59.61 | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (39),
% 250.88/59.61 | | | | | | | | | (41), (43), (46), (55), (61) are inconsistent by
% 250.88/59.61 | | | | | | | | | sub-proof #398.
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | Case 2:
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | (62) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1
% 250.88/59.61 | | | | | | | | | & op(e0, e4) = e1)
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | BETA: splitting (62) gives:
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | | Case 1:
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | (63) all_252_12 = e1 & op(e1, e4) = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | ALPHA: (63) implies:
% 250.88/59.61 | | | | | | | | | | (64) all_252_12 = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | REF_CLOSE: (16), (55), (64) are inconsistent by sub-proof
% 250.88/59.61 | | | | | | | | | | #554.
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | Case 2:
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | (65) all_252_20 = e1 & op(e0, e4) = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | ALPHA: (65) implies:
% 250.88/59.61 | | | | | | | | | | (66) all_252_20 = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | COMBINE_EQS: (41), (66) imply:
% 250.88/59.61 | | | | | | | | | | (67) e3 = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | COMBINE_EQS: (38), (67) imply:
% 250.88/59.61 | | | | | | | | | | (68) all_252_6 = e1
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11),
% 250.88/59.61 | | | | | | | | | | (12), (13), (14), (16), (17), (18), (19), (21),
% 250.88/59.61 | | | | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29),
% 250.88/59.61 | | | | | | | | | | (30), (31), (32), (33), (35), (36), (37), (39),
% 250.88/59.61 | | | | | | | | | | (41), (43), (46), (55), (68) are inconsistent by
% 250.88/59.61 | | | | | | | | | | sub-proof #398.
% 250.88/59.61 | | | | | | | | | |
% 250.88/59.61 | | | | | | | | | End of split
% 250.88/59.61 | | | | | | | | |
% 250.88/59.61 | | | | | | | | End of split
% 250.88/59.61 | | | | | | | |
% 250.88/59.61 | | | | | | | End of split
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | Case 2:
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | (69) all_252_20 = e4 & op(e0, e4) = e4
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | | REF_CLOSE: (28), (41), (69) are inconsistent by sub-proof #563.
% 250.88/59.61 | | | | | | |
% 250.88/59.61 | | | | | | End of split
% 250.88/59.61 | | | | | |
% 250.88/59.61 | | | | | End of split
% 250.88/59.61 | | | | |
% 250.88/59.61 | | | | End of split
% 250.88/59.61 | | | |
% 250.88/59.61 | | | Case 2:
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | (70) all_252_2 = e2 & op(e3, e4) = e2
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | ALPHA: (70) implies:
% 250.88/59.61 | | | | (71) all_252_2 = e2
% 250.88/59.61 | | | |
% 250.88/59.61 | | | | REF_CLOSE: (3), (5), (9), (23), (25), (27), (29), (31), (33), (36),
% 250.88/59.61 | | | | (39), (71) are inconsistent by sub-proof #571.
% 250.88/59.61 | | | |
% 250.88/59.61 | | | End of split
% 250.88/59.61 | | |
% 250.88/59.61 | | Case 2:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (72) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4)
% 250.88/59.61 | | | = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (14), (16), (18),
% 250.88/59.61 | | | (19), (21), (24), (26), (28), (30), (32), (37), (38), (41),
% 250.88/59.61 | | | (72) are inconsistent by sub-proof #349.
% 250.88/59.61 | | |
% 250.88/59.61 | | End of split
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (73) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.88/59.61 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.88/59.61 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.88/59.61 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.88/59.61 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.88/59.61 | |
% 250.88/59.61 | | ALPHA: (73) implies:
% 250.88/59.61 | | (74) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.88/59.61 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.88/59.61 | | op(e1, e0) = e0)
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (5), (6), (7), (9), (13), (22), (29), (31), (74) are inconsistent
% 250.88/59.61 | | by sub-proof #348.
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #348 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) ~ (e2 = e0)
% 250.88/59.61 (2) all_252_19 = e2
% 250.88/59.61 (3) ~ (e1 = e0)
% 250.88/59.61 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (5) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.61 | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) =
% 250.88/59.61 e0)
% 250.88/59.61 (6) op(e2, e0) = e1
% 250.88/59.61 (7) all_252_16 = e1
% 250.88/59.61 (8) op(e3, e0) = all_48_2
% 250.88/59.61 (9) ~ (all_48_2 = e0)
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (5) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (10) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.88/59.61 | | = e0)
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (3), (4), (7), (8), (9), (10) are inconsistent by sub-proof #397.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (11) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.88/59.61 | | = e0)
% 250.88/59.61 | |
% 250.88/59.61 | | BETA: splitting (11) gives:
% 250.88/59.61 | |
% 250.88/59.61 | | Case 1:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (12) all_252_18 = e0 & op(e2, e0) = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | ALPHA: (12) implies:
% 250.88/59.61 | | | (13) op(e2, e0) = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (3), (4), (6), (13) are inconsistent by sub-proof #901.
% 250.88/59.61 | | |
% 250.88/59.61 | | Case 2:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (14) all_252_19 = e0 & op(e1, e0) = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | ALPHA: (14) implies:
% 250.88/59.61 | | | (15) all_252_19 = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | COMBINE_EQS: (2), (15) imply:
% 250.88/59.61 | | | (16) e2 = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | SIMP: (16) implies:
% 250.88/59.61 | | | (17) e2 = e0
% 250.88/59.61 | | |
% 250.88/59.61 | | | REDUCE: (1), (17) imply:
% 250.88/59.61 | | | (18) $false
% 250.88/59.61 | | |
% 250.88/59.61 | | | CLOSE: (18) is inconsistent.
% 250.88/59.61 | | |
% 250.88/59.61 | | End of split
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #349 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = e2)
% 250.88/59.61 | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.61 (2) ~ (all_4_2 = e4)
% 250.88/59.61 (3) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.61 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.61 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.61 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.88/59.61 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.88/59.61 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.61 (5) ~ (e1 = e0)
% 250.88/59.61 (6) all_252_13 = e0
% 250.88/59.61 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (8) ~ (e3 = e2)
% 250.88/59.61 (9) ~ (e4 = e0)
% 250.88/59.61 (10) ~ (e2 = e1)
% 250.88/59.61 (11) ~ (e4 = e1)
% 250.88/59.61 (12) op(e1, e4) = all_16_2
% 250.88/59.61 (13) ~ (e3 = e0)
% 250.88/59.61 (14) ~ (e3 = e1)
% 250.88/59.61 (15) op(e1, e0) = e2
% 250.88/59.61 (16) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.61 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.61 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.61 (17) ~ (e4 = e3)
% 250.88/59.61 (18) op(e1, e2) = all_4_2
% 250.88/59.61 (19) ~ (e4 = e2)
% 250.88/59.61 (20) ~ (all_16_2 = e3)
% 250.88/59.61 (21) all_252_6 = e3
% 250.88/59.61 (22) all_252_20 = e3
% 250.88/59.61
% 250.88/59.61 Begin of proof
% 250.88/59.61 |
% 250.88/59.61 | BETA: splitting (1) gives:
% 250.88/59.61 |
% 250.88/59.61 | Case 1:
% 250.88/59.61 | |
% 250.88/59.61 | | (23) all_252_6 = e2 & op(e2, e4) = e2
% 250.88/59.61 | |
% 250.88/59.61 | | REF_CLOSE: (8), (21), (23) are inconsistent by sub-proof #450.
% 250.88/59.61 | |
% 250.88/59.61 | Case 2:
% 250.88/59.61 | |
% 250.88/59.61 | | (24) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4)
% 250.88/59.61 | | = e2)
% 250.88/59.61 | |
% 250.88/59.61 | | BETA: splitting (24) gives:
% 250.88/59.61 | |
% 250.88/59.61 | | Case 1:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (25) all_252_12 = e2 & op(e1, e4) = e2
% 250.88/59.61 | | |
% 250.88/59.61 | | | ALPHA: (25) implies:
% 250.88/59.61 | | | (26) all_252_12 = e2
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.88/59.61 | | | (14), (15), (16), (17), (18), (19), (20), (26) are inconsistent
% 250.88/59.61 | | | by sub-proof #392.
% 250.88/59.61 | | |
% 250.88/59.61 | | Case 2:
% 250.88/59.61 | | |
% 250.88/59.61 | | | (27) all_252_20 = e2 & op(e0, e4) = e2
% 250.88/59.61 | | |
% 250.88/59.61 | | | REF_CLOSE: (8), (22), (27) are inconsistent by sub-proof #560.
% 250.88/59.61 | | |
% 250.88/59.61 | | End of split
% 250.88/59.61 | |
% 250.88/59.61 | End of split
% 250.88/59.61 |
% 250.88/59.61 End of proof
% 250.88/59.61
% 250.88/59.61 Sub-proof #350 shows that the following formulas are inconsistent:
% 250.88/59.61 ----------------------------------------------------------------
% 250.88/59.61 (1) op(e0, e3) = e1
% 250.88/59.61 (2) ~ (all_4_2 = e4)
% 250.88/59.61 (3) ~ (all_10_2 = e4)
% 250.88/59.61 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.61 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.88/59.61 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.61 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 250.88/59.61 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 250.88/59.61 (all_252_16 = e3 & op(e4, e0) = e3)
% 250.88/59.61 (6) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.88/59.61 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.88/59.61 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.88/59.61 (7) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.88/59.61 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.88/59.61 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.88/59.61 (8) all_252_21 = e1
% 250.88/59.61 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.88/59.61 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.88/59.61 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.88/59.61 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.88/59.61 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.88/59.61 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.88/59.61 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.61 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 250.88/59.61 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.88/59.61 (12) all_252_6 = e0
% 250.88/59.61 (13) ~ (e2 = e0)
% 250.88/59.61 (14) all_252_19 = e2
% 250.88/59.61 (15) ~ (e1 = e0)
% 250.88/59.61 (16) all_252_13 = e0
% 250.88/59.61 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.88/59.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.88/59.61 (18) op(e2, e3) = all_10_2
% 250.88/59.61 (19) ~ (e3 = e2)
% 250.88/59.62 (20) ~ (e4 = e0)
% 250.88/59.62 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.88/59.62 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.88/59.62 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.88/59.62 (22) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.88/59.62 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.88/59.62 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.88/59.62 (23) op(e2, e0) = e1
% 250.88/59.62 (24) ~ (e2 = e1)
% 250.88/59.62 (25) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.88/59.62 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.88/59.62 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.88/59.62 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.88/59.62 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.62 op(e0, e1) = e0)))
% 250.88/59.62 (26) ~ (e4 = e1)
% 250.88/59.62 (27) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.88/59.62 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.88/59.62 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.88/59.62 (28) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.88/59.62 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.88/59.62 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.62 (29) op(e1, e4) = all_16_2
% 250.88/59.62 (30) ~ (e3 = e0)
% 250.88/59.62 (31) all_252_2 = e0
% 250.88/59.62 (32) ~ (e3 = e1)
% 250.88/59.62 (33) all_252_16 = e1
% 250.88/59.62 (34) op(e3, e1) = all_36_2
% 250.88/59.62 (35) op(e1, e0) = e2
% 250.88/59.62 (36) ~ (all_8_2 = e0)
% 250.88/59.62 (37) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.88/59.62 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.88/59.62 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.88/59.62 (38) ~ (all_36_2 = e0)
% 250.88/59.62 (39) op(e4, e4) = all_244_0
% 250.88/59.62 (40) ~ (e4 = e3)
% 250.88/59.62 (41) op(e0, e1) = all_20_2
% 250.88/59.62 (42) op(e3, e0) = all_48_2
% 250.88/59.62 (43) op(e1, e2) = all_4_2
% 250.88/59.62 (44) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.88/59.62 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.88/59.62 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.88/59.62 (45) ~ (all_48_2 = e0)
% 250.88/59.62 (46) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.88/59.62 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.88/59.62 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.88/59.62 (47) ~ (e4 = e2)
% 250.88/59.62 (48) op(e3, e2) = all_8_2
% 250.88/59.62 (49) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.88/59.62 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.88/59.62 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.88/59.62 (50) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.88/59.62 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.88/59.62 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.88/59.62 (51) ~ (all_20_2 = e4)
% 250.88/59.62 (52) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.88/59.62 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.88/59.62 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.88/59.62 (53) ~ (all_244_3 = e0)
% 250.88/59.62 (54) ~ (all_16_2 = e3)
% 250.88/59.62 (55) all_252_8 = e1
% 250.88/59.62 (56) ~ (all_244_0 = e3)
% 250.88/59.62 (57) op(e3, e3) = all_244_3
% 250.88/59.62 (58) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.88/59.62 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.88/59.62 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.88/59.62 (59) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.88/59.62 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.88/59.62 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.62 (60) ~ (all_4_2 = e0)
% 250.88/59.62 (61) all_252_20 = e3
% 250.88/59.62
% 250.88/59.62 Begin of proof
% 250.88/59.62 |
% 250.88/59.62 | BETA: splitting (50) gives:
% 250.88/59.62 |
% 250.88/59.62 | Case 1:
% 250.88/59.62 | |
% 250.88/59.62 | | (62) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 250.88/59.62 | | e2)
% 250.88/59.62 | |
% 250.88/59.62 | | BETA: splitting (62) gives:
% 250.88/59.62 | |
% 250.88/59.62 | | Case 1:
% 250.88/59.62 | | |
% 250.88/59.62 | | | (63) all_252_0 = e2 & op(e4, e4) = e2
% 250.88/59.62 | | |
% 250.88/59.62 | | | ALPHA: (63) implies:
% 250.88/59.62 | | | (64) all_252_0 = e2
% 250.88/59.62 | | |
% 250.88/59.62 | | | BETA: splitting (25) gives:
% 250.88/59.62 | | |
% 250.88/59.62 | | | Case 1:
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | (65) all_252_24 = e0 & op(e0, e0) = e0
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | ALPHA: (65) implies:
% 250.88/59.62 | | | | (66) all_252_24 = e0
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | BETA: splitting (59) gives:
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | Case 1:
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | (67) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3,
% 250.88/59.62 | | | | | e4) = e1)
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | BETA: splitting (67) gives:
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | Case 1:
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | (68) all_252_0 = e1 & op(e4, e4) = e1
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | REF_CLOSE: (24), (64), (68) are inconsistent by sub-proof #558.
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | Case 2:
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | (69) all_252_2 = e1 & op(e3, e4) = e1
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | REF_CLOSE: (15), (31), (69) are inconsistent by sub-proof #568.
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | End of split
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | Case 2:
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | (70) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1,
% 250.88/59.62 | | | | | e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | BETA: splitting (70) gives:
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | | Case 1:
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | (71) all_252_6 = e1 & op(e2, e4) = e1
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | ALPHA: (71) implies:
% 250.88/59.62 | | | | | | (72) all_252_6 = e1
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | REF_CLOSE: (2), (6), (7), (11), (13), (14), (15), (16), (17), (19),
% 250.88/59.62 | | | | | | (20), (22), (23), (24), (25), (26), (28), (29), (30),
% 250.88/59.62 | | | | | | (32), (33), (34), (35), (36), (37), (38), (40), (42),
% 250.88/59.62 | | | | | | (43), (45), (47), (48), (50), (52), (53), (54), (57),
% 250.88/59.62 | | | | | | (59), (61), (64), (72) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | #394.
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | Case 2:
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | (73) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 250.88/59.62 | | | | | | op(e0, e4) = e1)
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | BETA: splitting (73) gives:
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | | Case 1:
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | (74) all_252_12 = e1 & op(e1, e4) = e1
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | ALPHA: (74) implies:
% 250.88/59.62 | | | | | | | (75) all_252_12 = e1
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | BETA: splitting (4) gives:
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | | (76) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 250.88/59.62 | | | | | | | | op(e0, e3) = e4)
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | | REF_CLOSE: (1), (17), (26), (40), (61), (76) are inconsistent by
% 250.88/59.62 | | | | | | | | sub-proof #390.
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | | (77) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 250.88/59.62 | | | | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | | BETA: splitting (77) gives:
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | (78) all_252_22 = e4 & op(e0, e2) = e4
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | ALPHA: (78) implies:
% 250.88/59.62 | | | | | | | | | (79) all_252_22 = e4
% 250.88/59.62 | | | | | | | | | (80) op(e0, e2) = e4
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | BETA: splitting (27) gives:
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | (81) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0
% 250.88/59.62 | | | | | | | | | | & op(e3, e2) = e0)
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | BETA: splitting (81) gives:
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | (82) all_252_4 = e0 & op(e4, e2) = e0
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | ALPHA: (82) implies:
% 250.88/59.62 | | | | | | | | | | | (83) all_252_4 = e0
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | BETA: splitting (58) gives:
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | (84) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 250.88/59.62 | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | BETA: splitting (84) gives:
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | (85) all_252_4 = e2 & op(e4, e2) = e2
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | ALPHA: (85) implies:
% 250.88/59.62 | | | | | | | | | | | | | (86) all_252_4 = e2
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | COMBINE_EQS: (83), (86) imply:
% 250.88/59.62 | | | | | | | | | | | | | (87) e2 = e0
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | COMBINE_EQS: (64), (87) imply:
% 250.88/59.62 | | | | | | | | | | | | | (88) all_252_0 = e0
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | REF_CLOSE: (7), (13), (15), (17), (19), (20), (24), (26),
% 250.88/59.62 | | | | | | | | | | | | | (32), (34), (36), (38), (40), (42), (45), (47),
% 250.88/59.62 | | | | | | | | | | | | | (48), (50), (52), (53), (57), (59), (61), (88) are
% 250.88/59.62 | | | | | | | | | | | | | inconsistent by sub-proof #559.
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | (89) all_252_5 = e2 & op(e3, e2) = e2
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | ALPHA: (89) implies:
% 250.88/59.62 | | | | | | | | | | | | | (90) all_252_5 = e2
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | BETA: splitting (5) gives:
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | (91) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 250.88/59.62 | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | (92) all_252_0 = e3 & op(e4, e4) = e3
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | (93) op(e4, e4) = e3
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (56), (93) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | sub-proof #813.
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | (94) all_252_1 = e3 & op(e4, e3) = e3
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | (95) all_252_1 = e3
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | (96) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.88/59.62 | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (26), (75), (96) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | sub-proof #389.
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | (97) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.88/59.62 | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.88/59.62 | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | (98) all_252_14 = e4 & op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | (99) op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (43), (99) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | sub-proof #831.
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | (100) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.88/59.62 | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (101) all_252_15 = e4 & op(e1, e1) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (102) all_252_15 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (103) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (19), (20), (24), (26), (30), (32),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (40), (47), (49), (52), (59), (61), (64), (83),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (90), (103) are inconsistent by sub-proof #383.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (104) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (105) all_252_8 = e3 & op(e2, e2) = e3
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (106) all_252_8 = e3
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (106) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (107) e3 = e1
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (107) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (108) all_252_1 = e1
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (12), (13), (15), (16), (17), (18), (19), (20),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (24), (26), (29), (30), (32), (34), (35), (36),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (37), (38), (40), (42), (43), (44), (45), (47),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (48), (52), (53), (54), (57), (61), (64), (75),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (102), (108) are inconsistent by sub-proof #362.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (109) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (15), (16), (17), (20), (24),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (26), (32), (34), (35), (36), (37), (38), (40),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (42), (43), (45), (47), (48), (52), (53), (57),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (61), (64), (75), (80), (102), (109) are
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #361.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (110) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (111) op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (47), (111) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | sub-proof #829.
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | (112) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 250.88/59.62 | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 250.88/59.62 | | | | | | | | | | | | | | op(e4, e0) = e3)
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | (113) all_252_4 = e3 & op(e4, e2) = e3
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | REF_CLOSE: (30), (83), (113) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | #689.
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | (114) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 250.88/59.62 | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | (115) all_252_9 = e3 & op(e4, e1) = e3
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | (116) all_252_9 = e3
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | (117) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (118) all_252_0 = e4 & op(e4, e4) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (64), (118) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | | | #606.
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (119) all_252_1 = e4 & op(e4, e3) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (120) all_252_1 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (121) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (122) all_252_12 = e4 & op(e1, e4) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (123) all_252_12 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (123) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (124) e4 = e1
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (125) e4 = e1
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (125) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (126) all_252_1 = e1
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (26), (75), (121) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | sub-proof #389.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | (127) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (128) all_252_14 = e4 & op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (129) op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (43), (129) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (130) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (131) all_252_15 = e4 & op(e1, e1) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (132) all_252_15 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (12), (13), (15), (16), (17), (18), (19), (20),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (24), (26), (29), (30), (32), (34), (35), (36),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (40), (42), (43), (44), (45), (47),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (48), (52), (53), (54), (57), (61), (64), (75),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (126), (132) are inconsistent by sub-proof #362.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (133) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (134) op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (47), (134) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #829.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (135) all_252_13 = e4 & op(e1, e3) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (136) all_252_13 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (136) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | #407.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (137) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (138) all_252_14 = e4 & op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (139) op(e1, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (43), (139) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | (140) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | (141) all_252_15 = e4 & op(e1, e1) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | (142) all_252_15 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (143) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (19), (20), (24), (26), (30), (32),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (40), (47), (49), (52), (59), (61), (64), (83),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (90), (143) are inconsistent by sub-proof #383.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | (144) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (145) all_252_8 = e3 & op(e2, e2) = e3
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (55), (145) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | #474.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (146) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (12), (15), (16), (17), (20), (24),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (26), (32), (34), (35), (36), (37), (38), (40),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (45), (47), (48), (52), (53), (57),
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | (61), (64), (75), (80), (142), (146) are
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #361.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | (147) all_252_19 = e4 & op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | (148) op(e1, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (47), (148) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | | sub-proof #829.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | (149) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.88/59.62 | | | | | | | | | | | | | | | | | op(e4, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (150) all_252_4 = e4 & op(e4, e2) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (151) all_252_4 = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (151) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (152) e4 = e0
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | REDUCE: (20), (152) imply:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (153) $false
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | (154) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 250.88/59.62 | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (155) all_252_9 = e4 & op(e4, e1) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (116), (155) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | #360.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | (156) all_252_16 = e4 & op(e4, e0) = e4
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (33), (156) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | | | | #359.
% 250.88/59.62 | | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | (157) all_252_16 = e3 & op(e4, e0) = e3
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | | REF_CLOSE: (32), (33), (157) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | | | | #488.
% 250.88/59.62 | | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | (158) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 250.88/59.62 | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 250.88/59.62 | | | | | | | | | | | | op(e0, e2) = e2)
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | BETA: splitting (158) gives:
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | Case 1:
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | (159) all_252_8 = e2 & op(e2, e2) = e2
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | REF_CLOSE: (24), (55), (159) are inconsistent by sub-proof
% 250.88/59.62 | | | | | | | | | | | | | #788.
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | (160) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 250.88/59.62 | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (11), (15), (16), (17), (19), (20),
% 250.88/59.62 | | | | | | | | | | | | | (24), (26), (29), (30), (32), (35), (37), (40),
% 250.88/59.62 | | | | | | | | | | | | | (43), (47), (54), (79), (160) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | | | sub-proof #354.
% 250.88/59.62 | | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | (161) all_252_5 = e0 & op(e3, e2) = e0
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | | REF_CLOSE: (17), (36), (48), (161) are inconsistent by
% 250.88/59.62 | | | | | | | | | | | sub-proof #874.
% 250.88/59.62 | | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | (162) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 250.88/59.62 | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 250.88/59.62 | | | | | | | | | | e2) = e0)
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | | REF_CLOSE: (15), (17), (20), (43), (55), (60), (79), (162)
% 250.88/59.62 | | | | | | | | | | are inconsistent by sub-proof #353.
% 250.88/59.62 | | | | | | | | | |
% 250.88/59.62 | | | | | | | | | End of split
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | Case 2:
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | (163) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 =
% 250.88/59.62 | | | | | | | | | e4 & op(e0, e0) = e4)
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | | REF_CLOSE: (17), (20), (41), (51), (66), (163) are
% 250.88/59.62 | | | | | | | | | inconsistent by sub-proof #352.
% 250.88/59.62 | | | | | | | | |
% 250.88/59.62 | | | | | | | | End of split
% 250.88/59.62 | | | | | | | |
% 250.88/59.62 | | | | | | | End of split
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | Case 2:
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | (164) all_252_20 = e1 & op(e0, e4) = e1
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | | REF_CLOSE: (32), (61), (164) are inconsistent by sub-proof #565.
% 250.88/59.62 | | | | | | |
% 250.88/59.62 | | | | | | End of split
% 250.88/59.62 | | | | | |
% 250.88/59.62 | | | | | End of split
% 250.88/59.62 | | | | |
% 250.88/59.62 | | | | End of split
% 250.88/59.62 | | | |
% 250.88/59.62 | | | Case 2:
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | (165) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 250.88/59.62 | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) |
% 250.88/59.62 | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 &
% 250.88/59.62 | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.88/59.62 | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.88/59.62 | | | | op(e0, e1) = e0))
% 250.88/59.62 | | | |
% 250.88/59.62 | | | | REF_CLOSE: (7), (13), (14), (15), (17), (19), (20), (23), (24), (26),
% 250.88/59.62 | | | | (32), (33), (34), (36), (38), (40), (42), (45), (47), (48),
% 250.88/59.62 | | | | (50), (52), (53), (57), (59), (61), (64), (165) are
% 250.88/59.62 | | | | inconsistent by sub-proof #395.
% 250.88/59.62 | | | |
% 250.88/59.62 | | | End of split
% 250.88/59.62 | | |
% 250.88/59.62 | | Case 2:
% 250.88/59.62 | | |
% 250.94/59.62 | | | (166) all_252_2 = e2 & op(e3, e4) = e2
% 250.94/59.62 | | |
% 250.94/59.62 | | | ALPHA: (166) implies:
% 250.94/59.62 | | | (167) all_252_2 = e2
% 250.94/59.62 | | |
% 250.94/59.62 | | | REF_CLOSE: (7), (13), (17), (34), (36), (38), (42), (45), (48), (53),
% 250.94/59.62 | | | (57), (167) are inconsistent by sub-proof #571.
% 250.94/59.62 | | |
% 250.94/59.62 | | End of split
% 250.94/59.62 | |
% 250.94/59.62 | Case 2:
% 250.94/59.62 | |
% 250.94/59.62 | | (168) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4)
% 250.94/59.62 | | = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.94/59.62 | |
% 250.94/59.62 | | REF_CLOSE: (2), (6), (11), (12), (13), (15), (16), (17), (19), (20), (24),
% 250.94/59.62 | | (26), (29), (30), (31), (32), (35), (37), (40), (43), (47), (49),
% 250.94/59.62 | | (52), (54), (59), (168) are inconsistent by sub-proof #351.
% 250.94/59.62 | |
% 250.94/59.62 | End of split
% 250.94/59.62 |
% 250.94/59.62 End of proof
% 250.94/59.62
% 250.94/59.62 Sub-proof #351 shows that the following formulas are inconsistent:
% 250.94/59.62 ----------------------------------------------------------------
% 250.94/59.62 (1) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = e2)
% 250.94/59.62 | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.94/59.62 (2) ~ (all_4_2 = e4)
% 250.94/59.62 (3) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.62 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.62 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.62 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.62 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.62 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.62 (5) all_252_6 = e0
% 250.94/59.62 (6) ~ (e2 = e0)
% 250.94/59.62 (7) ~ (e1 = e0)
% 250.94/59.62 (8) all_252_13 = e0
% 250.94/59.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.62 (10) ~ (e3 = e2)
% 250.94/59.62 (11) ~ (e4 = e0)
% 250.94/59.62 (12) ~ (e2 = e1)
% 250.94/59.62 (13) ~ (e4 = e1)
% 250.94/59.62 (14) op(e1, e4) = all_16_2
% 250.94/59.62 (15) ~ (e3 = e0)
% 250.94/59.62 (16) all_252_2 = e0
% 250.94/59.63 (17) ~ (e3 = e1)
% 250.94/59.63 (18) op(e1, e0) = e2
% 250.94/59.63 (19) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.63 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.63 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (20) ~ (e4 = e3)
% 250.94/59.63 (21) op(e1, e2) = all_4_2
% 250.94/59.63 (22) ~ (e4 = e2)
% 250.94/59.63 (23) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.94/59.63 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.94/59.63 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.63 (24) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.63 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.63 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.63 (25) ~ (all_16_2 = e3)
% 250.94/59.63 (26) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.94/59.63 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.94/59.63 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (1) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (27) all_252_6 = e2 & op(e2, e4) = e2
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (5), (6), (27) are inconsistent by sub-proof #892.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4)
% 250.94/59.63 | | = e2)
% 250.94/59.63 | |
% 250.94/59.63 | | BETA: splitting (28) gives:
% 250.94/59.63 | |
% 250.94/59.63 | | Case 1:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (29) all_252_12 = e2 & op(e1, e4) = e2
% 250.94/59.63 | | |
% 250.94/59.63 | | | ALPHA: (29) implies:
% 250.94/59.63 | | | (30) all_252_12 = e2
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 250.94/59.63 | | | (15), (17), (18), (19), (20), (21), (22), (25), (30) are
% 250.94/59.63 | | | inconsistent by sub-proof #392.
% 250.94/59.63 | | |
% 250.94/59.63 | | Case 2:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (31) all_252_20 = e2 & op(e0, e4) = e2
% 250.94/59.63 | | |
% 250.94/59.63 | | | ALPHA: (31) implies:
% 250.94/59.63 | | | (32) all_252_20 = e2
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (5), (7), (9), (10), (11), (12), (13), (14), (15), (16), (17),
% 250.94/59.63 | | | (20), (22), (23), (24), (25), (26), (32) are inconsistent by
% 250.94/59.63 | | | sub-proof #538.
% 250.94/59.63 | | |
% 250.94/59.63 | | End of split
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #352 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (2) ~ (e4 = e0)
% 250.94/59.63 (3) all_252_24 = e0
% 250.94/59.63 (4) op(e0, e1) = all_20_2
% 250.94/59.63 (5) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.94/59.63 (6) ~ (all_20_2 = e4)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (5) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (7) all_252_23 = e4 & op(e0, e1) = e4
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #912.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (8) all_252_24 = e4 & op(e0, e0) = e4
% 250.94/59.63 | |
% 250.94/59.63 | | ALPHA: (8) implies:
% 250.94/59.63 | | (9) all_252_24 = e4
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #401.
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #353 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) all_252_22 = e4
% 250.94/59.63 (2) ~ (e1 = e0)
% 250.94/59.63 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (4) ~ (e4 = e0)
% 250.94/59.63 (5) op(e1, e2) = all_4_2
% 250.94/59.63 (6) all_252_8 = e1
% 250.94/59.63 (7) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = e0)
% 250.94/59.63 | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.94/59.63 (8) ~ (all_4_2 = e0)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (7) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (9) all_252_8 = e0 & op(e2, e2) = e0
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #873.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (10) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2)
% 250.94/59.63 | | = e0)
% 250.94/59.63 | |
% 250.94/59.63 | | BETA: splitting (10) gives:
% 250.94/59.63 | |
% 250.94/59.63 | | Case 1:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (11) all_252_14 = e0 & op(e1, e2) = e0
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (3), (5), (8), (11) are inconsistent by sub-proof #855.
% 250.94/59.63 | | |
% 250.94/59.63 | | Case 2:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (12) all_252_22 = e0 & op(e0, e2) = e0
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #444.
% 250.94/59.63 | | |
% 250.94/59.63 | | End of split
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #354 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) ~ (all_4_2 = e4)
% 250.94/59.63 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.63 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.63 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.63 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.63 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.63 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.63 (4) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.94/59.63 (5) all_252_22 = e4
% 250.94/59.63 (6) ~ (e1 = e0)
% 250.94/59.63 (7) all_252_13 = e0
% 250.94/59.63 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (9) ~ (e3 = e2)
% 250.94/59.63 (10) ~ (e4 = e0)
% 250.94/59.63 (11) ~ (e2 = e1)
% 250.94/59.63 (12) ~ (e4 = e1)
% 250.94/59.63 (13) op(e1, e4) = all_16_2
% 250.94/59.63 (14) ~ (e3 = e0)
% 250.94/59.63 (15) ~ (e3 = e1)
% 250.94/59.63 (16) op(e1, e0) = e2
% 250.94/59.63 (17) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.63 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.63 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (18) ~ (e4 = e3)
% 250.94/59.63 (19) op(e1, e2) = all_4_2
% 250.94/59.63 (20) ~ (e4 = e2)
% 250.94/59.63 (21) ~ (all_16_2 = e3)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (4) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (22) all_252_14 = e2 & op(e1, e2) = e2
% 250.94/59.63 | |
% 250.94/59.63 | | ALPHA: (22) implies:
% 250.94/59.63 | | (23) all_252_14 = e2
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 250.94/59.63 | | (15), (16), (17), (18), (19), (20), (21), (23) are inconsistent
% 250.94/59.63 | | by sub-proof #356.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (24) all_252_22 = e2 & op(e0, e2) = e2
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (5), (20), (24) are inconsistent by sub-proof #355.
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #355 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) all_252_22 = e2 & op(e0, e2) = e2
% 250.94/59.63 (2) all_252_22 = e4
% 250.94/59.63 (3) ~ (e4 = e2)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | ALPHA: (1) implies:
% 250.94/59.63 | (4) all_252_22 = e2
% 250.94/59.63 |
% 250.94/59.63 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.63 | (5) e4 = e2
% 250.94/59.63 |
% 250.94/59.63 | SIMP: (5) implies:
% 250.94/59.63 | (6) e4 = e2
% 250.94/59.63 |
% 250.94/59.63 | REDUCE: (3), (6) imply:
% 250.94/59.63 | (7) $false
% 250.94/59.63 |
% 250.94/59.63 | CLOSE: (7) is inconsistent.
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #356 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) ~ (all_4_2 = e4)
% 250.94/59.63 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.63 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.63 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.63 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.63 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.63 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.63 (4) ~ (e1 = e0)
% 250.94/59.63 (5) all_252_13 = e0
% 250.94/59.63 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (7) ~ (e3 = e2)
% 250.94/59.63 (8) ~ (e4 = e0)
% 250.94/59.63 (9) ~ (e2 = e1)
% 250.94/59.63 (10) ~ (e4 = e1)
% 250.94/59.63 (11) op(e1, e4) = all_16_2
% 250.94/59.63 (12) ~ (e3 = e0)
% 250.94/59.63 (13) ~ (e3 = e1)
% 250.94/59.63 (14) op(e1, e0) = e2
% 250.94/59.63 (15) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.63 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.63 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (16) ~ (e4 = e3)
% 250.94/59.63 (17) op(e1, e2) = all_4_2
% 250.94/59.63 (18) all_252_14 = e2
% 250.94/59.63 (19) ~ (e4 = e2)
% 250.94/59.63 (20) ~ (all_16_2 = e3)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (3) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (21) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 250.94/59.63 | | = e3)
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (5), (6), (11), (12), (20), (21) are inconsistent by sub-proof
% 250.94/59.63 | | #412.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (22) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1)
% 250.94/59.63 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.63 | |
% 250.94/59.63 | | BETA: splitting (22) gives:
% 250.94/59.63 | |
% 250.94/59.63 | | Case 1:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (23) all_252_14 = e3 & op(e1, e2) = e3
% 250.94/59.63 | | |
% 250.94/59.63 | | | ALPHA: (23) implies:
% 250.94/59.63 | | | (24) all_252_14 = e3
% 250.94/59.63 | | |
% 250.94/59.63 | | | COMBINE_EQS: (18), (24) imply:
% 250.94/59.63 | | | (25) e3 = e2
% 250.94/59.63 | | |
% 250.94/59.63 | | | REDUCE: (7), (25) imply:
% 250.94/59.63 | | | (26) $false
% 250.94/59.63 | | |
% 250.94/59.63 | | | CLOSE: (26) is inconsistent.
% 250.94/59.63 | | |
% 250.94/59.63 | | Case 2:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (27) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1,
% 250.94/59.63 | | | e0) = e3)
% 250.94/59.63 | | |
% 250.94/59.63 | | | BETA: splitting (27) gives:
% 250.94/59.63 | | |
% 250.94/59.63 | | | Case 1:
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | (28) all_252_15 = e3 & op(e1, e1) = e3
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | ALPHA: (28) implies:
% 250.94/59.63 | | | | (29) all_252_15 = e3
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | BETA: splitting (15) gives:
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | Case 1:
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | | (30) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 &
% 250.94/59.63 | | | | | op(e1, e3) = e4)
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | | BETA: splitting (30) gives:
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | | Case 1:
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | (31) all_252_12 = e4 & op(e1, e4) = e4
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | ALPHA: (31) implies:
% 250.94/59.63 | | | | | | (32) all_252_12 = e4
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | BETA: splitting (2) gives:
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | Case 1:
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | (33) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 &
% 250.94/59.63 | | | | | | | op(e1, e3) = e1)
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | BETA: splitting (33) gives:
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | Case 1:
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | (34) all_252_12 = e1 & op(e1, e4) = e1
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | REF_CLOSE: (10), (32), (34) are inconsistent by sub-proof #566.
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | Case 2:
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | (35) all_252_13 = e1 & op(e1, e3) = e1
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | REF_CLOSE: (4), (5), (35) are inconsistent by sub-proof #411.
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | End of split
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | Case 2:
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | (36) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 &
% 250.94/59.63 | | | | | | | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | BETA: splitting (36) gives:
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | | Case 1:
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | (37) all_252_14 = e1 & op(e1, e2) = e1
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | REF_CLOSE: (9), (18), (37) are inconsistent by sub-proof #753.
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | Case 2:
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | (38) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 &
% 250.94/59.63 | | | | | | | | op(e1, e0) = e1)
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | BETA: splitting (38) gives:
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | | Case 1:
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | | (39) all_252_15 = e1 & op(e1, e1) = e1
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | | REF_CLOSE: (13), (29), (39) are inconsistent by sub-proof
% 250.94/59.63 | | | | | | | | | #358.
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | Case 2:
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | | (40) all_252_19 = e1 & op(e1, e0) = e1
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | | REF_CLOSE: (6), (9), (14), (40) are inconsistent by sub-proof
% 250.94/59.63 | | | | | | | | | #408.
% 250.94/59.63 | | | | | | | | |
% 250.94/59.63 | | | | | | | | End of split
% 250.94/59.63 | | | | | | | |
% 250.94/59.63 | | | | | | | End of split
% 250.94/59.63 | | | | | | |
% 250.94/59.63 | | | | | | End of split
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | Case 2:
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | (41) all_252_13 = e4 & op(e1, e3) = e4
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | ALPHA: (41) implies:
% 250.94/59.63 | | | | | | (42) all_252_13 = e4
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | | REF_CLOSE: (5), (8), (42) are inconsistent by sub-proof #407.
% 250.94/59.63 | | | | | |
% 250.94/59.63 | | | | | End of split
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | Case 2:
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | | (43) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 250.94/59.63 | | | | | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | | REF_CLOSE: (1), (6), (14), (16), (17), (19), (29), (43) are
% 250.94/59.63 | | | | | inconsistent by sub-proof #357.
% 250.94/59.63 | | | | |
% 250.94/59.63 | | | | End of split
% 250.94/59.63 | | | |
% 250.94/59.63 | | | Case 2:
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | (44) all_252_19 = e3 & op(e1, e0) = e3
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | ALPHA: (44) implies:
% 250.94/59.63 | | | | (45) op(e1, e0) = e3
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | REF_CLOSE: (6), (7), (14), (45) are inconsistent by sub-proof #736.
% 250.94/59.63 | | | |
% 250.94/59.63 | | | End of split
% 250.94/59.63 | | |
% 250.94/59.63 | | End of split
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #357 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) ~ (all_4_2 = e4)
% 250.94/59.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (3) op(e1, e0) = e2
% 250.94/59.63 (4) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 250.94/59.63 | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (5) ~ (e4 = e3)
% 250.94/59.63 (6) op(e1, e2) = all_4_2
% 250.94/59.63 (7) all_252_15 = e3
% 250.94/59.63 (8) ~ (e4 = e2)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (4) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (9) all_252_14 = e4 & op(e1, e2) = e4
% 250.94/59.63 | |
% 250.94/59.63 | | ALPHA: (9) implies:
% 250.94/59.63 | | (10) op(e1, e2) = e4
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #831.
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0)
% 250.94/59.63 | | = e4)
% 250.94/59.63 | |
% 250.94/59.63 | | BETA: splitting (11) gives:
% 250.94/59.63 | |
% 250.94/59.63 | | Case 1:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (12) all_252_15 = e4 & op(e1, e1) = e4
% 250.94/59.63 | | |
% 250.94/59.63 | | | ALPHA: (12) implies:
% 250.94/59.63 | | | (13) all_252_15 = e4
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #675.
% 250.94/59.63 | | |
% 250.94/59.63 | | Case 2:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (14) all_252_19 = e4 & op(e1, e0) = e4
% 250.94/59.63 | | |
% 250.94/59.63 | | | ALPHA: (14) implies:
% 250.94/59.63 | | | (15) op(e1, e0) = e4
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (2), (3), (8), (15) are inconsistent by sub-proof #829.
% 250.94/59.63 | | |
% 250.94/59.63 | | End of split
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #358 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) all_252_15 = e1 & op(e1, e1) = e1
% 250.94/59.63 (2) all_252_15 = e3
% 250.94/59.63 (3) ~ (e3 = e1)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | ALPHA: (1) implies:
% 250.94/59.63 | (4) all_252_15 = e1
% 250.94/59.63 |
% 250.94/59.63 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.63 | (5) e3 = e1
% 250.94/59.63 |
% 250.94/59.63 | REDUCE: (3), (5) imply:
% 250.94/59.63 | (6) $false
% 250.94/59.63 |
% 250.94/59.63 | CLOSE: (6) is inconsistent.
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #359 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) all_252_16 = e4 & op(e4, e0) = e4
% 250.94/59.63 (2) all_252_16 = e1
% 250.94/59.63 (3) ~ (e4 = e1)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | ALPHA: (1) implies:
% 250.94/59.63 | (4) all_252_16 = e4
% 250.94/59.63 |
% 250.94/59.63 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.63 | (5) e4 = e1
% 250.94/59.63 |
% 250.94/59.63 | SIMP: (5) implies:
% 250.94/59.63 | (6) e4 = e1
% 250.94/59.63 |
% 250.94/59.63 | REDUCE: (3), (6) imply:
% 250.94/59.63 | (7) $false
% 250.94/59.63 |
% 250.94/59.63 | CLOSE: (7) is inconsistent.
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #360 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) all_252_9 = e4 & op(e4, e1) = e4
% 250.94/59.63 (2) all_252_9 = e3
% 250.94/59.63 (3) ~ (e4 = e3)
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | ALPHA: (1) implies:
% 250.94/59.63 | (4) all_252_9 = e4
% 250.94/59.63 |
% 250.94/59.63 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.63 | (5) e4 = e3
% 250.94/59.63 |
% 250.94/59.63 | REDUCE: (3), (5) imply:
% 250.94/59.63 | (6) $false
% 250.94/59.63 |
% 250.94/59.63 | CLOSE: (6) is inconsistent.
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #361 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) ~ (all_4_2 = e4)
% 250.94/59.63 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.63 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.63 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.63 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.94/59.63 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.94/59.63 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.94/59.63 (4) op(e0, e2) = e4
% 250.94/59.63 (5) all_252_6 = e0
% 250.94/59.63 (6) all_252_15 = e4
% 250.94/59.63 (7) ~ (e1 = e0)
% 250.94/59.63 (8) all_252_13 = e0
% 250.94/59.63 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (10) ~ (e4 = e0)
% 250.94/59.63 (11) all_252_0 = e2
% 250.94/59.63 (12) ~ (e2 = e1)
% 250.94/59.63 (13) ~ (e4 = e1)
% 250.94/59.63 (14) ~ (e3 = e1)
% 250.94/59.63 (15) op(e3, e1) = all_36_2
% 250.94/59.63 (16) op(e1, e0) = e2
% 250.94/59.63 (17) ~ (all_8_2 = e0)
% 250.94/59.63 (18) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.63 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.63 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (19) ~ (all_36_2 = e0)
% 250.94/59.63 (20) ~ (e4 = e3)
% 250.94/59.63 (21) op(e3, e0) = all_48_2
% 250.94/59.63 (22) op(e1, e2) = all_4_2
% 250.94/59.63 (23) ~ (all_48_2 = e0)
% 250.94/59.63 (24) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) =
% 250.94/59.63 e3)
% 250.94/59.63 (25) ~ (e4 = e2)
% 250.94/59.63 (26) op(e3, e2) = all_8_2
% 250.94/59.63 (27) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.63 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.63 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.63 (28) ~ (all_244_3 = e0)
% 250.94/59.63 (29) op(e3, e3) = all_244_3
% 250.94/59.63 (30) all_252_12 = e1
% 250.94/59.63 (31) all_252_20 = e3
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (24) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (32) all_252_14 = e3 & op(e1, e2) = e3
% 250.94/59.63 | |
% 250.94/59.63 | | ALPHA: (32) implies:
% 250.94/59.63 | | (33) all_252_14 = e3
% 250.94/59.63 | |
% 250.94/59.63 | | BETA: splitting (27) gives:
% 250.94/59.63 | |
% 250.94/59.63 | | Case 1:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (34) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4)
% 250.94/59.63 | | | = e4)
% 250.94/59.63 | | |
% 250.94/59.63 | | | BETA: splitting (34) gives:
% 250.94/59.63 | | |
% 250.94/59.63 | | | Case 1:
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | (35) all_252_0 = e4 & op(e4, e4) = e4
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | ALPHA: (35) implies:
% 250.94/59.63 | | | | (36) all_252_0 = e4
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | COMBINE_EQS: (11), (36) imply:
% 250.94/59.63 | | | | (37) e4 = e2
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | SIMP: (37) implies:
% 250.94/59.63 | | | | (38) e4 = e2
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | COMBINE_EQS: (6), (38) imply:
% 250.94/59.63 | | | | (39) all_252_15 = e2
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (12), (13), (14), (16), (18),
% 250.94/59.63 | | | | (22), (25), (33), (39) are inconsistent by sub-proof #406.
% 250.94/59.63 | | | |
% 250.94/59.63 | | | Case 2:
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | (40) all_252_2 = e4 & op(e3, e4) = e4
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | ALPHA: (40) implies:
% 250.94/59.63 | | | | (41) all_252_2 = e4
% 250.94/59.63 | | | |
% 250.94/59.63 | | | | REF_CLOSE: (3), (9), (10), (15), (17), (19), (21), (23), (26), (28),
% 250.94/59.63 | | | | (29), (41) are inconsistent by sub-proof #569.
% 250.94/59.63 | | | |
% 250.94/59.63 | | | End of split
% 250.94/59.63 | | |
% 250.94/59.63 | | Case 2:
% 250.94/59.63 | | |
% 250.94/59.63 | | | (42) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4)
% 250.94/59.63 | | | = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.63 | | |
% 250.94/59.63 | | | REF_CLOSE: (5), (10), (13), (20), (30), (31), (42) are inconsistent by
% 250.94/59.63 | | | sub-proof #552.
% 250.94/59.63 | | |
% 250.94/59.63 | | End of split
% 250.94/59.63 | |
% 250.94/59.63 | Case 2:
% 250.94/59.63 | |
% 250.94/59.63 | | (43) all_252_22 = e3 & op(e0, e2) = e3
% 250.94/59.63 | |
% 250.94/59.63 | | ALPHA: (43) implies:
% 250.94/59.63 | | (44) op(e0, e2) = e3
% 250.94/59.63 | |
% 250.94/59.63 | | REF_CLOSE: (4), (9), (20), (44) are inconsistent by sub-proof #857.
% 250.94/59.63 | |
% 250.94/59.63 | End of split
% 250.94/59.63 |
% 250.94/59.63 End of proof
% 250.94/59.63
% 250.94/59.63 Sub-proof #362 shows that the following formulas are inconsistent:
% 250.94/59.63 ----------------------------------------------------------------
% 250.94/59.63 (1) op(e0, e3) = e1
% 250.94/59.63 (2) ~ (all_4_2 = e4)
% 250.94/59.63 (3) ~ (all_10_2 = e4)
% 250.94/59.63 (4) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.63 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.63 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.63 (5) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.94/59.63 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.94/59.63 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.94/59.63 (6) all_252_21 = e1
% 250.94/59.63 (7) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.94/59.63 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.94/59.63 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.63 (8) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.94/59.63 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.63 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.63 (9) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.63 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.63 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.63 (10) all_252_6 = e0
% 250.94/59.63 (11) all_252_15 = e4
% 250.94/59.63 (12) ~ (e2 = e0)
% 250.94/59.63 (13) ~ (e1 = e0)
% 250.94/59.63 (14) all_252_13 = e0
% 250.94/59.63 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.63 (16) op(e2, e3) = all_10_2
% 250.94/59.63 (17) ~ (e3 = e2)
% 250.94/59.63 (18) ~ (e4 = e0)
% 250.94/59.63 (19) all_252_0 = e2
% 250.94/59.63 (20) all_252_1 = e1
% 250.94/59.63 (21) ~ (e2 = e1)
% 250.94/59.63 (22) ~ (e4 = e1)
% 250.94/59.63 (23) op(e1, e4) = all_16_2
% 250.94/59.63 (24) ~ (e3 = e0)
% 250.94/59.63 (25) ~ (e3 = e1)
% 250.94/59.63 (26) op(e3, e1) = all_36_2
% 250.94/59.63 (27) op(e1, e0) = e2
% 250.94/59.63 (28) ~ (all_8_2 = e0)
% 250.94/59.63 (29) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.63 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.63 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.63 (30) ~ (all_36_2 = e0)
% 250.94/59.63 (31) ~ (e4 = e3)
% 250.94/59.63 (32) op(e3, e0) = all_48_2
% 250.94/59.63 (33) op(e1, e2) = all_4_2
% 250.94/59.63 (34) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.94/59.63 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.63 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.63 (35) ~ (all_48_2 = e0)
% 250.94/59.63 (36) ~ (e4 = e2)
% 250.94/59.63 (37) op(e3, e2) = all_8_2
% 250.94/59.63 (38) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.63 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.63 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.63 (39) ~ (all_244_3 = e0)
% 250.94/59.63 (40) ~ (all_16_2 = e3)
% 250.94/59.63 (41) op(e3, e3) = all_244_3
% 250.94/59.63 (42) all_252_12 = e1
% 250.94/59.63 (43) all_252_20 = e3
% 250.94/59.63
% 250.94/59.63 Begin of proof
% 250.94/59.63 |
% 250.94/59.63 | BETA: splitting (7) gives:
% 250.94/59.63 |
% 250.94/59.63 | Case 1:
% 250.94/59.63 | |
% 250.94/59.63 | | (44) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.94/59.63 | | e4)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (44) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (45) all_252_1 = e4 & op(e4, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (20), (22), (45) are inconsistent by sub-proof #955.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (46) all_252_3 = e4 & op(e3, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (46) implies:
% 250.94/59.64 | | | (47) all_252_3 = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (38) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (48) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 250.94/59.64 | | | | e4) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (2), (4), (5), (9), (11), (13), (14), (15), (17), (18), (19),
% 250.94/59.64 | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 250.94/59.64 | | | | (32), (33), (35), (36), (37), (39), (40), (41), (48) are
% 250.94/59.64 | | | | inconsistent by sub-proof #403.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (49) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 250.94/59.64 | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | BETA: splitting (49) gives:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | Case 1:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (50) all_252_6 = e4 & op(e2, e4) = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | ALPHA: (50) implies:
% 250.94/59.64 | | | | | (51) all_252_6 = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | COMBINE_EQS: (10), (51) imply:
% 250.94/59.64 | | | | | (52) e4 = e0
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | COMBINE_EQS: (47), (52) imply:
% 250.94/59.64 | | | | | (53) all_252_3 = e0
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REF_CLOSE: (1), (6), (7), (8), (12), (14), (15), (17), (18), (21),
% 250.94/59.64 | | | | | (22), (24), (25), (31), (34), (36), (53) are inconsistent
% 250.94/59.64 | | | | | by sub-proof #365.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | Case 2:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (54) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.94/59.64 | | | | | op(e0, e4) = e4)
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | BETA: splitting (54) gives:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | Case 1:
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | (55) all_252_12 = e4 & op(e1, e4) = e4
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | ALPHA: (55) implies:
% 250.94/59.64 | | | | | | (56) all_252_12 = e4
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | COMBINE_EQS: (42), (56) imply:
% 250.94/59.64 | | | | | | (57) e4 = e1
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | SIMP: (57) implies:
% 250.94/59.64 | | | | | | (58) e4 = e1
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | COMBINE_EQS: (47), (58) imply:
% 250.94/59.64 | | | | | | (59) all_252_3 = e1
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | REF_CLOSE: (1), (3), (6), (7), (8), (12), (14), (15), (16), (17),
% 250.94/59.64 | | | | | | (18), (21), (22), (24), (25), (31), (34), (36), (59) are
% 250.94/59.64 | | | | | | inconsistent by sub-proof #363.
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | Case 2:
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | (60) all_252_20 = e4 & op(e0, e4) = e4
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | REF_CLOSE: (31), (43), (60) are inconsistent by sub-proof #563.
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | End of split
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | End of split
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (61) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.64 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (61) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (62) all_252_7 = e4 & op(e2, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (62) implies:
% 250.94/59.64 | | | (63) op(e2, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (3), (15), (16), (63) are inconsistent by sub-proof #953.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (64) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 250.94/59.64 | | | e3) = e4)
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (64) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (65) all_252_13 = e4 & op(e1, e3) = e4
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | ALPHA: (65) implies:
% 250.94/59.64 | | | | (66) all_252_13 = e4
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (14), (18), (66) are inconsistent by sub-proof #407.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (67) all_252_21 = e4 & op(e0, e3) = e4
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | ALPHA: (67) implies:
% 250.94/59.64 | | | | (68) op(e0, e3) = e4
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (1), (15), (22), (68) are inconsistent by sub-proof #828.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #363 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) ~ (all_10_2 = e4)
% 250.94/59.64 (3) all_252_21 = e1
% 250.94/59.64 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.94/59.64 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.94/59.64 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 (5) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.94/59.64 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.64 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 (6) ~ (e2 = e0)
% 250.94/59.64 (7) all_252_13 = e0
% 250.94/59.64 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (9) all_252_3 = e1
% 250.94/59.64 (10) op(e2, e3) = all_10_2
% 250.94/59.64 (11) ~ (e3 = e2)
% 250.94/59.64 (12) ~ (e4 = e0)
% 250.94/59.64 (13) ~ (e2 = e1)
% 250.94/59.64 (14) ~ (e4 = e1)
% 250.94/59.64 (15) ~ (e3 = e0)
% 250.94/59.64 (16) ~ (e3 = e1)
% 250.94/59.64 (17) ~ (e4 = e3)
% 250.94/59.64 (18) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.94/59.64 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.64 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (19) ~ (e4 = e2)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (5) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (20) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 250.94/59.64 | | e2)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (20) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (21) all_252_1 = e2 & op(e4, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (21) implies:
% 250.94/59.64 | | | (22) all_252_1 = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (4) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (23) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3,
% 250.94/59.64 | | | | e3) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | BETA: splitting (23) gives:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | Case 1:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (24) all_252_1 = e4 & op(e4, e3) = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | ALPHA: (24) implies:
% 250.94/59.64 | | | | | (25) all_252_1 = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | COMBINE_EQS: (22), (25) imply:
% 250.94/59.64 | | | | | (26) e4 = e2
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | SIMP: (26) implies:
% 250.94/59.64 | | | | | (27) e4 = e2
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REDUCE: (19), (27) imply:
% 250.94/59.64 | | | | | (28) $false
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | CLOSE: (28) is inconsistent.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | Case 2:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (29) all_252_3 = e4 & op(e3, e3) = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | ALPHA: (29) implies:
% 250.94/59.64 | | | | | (30) all_252_3 = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REF_CLOSE: (9), (14), (30) are inconsistent by sub-proof #772.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | End of split
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (31) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1,
% 250.94/59.64 | | | | e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (2), (3), (7), (8), (10), (12), (14), (31) are inconsistent
% 250.94/59.64 | | | | by sub-proof #364.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (32) all_252_3 = e2 & op(e3, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (9), (13), (32) are inconsistent by sub-proof #849.
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (33) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.94/59.64 | | e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (33) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (34) all_252_7 = e2 & op(e2, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (34) implies:
% 250.94/59.64 | | | (35) all_252_7 = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (4) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (36) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3,
% 250.94/59.64 | | | | e3) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | BETA: splitting (36) gives:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | Case 1:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (37) all_252_1 = e4 & op(e4, e3) = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | ALPHA: (37) implies:
% 250.94/59.64 | | | | | (38) all_252_1 = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | BETA: splitting (18) gives:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | Case 1:
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | (39) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 250.94/59.64 | | | | | | op(e3, e3) = e3)
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | REF_CLOSE: (9), (16), (17), (38), (39) are inconsistent by sub-proof
% 250.94/59.64 | | | | | | #884.
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | Case 2:
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | (40) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 250.94/59.64 | | | | | | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | | REF_CLOSE: (1), (7), (8), (11), (15), (16), (35), (40) are
% 250.94/59.64 | | | | | | inconsistent by sub-proof #378.
% 250.94/59.64 | | | | | |
% 250.94/59.64 | | | | | End of split
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | Case 2:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (41) all_252_3 = e4 & op(e3, e3) = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | ALPHA: (41) implies:
% 250.94/59.64 | | | | | (42) all_252_3 = e4
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REF_CLOSE: (9), (14), (42) are inconsistent by sub-proof #772.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | End of split
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (43) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1,
% 250.94/59.64 | | | | e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (2), (3), (7), (8), (10), (12), (14), (43) are inconsistent
% 250.94/59.64 | | | | by sub-proof #364.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (44) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0,
% 250.94/59.64 | | | e3) = e2)
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (44) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (45) all_252_13 = e2 & op(e1, e3) = e2
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (6), (7), (45) are inconsistent by sub-proof #376.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (46) all_252_21 = e2 & op(e0, e3) = e2
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (3), (13), (46) are inconsistent by sub-proof #375.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #364 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) ~ (all_10_2 = e4)
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) all_252_13 = e0
% 250.94/59.64 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (5) op(e2, e3) = all_10_2
% 250.94/59.64 (6) ~ (e4 = e0)
% 250.94/59.64 (7) ~ (e4 = e1)
% 250.94/59.64 (8) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.94/59.64 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (8) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (9) all_252_7 = e4 & op(e2, e3) = e4
% 250.94/59.64 | |
% 250.94/59.64 | | ALPHA: (9) implies:
% 250.94/59.64 | | (10) op(e2, e3) = e4
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #953.
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (11) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 250.94/59.64 | | = e4)
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (2), (3), (6), (7), (11) are inconsistent by sub-proof #366.
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #365 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 250.94/59.64 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.94/59.64 | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 (4) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.94/59.64 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.64 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 (5) ~ (e2 = e0)
% 250.94/59.64 (6) all_252_13 = e0
% 250.94/59.64 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (8) ~ (e3 = e2)
% 250.94/59.64 (9) ~ (e4 = e0)
% 250.94/59.64 (10) ~ (e2 = e1)
% 250.94/59.64 (11) ~ (e4 = e1)
% 250.94/59.64 (12) ~ (e3 = e0)
% 250.94/59.64 (13) ~ (e3 = e1)
% 250.94/59.64 (14) ~ (e4 = e3)
% 250.94/59.64 (15) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.94/59.64 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.64 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (16) ~ (e4 = e2)
% 250.94/59.64 (17) all_252_3 = e0
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (3) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (18) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 250.94/59.64 | | e4)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (18) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (19) all_252_1 = e4 & op(e4, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (19) implies:
% 250.94/59.64 | | | (20) all_252_1 = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 250.94/59.64 | | | (15), (16), (17), (20) are inconsistent by sub-proof #374.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (21) all_252_3 = e4 & op(e3, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (9), (17), (21) are inconsistent by sub-proof #373.
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (22) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.64 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (22) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (23) all_252_7 = e4 & op(e2, e3) = e4
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 250.94/59.64 | | | (15), (16), (17), (23) are inconsistent by sub-proof #368.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (24) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 250.94/59.64 | | | e3) = e4)
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (2), (6), (9), (11), (24) are inconsistent by sub-proof #366.
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #366 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_21 = e1
% 250.94/59.64 (2) all_252_13 = e0
% 250.94/59.64 (3) ~ (e4 = e0)
% 250.94/59.64 (4) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.64 (5) ~ (e4 = e1)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (4) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (6) all_252_13 = e4 & op(e1, e3) = e4
% 250.94/59.64 | |
% 250.94/59.64 | | ALPHA: (6) implies:
% 250.94/59.64 | | (7) all_252_13 = e4
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #407.
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (8) all_252_21 = e4 & op(e0, e3) = e4
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #367.
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #367 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_21 = e4 & op(e0, e3) = e4
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) ~ (e4 = e1)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_21 = e4
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e4 = e1
% 250.94/59.64 |
% 250.94/59.64 | SIMP: (5) implies:
% 250.94/59.64 | (6) e4 = e1
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (6) imply:
% 250.94/59.64 | (7) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (7) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #368 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.94/59.64 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.64 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 (4) ~ (e2 = e0)
% 250.94/59.64 (5) all_252_13 = e0
% 250.94/59.64 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (7) ~ (e3 = e2)
% 250.94/59.64 (8) ~ (e2 = e1)
% 250.94/59.64 (9) ~ (e3 = e0)
% 250.94/59.64 (10) ~ (e3 = e1)
% 250.94/59.64 (11) ~ (e4 = e3)
% 250.94/59.64 (12) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.94/59.64 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.64 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (13) ~ (e4 = e2)
% 250.94/59.64 (14) all_252_7 = e4 & op(e2, e3) = e4
% 250.94/59.64 (15) all_252_3 = e0
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (14) implies:
% 250.94/59.64 | (16) all_252_7 = e4
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (12) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (17) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 250.94/59.64 | | e3)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (17) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (18) all_252_1 = e3 & op(e4, e3) = e3
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (18) implies:
% 250.94/59.64 | | | (19) all_252_1 = e3
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (3) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (20) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3,
% 250.94/59.64 | | | | e3) = e2)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | BETA: splitting (20) gives:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | Case 1:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (21) all_252_1 = e2 & op(e4, e3) = e2
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REF_CLOSE: (7), (19), (21) are inconsistent by sub-proof #372.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | Case 2:
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | (22) all_252_3 = e2 & op(e3, e3) = e2
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | | REF_CLOSE: (4), (15), (22) are inconsistent by sub-proof #382.
% 250.94/59.64 | | | | |
% 250.94/59.64 | | | | End of split
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (23) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1,
% 250.94/59.64 | | | | e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (2), (4), (5), (8), (13), (16), (23) are inconsistent by
% 250.94/59.64 | | | | sub-proof #370.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (24) all_252_3 = e3 & op(e3, e3) = e3
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (9), (15), (24) are inconsistent by sub-proof #380.
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (25) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.64 | | e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (1), (5), (6), (9), (10), (11), (16), (25) are inconsistent by
% 250.94/59.64 | | sub-proof #369.
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #369 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) all_252_13 = e0
% 250.94/59.64 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (4) all_252_7 = e4
% 250.94/59.64 (5) ~ (e3 = e0)
% 250.94/59.64 (6) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.64 | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (7) ~ (e3 = e1)
% 250.94/59.64 (8) ~ (e4 = e3)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (6) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (9) all_252_7 = e3 & op(e2, e3) = e3
% 250.94/59.64 | |
% 250.94/59.64 | | ALPHA: (9) implies:
% 250.94/59.64 | | (10) all_252_7 = e3
% 250.94/59.64 | |
% 250.94/59.64 | | COMBINE_EQS: (4), (10) imply:
% 250.94/59.64 | | (11) e4 = e3
% 250.94/59.64 | |
% 250.94/59.64 | | SIMP: (11) implies:
% 250.94/59.64 | | (12) e4 = e3
% 250.94/59.64 | |
% 250.94/59.64 | | REDUCE: (8), (12) imply:
% 250.94/59.64 | | (13) $false
% 250.94/59.64 | |
% 250.94/59.64 | | CLOSE: (13) is inconsistent.
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (14) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.94/59.64 | | = e3)
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (1), (2), (3), (5), (7), (14) are inconsistent by sub-proof #379.
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #370 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.64 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) ~ (e2 = e0)
% 250.94/59.64 (4) all_252_13 = e0
% 250.94/59.64 (5) ~ (e2 = e1)
% 250.94/59.64 (6) all_252_7 = e4
% 250.94/59.64 (7) ~ (e4 = e2)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (1) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (8) all_252_7 = e2 & op(e2, e3) = e2
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (6), (7), (8) are inconsistent by sub-proof #371.
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (9) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.94/59.64 | | e2)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (9) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (10) all_252_13 = e2 & op(e1, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #376.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (11) all_252_21 = e2 & op(e0, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #375.
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #371 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_7 = e2 & op(e2, e3) = e2
% 250.94/59.64 (2) all_252_7 = e4
% 250.94/59.64 (3) ~ (e4 = e2)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_7 = e2
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e4 = e2
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (5) imply:
% 250.94/59.64 | (6) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (6) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #372 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_1 = e2 & op(e4, e3) = e2
% 250.94/59.64 (2) all_252_1 = e3
% 250.94/59.64 (3) ~ (e3 = e2)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_1 = e2
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e3 = e2
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (5) imply:
% 250.94/59.64 | (6) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (6) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #373 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_3 = e4 & op(e3, e3) = e4
% 250.94/59.64 (2) all_252_3 = e0
% 250.94/59.64 (3) ~ (e4 = e0)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_3 = e4
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e4 = e0
% 250.94/59.64 |
% 250.94/59.64 | SIMP: (5) implies:
% 250.94/59.64 | (6) e4 = e0
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (6) imply:
% 250.94/59.64 | (7) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (7) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #374 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 250.94/59.64 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 250.94/59.64 | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 (4) ~ (e2 = e0)
% 250.94/59.64 (5) all_252_13 = e0
% 250.94/59.64 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (7) ~ (e3 = e2)
% 250.94/59.64 (8) ~ (e2 = e1)
% 250.94/59.64 (9) ~ (e3 = e0)
% 250.94/59.64 (10) ~ (e3 = e1)
% 250.94/59.64 (11) ~ (e4 = e3)
% 250.94/59.64 (12) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.94/59.64 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.64 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (13) ~ (e4 = e2)
% 250.94/59.64 (14) all_252_1 = e4
% 250.94/59.64 (15) all_252_3 = e0
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (3) gives:
% 250.94/59.64 |
% 250.94/59.64 | Case 1:
% 250.94/59.64 | |
% 250.94/59.64 | | (16) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 250.94/59.64 | | e2)
% 250.94/59.64 | |
% 250.94/59.64 | | REF_CLOSE: (4), (13), (14), (15), (16) are inconsistent by sub-proof #381.
% 250.94/59.64 | |
% 250.94/59.64 | Case 2:
% 250.94/59.64 | |
% 250.94/59.64 | | (17) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.94/59.64 | | e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.94/59.64 | |
% 250.94/59.64 | | BETA: splitting (17) gives:
% 250.94/59.64 | |
% 250.94/59.64 | | Case 1:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (18) all_252_7 = e2 & op(e2, e3) = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | ALPHA: (18) implies:
% 250.94/59.64 | | | (19) all_252_7 = e2
% 250.94/59.64 | | |
% 250.94/59.64 | | | REF_CLOSE: (1), (5), (6), (7), (9), (10), (11), (12), (14), (15), (19) are
% 250.94/59.64 | | | inconsistent by sub-proof #377.
% 250.94/59.64 | | |
% 250.94/59.64 | | Case 2:
% 250.94/59.64 | | |
% 250.94/59.64 | | | (20) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0,
% 250.94/59.64 | | | e3) = e2)
% 250.94/59.64 | | |
% 250.94/59.64 | | | BETA: splitting (20) gives:
% 250.94/59.64 | | |
% 250.94/59.64 | | | Case 1:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (21) all_252_13 = e2 & op(e1, e3) = e2
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (4), (5), (21) are inconsistent by sub-proof #376.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | Case 2:
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | (22) all_252_21 = e2 & op(e0, e3) = e2
% 250.94/59.64 | | | |
% 250.94/59.64 | | | | REF_CLOSE: (2), (8), (22) are inconsistent by sub-proof #375.
% 250.94/59.64 | | | |
% 250.94/59.64 | | | End of split
% 250.94/59.64 | | |
% 250.94/59.64 | | End of split
% 250.94/59.64 | |
% 250.94/59.64 | End of split
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #375 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_21 = e2 & op(e0, e3) = e2
% 250.94/59.64 (2) all_252_21 = e1
% 250.94/59.64 (3) ~ (e2 = e1)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_21 = e2
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e2 = e1
% 250.94/59.64 |
% 250.94/59.64 | SIMP: (5) implies:
% 250.94/59.64 | (6) e2 = e1
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (6) imply:
% 250.94/59.64 | (7) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (7) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #376 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) all_252_13 = e2 & op(e1, e3) = e2
% 250.94/59.64 (2) all_252_13 = e0
% 250.94/59.64 (3) ~ (e2 = e0)
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | ALPHA: (1) implies:
% 250.94/59.64 | (4) all_252_13 = e2
% 250.94/59.64 |
% 250.94/59.64 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.64 | (5) e2 = e0
% 250.94/59.64 |
% 250.94/59.64 | REDUCE: (3), (5) imply:
% 250.94/59.64 | (6) $false
% 250.94/59.64 |
% 250.94/59.64 | CLOSE: (6) is inconsistent.
% 250.94/59.64 |
% 250.94/59.64 End of proof
% 250.94/59.64
% 250.94/59.64 Sub-proof #377 shows that the following formulas are inconsistent:
% 250.94/59.64 ----------------------------------------------------------------
% 250.94/59.64 (1) op(e0, e3) = e1
% 250.94/59.64 (2) all_252_13 = e0
% 250.94/59.64 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.64 (4) ~ (e3 = e2)
% 250.94/59.64 (5) all_252_7 = e2
% 250.94/59.64 (6) ~ (e3 = e0)
% 250.94/59.64 (7) ~ (e3 = e1)
% 250.94/59.64 (8) ~ (e4 = e3)
% 250.94/59.64 (9) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) |
% 250.94/59.64 (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.64 | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.64 (10) all_252_1 = e4
% 250.94/59.64 (11) all_252_3 = e0
% 250.94/59.64
% 250.94/59.64 Begin of proof
% 250.94/59.64 |
% 250.94/59.64 | BETA: splitting (9) gives:
% 250.94/59.64 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (12) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 250.94/59.65 | | e3)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (12) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (13) all_252_1 = e3 & op(e4, e3) = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (8), (10), (13) are inconsistent by sub-proof #946.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (14) all_252_3 = e3 & op(e3, e3) = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (6), (11), (14) are inconsistent by sub-proof #380.
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (15) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.94/59.65 | | e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (15) are inconsistent by
% 250.94/59.65 | | sub-proof #378.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #378 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) op(e0, e3) = e1
% 250.94/59.65 (2) all_252_13 = e0
% 250.94/59.65 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.65 (4) ~ (e3 = e2)
% 250.94/59.65 (5) all_252_7 = e2
% 250.94/59.65 (6) ~ (e3 = e0)
% 250.94/59.65 (7) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.65 | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.65 (8) ~ (e3 = e1)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (7) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (9) all_252_7 = e3 & op(e2, e3) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (9) implies:
% 250.94/59.65 | | (10) all_252_7 = e3
% 250.94/59.65 | |
% 250.94/59.65 | | COMBINE_EQS: (5), (10) imply:
% 250.94/59.65 | | (11) e3 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | REDUCE: (4), (11) imply:
% 250.94/59.65 | | (12) $false
% 250.94/59.65 | |
% 250.94/59.65 | | CLOSE: (12) is inconsistent.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (13) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3)
% 250.94/59.65 | | = e3)
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (2), (3), (6), (8), (13) are inconsistent by sub-proof #379.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #379 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) op(e0, e3) = e1
% 250.94/59.65 (2) all_252_13 = e0
% 250.94/59.65 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.65 (4) ~ (e3 = e0)
% 250.94/59.65 (5) ~ (e3 = e1)
% 250.94/59.65 (6) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (6) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (7) all_252_13 = e3 & op(e1, e3) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #883.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (8) all_252_21 = e3 & op(e0, e3) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (8) implies:
% 250.94/59.65 | | (9) op(e0, e3) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #590.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #380 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_3 = e3 & op(e3, e3) = e3
% 250.94/59.65 (2) all_252_3 = e0
% 250.94/59.65 (3) ~ (e3 = e0)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | ALPHA: (1) implies:
% 250.94/59.65 | (4) all_252_3 = e3
% 250.94/59.65 |
% 250.94/59.65 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.65 | (5) e3 = e0
% 250.94/59.65 |
% 250.94/59.65 | SIMP: (5) implies:
% 250.94/59.65 | (6) e3 = e0
% 250.94/59.65 |
% 250.94/59.65 | REDUCE: (3), (6) imply:
% 250.94/59.65 | (7) $false
% 250.94/59.65 |
% 250.94/59.65 | CLOSE: (7) is inconsistent.
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #381 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) ~ (e2 = e0)
% 250.94/59.65 (2) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.94/59.65 (3) ~ (e4 = e2)
% 250.94/59.65 (4) all_252_1 = e4
% 250.94/59.65 (5) all_252_3 = e0
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (2) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (6) all_252_1 = e2 & op(e4, e3) = e2
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (6) implies:
% 250.94/59.65 | | (7) all_252_1 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | COMBINE_EQS: (4), (7) imply:
% 250.94/59.65 | | (8) e4 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | REDUCE: (3), (8) imply:
% 250.94/59.65 | | (9) $false
% 250.94/59.65 | |
% 250.94/59.65 | | CLOSE: (9) is inconsistent.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (10) all_252_3 = e2 & op(e3, e3) = e2
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #382.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #382 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_3 = e2 & op(e3, e3) = e2
% 250.94/59.65 (2) all_252_3 = e0
% 250.94/59.65 (3) ~ (e2 = e0)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | ALPHA: (1) implies:
% 250.94/59.65 | (4) all_252_3 = e2
% 250.94/59.65 |
% 250.94/59.65 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.65 | (5) e2 = e0
% 250.94/59.65 |
% 250.94/59.65 | SIMP: (5) implies:
% 250.94/59.65 | (6) e2 = e0
% 250.94/59.65 |
% 250.94/59.65 | REDUCE: (3), (6) imply:
% 250.94/59.65 | (7) $false
% 250.94/59.65 |
% 250.94/59.65 | CLOSE: (7) is inconsistent.
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #383 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_4 = e0
% 250.94/59.65 (2) all_252_6 = e0
% 250.94/59.65 (3) ~ (e1 = e0)
% 250.94/59.65 (4) ~ (e3 = e2)
% 250.94/59.65 (5) ~ (e4 = e0)
% 250.94/59.65 (6) all_252_0 = e2
% 250.94/59.65 (7) ~ (e2 = e1)
% 250.94/59.65 (8) ~ (e4 = e1)
% 250.94/59.65 (9) all_252_5 = e2
% 250.94/59.65 (10) ~ (e3 = e0)
% 250.94/59.65 (11) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.94/59.65 (12) ~ (e3 = e1)
% 250.94/59.65 (13) ~ (e4 = e3)
% 250.94/59.65 (14) ~ (e4 = e2)
% 250.94/59.65 (15) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.94/59.65 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.94/59.65 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.65 (16) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.65 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.65 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65 (17) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.94/59.65 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.94/59.65 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.94/59.65 (18) all_252_20 = e3
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (11) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (19) all_252_4 = e3 & op(e4, e2) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #865.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (20) all_252_5 = e3 & op(e3, e2) = e3
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (20) implies:
% 250.94/59.65 | | (21) all_252_5 = e3
% 250.94/59.65 | |
% 250.94/59.65 | | COMBINE_EQS: (9), (21) imply:
% 250.94/59.65 | | (22) e3 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | SIMP: (22) implies:
% 250.94/59.65 | | (23) e3 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | COMBINE_EQS: (18), (23) imply:
% 250.94/59.65 | | (24) all_252_20 = e2
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 250.94/59.65 | | (16), (17), (24) are inconsistent by sub-proof #384.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #384 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_6 = e0
% 250.94/59.65 (2) ~ (e1 = e0)
% 250.94/59.65 (3) ~ (e3 = e2)
% 250.94/59.65 (4) ~ (e4 = e0)
% 250.94/59.65 (5) all_252_0 = e2
% 250.94/59.65 (6) ~ (e2 = e1)
% 250.94/59.65 (7) ~ (e4 = e1)
% 250.94/59.65 (8) ~ (e3 = e0)
% 250.94/59.65 (9) ~ (e3 = e1)
% 250.94/59.65 (10) all_252_20 = e2
% 250.94/59.65 (11) ~ (e4 = e3)
% 250.94/59.65 (12) ~ (e4 = e2)
% 250.94/59.65 (13) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.94/59.65 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.94/59.65 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.65 (14) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.65 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.65 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65 (15) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.94/59.65 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.94/59.65 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (15) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (16) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 250.94/59.65 | | e1)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (16) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (17) all_252_0 = e1 & op(e4, e4) = e1
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #558.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (18) all_252_2 = e1 & op(e3, e4) = e1
% 250.94/59.65 | | |
% 250.94/59.65 | | | ALPHA: (18) implies:
% 250.94/59.65 | | | (19) all_252_2 = e1
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 250.94/59.65 | | | (14), (19) are inconsistent by sub-proof #386.
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (20) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.94/59.65 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (20) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (21) all_252_6 = e1 & op(e2, e4) = e1
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (1), (2), (21) are inconsistent by sub-proof #545.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (22) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 250.94/59.65 | | | e4) = e1)
% 250.94/59.65 | | |
% 250.94/59.65 | | | BETA: splitting (22) gives:
% 250.94/59.65 | | |
% 250.94/59.65 | | | Case 1:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | (23) all_252_12 = e1 & op(e1, e4) = e1
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | ALPHA: (23) implies:
% 250.94/59.65 | | | | (24) all_252_12 = e1
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | BETA: splitting (13) gives:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | Case 1:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | (25) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 250.94/59.65 | | | | | e4) = e3)
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | BETA: splitting (25) gives:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | Case 1:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (26) all_252_0 = e3 & op(e4, e4) = e3
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | REF_CLOSE: (3), (5), (26) are inconsistent by sub-proof #897.
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | Case 2:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (27) all_252_2 = e3 & op(e3, e4) = e3
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | ALPHA: (27) implies:
% 250.94/59.65 | | | | | | (28) all_252_2 = e3
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | BETA: splitting (14) gives:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | Case 1:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (29) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 &
% 250.94/59.65 | | | | | | | op(e3, e4) = e4)
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | BETA: splitting (29) gives:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | Case 1:
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | (30) all_252_0 = e4 & op(e4, e4) = e4
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | REF_CLOSE: (5), (12), (30) are inconsistent by sub-proof #606.
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | Case 2:
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | (31) all_252_2 = e4 & op(e3, e4) = e4
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | ALPHA: (31) implies:
% 250.94/59.65 | | | | | | | | (32) all_252_2 = e4
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | REF_CLOSE: (11), (28), (32) are inconsistent by sub-proof #838.
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | End of split
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | Case 2:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (33) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 &
% 250.94/59.65 | | | | | | | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | BETA: splitting (33) gives:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | Case 1:
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | (34) all_252_6 = e4 & op(e2, e4) = e4
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | REF_CLOSE: (1), (4), (34) are inconsistent by sub-proof #387.
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | Case 2:
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | (35) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.94/59.65 | | | | | | | | op(e0, e4) = e4)
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | BETA: splitting (35) gives:
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | | Case 1:
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | | (36) all_252_12 = e4 & op(e1, e4) = e4
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | | ALPHA: (36) implies:
% 250.94/59.65 | | | | | | | | | (37) all_252_12 = e4
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | | REF_CLOSE: (7), (24), (37) are inconsistent by sub-proof #554.
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | Case 2:
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | | (38) all_252_20 = e4 & op(e0, e4) = e4
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | | REF_CLOSE: (10), (12), (38) are inconsistent by sub-proof
% 250.94/59.65 | | | | | | | | | #534.
% 250.94/59.65 | | | | | | | | |
% 250.94/59.65 | | | | | | | | End of split
% 250.94/59.65 | | | | | | | |
% 250.94/59.65 | | | | | | | End of split
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | End of split
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | End of split
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | Case 2:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | (39) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1,
% 250.94/59.65 | | | | | e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | BETA: splitting (39) gives:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | Case 1:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (40) all_252_6 = e3 & op(e2, e4) = e3
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | ALPHA: (40) implies:
% 250.94/59.65 | | | | | | (41) all_252_6 = e3
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | REF_CLOSE: (1), (8), (41) are inconsistent by sub-proof #691.
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | Case 2:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (42) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 250.94/59.65 | | | | | | op(e0, e4) = e3)
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | BETA: splitting (42) gives:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | Case 1:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (43) all_252_12 = e3 & op(e1, e4) = e3
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | ALPHA: (43) implies:
% 250.94/59.65 | | | | | | | (44) all_252_12 = e3
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | REF_CLOSE: (9), (24), (44) are inconsistent by sub-proof #385.
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | Case 2:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (45) all_252_20 = e3 & op(e0, e4) = e3
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | REF_CLOSE: (3), (10), (45) are inconsistent by sub-proof #539.
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | End of split
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | End of split
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | End of split
% 250.94/59.65 | | | |
% 250.94/59.65 | | | Case 2:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | (46) all_252_20 = e1 & op(e0, e4) = e1
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | REF_CLOSE: (6), (10), (46) are inconsistent by sub-proof #532.
% 250.94/59.65 | | | |
% 250.94/59.65 | | | End of split
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #385 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_12 = e3
% 250.94/59.65 (2) all_252_12 = e1
% 250.94/59.65 (3) ~ (e3 = e1)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | COMBINE_EQS: (1), (2) imply:
% 250.94/59.65 | (4) e3 = e1
% 250.94/59.65 |
% 250.94/59.65 | SIMP: (4) implies:
% 250.94/59.65 | (5) e3 = e1
% 250.94/59.65 |
% 250.94/59.65 | REDUCE: (3), (5) imply:
% 250.94/59.65 | (6) $false
% 250.94/59.65 |
% 250.94/59.65 | CLOSE: (6) is inconsistent.
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #386 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_6 = e0
% 250.94/59.65 (2) ~ (e3 = e2)
% 250.94/59.65 (3) ~ (e4 = e0)
% 250.94/59.65 (4) all_252_0 = e2
% 250.94/59.65 (5) all_252_2 = e1
% 250.94/59.65 (6) ~ (e4 = e1)
% 250.94/59.65 (7) ~ (e3 = e0)
% 250.94/59.65 (8) ~ (e3 = e1)
% 250.94/59.65 (9) all_252_20 = e2
% 250.94/59.65 (10) ~ (e4 = e3)
% 250.94/59.65 (11) ~ (e4 = e2)
% 250.94/59.65 (12) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.94/59.65 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.94/59.65 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.65 (13) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.65 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.65 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (12) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (14) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 250.94/59.65 | | e3)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (14) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (15) all_252_0 = e3 & op(e4, e4) = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #897.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (16) all_252_2 = e3 & op(e3, e4) = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | ALPHA: (16) implies:
% 250.94/59.65 | | | (17) all_252_2 = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (5), (8), (17) are inconsistent by sub-proof #388.
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (18) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.94/59.65 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (18) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (19) all_252_6 = e3 & op(e2, e4) = e3
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (1), (7), (19) are inconsistent by sub-proof #540.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (20) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 250.94/59.65 | | | e4) = e3)
% 250.94/59.65 | | |
% 250.94/59.65 | | | BETA: splitting (20) gives:
% 250.94/59.65 | | |
% 250.94/59.65 | | | Case 1:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | (21) all_252_12 = e3 & op(e1, e4) = e3
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | ALPHA: (21) implies:
% 250.94/59.65 | | | | (22) all_252_12 = e3
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | BETA: splitting (13) gives:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | Case 1:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 250.94/59.65 | | | | | e4) = e4)
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | REF_CLOSE: (4), (5), (6), (11), (23) are inconsistent by sub-proof
% 250.94/59.65 | | | | | #604.
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | Case 2:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | (24) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 250.94/59.65 | | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | BETA: splitting (24) gives:
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | | Case 1:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (25) all_252_6 = e4 & op(e2, e4) = e4
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | REF_CLOSE: (1), (3), (25) are inconsistent by sub-proof #387.
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | Case 2:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | (26) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.94/59.65 | | | | | | op(e0, e4) = e4)
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | BETA: splitting (26) gives:
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | | Case 1:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (27) all_252_12 = e4 & op(e1, e4) = e4
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | ALPHA: (27) implies:
% 250.94/59.65 | | | | | | | (28) all_252_12 = e4
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | COMBINE_EQS: (22), (28) imply:
% 250.94/59.65 | | | | | | | (29) e4 = e3
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | SIMP: (29) implies:
% 250.94/59.65 | | | | | | | (30) e4 = e3
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | REDUCE: (10), (30) imply:
% 250.94/59.65 | | | | | | | (31) $false
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | CLOSE: (31) is inconsistent.
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | Case 2:
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | (32) all_252_20 = e4 & op(e0, e4) = e4
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | | REF_CLOSE: (9), (11), (32) are inconsistent by sub-proof #534.
% 250.94/59.65 | | | | | | |
% 250.94/59.65 | | | | | | End of split
% 250.94/59.65 | | | | | |
% 250.94/59.65 | | | | | End of split
% 250.94/59.65 | | | | |
% 250.94/59.65 | | | | End of split
% 250.94/59.65 | | | |
% 250.94/59.65 | | | Case 2:
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | (33) all_252_20 = e3 & op(e0, e4) = e3
% 250.94/59.65 | | | |
% 250.94/59.65 | | | | REF_CLOSE: (2), (9), (33) are inconsistent by sub-proof #539.
% 250.94/59.65 | | | |
% 250.94/59.65 | | | End of split
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #387 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_6 = e4 & op(e2, e4) = e4
% 250.94/59.65 (2) all_252_6 = e0
% 250.94/59.65 (3) ~ (e4 = e0)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | ALPHA: (1) implies:
% 250.94/59.65 | (4) all_252_6 = e4
% 250.94/59.65 |
% 250.94/59.65 | COMBINE_EQS: (2), (4) imply:
% 250.94/59.65 | (5) e4 = e0
% 250.94/59.65 |
% 250.94/59.65 | REDUCE: (3), (5) imply:
% 250.94/59.65 | (6) $false
% 250.94/59.65 |
% 250.94/59.65 | CLOSE: (6) is inconsistent.
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #388 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_2 = e3
% 250.94/59.65 (2) all_252_2 = e1
% 250.94/59.65 (3) ~ (e3 = e1)
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | COMBINE_EQS: (1), (2) imply:
% 250.94/59.65 | (4) e3 = e1
% 250.94/59.65 |
% 250.94/59.65 | SIMP: (4) implies:
% 250.94/59.65 | (5) e3 = e1
% 250.94/59.65 |
% 250.94/59.65 | REDUCE: (3), (5) imply:
% 250.94/59.65 | (6) $false
% 250.94/59.65 |
% 250.94/59.65 | CLOSE: (6) is inconsistent.
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #389 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) all_252_13 = e0
% 250.94/59.65 (2) ~ (e4 = e0)
% 250.94/59.65 (3) ~ (e4 = e1)
% 250.94/59.65 (4) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 250.94/59.65 (5) all_252_12 = e1
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (4) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (6) all_252_12 = e4 & op(e1, e4) = e4
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (6) implies:
% 250.94/59.65 | | (7) all_252_12 = e4
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #554.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (8) all_252_13 = e4 & op(e1, e3) = e4
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (8) implies:
% 250.94/59.65 | | (9) all_252_13 = e4
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #407.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #390 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) op(e0, e3) = e1
% 250.94/59.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.65 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.94/59.65 (4) ~ (e4 = e1)
% 250.94/59.65 (5) ~ (e4 = e3)
% 250.94/59.65 (6) all_252_20 = e3
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (3) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (7) all_252_20 = e4 & op(e0, e4) = e4
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #563.
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (8) all_252_21 = e4 & op(e0, e3) = e4
% 250.94/59.65 | |
% 250.94/59.65 | | ALPHA: (8) implies:
% 250.94/59.65 | | (9) op(e0, e3) = e4
% 250.94/59.65 | |
% 250.94/59.65 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #828.
% 250.94/59.65 | |
% 250.94/59.65 | End of split
% 250.94/59.65 |
% 250.94/59.65 End of proof
% 250.94/59.65
% 250.94/59.65 Sub-proof #391 shows that the following formulas are inconsistent:
% 250.94/59.65 ----------------------------------------------------------------
% 250.94/59.65 (1) ~ (all_4_2 = e4)
% 250.94/59.65 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.65 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.65 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.65 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.94/59.65 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.94/59.65 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.94/59.65 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.65 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.65 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.65 (5) ~ (e2 = e0)
% 250.94/59.65 (6) all_252_19 = e2
% 250.94/59.65 (7) ~ (e1 = e0)
% 250.94/59.65 (8) all_252_13 = e0
% 250.94/59.65 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.65 (10) ~ (e3 = e2)
% 250.94/59.65 (11) ~ (e4 = e0)
% 250.94/59.65 (12) all_252_6 = e1
% 250.94/59.65 (13) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.94/59.65 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.94/59.65 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.94/59.65 (14) op(e2, e0) = e1
% 250.94/59.65 (15) ~ (e2 = e1)
% 250.94/59.65 (16) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.94/59.65 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.94/59.65 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.94/59.65 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.94/59.65 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.94/59.65 op(e0, e1) = e0)))
% 250.94/59.65 (17) ~ (e4 = e1)
% 250.94/59.65 (18) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.94/59.65 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.94/59.65 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.94/59.65 (19) op(e1, e4) = all_16_2
% 250.94/59.65 (20) ~ (e3 = e0)
% 250.94/59.65 (21) ~ (e3 = e1)
% 250.94/59.65 (22) all_252_16 = e1
% 250.94/59.65 (23) op(e3, e1) = all_36_2
% 250.94/59.65 (24) op(e1, e0) = e2
% 250.94/59.65 (25) ~ (all_8_2 = e0)
% 250.94/59.65 (26) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.94/59.65 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.94/59.65 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.94/59.65 (27) ~ (all_36_2 = e0)
% 250.94/59.65 (28) ~ (e4 = e3)
% 250.94/59.65 (29) op(e3, e0) = all_48_2
% 250.94/59.65 (30) op(e1, e2) = all_4_2
% 250.94/59.65 (31) ~ (all_48_2 = e0)
% 250.94/59.65 (32) ~ (e4 = e2)
% 250.94/59.65 (33) op(e3, e2) = all_8_2
% 250.94/59.65 (34) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.94/59.65 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.94/59.65 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.94/59.65 (35) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.94/59.65 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.94/59.65 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.94/59.65 (36) ~ (all_244_3 = e0)
% 250.94/59.65 (37) ~ (all_16_2 = e3)
% 250.94/59.65 (38) op(e3, e3) = all_244_3
% 250.94/59.65 (39) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.94/59.65 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.94/59.65 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.94/59.65 (40) all_252_20 = e3
% 250.94/59.65
% 250.94/59.65 Begin of proof
% 250.94/59.65 |
% 250.94/59.65 | BETA: splitting (34) gives:
% 250.94/59.65 |
% 250.94/59.65 | Case 1:
% 250.94/59.65 | |
% 250.94/59.65 | | (41) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 250.94/59.65 | | e2)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (41) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (42) all_252_0 = e2 & op(e4, e4) = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | ALPHA: (42) implies:
% 250.94/59.65 | | | (43) all_252_0 = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.94/59.65 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 250.94/59.65 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 250.94/59.65 | | | (33), (34), (35), (36), (37), (38), (39), (40), (43) are
% 250.94/59.65 | | | inconsistent by sub-proof #394.
% 250.94/59.65 | | |
% 250.94/59.65 | | Case 2:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (44) all_252_2 = e2 & op(e3, e4) = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | ALPHA: (44) implies:
% 250.94/59.65 | | | (45) all_252_2 = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | REF_CLOSE: (3), (5), (9), (23), (25), (27), (29), (31), (33), (36), (38),
% 250.94/59.65 | | | (45) are inconsistent by sub-proof #571.
% 250.94/59.65 | | |
% 250.94/59.65 | | End of split
% 250.94/59.65 | |
% 250.94/59.65 | Case 2:
% 250.94/59.65 | |
% 250.94/59.65 | | (46) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.94/59.65 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.94/59.65 | |
% 250.94/59.65 | | BETA: splitting (46) gives:
% 250.94/59.65 | |
% 250.94/59.65 | | Case 1:
% 250.94/59.65 | | |
% 250.94/59.65 | | | (47) all_252_6 = e2 & op(e2, e4) = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | ALPHA: (47) implies:
% 250.94/59.65 | | | (48) all_252_6 = e2
% 250.94/59.65 | | |
% 250.94/59.65 | | | COMBINE_EQS: (12), (48) imply:
% 250.94/59.65 | | | (49) e2 = e1
% 250.94/59.65 | | |
% 250.94/59.65 | | | SIMP: (49) implies:
% 250.94/59.65 | | | (50) e2 = e1
% 250.94/59.65 | | |
% 250.94/59.66 | | | REDUCE: (15), (50) imply:
% 250.94/59.66 | | | (51) $false
% 250.94/59.66 | | |
% 250.94/59.66 | | | CLOSE: (51) is inconsistent.
% 250.94/59.66 | | |
% 250.94/59.66 | | Case 2:
% 250.94/59.66 | | |
% 250.94/59.66 | | | (52) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 250.94/59.66 | | | e4) = e2)
% 250.94/59.66 | | |
% 250.94/59.66 | | | BETA: splitting (52) gives:
% 250.94/59.66 | | |
% 250.94/59.66 | | | Case 1:
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | (53) all_252_12 = e2 & op(e1, e4) = e2
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | ALPHA: (53) implies:
% 250.94/59.66 | | | | (54) all_252_12 = e2
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (15), (17), (19),
% 250.94/59.66 | | | | (20), (21), (24), (26), (28), (30), (32), (37), (54) are
% 250.94/59.66 | | | | inconsistent by sub-proof #392.
% 250.94/59.66 | | | |
% 250.94/59.66 | | | Case 2:
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | (55) all_252_20 = e2 & op(e0, e4) = e2
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | ALPHA: (55) implies:
% 250.94/59.66 | | | | (56) all_252_20 = e2
% 250.94/59.66 | | | |
% 250.94/59.66 | | | | REF_CLOSE: (10), (40), (56) are inconsistent by sub-proof #520.
% 250.94/59.66 | | | |
% 250.94/59.66 | | | End of split
% 250.94/59.66 | | |
% 250.94/59.66 | | End of split
% 250.94/59.66 | |
% 250.94/59.66 | End of split
% 250.94/59.66 |
% 250.94/59.66 End of proof
% 250.94/59.66
% 250.94/59.66 Sub-proof #392 shows that the following formulas are inconsistent:
% 250.94/59.66 ----------------------------------------------------------------
% 250.94/59.66 (1) ~ (all_4_2 = e4)
% 250.94/59.66 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.94/59.66 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.94/59.66 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.94/59.66 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.94/59.66 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.94/59.66 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.94/59.66 (4) all_252_12 = e2
% 250.94/59.66 (5) ~ (e1 = e0)
% 250.94/59.66 (6) all_252_13 = e0
% 250.94/59.66 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.94/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.94/59.66 (8) ~ (e3 = e2)
% 250.94/59.66 (9) ~ (e4 = e0)
% 250.94/59.66 (10) ~ (e2 = e1)
% 250.94/59.66 (11) ~ (e4 = e1)
% 250.98/59.66 (12) op(e1, e4) = all_16_2
% 250.98/59.66 (13) ~ (e3 = e0)
% 250.98/59.66 (14) ~ (e3 = e1)
% 250.98/59.66 (15) op(e1, e0) = e2
% 250.98/59.66 (16) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.66 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.66 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.66 (17) ~ (e4 = e3)
% 250.98/59.66 (18) op(e1, e2) = all_4_2
% 250.98/59.66 (19) ~ (e4 = e2)
% 250.98/59.66 (20) ~ (all_16_2 = e3)
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | BETA: splitting (16) gives:
% 250.98/59.66 |
% 250.98/59.66 | Case 1:
% 250.98/59.66 | |
% 250.98/59.66 | | (21) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 250.98/59.66 | | = e4)
% 250.98/59.66 | |
% 250.98/59.66 | | BETA: splitting (21) gives:
% 250.98/59.66 | |
% 250.98/59.66 | | Case 1:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (22) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.66 | | |
% 250.98/59.66 | | | REF_CLOSE: (4), (19), (22) are inconsistent by sub-proof #561.
% 250.98/59.66 | | |
% 250.98/59.66 | | Case 2:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (23) all_252_13 = e4 & op(e1, e3) = e4
% 250.98/59.66 | | |
% 250.98/59.66 | | | REF_CLOSE: (6), (9), (23) are inconsistent by sub-proof #413.
% 250.98/59.66 | | |
% 250.98/59.66 | | End of split
% 250.98/59.66 | |
% 250.98/59.66 | Case 2:
% 250.98/59.66 | |
% 250.98/59.66 | | (24) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1)
% 250.98/59.66 | | = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.66 | |
% 250.98/59.66 | | BETA: splitting (24) gives:
% 250.98/59.66 | |
% 250.98/59.66 | | Case 1:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (25) all_252_14 = e4 & op(e1, e2) = e4
% 250.98/59.66 | | |
% 250.98/59.66 | | | ALPHA: (25) implies:
% 250.98/59.66 | | | (26) op(e1, e2) = e4
% 250.98/59.66 | | |
% 250.98/59.66 | | | REF_CLOSE: (1), (7), (18), (26) are inconsistent by sub-proof #831.
% 250.98/59.66 | | |
% 250.98/59.66 | | Case 2:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (27) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.66 | | | e0) = e4)
% 250.98/59.66 | | |
% 250.98/59.66 | | | BETA: splitting (27) gives:
% 250.98/59.66 | | |
% 250.98/59.66 | | | Case 1:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | (28) all_252_15 = e4 & op(e1, e1) = e4
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | ALPHA: (28) implies:
% 250.98/59.66 | | | | (29) all_252_15 = e4
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | BETA: splitting (3) gives:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | Case 1:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | (30) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 &
% 250.98/59.66 | | | | | op(e1, e3) = e3)
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | BETA: splitting (30) gives:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | Case 1:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | (31) all_252_12 = e3 & op(e1, e4) = e3
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | REF_CLOSE: (7), (12), (20), (31) are inconsistent by sub-proof #895.
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | Case 2:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | (32) all_252_13 = e3 & op(e1, e3) = e3
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | REF_CLOSE: (6), (13), (32) are inconsistent by sub-proof #883.
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | End of split
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | Case 2:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | (33) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 250.98/59.66 | | | | | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | BETA: splitting (33) gives:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | Case 1:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | (34) all_252_14 = e3 & op(e1, e2) = e3
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | ALPHA: (34) implies:
% 250.98/59.66 | | | | | | (35) all_252_14 = e3
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | BETA: splitting (2) gives:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | Case 1:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | (36) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 &
% 250.98/59.66 | | | | | | | op(e1, e3) = e1)
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | BETA: splitting (36) gives:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | Case 1:
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | (37) all_252_12 = e1 & op(e1, e4) = e1
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | REF_CLOSE: (4), (10), (37) are inconsistent by sub-proof #393.
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | Case 2:
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | (38) all_252_13 = e1 & op(e1, e3) = e1
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | ALPHA: (38) implies:
% 250.98/59.66 | | | | | | | | (39) all_252_13 = e1
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | REF_CLOSE: (5), (6), (39) are inconsistent by sub-proof #943.
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | End of split
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | Case 2:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | (40) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 &
% 250.98/59.66 | | | | | | | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | BETA: splitting (40) gives:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | Case 1:
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | (41) all_252_14 = e1 & op(e1, e2) = e1
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | REF_CLOSE: (14), (35), (41) are inconsistent by sub-proof #410.
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | Case 2:
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | (42) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 &
% 250.98/59.66 | | | | | | | | op(e1, e0) = e1)
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | BETA: splitting (42) gives:
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | | Case 1:
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | (43) all_252_15 = e1 & op(e1, e1) = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | ALPHA: (43) implies:
% 250.98/59.66 | | | | | | | | | (44) all_252_15 = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | COMBINE_EQS: (29), (44) imply:
% 250.98/59.66 | | | | | | | | | (45) e4 = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | SIMP: (45) implies:
% 250.98/59.66 | | | | | | | | | (46) e4 = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | REDUCE: (11), (46) imply:
% 250.98/59.66 | | | | | | | | | (47) $false
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | CLOSE: (47) is inconsistent.
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | Case 2:
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | (48) all_252_19 = e1 & op(e1, e0) = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | ALPHA: (48) implies:
% 250.98/59.66 | | | | | | | | | (49) op(e1, e0) = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | GROUND_INST: instantiating (7) with e1, e2, e0, e1, simplifying
% 250.98/59.66 | | | | | | | | | with (15), (49) gives:
% 250.98/59.66 | | | | | | | | | (50) e2 = e1
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | REDUCE: (10), (50) imply:
% 250.98/59.66 | | | | | | | | | (51) $false
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | | CLOSE: (51) is inconsistent.
% 250.98/59.66 | | | | | | | | |
% 250.98/59.66 | | | | | | | | End of split
% 250.98/59.66 | | | | | | | |
% 250.98/59.66 | | | | | | | End of split
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | End of split
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | Case 2:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | (52) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 250.98/59.66 | | | | | | op(e1, e0) = e3)
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | BETA: splitting (52) gives:
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | | Case 1:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | (53) all_252_15 = e3 & op(e1, e1) = e3
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | REF_CLOSE: (17), (29), (53) are inconsistent by sub-proof #486.
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | Case 2:
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | (54) all_252_19 = e3 & op(e1, e0) = e3
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | ALPHA: (54) implies:
% 250.98/59.66 | | | | | | | (55) op(e1, e0) = e3
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | | REF_CLOSE: (7), (8), (15), (55) are inconsistent by sub-proof
% 250.98/59.66 | | | | | | | #736.
% 250.98/59.66 | | | | | | |
% 250.98/59.66 | | | | | | End of split
% 250.98/59.66 | | | | | |
% 250.98/59.66 | | | | | End of split
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | End of split
% 250.98/59.66 | | | |
% 250.98/59.66 | | | Case 2:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | (56) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | ALPHA: (56) implies:
% 250.98/59.66 | | | | (57) op(e1, e0) = e4
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | GROUND_INST: instantiating (7) with e2, e4, e0, e1, simplifying with
% 250.98/59.66 | | | | (15), (57) gives:
% 250.98/59.66 | | | | (58) e4 = e2
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | REDUCE: (19), (58) imply:
% 250.98/59.66 | | | | (59) $false
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | CLOSE: (59) is inconsistent.
% 250.98/59.66 | | | |
% 250.98/59.66 | | | End of split
% 250.98/59.66 | | |
% 250.98/59.66 | | End of split
% 250.98/59.66 | |
% 250.98/59.66 | End of split
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #393 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) all_252_12 = e1 & op(e1, e4) = e1
% 250.98/59.66 (2) all_252_12 = e2
% 250.98/59.66 (3) ~ (e2 = e1)
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | ALPHA: (1) implies:
% 250.98/59.66 | (4) all_252_12 = e1
% 250.98/59.66 |
% 250.98/59.66 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.66 | (5) e2 = e1
% 250.98/59.66 |
% 250.98/59.66 | SIMP: (5) implies:
% 250.98/59.66 | (6) e2 = e1
% 250.98/59.66 |
% 250.98/59.66 | REDUCE: (3), (6) imply:
% 250.98/59.66 | (7) $false
% 250.98/59.66 |
% 250.98/59.66 | CLOSE: (7) is inconsistent.
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #394 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) ~ (all_4_2 = e4)
% 250.98/59.66 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.66 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.66 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.66 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.66 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.66 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.66 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.66 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.66 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.66 (5) ~ (e2 = e0)
% 250.98/59.66 (6) all_252_19 = e2
% 250.98/59.66 (7) ~ (e1 = e0)
% 250.98/59.66 (8) all_252_13 = e0
% 250.98/59.66 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.66 (10) ~ (e3 = e2)
% 250.98/59.66 (11) ~ (e4 = e0)
% 250.98/59.66 (12) all_252_0 = e2
% 250.98/59.66 (13) all_252_6 = e1
% 250.98/59.66 (14) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.98/59.66 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.98/59.66 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.66 (15) op(e2, e0) = e1
% 250.98/59.66 (16) ~ (e2 = e1)
% 250.98/59.66 (17) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.98/59.66 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.66 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.98/59.66 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.98/59.66 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.98/59.66 op(e0, e1) = e0)))
% 250.98/59.66 (18) ~ (e4 = e1)
% 250.98/59.66 (19) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.98/59.66 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.66 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.66 (20) op(e1, e4) = all_16_2
% 250.98/59.66 (21) ~ (e3 = e0)
% 250.98/59.66 (22) ~ (e3 = e1)
% 250.98/59.66 (23) all_252_16 = e1
% 250.98/59.66 (24) op(e3, e1) = all_36_2
% 250.98/59.66 (25) op(e1, e0) = e2
% 250.98/59.66 (26) ~ (all_8_2 = e0)
% 250.98/59.66 (27) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.66 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.66 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.66 (28) ~ (all_36_2 = e0)
% 250.98/59.66 (29) ~ (e4 = e3)
% 250.98/59.66 (30) op(e3, e0) = all_48_2
% 250.98/59.66 (31) op(e1, e2) = all_4_2
% 250.98/59.66 (32) ~ (all_48_2 = e0)
% 250.98/59.66 (33) ~ (e4 = e2)
% 250.98/59.66 (34) op(e3, e2) = all_8_2
% 250.98/59.66 (35) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.98/59.66 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.98/59.66 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.98/59.66 (36) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.66 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.66 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.66 (37) ~ (all_244_3 = e0)
% 250.98/59.66 (38) ~ (all_16_2 = e3)
% 250.98/59.66 (39) op(e3, e3) = all_244_3
% 250.98/59.66 (40) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.98/59.66 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.98/59.66 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.98/59.66 (41) all_252_20 = e3
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | BETA: splitting (17) gives:
% 250.98/59.66 |
% 250.98/59.66 | Case 1:
% 250.98/59.66 | |
% 250.98/59.66 | | (42) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | ALPHA: (42) implies:
% 250.98/59.66 | | (43) all_252_24 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | BETA: splitting (36) gives:
% 250.98/59.66 | |
% 250.98/59.66 | | Case 1:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (44) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4)
% 250.98/59.66 | | | = e4)
% 250.98/59.66 | | |
% 250.98/59.66 | | | REF_CLOSE: (3), (9), (11), (12), (24), (26), (28), (30), (32), (33), (34),
% 250.98/59.66 | | | (37), (39), (44) are inconsistent by sub-proof #555.
% 250.98/59.66 | | |
% 250.98/59.66 | | Case 2:
% 250.98/59.66 | | |
% 250.98/59.66 | | | (45) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4)
% 250.98/59.66 | | | = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.66 | | |
% 250.98/59.66 | | | BETA: splitting (45) gives:
% 250.98/59.66 | | |
% 250.98/59.66 | | | Case 1:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | (46) all_252_6 = e4 & op(e2, e4) = e4
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | REF_CLOSE: (13), (18), (46) are inconsistent by sub-proof #414.
% 250.98/59.66 | | | |
% 250.98/59.66 | | | Case 2:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | (47) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 250.98/59.66 | | | | e4) = e4)
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | BETA: splitting (47) gives:
% 250.98/59.66 | | | |
% 250.98/59.66 | | | | Case 1:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | (48) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | ALPHA: (48) implies:
% 250.98/59.66 | | | | | (49) all_252_12 = e4
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13),
% 250.98/59.66 | | | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 250.98/59.66 | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 250.98/59.66 | | | | | (36), (37), (38), (39), (41), (43), (49) are inconsistent
% 250.98/59.66 | | | | | by sub-proof #398.
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | Case 2:
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | (50) all_252_20 = e4 & op(e0, e4) = e4
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | | REF_CLOSE: (29), (41), (50) are inconsistent by sub-proof #563.
% 250.98/59.66 | | | | |
% 250.98/59.66 | | | | End of split
% 250.98/59.66 | | | |
% 250.98/59.66 | | | End of split
% 250.98/59.66 | | |
% 250.98/59.66 | | End of split
% 250.98/59.66 | |
% 250.98/59.66 | Case 2:
% 250.98/59.66 | |
% 250.98/59.66 | | (51) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.98/59.66 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.98/59.66 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.98/59.66 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0,
% 250.98/59.66 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (11), (12), (15), (16), (18),
% 250.98/59.66 | | (22), (23), (24), (26), (28), (29), (30), (32), (33), (34), (35),
% 250.98/59.66 | | (36), (37), (39), (40), (41), (51) are inconsistent by sub-proof
% 250.98/59.66 | | #395.
% 250.98/59.66 | |
% 250.98/59.66 | End of split
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #395 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.66 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.66 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.66 (2) ~ (e2 = e0)
% 250.98/59.66 (3) all_252_19 = e2
% 250.98/59.66 (4) ~ (e1 = e0)
% 250.98/59.66 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.66 (6) ~ (e3 = e2)
% 250.98/59.66 (7) ~ (e4 = e0)
% 250.98/59.66 (8) all_252_0 = e2
% 250.98/59.66 (9) op(e2, e0) = e1
% 250.98/59.66 (10) ~ (e2 = e1)
% 250.98/59.66 (11) ~ (e4 = e1)
% 250.98/59.66 (12) ~ (e3 = e1)
% 250.98/59.66 (13) all_252_16 = e1
% 250.98/59.66 (14) op(e3, e1) = all_36_2
% 250.98/59.66 (15) ~ (all_8_2 = e0)
% 250.98/59.66 (16) ~ (all_36_2 = e0)
% 250.98/59.66 (17) ~ (e4 = e3)
% 250.98/59.66 (18) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) =
% 250.98/59.66 e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.98/59.66 op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) |
% 250.98/59.66 (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) =
% 250.98/59.66 e0) | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.98/59.66 (19) op(e3, e0) = all_48_2
% 250.98/59.66 (20) ~ (all_48_2 = e0)
% 250.98/59.66 (21) ~ (e4 = e2)
% 250.98/59.66 (22) op(e3, e2) = all_8_2
% 250.98/59.66 (23) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.98/59.66 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.98/59.66 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.98/59.66 (24) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.66 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.66 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.66 (25) ~ (all_244_3 = e0)
% 250.98/59.66 (26) op(e3, e3) = all_244_3
% 250.98/59.66 (27) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.98/59.66 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.98/59.66 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.98/59.66 (28) all_252_20 = e3
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | ALPHA: (18) implies:
% 250.98/59.66 | (29) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) =
% 250.98/59.66 | e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 &
% 250.98/59.66 | op(e1, e0) = e0)
% 250.98/59.66 |
% 250.98/59.66 | BETA: splitting (29) gives:
% 250.98/59.66 |
% 250.98/59.66 | Case 1:
% 250.98/59.66 | |
% 250.98/59.66 | | (30) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0)
% 250.98/59.66 | | = e0)
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (4), (5), (13), (19), (20), (30) are inconsistent by sub-proof
% 250.98/59.66 | | #397.
% 250.98/59.66 | |
% 250.98/59.66 | Case 2:
% 250.98/59.66 | |
% 250.98/59.66 | | (31) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.98/59.66 | | = e0)
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 250.98/59.66 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 250.98/59.66 | | (26), (27), (28), (31) are inconsistent by sub-proof #396.
% 250.98/59.66 | |
% 250.98/59.66 | End of split
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #396 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.66 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.66 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.66 (2) ~ (e2 = e0)
% 250.98/59.66 (3) all_252_19 = e2
% 250.98/59.66 (4) ~ (e1 = e0)
% 250.98/59.66 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.66 (6) ~ (e3 = e2)
% 250.98/59.66 (7) ~ (e4 = e0)
% 250.98/59.66 (8) all_252_0 = e2
% 250.98/59.66 (9) op(e2, e0) = e1
% 250.98/59.66 (10) ~ (e2 = e1)
% 250.98/59.66 (11) ~ (e4 = e1)
% 250.98/59.66 (12) ~ (e3 = e1)
% 250.98/59.66 (13) op(e3, e1) = all_36_2
% 250.98/59.66 (14) ~ (all_8_2 = e0)
% 250.98/59.66 (15) ~ (all_36_2 = e0)
% 250.98/59.66 (16) ~ (e4 = e3)
% 250.98/59.66 (17) op(e3, e0) = all_48_2
% 250.98/59.66 (18) ~ (all_48_2 = e0)
% 250.98/59.66 (19) ~ (e4 = e2)
% 250.98/59.66 (20) op(e3, e2) = all_8_2
% 250.98/59.66 (21) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) =
% 250.98/59.66 e0)
% 250.98/59.66 (22) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.98/59.66 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.98/59.66 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.98/59.66 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.66 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.66 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.66 (24) ~ (all_244_3 = e0)
% 250.98/59.66 (25) op(e3, e3) = all_244_3
% 250.98/59.66 (26) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.98/59.66 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.98/59.66 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.98/59.66 (27) all_252_20 = e3
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | BETA: splitting (21) gives:
% 250.98/59.66 |
% 250.98/59.66 | Case 1:
% 250.98/59.66 | |
% 250.98/59.66 | | (28) all_252_18 = e0 & op(e2, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | ALPHA: (28) implies:
% 250.98/59.66 | | (29) op(e2, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (4), (5), (9), (29) are inconsistent by sub-proof #901.
% 250.98/59.66 | |
% 250.98/59.66 | Case 2:
% 250.98/59.66 | |
% 250.98/59.66 | | (30) all_252_19 = e0 & op(e1, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | ALPHA: (30) implies:
% 250.98/59.66 | | (31) all_252_19 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | COMBINE_EQS: (3), (31) imply:
% 250.98/59.66 | | (32) e2 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 250.98/59.66 | | (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 250.98/59.66 | | (27), (32) are inconsistent by sub-proof #493.
% 250.98/59.66 | |
% 250.98/59.66 | End of split
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #397 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) ~ (e1 = e0)
% 250.98/59.66 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.66 (3) all_252_16 = e1
% 250.98/59.66 (4) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.66 (5) op(e3, e0) = all_48_2
% 250.98/59.66 (6) ~ (all_48_2 = e0)
% 250.98/59.66
% 250.98/59.66 Begin of proof
% 250.98/59.66 |
% 250.98/59.66 | BETA: splitting (4) gives:
% 250.98/59.66 |
% 250.98/59.66 | Case 1:
% 250.98/59.66 | |
% 250.98/59.66 | | (7) all_252_16 = e0 & op(e4, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | ALPHA: (7) implies:
% 250.98/59.66 | | (8) all_252_16 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | COMBINE_EQS: (3), (8) imply:
% 250.98/59.66 | | (9) e1 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | SIMP: (9) implies:
% 250.98/59.66 | | (10) e1 = e0
% 250.98/59.66 | |
% 250.98/59.66 | | REDUCE: (1), (10) imply:
% 250.98/59.66 | | (11) $false
% 250.98/59.66 | |
% 250.98/59.66 | | CLOSE: (11) is inconsistent.
% 250.98/59.66 | |
% 250.98/59.66 | Case 2:
% 250.98/59.66 | |
% 250.98/59.66 | | (12) all_252_17 = e0 & op(e3, e0) = e0
% 250.98/59.66 | |
% 250.98/59.66 | | REF_CLOSE: (2), (5), (6), (12) are inconsistent by sub-proof #573.
% 250.98/59.66 | |
% 250.98/59.66 | End of split
% 250.98/59.66 |
% 250.98/59.66 End of proof
% 250.98/59.66
% 250.98/59.66 Sub-proof #398 shows that the following formulas are inconsistent:
% 250.98/59.66 ----------------------------------------------------------------
% 250.98/59.66 (1) ~ (all_4_2 = e4)
% 250.98/59.66 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.66 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.66 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.66 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.66 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.66 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.66 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.66 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.66 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.66 (5) ~ (e1 = e0)
% 250.98/59.66 (6) all_252_13 = e0
% 250.98/59.66 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.66 (8) ~ (e3 = e2)
% 250.98/59.66 (9) ~ (e4 = e0)
% 250.98/59.66 (10) all_252_0 = e2
% 250.98/59.66 (11) all_252_6 = e1
% 250.98/59.66 (12) all_252_12 = e4
% 250.98/59.66 (13) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.98/59.66 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.98/59.66 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.66 (14) op(e2, e0) = e1
% 250.98/59.66 (15) ~ (e2 = e1)
% 250.98/59.66 (16) ~ (e4 = e1)
% 250.98/59.67 (17) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.98/59.67 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.67 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.67 (18) op(e1, e4) = all_16_2
% 250.98/59.67 (19) ~ (e3 = e0)
% 250.98/59.67 (20) ~ (e3 = e1)
% 250.98/59.67 (21) all_252_16 = e1
% 250.98/59.67 (22) all_252_24 = e0
% 250.98/59.67 (23) op(e3, e1) = all_36_2
% 250.98/59.67 (24) op(e1, e0) = e2
% 250.98/59.67 (25) ~ (all_8_2 = e0)
% 250.98/59.67 (26) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 (27) ~ (all_36_2 = e0)
% 250.98/59.67 (28) ~ (e4 = e3)
% 250.98/59.67 (29) op(e3, e0) = all_48_2
% 250.98/59.67 (30) op(e1, e2) = all_4_2
% 250.98/59.67 (31) ~ (all_48_2 = e0)
% 250.98/59.67 (32) ~ (e4 = e2)
% 250.98/59.67 (33) op(e3, e2) = all_8_2
% 250.98/59.67 (34) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.67 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.67 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.67 (35) ~ (all_244_3 = e0)
% 250.98/59.67 (36) ~ (all_16_2 = e3)
% 250.98/59.67 (37) op(e3, e3) = all_244_3
% 250.98/59.67 (38) all_252_20 = e3
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (13) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0)
% 250.98/59.67 | | = e3)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (39) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (40) all_252_16 = e3 & op(e4, e0) = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (20), (21), (40) are inconsistent by sub-proof #488.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (41) all_252_17 = e3 & op(e3, e0) = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (41) implies:
% 250.98/59.67 | | | (42) all_252_17 = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (17) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (43) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3,
% 250.98/59.67 | | | | e0) = e4)
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | BETA: splitting (43) gives:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | Case 1:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (44) all_252_16 = e4 & op(e4, e0) = e4
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | ALPHA: (44) implies:
% 250.98/59.67 | | | | | (45) all_252_16 = e4
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | COMBINE_EQS: (21), (45) imply:
% 250.98/59.67 | | | | | (46) e4 = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | SIMP: (46) implies:
% 250.98/59.67 | | | | | (47) e4 = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 250.98/59.67 | | | | | (12), (15), (16), (18), (19), (20), (23), (24), (25), (26),
% 250.98/59.67 | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 250.98/59.67 | | | | | (37), (38), (47) are inconsistent by sub-proof #402.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | Case 2:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (48) all_252_17 = e4 & op(e3, e0) = e4
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (28), (42), (48) are inconsistent by sub-proof #837.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | End of split
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (49) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.67 | | | | e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | BETA: splitting (49) gives:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | Case 1:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (50) all_252_18 = e4 & op(e2, e0) = e4
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | ALPHA: (50) implies:
% 250.98/59.67 | | | | | (51) op(e2, e0) = e4
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | GROUND_INST: instantiating (7) with e1, e4, e0, e2, simplifying with
% 250.98/59.67 | | | | | (14), (51) gives:
% 250.98/59.67 | | | | | (52) e4 = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 250.98/59.67 | | | | | (12), (15), (16), (18), (19), (20), (23), (24), (25), (26),
% 250.98/59.67 | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 250.98/59.67 | | | | | (37), (38), (52) are inconsistent by sub-proof #402.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | Case 2:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (53) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 &
% 250.98/59.67 | | | | | op(e0, e0) = e4)
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (7), (9), (22), (24), (32), (53) are inconsistent by
% 250.98/59.67 | | | | | sub-proof #400.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | End of split
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (54) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0)
% 250.98/59.67 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (54) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (55) all_252_18 = e3 & op(e2, e0) = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (55) implies:
% 250.98/59.67 | | | (56) op(e2, e0) = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (7), (14), (20), (56) are inconsistent by sub-proof #399.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (57) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0,
% 250.98/59.67 | | | e0) = e3)
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (57) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (58) all_252_19 = e3 & op(e1, e0) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (58) implies:
% 250.98/59.67 | | | | (59) op(e1, e0) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (7), (8), (24), (59) are inconsistent by sub-proof #736.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (60) all_252_24 = e3 & op(e0, e0) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (60) implies:
% 250.98/59.67 | | | | (61) all_252_24 = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | COMBINE_EQS: (22), (61) imply:
% 250.98/59.67 | | | | (62) e3 = e0
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REDUCE: (19), (62) imply:
% 250.98/59.67 | | | | (63) $false
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | CLOSE: (63) is inconsistent.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #399 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (2) op(e2, e0) = e3
% 250.98/59.67 (3) op(e2, e0) = e1
% 250.98/59.67 (4) ~ (e3 = e1)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | GROUND_INST: instantiating (1) with e1, e3, e0, e2, simplifying with (2), (3)
% 250.98/59.67 | gives:
% 250.98/59.67 | (5) e3 = e1
% 250.98/59.67 |
% 250.98/59.67 | REDUCE: (4), (5) imply:
% 250.98/59.67 | (6) $false
% 250.98/59.67 |
% 250.98/59.67 | CLOSE: (6) is inconsistent.
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #400 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (2) ~ (e4 = e0)
% 250.98/59.67 (3) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.67 (4) all_252_24 = e0
% 250.98/59.67 (5) op(e1, e0) = e2
% 250.98/59.67 (6) ~ (e4 = e2)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (3) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (7) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.67 | |
% 250.98/59.67 | | ALPHA: (7) implies:
% 250.98/59.67 | | (8) op(e1, e0) = e4
% 250.98/59.67 | |
% 250.98/59.67 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #829.
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (9) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.67 | |
% 250.98/59.67 | | ALPHA: (9) implies:
% 250.98/59.67 | | (10) all_252_24 = e4
% 250.98/59.67 | |
% 250.98/59.67 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #401.
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #401 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) all_252_24 = e4
% 250.98/59.67 (2) all_252_24 = e0
% 250.98/59.67 (3) ~ (e4 = e0)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.67 | (4) e4 = e0
% 250.98/59.67 |
% 250.98/59.67 | SIMP: (4) implies:
% 250.98/59.67 | (5) e4 = e0
% 250.98/59.67 |
% 250.98/59.67 | REDUCE: (3), (5) imply:
% 250.98/59.67 | (6) $false
% 250.98/59.67 |
% 250.98/59.67 | CLOSE: (6) is inconsistent.
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #402 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) ~ (all_4_2 = e4)
% 250.98/59.67 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.67 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.67 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.67 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.67 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.67 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.67 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.67 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.67 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.67 (5) ~ (e1 = e0)
% 250.98/59.67 (6) all_252_13 = e0
% 250.98/59.67 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (8) ~ (e3 = e2)
% 250.98/59.67 (9) ~ (e4 = e0)
% 250.98/59.67 (10) all_252_0 = e2
% 250.98/59.67 (11) all_252_6 = e1
% 250.98/59.67 (12) all_252_12 = e4
% 250.98/59.67 (13) ~ (e2 = e1)
% 250.98/59.67 (14) ~ (e4 = e1)
% 250.98/59.67 (15) e4 = e1
% 250.98/59.67 (16) op(e1, e4) = all_16_2
% 250.98/59.67 (17) ~ (e3 = e0)
% 250.98/59.67 (18) ~ (e3 = e1)
% 250.98/59.67 (19) op(e3, e1) = all_36_2
% 250.98/59.67 (20) op(e1, e0) = e2
% 250.98/59.67 (21) ~ (all_8_2 = e0)
% 250.98/59.67 (22) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 (23) ~ (all_36_2 = e0)
% 250.98/59.67 (24) ~ (e4 = e3)
% 250.98/59.67 (25) op(e3, e0) = all_48_2
% 250.98/59.67 (26) op(e1, e2) = all_4_2
% 250.98/59.67 (27) ~ (all_48_2 = e0)
% 250.98/59.67 (28) ~ (e4 = e2)
% 250.98/59.67 (29) op(e3, e2) = all_8_2
% 250.98/59.67 (30) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.67 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.67 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.67 (31) ~ (all_244_3 = e0)
% 250.98/59.67 (32) ~ (all_16_2 = e3)
% 250.98/59.67 (33) op(e3, e3) = all_244_3
% 250.98/59.67 (34) all_252_20 = e3
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | COMBINE_EQS: (12), (15) imply:
% 250.98/59.67 | (35) all_252_12 = e1
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (22) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (36) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 250.98/59.67 | | = e4)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (36) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (37) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (12), (14), (35) are inconsistent by sub-proof #554.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (38) all_252_13 = e4 & op(e1, e3) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (6), (9), (38) are inconsistent by sub-proof #413.
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (39) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1)
% 250.98/59.67 | | = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (39) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (40) all_252_14 = e4 & op(e1, e2) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (40) implies:
% 250.98/59.67 | | | (41) op(e1, e2) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (1), (7), (26), (41) are inconsistent by sub-proof #831.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (42) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.67 | | | e0) = e4)
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (42) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (43) all_252_15 = e4 & op(e1, e1) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (43) implies:
% 250.98/59.67 | | | | (44) all_252_15 = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | BETA: splitting (30) gives:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | Case 1:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (45) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 250.98/59.67 | | | | | e4) = e4)
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13),
% 250.98/59.67 | | | | | (14), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 250.98/59.67 | | | | | (26), (27), (28), (29), (31), (32), (33), (44), (45) are
% 250.98/59.67 | | | | | inconsistent by sub-proof #403.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | Case 2:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (46) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 250.98/59.67 | | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | BETA: splitting (46) gives:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | Case 1:
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | (47) all_252_6 = e4 & op(e2, e4) = e4
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | REF_CLOSE: (11), (14), (47) are inconsistent by sub-proof #414.
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | Case 2:
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | (48) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 250.98/59.67 | | | | | | op(e0, e4) = e4)
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | BETA: splitting (48) gives:
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | Case 1:
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | | (49) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | | REF_CLOSE: (12), (14), (35) are inconsistent by sub-proof #554.
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | Case 2:
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | | (50) all_252_20 = e4 & op(e0, e4) = e4
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | | REF_CLOSE: (24), (34), (50) are inconsistent by sub-proof #563.
% 250.98/59.67 | | | | | | |
% 250.98/59.67 | | | | | | End of split
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | End of split
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | End of split
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (51) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (51) implies:
% 250.98/59.67 | | | | (52) op(e1, e0) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (7), (20), (28), (52) are inconsistent by sub-proof #829.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #403 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) ~ (all_4_2 = e4)
% 250.98/59.67 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.67 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.67 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.67 (3) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.67 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.67 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.67 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.67 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.67 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.67 (5) all_252_15 = e4
% 250.98/59.67 (6) ~ (e1 = e0)
% 250.98/59.67 (7) all_252_13 = e0
% 250.98/59.67 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (9) ~ (e3 = e2)
% 250.98/59.67 (10) ~ (e4 = e0)
% 250.98/59.67 (11) all_252_0 = e2
% 250.98/59.67 (12) ~ (e2 = e1)
% 250.98/59.67 (13) ~ (e4 = e1)
% 250.98/59.67 (14) op(e1, e4) = all_16_2
% 250.98/59.67 (15) ~ (e3 = e0)
% 250.98/59.67 (16) ~ (e3 = e1)
% 250.98/59.67 (17) op(e3, e1) = all_36_2
% 250.98/59.67 (18) op(e1, e0) = e2
% 250.98/59.67 (19) ~ (all_8_2 = e0)
% 250.98/59.67 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.67 (21) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 (22) ~ (all_36_2 = e0)
% 250.98/59.67 (23) op(e3, e0) = all_48_2
% 250.98/59.67 (24) op(e1, e2) = all_4_2
% 250.98/59.67 (25) ~ (all_48_2 = e0)
% 250.98/59.67 (26) ~ (e4 = e2)
% 250.98/59.67 (27) op(e3, e2) = all_8_2
% 250.98/59.67 (28) ~ (all_244_3 = e0)
% 250.98/59.67 (29) ~ (all_16_2 = e3)
% 250.98/59.67 (30) op(e3, e3) = all_244_3
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (20) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (31) all_252_0 = e4 & op(e4, e4) = e4
% 250.98/59.67 | |
% 250.98/59.67 | | ALPHA: (31) implies:
% 250.98/59.67 | | (32) all_252_0 = e4
% 250.98/59.67 | |
% 250.98/59.67 | | COMBINE_EQS: (11), (32) imply:
% 250.98/59.67 | | (33) e4 = e2
% 250.98/59.67 | |
% 250.98/59.67 | | SIMP: (33) implies:
% 250.98/59.67 | | (34) e4 = e2
% 250.98/59.67 | |
% 250.98/59.67 | | COMBINE_EQS: (5), (34) imply:
% 250.98/59.67 | | (35) all_252_15 = e2
% 250.98/59.67 | |
% 250.98/59.67 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 250.98/59.67 | | (16), (18), (21), (24), (26), (29), (35) are inconsistent by
% 250.98/59.67 | | sub-proof #404.
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (36) all_252_2 = e4 & op(e3, e4) = e4
% 250.98/59.67 | |
% 250.98/59.67 | | ALPHA: (36) implies:
% 250.98/59.67 | | (37) all_252_2 = e4
% 250.98/59.67 | |
% 250.98/59.67 | | REF_CLOSE: (3), (8), (10), (17), (19), (22), (23), (25), (27), (28), (30),
% 250.98/59.67 | | (37) are inconsistent by sub-proof #569.
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #404 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) ~ (all_4_2 = e4)
% 250.98/59.67 (2) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.67 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.67 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.67 (3) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.67 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.67 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.67 (4) ~ (e1 = e0)
% 250.98/59.67 (5) all_252_13 = e0
% 250.98/59.67 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (7) ~ (e3 = e2)
% 250.98/59.67 (8) ~ (e4 = e0)
% 250.98/59.67 (9) ~ (e2 = e1)
% 250.98/59.67 (10) ~ (e4 = e1)
% 250.98/59.67 (11) op(e1, e4) = all_16_2
% 250.98/59.67 (12) ~ (e3 = e0)
% 250.98/59.67 (13) ~ (e3 = e1)
% 250.98/59.67 (14) op(e1, e0) = e2
% 250.98/59.67 (15) all_252_15 = e2
% 250.98/59.67 (16) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 (17) op(e1, e2) = all_4_2
% 250.98/59.67 (18) ~ (e4 = e2)
% 250.98/59.67 (19) ~ (all_16_2 = e3)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (3) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (20) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 250.98/59.67 | | = e3)
% 250.98/59.67 | |
% 250.98/59.67 | | REF_CLOSE: (5), (6), (11), (12), (19), (20) are inconsistent by sub-proof
% 250.98/59.67 | | #412.
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (21) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1)
% 250.98/59.67 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (21) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (22) all_252_14 = e3 & op(e1, e2) = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (22) implies:
% 250.98/59.67 | | | (23) all_252_14 = e3
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (13), (14), (15),
% 250.98/59.67 | | | (16), (17), (18), (23) are inconsistent by sub-proof #406.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (24) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1,
% 250.98/59.67 | | | e0) = e3)
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (24) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (25) all_252_15 = e3 & op(e1, e1) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (7), (15), (25) are inconsistent by sub-proof #405.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (26) all_252_19 = e3 & op(e1, e0) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (26) implies:
% 250.98/59.67 | | | | (27) op(e1, e0) = e3
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (6), (7), (14), (27) are inconsistent by sub-proof #736.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #405 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) all_252_15 = e3 & op(e1, e1) = e3
% 250.98/59.67 (2) all_252_15 = e2
% 250.98/59.67 (3) ~ (e3 = e2)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | ALPHA: (1) implies:
% 250.98/59.67 | (4) all_252_15 = e3
% 250.98/59.67 |
% 250.98/59.67 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.67 | (5) e3 = e2
% 250.98/59.67 |
% 250.98/59.67 | REDUCE: (3), (5) imply:
% 250.98/59.67 | (6) $false
% 250.98/59.67 |
% 250.98/59.67 | CLOSE: (6) is inconsistent.
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #406 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) all_252_14 = e3
% 250.98/59.67 (2) ~ (all_4_2 = e4)
% 250.98/59.67 (3) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 250.98/59.67 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 250.98/59.67 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.67 (4) ~ (e1 = e0)
% 250.98/59.67 (5) all_252_13 = e0
% 250.98/59.67 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.67 (7) ~ (e4 = e0)
% 250.98/59.67 (8) ~ (e2 = e1)
% 250.98/59.67 (9) ~ (e4 = e1)
% 250.98/59.67 (10) ~ (e3 = e1)
% 250.98/59.67 (11) op(e1, e0) = e2
% 250.98/59.67 (12) all_252_15 = e2
% 250.98/59.67 (13) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.67 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.67 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 (14) op(e1, e2) = all_4_2
% 250.98/59.67 (15) ~ (e4 = e2)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | BETA: splitting (13) gives:
% 250.98/59.67 |
% 250.98/59.67 | Case 1:
% 250.98/59.67 | |
% 250.98/59.67 | | (16) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 250.98/59.67 | | = e4)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (16) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (17) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (17) implies:
% 250.98/59.67 | | | (18) all_252_12 = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (3) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (19) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1,
% 250.98/59.67 | | | | e3) = e1)
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | BETA: splitting (19) gives:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | Case 1:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (20) all_252_12 = e1 & op(e1, e4) = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (9), (18), (20) are inconsistent by sub-proof #566.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | Case 2:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (21) all_252_13 = e1 & op(e1, e3) = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (4), (5), (21) are inconsistent by sub-proof #411.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | End of split
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (22) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1,
% 250.98/59.67 | | | | e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | BETA: splitting (22) gives:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | Case 1:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (23) all_252_14 = e1 & op(e1, e2) = e1
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | REF_CLOSE: (1), (10), (23) are inconsistent by sub-proof #410.
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | Case 2:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | (24) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 &
% 250.98/59.67 | | | | | op(e1, e0) = e1)
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | BETA: splitting (24) gives:
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | | Case 1:
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | (25) all_252_15 = e1 & op(e1, e1) = e1
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | REF_CLOSE: (8), (12), (25) are inconsistent by sub-proof #409.
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | Case 2:
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | (26) all_252_19 = e1 & op(e1, e0) = e1
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | | REF_CLOSE: (6), (8), (11), (26) are inconsistent by sub-proof #408.
% 250.98/59.67 | | | | | |
% 250.98/59.67 | | | | | End of split
% 250.98/59.67 | | | | |
% 250.98/59.67 | | | | End of split
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (27) all_252_13 = e4 & op(e1, e3) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (27) implies:
% 250.98/59.67 | | | (28) all_252_13 = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (5), (7), (28) are inconsistent by sub-proof #407.
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | Case 2:
% 250.98/59.67 | |
% 250.98/59.67 | | (29) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1)
% 250.98/59.67 | | = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.67 | |
% 250.98/59.67 | | BETA: splitting (29) gives:
% 250.98/59.67 | |
% 250.98/59.67 | | Case 1:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (30) all_252_14 = e4 & op(e1, e2) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | ALPHA: (30) implies:
% 250.98/59.67 | | | (31) op(e1, e2) = e4
% 250.98/59.67 | | |
% 250.98/59.67 | | | REF_CLOSE: (2), (6), (14), (31) are inconsistent by sub-proof #831.
% 250.98/59.67 | | |
% 250.98/59.67 | | Case 2:
% 250.98/59.67 | | |
% 250.98/59.67 | | | (32) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.67 | | | e0) = e4)
% 250.98/59.67 | | |
% 250.98/59.67 | | | BETA: splitting (32) gives:
% 250.98/59.67 | | |
% 250.98/59.67 | | | Case 1:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (33) all_252_15 = e4 & op(e1, e1) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (33) implies:
% 250.98/59.67 | | | | (34) all_252_15 = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (12), (15), (34) are inconsistent by sub-proof #470.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | Case 2:
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | (35) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | ALPHA: (35) implies:
% 250.98/59.67 | | | | (36) op(e1, e0) = e4
% 250.98/59.67 | | | |
% 250.98/59.67 | | | | REF_CLOSE: (6), (11), (15), (36) are inconsistent by sub-proof #829.
% 250.98/59.67 | | | |
% 250.98/59.67 | | | End of split
% 250.98/59.67 | | |
% 250.98/59.67 | | End of split
% 250.98/59.67 | |
% 250.98/59.67 | End of split
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #407 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.67 (1) all_252_13 = e4
% 250.98/59.67 (2) all_252_13 = e0
% 250.98/59.67 (3) ~ (e4 = e0)
% 250.98/59.67
% 250.98/59.67 Begin of proof
% 250.98/59.67 |
% 250.98/59.67 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.67 | (4) e4 = e0
% 250.98/59.67 |
% 250.98/59.67 | SIMP: (4) implies:
% 250.98/59.67 | (5) e4 = e0
% 250.98/59.67 |
% 250.98/59.67 | REDUCE: (3), (5) imply:
% 250.98/59.67 | (6) $false
% 250.98/59.67 |
% 250.98/59.67 | CLOSE: (6) is inconsistent.
% 250.98/59.67 |
% 250.98/59.67 End of proof
% 250.98/59.67
% 250.98/59.67 Sub-proof #408 shows that the following formulas are inconsistent:
% 250.98/59.67 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_19 = e1 & op(e1, e0) = e1
% 250.98/59.68 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (3) op(e1, e0) = e2
% 250.98/59.68 (4) ~ (e2 = e1)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (5) op(e1, e0) = e1
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (2) with e1, e2, e0, e1, simplifying with (3), (5)
% 250.98/59.68 | gives:
% 250.98/59.68 | (6) e2 = e1
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (4), (6) imply:
% 250.98/59.68 | (7) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (7) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #409 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_15 = e1 & op(e1, e1) = e1
% 250.98/59.68 (2) all_252_15 = e2
% 250.98/59.68 (3) ~ (e2 = e1)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (4) all_252_15 = e1
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.68 | (5) e2 = e1
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #410 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_14 = e1 & op(e1, e2) = e1
% 250.98/59.68 (2) all_252_14 = e3
% 250.98/59.68 (3) ~ (e3 = e1)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (4) all_252_14 = e1
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.68 | (5) e3 = e1
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #411 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_13 = e1 & op(e1, e3) = e1
% 250.98/59.68 (2) all_252_13 = e0
% 250.98/59.68 (3) ~ (e1 = e0)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (4) all_252_13 = e1
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.68 | (5) e1 = e0
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #412 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 250.98/59.68 (2) all_252_13 = e0
% 250.98/59.68 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (4) op(e1, e4) = all_16_2
% 250.98/59.68 (5) ~ (e3 = e0)
% 250.98/59.68 (6) ~ (all_16_2 = e3)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | BETA: splitting (1) gives:
% 250.98/59.68 |
% 250.98/59.68 | Case 1:
% 250.98/59.68 | |
% 250.98/59.68 | | (7) all_252_12 = e3 & op(e1, e4) = e3
% 250.98/59.68 | |
% 250.98/59.68 | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #895.
% 250.98/59.68 | |
% 250.98/59.68 | Case 2:
% 250.98/59.68 | |
% 250.98/59.68 | | (8) all_252_13 = e3 & op(e1, e3) = e3
% 250.98/59.68 | |
% 250.98/59.68 | | ALPHA: (8) implies:
% 250.98/59.68 | | (9) all_252_13 = e3
% 250.98/59.68 | |
% 250.98/59.68 | | COMBINE_EQS: (2), (9) imply:
% 250.98/59.68 | | (10) e3 = e0
% 250.98/59.68 | |
% 250.98/59.68 | | SIMP: (10) implies:
% 250.98/59.68 | | (11) e3 = e0
% 250.98/59.68 | |
% 250.98/59.68 | | REDUCE: (5), (11) imply:
% 250.98/59.68 | | (12) $false
% 250.98/59.68 | |
% 250.98/59.68 | | CLOSE: (12) is inconsistent.
% 250.98/59.68 | |
% 250.98/59.68 | End of split
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #413 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_13 = e4 & op(e1, e3) = e4
% 250.98/59.68 (2) all_252_13 = e0
% 250.98/59.68 (3) ~ (e4 = e0)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (4) all_252_13 = e4
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.68 | (5) e4 = e0
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #414 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_6 = e4 & op(e2, e4) = e4
% 250.98/59.68 (2) all_252_6 = e1
% 250.98/59.68 (3) ~ (e4 = e1)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | ALPHA: (1) implies:
% 250.98/59.68 | (4) all_252_6 = e4
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.68 | (5) e4 = e1
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #415 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (2) op(e2, e0) = e1
% 250.98/59.68 (3) ~ (e2 = e1)
% 250.98/59.68 (4) op(e2, e0) = all_40_2
% 250.98/59.68 (5) op(e2, e0) = e2
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (1) with all_40_2, e1, e0, e2, simplifying with
% 250.98/59.68 | (2), (4) gives:
% 250.98/59.68 | (6) all_40_2 = e1
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (1) with all_40_2, e2, e0, e2, simplifying with
% 250.98/59.68 | (4), (5) gives:
% 250.98/59.68 | (7) all_40_2 = e2
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (6), (7) imply:
% 250.98/59.68 | (8) e2 = e1
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (8) imply:
% 250.98/59.68 | (9) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (9) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #416 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) ~ (all_48_2 = e2)
% 250.98/59.68 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (3) op(e3, e0) = e2
% 250.98/59.68 (4) op(e3, e0) = all_114_1
% 250.98/59.68 (5) op(e3, e0) = all_48_2
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (2) with all_48_2, all_114_1, e0, e3, simplifying
% 250.98/59.68 | with (4), (5) gives:
% 250.98/59.68 | (6) all_114_1 = all_48_2
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (2) with e2, all_114_1, e0, e3, simplifying with
% 250.98/59.68 | (3), (4) gives:
% 250.98/59.68 | (7) all_114_1 = e2
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (6), (7) imply:
% 250.98/59.68 | (8) all_48_2 = e2
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (1), (8) imply:
% 250.98/59.68 | (9) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (9) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #417 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) ~ (e2 = e0)
% 250.98/59.68 (2) op(all_38_2, all_4_2) = e1
% 250.98/59.68 (3) all_252_13 = e0
% 250.98/59.68 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (5) op(e2, e2) = all_244_8
% 250.98/59.68 (6) op(e2, e1) = all_38_2
% 250.98/59.68 (7) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 250.98/59.68 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 250.98/59.68 | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.98/59.68 (8) op(e1, e0) = all_34_2
% 250.98/59.68 (9) op(e4, e2) = all_6_2
% 250.98/59.68 (10) ~ (all_34_2 = e2)
% 250.98/59.68 (11) ~ (e2 = e1)
% 250.98/59.68 (12) op(e0, e2) = all_28_2
% 250.98/59.68 (13) ~ (all_28_2 = e1)
% 250.98/59.68 (14) ~ (all_6_2 = e1)
% 250.98/59.68 (15) op(e1, e4) = all_16_2
% 250.98/59.68 (16) ~ (all_16_2 = e2)
% 250.98/59.68 (17) ~ (all_8_2 = e1)
% 250.98/59.68 (18) op(e1, e1) = all_244_15
% 250.98/59.68 (19) op(e1, e2) = all_4_2
% 250.98/59.68 (20) ~ (all_244_15 = e2)
% 250.98/59.68 (21) op(e3, e2) = all_8_2
% 250.98/59.68 (22) ~ (all_244_8 = all_28_2)
% 250.98/59.68 (23) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.98/59.68 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.98/59.68 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.98/59.68 (24) op(e1, e2) = all_230_1
% 250.98/59.68 (25) op(e2, e1) = e0
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | BETA: splitting (23) gives:
% 250.98/59.68 |
% 250.98/59.68 | Case 1:
% 250.98/59.68 | |
% 250.98/59.68 | | (26) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 250.98/59.68 | | = e2)
% 250.98/59.68 | |
% 250.98/59.68 | | BETA: splitting (26) gives:
% 250.98/59.68 | |
% 250.98/59.68 | | Case 1:
% 250.98/59.68 | | |
% 250.98/59.68 | | | (27) all_252_12 = e2 & op(e1, e4) = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | ALPHA: (27) implies:
% 250.98/59.68 | | | (28) op(e1, e4) = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | GROUND_INST: instantiating (4) with all_16_2, e2, e4, e1, simplifying with
% 250.98/59.68 | | | (15), (28) gives:
% 250.98/59.68 | | | (29) all_16_2 = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | REDUCE: (16), (29) imply:
% 250.98/59.68 | | | (30) $false
% 250.98/59.68 | | |
% 250.98/59.68 | | | CLOSE: (30) is inconsistent.
% 250.98/59.68 | | |
% 250.98/59.68 | | Case 2:
% 250.98/59.68 | | |
% 250.98/59.68 | | | (31) all_252_13 = e2 & op(e1, e3) = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | ALPHA: (31) implies:
% 250.98/59.68 | | | (32) all_252_13 = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | REF_CLOSE: (1), (3), (32) are inconsistent by sub-proof #418.
% 250.98/59.68 | | |
% 250.98/59.68 | | End of split
% 250.98/59.68 | |
% 250.98/59.68 | Case 2:
% 250.98/59.68 | |
% 250.98/59.68 | | (33) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 250.98/59.68 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.98/59.68 | |
% 250.98/59.68 | | BETA: splitting (33) gives:
% 250.98/59.68 | |
% 250.98/59.68 | | Case 1:
% 250.98/59.68 | | |
% 250.98/59.68 | | | (34) all_252_14 = e2 & op(e1, e2) = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | ALPHA: (34) implies:
% 250.98/59.68 | | | (35) all_252_14 = e2
% 250.98/59.68 | | | (36) op(e1, e2) = e2
% 250.98/59.68 | | |
% 250.98/59.68 | | | BETA: splitting (7) gives:
% 250.98/59.68 | | |
% 250.98/59.68 | | | Case 1:
% 250.98/59.68 | | | |
% 250.98/59.68 | | | | (37) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3,
% 250.98/59.68 | | | | e2) = e1)
% 250.98/59.68 | | | |
% 250.98/59.68 | | | | REF_CLOSE: (4), (9), (14), (17), (21), (37) are inconsistent by
% 250.98/59.68 | | | | sub-proof #928.
% 250.98/59.68 | | | |
% 250.98/59.68 | | | Case 2:
% 250.98/59.68 | | | |
% 250.98/59.68 | | | | (38) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1,
% 250.98/59.68 | | | | e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.98/59.68 | | | |
% 250.98/59.68 | | | | BETA: splitting (38) gives:
% 250.98/59.68 | | | |
% 250.98/59.68 | | | | Case 1:
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | (39) all_252_8 = e1 & op(e2, e2) = e1
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | ALPHA: (39) implies:
% 250.98/59.68 | | | | | (40) op(e2, e2) = e1
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | GROUND_INST: instantiating (4) with all_4_2, all_230_1, e2, e1,
% 250.98/59.68 | | | | | simplifying with (19), (24) gives:
% 250.98/59.68 | | | | | (41) all_230_1 = all_4_2
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | GROUND_INST: instantiating (4) with e2, all_230_1, e2, e1, simplifying
% 250.98/59.68 | | | | | with (24), (36) gives:
% 250.98/59.68 | | | | | (42) all_230_1 = e2
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | GROUND_INST: instantiating (4) with all_38_2, e0, e1, e2, simplifying
% 250.98/59.68 | | | | | with (6), (25) gives:
% 250.98/59.68 | | | | | (43) all_38_2 = e0
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | GROUND_INST: instantiating (4) with all_244_8, e1, e2, e2, simplifying
% 250.98/59.68 | | | | | with (5), (40) gives:
% 250.98/59.68 | | | | | (44) all_244_8 = e1
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | COMBINE_EQS: (41), (42) imply:
% 250.98/59.68 | | | | | (45) all_4_2 = e2
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | SIMP: (45) implies:
% 250.98/59.68 | | | | | (46) all_4_2 = e2
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | REDUCE: (22), (44) imply:
% 250.98/59.68 | | | | | (47) ~ (all_28_2 = e1)
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | REDUCE: (2), (43), (46) imply:
% 250.98/59.68 | | | | | (48) op(e0, e2) = e1
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | REF_CLOSE: (4), (12), (13), (48) are inconsistent by sub-proof #907.
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | Case 2:
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | (49) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 250.98/59.68 | | | | | op(e0, e2) = e1)
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | | REF_CLOSE: (4), (11), (12), (13), (35), (49) are inconsistent by
% 250.98/59.68 | | | | | sub-proof #471.
% 250.98/59.68 | | | | |
% 250.98/59.68 | | | | End of split
% 250.98/59.68 | | | |
% 250.98/59.68 | | | End of split
% 250.98/59.68 | | |
% 250.98/59.68 | | Case 2:
% 250.98/59.68 | | |
% 250.98/59.68 | | | (50) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 250.98/59.68 | | | e0) = e2)
% 250.98/59.68 | | |
% 250.98/59.68 | | | REF_CLOSE: (4), (8), (10), (18), (20), (50) are inconsistent by sub-proof
% 250.98/59.68 | | | #819.
% 250.98/59.68 | | |
% 250.98/59.68 | | End of split
% 250.98/59.68 | |
% 250.98/59.68 | End of split
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #418 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) all_252_13 = e2
% 250.98/59.68 (2) all_252_13 = e0
% 250.98/59.68 (3) ~ (e2 = e0)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.68 | (4) e2 = e0
% 250.98/59.68 |
% 250.98/59.68 | SIMP: (4) implies:
% 250.98/59.68 | (5) e2 = e0
% 250.98/59.68 |
% 250.98/59.68 | REDUCE: (3), (5) imply:
% 250.98/59.68 | (6) $false
% 250.98/59.68 |
% 250.98/59.68 | CLOSE: (6) is inconsistent.
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #419 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) op(all_62_2, e4) = e3
% 250.98/59.68 (2) ~ (all_8_2 = e4)
% 250.98/59.68 (3) ( ~ (all_52_0 = e2) & op(e4, all_52_1) = all_52_0 & op(e1, e4) = all_52_1
% 250.98/59.68 & $i(all_52_0) & $i(all_52_1)) | ( ~ (all_52_1 = e0) & op(e1, e4) =
% 250.98/59.68 all_52_1 & $i(all_52_1))
% 250.98/59.68 (4) ~ (all_4_2 = e4)
% 250.98/59.68 (5) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.68 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.68 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.68 (6) op(e3, all_16_2) = e1
% 250.98/59.68 (7) op(e4, e0) = all_30_2
% 250.98/59.68 (8) ~ (e2 = e0)
% 250.98/59.68 (9) ~ (e1 = e0)
% 250.98/59.68 (10) op(e3, e4) = e0
% 250.98/59.68 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (12) ~ (e3 = e2)
% 250.98/59.68 (13) ~ (e4 = e0)
% 250.98/59.68 (14) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 250.98/59.68 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 250.98/59.68 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 250.98/59.68 (15) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.98/59.68 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.98/59.68 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.98/59.68 (16) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.98/59.68 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.98/59.68 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.68 (17) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.98/59.68 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.98/59.68 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.68 (18) ~ (all_244_15 = e4)
% 250.98/59.68 (19) ~ (e2 = e1)
% 250.98/59.68 (20) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.98/59.68 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.68 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.98/59.68 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.98/59.68 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.98/59.68 op(e0, e1) = e0)))
% 250.98/59.68 (21) ~ (e4 = e1)
% 250.98/59.68 (22) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.98/59.68 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.68 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.68 (23) op(e1, e4) = all_16_2
% 250.98/59.68 (24) all_252_10 = e4
% 250.98/59.68 (25) op(e1, e3) = all_62_2
% 250.98/59.68 (26) ~ (e3 = e0)
% 250.98/59.68 (27) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.98/59.68 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.98/59.68 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.98/59.68 (28) all_252_2 = e0
% 250.98/59.68 (29) ~ (e3 = e1)
% 250.98/59.68 (30) op(e3, e1) = all_36_2
% 250.98/59.68 (31) ~ (all_8_2 = e1)
% 250.98/59.68 (32) op(all_40_2, e0) = e2
% 250.98/59.68 (33) ~ (all_48_2 = all_8_2)
% 250.98/59.68 (34) ~ (all_8_2 = e0)
% 250.98/59.68 (35) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.98/59.68 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.98/59.68 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.98/59.68 (36) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.68 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.68 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.68 (37) op(e1, e4) = all_36_1
% 250.98/59.68 (38) ~ (all_244_15 = e3)
% 250.98/59.68 (39) op(e3, e1) = e4
% 250.98/59.68 (40) ~ (all_36_2 = e0)
% 250.98/59.68 (41) op(e4, e4) = all_244_0
% 250.98/59.68 (42) ~ (all_48_2 = e4)
% 250.98/59.68 (43) ~ (e4 = e3)
% 250.98/59.68 (44) op(e1, e1) = all_244_15
% 250.98/59.68 (45) op(e3, e0) = all_48_2
% 250.98/59.68 (46) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.98/59.68 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.98/59.68 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.98/59.68 (47) op(all_48_2, e0) = e3
% 250.98/59.68 (48) op(e1, e2) = all_4_2
% 250.98/59.68 (49) op(e3, all_30_2) = e4
% 250.98/59.68 (50) ~ (all_48_2 = e0)
% 250.98/59.68 (51) op(all_244_3, all_244_3) = e3
% 250.98/59.68 (52) ~ (e4 = e2)
% 250.98/59.68 (53) op(e3, e2) = all_8_2
% 250.98/59.68 (54) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.98/59.68 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.98/59.68 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.98/59.68 (55) ~ (all_244_3 = e0)
% 250.98/59.68 (56) op(e2, e0) = all_40_2
% 250.98/59.68 (57) ~ (all_244_0 = e3)
% 250.98/59.68 (58) op(e3, e3) = all_244_3
% 250.98/59.68 (59) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.68 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.68 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.68
% 250.98/59.68 Begin of proof
% 250.98/59.68 |
% 250.98/59.68 | GROUND_INST: instantiating (11) with all_16_2, all_36_1, e4, e1, simplifying
% 250.98/59.68 | with (23), (37) gives:
% 250.98/59.68 | (60) all_36_1 = all_16_2
% 250.98/59.68 |
% 250.98/59.68 | BETA: splitting (3) gives:
% 250.98/59.68 |
% 250.98/59.68 | Case 1:
% 250.98/59.68 | |
% 250.98/59.68 | | (61) ~ (all_52_0 = e2) & op(e4, all_52_1) = all_52_0 & op(e1, e4) =
% 250.98/59.68 | | all_52_1 & $i(all_52_0) & $i(all_52_1)
% 250.98/59.68 | |
% 250.98/59.68 | | ALPHA: (61) implies:
% 250.98/59.68 | | (62) op(e1, e4) = all_52_1
% 250.98/59.68 | |
% 250.98/59.68 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.98/59.68 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.98/59.68 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.98/59.68 | | (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 250.98/59.68 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 250.98/59.68 | | (59), (62) are inconsistent by sub-proof #420.
% 250.98/59.68 | |
% 250.98/59.68 | Case 2:
% 250.98/59.68 | |
% 250.98/59.68 | | (63) ~ (all_52_1 = e0) & op(e1, e4) = all_52_1 & $i(all_52_1)
% 250.98/59.68 | |
% 250.98/59.68 | | ALPHA: (63) implies:
% 250.98/59.68 | | (64) op(e1, e4) = all_52_1
% 250.98/59.68 | |
% 250.98/59.68 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 250.98/59.68 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 250.98/59.68 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 250.98/59.68 | | (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 250.98/59.68 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 250.98/59.68 | | (59), (64) are inconsistent by sub-proof #420.
% 250.98/59.68 | |
% 250.98/59.68 | End of split
% 250.98/59.68 |
% 250.98/59.68 End of proof
% 250.98/59.68
% 250.98/59.68 Sub-proof #420 shows that the following formulas are inconsistent:
% 250.98/59.68 ----------------------------------------------------------------
% 250.98/59.68 (1) op(all_62_2, e4) = e3
% 250.98/59.68 (2) ~ (all_8_2 = e4)
% 250.98/59.68 (3) ~ (all_4_2 = e4)
% 250.98/59.68 (4) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.68 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.68 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.68 (5) op(e3, all_16_2) = e1
% 250.98/59.68 (6) op(e4, e0) = all_30_2
% 250.98/59.68 (7) ~ (e2 = e0)
% 250.98/59.68 (8) ~ (e1 = e0)
% 250.98/59.68 (9) op(e3, e4) = e0
% 250.98/59.68 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.68 (11) ~ (e3 = e2)
% 250.98/59.68 (12) ~ (e4 = e0)
% 250.98/59.68 (13) ~ (all_30_2 = e2) | ( ~ (all_30_0 = e3) & op(e2, all_30_1) = all_30_0 &
% 250.98/59.68 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 250.98/59.68 e1) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 250.98/59.68 (14) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 250.98/59.68 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 250.98/59.68 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.98/59.68 (15) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.98/59.68 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.98/59.68 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.68 (16) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 250.98/59.68 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 250.98/59.68 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.68 (17) ~ (all_244_15 = e4)
% 250.98/59.68 (18) ~ (e2 = e1)
% 250.98/59.68 (19) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.98/59.68 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.68 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.98/59.68 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.98/59.68 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.98/59.68 op(e0, e1) = e0)))
% 250.98/59.68 (20) ~ (e4 = e1)
% 250.98/59.68 (21) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 250.98/59.68 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 250.98/59.68 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.68 (22) op(e1, e4) = all_16_2
% 250.98/59.68 (23) all_252_10 = e4
% 250.98/59.68 (24) op(e1, e3) = all_62_2
% 250.98/59.68 (25) ~ (e3 = e0)
% 250.98/59.68 (26) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.98/59.68 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.98/59.68 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.98/59.68 (27) all_252_2 = e0
% 250.98/59.68 (28) ~ (e3 = e1)
% 250.98/59.68 (29) op(e3, e1) = all_36_2
% 250.98/59.68 (30) ~ (all_8_2 = e1)
% 250.98/59.68 (31) op(all_40_2, e0) = e2
% 250.98/59.68 (32) ~ (all_48_2 = all_8_2)
% 250.98/59.68 (33) ~ (all_8_2 = e0)
% 250.98/59.68 (34) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 250.98/59.68 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 250.98/59.68 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.98/59.68 (35) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.68 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.68 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.68 (36) ~ (all_244_15 = e3)
% 250.98/59.68 (37) op(e3, e1) = e4
% 250.98/59.68 (38) ~ (all_36_2 = e0)
% 250.98/59.68 (39) op(e4, e4) = all_244_0
% 250.98/59.68 (40) ~ (all_48_2 = e4)
% 250.98/59.68 (41) ~ (e4 = e3)
% 250.98/59.68 (42) op(e1, e1) = all_244_15
% 250.98/59.68 (43) op(e3, e0) = all_48_2
% 250.98/59.69 (44) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.98/59.69 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.98/59.69 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.98/59.69 (45) op(all_48_2, e0) = e3
% 250.98/59.69 (46) op(e1, e2) = all_4_2
% 250.98/59.69 (47) op(e3, all_30_2) = e4
% 250.98/59.69 (48) ~ (all_48_2 = e0)
% 250.98/59.69 (49) op(all_244_3, all_244_3) = e3
% 250.98/59.69 (50) ~ (e4 = e2)
% 250.98/59.69 (51) op(e3, e2) = all_8_2
% 250.98/59.69 (52) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.98/59.69 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.98/59.69 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.98/59.69 (53) ~ (all_244_3 = e0)
% 250.98/59.69 (54) op(e2, e0) = all_40_2
% 250.98/59.69 (55) op(e1, e4) = all_52_1
% 250.98/59.69 (56) ~ (all_244_0 = e3)
% 250.98/59.69 (57) op(e3, e3) = all_244_3
% 250.98/59.69 (58) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.69 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.69 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.69
% 250.98/59.69 Begin of proof
% 250.98/59.69 |
% 250.98/59.69 | GROUND_INST: instantiating (10) with all_16_2, all_52_1, e4, e1, simplifying
% 250.98/59.69 | with (22), (55) gives:
% 250.98/59.69 | (59) all_52_1 = all_16_2
% 250.98/59.69 |
% 250.98/59.69 | BETA: splitting (13) gives:
% 250.98/59.69 |
% 250.98/59.69 | Case 1:
% 250.98/59.69 | |
% 250.98/59.69 | | (60) ~ (all_30_2 = e2)
% 250.98/59.69 | |
% 250.98/59.69 | | BETA: splitting (26) gives:
% 250.98/59.69 | |
% 250.98/59.69 | | Case 1:
% 250.98/59.69 | | |
% 250.98/59.69 | | | (61) ~ (all_40_2 = e4)
% 250.98/59.69 | | |
% 250.98/59.69 | | | BETA: splitting (34) gives:
% 250.98/59.69 | | |
% 250.98/59.69 | | | Case 1:
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | (62) ~ (all_48_2 = e1)
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | BETA: splitting (15) gives:
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | Case 1:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | (63) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3,
% 250.98/59.69 | | | | | e3) = e1)
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | REF_CLOSE: (8), (9), (10), (36), (42), (49), (57), (63) are
% 250.98/59.69 | | | | | inconsistent by sub-proof #465.
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | Case 2:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | (64) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3,
% 250.98/59.69 | | | | | e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | BETA: splitting (64) gives:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | Case 1:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (65) all_252_5 = e1 & op(e3, e2) = e1
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | ALPHA: (65) implies:
% 250.98/59.69 | | | | | | (66) op(e3, e2) = e1
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | REF_CLOSE: (10), (30), (51), (66) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | #929.
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | Case 2:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (67) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 250.98/59.69 | | | | | | op(e3, e0) = e1)
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | BETA: splitting (67) gives:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | Case 1:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (68) all_252_10 = e1 & op(e3, e1) = e1
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | ALPHA: (68) implies:
% 250.98/59.69 | | | | | | | (69) all_252_10 = e1
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | REF_CLOSE: (20), (23), (69) are inconsistent by sub-proof #434.
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | Case 2:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (70) all_252_17 = e1 & op(e3, e0) = e1
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | ALPHA: (70) implies:
% 250.98/59.69 | | | | | | | (71) op(e3, e0) = e1
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | GROUND_INST: instantiating (10) with all_48_2, e1, e0, e3,
% 250.98/59.69 | | | | | | | simplifying with (43), (71) gives:
% 250.98/59.69 | | | | | | | (72) all_48_2 = e1
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | REDUCE: (62), (72) imply:
% 250.98/59.69 | | | | | | | (73) $false
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | CLOSE: (73) is inconsistent.
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | End of split
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | End of split
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | End of split
% 250.98/59.69 | | | |
% 250.98/59.69 | | | Case 2:
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | (74) all_48_2 = e1
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | REDUCE: (32), (74) imply:
% 250.98/59.69 | | | | (75) ~ (all_8_2 = e1)
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | REDUCE: (40), (74) imply:
% 250.98/59.69 | | | | (76) ~ (e4 = e1)
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | REDUCE: (45), (74) imply:
% 250.98/59.69 | | | | (77) op(e1, e0) = e3
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | REDUCE: (43), (74) imply:
% 250.98/59.69 | | | | (78) op(e3, e0) = e1
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | BETA: splitting (16) gives:
% 250.98/59.69 | | | |
% 250.98/59.69 | | | | Case 1:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | (79) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 &
% 250.98/59.69 | | | | | op(e3, e0) = e3)
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | BETA: splitting (79) gives:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | Case 1:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (80) all_252_16 = e3 & op(e4, e0) = e3
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | ALPHA: (80) implies:
% 250.98/59.69 | | | | | | (81) all_252_16 = e3
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | BETA: splitting (21) gives:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | Case 1:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (82) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 &
% 250.98/59.69 | | | | | | | op(e3, e0) = e4)
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | BETA: splitting (82) gives:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (83) all_252_16 = e4 & op(e4, e0) = e4
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | REF_CLOSE: (41), (81), (83) are inconsistent by sub-proof #483.
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (84) all_252_17 = e4 & op(e3, e0) = e4
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | ALPHA: (84) implies:
% 250.98/59.69 | | | | | | | | (85) all_252_17 = e4
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (15), (18), (20), (23),
% 250.98/59.69 | | | | | | | | (25), (27), (28), (29), (30), (33), (37), (38), (41),
% 250.98/59.69 | | | | | | | | (43), (48), (50), (51), (52), (53), (57), (58), (85)
% 250.98/59.69 | | | | | | | | are inconsistent by sub-proof #431.
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | End of split
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | Case 2:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (86) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 &
% 250.98/59.69 | | | | | | | op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | BETA: splitting (86) gives:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (87) all_252_18 = e4 & op(e2, e0) = e4
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | REF_CLOSE: (10), (54), (61), (87) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | #934.
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (88) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 &
% 250.98/59.69 | | | | | | | | op(e0, e0) = e4)
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | BETA: splitting (88) gives:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (89) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (17), (22), (24),
% 250.98/59.69 | | | | | | | | | (35), (39), (41), (42), (44), (46), (56), (77),
% 250.98/59.69 | | | | | | | | | (89) are inconsistent by sub-proof #428.
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (90) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | ALPHA: (90) implies:
% 250.98/59.69 | | | | | | | | | (91) all_252_24 = e4
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | BETA: splitting (14) gives:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (92) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 =
% 250.98/59.69 | | | | | | | | | | e2 & op(e3, e0) = e2)
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | REF_CLOSE: (6), (10), (18), (60), (78), (92) are inconsistent
% 250.98/59.69 | | | | | | | | | | by sub-proof #426.
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (93) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 =
% 250.98/59.69 | | | | | | | | | | e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0,
% 250.98/59.69 | | | | | | | | | | e0) = e2)
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | BETA: splitting (93) gives:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (94) all_252_18 = e2 & op(e2, e0) = e2
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | ALPHA: (94) implies:
% 250.98/59.69 | | | | | | | | | | | (95) all_252_18 = e2
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (19) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (96) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (12), (91), (96) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | #437.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (97) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.69 | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.98/59.69 | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 250.98/59.69 | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.98/59.69 | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 250.98/59.69 | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (97) implies:
% 250.98/59.69 | | | | | | | | | | | | (98) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.69 | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 250.98/59.69 | | | | | | | | | | | | = e0)
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | BETA: splitting (98) gives:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (99) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | REF_CLOSE: (10), (25), (43), (48), (81), (99) are
% 250.98/59.69 | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (100) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.98/59.69 | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | BETA: splitting (100) gives:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (101) all_252_18 = e0 & op(e2, e0) = e0
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | ALPHA: (101) implies:
% 250.98/59.69 | | | | | | | | | | | | | | (102) all_252_18 = e0
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | COMBINE_EQS: (95), (102) imply:
% 250.98/59.69 | | | | | | | | | | | | | | (103) e2 = e0
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | REDUCE: (7), (103) imply:
% 250.98/59.69 | | | | | | | | | | | | | | (104) $false
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | CLOSE: (104) is inconsistent.
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (105) all_252_19 = e0 & op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | ALPHA: (105) implies:
% 250.98/59.69 | | | | | | | | | | | | | | (106) op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | REF_CLOSE: (10), (25), (77), (106) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | | | sub-proof #438.
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (107) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 250.98/59.69 | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (107) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (108) all_252_19 = e2 & op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (108) implies:
% 250.98/59.69 | | | | | | | | | | | | (109) op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (10), (11), (77), (109) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | sub-proof #736.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (110) all_252_24 = e2 & op(e0, e0) = e2
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (50), (91), (110) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | #476.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | End of split
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | End of split
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | End of split
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | Case 2:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (111) all_252_17 = e3 & op(e3, e0) = e3
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | REF_CLOSE: (10), (28), (78), (111) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | #436.
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | End of split
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | Case 2:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | (112) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 &
% 250.98/59.69 | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | BETA: splitting (112) gives:
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | | Case 1:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (113) all_252_18 = e3 & op(e2, e0) = e3
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | ALPHA: (113) implies:
% 250.98/59.69 | | | | | | (114) all_252_18 = e3
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | BETA: splitting (14) gives:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | Case 1:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (115) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 &
% 250.98/59.69 | | | | | | | op(e3, e0) = e2)
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | REF_CLOSE: (6), (10), (18), (60), (78), (115) are inconsistent by
% 250.98/59.69 | | | | | | | sub-proof #426.
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | Case 2:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (116) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 &
% 250.98/59.69 | | | | | | | op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | BETA: splitting (116) gives:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (117) all_252_18 = e2 & op(e2, e0) = e2
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | ALPHA: (117) implies:
% 250.98/59.69 | | | | | | | | (118) all_252_18 = e2
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | REF_CLOSE: (11), (114), (118) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | #786.
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (119) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2
% 250.98/59.69 | | | | | | | | & op(e0, e0) = e2)
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | BETA: splitting (119) gives:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (120) all_252_19 = e2 & op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | ALPHA: (120) implies:
% 250.98/59.69 | | | | | | | | | (121) op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | REF_CLOSE: (10), (11), (77), (121) are inconsistent by
% 250.98/59.69 | | | | | | | | | sub-proof #736.
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (122) all_252_24 = e2 & op(e0, e0) = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | ALPHA: (122) implies:
% 250.98/59.69 | | | | | | | | | (123) all_252_24 = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | BETA: splitting (19) gives:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (124) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | REF_CLOSE: (7), (123), (124) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | #424.
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (125) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.69 | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.98/59.69 | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) =
% 250.98/59.69 | | | | | | | | | | e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.98/59.69 | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 250.98/59.69 | | | | | | | | | | = e0 & op(e0, e1) = e0))
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | ALPHA: (125) implies:
% 250.98/59.69 | | | | | | | | | | (126) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.98/59.69 | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.98/59.69 | | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | BETA: splitting (126) gives:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (127) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (127) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (128) all_252_16 = e0 & op(e4, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (128) implies:
% 250.98/59.69 | | | | | | | | | | | | (129) all_252_16 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | BETA: splitting (21) gives:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (130) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (12), (15), (18), (20),
% 250.98/59.69 | | | | | | | | | | | | | (23), (25), (27), (28), (29), (30), (33), (37),
% 250.98/59.69 | | | | | | | | | | | | | (38), (41), (43), (48), (50), (51), (52), (53),
% 250.98/59.69 | | | | | | | | | | | | | (57), (58), (129), (130) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | | sub-proof #423.
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (131) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19
% 250.98/59.69 | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) | (all_252_24 = e4 &
% 250.98/59.69 | | | | | | | | | | | | | op(e0, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | BETA: splitting (131) gives:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (132) all_252_18 = e4 & op(e2, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | REF_CLOSE: (10), (54), (61), (132) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | | | sub-proof #934.
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (133) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24
% 250.98/59.69 | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | (134) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | (135) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (123), (135) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | | | | | #424.
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (17), (22), (24),
% 250.98/59.69 | | | | | | | | | | | | | | | | (35), (39), (41), (42), (44), (46), (56), (77),
% 250.98/59.69 | | | | | | | | | | | | | | | | (134) are inconsistent by sub-proof #428.
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | (136) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 250.98/59.69 | | | | | | | | | | | | | | | (137) all_252_24 = e4
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | REF_CLOSE: (50), (123), (137) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | | | | #492.
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (138) all_252_17 = e0 & op(e3, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (10), (43), (48), (138) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | sub-proof #573.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (139) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.98/59.69 | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (139) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (140) all_252_18 = e0 & op(e2, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (140) implies:
% 250.98/59.69 | | | | | | | | | | | | (141) all_252_18 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (25), (114), (141) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | #422.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (142) all_252_19 = e0 & op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (142) implies:
% 250.98/59.69 | | | | | | | | | | | | (143) op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (10), (25), (77), (143) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | sub-proof #438.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | End of split
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | End of split
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | End of split
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | Case 2:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | (144) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 250.98/59.69 | | | | | | op(e0, e0) = e3)
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | BETA: splitting (144) gives:
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | | Case 1:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (145) all_252_19 = e3 & op(e1, e0) = e3
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | ALPHA: (145) implies:
% 250.98/59.69 | | | | | | | (146) all_252_19 = e3
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (17), (22), (24), (35),
% 250.98/59.69 | | | | | | | (39), (41), (42), (44), (46), (56), (146) are
% 250.98/59.69 | | | | | | | inconsistent by sub-proof #429.
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | Case 2:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | (147) all_252_24 = e3 & op(e0, e0) = e3
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | ALPHA: (147) implies:
% 250.98/59.69 | | | | | | | (148) all_252_24 = e3
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | BETA: splitting (14) gives:
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (149) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2
% 250.98/59.69 | | | | | | | | & op(e3, e0) = e2)
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | REF_CLOSE: (6), (10), (18), (60), (78), (149) are inconsistent
% 250.98/59.69 | | | | | | | | by sub-proof #426.
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | (150) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2
% 250.98/59.69 | | | | | | | | & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) =
% 250.98/59.69 | | | | | | | | e2)
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | BETA: splitting (150) gives:
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (151) all_252_18 = e2 & op(e2, e0) = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | ALPHA: (151) implies:
% 250.98/59.69 | | | | | | | | | (152) all_252_18 = e2
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | BETA: splitting (19) gives:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (153) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | REF_CLOSE: (25), (148), (153) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | #533.
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (154) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.69 | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 250.98/59.69 | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) =
% 250.98/59.69 | | | | | | | | | | e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 250.98/59.69 | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 250.98/59.69 | | | | | | | | | | = e0 & op(e0, e1) = e0))
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | ALPHA: (154) implies:
% 250.98/59.69 | | | | | | | | | | (155) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 =
% 250.98/59.69 | | | | | | | | | | e0 & op(e3, e0) = e0) | (all_252_18 = e0 & op(e2,
% 250.98/59.69 | | | | | | | | | | e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | BETA: splitting (155) gives:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (156) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (156) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (157) all_252_16 = e0 & op(e4, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (157) implies:
% 250.98/59.69 | | | | | | | | | | | | (158) all_252_16 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | BETA: splitting (21) gives:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (159) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17
% 250.98/59.69 | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (12), (15), (18), (20),
% 250.98/59.69 | | | | | | | | | | | | | (23), (25), (27), (28), (29), (30), (33), (37),
% 250.98/59.69 | | | | | | | | | | | | | (38), (41), (43), (48), (50), (51), (52), (53),
% 250.98/59.69 | | | | | | | | | | | | | (57), (58), (158), (159) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | | sub-proof #423.
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | (160) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19
% 250.98/59.69 | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) | (all_252_24 = e4 &
% 250.98/59.69 | | | | | | | | | | | | | op(e0, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | BETA: splitting (160) gives:
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (161) all_252_18 = e4 & op(e2, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | REF_CLOSE: (10), (54), (61), (161) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | | | sub-proof #934.
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | (162) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24
% 250.98/59.69 | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | (163) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | (164) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | REF_CLOSE: (25), (148), (164) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | | | | | #533.
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (17), (22), (24),
% 250.98/59.69 | | | | | | | | | | | | | | | | (35), (39), (41), (42), (44), (46), (56), (77),
% 250.98/59.69 | | | | | | | | | | | | | | | | (163) are inconsistent by sub-proof #428.
% 250.98/59.69 | | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | (165) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | | REF_CLOSE: (41), (148), (165) are inconsistent by sub-proof
% 250.98/59.69 | | | | | | | | | | | | | | | #421.
% 250.98/59.69 | | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (166) all_252_17 = e0 & op(e3, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (10), (43), (48), (166) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | sub-proof #573.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | (167) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 250.98/59.69 | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | BETA: splitting (167) gives:
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (168) all_252_18 = e0 & op(e2, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (168) implies:
% 250.98/59.69 | | | | | | | | | | | | (169) all_252_18 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | COMBINE_EQS: (152), (169) imply:
% 250.98/59.69 | | | | | | | | | | | | (170) e2 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | SIMP: (170) implies:
% 250.98/59.69 | | | | | | | | | | | | (171) e2 = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REDUCE: (7), (171) imply:
% 250.98/59.69 | | | | | | | | | | | | (172) $false
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | (173) all_252_19 = e0 & op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | ALPHA: (173) implies:
% 250.98/59.69 | | | | | | | | | | | | (174) op(e1, e0) = e0
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | | REF_CLOSE: (10), (25), (77), (174) are inconsistent by
% 250.98/59.69 | | | | | | | | | | | | sub-proof #438.
% 250.98/59.69 | | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | (175) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 =
% 250.98/59.69 | | | | | | | | | e2 & op(e0, e0) = e2)
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | BETA: splitting (175) gives:
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 1:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (176) all_252_19 = e2 & op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | ALPHA: (176) implies:
% 250.98/59.69 | | | | | | | | | | (177) op(e1, e0) = e2
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | REF_CLOSE: (10), (11), (77), (177) are inconsistent by
% 250.98/59.69 | | | | | | | | | | sub-proof #736.
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | Case 2:
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | (178) all_252_24 = e2 & op(e0, e0) = e2
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | ALPHA: (178) implies:
% 250.98/59.69 | | | | | | | | | | (179) all_252_24 = e2
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | COMBINE_EQS: (148), (179) imply:
% 250.98/59.69 | | | | | | | | | | (180) e3 = e2
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | REDUCE: (11), (180) imply:
% 250.98/59.69 | | | | | | | | | | (181) $false
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | | CLOSE: (181) is inconsistent.
% 250.98/59.69 | | | | | | | | | |
% 250.98/59.69 | | | | | | | | | End of split
% 250.98/59.69 | | | | | | | | |
% 250.98/59.69 | | | | | | | | End of split
% 250.98/59.69 | | | | | | | |
% 250.98/59.69 | | | | | | | End of split
% 250.98/59.69 | | | | | | |
% 250.98/59.69 | | | | | | End of split
% 250.98/59.69 | | | | | |
% 250.98/59.69 | | | | | End of split
% 250.98/59.69 | | | | |
% 250.98/59.69 | | | | End of split
% 250.98/59.69 | | | |
% 250.98/59.69 | | | End of split
% 250.98/59.69 | | |
% 250.98/59.69 | | Case 2:
% 250.98/59.69 | | |
% 250.98/59.69 | | | (182) all_40_2 = e4
% 250.98/59.69 | | |
% 250.98/59.69 | | | REDUCE: (31), (182) imply:
% 250.98/59.69 | | | (183) op(e4, e0) = e2
% 250.98/59.69 | | |
% 250.98/59.69 | | | REF_CLOSE: (6), (10), (60), (183) are inconsistent by sub-proof #830.
% 250.98/59.69 | | |
% 250.98/59.69 | | End of split
% 250.98/59.69 | |
% 250.98/59.69 | Case 2:
% 250.98/59.69 | |
% 250.98/59.69 | | (184) all_30_2 = e2
% 250.98/59.69 | |
% 250.98/59.69 | | REDUCE: (47), (184) imply:
% 250.98/59.69 | | (185) op(e3, e2) = e4
% 250.98/59.69 | |
% 250.98/59.69 | | REF_CLOSE: (2), (10), (51), (185) are inconsistent by sub-proof #502.
% 250.98/59.69 | |
% 250.98/59.69 | End of split
% 250.98/59.69 |
% 250.98/59.69 End of proof
% 250.98/59.69
% 250.98/59.69 Sub-proof #421 shows that the following formulas are inconsistent:
% 250.98/59.69 ----------------------------------------------------------------
% 250.98/59.69 (1) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.69 (2) all_252_24 = e3
% 250.98/59.69 (3) ~ (e4 = e3)
% 250.98/59.69
% 250.98/59.69 Begin of proof
% 250.98/59.69 |
% 250.98/59.69 | ALPHA: (1) implies:
% 250.98/59.69 | (4) all_252_24 = e4
% 250.98/59.69 |
% 250.98/59.69 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.69 | (5) e4 = e3
% 250.98/59.69 |
% 250.98/59.69 | SIMP: (5) implies:
% 250.98/59.69 | (6) e4 = e3
% 250.98/59.69 |
% 250.98/59.69 | REDUCE: (3), (6) imply:
% 250.98/59.69 | (7) $false
% 250.98/59.69 |
% 250.98/59.69 | CLOSE: (7) is inconsistent.
% 250.98/59.69 |
% 250.98/59.69 End of proof
% 250.98/59.69
% 250.98/59.69 Sub-proof #422 shows that the following formulas are inconsistent:
% 250.98/59.69 ----------------------------------------------------------------
% 250.98/59.69 (1) all_252_18 = e3
% 250.98/59.69 (2) all_252_18 = e0
% 250.98/59.69 (3) ~ (e3 = e0)
% 250.98/59.69
% 250.98/59.69 Begin of proof
% 250.98/59.69 |
% 250.98/59.69 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.69 | (4) e3 = e0
% 250.98/59.69 |
% 250.98/59.69 | SIMP: (4) implies:
% 250.98/59.69 | (5) e3 = e0
% 250.98/59.69 |
% 250.98/59.69 | REDUCE: (3), (5) imply:
% 250.98/59.69 | (6) $false
% 250.98/59.69 |
% 250.98/59.69 | CLOSE: (6) is inconsistent.
% 250.98/59.69 |
% 250.98/59.69 End of proof
% 250.98/59.69
% 250.98/59.69 Sub-proof #423 shows that the following formulas are inconsistent:
% 250.98/59.69 ----------------------------------------------------------------
% 250.98/59.69 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.69 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.69 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.69 (2) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.98/59.69 (3) ~ (e2 = e0)
% 250.98/59.69 (4) ~ (e1 = e0)
% 250.98/59.69 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.69 (6) ~ (e3 = e2)
% 250.98/59.69 (7) ~ (e4 = e0)
% 250.98/59.69 (8) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 250.98/59.69 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.98/59.69 | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.69 (9) ~ (e2 = e1)
% 250.98/59.69 (10) ~ (e4 = e1)
% 250.98/59.70 (11) all_252_10 = e4
% 250.98/59.70 (12) ~ (e3 = e0)
% 250.98/59.70 (13) all_252_2 = e0
% 250.98/59.70 (14) ~ (e3 = e1)
% 250.98/59.70 (15) op(e3, e1) = all_36_2
% 250.98/59.70 (16) ~ (all_8_2 = e1)
% 250.98/59.70 (17) ~ (all_8_2 = e0)
% 250.98/59.70 (18) op(e3, e1) = e4
% 250.98/59.70 (19) ~ (all_36_2 = e0)
% 250.98/59.70 (20) ~ (e4 = e3)
% 250.98/59.70 (21) op(e3, e0) = all_48_2
% 250.98/59.70 (22) ~ (all_48_2 = e0)
% 250.98/59.70 (23) all_252_16 = e0
% 250.98/59.70 (24) ~ (e4 = e2)
% 250.98/59.70 (25) op(e3, e2) = all_8_2
% 250.98/59.70 (26) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.98/59.70 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.98/59.70 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.98/59.70 (27) ~ (all_244_3 = e0)
% 250.98/59.70 (28) op(e3, e3) = all_244_3
% 250.98/59.70 (29) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.70 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.70 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (2) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (30) all_252_16 = e4 & op(e4, e0) = e4
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (30) implies:
% 250.98/59.70 | | (31) all_252_16 = e4
% 250.98/59.70 | |
% 250.98/59.70 | | COMBINE_EQS: (23), (31) imply:
% 250.98/59.70 | | (32) e4 = e0
% 250.98/59.70 | |
% 250.98/59.70 | | REDUCE: (7), (32) imply:
% 250.98/59.70 | | (33) $false
% 250.98/59.70 | |
% 250.98/59.70 | | CLOSE: (33) is inconsistent.
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (34) all_252_17 = e4 & op(e3, e0) = e4
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (34) implies:
% 250.98/59.70 | | (35) all_252_17 = e4
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 250.98/59.70 | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 250.98/59.70 | | (27), (28), (29), (35) are inconsistent by sub-proof #431.
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #424 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.70 (2) all_252_24 = e2
% 250.98/59.70 (3) ~ (e2 = e0)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (1) implies:
% 250.98/59.70 | (4) all_252_24 = e0
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.70 | (5) e2 = e0
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (3), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #425 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_16 = e3
% 250.98/59.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (3) ~ (e3 = e0)
% 250.98/59.70 (4) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.70 (5) op(e3, e0) = all_48_2
% 250.98/59.70 (6) ~ (all_48_2 = e0)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (4) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (7) all_252_16 = e0 & op(e4, e0) = e0
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (7) implies:
% 250.98/59.70 | | (8) all_252_16 = e0
% 250.98/59.70 | |
% 250.98/59.70 | | COMBINE_EQS: (1), (8) imply:
% 250.98/59.70 | | (9) e3 = e0
% 250.98/59.70 | |
% 250.98/59.70 | | SIMP: (9) implies:
% 250.98/59.70 | | (10) e3 = e0
% 250.98/59.70 | |
% 250.98/59.70 | | REDUCE: (3), (10) imply:
% 250.98/59.70 | | (11) $false
% 250.98/59.70 | |
% 250.98/59.70 | | CLOSE: (11) is inconsistent.
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (12) all_252_17 = e0 & op(e3, e0) = e0
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (2), (5), (6), (12) are inconsistent by sub-proof #573.
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #426 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) op(e4, e0) = all_30_2
% 250.98/59.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (3) ~ (e2 = e1)
% 250.98/59.70 (4) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.70 (5) ~ (all_30_2 = e2)
% 250.98/59.70 (6) op(e3, e0) = e1
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (4) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (7) all_252_16 = e2 & op(e4, e0) = e2
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (7) implies:
% 250.98/59.70 | | (8) op(e4, e0) = e2
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #830.
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (9) all_252_17 = e2 & op(e3, e0) = e2
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (9) implies:
% 250.98/59.70 | | (10) op(e3, e0) = e2
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #427.
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #427 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (2) op(e3, e0) = e2
% 250.98/59.70 (3) op(e3, e0) = e1
% 250.98/59.70 (4) ~ (e2 = e1)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | GROUND_INST: instantiating (1) with e1, e2, e0, e3, simplifying with (2), (3)
% 250.98/59.70 | gives:
% 250.98/59.70 | (5) e2 = e1
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (4), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #428 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) op(all_62_2, e4) = e3
% 250.98/59.70 (2) ~ (all_4_2 = e4)
% 250.98/59.70 (3) op(e3, all_16_2) = e1
% 250.98/59.70 (4) ~ (e1 = e0)
% 250.98/59.70 (5) op(e3, e4) = e0
% 250.98/59.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (7) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.70 (8) ~ (all_244_15 = e4)
% 250.98/59.70 (9) op(e1, e4) = all_16_2
% 250.98/59.70 (10) op(e1, e3) = all_62_2
% 250.98/59.70 (11) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.70 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.70 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.70 (12) op(e4, e4) = all_244_0
% 250.98/59.70 (13) ~ (e4 = e3)
% 250.98/59.70 (14) op(e1, e1) = all_244_15
% 250.98/59.70 (15) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.98/59.70 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.98/59.70 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.98/59.70 (16) op(e1, e2) = all_4_2
% 250.98/59.70 (17) op(e1, e0) = e3
% 250.98/59.70 (18) ~ (all_244_0 = e3)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (7) implies:
% 250.98/59.70 | (19) all_252_19 = e4
% 250.98/59.70 | (20) op(e1, e0) = e4
% 250.98/59.70 |
% 250.98/59.70 | GROUND_INST: instantiating (6) with e3, e4, e0, e1, simplifying with (17),
% 250.98/59.70 | (20) gives:
% 250.98/59.70 | (21) e4 = e3
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (19), (21) imply:
% 250.98/59.70 | (22) all_252_19 = e3
% 250.98/59.70 |
% 250.98/59.70 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 250.98/59.70 | (14), (15), (16), (18), (22) are inconsistent by sub-proof #429.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #429 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) op(all_62_2, e4) = e3
% 250.98/59.70 (2) ~ (all_4_2 = e4)
% 250.98/59.70 (3) op(e3, all_16_2) = e1
% 250.98/59.70 (4) ~ (e1 = e0)
% 250.98/59.70 (5) op(e3, e4) = e0
% 250.98/59.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (7) ~ (all_244_15 = e4)
% 250.98/59.70 (8) op(e1, e4) = all_16_2
% 250.98/59.70 (9) op(e1, e3) = all_62_2
% 250.98/59.70 (10) all_252_19 = e3
% 250.98/59.70 (11) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.70 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.70 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.70 (12) op(e4, e4) = all_244_0
% 250.98/59.70 (13) ~ (e4 = e3)
% 250.98/59.70 (14) op(e1, e1) = all_244_15
% 250.98/59.70 (15) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 250.98/59.70 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 250.98/59.70 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.98/59.70 (16) op(e1, e2) = all_4_2
% 250.98/59.70 (17) ~ (all_244_0 = e3)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (15) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (18) ~ (all_62_2 = e4)
% 250.98/59.70 | |
% 250.98/59.70 | | BETA: splitting (11) gives:
% 250.98/59.70 | |
% 250.98/59.70 | | Case 1:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (19) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 250.98/59.70 | | | e3) = e4)
% 250.98/59.70 | | |
% 250.98/59.70 | | | BETA: splitting (19) gives:
% 250.98/59.70 | | |
% 250.98/59.70 | | | Case 1:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (20) all_252_12 = e4 & op(e1, e4) = e4
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | ALPHA: (20) implies:
% 250.98/59.70 | | | | (21) op(e1, e4) = e4
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | GROUND_INST: instantiating (6) with all_16_2, e4, e4, e1, simplifying
% 250.98/59.70 | | | | with (8), (21) gives:
% 250.98/59.70 | | | | (22) all_16_2 = e4
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | REDUCE: (3), (22) imply:
% 250.98/59.70 | | | | (23) op(e3, e4) = e1
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | REF_CLOSE: (4), (5), (6), (23) are inconsistent by sub-proof #607.
% 250.98/59.70 | | | |
% 250.98/59.70 | | | Case 2:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (24) all_252_13 = e4 & op(e1, e3) = e4
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | REF_CLOSE: (6), (9), (18), (24) are inconsistent by sub-proof #952.
% 250.98/59.70 | | | |
% 250.98/59.70 | | | End of split
% 250.98/59.70 | | |
% 250.98/59.70 | | Case 2:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (25) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 250.98/59.70 | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.70 | | |
% 250.98/59.70 | | | REF_CLOSE: (2), (6), (7), (10), (13), (14), (16), (25) are inconsistent by
% 250.98/59.70 | | | sub-proof #430.
% 250.98/59.70 | | |
% 250.98/59.70 | | End of split
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (26) all_62_2 = e4
% 250.98/59.70 | |
% 250.98/59.70 | | REDUCE: (1), (26) imply:
% 250.98/59.70 | | (27) op(e4, e4) = e3
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (6), (12), (17), (27) are inconsistent by sub-proof #813.
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #430 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) ~ (all_4_2 = e4)
% 250.98/59.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (3) ~ (all_244_15 = e4)
% 250.98/59.70 (4) all_252_19 = e3
% 250.98/59.70 (5) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 250.98/59.70 | (all_252_19 = e4 & op(e1, e0) = e4)
% 250.98/59.70 (6) ~ (e4 = e3)
% 250.98/59.70 (7) op(e1, e1) = all_244_15
% 250.98/59.70 (8) op(e1, e2) = all_4_2
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (5) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (9) all_252_14 = e4 & op(e1, e2) = e4
% 250.98/59.70 | |
% 250.98/59.70 | | ALPHA: (9) implies:
% 250.98/59.70 | | (10) op(e1, e2) = e4
% 250.98/59.70 | |
% 250.98/59.70 | | REF_CLOSE: (1), (2), (8), (10) are inconsistent by sub-proof #831.
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0)
% 250.98/59.70 | | = e4)
% 250.98/59.70 | |
% 250.98/59.70 | | BETA: splitting (11) gives:
% 250.98/59.70 | |
% 250.98/59.70 | | Case 1:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (12) all_252_15 = e4 & op(e1, e1) = e4
% 250.98/59.70 | | |
% 250.98/59.70 | | | ALPHA: (12) implies:
% 250.98/59.70 | | | (13) op(e1, e1) = e4
% 250.98/59.70 | | |
% 250.98/59.70 | | | REF_CLOSE: (2), (3), (7), (13) are inconsistent by sub-proof #756.
% 250.98/59.70 | | |
% 250.98/59.70 | | Case 2:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (14) all_252_19 = e4 & op(e1, e0) = e4
% 250.98/59.70 | | |
% 250.98/59.70 | | | ALPHA: (14) implies:
% 250.98/59.70 | | | (15) all_252_19 = e4
% 250.98/59.70 | | |
% 250.98/59.70 | | | COMBINE_EQS: (4), (15) imply:
% 250.98/59.70 | | | (16) e4 = e3
% 250.98/59.70 | | |
% 250.98/59.70 | | | SIMP: (16) implies:
% 250.98/59.70 | | | (17) e4 = e3
% 250.98/59.70 | | |
% 250.98/59.70 | | | REDUCE: (6), (17) imply:
% 250.98/59.70 | | | (18) $false
% 250.98/59.70 | | |
% 250.98/59.70 | | | CLOSE: (18) is inconsistent.
% 250.98/59.70 | | |
% 250.98/59.70 | | End of split
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #431 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.70 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.70 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.70 (2) ~ (e2 = e0)
% 250.98/59.70 (3) ~ (e1 = e0)
% 250.98/59.70 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (5) ~ (e3 = e2)
% 250.98/59.70 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 250.98/59.70 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 250.98/59.70 | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.70 (7) ~ (e2 = e1)
% 250.98/59.70 (8) all_252_17 = e4
% 250.98/59.70 (9) ~ (e4 = e1)
% 250.98/59.70 (10) all_252_10 = e4
% 250.98/59.70 (11) ~ (e3 = e0)
% 250.98/59.70 (12) all_252_2 = e0
% 250.98/59.70 (13) ~ (e3 = e1)
% 250.98/59.70 (14) op(e3, e1) = all_36_2
% 250.98/59.70 (15) ~ (all_8_2 = e1)
% 250.98/59.70 (16) ~ (all_8_2 = e0)
% 250.98/59.70 (17) op(e3, e1) = e4
% 250.98/59.70 (18) ~ (all_36_2 = e0)
% 250.98/59.70 (19) ~ (e4 = e3)
% 250.98/59.70 (20) op(e3, e0) = all_48_2
% 250.98/59.70 (21) ~ (all_48_2 = e0)
% 250.98/59.70 (22) ~ (e4 = e2)
% 250.98/59.70 (23) op(e3, e2) = all_8_2
% 250.98/59.70 (24) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.98/59.70 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) =
% 250.98/59.70 e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.98/59.70 (25) ~ (all_244_3 = e0)
% 250.98/59.70 (26) op(e3, e3) = all_244_3
% 250.98/59.70 (27) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.70 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.70 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | BETA: splitting (6) gives:
% 250.98/59.70 |
% 250.98/59.70 | Case 1:
% 250.98/59.70 | |
% 250.98/59.70 | | (28) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 250.98/59.70 | | e1)
% 250.98/59.70 | |
% 250.98/59.70 | | BETA: splitting (28) gives:
% 250.98/59.70 | |
% 250.98/59.70 | | Case 1:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (29) all_252_2 = e1 & op(e3, e4) = e1
% 250.98/59.70 | | |
% 250.98/59.70 | | | REF_CLOSE: (3), (12), (29) are inconsistent by sub-proof #568.
% 250.98/59.70 | | |
% 250.98/59.70 | | Case 2:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (30) all_252_3 = e1 & op(e3, e3) = e1
% 250.98/59.70 | | |
% 250.98/59.70 | | | ALPHA: (30) implies:
% 250.98/59.70 | | | (31) all_252_3 = e1
% 250.98/59.70 | | |
% 250.98/59.70 | | | BETA: splitting (24) gives:
% 250.98/59.70 | | |
% 250.98/59.70 | | | Case 1:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (32) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3,
% 250.98/59.70 | | | | e3) = e3)
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | BETA: splitting (32) gives:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | Case 1:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | (33) all_252_2 = e3 & op(e3, e4) = e3
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | REF_CLOSE: (11), (12), (33) are inconsistent by sub-proof #541.
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | Case 2:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | (34) all_252_3 = e3 & op(e3, e3) = e3
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | REF_CLOSE: (13), (31), (34) are inconsistent by sub-proof #775.
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | End of split
% 250.98/59.70 | | | |
% 250.98/59.70 | | | Case 2:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (35) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3,
% 250.98/59.70 | | | | e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | BETA: splitting (35) gives:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | Case 1:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | (36) all_252_5 = e3 & op(e3, e2) = e3
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | ALPHA: (36) implies:
% 250.98/59.70 | | | | | (37) all_252_5 = e3
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | BETA: splitting (27) gives:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | Case 1:
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | (38) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 &
% 250.98/59.70 | | | | | | op(e3, e3) = e2)
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | REF_CLOSE: (1), (2), (4), (7), (14), (16), (18), (20), (21), (23),
% 250.98/59.70 | | | | | | (25), (26), (31), (38) are inconsistent by sub-proof
% 250.98/59.70 | | | | | | #504.
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | Case 2:
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | (39) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 &
% 250.98/59.70 | | | | | | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | BETA: splitting (39) gives:
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | Case 1:
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | | (40) all_252_5 = e2 & op(e3, e2) = e2
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | | REF_CLOSE: (5), (37), (40) are inconsistent by sub-proof #862.
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | Case 2:
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | | (41) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 250.98/59.70 | | | | | | | op(e3, e0) = e2)
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | | BETA: splitting (41) gives:
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | | Case 1:
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | | (42) all_252_10 = e2 & op(e3, e1) = e2
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | | REF_CLOSE: (10), (22), (42) are inconsistent by sub-proof #433.
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | Case 2:
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | | (43) all_252_17 = e2 & op(e3, e0) = e2
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | | REF_CLOSE: (8), (22), (43) are inconsistent by sub-proof #432.
% 250.98/59.70 | | | | | | | |
% 250.98/59.70 | | | | | | | End of split
% 250.98/59.70 | | | | | | |
% 250.98/59.70 | | | | | | End of split
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | End of split
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | Case 2:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | (44) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 &
% 250.98/59.70 | | | | | op(e3, e0) = e3)
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | BETA: splitting (44) gives:
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | | Case 1:
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | (45) all_252_10 = e3 & op(e3, e1) = e3
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | ALPHA: (45) implies:
% 250.98/59.70 | | | | | | (46) op(e3, e1) = e3
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | REF_CLOSE: (4), (14), (17), (19), (46) are inconsistent by sub-proof
% 250.98/59.70 | | | | | | #614.
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | Case 2:
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | (47) all_252_17 = e3 & op(e3, e0) = e3
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | | REF_CLOSE: (8), (19), (47) are inconsistent by sub-proof #443.
% 250.98/59.70 | | | | | |
% 250.98/59.70 | | | | | End of split
% 250.98/59.70 | | | | |
% 250.98/59.70 | | | | End of split
% 250.98/59.70 | | | |
% 250.98/59.70 | | | End of split
% 250.98/59.70 | | |
% 250.98/59.70 | | End of split
% 250.98/59.70 | |
% 250.98/59.70 | Case 2:
% 250.98/59.70 | |
% 250.98/59.70 | | (48) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.98/59.70 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.70 | |
% 250.98/59.70 | | BETA: splitting (48) gives:
% 250.98/59.70 | |
% 250.98/59.70 | | Case 1:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (49) all_252_5 = e1 & op(e3, e2) = e1
% 250.98/59.70 | | |
% 250.98/59.70 | | | ALPHA: (49) implies:
% 250.98/59.70 | | | (50) op(e3, e2) = e1
% 250.98/59.70 | | |
% 250.98/59.70 | | | REF_CLOSE: (4), (15), (23), (50) are inconsistent by sub-proof #929.
% 250.98/59.70 | | |
% 250.98/59.70 | | Case 2:
% 250.98/59.70 | | |
% 250.98/59.70 | | | (51) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 250.98/59.70 | | | e0) = e1)
% 250.98/59.70 | | |
% 250.98/59.70 | | | BETA: splitting (51) gives:
% 250.98/59.70 | | |
% 250.98/59.70 | | | Case 1:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (52) all_252_10 = e1 & op(e3, e1) = e1
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | REF_CLOSE: (9), (10), (52) are inconsistent by sub-proof #631.
% 250.98/59.70 | | | |
% 250.98/59.70 | | | Case 2:
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | (53) all_252_17 = e1 & op(e3, e0) = e1
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | ALPHA: (53) implies:
% 250.98/59.70 | | | | (54) all_252_17 = e1
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | COMBINE_EQS: (8), (54) imply:
% 250.98/59.70 | | | | (55) e4 = e1
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | REDUCE: (9), (55) imply:
% 250.98/59.70 | | | | (56) $false
% 250.98/59.70 | | | |
% 250.98/59.70 | | | | CLOSE: (56) is inconsistent.
% 250.98/59.70 | | | |
% 250.98/59.70 | | | End of split
% 250.98/59.70 | | |
% 250.98/59.70 | | End of split
% 250.98/59.70 | |
% 250.98/59.70 | End of split
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #432 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_17 = e2 & op(e3, e0) = e2
% 250.98/59.70 (2) all_252_17 = e4
% 250.98/59.70 (3) ~ (e4 = e2)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (1) implies:
% 250.98/59.70 | (4) all_252_17 = e2
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.70 | (5) e4 = e2
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (3), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #433 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_10 = e2 & op(e3, e1) = e2
% 250.98/59.70 (2) all_252_10 = e4
% 250.98/59.70 (3) ~ (e4 = e2)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (1) implies:
% 250.98/59.70 | (4) all_252_10 = e2
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.70 | (5) e4 = e2
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (3), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #434 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_10 = e4
% 250.98/59.70 (2) all_252_10 = e1
% 250.98/59.70 (3) ~ (e4 = e1)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.70 | (4) e4 = e1
% 250.98/59.70 |
% 250.98/59.70 | SIMP: (4) implies:
% 250.98/59.70 | (5) e4 = e1
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (3), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #435 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (2) op(e3, e1) = all_36_2
% 250.98/59.70 (3) op(e3, e1) = e4
% 250.98/59.70 (4) ~ (all_36_2 = e4)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | GROUND_INST: instantiating (1) with all_36_2, e4, e1, e3, simplifying with
% 250.98/59.70 | (2), (3) gives:
% 250.98/59.70 | (5) all_36_2 = e4
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (4), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #436 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_17 = e3 & op(e3, e0) = e3
% 250.98/59.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (3) op(e3, e0) = e1
% 250.98/59.70 (4) ~ (e3 = e1)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (1) implies:
% 250.98/59.70 | (5) op(e3, e0) = e3
% 250.98/59.70 |
% 250.98/59.70 | GROUND_INST: instantiating (2) with e1, e3, e0, e3, simplifying with (3), (5)
% 250.98/59.70 | gives:
% 250.98/59.70 | (6) e3 = e1
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (4), (6) imply:
% 250.98/59.70 | (7) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (7) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #437 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) all_252_24 = e0 & op(e0, e0) = e0
% 250.98/59.70 (2) all_252_24 = e4
% 250.98/59.70 (3) ~ (e4 = e0)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | ALPHA: (1) implies:
% 250.98/59.70 | (4) all_252_24 = e0
% 250.98/59.70 |
% 250.98/59.70 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.70 | (5) e4 = e0
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (3), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #438 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (2) op(e1, e0) = e3
% 250.98/59.70 (3) op(e1, e0) = e0
% 250.98/59.70 (4) ~ (e3 = e0)
% 250.98/59.70
% 250.98/59.70 Begin of proof
% 250.98/59.70 |
% 250.98/59.70 | GROUND_INST: instantiating (1) with e3, e0, e0, e1, simplifying with (2), (3)
% 250.98/59.70 | gives:
% 250.98/59.70 | (5) e3 = e0
% 250.98/59.70 |
% 250.98/59.70 | REDUCE: (4), (5) imply:
% 250.98/59.70 | (6) $false
% 250.98/59.70 |
% 250.98/59.70 | CLOSE: (6) is inconsistent.
% 250.98/59.70 |
% 250.98/59.70 End of proof
% 250.98/59.70
% 250.98/59.70 Sub-proof #439 shows that the following formulas are inconsistent:
% 250.98/59.70 ----------------------------------------------------------------
% 250.98/59.70 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.70 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.70 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.70 (2) all_252_6 = e2
% 250.98/59.70 (3) ~ (e2 = e0)
% 250.98/59.70 (4) ~ (e1 = e0)
% 250.98/59.70 (5) op(e3, e4) = e0
% 250.98/59.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.70 (7) ~ (e3 = e2)
% 250.98/59.70 (8) ~ (e4 = e0)
% 250.98/59.70 (9) ~ (e2 = e1)
% 250.98/59.70 (10) ~ (e4 = e1)
% 250.98/59.70 (11) all_252_16 = e2
% 250.98/59.70 (12) op(e1, e4) = all_16_2
% 250.98/59.70 (13) ~ (e3 = e0)
% 250.98/59.70 (14) all_252_2 = e0
% 250.98/59.70 (15) ~ (e3 = e1)
% 250.98/59.70 (16) op(e3, e1) = all_36_2
% 250.98/59.70 (17) ~ (all_16_2 = e2)
% 250.98/59.70 (18) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) =
% 250.98/59.70 e0)
% 250.98/59.71 (19) ~ (all_8_2 = e0)
% 250.98/59.71 (20) ~ (all_36_2 = e0)
% 250.98/59.71 (21) ~ (e4 = e3)
% 250.98/59.71 (22) op(e3, e0) = all_48_2
% 250.98/59.71 (23) ~ (all_48_2 = e0)
% 250.98/59.71 (24) ~ (e4 = e2)
% 250.98/59.71 (25) op(e3, e2) = all_8_2
% 250.98/59.71 (26) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.98/59.71 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.98/59.71 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.98/59.71 (27) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.98/59.71 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.98/59.71 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.98/59.71 (28) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.71 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.71 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.71 (29) ~ (all_244_3 = e0)
% 250.98/59.71 (30) ~ (all_16_2 = e3)
% 250.98/59.71 (31) op(e3, e3) = all_244_3
% 250.98/59.71 (32) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.98/59.71 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.98/59.71 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.98/59.71 (33) all_252_20 = e3
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | BETA: splitting (18) gives:
% 250.98/59.71 |
% 250.98/59.71 | Case 1:
% 250.98/59.71 | |
% 250.98/59.71 | | (34) all_252_16 = e0 & op(e4, e0) = e0
% 250.98/59.71 | |
% 250.98/59.71 | | ALPHA: (34) implies:
% 250.98/59.71 | | (35) all_252_16 = e0
% 250.98/59.71 | |
% 250.98/59.71 | | COMBINE_EQS: (11), (35) imply:
% 250.98/59.71 | | (36) e2 = e0
% 250.98/59.71 | |
% 250.98/59.71 | | COMBINE_EQS: (2), (36) imply:
% 250.98/59.71 | | (37) all_252_6 = e0
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 250.98/59.71 | | (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 250.98/59.71 | | (27), (28), (29), (30), (31), (32), (33), (37) are inconsistent
% 250.98/59.71 | | by sub-proof #537.
% 250.98/59.71 | |
% 250.98/59.71 | Case 2:
% 250.98/59.71 | |
% 250.98/59.71 | | (38) all_252_17 = e0 & op(e3, e0) = e0
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (6), (22), (23), (38) are inconsistent by sub-proof #573.
% 250.98/59.71 | |
% 250.98/59.71 | End of split
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #440 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (2) op(e3, e0) = e4
% 250.98/59.71 (3) ~ (e2 = e1)
% 250.98/59.71 (4) ~ (e4 = e1)
% 250.98/59.71 (5) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.71 (6) all_252_16 = e2
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | BETA: splitting (5) gives:
% 250.98/59.71 |
% 250.98/59.71 | Case 1:
% 250.98/59.71 | |
% 250.98/59.71 | | (7) all_252_16 = e1 & op(e4, e0) = e1
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #442.
% 250.98/59.71 | |
% 250.98/59.71 | Case 2:
% 250.98/59.71 | |
% 250.98/59.71 | | (8) all_252_17 = e1 & op(e3, e0) = e1
% 250.98/59.71 | |
% 250.98/59.71 | | ALPHA: (8) implies:
% 250.98/59.71 | | (9) op(e3, e0) = e1
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #441.
% 250.98/59.71 | |
% 250.98/59.71 | End of split
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #441 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (2) op(e3, e0) = e4
% 250.98/59.71 (3) op(e3, e0) = e1
% 250.98/59.71 (4) ~ (e4 = e1)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | GROUND_INST: instantiating (1) with e1, e4, e0, e3, simplifying with (2), (3)
% 250.98/59.71 | gives:
% 250.98/59.71 | (5) e4 = e1
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (4), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #442 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_16 = e1 & op(e4, e0) = e1
% 250.98/59.71 (2) all_252_16 = e2
% 250.98/59.71 (3) ~ (e2 = e1)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_16 = e1
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e2 = e1
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #443 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_17 = e3 & op(e3, e0) = e3
% 250.98/59.71 (2) all_252_17 = e4
% 250.98/59.71 (3) ~ (e4 = e3)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_17 = e3
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e4 = e3
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #444 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_22 = e0 & op(e0, e2) = e0
% 250.98/59.71 (2) all_252_22 = e4
% 250.98/59.71 (3) ~ (e4 = e0)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_22 = e0
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e4 = e0
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #445 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_22 = e2 & op(e0, e2) = e2
% 250.98/59.71 (2) all_252_22 = e4
% 250.98/59.71 (3) ~ (e4 = e2)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_22 = e2
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e4 = e2
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #446 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_22 = e1 & op(e0, e2) = e1
% 250.98/59.71 (2) all_252_22 = e4
% 250.98/59.71 (3) ~ (e4 = e1)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_22 = e1
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e4 = e1
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #447 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_14 = e3
% 250.98/59.71 (2) all_252_14 = e2
% 250.98/59.71 (3) ~ (e3 = e2)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.71 | (4) e3 = e2
% 250.98/59.71 |
% 250.98/59.71 | SIMP: (4) implies:
% 250.98/59.71 | (5) e3 = e2
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #448 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_18 = e4
% 250.98/59.71 (2) all_252_18 = e1
% 250.98/59.71 (3) ~ (e4 = e1)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (1), (2) imply:
% 250.98/59.71 | (4) e4 = e1
% 250.98/59.71 |
% 250.98/59.71 | SIMP: (4) implies:
% 250.98/59.71 | (5) e4 = e1
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #449 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_11 = e3 & op(e2, e1) = e3
% 250.98/59.71 (2) all_252_11 = e1
% 250.98/59.71 (3) ~ (e3 = e1)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_11 = e3
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e3 = e1
% 250.98/59.71 |
% 250.98/59.71 | SIMP: (5) implies:
% 250.98/59.71 | (6) e3 = e1
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (6) imply:
% 250.98/59.71 | (7) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (7) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #450 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_6 = e2 & op(e2, e4) = e2
% 250.98/59.71 (2) all_252_6 = e3
% 250.98/59.71 (3) ~ (e3 = e2)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (4) all_252_6 = e2
% 250.98/59.71 |
% 250.98/59.71 | COMBINE_EQS: (2), (4) imply:
% 250.98/59.71 | (5) e3 = e2
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (3), (5) imply:
% 250.98/59.71 | (6) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (6) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #451 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (2) op(e4, e2) = all_6_2
% 250.98/59.71 (3) ~ (all_6_2 = e2)
% 250.98/59.71 (4) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.98/59.71 (5) all_252_5 = e4
% 250.98/59.71 (6) ~ (e4 = e2)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | BETA: splitting (4) gives:
% 250.98/59.71 |
% 250.98/59.71 | Case 1:
% 250.98/59.71 | |
% 250.98/59.71 | | (7) all_252_4 = e2 & op(e4, e2) = e2
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #453.
% 250.98/59.71 | |
% 250.98/59.71 | Case 2:
% 250.98/59.71 | |
% 250.98/59.71 | | (8) all_252_5 = e2 & op(e3, e2) = e2
% 250.98/59.71 | |
% 250.98/59.71 | | ALPHA: (8) implies:
% 250.98/59.71 | | (9) all_252_5 = e2
% 250.98/59.71 | |
% 250.98/59.71 | | COMBINE_EQS: (5), (9) imply:
% 250.98/59.71 | | (10) e4 = e2
% 250.98/59.71 | |
% 250.98/59.71 | | REDUCE: (6), (10) imply:
% 250.98/59.71 | | (11) $false
% 250.98/59.71 | |
% 250.98/59.71 | | CLOSE: (11) is inconsistent.
% 250.98/59.71 | |
% 250.98/59.71 | End of split
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #452 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 250.98/59.71 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.71 | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.71 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (3) ~ (e4 = e0)
% 250.98/59.71 (4) ~ (all_244_3 = e4)
% 250.98/59.71 (5) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.98/59.71 (6) op(e3, e1) = all_36_2
% 250.98/59.71 (7) ~ (all_8_2 = e0)
% 250.98/59.71 (8) ~ (all_36_2 = e0)
% 250.98/59.71 (9) op(e3, e0) = all_48_2
% 250.98/59.71 (10) ~ (all_48_2 = e0)
% 250.98/59.71 (11) op(e3, e2) = all_8_2
% 250.98/59.71 (12) ~ (all_244_3 = e0)
% 250.98/59.71 (13) op(e3, e3) = all_244_3
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | BETA: splitting (5) gives:
% 250.98/59.71 |
% 250.98/59.71 | Case 1:
% 250.98/59.71 | |
% 250.98/59.71 | | (14) all_252_2 = e4 & op(e3, e4) = e4
% 250.98/59.71 | |
% 250.98/59.71 | | ALPHA: (14) implies:
% 250.98/59.71 | | (15) all_252_2 = e4
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (15)
% 250.98/59.71 | | are inconsistent by sub-proof #569.
% 250.98/59.71 | |
% 250.98/59.71 | Case 2:
% 250.98/59.71 | |
% 250.98/59.71 | | (16) all_252_3 = e4 & op(e3, e3) = e4
% 250.98/59.71 | |
% 250.98/59.71 | | REF_CLOSE: (2), (4), (13), (16) are inconsistent by sub-proof #846.
% 250.98/59.71 | |
% 250.98/59.71 | End of split
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #453 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) all_252_4 = e2 & op(e4, e2) = e2
% 250.98/59.71 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (3) op(e4, e2) = all_6_2
% 250.98/59.71 (4) ~ (all_6_2 = e2)
% 250.98/59.71
% 250.98/59.71 Begin of proof
% 250.98/59.71 |
% 250.98/59.71 | ALPHA: (1) implies:
% 250.98/59.71 | (5) op(e4, e2) = e2
% 250.98/59.71 |
% 250.98/59.71 | GROUND_INST: instantiating (2) with all_6_2, e2, e2, e4, simplifying with (3),
% 250.98/59.71 | (5) gives:
% 250.98/59.71 | (6) all_6_2 = e2
% 250.98/59.71 |
% 250.98/59.71 | REDUCE: (4), (6) imply:
% 250.98/59.71 | (7) $false
% 250.98/59.71 |
% 250.98/59.71 | CLOSE: (7) is inconsistent.
% 250.98/59.71 |
% 250.98/59.71 End of proof
% 250.98/59.71
% 250.98/59.71 Sub-proof #454 shows that the following formulas are inconsistent:
% 250.98/59.71 ----------------------------------------------------------------
% 250.98/59.71 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) |
% 250.98/59.71 (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = e2) |
% 250.98/59.71 (all_252_16 = e2 & op(e4, e0) = e2)
% 250.98/59.71 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 250.98/59.71 all_250_23 = e0
% 250.98/59.71 (3) all_32_2 = all_20_2
% 250.98/59.71 (4) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 250.98/59.71 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 250.98/59.71 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 250.98/59.71 (5) ~ (all_4_2 = e4)
% 250.98/59.71 (6) ~ (all_178_2 = e3) | ( ~ (all_178_0 = e4) & op(e3, all_178_1) =
% 250.98/59.71 all_178_0 & op(e0, e3) = all_178_1 & $i(all_178_0) & $i(all_178_1)) | (
% 250.98/59.71 ~ (all_178_1 = e1) & op(e0, e3) = all_178_1 & $i(all_178_1))
% 250.98/59.71 (7) ~ (all_10_2 = e4)
% 250.98/59.71 (8) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.98/59.71 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 250.98/59.71 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 250.98/59.71 (9) op(all_4_2, e2) = e1
% 250.98/59.71 (10) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3)
% 250.98/59.71 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) =
% 250.98/59.71 e3) | (all_252_16 = e3 & op(e4, e0) = e3)
% 250.98/59.71 (11) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.98/59.71 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 250.98/59.71 e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 250.98/59.71 (12) op(all_6_2, e2) = e4
% 250.98/59.71 (13) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 250.98/59.71 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 250.98/59.71 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 250.98/59.71 (14) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.98/59.71 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 250.98/59.71 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 250.98/59.71 (15) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.71 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.98/59.71 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 250.98/59.71 (16) op(e4, e0) = all_30_2
% 250.98/59.71 (17) all_250_8 = all_36_2
% 250.98/59.71 (18) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 250.98/59.71 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 250.98/59.71 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 250.98/59.71 (19) ~ (all_138_2 = e0) | ( ~ (all_138_0 = e4) & op(e3, e0) = all_138_1 &
% 250.98/59.71 op(e0, all_138_1) = all_138_0 & $i(all_138_0) & $i(all_138_1)) | ( ~
% 250.98/59.71 (all_138_1 = e1) & op(e3, e0) = all_138_1 & $i(all_138_1))
% 250.98/59.71 (20) ~ (all_244_8 = all_6_2)
% 250.98/59.71 (21) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 250.98/59.71 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 250.98/59.71 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 250.98/59.71 (22) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 250.98/59.71 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 250.98/59.71 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 250.98/59.71 (23) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 250.98/59.71 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 250.98/59.71 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 250.98/59.71 (24) all_94_2 = all_38_2
% 250.98/59.71 (25) all_162_2 = all_28_2
% 250.98/59.71 (26) op(all_62_2, all_36_2) = e3
% 250.98/59.71 (27) op(all_38_2, e1) = e2
% 250.98/59.71 (28) ~ (all_64_2 = e3)
% 250.98/59.71 (29) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 250.98/59.71 all_250_15 = e0
% 250.98/59.71 (30) ~ (all_28_2 = all_6_2)
% 250.98/59.71 (31) ~ (e2 = e0)
% 250.98/59.71 (32) op(all_38_2, all_4_2) = e1
% 250.98/59.71 (33) ~ (e1 = e0)
% 250.98/59.71 (34) ~ (all_22_2 = e3)
% 250.98/59.71 (35) ~ (all_28_2 = e3)
% 250.98/59.71 (36) ~ (all_62_2 = all_22_2)
% 250.98/59.71 (37) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 250.98/59.71 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 250.98/59.71 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 250.98/59.71 (38) op(e3, e4) = e0
% 250.98/59.71 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 250.98/59.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 250.98/59.71 (40) op(e2, e3) = all_10_2
% 250.98/59.71 (41) ~ (e3 = e2)
% 250.98/59.71 (42) op(e0, e0) = all_244_24
% 250.98/59.71 (43) ~ (e4 = e0)
% 250.98/59.71 (44) ~ (all_30_2 = all_6_2)
% 250.98/59.71 (45) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 250.98/59.71 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 250.98/59.71 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 250.98/59.71 (46) op(e2, e2) = all_244_8
% 250.98/59.71 (47) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 250.98/59.71 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 250.98/59.71 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 250.98/59.71 (48) op(e2, e1) = all_38_2
% 250.98/59.71 (49) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 250.98/59.71 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 250.98/59.71 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 250.98/59.71 (50) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 250.98/59.71 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 250.98/59.71 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 250.98/59.71 (51) ~ (all_36_2 = all_20_2)
% 250.98/59.71 (52) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4)
% 250.98/59.71 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) =
% 250.98/59.71 e4) | (all_252_16 = e4 & op(e4, e0) = e4)
% 250.98/59.71 (53) ~ (all_64_2 = all_40_2)
% 250.98/59.71 (54) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 250.98/59.71 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 250.98/59.71 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 250.98/59.71 (55) op(e1, e0) = all_34_2
% 250.98/59.71 (56) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 250.98/59.71 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 250.98/59.71 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 250.98/59.71 (57) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 250.98/59.71 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 250.98/59.71 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 250.98/59.71 (58) op(e4, e2) = all_6_2
% 250.98/59.71 (59) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.98/59.71 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 250.98/59.71 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 250.98/59.71 (60) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 250.98/59.71 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 250.98/59.71 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 250.98/59.71 (61) all_78_2 = all_10_2
% 250.98/59.71 (62) ~ (e2 = e1)
% 250.98/59.71 (63) op(all_26_2, e1) = e4
% 250.98/59.71 (64) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 250.98/59.71 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 250.98/59.71 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 250.98/59.71 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 250.98/59.71 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 250.98/59.71 op(e0, e1) = e0)))
% 250.98/59.71 (65) op(e0, e2) = all_28_2
% 250.98/59.71 (66) ~ (e4 = e1)
% 250.98/59.71 (67) op(all_6_2, all_64_2) = e2
% 250.98/59.71 (68) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 250.98/59.71 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 250.98/59.71 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 250.98/59.71 (69) ~ (all_244_8 = all_10_2)
% 250.98/59.71 (70) ~ (all_6_2 = e1)
% 250.98/59.71 (71) ~ (all_244_8 = all_38_2)
% 250.98/59.71 (72) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 250.98/59.71 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 250.98/59.71 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 250.98/59.71 (73) all_80_2 = all_6_2
% 250.98/59.71 (74) all_250_21 = all_22_2
% 250.98/59.71 (75) all_50_2 = all_4_2
% 250.98/59.71 (76) op(all_34_2, e0) = e1
% 250.98/59.71 (77) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 250.98/59.71 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 250.98/59.71 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 250.98/59.71 (78) op(e1, e4) = all_16_2
% 250.98/59.71 (79) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 250.98/59.71 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 250.98/59.71 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 250.98/59.71 (80) ~ (all_28_2 = all_20_2)
% 250.98/59.71 (81) all_178_2 = all_40_2
% 250.98/59.71 (82) op(e1, e3) = all_62_2
% 250.98/59.71 (83) ~ (all_244_0 = all_26_2)
% 250.98/59.71 (84) ~ (e3 = e0)
% 250.98/59.71 (85) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 250.98/59.71 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 250.98/59.71 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 250.98/59.71 (86) ~ (all_40_2 = all_10_2)
% 250.98/59.71 (87) all_250_10 = e4 | all_250_10 = e3 | all_250_10 = e2 | all_250_10 = e1 |
% 250.98/59.71 all_250_10 = e0
% 250.98/59.71 (88) op(all_84_2, e0) = e3
% 250.98/59.71 (89) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 250.98/59.71 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 250.98/59.71 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 250.98/59.71 (90) ~ (all_244_3 = all_10_2)
% 250.98/59.71 (91) ~ (all_48_2 = all_36_2)
% 250.98/59.71 (92) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 250.98/59.71 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 250.98/59.71 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 250.98/59.71 (93) all_252_2 = e0
% 250.98/59.71 (94) ~ (all_30_2 = e2)
% 250.98/59.71 (95) all_70_2 = all_62_2
% 250.98/59.71 (96) ~ (e3 = e1)
% 250.98/59.71 (97) op(all_48_2, all_22_2) = e0
% 250.98/59.71 (98) op(e3, e1) = all_36_2
% 250.98/59.71 (99) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 250.98/59.71 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 250.98/59.71 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 250.98/59.71 (100) ~ (all_16_2 = e2)
% 250.98/59.71 (101) ~ (all_8_2 = e1)
% 250.98/59.71 (102) op(all_40_2, e0) = e2
% 250.98/59.71 (103) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 250.98/59.71 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 250.98/59.71 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 250.98/59.71 (104) ~ (all_22_2 = e1)
% 250.98/59.71 (105) ~ (all_244_8 = all_40_2)
% 250.98/59.71 (106) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 250.98/59.71 all_250_8 = e0
% 250.98/59.71 (107) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 250.98/59.71 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 250.98/59.71 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 250.98/59.71 (108) op(e0, all_84_2) = e4
% 250.98/59.71 (109) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 250.98/59.71 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 250.98/59.71 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 250.98/59.71 (110) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 250.98/59.71 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 250.98/59.71 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 250.98/59.71 (111) ~ (all_40_2 = all_34_2)
% 250.98/59.71 (112) ~ (all_244_15 = all_38_2)
% 250.98/59.71 (113) ~ (all_48_2 = all_8_2)
% 250.98/59.71 (114) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 250.98/59.71 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 250.98/59.71 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 250.98/59.71 (115) ~ (all_36_2 = all_26_2)
% 250.98/59.71 (116) ~ (all_8_2 = e0)
% 250.98/59.71 (117) all_44_2 = all_26_2
% 250.98/59.71 (118) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0)
% 250.98/59.71 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) =
% 250.98/59.71 e0) | (all_252_16 = e0 & op(e4, e0) = e0)
% 250.98/59.71 (119) ~ (all_244_15 = all_34_2)
% 250.98/59.71 (120) all_250_10 = all_64_2
% 250.98/59.71 (121) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 250.98/59.71 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 250.98/59.71 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 250.98/59.71 (122) all_138_2 = all_10_2
% 250.98/59.71 (123) op(all_22_2, e3) = e0
% 250.98/59.71 (124) all_68_2 = all_22_2
% 250.98/59.71 (125) op(e0, e3) = all_22_2
% 250.98/59.72 (126) ~ (all_28_2 = all_22_2)
% 250.98/59.72 (127) all_242_2 = all_38_2
% 250.98/59.72 (128) op(all_34_2, all_20_2) = e0
% 250.98/59.72 (129) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 250.98/59.72 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 250.98/59.72 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 250.98/59.72 (130) op(all_62_2, e3) = e1
% 250.98/59.72 (131) op(e4, e1) = all_26_2
% 250.98/59.72 (132) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 250.98/59.72 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 250.98/59.72 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 250.98/59.72 (133) ~ (all_64_2 = all_38_2)
% 250.98/59.72 (134) op(all_10_2, e3) = e2
% 250.98/59.72 (135) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 250.98/59.72 all_250_21 = e0
% 250.98/59.72 (136) ~ (all_62_2 = all_16_2)
% 250.98/59.72 (137) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 250.98/59.72 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 250.98/59.72 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 250.98/59.72 (138) ~ (all_8_2 = all_6_2)
% 250.98/59.72 (139) ~ (all_36_2 = e0)
% 250.98/59.72 (140) all_250_15 = all_16_2
% 250.98/59.72 (141) op(e4, e4) = all_244_0
% 250.98/59.72 (142) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.72 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 250.98/59.72 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 250.98/59.72 (143) ~ (e4 = e3)
% 250.98/59.72 (144) op(e1, e1) = all_244_15
% 250.98/59.72 (145) ~ (all_64_2 = e0)
% 250.98/59.72 (146) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 250.98/59.72 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 250.98/59.72 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 250.98/59.72 (147) op(e0, e1) = all_20_2
% 250.98/59.72 (148) op(e3, e0) = all_48_2
% 250.98/59.72 (149) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 250.98/59.72 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 250.98/59.72 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 250.98/59.72 (150) op(all_48_2, e0) = e3
% 250.98/59.72 (151) ~ (all_38_2 = all_36_2)
% 250.98/59.72 (152) ~ (all_26_2 = e3)
% 250.98/59.72 (153) all_82_2 = all_28_2
% 250.98/59.72 (154) op(e1, e2) = all_4_2
% 250.98/59.72 (155) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 250.98/59.72 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 250.98/59.72 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 250.98/59.72 (156) ~ (all_28_2 = all_8_2)
% 250.98/59.72 (157) ~ (all_48_2 = e0)
% 250.98/59.72 (158) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 250.98/59.72 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 250.98/59.72 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 250.98/59.72 (159) op(e4, e3) = all_84_2
% 250.98/59.72 (160) all_86_2 = all_40_2
% 250.98/59.72 (161) op(all_244_3, all_244_3) = e3
% 250.98/59.72 (162) op(e2, e4) = all_64_2
% 250.98/59.72 (163) ~ (all_22_2 = all_10_2)
% 250.98/59.72 (164) ~ (all_6_2 = all_4_2)
% 250.98/59.72 (165) ~ (e4 = e2)
% 250.98/59.72 (166) ~ (all_22_2 = all_20_2)
% 250.98/59.72 (167) op(e3, e2) = all_8_2
% 250.98/59.72 (168) ~ (all_34_2 = all_16_2)
% 250.98/59.72 (169) ~ (all_64_2 = all_16_2)
% 250.98/59.72 (170) op(all_36_2, e1) = e3
% 250.98/59.72 (171) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 250.98/59.72 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 250.98/59.72 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 250.98/59.72 (172) ~ (all_38_2 = all_10_2)
% 250.98/59.72 (173) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 250.98/59.72 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 250.98/59.72 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 250.98/59.72 (174) ~ (all_244_15 = all_36_2)
% 250.98/59.72 (175) ~ (all_20_2 = e4)
% 250.98/59.72 (176) ~ (all_244_24 = all_22_2)
% 250.98/59.72 (177) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 250.98/59.72 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 250.98/59.72 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 250.98/59.72 (178) ~ (all_244_3 = e0)
% 250.98/59.72 (179) op(e2, e0) = all_40_2
% 250.98/59.72 (180) ~ (all_20_2 = e3)
% 250.98/59.72 (181) ~ (all_16_2 = e3)
% 250.98/59.72 (182) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 250.98/59.72 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 250.98/59.72 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 250.98/59.72 (183) ~ (all_244_0 = e3)
% 250.98/59.72 (184) op(e3, e3) = all_244_3
% 250.98/59.72 (185) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 250.98/59.72 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 250.98/59.72 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 250.98/59.72 (186) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 250.98/59.72 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 250.98/59.72 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 250.98/59.72 (187) all_90_2 = all_22_2
% 250.98/59.72 (188) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 250.98/59.72 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 250.98/59.72 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 250.98/59.72 (189) op(all_26_2, all_16_2) = e1
% 250.98/59.72 (190) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 250.98/59.72 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 250.98/59.72 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 250.98/59.72 (191) all_46_2 = all_36_2
% 250.98/59.72 (192) op(e4, e0) = all_146_1
% 250.98/59.72 (193) op(all_22_2, all_48_2) = e3
% 250.98/59.72 (194) ~ (all_16_2 = e0)
% 250.98/59.72 (195) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 250.98/59.72 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 250.98/59.72 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 250.98/59.72 (196) all_250_23 = all_20_2
% 250.98/59.72 (197) all_252_20 = e3
% 250.98/59.72
% 250.98/59.72 Begin of proof
% 250.98/59.72 |
% 250.98/59.72 | GROUND_INST: instantiating (39) with all_30_2, all_146_1, e0, e4, simplifying
% 250.98/59.72 | with (16), (192) gives:
% 250.98/59.72 | (198) all_146_1 = all_30_2
% 250.98/59.72 |
% 250.98/59.72 | BETA: splitting (85) gives:
% 250.98/59.72 |
% 250.98/59.72 | Case 1:
% 250.98/59.72 | |
% 250.98/59.72 | | (199) ~ (all_32_2 = e2)
% 250.98/59.72 | |
% 250.98/59.72 | | REDUCE: (3), (199) imply:
% 250.98/59.72 | | (200) ~ (all_20_2 = e2)
% 250.98/59.72 | |
% 250.98/59.72 | | BETA: splitting (60) gives:
% 250.98/59.72 | |
% 250.98/59.72 | | Case 1:
% 250.98/59.72 | | |
% 250.98/59.72 | | | (201) ~ (all_34_2 = e2)
% 250.98/59.72 | | |
% 250.98/59.72 | | | BETA: splitting (23) gives:
% 250.98/59.72 | | |
% 250.98/59.72 | | | Case 1:
% 250.98/59.72 | | | |
% 250.98/59.72 | | | | (202) ~ (all_36_2 = e4)
% 250.98/59.72 | | | |
% 250.98/59.72 | | | | BETA: splitting (50) gives:
% 250.98/59.72 | | | |
% 250.98/59.72 | | | | Case 1:
% 250.98/59.72 | | | | |
% 250.98/59.72 | | | | | (203) ~ (all_38_2 = e4)
% 250.98/59.72 | | | | |
% 250.98/59.72 | | | | | BETA: splitting (92) gives:
% 250.98/59.72 | | | | |
% 250.98/59.72 | | | | | Case 1:
% 250.98/59.72 | | | | | |
% 250.98/59.72 | | | | | | (204) ~ (all_40_2 = e4)
% 250.98/59.72 | | | | | |
% 250.98/59.72 | | | | | | BETA: splitting (21) gives:
% 250.98/59.72 | | | | | |
% 250.98/59.72 | | | | | | Case 1:
% 250.98/59.72 | | | | | | |
% 250.98/59.72 | | | | | | | (205) ~ (all_44_2 = e2)
% 250.98/59.72 | | | | | | |
% 250.98/59.72 | | | | | | | REDUCE: (117), (205) imply:
% 250.98/59.72 | | | | | | | (206) ~ (all_26_2 = e2)
% 250.98/59.72 | | | | | | |
% 250.98/59.72 | | | | | | | BETA: splitting (110) gives:
% 250.98/59.72 | | | | | | |
% 250.98/59.72 | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | |
% 250.98/59.72 | | | | | | | | (207) ~ (all_46_2 = e2)
% 250.98/59.72 | | | | | | | |
% 250.98/59.72 | | | | | | | | REDUCE: (191), (207) imply:
% 250.98/59.72 | | | | | | | | (208) ~ (all_36_2 = e2)
% 250.98/59.72 | | | | | | | |
% 250.98/59.72 | | | | | | | | BETA: splitting (121) gives:
% 250.98/59.72 | | | | | | | |
% 250.98/59.72 | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | |
% 250.98/59.72 | | | | | | | | | (209) ~ (all_48_2 = e1)
% 250.98/59.72 | | | | | | | | |
% 250.98/59.72 | | | | | | | | | BETA: splitting (195) gives:
% 250.98/59.72 | | | | | | | | |
% 250.98/59.72 | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | (210) ~ (all_50_2 = e3)
% 250.98/59.72 | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | REDUCE: (75), (210) imply:
% 250.98/59.72 | | | | | | | | | | (211) ~ (all_4_2 = e3)
% 250.98/59.72 | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | BETA: splitting (149) gives:
% 250.98/59.72 | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | (212) ~ (all_62_2 = e4)
% 250.98/59.72 | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | BETA: splitting (54) gives:
% 250.98/59.72 | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | (213) ~ (all_68_2 = e4)
% 250.98/59.72 | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | REDUCE: (124), (213) imply:
% 250.98/59.72 | | | | | | | | | | | | (214) ~ (all_22_2 = e4)
% 250.98/59.72 | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | BETA: splitting (114) gives:
% 250.98/59.72 | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | (215) ~ (all_70_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | REDUCE: (95), (215) imply:
% 250.98/59.72 | | | | | | | | | | | | | (216) ~ (all_62_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | BETA: splitting (99) gives:
% 250.98/59.72 | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | (217) ~ (all_78_2 = e1)
% 250.98/59.72 | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | REDUCE: (61), (217) imply:
% 250.98/59.72 | | | | | | | | | | | | | | (218) ~ (all_10_2 = e1)
% 250.98/59.72 | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 250.98/59.72 | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | (219) ~ (all_82_2 = e1)
% 250.98/59.72 | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | REDUCE: (153), (219) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | (220) ~ (all_28_2 = e1)
% 250.98/59.72 | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 250.98/59.72 | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | (221) ~ (all_80_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (73), (221) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (222) ~ (all_6_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | (223) ~ (all_86_2 = e3)
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | REDUCE: (160), (223) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | (224) ~ (all_40_2 = e3)
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (225) ~ (all_90_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (187), (225) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (226) ~ (all_22_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (39), (74), (97), (104), (135), (150),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (214), (226) are inconsistent by sub-proof #957.
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (227) all_90_2 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (228) ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | op(e2, all_90_1) = all_90_0 & $i(all_90_0) &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | $i(all_90_1)) | ( ~ (all_90_1 = e1) & op(e3, e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | = all_90_1 & $i(all_90_1))
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (227) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (229) all_22_2 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | SIMP: (229) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (230) all_22_2 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (176), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (231) ~ (all_244_24 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (126), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (232) ~ (all_28_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (166), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (233) ~ (all_20_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (163), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (234) ~ (all_10_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (235) ~ (all_10_2 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (214), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (236) ~ (e4 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (34), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (237) ~ (e3 = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REDUCE: (123), (230) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (238) op(e2, e3) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (239) ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | op(e2, all_90_1) = all_90_0 & $i(all_90_0) &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | $i(all_90_1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (240) op(e3, e2) = all_90_1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (241) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (242) all_252_20 = e2 & op(e0, e4) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (242) are inconsistent by sub-proof
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | #560.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (243) all_252_21 = e2 & op(e0, e3) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (244) all_252_21 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_10_2, e0, e3, e2,
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (40), (238) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (245) all_10_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_8_2, all_90_1, e2, e3,
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (167), (240) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (246) all_90_1 = all_8_2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (245) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (247) all_138_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (245) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_244_8 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11), (13), (18), (19), (24), (27),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (35), (37), (38), (39), (40), (41), (46), (47),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (48), (49), (55), (57), (58), (62), (64), (65),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (66), (70), (72), (78), (79), (82), (84), (86),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (93), (96), (98), (100), (101), (103), (104),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (116), (125), (129), (134), (139), (143), (147),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (148), (157), (165), (171), (172), (173), (175),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (177), (178), (179), (180), (181), (182), (184),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (190), (197), (201), (202), (203), (204), (208),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (214), (216), (218), (220), (222), (224), (235),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (240), (244), (245), (246), (247), (248) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (249) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (250) all_252_22 = e2 & op(e0, e2) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (65), (232), (250) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | sub-proof #979.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (251) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (147), (200), (231), (251) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (252) ~ (all_90_1 = e1) & op(e3, e2) = all_90_1 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | $i(all_90_1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (253) ~ (all_90_1 = e1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (254) op(e3, e2) = all_90_1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (255) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (256) all_252_20 = e2 & op(e0, e4) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (256) are inconsistent by sub-proof
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | #560.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (257) all_252_21 = e2 & op(e0, e3) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (258) all_252_21 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_10_2, e0, e3, e2,
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (40), (238) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (259) all_10_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_8_2, all_90_1, e2, e3,
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (167), (254) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (260) all_90_1 = all_8_2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (259) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (261) all_138_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (259) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (262) ~ (all_244_8 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11), (13), (18), (19), (24), (27),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (35), (37), (38), (39), (40), (41), (46), (47),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (48), (49), (55), (57), (58), (62), (64), (65),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (66), (70), (72), (78), (79), (82), (84), (86),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (93), (96), (98), (100), (101), (103), (104),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (116), (125), (129), (134), (139), (143), (147),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (148), (157), (165), (171), (172), (173), (175),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (177), (178), (179), (180), (181), (182), (184),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (190), (197), (201), (202), (203), (204), (208),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (214), (216), (218), (220), (222), (224), (235),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (254), (258), (259), (260), (261), (262) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (263) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (264) all_252_22 = e2 & op(e0, e2) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (65), (232), (264) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | sub-proof #979.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (265) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (147), (200), (231), (265) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | (266) all_86_2 = e3
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (34), (39), (46), (74), (81), (97), (102),
% 250.98/59.72 | | | | | | | | | | | | | | | | | (104), (105), (135), (137), (148), (150), (160),
% 250.98/59.72 | | | | | | | | | | | | | | | | | (187), (193), (214), (266) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | sub-proof #876.
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | (267) all_80_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (267) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (268) all_6_2 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (20), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (269) ~ (all_244_8 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (44), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (270) ~ (all_30_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (30), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (271) ~ (all_28_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (164), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (272) ~ (all_4_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | (273) ~ (all_4_2 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (70), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (274) ~ (e1 = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (12), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (275) op(e0, e2) = e4
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | REDUCE: (58), (268) imply:
% 250.98/59.72 | | | | | | | | | | | | | | | | (276) op(e4, e2) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | (277) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (278) all_252_0 = e0 & op(e4, e4) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (279) all_252_0 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (148), (157),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (165), (167), (173), (177), (178), (184), (190),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (197), (279) are inconsistent by sub-proof #559.
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (280) all_252_1 = e0 & op(e4, e3) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (281) all_252_1 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | (282) op(e4, e3) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | (283) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (284) all_252_0 = e2 & op(e4, e4) = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | (285) all_252_0 = e2
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | (286) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | (287) all_252_1 = e4 & op(e4, e3) = e4
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (281), (287) are inconsistent by sub-proof
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | #898.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | (288) all_252_3 = e4 & op(e3, e3) = e4
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | (289) all_252_3 = e4
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | (290) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | (291) all_252_1 = e1 & op(e4, e3) = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (281), (291) are inconsistent by sub-proof
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | (292) all_252_3 = e1 & op(e3, e3) = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (289), (292) are inconsistent by sub-proof
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | #890.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | (293) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | (294) all_252_7 = e1 & op(e2, e3) = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | (295) op(e2, e3) = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (40), (218), (295) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #948.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_252_13 = e1 & op(e1, e3) = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_252_13 = e1
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (299) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (84), (141), (183), (281), (299) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #511.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (300) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_252_4 = e3 & op(e4, e2) = e3
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_252_4 = e3
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) op(e4, e2) = e3
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (304) are
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #497.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_252_8 = e0 & op(e2, e2) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) op(e2, e2) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (46), (269), (307) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_252_14 = e0 & op(e1, e2) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (154), (273), (309) are inconsistent by
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #855.
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_252_22 = e0 & op(e0, e2) = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_252_22 = e0
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_252_20 = e4 & op(e0, e4) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (197), (313) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_252_21 = e4 & op(e0, e3) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (125), (214), (314) are inconsistent by
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_252_22 = e4 & op(e0, e2) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_252_22 = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (311), (317) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #528.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_252_23 = e4 & op(e0, e1) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (319) are inconsistent by
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_252_24 = e4 & op(e0, e0) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_252_24 = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_252_1 = e3 & op(e4, e3) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_252_1 = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (324) imply:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) e3 = e0
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) e3 = e0
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (326) imply:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_4 = e0
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (327) are
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_252_3 = e3 & op(e3, e3) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (289), (328) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_252_7 = e3 & op(e2, e3) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_252_7 = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_252_20 = e2 & op(e0, e4) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (333) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_252_21 = e2 & op(e0, e3) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) all_252_21 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (39), (159), (165), (282), (289), (336) are
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_252_7 = e2 & op(e2, e3) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_252_7 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (339) imply:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) e3 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (340) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) e3 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (341) imply:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_252_20 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (33), (35), (39), (41), (43), (62),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (79), (84), (96), (103), (104),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (143), (147), (165), (175), (180), (214),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335), (342) are inconsistent by sub-proof #524.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) all_252_13 = e2 & op(e1, e3) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) op(e1, e3) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (82), (216), (345) are inconsistent by
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #972.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (276), (302),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) are inconsistent by sub-proof #494.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_252_22 = e2 & op(e0, e2) = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_252_22 = e2
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (348) imply:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) e2 = e0
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (148), (157),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (173), (177), (178), (184), (190),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (285), (349) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #493.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (165), (200), (321), (350) are
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #491.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_252_13 = e3 & op(e1, e3) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (298), (352) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #944.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_252_21 = e3 & op(e0, e3) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (39), (125), (353) are inconsistent by
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #959.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_252_9 = e3 & op(e4, e1) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) op(e4, e1) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (131), (152), (356) are inconsistent by
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_252_16 = e3 & op(e4, e0) = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_252_16 = e3
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (359) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_252_0 = e4 & op(e4, e4) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (285), (360) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #606.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_252_1 = e4 & op(e4, e3) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (281), (361) are inconsistent by sub-proof
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #898.
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 &
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_252_4 = e4 & op(e4, e2) = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_252_4 = e4
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 250.98/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (365) are
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #497.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_252_8 = e0 & op(e2, e2) = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) op(e2, e2) = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (46), (269), (368) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (154), (273), (370) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #855.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_252_22 = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (197), (374) are inconsistent by sub-proof
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (125), (214), (375) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_252_22 = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (378) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) e4 = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (379) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) e4 = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (380) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_252_4 = e0
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (381) are
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (383) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (384) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_252_24 = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (38), (39), (66), (289), (386) are
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_252_5 = e1 & op(e3, e2) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) op(e3, e2) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (101), (167), (389) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_252_10 = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (285), (394) are inconsistent by sub-proof
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #558.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) all_252_1 = e1 & op(e4, e3) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (281), (395) are inconsistent by sub-proof
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (396) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) all_252_4 = e1 & op(e4, e2) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (397) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) op(e4, e2) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (58), (70), (398) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #930.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_252_9 = e1 & op(e4, e1) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_252_9 = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) op(e4, e1) = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (403) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_252_9 = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (405) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) e4 = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (406) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) $false
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (407) is inconsistent.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (202), (408) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_252_11 = e4 & op(e2, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) op(e2, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (203), (411) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #935.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_252_15 = e4 & op(e1, e1) = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_252_15 = e4
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_252_20 = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (417) are inconsistent by sub-proof
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_252_21 = e2 & op(e0, e3) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_252_21 = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_252_9 = e3 & op(e4, e1) = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (96), (402), (421) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_252_10 = e3 & op(e3, e1) = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_252_10 = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (423) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) e3 = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (358), (424) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_252_16 = e1
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (84), (141), (183), (281), (426) are
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #511.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_252_4 = e3 & op(e4, e2) = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_252_4 = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (428) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) e4 = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (429) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) $false
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_252_9 = e3 & op(e4, e1) = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (96), (402), (431) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (357), (425) are inconsistent by sub-proof
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #488.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_252_11 = e3 & op(e2, e1) = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_252_11 = e3
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_252_9 = e2 & op(e4, e1) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) op(e4, e1) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (62), (402), (437) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #785.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_252_10 = e2 & op(e3, e1) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) op(e3, e1) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (208), (439) are inconsistent by
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_252_11 = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (434), (442) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) e3 = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (443) imply:
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_252_20 = e2
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (33), (35), (39), (41), (43), (62),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (79), (84), (96), (103), (104),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (143), (147), (165), (175), (180), (214),
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419), (444) are inconsistent by sub-proof #524.
% 251.13/59.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (445) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (414), (446) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #487.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) op(e0, e1) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (200), (448) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #985.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (414), (450) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #486.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_252_23 = e3 & op(e0, e1) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) op(e0, e1) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (180), (452) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (148), (157),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (173), (177), (178), (184), (190),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (285), (372), (454) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #485.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (165), (200), (385), (455) are
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #491.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (456) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_252_16 = e1 & op(e4, e0) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (358), (457) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) op(e3, e0) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (148), (209), (459) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (461) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_252_9 = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (285), (464) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #558.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_252_1 = e1 & op(e4, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (281), (465) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_252_4 = e1 & op(e4, e2) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (467) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) op(e4, e2) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (58), (70), (468) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #930.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (469) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_252_9 = e1 & op(e4, e1) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (462), (470) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #923.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_252_16 = e1 & op(e4, e0) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (358), (471) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_252_16 = e4 & op(e4, e0) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (358), (472) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #483.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | (474) op(e0, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (104), (125), (474) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #714.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | (475) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (40), (82), (125), (212), (214), (475)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #771.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | (476) all_252_1 = e2 & op(e4, e3) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | (477) op(e4, e3) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (39), (159), (282), (477) are inconsistent
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | by sub-proof #850.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | (478) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | (479) all_252_4 = e2 & op(e4, e2) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | (480) all_252_4 = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | (481) op(e4, e2) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | (482) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (482) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | (483) all_252_1 = e4 & op(e4, e3) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (281), (483) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | #898.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | (484) all_252_3 = e4 & op(e3, e3) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | (485) all_252_3 = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | (486) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (487) all_252_1 = e1 & op(e4, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (281), (487) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (488) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (489) all_252_3 = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (485), (489) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | #772.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | (490) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (491) all_252_7 = e1 & op(e2, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (492) op(e2, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (40), (218), (492) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #948.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | (493) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_252_13 = e1 & op(e1, e3) = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_252_13 = e1
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (496) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (496) are
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #497.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (497) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (497) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_252_8 = e0 & op(e2, e2) = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (498) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) op(e2, e2) = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (46), (269), (499) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (154), (273), (501) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #855.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_252_22 = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (504) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (197), (505) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (125), (214), (506) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_252_22 = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (503), (509) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #528.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (510) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (511) are inconsistent by
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (512) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_252_24 = e4
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_252_1 = e3 & op(e4, e3) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (281), (515) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #840.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_252_3 = e3 & op(e3, e3) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (485), (516) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #482.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (517) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_252_7 = e3 & op(e2, e3) = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (518) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_252_7 = e3
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (520) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (521) are inconsistent by sub-proof
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_252_21 = e2 & op(e0, e3) = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (522) implies:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_252_21 = e2
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with e0, e2, e2, e4,
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (276), (481) gives:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) e2 = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (525) imply:
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) all_252_4 = e0
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (526) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) all_252_3 = e0 & op(e3, e3) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) op(e3, e3) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (178), (184), (528) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #973.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) all_252_7 = e0 & op(e2, e3) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (519), (530) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #887.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_252_13 = e0 & op(e1, e3) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_252_13 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (495), (533) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #943.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_252_21 = e0 & op(e0, e3) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_252_21 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (523), (535) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) e2 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (536) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_252_4 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (537) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_252_22 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (503), (540) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) e2 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (541) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) e2 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (542) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_252_4 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (543) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (165), (200), (513), (544) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #491.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_252_13 = e3 & op(e1, e3) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (495), (546) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #944.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_252_21 = e3 & op(e0, e3) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (39), (125), (547) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #959.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | (549) op(e0, e3) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (104), (125), (549) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #714.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (550) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (40), (82), (125), (212), (214), (550)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #771.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | (551) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (94), (131), (206), (551) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | (552) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | op(e4, e0) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | BETA: splitting (552) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (553) all_252_4 = e0 & op(e4, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (554) all_252_4 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (554) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | (555) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | e0 & op(e4, e0) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | (556) all_252_9 = e0 & op(e4, e1) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | (557) all_252_9 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | (558) op(e4, e1) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | (559) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (560) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (557), (560) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | #481.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (561) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (202), (561) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | (562) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (563) all_252_11 = e4 & op(e2, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (564) op(e2, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (203), (564) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | sub-proof #935.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | (565) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | (566) all_252_15 = e4 & op(e1, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | (567) all_252_15 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | (568) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (39), (98), (208), (558), (568) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #580.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | (569) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | (570) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | (571) all_252_11 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | (572) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (78), (82), (100), (216), (572) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | (573) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (573) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_252_14 = e2 & op(e1, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (574) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_252_14 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_252_9 = e3 & op(e4, e1) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) op(e4, e1) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (131), (152), (578) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_252_10 = e3 & op(e3, e1) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (579) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_252_10 = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) op(e3, e1) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (58), (70), (101), (167), (582) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #928.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_252_8 = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) op(e3, e4) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (38), (39), (588) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #607.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_252_3 = e1
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (591) are
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #497.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (592) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_252_8 = e0 & op(e2, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (593) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) op(e2, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (46), (269), (594) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (154), (273), (596) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #855.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) all_252_22 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) op(e0, e2) = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (601) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) all_252_6 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (604) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_252_0 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (606) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (197), (607) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #553.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (125), (214), (608) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (609) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (598), (610) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #480.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (612) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (613) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_252_24 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_252_4 = e3 & op(e4, e2) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_252_4 = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) op(e4, e2) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (619) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_252_20 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (621) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_252_21 = e2 & op(e0, e3) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_252_21 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_252_4 = e4 & op(e4, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_252_4 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (617), (626) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #479.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_252_5 = e4 & op(e3, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_252_5 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_252_4 = e2 & op(e4, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (630) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_252_4 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (617), (631) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) e3 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (632) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_252_20 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (33), (35), (39), (41), (43), (62),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (79), (84), (96), (103), (104),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (143), (147), (165), (175), (180), (214),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623), (633) are inconsistent by sub-proof #524.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_252_5 = e2 & op(e3, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_252_5 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (628), (635) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) all_252_8 = e2 & op(e2, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (39), (41), (62), (78), (98), (100),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (139), (148), (157), (165), (167), (173),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (197), (585), (602), (605), (637)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #477.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (11), (13), (25), (31), (33), (35),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (40), (41), (48), (49), (55), (57),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (59), (62), (63), (65), (68), (70), (78),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (96), (98), (100), (101), (103),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (116), (125), (126), (129), (131), (139),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (146), (147), (148), (152), (154), (156), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (162), (165), (167), (169), (173), (178),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179), (182), (184), (185), (186), (189), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (201), (202), (203), (204), (208), (209),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (216), (220), (271), (275), (276), (617),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) are inconsistent by sub-proof #494.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_252_22 = e2
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (598), (640) imply:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) e2 = e0
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (148), (157),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (173), (177), (178), (184), (190),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (605), (641) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #493.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (643) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_252_8 = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (58), (62), (65), (66), (70), (101),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (220), (575), (644) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (645) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_252_14 = e4 & op(e1, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) op(e1, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (154), (647) are inconsistent by
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (598), (648) are inconsistent by sub-proof
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #480.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (147), (148),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (165), (167), (173), (177), (178), (184),
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (197), (200), (598), (605), (614), (649)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #475.
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_252_5 = e3 & op(e3, e2) = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_252_5 = e3
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.13/59.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (39), (43), (66), (98), (116), (139), (148),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (178), (184), (590), (652) are
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #503.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) all_252_5 = e4 & op(e3, e2) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (651), (654) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #680.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (655) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) op(e3, e1) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (143), (581), (657) are inconsistent
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #614.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_252_17 = e4 & op(e3, e0) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (658) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_252_17 = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_252_20 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (662) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_252_21 = e2 & op(e0, e3) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (663) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_252_21 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (665) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_252_2 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (39), (98), (116), (139), (148),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (178), (184), (667) are inconsistent
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #571.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_252_3 = e2 & op(e3, e3) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (668) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_252_3 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (590), (669) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) e2 = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (670) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) e2 = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (605), (671) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_252_0 = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (39), (41), (62), (78), (98), (100),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (139), (148), (157), (165), (167), (173),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178), (184), (197), (602), (672) are inconsistent
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #518.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (673) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_252_5 = e2 & op(e3, e2) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_252_5 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (651), (675) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) e3 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (676) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_252_20 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (33), (35), (39), (41), (43), (62),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (79), (84), (96), (103), (104),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (143), (147), (165), (175), (180), (214),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664), (677) are inconsistent by sub-proof #524.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_252_10 = e2 & op(e3, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (679) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) op(e3, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (98), (208), (680) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_252_17 = e2 & op(e3, e0) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (681) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_252_17 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (659), (682) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) e4 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (683) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) e4 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (684) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) $false
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (685) is inconsistent.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (39), (41), (43), (62), (66),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (116), (139), (143), (147), (148),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (165), (167), (173), (177), (178), (184),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (197), (200), (598), (605), (614), (686)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #475.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (687) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_252_8 = e3 & op(e2, e2) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (585), (688) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #474.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_252_14 = e3 & op(e1, e2) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (154), (211), (690) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #858.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_252_22 = e3 & op(e0, e2) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (691) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) op(e0, e2) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (65), (84), (599), (692) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #473.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_252_2 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (39), (98), (116), (139), (148),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (178), (184), (694) are inconsistent
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #571.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (695) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (696) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_252_6 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (602), (697) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #833.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (698) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (78), (100), (699) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #926.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (197), (700) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (701) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) op(e2, e3) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (40), (702) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (703) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (704) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_252_8 = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (49), (58), (62), (65), (66), (70), (101),
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (220), (575), (705) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (179), (203), (204), (706) are
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #933.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (707) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) all_252_5 = e1 & op(e3, e2) = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (708) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) op(e3, e2) = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (101), (167), (709) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (580), (711) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #472.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (712) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) op(e3, e0) = e1
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (148), (209), (713) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (62), (65), (220), (575), (714) are
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #471.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_252_11 = e3 & op(e2, e1) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_252_11 = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (571), (717) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) e3 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (718) imply:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) $false
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (719) is inconsistent.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (720) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_252_15 = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (567), (722) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #675.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_252_23 = e3 & op(e0, e1) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) op(e0, e1) = e3
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (180), (724) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (725) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (725) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (567), (726) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | #487.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_252_19 = e2 & op(e1, e0) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (727) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) op(e1, e0) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (55), (201), (728) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #909.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | (729) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_252_15 = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (567), (731) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | #470.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (732) implies:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | (733) op(e0, e1) = e2
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (200), (733) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #985.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | (734) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (147), (175), (734) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | (735) all_252_16 = e0 & op(e4, e0) = e0
% 251.13/59.76 | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (270), (735) are inconsistent by
% 251.13/59.76 | | | | | | | | | | | | | | | | | | | sub-proof #469.
% 251.13/59.76 | | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | (736) all_82_2 = e1
% 251.13/59.76 | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | | REF_CLOSE: (2), (39), (76), (80), (128), (153), (175), (180),
% 251.13/59.76 | | | | | | | | | | | | | | | (196), (200), (736) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | | | | | | | | | | #779.
% 251.13/59.76 | | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | (737) all_78_2 = e1
% 251.13/59.76 | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | | REF_CLOSE: (39), (61), (82), (134), (216), (737) are
% 251.13/59.76 | | | | | | | | | | | | | | inconsistent by sub-proof #971.
% 251.13/59.76 | | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | (738) all_70_2 = e2
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | COMBINE_EQS: (95), (738) imply:
% 251.13/59.76 | | | | | | | | | | | | | (739) all_62_2 = e2
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | SIMP: (739) implies:
% 251.13/59.76 | | | | | | | | | | | | | (740) all_62_2 = e2
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | | REF_CLOSE: (34), (36), (39), (74), (97), (104), (135), (150),
% 251.13/59.76 | | | | | | | | | | | | | (214), (740) are inconsistent by sub-proof #852.
% 251.13/59.76 | | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | (741) all_68_2 = e4
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | COMBINE_EQS: (124), (741) imply:
% 251.13/59.76 | | | | | | | | | | | | (742) all_22_2 = e4
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | SIMP: (742) implies:
% 251.13/59.76 | | | | | | | | | | | | (743) all_22_2 = e4
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | REF_CLOSE: (34), (39), (42), (88), (108), (123), (159), (743)
% 251.13/59.76 | | | | | | | | | | | | are inconsistent by sub-proof #467.
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | (744) all_62_2 = e4
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | REDUCE: (136), (744) imply:
% 251.13/59.76 | | | | | | | | | | | (745) ~ (all_16_2 = e4)
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | SIMP: (745) implies:
% 251.13/59.76 | | | | | | | | | | | (746) ~ (all_16_2 = e4)
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | REF_CLOSE: (29), (39), (63), (100), (140), (181), (189),
% 251.13/59.76 | | | | | | | | | | | (194), (746) are inconsistent by sub-proof #466.
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | (747) all_50_2 = e3
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | COMBINE_EQS: (75), (747) imply:
% 251.13/59.76 | | | | | | | | | | (748) all_4_2 = e3
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | REDUCE: (9), (748) imply:
% 251.13/59.76 | | | | | | | | | | (749) op(e3, e2) = e1
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | REF_CLOSE: (39), (101), (167), (749) are inconsistent by
% 251.13/59.76 | | | | | | | | | | sub-proof #929.
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | (750) all_48_2 = e1
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | REDUCE: (91), (750) imply:
% 251.13/59.76 | | | | | | | | | (751) ~ (all_36_2 = e1)
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | SIMP: (751) implies:
% 251.13/59.76 | | | | | | | | | (752) ~ (all_36_2 = e1)
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | REF_CLOSE: (17), (26), (39), (106), (130), (139), (202),
% 251.13/59.76 | | | | | | | | | (208), (752) are inconsistent by sub-proof #658.
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | End of split
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | (753) all_46_2 = e2
% 251.13/59.76 | | | | | | | | (754) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.76 | | | | | | | | op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1))
% 251.13/59.76 | | | | | | | | | ( ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 &
% 251.13/59.76 | | | | | | | | $i(all_46_1))
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | COMBINE_EQS: (191), (753) imply:
% 251.13/59.76 | | | | | | | | (755) all_36_2 = e2
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | SIMP: (755) implies:
% 251.13/59.76 | | | | | | | | (756) all_36_2 = e2
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (174), (756) imply:
% 251.13/59.76 | | | | | | | | (757) ~ (all_244_15 = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (151), (756) imply:
% 251.13/59.76 | | | | | | | | (758) ~ (all_38_2 = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (115), (756) imply:
% 251.13/59.76 | | | | | | | | (759) ~ (all_26_2 = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (51), (756) imply:
% 251.13/59.76 | | | | | | | | (760) ~ (all_20_2 = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (26), (756) imply:
% 251.13/59.76 | | | | | | | | (761) op(all_62_2, e2) = e3
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (170), (756) imply:
% 251.13/59.76 | | | | | | | | (762) op(e2, e1) = e3
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REF_CLOSE: (32), (33), (38), (39), (41), (46), (48), (59), (62),
% 251.13/59.76 | | | | | | | | (71), (78), (82), (95), (100), (101), (112), (113),
% 251.13/59.76 | | | | | | | | (114), (121), (131), (142), (144), (147), (148),
% 251.13/59.76 | | | | | | | | (150), (154), (161), (167), (182), (184), (200),
% 251.13/59.76 | | | | | | | | (206), (754), (757), (758), (761), (762) are
% 251.13/59.76 | | | | | | | | inconsistent by sub-proof #460.
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | End of split
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | Case 2:
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | (763) all_44_2 = e2
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | REF_CLOSE: (39), (48), (63), (117), (203), (763) are inconsistent
% 251.13/59.76 | | | | | | | by sub-proof #732.
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | End of split
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | Case 2:
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | (764) all_40_2 = e4
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | REDUCE: (102), (764) imply:
% 251.13/59.76 | | | | | | (765) op(e4, e0) = e2
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | REF_CLOSE: (16), (39), (94), (765) are inconsistent by sub-proof
% 251.13/59.76 | | | | | | #830.
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | End of split
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | Case 2:
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | (766) all_38_2 = e4
% 251.13/59.76 | | | | | (767) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1,
% 251.13/59.76 | | | | | e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 251.13/59.76 | | | | | (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | REF_CLOSE: (11), (12), (27), (31), (39), (67), (78), (83), (98),
% 251.13/59.76 | | | | | (100), (107), (116), (127), (131), (133), (139), (141),
% 251.13/59.76 | | | | | (148), (152), (157), (162), (167), (173), (178), (184),
% 251.13/59.76 | | | | | (197), (766), (767) are inconsistent by sub-proof #456.
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | End of split
% 251.13/59.76 | | | |
% 251.13/59.76 | | | Case 2:
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | (768) all_36_2 = e4
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | REDUCE: (170), (768) imply:
% 251.13/59.76 | | | | (769) op(e4, e1) = e3
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | REF_CLOSE: (39), (131), (152), (769) are inconsistent by sub-proof #834.
% 251.13/59.76 | | | |
% 251.13/59.76 | | | End of split
% 251.13/59.76 | | |
% 251.13/59.76 | | Case 2:
% 251.13/59.76 | | |
% 251.13/59.76 | | | (770) all_34_2 = e2
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (119), (770) imply:
% 251.13/59.76 | | | (771) ~ (all_244_15 = e2)
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (111), (770) imply:
% 251.13/59.76 | | | (772) ~ (all_40_2 = e2)
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (168), (770) imply:
% 251.13/59.76 | | | (773) ~ (all_16_2 = e2)
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (76), (770) imply:
% 251.13/59.76 | | | (774) op(e2, e0) = e1
% 251.13/59.76 | | |
% 251.13/59.76 | | | GROUND_INST: instantiating (39) with all_40_2, e1, e0, e2, simplifying
% 251.13/59.76 | | | with (179), (774) gives:
% 251.13/59.76 | | | (775) all_40_2 = e1
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (53), (775) imply:
% 251.13/59.76 | | | (776) ~ (all_64_2 = e1)
% 251.13/59.76 | | |
% 251.13/59.76 | | | REDUCE: (772), (775) imply:
% 251.13/59.76 | | | (777) ~ (e2 = e1)
% 251.13/59.76 | | |
% 251.13/59.76 | | | BETA: splitting (50) gives:
% 251.13/59.76 | | |
% 251.13/59.76 | | | Case 1:
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | (778) ~ (all_38_2 = e4)
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | BETA: splitting (110) gives:
% 251.13/59.76 | | | |
% 251.13/59.76 | | | | Case 1:
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | (779) ~ (all_46_2 = e2)
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | REDUCE: (191), (779) imply:
% 251.13/59.76 | | | | | (780) ~ (all_36_2 = e2)
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | BETA: splitting (21) gives:
% 251.13/59.76 | | | | |
% 251.13/59.76 | | | | | Case 1:
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | (781) ~ (all_44_2 = e2)
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | REDUCE: (117), (781) imply:
% 251.13/59.76 | | | | | | (782) ~ (all_26_2 = e2)
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | BETA: splitting (142) gives:
% 251.13/59.76 | | | | | |
% 251.13/59.76 | | | | | | Case 1:
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | (783) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 &
% 251.13/59.76 | | | | | | | op(e3, e1) = e2)
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | REF_CLOSE: (39), (98), (131), (780), (782), (783) are inconsistent
% 251.13/59.76 | | | | | | | by sub-proof #969.
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | Case 2:
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | (784) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 &
% 251.13/59.76 | | | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | BETA: splitting (784) gives:
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | (785) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | ALPHA: (785) implies:
% 251.13/59.76 | | | | | | | | (786) op(e2, e1) = e2
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | GROUND_INST: instantiating (39) with all_38_2, e2, e1, e2,
% 251.13/59.76 | | | | | | | | simplifying with (48), (786) gives:
% 251.13/59.76 | | | | | | | | (787) all_38_2 = e2
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REDUCE: (133), (787) imply:
% 251.13/59.76 | | | | | | | | (788) ~ (all_64_2 = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | BETA: splitting (87) gives:
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | (789) all_250_10 = e4
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | COMBINE_EQS: (120), (789) imply:
% 251.13/59.76 | | | | | | | | | (790) all_64_2 = e4
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | REDUCE: (169), (790) imply:
% 251.13/59.76 | | | | | | | | | (791) ~ (all_16_2 = e4)
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | SIMP: (791) implies:
% 251.13/59.76 | | | | | | | | | (792) ~ (all_16_2 = e4)
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | REF_CLOSE: (29), (39), (63), (100), (140), (181), (189),
% 251.13/59.76 | | | | | | | | | (194), (792) are inconsistent by sub-proof #466.
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | (793) all_250_10 = e3 | all_250_10 = e2 | all_250_10 = e1 |
% 251.13/59.76 | | | | | | | | | all_250_10 = e0
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | BETA: splitting (793) gives:
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | (794) all_250_10 = e3
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | COMBINE_EQS: (120), (794) imply:
% 251.13/59.76 | | | | | | | | | | (795) all_64_2 = e3
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | REDUCE: (28), (795) imply:
% 251.13/59.76 | | | | | | | | | | (796) $false
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | CLOSE: (796) is inconsistent.
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | (797) all_250_10 = e2 | all_250_10 = e1 | all_250_10 = e0
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | BETA: splitting (797) gives:
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | (798) all_250_10 = e2
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | COMBINE_EQS: (120), (798) imply:
% 251.13/59.76 | | | | | | | | | | | (799) all_64_2 = e2
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | REDUCE: (788), (799) imply:
% 251.13/59.76 | | | | | | | | | | | (800) $false
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | CLOSE: (800) is inconsistent.
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | (801) all_250_10 = e1 | all_250_10 = e0
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | BETA: splitting (801) gives:
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | Case 1:
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | (802) all_250_10 = e1
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | COMBINE_EQS: (120), (802) imply:
% 251.13/59.76 | | | | | | | | | | | | (803) all_64_2 = e1
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | REDUCE: (776), (803) imply:
% 251.13/59.76 | | | | | | | | | | | | (804) $false
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | CLOSE: (804) is inconsistent.
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | (805) all_250_10 = e0
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | COMBINE_EQS: (120), (805) imply:
% 251.13/59.76 | | | | | | | | | | | | (806) all_64_2 = e0
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | REDUCE: (145), (806) imply:
% 251.13/59.76 | | | | | | | | | | | | (807) $false
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | | CLOSE: (807) is inconsistent.
% 251.13/59.76 | | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | | |
% 251.13/59.76 | | | | | | | | | End of split
% 251.13/59.76 | | | | | | | | |
% 251.13/59.76 | | | | | | | | End of split
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | Case 2:
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | (808) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2
% 251.13/59.76 | | | | | | | | & op(e0, e1) = e2)
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | | REF_CLOSE: (39), (144), (147), (200), (771), (808) are
% 251.13/59.76 | | | | | | | | inconsistent by sub-proof #965.
% 251.13/59.76 | | | | | | | |
% 251.13/59.76 | | | | | | | End of split
% 251.13/59.76 | | | | | | |
% 251.13/59.76 | | | | | | End of split
% 251.13/59.76 | | | | | |
% 251.13/59.77 | | | | | Case 2:
% 251.13/59.77 | | | | | |
% 251.13/59.77 | | | | | | (809) all_44_2 = e2
% 251.13/59.77 | | | | | |
% 251.13/59.77 | | | | | | REF_CLOSE: (39), (48), (63), (117), (778), (809) are inconsistent by
% 251.13/59.77 | | | | | | sub-proof #732.
% 251.13/59.77 | | | | | |
% 251.13/59.77 | | | | | End of split
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | Case 2:
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | (810) all_46_2 = e2
% 251.13/59.77 | | | | | (811) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1,
% 251.13/59.77 | | | | | e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 251.13/59.77 | | | | | (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | COMBINE_EQS: (191), (810) imply:
% 251.13/59.77 | | | | | (812) all_36_2 = e2
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | SIMP: (812) implies:
% 251.13/59.77 | | | | | (813) all_36_2 = e2
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REDUCE: (151), (813) imply:
% 251.13/59.77 | | | | | (814) ~ (all_38_2 = e2)
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REDUCE: (115), (813) imply:
% 251.13/59.77 | | | | | (815) ~ (all_26_2 = e2)
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | SIMP: (815) implies:
% 251.13/59.77 | | | | | (816) ~ (all_26_2 = e2)
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REDUCE: (51), (813) imply:
% 251.13/59.77 | | | | | (817) ~ (all_20_2 = e2)
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REDUCE: (26), (813) imply:
% 251.13/59.77 | | | | | (818) op(all_62_2, e2) = e3
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REDUCE: (170), (813) imply:
% 251.13/59.77 | | | | | (819) op(e2, e1) = e3
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | | REF_CLOSE: (32), (33), (38), (39), (41), (46), (48), (59), (62), (71),
% 251.13/59.77 | | | | | (78), (82), (95), (100), (101), (112), (113), (114), (121),
% 251.13/59.77 | | | | | (131), (142), (144), (147), (148), (150), (154), (161),
% 251.13/59.77 | | | | | (167), (182), (184), (200), (771), (811), (814), (816),
% 251.13/59.77 | | | | | (818), (819) are inconsistent by sub-proof #460.
% 251.13/59.77 | | | | |
% 251.13/59.77 | | | | End of split
% 251.13/59.77 | | | |
% 251.13/59.77 | | | Case 2:
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | (820) all_38_2 = e4
% 251.13/59.77 | | | | (821) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1, e4)
% 251.13/59.77 | | | | = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.77 | | | | e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | REF_CLOSE: (11), (12), (27), (31), (39), (67), (78), (83), (98), (100),
% 251.13/59.77 | | | | (107), (116), (127), (131), (133), (139), (141), (148),
% 251.13/59.77 | | | | (152), (157), (162), (167), (173), (178), (184), (197),
% 251.13/59.77 | | | | (820), (821) are inconsistent by sub-proof #456.
% 251.13/59.77 | | | |
% 251.13/59.77 | | | End of split
% 251.13/59.77 | | |
% 251.13/59.77 | | End of split
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (822) all_32_2 = e2
% 251.13/59.77 | |
% 251.13/59.77 | | COMBINE_EQS: (3), (822) imply:
% 251.13/59.77 | | (823) all_20_2 = e2
% 251.13/59.77 | |
% 251.13/59.77 | | REDUCE: (166), (823) imply:
% 251.13/59.77 | | (824) ~ (all_22_2 = e2)
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (34), (39), (42), (54), (74), (88), (97), (104), (108), (123),
% 251.13/59.77 | | (124), (135), (150), (159), (824) are inconsistent by sub-proof
% 251.13/59.77 | | #455.
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #455 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) ~ (all_22_2 = e2)
% 251.13/59.77 (2) ~ (all_22_2 = e3)
% 251.13/59.77 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (4) op(e0, e0) = all_244_24
% 251.13/59.77 (5) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.77 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.77 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.77 (6) all_250_21 = all_22_2
% 251.13/59.77 (7) op(all_84_2, e0) = e3
% 251.13/59.77 (8) op(all_48_2, all_22_2) = e0
% 251.13/59.77 (9) ~ (all_22_2 = e1)
% 251.13/59.77 (10) op(e0, all_84_2) = e4
% 251.13/59.77 (11) op(all_22_2, e3) = e0
% 251.13/59.77 (12) all_68_2 = all_22_2
% 251.13/59.77 (13) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.77 all_250_21 = e0
% 251.13/59.77 (14) op(all_48_2, e0) = e3
% 251.13/59.77 (15) op(e4, e3) = all_84_2
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (5) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (16) ~ (all_68_2 = e4)
% 251.13/59.77 | |
% 251.13/59.77 | | REDUCE: (12), (16) imply:
% 251.13/59.77 | | (17) ~ (all_22_2 = e4)
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (13), (14), (17) are inconsistent
% 251.13/59.77 | | by sub-proof #957.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (18) all_68_2 = e4
% 251.13/59.77 | |
% 251.13/59.77 | | COMBINE_EQS: (12), (18) imply:
% 251.13/59.77 | | (19) all_22_2 = e4
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (2), (3), (4), (7), (10), (11), (15), (19) are inconsistent by
% 251.13/59.77 | | sub-proof #467.
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #456 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.77 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.77 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.77 (2) op(all_6_2, e2) = e4
% 251.13/59.77 (3) op(all_38_2, e1) = e2
% 251.13/59.77 (4) ~ (e2 = e0)
% 251.13/59.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (6) op(all_6_2, all_64_2) = e2
% 251.13/59.77 (7) ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1, e4) = all_38_1
% 251.13/59.77 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e4) =
% 251.13/59.77 all_38_1 & $i(all_38_1))
% 251.13/59.77 (8) op(e1, e4) = all_16_2
% 251.13/59.77 (9) ~ (all_244_0 = all_26_2)
% 251.13/59.77 (10) op(e3, e1) = all_36_2
% 251.13/59.77 (11) ~ (all_16_2 = e2)
% 251.13/59.77 (12) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 251.13/59.77 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 251.13/59.77 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 251.13/59.77 (13) ~ (all_8_2 = e0)
% 251.13/59.77 (14) all_38_2 = e4
% 251.13/59.77 (15) all_242_2 = all_38_2
% 251.13/59.77 (16) op(e4, e1) = all_26_2
% 251.13/59.77 (17) ~ (all_64_2 = all_38_2)
% 251.13/59.77 (18) ~ (all_36_2 = e0)
% 251.13/59.77 (19) op(e4, e4) = all_244_0
% 251.13/59.77 (20) op(e3, e0) = all_48_2
% 251.13/59.77 (21) ~ (all_26_2 = e3)
% 251.13/59.77 (22) ~ (all_48_2 = e0)
% 251.13/59.77 (23) op(e2, e4) = all_64_2
% 251.13/59.77 (24) op(e3, e2) = all_8_2
% 251.13/59.77 (25) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.77 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.77 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.77 (26) ~ (all_244_3 = e0)
% 251.13/59.77 (27) op(e3, e3) = all_244_3
% 251.13/59.77 (28) all_252_20 = e3
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | COMBINE_EQS: (14), (15) imply:
% 251.13/59.77 | (29) all_242_2 = e4
% 251.13/59.77 |
% 251.13/59.77 | REDUCE: (14), (17) imply:
% 251.13/59.77 | (30) ~ (all_64_2 = e4)
% 251.13/59.77 |
% 251.13/59.77 | REDUCE: (3), (14) imply:
% 251.13/59.77 | (31) op(e4, e1) = e2
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (7) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (32) ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 & op(e1, e4) =
% 251.13/59.77 | | all_38_1 & $i(all_38_0) & $i(all_38_1)
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (32) implies:
% 251.13/59.77 | | (33) op(e1, e4) = all_38_1
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 251.13/59.77 | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 251.13/59.77 | | (29), (30), (31), (33) are inconsistent by sub-proof #457.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (34) ~ (all_38_1 = e3) & op(e1, e4) = all_38_1 & $i(all_38_1)
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (34) implies:
% 251.13/59.77 | | (35) op(e1, e4) = all_38_1
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 251.13/59.77 | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 251.13/59.77 | | (29), (30), (31), (35) are inconsistent by sub-proof #457.
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #457 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) all_242_2 = e4
% 251.13/59.77 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.77 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.77 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.77 (3) op(all_6_2, e2) = e4
% 251.13/59.77 (4) ~ (e2 = e0)
% 251.13/59.77 (5) op(e4, e1) = e2
% 251.13/59.77 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (7) op(all_6_2, all_64_2) = e2
% 251.13/59.77 (8) op(e1, e4) = all_16_2
% 251.13/59.77 (9) ~ (all_244_0 = all_26_2)
% 251.13/59.77 (10) op(e3, e1) = all_36_2
% 251.13/59.77 (11) ~ (all_16_2 = e2)
% 251.13/59.77 (12) ~ (all_242_2 = e4) | ( ~ (all_242_0 = e3) & op(e4, all_242_1) =
% 251.13/59.77 all_242_0 & op(e1, e4) = all_242_1 & $i(all_242_0) & $i(all_242_1)) |
% 251.13/59.77 ( ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1))
% 251.13/59.77 (13) ~ (all_8_2 = e0)
% 251.13/59.77 (14) op(e1, e4) = all_38_1
% 251.13/59.77 (15) op(e4, e1) = all_26_2
% 251.13/59.77 (16) ~ (all_36_2 = e0)
% 251.13/59.77 (17) op(e4, e4) = all_244_0
% 251.13/59.77 (18) op(e3, e0) = all_48_2
% 251.13/59.77 (19) ~ (all_26_2 = e3)
% 251.13/59.77 (20) ~ (all_48_2 = e0)
% 251.13/59.77 (21) op(e2, e4) = all_64_2
% 251.13/59.77 (22) op(e3, e2) = all_8_2
% 251.13/59.77 (23) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.77 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.77 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.77 (24) ~ (all_244_3 = e0)
% 251.13/59.77 (25) op(e3, e3) = all_244_3
% 251.13/59.77 (26) ~ (all_64_2 = e4)
% 251.13/59.77 (27) all_252_20 = e3
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (12) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (28) ~ (all_242_2 = e4)
% 251.13/59.77 | |
% 251.13/59.77 | | REDUCE: (1), (28) imply:
% 251.13/59.77 | | (29) $false
% 251.13/59.77 | |
% 251.13/59.77 | | CLOSE: (29) is inconsistent.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (30) ( ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 251.13/59.77 | | all_242_1 & $i(all_242_0) & $i(all_242_1)) | ( ~ (all_242_1 = e0)
% 251.13/59.77 | | & op(e1, e4) = all_242_1 & $i(all_242_1))
% 251.13/59.77 | |
% 251.13/59.77 | | GROUND_INST: instantiating (6) with all_16_2, all_38_1, e4, e1, simplifying
% 251.13/59.77 | | with (8), (14) gives:
% 251.13/59.77 | | (31) all_38_1 = all_16_2
% 251.13/59.77 | |
% 251.13/59.77 | | GROUND_INST: instantiating (6) with all_26_2, e2, e1, e4, simplifying with
% 251.13/59.77 | | (5), (15) gives:
% 251.13/59.77 | | (32) all_26_2 = e2
% 251.13/59.77 | |
% 251.13/59.77 | | REDUCE: (9), (32) imply:
% 251.13/59.77 | | (33) ~ (all_244_0 = e2)
% 251.13/59.77 | |
% 251.13/59.77 | | REDUCE: (19), (32) imply:
% 251.13/59.77 | | (34) ~ (e3 = e2)
% 251.13/59.77 | |
% 251.13/59.77 | | SIMP: (34) implies:
% 251.13/59.77 | | (35) ~ (e3 = e2)
% 251.13/59.77 | |
% 251.13/59.77 | | BETA: splitting (30) gives:
% 251.13/59.77 | |
% 251.13/59.77 | | Case 1:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (36) ~ (all_242_0 = e3) & op(e4, all_242_1) = all_242_0 & op(e1, e4) =
% 251.13/59.77 | | | all_242_1 & $i(all_242_0) & $i(all_242_1)
% 251.13/59.77 | | |
% 251.13/59.77 | | | ALPHA: (36) implies:
% 251.13/59.77 | | | (37) op(e1, e4) = all_242_1
% 251.13/59.77 | | |
% 251.13/59.77 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (13), (16), (17),
% 251.13/59.77 | | | (18), (20), (21), (22), (23), (24), (25), (26), (27), (33),
% 251.13/59.77 | | | (35), (37) are inconsistent by sub-proof #458.
% 251.13/59.77 | | |
% 251.13/59.77 | | Case 2:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (38) ~ (all_242_1 = e0) & op(e1, e4) = all_242_1 & $i(all_242_1)
% 251.13/59.77 | | |
% 251.13/59.77 | | | ALPHA: (38) implies:
% 251.13/59.77 | | | (39) op(e1, e4) = all_242_1
% 251.13/59.77 | | |
% 251.13/59.77 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (13), (16), (17),
% 251.13/59.77 | | | (18), (20), (21), (22), (23), (24), (25), (26), (27), (33),
% 251.13/59.77 | | | (35), (39) are inconsistent by sub-proof #458.
% 251.13/59.77 | | |
% 251.13/59.77 | | End of split
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #458 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.77 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.77 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.77 (2) op(all_6_2, e2) = e4
% 251.13/59.77 (3) ~ (e2 = e0)
% 251.13/59.77 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (5) ~ (e3 = e2)
% 251.13/59.77 (6) ~ (all_244_0 = e2)
% 251.13/59.77 (7) op(all_6_2, all_64_2) = e2
% 251.13/59.77 (8) op(e1, e4) = all_16_2
% 251.13/59.77 (9) op(e3, e1) = all_36_2
% 251.13/59.77 (10) ~ (all_16_2 = e2)
% 251.13/59.77 (11) ~ (all_8_2 = e0)
% 251.13/59.77 (12) op(e1, e4) = all_242_1
% 251.13/59.77 (13) ~ (all_36_2 = e0)
% 251.13/59.77 (14) op(e4, e4) = all_244_0
% 251.13/59.77 (15) op(e3, e0) = all_48_2
% 251.13/59.77 (16) ~ (all_48_2 = e0)
% 251.13/59.77 (17) op(e2, e4) = all_64_2
% 251.13/59.77 (18) op(e3, e2) = all_8_2
% 251.13/59.77 (19) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.77 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.77 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.77 (20) ~ (all_244_3 = e0)
% 251.13/59.77 (21) op(e3, e3) = all_244_3
% 251.13/59.77 (22) ~ (all_64_2 = e4)
% 251.13/59.77 (23) all_252_20 = e3
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (19) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (24) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.13/59.77 | | e2)
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (3), (4), (6), (9), (11), (13), (14), (15), (16), (18),
% 251.13/59.77 | | (20), (21), (24) are inconsistent by sub-proof #459.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (25) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.77 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.77 | |
% 251.13/59.77 | | BETA: splitting (25) gives:
% 251.13/59.77 | |
% 251.13/59.77 | | Case 1:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (26) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.77 | | |
% 251.13/59.77 | | | ALPHA: (26) implies:
% 251.13/59.77 | | | (27) op(e2, e4) = e2
% 251.13/59.77 | | |
% 251.13/59.77 | | | REF_CLOSE: (2), (4), (7), (17), (22), (27) are inconsistent by sub-proof
% 251.13/59.77 | | | #790.
% 251.13/59.77 | | |
% 251.13/59.77 | | Case 2:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 251.13/59.77 | | | e4) = e2)
% 251.13/59.77 | | |
% 251.13/59.77 | | | BETA: splitting (28) gives:
% 251.13/59.77 | | |
% 251.13/59.77 | | | Case 1:
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | (29) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | ALPHA: (29) implies:
% 251.13/59.77 | | | | (30) op(e1, e4) = e2
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | REF_CLOSE: (4), (8), (10), (12), (30) are inconsistent by sub-proof
% 251.13/59.77 | | | | #600.
% 251.13/59.77 | | | |
% 251.13/59.77 | | | Case 2:
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | (31) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | ALPHA: (31) implies:
% 251.13/59.77 | | | | (32) all_252_20 = e2
% 251.13/59.77 | | | |
% 251.13/59.77 | | | | REF_CLOSE: (5), (23), (32) are inconsistent by sub-proof #520.
% 251.13/59.77 | | | |
% 251.13/59.77 | | | End of split
% 251.13/59.77 | | |
% 251.13/59.77 | | End of split
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #459 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.77 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.77 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.77 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.77 (3) ~ (e2 = e0)
% 251.13/59.77 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (5) ~ (all_244_0 = e2)
% 251.13/59.77 (6) op(e3, e1) = all_36_2
% 251.13/59.77 (7) ~ (all_8_2 = e0)
% 251.13/59.77 (8) ~ (all_36_2 = e0)
% 251.13/59.77 (9) op(e4, e4) = all_244_0
% 251.13/59.77 (10) op(e3, e0) = all_48_2
% 251.13/59.77 (11) ~ (all_48_2 = e0)
% 251.13/59.77 (12) op(e3, e2) = all_8_2
% 251.13/59.77 (13) ~ (all_244_3 = e0)
% 251.13/59.77 (14) op(e3, e3) = all_244_3
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (1) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (15) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (15) implies:
% 251.13/59.77 | | (16) op(e4, e4) = e2
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (4), (5), (9), (16) are inconsistent by sub-proof #809.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (17) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (17) implies:
% 251.13/59.77 | | (18) all_252_2 = e2
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), (18)
% 251.13/59.77 | | are inconsistent by sub-proof #571.
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #460 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) ~ (all_26_2 = e2)
% 251.13/59.77 (2) op(all_38_2, all_4_2) = e1
% 251.13/59.77 (3) ~ (e1 = e0)
% 251.13/59.77 (4) op(e3, e4) = e0
% 251.13/59.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (6) ~ (e3 = e2)
% 251.13/59.77 (7) op(e2, e2) = all_244_8
% 251.13/59.77 (8) op(e2, e1) = all_38_2
% 251.13/59.77 (9) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 251.13/59.77 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 251.13/59.77 | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.77 (10) ~ (e2 = e1)
% 251.13/59.77 (11) op(all_62_2, e2) = e3
% 251.13/59.77 (12) ~ (all_244_8 = all_38_2)
% 251.13/59.77 (13) op(e1, e4) = all_16_2
% 251.13/59.77 (14) op(e1, e3) = all_62_2
% 251.13/59.77 (15) all_70_2 = all_62_2
% 251.13/59.77 (16) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.77 all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1,
% 251.13/59.77 e2) = all_46_1 & $i(all_46_1))
% 251.13/59.77 (17) op(e2, e1) = e3
% 251.13/59.77 (18) ~ (all_16_2 = e2)
% 251.13/59.77 (19) ~ (all_8_2 = e1)
% 251.13/59.77 (20) ~ (all_38_2 = e2)
% 251.13/59.77 (21) ~ (all_244_15 = all_38_2)
% 251.13/59.77 (22) ~ (all_48_2 = all_8_2)
% 251.13/59.77 (23) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.77 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.77 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.77 (24) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.13/59.77 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.13/59.77 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.13/59.77 (25) op(e4, e1) = all_26_2
% 251.13/59.77 (26) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.77 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.77 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.77 (27) op(e1, e1) = all_244_15
% 251.13/59.77 (28) op(e0, e1) = all_20_2
% 251.13/59.77 (29) op(e3, e0) = all_48_2
% 251.13/59.77 (30) op(all_48_2, e0) = e3
% 251.13/59.77 (31) op(e1, e2) = all_4_2
% 251.13/59.77 (32) op(all_244_3, all_244_3) = e3
% 251.13/59.77 (33) ~ (all_244_15 = e2)
% 251.13/59.77 (34) op(e3, e2) = all_8_2
% 251.13/59.77 (35) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.77 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.77 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.77 (36) op(e3, e3) = all_244_3
% 251.13/59.77 (37) ~ (all_20_2 = e2)
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (16) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (38) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.77 | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (38) implies:
% 251.13/59.77 | | (39) op(e1, e2) = all_46_1
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.77 | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.13/59.77 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 251.13/59.77 | | (36), (37), (39) are inconsistent by sub-proof #461.
% 251.13/59.77 | |
% 251.13/59.77 | Case 2:
% 251.13/59.77 | |
% 251.13/59.77 | | (40) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1)
% 251.13/59.77 | |
% 251.13/59.77 | | ALPHA: (40) implies:
% 251.13/59.77 | | (41) op(e1, e2) = all_46_1
% 251.13/59.77 | |
% 251.13/59.77 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.77 | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.13/59.77 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 251.13/59.77 | | (36), (37), (41) are inconsistent by sub-proof #461.
% 251.13/59.77 | |
% 251.13/59.77 | End of split
% 251.13/59.77 |
% 251.13/59.77 End of proof
% 251.13/59.77
% 251.13/59.77 Sub-proof #461 shows that the following formulas are inconsistent:
% 251.13/59.77 ----------------------------------------------------------------
% 251.13/59.77 (1) ~ (all_26_2 = e2)
% 251.13/59.77 (2) op(all_38_2, all_4_2) = e1
% 251.13/59.77 (3) ~ (e1 = e0)
% 251.13/59.77 (4) op(e3, e4) = e0
% 251.13/59.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.77 (6) ~ (e3 = e2)
% 251.13/59.77 (7) op(e2, e2) = all_244_8
% 251.13/59.77 (8) op(e2, e1) = all_38_2
% 251.13/59.77 (9) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 251.13/59.77 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 251.13/59.77 | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.77 (10) ~ (e2 = e1)
% 251.13/59.77 (11) op(all_62_2, e2) = e3
% 251.13/59.77 (12) ~ (all_244_8 = all_38_2)
% 251.13/59.77 (13) op(e1, e4) = all_16_2
% 251.13/59.77 (14) op(e1, e3) = all_62_2
% 251.13/59.77 (15) all_70_2 = all_62_2
% 251.13/59.77 (16) op(e2, e1) = e3
% 251.13/59.77 (17) ~ (all_16_2 = e2)
% 251.13/59.77 (18) ~ (all_8_2 = e1)
% 251.13/59.77 (19) ~ (all_38_2 = e2)
% 251.13/59.77 (20) ~ (all_244_15 = all_38_2)
% 251.13/59.77 (21) ~ (all_48_2 = all_8_2)
% 251.13/59.77 (22) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.77 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.77 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.77 (23) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.13/59.77 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.13/59.77 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.13/59.77 (24) op(e4, e1) = all_26_2
% 251.13/59.77 (25) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.77 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.77 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.77 (26) op(e1, e1) = all_244_15
% 251.13/59.77 (27) op(e0, e1) = all_20_2
% 251.13/59.77 (28) op(e3, e0) = all_48_2
% 251.13/59.77 (29) op(e1, e2) = all_46_1
% 251.13/59.77 (30) op(all_48_2, e0) = e3
% 251.13/59.77 (31) op(e1, e2) = all_4_2
% 251.13/59.77 (32) op(all_244_3, all_244_3) = e3
% 251.13/59.77 (33) ~ (all_244_15 = e2)
% 251.13/59.77 (34) op(e3, e2) = all_8_2
% 251.13/59.77 (35) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.77 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.77 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.77 (36) op(e3, e3) = all_244_3
% 251.13/59.77 (37) ~ (all_20_2 = e2)
% 251.13/59.77
% 251.13/59.77 Begin of proof
% 251.13/59.77 |
% 251.13/59.77 | BETA: splitting (25) gives:
% 251.13/59.77 |
% 251.13/59.77 | Case 1:
% 251.13/59.77 | |
% 251.13/59.77 | | (38) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.77 | | e2)
% 251.13/59.77 | |
% 251.13/59.77 | | BETA: splitting (38) gives:
% 251.13/59.77 | |
% 251.13/59.77 | | Case 1:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (39) all_252_9 = e2 & op(e4, e1) = e2
% 251.13/59.77 | | |
% 251.13/59.77 | | | REF_CLOSE: (1), (5), (24), (39) are inconsistent by sub-proof #970.
% 251.13/59.77 | | |
% 251.13/59.77 | | Case 2:
% 251.13/59.77 | | |
% 251.13/59.77 | | | (40) all_252_10 = e2 & op(e3, e1) = e2
% 251.13/59.77 | | |
% 251.13/59.77 | | | ALPHA: (40) implies:
% 251.13/59.77 | | | (41) all_252_10 = e2
% 251.13/59.77 | | |
% 251.13/59.78 | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 251.13/59.78 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.13/59.78 | | | (26), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 251.13/59.78 | | | (41) are inconsistent by sub-proof #463.
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (42) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.13/59.78 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.78 | |
% 251.13/59.78 | | BETA: splitting (42) gives:
% 251.13/59.78 | |
% 251.13/59.78 | | Case 1:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (43) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (5), (6), (8), (16), (43) are inconsistent by sub-proof #462.
% 251.13/59.78 | | |
% 251.13/59.78 | | Case 2:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (44) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.78 | | | e1) = e2)
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (5), (26), (27), (33), (37), (44) are inconsistent by sub-proof
% 251.13/59.78 | | | #965.
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #462 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (3) ~ (e3 = e2)
% 251.13/59.78 (4) op(e2, e1) = all_38_2
% 251.13/59.78 (5) op(e2, e1) = e3
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (6) op(e2, e1) = e2
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_38_2, e2, e1, e2, simplifying with
% 251.13/59.78 | (4), (6) gives:
% 251.13/59.78 | (7) all_38_2 = e2
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_38_2, e3, e1, e2, simplifying with
% 251.13/59.78 | (4), (5) gives:
% 251.13/59.78 | (8) all_38_2 = e3
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (7), (8) imply:
% 251.13/59.78 | (9) e3 = e2
% 251.13/59.78 |
% 251.13/59.78 | SIMP: (9) implies:
% 251.13/59.78 | (10) e3 = e2
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (10) imply:
% 251.13/59.78 | (11) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (11) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #463 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) op(all_38_2, all_4_2) = e1
% 251.13/59.78 (2) ~ (e1 = e0)
% 251.13/59.78 (3) op(e3, e4) = e0
% 251.13/59.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (5) op(e2, e2) = all_244_8
% 251.13/59.78 (6) op(e2, e1) = all_38_2
% 251.13/59.78 (7) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 251.13/59.78 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 251.13/59.78 | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.78 (8) ~ (e2 = e1)
% 251.13/59.78 (9) op(all_62_2, e2) = e3
% 251.13/59.78 (10) ~ (all_244_8 = all_38_2)
% 251.13/59.78 (11) op(e1, e4) = all_16_2
% 251.13/59.78 (12) op(e1, e3) = all_62_2
% 251.13/59.78 (13) all_70_2 = all_62_2
% 251.13/59.78 (14) op(e2, e1) = e3
% 251.13/59.78 (15) ~ (all_16_2 = e2)
% 251.13/59.78 (16) ~ (all_8_2 = e1)
% 251.13/59.78 (17) ~ (all_38_2 = e2)
% 251.13/59.78 (18) ~ (all_244_15 = all_38_2)
% 251.13/59.78 (19) ~ (all_48_2 = all_8_2)
% 251.13/59.78 (20) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.78 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.78 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.78 (21) all_252_10 = e2
% 251.13/59.78 (22) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.13/59.78 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.13/59.78 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.13/59.78 (23) op(e1, e1) = all_244_15
% 251.13/59.78 (24) op(e3, e0) = all_48_2
% 251.13/59.78 (25) op(e1, e2) = all_46_1
% 251.13/59.78 (26) op(all_48_2, e0) = e3
% 251.13/59.78 (27) op(e1, e2) = all_4_2
% 251.13/59.78 (28) op(all_244_3, all_244_3) = e3
% 251.13/59.78 (29) ~ (all_244_15 = e2)
% 251.13/59.78 (30) op(e3, e2) = all_8_2
% 251.13/59.78 (31) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.78 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.78 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.78 (32) op(e3, e3) = all_244_3
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (4) with all_4_2, all_46_1, e2, e1, simplifying
% 251.13/59.78 | with (25), (27) gives:
% 251.13/59.78 | (33) all_46_1 = all_4_2
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (4) with all_38_2, e3, e1, e2, simplifying with
% 251.13/59.78 | (6), (14) gives:
% 251.13/59.78 | (34) all_38_2 = e3
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (10), (34) imply:
% 251.13/59.78 | (35) ~ (all_244_8 = e3)
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (18), (34) imply:
% 251.13/59.78 | (36) ~ (all_244_15 = e3)
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (17), (34) imply:
% 251.13/59.78 | (37) ~ (e3 = e2)
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (1), (34) imply:
% 251.13/59.78 | (38) op(e3, all_4_2) = e1
% 251.13/59.78 |
% 251.13/59.78 | BETA: splitting (22) gives:
% 251.13/59.78 |
% 251.13/59.78 | Case 1:
% 251.13/59.78 | |
% 251.13/59.78 | | (39) ~ (all_48_2 = e1)
% 251.13/59.78 | |
% 251.13/59.78 | | BETA: splitting (7) gives:
% 251.13/59.78 | |
% 251.13/59.78 | | Case 1:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (40) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3)
% 251.13/59.78 | | | = e1)
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (2), (3), (4), (23), (28), (32), (36), (40) are inconsistent by
% 251.13/59.78 | | | sub-proof #465.
% 251.13/59.78 | | |
% 251.13/59.78 | | Case 2:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (41) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1)
% 251.13/59.78 | | | = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.78 | | |
% 251.13/59.78 | | | BETA: splitting (41) gives:
% 251.13/59.78 | | |
% 251.13/59.78 | | | Case 1:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | (42) all_252_5 = e1 & op(e3, e2) = e1
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | ALPHA: (42) implies:
% 251.13/59.78 | | | | (43) op(e3, e2) = e1
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | REF_CLOSE: (4), (16), (30), (43) are inconsistent by sub-proof #929.
% 251.13/59.78 | | | |
% 251.13/59.78 | | | Case 2:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | (44) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 251.13/59.78 | | | | e0) = e1)
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | BETA: splitting (44) gives:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | Case 1:
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | (45) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | REF_CLOSE: (8), (21), (45) are inconsistent by sub-proof #464.
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | Case 2:
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | (46) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | ALPHA: (46) implies:
% 251.13/59.78 | | | | | (47) op(e3, e0) = e1
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | REF_CLOSE: (4), (24), (39), (47) are inconsistent by sub-proof #889.
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | End of split
% 251.13/59.78 | | | |
% 251.13/59.78 | | | End of split
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (48) all_48_2 = e1
% 251.13/59.78 | |
% 251.13/59.78 | | REDUCE: (19), (48) imply:
% 251.13/59.78 | | (49) ~ (all_8_2 = e1)
% 251.13/59.78 | |
% 251.13/59.78 | | REDUCE: (26), (48) imply:
% 251.13/59.78 | | (50) op(e1, e0) = e3
% 251.13/59.78 | |
% 251.13/59.78 | | BETA: splitting (20) gives:
% 251.13/59.78 | |
% 251.13/59.78 | | Case 1:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (51) ~ (all_70_2 = e2)
% 251.13/59.78 | | |
% 251.13/59.78 | | | REDUCE: (13), (51) imply:
% 251.13/59.78 | | | (52) ~ (all_62_2 = e2)
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (4), (11), (12), (15), (16), (23), (27), (29), (30), (31),
% 251.13/59.78 | | | (37), (38), (50), (52) are inconsistent by sub-proof #735.
% 251.13/59.78 | | |
% 251.13/59.78 | | Case 2:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (53) all_70_2 = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | COMBINE_EQS: (13), (53) imply:
% 251.13/59.78 | | | (54) all_62_2 = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | SIMP: (54) implies:
% 251.13/59.78 | | | (55) all_62_2 = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | REDUCE: (9), (55) imply:
% 251.13/59.78 | | | (56) op(e2, e2) = e3
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (4), (5), (35), (56) are inconsistent by sub-proof #877.
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #464 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.78 (2) all_252_10 = e2
% 251.13/59.78 (3) ~ (e2 = e1)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (4) all_252_10 = e1
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.78 | (5) e2 = e1
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (5) imply:
% 251.13/59.78 | (6) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (6) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #465 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) ~ (e1 = e0)
% 251.13/59.78 (2) op(e3, e4) = e0
% 251.13/59.78 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (4) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.78 (5) ~ (all_244_15 = e3)
% 251.13/59.78 (6) op(e1, e1) = all_244_15
% 251.13/59.78 (7) op(all_244_3, all_244_3) = e3
% 251.13/59.78 (8) op(e3, e3) = all_244_3
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | BETA: splitting (4) gives:
% 251.13/59.78 |
% 251.13/59.78 | Case 1:
% 251.13/59.78 | |
% 251.13/59.78 | | (9) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | ALPHA: (9) implies:
% 251.13/59.78 | | (10) op(e3, e4) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #607.
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (11) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | REF_CLOSE: (3), (5), (6), (7), (8), (11) are inconsistent by sub-proof #632.
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #466 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 |
% 251.13/59.78 all_250_15 = e0
% 251.13/59.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (3) op(all_26_2, e1) = e4
% 251.13/59.78 (4) ~ (all_16_2 = e4)
% 251.13/59.78 (5) ~ (all_16_2 = e2)
% 251.13/59.78 (6) all_250_15 = all_16_2
% 251.13/59.78 (7) ~ (all_16_2 = e3)
% 251.13/59.78 (8) op(all_26_2, all_16_2) = e1
% 251.13/59.78 (9) ~ (all_16_2 = e0)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | BETA: splitting (1) gives:
% 251.13/59.78 |
% 251.13/59.78 | Case 1:
% 251.13/59.78 | |
% 251.13/59.78 | | (10) all_250_15 = e4
% 251.13/59.78 | |
% 251.13/59.78 | | COMBINE_EQS: (6), (10) imply:
% 251.13/59.78 | | (11) all_16_2 = e4
% 251.13/59.78 | |
% 251.13/59.78 | | REDUCE: (4), (11) imply:
% 251.13/59.78 | | (12) $false
% 251.13/59.78 | |
% 251.13/59.78 | | CLOSE: (12) is inconsistent.
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (13) ~ (all_250_15 = e4)
% 251.13/59.78 | | (14) all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 | all_250_15 =
% 251.13/59.78 | | e0
% 251.13/59.78 | |
% 251.13/59.78 | | BETA: splitting (14) gives:
% 251.13/59.78 | |
% 251.13/59.78 | | Case 1:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (15) all_250_15 = e3
% 251.13/59.78 | | |
% 251.13/59.78 | | | COMBINE_EQS: (6), (15) imply:
% 251.13/59.78 | | | (16) all_16_2 = e3
% 251.13/59.78 | | |
% 251.13/59.78 | | | REDUCE: (7), (16) imply:
% 251.13/59.78 | | | (17) $false
% 251.13/59.78 | | |
% 251.13/59.78 | | | CLOSE: (17) is inconsistent.
% 251.13/59.78 | | |
% 251.13/59.78 | | Case 2:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (18) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = e0
% 251.13/59.78 | | |
% 251.13/59.78 | | | BETA: splitting (18) gives:
% 251.13/59.78 | | |
% 251.13/59.78 | | | Case 1:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | (19) all_250_15 = e2
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | COMBINE_EQS: (6), (19) imply:
% 251.13/59.78 | | | | (20) all_16_2 = e2
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | REDUCE: (5), (20) imply:
% 251.13/59.78 | | | | (21) $false
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | CLOSE: (21) is inconsistent.
% 251.13/59.78 | | | |
% 251.13/59.78 | | | Case 2:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | (22) all_250_15 = e1 | all_250_15 = e0
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | BETA: splitting (22) gives:
% 251.13/59.78 | | | |
% 251.13/59.78 | | | | Case 1:
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | (23) all_250_15 = e1
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | COMBINE_EQS: (6), (23) imply:
% 251.13/59.78 | | | | | (24) all_16_2 = e1
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | REDUCE: (4), (24) imply:
% 251.13/59.78 | | | | | (25) ~ (e4 = e1)
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | SIMP: (25) implies:
% 251.13/59.78 | | | | | (26) ~ (e4 = e1)
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | REF_CLOSE: (2), (3), (8), (24), (26) are inconsistent by sub-proof
% 251.13/59.78 | | | | | #510.
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | Case 2:
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | (27) all_250_15 = e0
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | COMBINE_EQS: (6), (27) imply:
% 251.13/59.78 | | | | | (28) all_16_2 = e0
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | REDUCE: (9), (28) imply:
% 251.13/59.78 | | | | | (29) $false
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | | CLOSE: (29) is inconsistent.
% 251.13/59.78 | | | | |
% 251.13/59.78 | | | | End of split
% 251.13/59.78 | | | |
% 251.13/59.78 | | | End of split
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #467 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) ~ (all_22_2 = e3)
% 251.13/59.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (3) op(e0, e0) = all_244_24
% 251.13/59.78 (4) op(all_84_2, e0) = e3
% 251.13/59.78 (5) all_22_2 = e4
% 251.13/59.78 (6) op(e0, all_84_2) = e4
% 251.13/59.78 (7) op(all_22_2, e3) = e0
% 251.13/59.78 (8) op(e4, e3) = all_84_2
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (1), (5) imply:
% 251.13/59.78 | (9) ~ (e4 = e3)
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (5), (7) imply:
% 251.13/59.78 | (10) op(e4, e3) = e0
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_84_2, e0, e3, e4, simplifying with
% 251.13/59.78 | (8), (10) gives:
% 251.13/59.78 | (11) all_84_2 = e0
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (4), (11) imply:
% 251.13/59.78 | (12) op(e0, e0) = e3
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (6), (11) imply:
% 251.13/59.78 | (13) op(e0, e0) = e4
% 251.13/59.78 |
% 251.13/59.78 | REF_CLOSE: (2), (3), (9), (12), (13) are inconsistent by sub-proof #468.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #468 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (2) op(e0, e0) = all_244_24
% 251.13/59.78 (3) op(e0, e0) = e3
% 251.13/59.78 (4) op(e0, e0) = e4
% 251.13/59.78 (5) ~ (e4 = e3)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (1) with all_244_24, e3, e0, e0, simplifying with
% 251.13/59.78 | (2), (3) gives:
% 251.13/59.78 | (6) all_244_24 = e3
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (1) with all_244_24, e4, e0, e0, simplifying with
% 251.13/59.78 | (2), (4) gives:
% 251.13/59.78 | (7) all_244_24 = e4
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (6), (7) imply:
% 251.13/59.78 | (8) e4 = e3
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (5), (8) imply:
% 251.13/59.78 | (9) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (9) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #469 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_16 = e0 & op(e4, e0) = e0
% 251.13/59.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (3) op(e4, e0) = all_30_2
% 251.13/59.78 (4) ~ (all_30_2 = e0)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (5) op(e4, e0) = e0
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_30_2, e0, e0, e4, simplifying with
% 251.13/59.78 | (3), (5) gives:
% 251.13/59.78 | (6) all_30_2 = e0
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (4), (6) imply:
% 251.13/59.78 | (7) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (7) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #470 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_15 = e4
% 251.13/59.78 (2) all_252_15 = e2
% 251.13/59.78 (3) ~ (e4 = e2)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.78 | (4) e4 = e2
% 251.13/59.78 |
% 251.13/59.78 | SIMP: (4) implies:
% 251.13/59.78 | (5) e4 = e2
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (5) imply:
% 251.13/59.78 | (6) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (6) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #471 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (2) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.78 (3) ~ (e2 = e1)
% 251.13/59.78 (4) op(e0, e2) = all_28_2
% 251.13/59.78 (5) ~ (all_28_2 = e1)
% 251.13/59.78 (6) all_252_14 = e2
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | BETA: splitting (2) gives:
% 251.13/59.78 |
% 251.13/59.78 | Case 1:
% 251.13/59.78 | |
% 251.13/59.78 | | (7) all_252_14 = e1 & op(e1, e2) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | ALPHA: (7) implies:
% 251.13/59.78 | | (8) all_252_14 = e1
% 251.13/59.78 | |
% 251.13/59.78 | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #861.
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (9) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | ALPHA: (9) implies:
% 251.13/59.78 | | (10) op(e0, e2) = e1
% 251.13/59.78 | |
% 251.13/59.78 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #907.
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #472 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.78 (2) all_252_10 = e3
% 251.13/59.78 (3) ~ (e3 = e1)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (4) all_252_10 = e1
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.78 | (5) e3 = e1
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (5) imply:
% 251.13/59.78 | (6) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (6) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #473 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) op(e0, e2) = e3
% 251.13/59.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (3) op(e0, e2) = all_28_2
% 251.13/59.78 (4) op(e0, e2) = e0
% 251.13/59.78 (5) ~ (e3 = e0)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_28_2, e0, e2, e0, simplifying with
% 251.13/59.78 | (3), (4) gives:
% 251.13/59.78 | (6) all_28_2 = e0
% 251.13/59.78 |
% 251.13/59.78 | GROUND_INST: instantiating (2) with all_28_2, e3, e2, e0, simplifying with
% 251.13/59.78 | (1), (3) gives:
% 251.13/59.78 | (7) all_28_2 = e3
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (6), (7) imply:
% 251.13/59.78 | (8) e3 = e0
% 251.13/59.78 |
% 251.13/59.78 | SIMP: (8) implies:
% 251.13/59.78 | (9) e3 = e0
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (5), (9) imply:
% 251.13/59.78 | (10) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (10) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #474 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_8 = e3 & op(e2, e2) = e3
% 251.13/59.78 (2) all_252_8 = e1
% 251.13/59.78 (3) ~ (e3 = e1)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (4) all_252_8 = e3
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.78 | (5) e3 = e1
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (5) imply:
% 251.13/59.78 | (6) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (6) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #475 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.78 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.78 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.78 (2) ~ (e2 = e0)
% 251.13/59.78 (3) ~ (e1 = e0)
% 251.13/59.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (5) ~ (e3 = e2)
% 251.13/59.78 (6) ~ (e4 = e0)
% 251.13/59.78 (7) all_252_0 = e2
% 251.13/59.78 (8) all_252_22 = e0
% 251.13/59.78 (9) ~ (e2 = e1)
% 251.13/59.78 (10) ~ (e4 = e1)
% 251.13/59.78 (11) ~ (e3 = e1)
% 251.13/59.78 (12) op(e3, e1) = all_36_2
% 251.13/59.78 (13) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) =
% 251.13/59.78 e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.78 (14) ~ (all_8_2 = e0)
% 251.13/59.78 (15) ~ (all_36_2 = e0)
% 251.13/59.78 (16) ~ (e4 = e3)
% 251.13/59.78 (17) op(e0, e1) = all_20_2
% 251.13/59.78 (18) op(e3, e0) = all_48_2
% 251.13/59.78 (19) ~ (all_48_2 = e0)
% 251.13/59.78 (20) ~ (e4 = e2)
% 251.13/59.78 (21) op(e3, e2) = all_8_2
% 251.13/59.78 (22) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.78 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.78 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.78 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.78 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.78 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.78 (24) all_252_24 = e4
% 251.13/59.78 (25) ~ (all_244_3 = e0)
% 251.13/59.78 (26) op(e3, e3) = all_244_3
% 251.13/59.78 (27) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.78 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.78 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.78 (28) ~ (all_20_2 = e2)
% 251.13/59.78 (29) all_252_20 = e3
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | BETA: splitting (13) gives:
% 251.13/59.78 |
% 251.13/59.78 | Case 1:
% 251.13/59.78 | |
% 251.13/59.78 | | (30) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.78 | |
% 251.13/59.78 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.78 | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (25), (26),
% 251.13/59.78 | | (27), (29), (30) are inconsistent by sub-proof #485.
% 251.13/59.78 | |
% 251.13/59.78 | Case 2:
% 251.13/59.78 | |
% 251.13/59.78 | | (31) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0)
% 251.13/59.78 | | = e2)
% 251.13/59.78 | |
% 251.13/59.78 | | BETA: splitting (31) gives:
% 251.13/59.78 | |
% 251.13/59.78 | | Case 1:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (32) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | ALPHA: (32) implies:
% 251.13/59.78 | | | (33) op(e0, e1) = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (4), (17), (28), (33) are inconsistent by sub-proof #985.
% 251.13/59.78 | | |
% 251.13/59.78 | | Case 2:
% 251.13/59.78 | | |
% 251.13/59.78 | | | (34) all_252_24 = e2 & op(e0, e0) = e2
% 251.13/59.78 | | |
% 251.13/59.78 | | | REF_CLOSE: (20), (24), (34) are inconsistent by sub-proof #476.
% 251.13/59.78 | | |
% 251.13/59.78 | | End of split
% 251.13/59.78 | |
% 251.13/59.78 | End of split
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #476 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_24 = e2 & op(e0, e0) = e2
% 251.13/59.78 (2) all_252_24 = e4
% 251.13/59.78 (3) ~ (e4 = e2)
% 251.13/59.78
% 251.13/59.78 Begin of proof
% 251.13/59.78 |
% 251.13/59.78 | ALPHA: (1) implies:
% 251.13/59.78 | (4) all_252_24 = e2
% 251.13/59.78 |
% 251.13/59.78 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.78 | (5) e4 = e2
% 251.13/59.78 |
% 251.13/59.78 | REDUCE: (3), (5) imply:
% 251.13/59.78 | (6) $false
% 251.13/59.78 |
% 251.13/59.78 | CLOSE: (6) is inconsistent.
% 251.13/59.78 |
% 251.13/59.78 End of proof
% 251.13/59.78
% 251.13/59.78 Sub-proof #477 shows that the following formulas are inconsistent:
% 251.13/59.78 ----------------------------------------------------------------
% 251.13/59.78 (1) all_252_6 = e4
% 251.13/59.78 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.78 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.78 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.78 (3) ~ (e2 = e0)
% 251.13/59.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.78 (5) ~ (e3 = e2)
% 251.13/59.78 (6) all_252_0 = e2
% 251.13/59.78 (7) ~ (e2 = e1)
% 251.13/59.78 (8) op(e1, e4) = all_16_2
% 251.13/59.78 (9) op(e3, e1) = all_36_2
% 251.13/59.78 (10) ~ (all_16_2 = e2)
% 251.13/59.78 (11) ~ (all_8_2 = e0)
% 251.13/59.78 (12) all_252_8 = e2 & op(e2, e2) = e2
% 251.13/59.78 (13) ~ (all_36_2 = e0)
% 251.13/59.78 (14) op(e3, e0) = all_48_2
% 251.13/59.78 (15) ~ (all_48_2 = e0)
% 251.13/59.78 (16) ~ (e4 = e2)
% 251.13/59.78 (17) op(e3, e2) = all_8_2
% 251.13/59.79 (18) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.79 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.79 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.79 (19) ~ (all_244_3 = e0)
% 251.13/59.79 (20) all_252_8 = e1
% 251.13/59.79 (21) op(e3, e3) = all_244_3
% 251.13/59.79 (22) all_252_20 = e3
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (12) implies:
% 251.13/59.79 | (23) all_252_8 = e2
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (20), (23) imply:
% 251.13/59.79 | (24) e2 = e1
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (24) implies:
% 251.13/59.79 | (25) e2 = e1
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (6), (25) imply:
% 251.13/59.79 | (26) all_252_0 = e1
% 251.13/59.79 |
% 251.13/59.79 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 251.13/59.79 | (15), (16), (17), (18), (19), (21), (22), (26) are inconsistent by
% 251.13/59.79 | sub-proof #518.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #478 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_5 = e4
% 251.13/59.79 (2) all_252_5 = e2
% 251.13/59.79 (3) ~ (e4 = e2)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.79 | (4) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (4) implies:
% 251.13/59.79 | (5) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #479 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_4 = e4
% 251.13/59.79 (2) all_252_4 = e3
% 251.13/59.79 (3) ~ (e4 = e3)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.79 | (4) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (4) implies:
% 251.13/59.79 | (5) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #480 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.79 (2) all_252_22 = e0
% 251.13/59.79 (3) ~ (e4 = e0)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_22 = e4
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e0
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #481 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.79 (2) all_252_9 = e0
% 251.13/59.79 (3) ~ (e4 = e0)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_9 = e4
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e0
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (5) implies:
% 251.13/59.79 | (6) e4 = e0
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (6) imply:
% 251.13/59.79 | (7) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (7) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #482 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_3 = e3 & op(e3, e3) = e3
% 251.13/59.79 (2) all_252_3 = e4
% 251.13/59.79 (3) ~ (e4 = e3)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_3 = e3
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (5) implies:
% 251.13/59.79 | (6) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (6) imply:
% 251.13/59.79 | (7) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (7) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #483 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_16 = e4 & op(e4, e0) = e4
% 251.13/59.79 (2) all_252_16 = e3
% 251.13/59.79 (3) ~ (e4 = e3)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_16 = e4
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #484 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_16 = e1 & op(e4, e0) = e1
% 251.13/59.79 (2) all_252_16 = e3
% 251.13/59.79 (3) ~ (e3 = e1)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_16 = e1
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e3 = e1
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #485 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.79 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.79 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.79 (2) ~ (e2 = e0)
% 251.13/59.79 (3) ~ (e1 = e0)
% 251.13/59.79 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (5) ~ (e3 = e2)
% 251.13/59.79 (6) ~ (e4 = e0)
% 251.13/59.79 (7) all_252_0 = e2
% 251.13/59.79 (8) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.79 (9) all_252_22 = e0
% 251.13/59.79 (10) ~ (e2 = e1)
% 251.13/59.79 (11) ~ (e4 = e1)
% 251.13/59.79 (12) ~ (e3 = e1)
% 251.13/59.79 (13) op(e3, e1) = all_36_2
% 251.13/59.79 (14) ~ (all_8_2 = e0)
% 251.13/59.79 (15) ~ (all_36_2 = e0)
% 251.13/59.79 (16) ~ (e4 = e3)
% 251.13/59.79 (17) op(e3, e0) = all_48_2
% 251.13/59.79 (18) ~ (all_48_2 = e0)
% 251.13/59.79 (19) ~ (e4 = e2)
% 251.13/59.79 (20) op(e3, e2) = all_8_2
% 251.13/59.79 (21) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.79 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.79 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.79 (22) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.79 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.79 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.79 (23) ~ (all_244_3 = e0)
% 251.13/59.79 (24) op(e3, e3) = all_244_3
% 251.13/59.79 (25) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.79 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.79 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.79 (26) all_252_20 = e3
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (8) implies:
% 251.13/59.79 | (27) all_252_22 = e2
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (9), (27) imply:
% 251.13/59.79 | (28) e2 = e0
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (7), (28) imply:
% 251.13/59.79 | (29) all_252_0 = e0
% 251.13/59.79 |
% 251.13/59.79 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 251.13/59.79 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 251.13/59.79 | (29) are inconsistent by sub-proof #559.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #486 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.79 (2) all_252_15 = e4
% 251.13/59.79 (3) ~ (e4 = e3)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_15 = e3
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e3
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #487 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.79 (2) all_252_15 = e4
% 251.13/59.79 (3) ~ (e4 = e2)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_15 = e2
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #488 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_16 = e3 & op(e4, e0) = e3
% 251.13/59.79 (2) all_252_16 = e1
% 251.13/59.79 (3) ~ (e3 = e1)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_16 = e3
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e3 = e1
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (5) implies:
% 251.13/59.79 | (6) e3 = e1
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (6) imply:
% 251.13/59.79 | (7) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (7) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #489 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_9 = e3 & op(e4, e1) = e3
% 251.13/59.79 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (3) op(e4, e1) = e1
% 251.13/59.79 (4) ~ (e3 = e1)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (5) op(e4, e1) = e3
% 251.13/59.79 |
% 251.13/59.79 | GROUND_INST: instantiating (2) with e1, e3, e1, e4, simplifying with (3), (5)
% 251.13/59.79 | gives:
% 251.13/59.79 | (6) e3 = e1
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (4), (6) imply:
% 251.13/59.79 | (7) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (7) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #490 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_3 = e4
% 251.13/59.79 (2) ~ (e1 = e0)
% 251.13/59.79 (3) op(e3, e4) = e0
% 251.13/59.79 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (5) ~ (e4 = e1)
% 251.13/59.79 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | BETA: splitting (6) gives:
% 251.13/59.79 |
% 251.13/59.79 | Case 1:
% 251.13/59.79 | |
% 251.13/59.79 | | (7) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.79 | |
% 251.13/59.79 | | ALPHA: (7) implies:
% 251.13/59.79 | | (8) op(e3, e4) = e1
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #607.
% 251.13/59.79 | |
% 251.13/59.79 | Case 2:
% 251.13/59.79 | |
% 251.13/59.79 | | (9) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #890.
% 251.13/59.79 | |
% 251.13/59.79 | End of split
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #491 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (2) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.79 (3) op(e0, e1) = all_20_2
% 251.13/59.79 (4) ~ (e4 = e2)
% 251.13/59.79 (5) all_252_24 = e4
% 251.13/59.79 (6) ~ (all_20_2 = e2)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | BETA: splitting (2) gives:
% 251.13/59.79 |
% 251.13/59.79 | Case 1:
% 251.13/59.79 | |
% 251.13/59.79 | | (7) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | ALPHA: (7) implies:
% 251.13/59.79 | | (8) op(e0, e1) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #985.
% 251.13/59.79 | |
% 251.13/59.79 | Case 2:
% 251.13/59.79 | |
% 251.13/59.79 | | (9) all_252_24 = e2 & op(e0, e0) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | ALPHA: (9) implies:
% 251.13/59.79 | | (10) all_252_24 = e2
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #492.
% 251.13/59.79 | |
% 251.13/59.79 | End of split
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #492 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_24 = e4
% 251.13/59.79 (2) all_252_24 = e2
% 251.13/59.79 (3) ~ (e4 = e2)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.79 | (4) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (4) implies:
% 251.13/59.79 | (5) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #493 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.79 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.79 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.79 (2) e2 = e0
% 251.13/59.79 (3) ~ (e2 = e0)
% 251.13/59.79 (4) ~ (e1 = e0)
% 251.13/59.79 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (6) ~ (e3 = e2)
% 251.13/59.79 (7) ~ (e4 = e0)
% 251.13/59.79 (8) all_252_0 = e2
% 251.13/59.79 (9) ~ (e2 = e1)
% 251.13/59.79 (10) ~ (e4 = e1)
% 251.13/59.79 (11) ~ (e3 = e1)
% 251.13/59.79 (12) op(e3, e1) = all_36_2
% 251.13/59.79 (13) ~ (all_8_2 = e0)
% 251.13/59.79 (14) ~ (all_36_2 = e0)
% 251.13/59.79 (15) ~ (e4 = e3)
% 251.13/59.79 (16) op(e3, e0) = all_48_2
% 251.13/59.79 (17) ~ (all_48_2 = e0)
% 251.13/59.79 (18) ~ (e4 = e2)
% 251.13/59.79 (19) op(e3, e2) = all_8_2
% 251.13/59.79 (20) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.79 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.79 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.79 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.79 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.79 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.79 (22) ~ (all_244_3 = e0)
% 251.13/59.79 (23) op(e3, e3) = all_244_3
% 251.13/59.79 (24) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.79 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.79 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.79 (25) all_252_20 = e3
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | SIMP: (2) implies:
% 251.13/59.79 | (26) e2 = e0
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (8), (26) imply:
% 251.13/59.79 | (27) all_252_0 = e0
% 251.13/59.79 |
% 251.13/59.79 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 251.13/59.79 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 251.13/59.79 | (27) are inconsistent by sub-proof #559.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #494 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 251.13/59.79 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 251.13/59.79 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.13/59.79 (2) ~ (all_10_2 = e4)
% 251.13/59.79 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.79 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.79 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.79 (4) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.79 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.79 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.79 (5) op(e0, e2) = e4
% 251.13/59.79 (6) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.79 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.13/59.79 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.79 (7) all_162_2 = all_28_2
% 251.13/59.79 (8) ~ (e2 = e0)
% 251.13/59.79 (9) ~ (e1 = e0)
% 251.13/59.79 (10) ~ (all_28_2 = e3)
% 251.13/59.79 (11) op(e3, e4) = e0
% 251.13/59.79 (12) ~ (all_62_2 = e2)
% 251.13/59.79 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (14) op(e2, e3) = all_10_2
% 251.13/59.79 (15) ~ (e3 = e2)
% 251.13/59.79 (16) op(e2, e1) = all_38_2
% 251.13/59.79 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.79 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.79 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.79 (18) op(e1, e0) = all_34_2
% 251.13/59.79 (19) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.13/59.79 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.79 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.79 (20) ~ (all_40_2 = e4)
% 251.13/59.79 (21) ~ (all_36_2 = e2)
% 251.13/59.79 (22) op(e4, e2) = all_6_2
% 251.13/59.79 (23) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.79 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.13/59.79 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.79 (24) ~ (all_34_2 = e2)
% 251.13/59.79 (25) ~ (e2 = e1)
% 251.13/59.79 (26) op(all_26_2, e1) = e4
% 251.13/59.79 (27) op(e0, e2) = all_28_2
% 251.13/59.79 (28) ~ (all_28_2 = e1)
% 251.13/59.79 (29) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.13/59.79 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.13/59.79 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.13/59.79 (30) ~ (all_6_2 = e1)
% 251.13/59.79 (31) op(e1, e4) = all_16_2
% 251.13/59.79 (32) op(e4, e2) = e0
% 251.13/59.79 (33) ~ (all_28_2 = all_20_2)
% 251.13/59.79 (34) op(e1, e3) = all_62_2
% 251.13/59.79 (35) ~ (e3 = e0)
% 251.13/59.79 (36) all_252_4 = e3
% 251.13/59.79 (37) ~ (all_36_2 = e4)
% 251.13/59.79 (38) ~ (e3 = e1)
% 251.13/59.79 (39) op(e4, e2) = e3
% 251.13/59.79 (40) op(e3, e1) = all_36_2
% 251.13/59.79 (41) ~ (all_16_2 = e2)
% 251.13/59.79 (42) ~ (all_8_2 = e1)
% 251.13/59.79 (43) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.79 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.79 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.79 (44) ~ (all_22_2 = e1)
% 251.13/59.79 (45) ~ (all_8_2 = e0)
% 251.13/59.79 (46) ~ (all_38_2 = e4)
% 251.13/59.79 (47) op(e0, e3) = all_22_2
% 251.13/59.79 (48) ~ (all_28_2 = all_22_2)
% 251.13/59.79 (49) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.79 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.79 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.79 (50) op(e4, e1) = all_26_2
% 251.13/59.79 (51) ~ (all_36_2 = e0)
% 251.13/59.79 (52) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.13/59.79 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.13/59.79 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.13/59.79 (53) op(e0, e1) = all_20_2
% 251.13/59.79 (54) op(e3, e0) = all_48_2
% 251.13/59.79 (55) ~ (all_26_2 = e3)
% 251.13/59.79 (56) op(e1, e2) = all_4_2
% 251.13/59.79 (57) ~ (all_28_2 = all_8_2)
% 251.13/59.79 (58) ~ (all_48_2 = e0)
% 251.13/59.79 (59) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.79 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.79 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.79 (60) ~ (all_48_2 = e1)
% 251.13/59.79 (61) op(e2, e4) = all_64_2
% 251.13/59.79 (62) ~ (e4 = e2)
% 251.13/59.79 (63) op(e3, e2) = all_8_2
% 251.13/59.79 (64) ~ (all_64_2 = all_16_2)
% 251.13/59.79 (65) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.79 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.79 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.79 (66) ~ (all_244_3 = e0)
% 251.13/59.79 (67) op(e2, e0) = all_40_2
% 251.13/59.79 (68) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.79 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.79 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.79 (69) ~ (all_28_2 = e0)
% 251.13/59.79 (70) op(e3, e3) = all_244_3
% 251.13/59.79 (71) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.79 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.79 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.79 (72) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.13/59.79 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.79 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 251.13/59.79 (73) ~ (all_4_2 = e3)
% 251.13/59.79 (74) op(all_26_2, all_16_2) = e1
% 251.13/59.79 (75) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.79 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.79 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.79 (76) all_252_20 = e3
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | GROUND_INST: instantiating (13) with e0, e3, e2, e4, simplifying with (32),
% 251.13/59.79 | (39) gives:
% 251.13/59.79 | (77) e3 = e0
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (36), (77) imply:
% 251.13/59.79 | (78) all_252_4 = e0
% 251.13/59.79 |
% 251.13/59.79 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.79 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.13/59.79 | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 251.13/59.79 | (37), (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 251.13/59.79 | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 251.13/59.79 | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 251.13/59.79 | (71), (72), (73), (74), (75), (76), (78) are inconsistent by
% 251.13/59.79 | sub-proof #498.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #495 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_3 = e4
% 251.13/59.79 (2) ~ (e2 = e0)
% 251.13/59.79 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.79 (4) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.13/59.79 (5) op(e4, e3) = all_84_2
% 251.13/59.79 (6) ~ (e4 = e2)
% 251.13/59.79 (7) op(e4, e3) = e0
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | BETA: splitting (4) gives:
% 251.13/59.79 |
% 251.13/59.79 | Case 1:
% 251.13/59.79 | |
% 251.13/59.79 | | (8) all_252_1 = e2 & op(e4, e3) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | ALPHA: (8) implies:
% 251.13/59.79 | | (9) op(e4, e3) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #850.
% 251.13/59.79 | |
% 251.13/59.79 | Case 2:
% 251.13/59.79 | |
% 251.13/59.79 | | (10) all_252_3 = e2 & op(e3, e3) = e2
% 251.13/59.79 | |
% 251.13/59.79 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #496.
% 251.13/59.79 | |
% 251.13/59.79 | End of split
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #496 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) all_252_3 = e2 & op(e3, e3) = e2
% 251.13/59.79 (2) all_252_3 = e4
% 251.13/59.79 (3) ~ (e4 = e2)
% 251.13/59.79
% 251.13/59.79 Begin of proof
% 251.13/59.79 |
% 251.13/59.79 | ALPHA: (1) implies:
% 251.13/59.79 | (4) all_252_3 = e2
% 251.13/59.79 |
% 251.13/59.79 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.79 | (5) e4 = e2
% 251.13/59.79 |
% 251.13/59.79 | REDUCE: (3), (5) imply:
% 251.13/59.79 | (6) $false
% 251.13/59.79 |
% 251.13/59.79 | CLOSE: (6) is inconsistent.
% 251.13/59.79 |
% 251.13/59.79 End of proof
% 251.13/59.79
% 251.13/59.79 Sub-proof #497 shows that the following formulas are inconsistent:
% 251.13/59.79 ----------------------------------------------------------------
% 251.13/59.79 (1) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 251.13/59.79 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 251.13/59.79 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.13/59.79 (2) ~ (all_10_2 = e4)
% 251.13/59.79 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.79 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.79 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.80 (4) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.80 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.80 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.80 (5) op(e0, e2) = e4
% 251.13/59.80 (6) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.80 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.13/59.80 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.80 (7) all_162_2 = all_28_2
% 251.13/59.80 (8) ~ (e2 = e0)
% 251.13/59.80 (9) ~ (e1 = e0)
% 251.13/59.80 (10) ~ (all_28_2 = e3)
% 251.13/59.80 (11) op(e3, e4) = e0
% 251.13/59.80 (12) ~ (all_62_2 = e2)
% 251.13/59.80 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.80 (14) op(e2, e3) = all_10_2
% 251.13/59.80 (15) ~ (e3 = e2)
% 251.13/59.80 (16) op(e2, e1) = all_38_2
% 251.13/59.80 (17) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.80 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.80 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.80 (18) op(e1, e0) = all_34_2
% 251.13/59.80 (19) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.13/59.80 (20) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.13/59.80 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.80 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.80 (21) ~ (all_40_2 = e4)
% 251.13/59.80 (22) ~ (all_36_2 = e2)
% 251.13/59.80 (23) op(e4, e2) = all_6_2
% 251.13/59.80 (24) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.80 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.13/59.80 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.80 (25) ~ (all_34_2 = e2)
% 251.13/59.80 (26) ~ (e2 = e1)
% 251.13/59.80 (27) op(all_26_2, e1) = e4
% 251.13/59.80 (28) op(e0, e2) = all_28_2
% 251.13/59.80 (29) ~ (all_28_2 = e1)
% 251.13/59.80 (30) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.13/59.80 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.13/59.80 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.13/59.80 (31) ~ (all_6_2 = e1)
% 251.13/59.80 (32) op(e1, e4) = all_16_2
% 251.13/59.80 (33) ~ (all_28_2 = all_20_2)
% 251.13/59.80 (34) op(e1, e3) = all_62_2
% 251.13/59.80 (35) ~ (e3 = e0)
% 251.13/59.80 (36) ~ (all_36_2 = e4)
% 251.13/59.80 (37) ~ (e3 = e1)
% 251.13/59.80 (38) op(e3, e1) = all_36_2
% 251.13/59.80 (39) ~ (all_16_2 = e2)
% 251.13/59.80 (40) ~ (all_8_2 = e1)
% 251.13/59.80 (41) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.80 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.80 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.80 (42) ~ (all_22_2 = e1)
% 251.13/59.80 (43) ~ (all_8_2 = e0)
% 251.13/59.80 (44) ~ (all_38_2 = e4)
% 251.13/59.80 (45) op(e0, e3) = all_22_2
% 251.13/59.80 (46) ~ (all_28_2 = all_22_2)
% 251.13/59.80 (47) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.80 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.80 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.80 (48) op(e4, e1) = all_26_2
% 251.13/59.80 (49) ~ (all_36_2 = e0)
% 251.13/59.80 (50) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.13/59.80 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.13/59.80 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.13/59.80 (51) op(e0, e1) = all_20_2
% 251.13/59.80 (52) op(e3, e0) = all_48_2
% 251.13/59.80 (53) ~ (all_26_2 = e3)
% 251.13/59.80 (54) op(e1, e2) = all_4_2
% 251.13/59.80 (55) ~ (all_28_2 = all_8_2)
% 251.13/59.80 (56) ~ (all_48_2 = e0)
% 251.13/59.80 (57) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.80 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.80 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.80 (58) ~ (all_48_2 = e1)
% 251.13/59.80 (59) op(e2, e4) = all_64_2
% 251.13/59.80 (60) ~ (e4 = e2)
% 251.13/59.80 (61) op(e3, e2) = all_8_2
% 251.13/59.80 (62) ~ (all_64_2 = all_16_2)
% 251.13/59.80 (63) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.80 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.80 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.80 (64) ~ (all_244_3 = e0)
% 251.13/59.80 (65) op(e2, e0) = all_40_2
% 251.13/59.80 (66) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.80 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.80 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.80 (67) ~ (all_28_2 = e0)
% 251.13/59.80 (68) op(e3, e3) = all_244_3
% 251.13/59.80 (69) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.80 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.80 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.80 (70) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.13/59.80 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.80 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 251.13/59.80 (71) ~ (all_4_2 = e3)
% 251.13/59.80 (72) op(all_26_2, all_16_2) = e1
% 251.13/59.80 (73) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.80 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.80 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.80 (74) all_252_20 = e3
% 251.13/59.80
% 251.13/59.80 Begin of proof
% 251.13/59.80 |
% 251.13/59.80 | BETA: splitting (19) gives:
% 251.13/59.80 |
% 251.13/59.80 | Case 1:
% 251.13/59.80 | |
% 251.13/59.80 | | (75) all_252_4 = e0 & op(e4, e2) = e0
% 251.13/59.80 | |
% 251.13/59.80 | | ALPHA: (75) implies:
% 251.13/59.80 | | (76) all_252_4 = e0
% 251.13/59.80 | |
% 251.13/59.80 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.80 | | (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 251.13/59.80 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 251.13/59.80 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 251.13/59.80 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 251.13/59.80 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 251.13/59.80 | | (69), (70), (71), (72), (73), (74), (76) are inconsistent by
% 251.13/59.80 | | sub-proof #498.
% 251.13/59.80 | |
% 251.13/59.80 | Case 2:
% 251.13/59.80 | |
% 251.13/59.80 | | (77) all_252_5 = e0 & op(e3, e2) = e0
% 251.13/59.80 | |
% 251.13/59.80 | | REF_CLOSE: (13), (43), (61), (77) are inconsistent by sub-proof #874.
% 251.13/59.80 | |
% 251.13/59.80 | End of split
% 251.13/59.80 |
% 251.13/59.80 End of proof
% 251.13/59.80
% 251.13/59.80 Sub-proof #498 shows that the following formulas are inconsistent:
% 251.13/59.80 ----------------------------------------------------------------
% 251.13/59.80 (1) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 251.13/59.80 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 251.13/59.80 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.13/59.80 (2) ~ (all_10_2 = e4)
% 251.13/59.80 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.80 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.80 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.80 (4) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.80 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.80 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.80 (5) all_252_4 = e0
% 251.13/59.80 (6) op(e0, e2) = e4
% 251.13/59.80 (7) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.80 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.13/59.80 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.80 (8) all_162_2 = all_28_2
% 251.13/59.80 (9) ~ (e2 = e0)
% 251.13/59.80 (10) ~ (e1 = e0)
% 251.13/59.80 (11) ~ (all_28_2 = e3)
% 251.13/59.80 (12) op(e3, e4) = e0
% 251.13/59.80 (13) ~ (all_62_2 = e2)
% 251.13/59.80 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.80 (15) op(e2, e3) = all_10_2
% 251.13/59.80 (16) ~ (e3 = e2)
% 251.13/59.80 (17) op(e2, e1) = all_38_2
% 251.13/59.80 (18) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.80 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.80 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.80 (19) op(e1, e0) = all_34_2
% 251.13/59.80 (20) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.13/59.80 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.80 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.80 (21) ~ (all_40_2 = e4)
% 251.13/59.80 (22) ~ (all_36_2 = e2)
% 251.13/59.80 (23) op(e4, e2) = all_6_2
% 251.13/59.80 (24) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.80 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.13/59.80 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.80 (25) ~ (all_34_2 = e2)
% 251.13/59.80 (26) ~ (e2 = e1)
% 251.13/59.80 (27) op(all_26_2, e1) = e4
% 251.13/59.80 (28) op(e0, e2) = all_28_2
% 251.13/59.80 (29) ~ (all_28_2 = e1)
% 251.13/59.80 (30) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.13/59.80 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.13/59.80 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.13/59.80 (31) ~ (all_6_2 = e1)
% 251.13/59.80 (32) op(e1, e4) = all_16_2
% 251.13/59.80 (33) ~ (all_28_2 = all_20_2)
% 251.13/59.80 (34) op(e1, e3) = all_62_2
% 251.13/59.80 (35) ~ (e3 = e0)
% 251.13/59.80 (36) ~ (all_36_2 = e4)
% 251.13/59.80 (37) ~ (e3 = e1)
% 251.13/59.80 (38) op(e3, e1) = all_36_2
% 251.13/59.80 (39) ~ (all_16_2 = e2)
% 251.13/59.80 (40) ~ (all_8_2 = e1)
% 251.13/59.80 (41) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.80 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.80 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.80 (42) ~ (all_22_2 = e1)
% 251.13/59.80 (43) ~ (all_8_2 = e0)
% 251.13/59.80 (44) ~ (all_38_2 = e4)
% 251.13/59.80 (45) op(e0, e3) = all_22_2
% 251.13/59.80 (46) ~ (all_28_2 = all_22_2)
% 251.13/59.80 (47) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.80 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.80 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.80 (48) op(e4, e1) = all_26_2
% 251.13/59.80 (49) ~ (all_36_2 = e0)
% 251.13/59.80 (50) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.13/59.80 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.13/59.80 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.13/59.80 (51) op(e0, e1) = all_20_2
% 251.13/59.80 (52) op(e3, e0) = all_48_2
% 251.13/59.80 (53) ~ (all_26_2 = e3)
% 251.13/59.80 (54) op(e1, e2) = all_4_2
% 251.13/59.80 (55) ~ (all_28_2 = all_8_2)
% 251.13/59.80 (56) ~ (all_48_2 = e0)
% 251.13/59.80 (57) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.80 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.80 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.80 (58) ~ (all_48_2 = e1)
% 251.13/59.80 (59) op(e2, e4) = all_64_2
% 251.13/59.80 (60) ~ (e4 = e2)
% 251.13/59.80 (61) op(e3, e2) = all_8_2
% 251.13/59.80 (62) ~ (all_64_2 = all_16_2)
% 251.13/59.80 (63) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.80 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.80 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.80 (64) ~ (all_244_3 = e0)
% 251.13/59.80 (65) op(e2, e0) = all_40_2
% 251.13/59.80 (66) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.80 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.80 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.80 (67) ~ (all_28_2 = e0)
% 251.13/59.80 (68) op(e3, e3) = all_244_3
% 251.13/59.80 (69) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.80 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.80 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.80 (70) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.13/59.80 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.80 e2) | (all_252_17 = e2 & op(e3, e0) = e2)
% 251.13/59.80 (71) ~ (all_4_2 = e3)
% 251.13/59.80 (72) op(all_26_2, all_16_2) = e1
% 251.13/59.80 (73) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.80 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.80 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.80 (74) all_252_20 = e3
% 251.13/59.80
% 251.13/59.80 Begin of proof
% 251.13/59.80 |
% 251.13/59.80 | GROUND_INST: instantiating (14) with all_28_2, e4, e2, e0, simplifying with
% 251.13/59.80 | (6), (28) gives:
% 251.13/59.80 | (75) all_28_2 = e4
% 251.13/59.80 |
% 251.13/59.80 | COMBINE_EQS: (8), (75) imply:
% 251.13/59.80 | (76) all_162_2 = e4
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (46), (75) imply:
% 251.13/59.80 | (77) ~ (all_22_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | SIMP: (77) implies:
% 251.13/59.80 | (78) ~ (all_22_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (33), (75) imply:
% 251.13/59.80 | (79) ~ (all_20_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | SIMP: (79) implies:
% 251.13/59.80 | (80) ~ (all_20_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (55), (75) imply:
% 251.13/59.80 | (81) ~ (all_8_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | SIMP: (81) implies:
% 251.13/59.80 | (82) ~ (all_8_2 = e4)
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (11), (75) imply:
% 251.13/59.80 | (83) ~ (e4 = e3)
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (29), (75) imply:
% 251.13/59.80 | (84) ~ (e4 = e1)
% 251.13/59.80 |
% 251.13/59.80 | REDUCE: (67), (75) imply:
% 251.13/59.80 | (85) ~ (e4 = e0)
% 251.13/59.80 |
% 251.13/59.80 | BETA: splitting (47) gives:
% 251.13/59.80 |
% 251.13/59.80 | Case 1:
% 251.13/59.80 | |
% 251.13/59.80 | | (86) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 251.13/59.80 | | e4)
% 251.13/59.80 | |
% 251.13/59.80 | | BETA: splitting (86) gives:
% 251.13/59.80 | |
% 251.13/59.80 | | Case 1:
% 251.13/59.80 | | |
% 251.13/59.80 | | | (87) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | ALPHA: (87) implies:
% 251.13/59.80 | | | (88) all_252_6 = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | BETA: splitting (1) gives:
% 251.13/59.80 | | |
% 251.13/59.80 | | | Case 1:
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | (89) ~ (all_162_2 = e4)
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | REDUCE: (76), (89) imply:
% 251.13/59.80 | | | | (90) $false
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | CLOSE: (90) is inconsistent.
% 251.13/59.80 | | | |
% 251.13/59.80 | | | Case 2:
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | (91) ( ~ (all_162_0 = e1) & op(e4, all_162_1) = all_162_0 & op(e2,
% 251.13/59.80 | | | | e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | ( ~
% 251.13/59.80 | | | | (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | BETA: splitting (91) gives:
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | Case 1:
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | (92) ~ (all_162_0 = e1) & op(e4, all_162_1) = all_162_0 & op(e2,
% 251.13/59.80 | | | | | e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | ALPHA: (92) implies:
% 251.13/59.80 | | | | | (93) op(e2, e4) = all_162_1
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | REF_CLOSE: (4), (9), (10), (12), (14), (16), (26), (27), (32), (37),
% 251.13/59.80 | | | | | (38), (39), (43), (49), (52), (56), (59), (60), (61), (62),
% 251.13/59.80 | | | | | (63), (64), (68), (72), (73), (74), (84), (87), (88), (93)
% 251.13/59.80 | | | | | are inconsistent by sub-proof #508.
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | Case 2:
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | (94) ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1)
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | ALPHA: (94) implies:
% 251.13/59.80 | | | | | (95) op(e2, e4) = all_162_1
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | REF_CLOSE: (4), (9), (10), (12), (14), (16), (26), (27), (32), (37),
% 251.13/59.80 | | | | | (38), (39), (43), (49), (52), (56), (59), (60), (61), (62),
% 251.13/59.80 | | | | | (63), (64), (68), (72), (73), (74), (84), (87), (88), (95)
% 251.13/59.80 | | | | | are inconsistent by sub-proof #508.
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | End of split
% 251.13/59.80 | | | |
% 251.13/59.80 | | | End of split
% 251.13/59.80 | | |
% 251.13/59.80 | | Case 2:
% 251.13/59.80 | | |
% 251.13/59.80 | | | (96) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | ALPHA: (96) implies:
% 251.13/59.80 | | | (97) op(e2, e3) = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | REF_CLOSE: (2), (14), (15), (97) are inconsistent by sub-proof #953.
% 251.13/59.80 | | |
% 251.13/59.80 | | End of split
% 251.13/59.80 | |
% 251.13/59.80 | Case 2:
% 251.13/59.80 | |
% 251.13/59.80 | | (98) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.80 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.80 | |
% 251.13/59.80 | | BETA: splitting (98) gives:
% 251.13/59.80 | |
% 251.13/59.80 | | Case 1:
% 251.13/59.80 | | |
% 251.13/59.80 | | | (99) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | ALPHA: (99) implies:
% 251.13/59.80 | | | (100) all_252_8 = e4
% 251.13/59.80 | | |
% 251.13/59.80 | | | BETA: splitting (57) gives:
% 251.13/59.80 | | |
% 251.13/59.80 | | | Case 1:
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | (101) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3,
% 251.13/59.80 | | | | e2) = e3)
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | BETA: splitting (101) gives:
% 251.13/59.80 | | | |
% 251.13/59.80 | | | | Case 1:
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | (102) all_252_4 = e3 & op(e4, e2) = e3
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | REF_CLOSE: (5), (35), (102) are inconsistent by sub-proof #865.
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | Case 2:
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | (103) all_252_5 = e3 & op(e3, e2) = e3
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | ALPHA: (103) implies:
% 251.13/59.80 | | | | | (104) all_252_5 = e3
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | BETA: splitting (69) gives:
% 251.13/59.80 | | | | |
% 251.13/59.80 | | | | | Case 1:
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | (105) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 &
% 251.13/59.80 | | | | | | op(e3, e2) = e2)
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | BETA: splitting (105) gives:
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | Case 1:
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | (106) all_252_4 = e2 & op(e4, e2) = e2
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | REF_CLOSE: (5), (9), (106) are inconsistent by sub-proof #863.
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | Case 2:
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | (107) all_252_5 = e2 & op(e3, e2) = e2
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | ALPHA: (107) implies:
% 251.13/59.80 | | | | | | | (108) all_252_5 = e2
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | REF_CLOSE: (16), (104), (108) are inconsistent by sub-proof #507.
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | End of split
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | Case 2:
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | (109) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 &
% 251.13/59.80 | | | | | | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | BETA: splitting (109) gives:
% 251.13/59.80 | | | | | |
% 251.13/59.80 | | | | | | Case 1:
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | (110) all_252_8 = e2 & op(e2, e2) = e2
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | REF_CLOSE: (60), (100), (110) are inconsistent by sub-proof #642.
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | Case 2:
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | (111) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 251.13/59.80 | | | | | | | op(e0, e2) = e2)
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | BETA: splitting (111) gives:
% 251.13/59.80 | | | | | | |
% 251.13/59.80 | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | (112) all_252_14 = e2 & op(e1, e2) = e2
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | ALPHA: (112) implies:
% 251.13/59.80 | | | | | | | | (113) all_252_14 = e2
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | REF_CLOSE: (14), (18), (23), (26), (28), (29), (31), (40), (61),
% 251.13/59.80 | | | | | | | | (84), (100), (113) are inconsistent by sub-proof
% 251.13/59.80 | | | | | | | | #506.
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | (114) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | ALPHA: (114) implies:
% 251.13/59.80 | | | | | | | | (115) all_252_22 = e2
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | BETA: splitting (3) gives:
% 251.13/59.80 | | | | | | | |
% 251.13/59.80 | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | (116) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 =
% 251.13/59.80 | | | | | | | | | e4 & op(e0, e3) = e4)
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | BETA: splitting (116) gives:
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | (117) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | REF_CLOSE: (74), (83), (117) are inconsistent by sub-proof
% 251.13/59.80 | | | | | | | | | | #553.
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | (118) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | REF_CLOSE: (14), (45), (78), (118) are inconsistent by
% 251.13/59.80 | | | | | | | | | | sub-proof #805.
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | End of split
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | (119) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 =
% 251.13/59.80 | | | | | | | | | e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0,
% 251.13/59.80 | | | | | | | | | e0) = e4)
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | BETA: splitting (119) gives:
% 251.13/59.80 | | | | | | | | |
% 251.13/59.80 | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | (120) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | ALPHA: (120) implies:
% 251.13/59.80 | | | | | | | | | | (121) all_252_22 = e4
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | COMBINE_EQS: (115), (121) imply:
% 251.13/59.80 | | | | | | | | | | (122) e4 = e2
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | REDUCE: (60), (122) imply:
% 251.13/59.80 | | | | | | | | | | (123) $false
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | CLOSE: (123) is inconsistent.
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | (124) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 =
% 251.13/59.80 | | | | | | | | | | e4 & op(e0, e0) = e4)
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | BETA: splitting (124) gives:
% 251.13/59.80 | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | (125) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | REF_CLOSE: (14), (51), (80), (125) are inconsistent by
% 251.13/59.80 | | | | | | | | | | | sub-proof #912.
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | (126) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | ALPHA: (126) implies:
% 251.13/59.80 | | | | | | | | | | | (127) all_252_24 = e4
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | BETA: splitting (66) gives:
% 251.13/59.80 | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | (128) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 251.13/59.80 | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | REF_CLOSE: (13), (14), (32), (34), (39), (128) are
% 251.13/59.80 | | | | | | | | | | | | inconsistent by sub-proof #925.
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | (129) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 251.13/59.80 | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 251.13/59.80 | | | | | | | | | | | | op(e1, e0) = e2)
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | BETA: splitting (129) gives:
% 251.13/59.80 | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | (130) all_252_14 = e2 & op(e1, e2) = e2
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | ALPHA: (130) implies:
% 251.13/59.80 | | | | | | | | | | | | | (131) all_252_14 = e2
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | REF_CLOSE: (14), (18), (23), (26), (28), (29), (31), (40),
% 251.13/59.80 | | | | | | | | | | | | | (61), (84), (100), (131) are inconsistent by
% 251.13/59.80 | | | | | | | | | | | | | sub-proof #506.
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | (132) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 251.13/59.80 | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.80 | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | (133) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.80 | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | ALPHA: (133) implies:
% 251.13/59.80 | | | | | | | | | | | | | | (134) all_252_15 = e2
% 251.13/59.80 | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 251.13/59.80 | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | (135) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 251.13/59.80 | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 251.13/59.80 | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 251.13/59.80 | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | (136) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.80 | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 251.13/59.80 | | | | | | | | | | | | | | | | (137) all_252_9 = e4
% 251.13/59.80 | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 251.13/59.80 | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | (138) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 251.13/59.80 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (139) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (74), (139) are inconsistent by sub-proof
% 251.13/59.80 | | | | | | | | | | | | | | | | | | #565.
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (140) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (141) op(e0, e3) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (45), (141) are inconsistent by
% 251.13/59.80 | | | | | | | | | | | | | | | | | | sub-proof #714.
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | (142) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 251.13/59.80 | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 251.13/59.80 | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 251.13/59.80 | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (143) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (144) op(e0, e2) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (28), (29), (144) are inconsistent by
% 251.13/59.80 | | | | | | | | | | | | | | | | | | sub-proof #907.
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | (145) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 251.13/59.80 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 251.13/59.80 | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.80 | | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | | (146) all_252_23 = e1 & op(e0, e1) = e1
% 251.13/59.80 | | | | | | | | | | | | | | | | | | |
% 251.13/59.80 | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | (147) all_252_23 = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | (148) op(e0, e1) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | (149) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | (150) all_252_9 = e0 & op(e4, e1) = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (137), (150) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | #505.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | (151) all_252_10 = e0 & op(e3, e1) = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (38), (49), (151) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | sub-proof #726.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | (152) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | (153) all_252_11 = e0 & op(e2, e1) = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | (154) all_252_11 = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_9 = e3 & op(e4, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (157) op(e4, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (48), (53), (157) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_10 = e3 & op(e3, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_10 = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (160) op(e3, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | (161) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (163) op(e3, e4) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (14), (163) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #607.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_252_3 = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (14), (26), (38), (43), (49), (52),
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (61), (64), (68), (165), (166) are
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #504.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (167) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 &
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_5 = e2 & op(e3, e2) = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (104), (168) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | #862.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_10 = e2 & op(e3, e1) = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) op(e3, e1) = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (38), (171) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_17 = e2 & op(e3, e0) = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_17 = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (38), (43), (49), (52), (56), (61),
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (68), (84), (85), (165), (174) are
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #503.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_252_5 = e4 & op(e3, e2) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) op(e3, e2) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (61), (82), (177) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #502.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) op(e3, e1) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (38), (83), (160), (180) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #614.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_17 = e4 & op(e3, e0) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_17 = e4
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (182) imply:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) e4 = e2
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (183) imply:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) $false
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 =
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 &
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_5 = e1 & op(e3, e2) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (187) op(e3, e2) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (61), (187) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #929.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | (188) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_10 = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (159), (190) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | #693.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (192) op(e3, e0) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (52), (58), (192) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | (193) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_11 = e3 & op(e2, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (154), (194) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | #725.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | (195) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (134), (196) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | #501.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_23 = e3 & op(e0, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | (198) op(e0, e1) = e3
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (37), (148), (198) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #915.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | (199) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | (200) all_252_15 = e0 & op(e1, e1) = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (134), (200) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | #500.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | (201) all_252_23 = e0 & op(e0, e1) = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | (202) all_252_23 = e0
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (147), (202) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | | #515.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | (203) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (127), (203) are inconsistent by sub-proof
% 251.13/59.81 | | | | | | | | | | | | | | | | | | | #499.
% 251.13/59.81 | | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | (204) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.81 | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (36), (38), (204) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | | | sub-proof #914.
% 251.13/59.81 | | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | (205) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 251.13/59.81 | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 251.13/59.81 | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 251.13/59.81 | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (44), (51), (60), (80), (134), (205)
% 251.13/59.81 | | | | | | | | | | | | | | | are inconsistent by sub-proof #911.
% 251.13/59.81 | | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | Case 2:
% 251.13/59.81 | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | (206) all_252_19 = e2 & op(e1, e0) = e2
% 251.13/59.81 | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | ALPHA: (206) implies:
% 251.13/59.81 | | | | | | | | | | | | | | (207) op(e1, e0) = e2
% 251.13/59.81 | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (25), (207) are inconsistent by
% 251.13/59.81 | | | | | | | | | | | | | | sub-proof #909.
% 251.13/59.81 | | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | | |
% 251.13/59.81 | | | | | | | | | End of split
% 251.13/59.81 | | | | | | | | |
% 251.13/59.81 | | | | | | | | End of split
% 251.13/59.81 | | | | | | | |
% 251.13/59.81 | | | | | | | End of split
% 251.13/59.81 | | | | | | |
% 251.13/59.81 | | | | | | End of split
% 251.13/59.81 | | | | | |
% 251.13/59.81 | | | | | End of split
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | End of split
% 251.13/59.81 | | | |
% 251.13/59.81 | | | Case 2:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | (208) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1,
% 251.13/59.81 | | | | e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | BETA: splitting (208) gives:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | Case 1:
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | | (209) all_252_8 = e3 & op(e2, e2) = e3
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | | ALPHA: (209) implies:
% 251.13/59.81 | | | | | (210) all_252_8 = e3
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | | REF_CLOSE: (83), (100), (210) are inconsistent by sub-proof #936.
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | Case 2:
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | | (211) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 251.13/59.81 | | | | | op(e0, e2) = e3)
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | | REF_CLOSE: (6), (14), (54), (71), (83), (211) are inconsistent by
% 251.13/59.81 | | | | | sub-proof #856.
% 251.13/59.81 | | | | |
% 251.13/59.81 | | | | End of split
% 251.13/59.81 | | | |
% 251.13/59.81 | | | End of split
% 251.13/59.81 | | |
% 251.13/59.81 | | Case 2:
% 251.13/59.81 | | |
% 251.13/59.81 | | | (212) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 251.13/59.81 | | | e0) = e4)
% 251.13/59.81 | | |
% 251.13/59.81 | | | REF_CLOSE: (14), (17), (21), (44), (65), (212) are inconsistent by
% 251.13/59.81 | | | sub-proof #933.
% 251.13/59.81 | | |
% 251.13/59.81 | | End of split
% 251.13/59.81 | |
% 251.13/59.81 | End of split
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #499 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.81 (2) all_252_24 = e4
% 251.13/59.81 (3) ~ (e4 = e1)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | ALPHA: (1) implies:
% 251.13/59.81 | (4) all_252_24 = e1
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.81 | (5) e4 = e1
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (5) imply:
% 251.13/59.81 | (6) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (6) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #500 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_15 = e0 & op(e1, e1) = e0
% 251.13/59.81 (2) all_252_15 = e2
% 251.13/59.81 (3) ~ (e2 = e0)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | ALPHA: (1) implies:
% 251.13/59.81 | (4) all_252_15 = e0
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.81 | (5) e2 = e0
% 251.13/59.81 |
% 251.13/59.81 | SIMP: (5) implies:
% 251.13/59.81 | (6) e2 = e0
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (6) imply:
% 251.13/59.81 | (7) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (7) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #501 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.81 (2) all_252_15 = e2
% 251.13/59.81 (3) ~ (e3 = e2)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | ALPHA: (1) implies:
% 251.13/59.81 | (4) all_252_15 = e3
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.81 | (5) e3 = e2
% 251.13/59.81 |
% 251.13/59.81 | SIMP: (5) implies:
% 251.13/59.81 | (6) e3 = e2
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (6) imply:
% 251.13/59.81 | (7) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (7) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #502 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (2) op(e3, e2) = all_8_2
% 251.13/59.81 (3) op(e3, e2) = e4
% 251.13/59.81 (4) ~ (all_8_2 = e4)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | GROUND_INST: instantiating (1) with all_8_2, e4, e2, e3, simplifying with (2),
% 251.13/59.81 | (3) gives:
% 251.13/59.81 | (5) all_8_2 = e4
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (4), (5) imply:
% 251.13/59.81 | (6) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (6) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #503 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.81 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.81 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.81 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (3) all_252_3 = e1
% 251.13/59.81 (4) ~ (e4 = e0)
% 251.13/59.81 (5) ~ (e4 = e1)
% 251.13/59.81 (6) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.13/59.81 (7) op(e3, e1) = all_36_2
% 251.13/59.81 (8) ~ (all_8_2 = e0)
% 251.13/59.81 (9) ~ (all_36_2 = e0)
% 251.13/59.81 (10) op(e3, e0) = all_48_2
% 251.13/59.81 (11) ~ (all_48_2 = e0)
% 251.13/59.81 (12) op(e3, e2) = all_8_2
% 251.13/59.81 (13) ~ (all_244_3 = e0)
% 251.13/59.81 (14) op(e3, e3) = all_244_3
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | BETA: splitting (6) gives:
% 251.13/59.81 |
% 251.13/59.81 | Case 1:
% 251.13/59.81 | |
% 251.13/59.81 | | (15) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.81 | |
% 251.13/59.81 | | ALPHA: (15) implies:
% 251.13/59.81 | | (16) all_252_2 = e4
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (13), (14), (16)
% 251.13/59.81 | | are inconsistent by sub-proof #569.
% 251.13/59.81 | |
% 251.13/59.81 | Case 2:
% 251.13/59.81 | |
% 251.13/59.81 | | (17) all_252_3 = e4 & op(e3, e3) = e4
% 251.13/59.81 | |
% 251.13/59.81 | | ALPHA: (17) implies:
% 251.13/59.81 | | (18) all_252_3 = e4
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (3), (5), (18) are inconsistent by sub-proof #772.
% 251.13/59.81 | |
% 251.13/59.81 | End of split
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #504 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.81 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.81 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.81 (2) ~ (e2 = e0)
% 251.13/59.81 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (4) all_252_3 = e1
% 251.13/59.81 (5) ~ (e2 = e1)
% 251.13/59.81 (6) op(e3, e1) = all_36_2
% 251.13/59.81 (7) ~ (all_8_2 = e0)
% 251.13/59.81 (8) ~ (all_36_2 = e0)
% 251.13/59.81 (9) op(e3, e0) = all_48_2
% 251.13/59.81 (10) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.13/59.81 (11) ~ (all_48_2 = e0)
% 251.13/59.81 (12) op(e3, e2) = all_8_2
% 251.13/59.81 (13) ~ (all_244_3 = e0)
% 251.13/59.81 (14) op(e3, e3) = all_244_3
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | BETA: splitting (10) gives:
% 251.13/59.81 |
% 251.13/59.81 | Case 1:
% 251.13/59.81 | |
% 251.13/59.81 | | (15) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.81 | |
% 251.13/59.81 | | ALPHA: (15) implies:
% 251.13/59.81 | | (16) all_252_2 = e2
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (12), (13), (14), (16)
% 251.13/59.81 | | are inconsistent by sub-proof #571.
% 251.13/59.81 | |
% 251.13/59.81 | Case 2:
% 251.13/59.81 | |
% 251.13/59.81 | | (17) all_252_3 = e2 & op(e3, e3) = e2
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (4), (5), (17) are inconsistent by sub-proof #849.
% 251.13/59.81 | |
% 251.13/59.81 | End of split
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #505 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_9 = e0 & op(e4, e1) = e0
% 251.13/59.81 (2) all_252_9 = e4
% 251.13/59.81 (3) ~ (e4 = e0)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | ALPHA: (1) implies:
% 251.13/59.81 | (4) all_252_9 = e0
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.81 | (5) e4 = e0
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (5) imply:
% 251.13/59.81 | (6) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (6) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #506 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_8 = e4
% 251.13/59.81 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (3) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 251.13/59.81 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 251.13/59.81 | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.81 (4) op(e4, e2) = all_6_2
% 251.13/59.81 (5) ~ (e2 = e1)
% 251.13/59.81 (6) op(e0, e2) = all_28_2
% 251.13/59.81 (7) ~ (e4 = e1)
% 251.13/59.81 (8) ~ (all_28_2 = e1)
% 251.13/59.81 (9) ~ (all_6_2 = e1)
% 251.13/59.81 (10) ~ (all_8_2 = e1)
% 251.13/59.81 (11) all_252_14 = e2
% 251.13/59.81 (12) op(e3, e2) = all_8_2
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | BETA: splitting (3) gives:
% 251.13/59.81 |
% 251.13/59.81 | Case 1:
% 251.13/59.81 | |
% 251.13/59.81 | | (13) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 251.13/59.81 | | e1)
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (2), (4), (9), (10), (12), (13) are inconsistent by sub-proof
% 251.13/59.81 | | #928.
% 251.13/59.81 | |
% 251.13/59.81 | Case 2:
% 251.13/59.81 | |
% 251.13/59.81 | | (14) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.81 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.81 | |
% 251.13/59.81 | | BETA: splitting (14) gives:
% 251.13/59.81 | |
% 251.13/59.81 | | Case 1:
% 251.13/59.81 | | |
% 251.13/59.81 | | | (15) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.81 | | |
% 251.13/59.81 | | | REF_CLOSE: (1), (7), (15) are inconsistent by sub-proof #644.
% 251.13/59.81 | | |
% 251.13/59.81 | | Case 2:
% 251.13/59.81 | | |
% 251.13/59.81 | | | (16) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 251.13/59.81 | | | e2) = e1)
% 251.13/59.81 | | |
% 251.13/59.81 | | | BETA: splitting (16) gives:
% 251.13/59.81 | | |
% 251.13/59.81 | | | Case 1:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | (17) all_252_14 = e1 & op(e1, e2) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | REF_CLOSE: (5), (11), (17) are inconsistent by sub-proof #753.
% 251.13/59.81 | | | |
% 251.13/59.81 | | | Case 2:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | (18) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | ALPHA: (18) implies:
% 251.13/59.81 | | | | (19) op(e0, e2) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | REF_CLOSE: (2), (6), (8), (19) are inconsistent by sub-proof #907.
% 251.13/59.81 | | | |
% 251.13/59.81 | | | End of split
% 251.13/59.81 | | |
% 251.13/59.81 | | End of split
% 251.13/59.81 | |
% 251.13/59.81 | End of split
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #507 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_5 = e3
% 251.13/59.81 (2) all_252_5 = e2
% 251.13/59.81 (3) ~ (e3 = e2)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.81 | (4) e3 = e2
% 251.13/59.81 |
% 251.13/59.81 | SIMP: (4) implies:
% 251.13/59.81 | (5) e3 = e2
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (5) imply:
% 251.13/59.81 | (6) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (6) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #508 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_6 = e4
% 251.13/59.81 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.81 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.81 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.81 (3) ~ (e2 = e0)
% 251.13/59.81 (4) ~ (e1 = e0)
% 251.13/59.81 (5) op(e3, e4) = e0
% 251.13/59.81 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (7) ~ (e3 = e2)
% 251.13/59.81 (8) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.81 (9) ~ (e2 = e1)
% 251.13/59.81 (10) op(all_26_2, e1) = e4
% 251.13/59.81 (11) ~ (e4 = e1)
% 251.13/59.81 (12) op(e1, e4) = all_16_2
% 251.13/59.81 (13) ~ (e3 = e1)
% 251.13/59.81 (14) op(e3, e1) = all_36_2
% 251.13/59.81 (15) ~ (all_16_2 = e2)
% 251.13/59.81 (16) ~ (all_8_2 = e0)
% 251.13/59.81 (17) ~ (all_36_2 = e0)
% 251.13/59.81 (18) op(e3, e0) = all_48_2
% 251.13/59.81 (19) ~ (all_48_2 = e0)
% 251.13/59.81 (20) op(e2, e4) = all_64_2
% 251.13/59.81 (21) ~ (e4 = e2)
% 251.13/59.81 (22) op(e3, e2) = all_8_2
% 251.13/59.81 (23) ~ (all_64_2 = all_16_2)
% 251.13/59.81 (24) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.81 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.81 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.81 (25) ~ (all_244_3 = e0)
% 251.13/59.81 (26) op(e2, e4) = all_162_1
% 251.13/59.81 (27) op(e3, e3) = all_244_3
% 251.13/59.81 (28) op(all_26_2, all_16_2) = e1
% 251.13/59.81 (29) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.81 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.81 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.81 (30) all_252_20 = e3
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | BETA: splitting (29) gives:
% 251.13/59.81 |
% 251.13/59.81 | Case 1:
% 251.13/59.81 | |
% 251.13/59.81 | | (31) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 251.13/59.81 | | e1)
% 251.13/59.81 | |
% 251.13/59.81 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (14), (15), (16),
% 251.13/59.81 | | (17), (18), (19), (21), (22), (24), (25), (27), (30), (31) are
% 251.13/59.81 | | inconsistent by sub-proof #517.
% 251.13/59.81 | |
% 251.13/59.81 | Case 2:
% 251.13/59.81 | |
% 251.13/59.81 | | (32) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.81 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.81 | |
% 251.13/59.81 | | BETA: splitting (32) gives:
% 251.13/59.81 | |
% 251.13/59.81 | | Case 1:
% 251.13/59.81 | | |
% 251.13/59.81 | | | (33) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.81 | | |
% 251.13/59.81 | | | REF_CLOSE: (1), (11), (33) are inconsistent by sub-proof #903.
% 251.13/59.81 | | |
% 251.13/59.81 | | Case 2:
% 251.13/59.81 | | |
% 251.13/59.81 | | | (34) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 251.13/59.81 | | | e4) = e1)
% 251.13/59.81 | | |
% 251.13/59.81 | | | BETA: splitting (34) gives:
% 251.13/59.81 | | |
% 251.13/59.81 | | | Case 1:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | (35) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | ALPHA: (35) implies:
% 251.13/59.81 | | | | (36) op(e1, e4) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | ALPHA: (8) implies:
% 251.13/59.81 | | | | (37) op(e2, e4) = e4
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | GROUND_INST: instantiating (6) with all_16_2, e1, e4, e1, simplifying
% 251.13/59.81 | | | | with (12), (36) gives:
% 251.13/59.81 | | | | (38) all_16_2 = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | GROUND_INST: instantiating (6) with all_64_2, all_162_1, e4, e2,
% 251.13/59.81 | | | | simplifying with (20), (26) gives:
% 251.13/59.81 | | | | (39) all_162_1 = all_64_2
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | GROUND_INST: instantiating (6) with e4, all_162_1, e4, e2, simplifying
% 251.13/59.81 | | | | with (26), (37) gives:
% 251.13/59.81 | | | | (40) all_162_1 = e4
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | COMBINE_EQS: (39), (40) imply:
% 251.13/59.81 | | | | (41) all_64_2 = e4
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | SIMP: (41) implies:
% 251.13/59.81 | | | | (42) all_64_2 = e4
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | REF_CLOSE: (6), (10), (11), (28), (38) are inconsistent by sub-proof
% 251.13/59.81 | | | | #510.
% 251.13/59.81 | | | |
% 251.13/59.81 | | | Case 2:
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | (43) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.81 | | | |
% 251.13/59.81 | | | | REF_CLOSE: (13), (30), (43) are inconsistent by sub-proof #509.
% 251.13/59.81 | | | |
% 251.13/59.81 | | | End of split
% 251.13/59.81 | | |
% 251.13/59.81 | | End of split
% 251.13/59.81 | |
% 251.13/59.81 | End of split
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #509 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.81 (2) all_252_20 = e3
% 251.13/59.81 (3) ~ (e3 = e1)
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | ALPHA: (1) implies:
% 251.13/59.81 | (4) all_252_20 = e1
% 251.13/59.81 |
% 251.13/59.81 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.81 | (5) e3 = e1
% 251.13/59.81 |
% 251.13/59.81 | SIMP: (5) implies:
% 251.13/59.81 | (6) e3 = e1
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (3), (6) imply:
% 251.13/59.81 | (7) $false
% 251.13/59.81 |
% 251.13/59.81 | CLOSE: (7) is inconsistent.
% 251.13/59.81 |
% 251.13/59.81 End of proof
% 251.13/59.81
% 251.13/59.81 Sub-proof #510 shows that the following formulas are inconsistent:
% 251.13/59.81 ----------------------------------------------------------------
% 251.13/59.81 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.81 (2) op(all_26_2, e1) = e4
% 251.13/59.81 (3) ~ (e4 = e1)
% 251.13/59.81 (4) all_16_2 = e1
% 251.13/59.81 (5) op(all_26_2, all_16_2) = e1
% 251.13/59.81
% 251.13/59.81 Begin of proof
% 251.13/59.81 |
% 251.13/59.81 | REDUCE: (4), (5) imply:
% 251.13/59.81 | (6) op(all_26_2, e1) = e1
% 251.13/59.81 |
% 251.13/59.81 | GROUND_INST: instantiating (1) with e4, e1, e1, all_26_2, simplifying with
% 251.13/59.81 | (2), (6) gives:
% 251.13/59.82 | (7) e4 = e1
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (3), (7) imply:
% 251.13/59.82 | (8) $false
% 251.13/59.82 |
% 251.13/59.82 | CLOSE: (8) is inconsistent.
% 251.13/59.82 |
% 251.13/59.82 End of proof
% 251.13/59.82
% 251.13/59.82 Sub-proof #511 shows that the following formulas are inconsistent:
% 251.13/59.82 ----------------------------------------------------------------
% 251.13/59.82 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.82 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3)
% 251.13/59.82 (3) ~ (e3 = e0)
% 251.13/59.82 (4) op(e4, e4) = all_244_0
% 251.13/59.82 (5) all_252_1 = e0
% 251.13/59.82 (6) ~ (all_244_0 = e3)
% 251.13/59.82
% 251.13/59.82 Begin of proof
% 251.13/59.82 |
% 251.13/59.82 | BETA: splitting (2) gives:
% 251.13/59.82 |
% 251.13/59.82 | Case 1:
% 251.13/59.82 | |
% 251.13/59.82 | | (7) all_252_0 = e3 & op(e4, e4) = e3
% 251.13/59.82 | |
% 251.13/59.82 | | ALPHA: (7) implies:
% 251.13/59.82 | | (8) op(e4, e4) = e3
% 251.13/59.82 | |
% 251.13/59.82 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #813.
% 251.13/59.82 | |
% 251.13/59.82 | Case 2:
% 251.13/59.82 | |
% 251.13/59.82 | | (9) all_252_1 = e3 & op(e4, e3) = e3
% 251.13/59.82 | |
% 251.13/59.82 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #840.
% 251.13/59.82 | |
% 251.13/59.82 | End of split
% 251.13/59.82 |
% 251.13/59.82 End of proof
% 251.13/59.82
% 251.13/59.82 Sub-proof #512 shows that the following formulas are inconsistent:
% 251.13/59.82 ----------------------------------------------------------------
% 251.13/59.82 (1) all_252_21 = e2
% 251.13/59.82 (2) ~ (all_10_2 = e1)
% 251.13/59.82 (3) ~ (all_10_2 = e4)
% 251.13/59.82 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.82 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.82 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.82 (5) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.82 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.82 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.82 (6) ~ (all_244_8 = e0)
% 251.13/59.82 (7) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.82 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.13/59.82 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.82 (8) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 251.13/59.82 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 251.13/59.82 | (all_252_18 = e0 & op(e2, e0) = e0)
% 251.13/59.82 (9) ~ (all_138_2 = e0) | ( ~ (all_138_0 = e4) & op(e3, e0) = all_138_1 &
% 251.13/59.82 op(e0, all_138_1) = all_138_0 & $i(all_138_0) & $i(all_138_1)) | ( ~
% 251.13/59.82 (all_138_1 = e1) & op(e3, e0) = all_138_1 & $i(all_138_1))
% 251.13/59.82 (10) ~ (all_40_2 = e3)
% 251.13/59.82 (11) all_94_2 = all_38_2
% 251.13/59.82 (12) op(all_38_2, e1) = e2
% 251.13/59.82 (13) ~ (all_28_2 = e3)
% 251.13/59.82 (14) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.82 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.82 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.82 (15) op(e3, e4) = e0
% 251.13/59.82 (16) ~ (all_62_2 = e2)
% 251.13/59.82 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.82 (18) op(e2, e3) = all_10_2
% 251.13/59.82 (19) ~ (e3 = e2)
% 251.13/59.82 (20) op(e2, e2) = all_244_8
% 251.13/59.82 (21) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.13/59.82 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.13/59.82 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.13/59.82 (22) op(e2, e1) = all_38_2
% 251.13/59.82 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.82 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.82 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.82 (24) op(e1, e0) = all_34_2
% 251.13/59.82 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.13/59.82 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.82 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.82 (26) ~ (all_40_2 = e4)
% 251.13/59.82 (27) ~ (all_36_2 = e2)
% 251.13/59.82 (28) op(e4, e2) = all_6_2
% 251.13/59.82 (29) ~ (all_34_2 = e2)
% 251.13/59.82 (30) ~ (e2 = e1)
% 251.13/59.82 (31) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.82 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.82 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.82 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.82 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.82 op(e0, e1) = e0)))
% 251.13/59.82 (32) op(e0, e2) = all_28_2
% 251.13/59.82 (33) ~ (e4 = e1)
% 251.13/59.82 (34) ~ (all_28_2 = e1)
% 251.13/59.82 (35) ~ (all_6_2 = e1)
% 251.13/59.82 (36) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.13/59.82 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.13/59.82 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.13/59.82 (37) op(e1, e4) = all_16_2
% 251.13/59.82 (38) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.82 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.82 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.82 (39) op(e1, e3) = all_62_2
% 251.13/59.82 (40) ~ (e3 = e0)
% 251.13/59.82 (41) ~ (all_40_2 = all_10_2)
% 251.13/59.82 (42) all_252_2 = e0
% 251.13/59.82 (43) ~ (all_36_2 = e4)
% 251.13/59.82 (44) ~ (all_22_2 = e4)
% 251.13/59.82 (45) ~ (e3 = e1)
% 251.13/59.82 (46) op(e3, e1) = all_36_2
% 251.13/59.82 (47) ~ (all_16_2 = e2)
% 251.13/59.82 (48) ~ (all_8_2 = e1)
% 251.13/59.82 (49) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.82 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.82 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.82 (50) ~ (all_22_2 = e1)
% 251.13/59.82 (51) ~ (all_8_2 = e0)
% 251.13/59.82 (52) ~ (all_38_2 = e4)
% 251.13/59.82 (53) op(e0, e3) = all_22_2
% 251.13/59.82 (54) op(e3, e2) = all_90_1
% 251.13/59.82 (55) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.82 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.82 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.82 (56) op(all_10_2, e3) = e2
% 251.13/59.82 (57) ~ (all_36_2 = e0)
% 251.13/59.82 (58) ~ (e4 = e3)
% 251.13/59.82 (59) op(e0, e1) = all_20_2
% 251.13/59.82 (60) op(e3, e0) = all_48_2
% 251.13/59.82 (61) ~ (all_48_2 = e0)
% 251.13/59.82 (62) ~ (e4 = e2)
% 251.13/59.82 (63) ~ (all_6_2 = e0)
% 251.13/59.82 (64) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.82 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.82 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.82 (65) ~ (all_38_2 = all_10_2)
% 251.13/59.82 (66) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.82 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.82 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.82 (67) ~ (all_20_2 = e4)
% 251.13/59.82 (68) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.82 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.82 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.82 (69) ~ (all_244_3 = e0)
% 251.13/59.82 (70) op(e2, e0) = all_40_2
% 251.13/59.82 (71) ~ (all_20_2 = e3)
% 251.13/59.82 (72) ~ (all_16_2 = e3)
% 251.13/59.82 (73) all_10_2 = e0
% 251.13/59.82 (74) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.82 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.82 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.82 (75) all_138_2 = e0
% 251.13/59.82 (76) op(e3, e3) = all_244_3
% 251.13/59.82 (77) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.82 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.82 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.82 (78) all_90_1 = all_8_2
% 251.13/59.82 (79) ~ (all_10_2 = e2)
% 251.13/59.82 (80) all_252_20 = e3
% 251.13/59.82
% 251.13/59.82 Begin of proof
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (41), (73) imply:
% 251.13/59.82 | (81) ~ (all_40_2 = e0)
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (65), (73) imply:
% 251.13/59.82 | (82) ~ (all_38_2 = e0)
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (3), (73) imply:
% 251.13/59.82 | (83) ~ (e4 = e0)
% 251.13/59.82 |
% 251.13/59.82 | SIMP: (83) implies:
% 251.13/59.82 | (84) ~ (e4 = e0)
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (73), (79) imply:
% 251.13/59.82 | (85) ~ (e2 = e0)
% 251.13/59.82 |
% 251.13/59.82 | SIMP: (85) implies:
% 251.13/59.82 | (86) ~ (e2 = e0)
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (2), (73) imply:
% 251.13/59.82 | (87) ~ (e1 = e0)
% 251.13/59.82 |
% 251.13/59.82 | SIMP: (87) implies:
% 251.13/59.82 | (88) ~ (e1 = e0)
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (56), (73) imply:
% 251.13/59.82 | (89) op(e0, e3) = e2
% 251.13/59.82 |
% 251.13/59.82 | REDUCE: (54), (78) imply:
% 251.13/59.82 | (90) op(e3, e2) = all_8_2
% 251.13/59.82 |
% 251.13/59.82 | BETA: splitting (9) gives:
% 251.13/59.82 |
% 251.13/59.82 | Case 1:
% 251.13/59.82 | |
% 251.13/59.82 | | (91) ~ (all_138_2 = e0)
% 251.13/59.82 | |
% 251.13/59.82 | | REDUCE: (75), (91) imply:
% 251.13/59.82 | | (92) $false
% 251.13/59.82 | |
% 251.13/59.82 | | CLOSE: (92) is inconsistent.
% 251.13/59.82 | |
% 251.13/59.82 | Case 2:
% 251.13/59.82 | |
% 251.13/59.82 | | (93) ( ~ (all_138_0 = e4) & op(e3, e0) = all_138_1 & op(e0, all_138_1) =
% 251.13/59.82 | | all_138_0 & $i(all_138_0) & $i(all_138_1)) | ( ~ (all_138_1 = e1)
% 251.13/59.82 | | & op(e3, e0) = all_138_1 & $i(all_138_1))
% 251.13/59.82 | |
% 251.13/59.82 | | BETA: splitting (8) gives:
% 251.13/59.82 | |
% 251.13/59.82 | | Case 1:
% 251.13/59.82 | | |
% 251.13/59.82 | | | (94) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3)
% 251.13/59.82 | | | = e0)
% 251.13/59.82 | | |
% 251.13/59.82 | | | BETA: splitting (94) gives:
% 251.13/59.82 | | |
% 251.13/59.82 | | | Case 1:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | (95) all_252_6 = e0 & op(e2, e4) = e0
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | ALPHA: (95) implies:
% 251.13/59.82 | | | | (96) all_252_6 = e0
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | REF_CLOSE: (5), (15), (17), (19), (30), (33), (37), (40), (42), (45),
% 251.13/59.82 | | | | (46), (47), (51), (57), (58), (60), (61), (62), (64), (66),
% 251.13/59.82 | | | | (68), (69), (72), (76), (77), (80), (84), (86), (88), (90),
% 251.13/59.82 | | | | (96) are inconsistent by sub-proof #537.
% 251.13/59.82 | | | |
% 251.13/59.82 | | | Case 2:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | (97) all_252_7 = e0 & op(e2, e3) = e0
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | ALPHA: (97) implies:
% 251.13/59.82 | | | | (98) all_252_7 = e0
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | BETA: splitting (93) gives:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | Case 1:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | (99) ~ (all_138_0 = e4) & op(e3, e0) = all_138_1 & op(e0,
% 251.13/59.82 | | | | | all_138_1) = all_138_0 & $i(all_138_0) & $i(all_138_1)
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | ALPHA: (99) implies:
% 251.13/59.82 | | | | | (100) op(e3, e0) = all_138_1
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 251.13/59.82 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.13/59.82 | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 251.13/59.82 | | | | | (35), (36), (37), (38), (39), (40), (43), (44), (45), (46),
% 251.13/59.82 | | | | | (47), (48), (49), (50), (51), (52), (53), (55), (57), (58),
% 251.13/59.82 | | | | | (59), (60), (61), (62), (63), (66), (67), (68), (69), (70),
% 251.13/59.82 | | | | | (71), (74), (76), (77), (80), (82), (84), (86), (88), (89),
% 251.13/59.82 | | | | | (90), (98), (100) are inconsistent by sub-proof #513.
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | Case 2:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | (101) ~ (all_138_1 = e1) & op(e3, e0) = all_138_1 & $i(all_138_1)
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | ALPHA: (101) implies:
% 251.13/59.82 | | | | | (102) op(e3, e0) = all_138_1
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 251.13/59.82 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.13/59.82 | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 251.13/59.82 | | | | | (35), (36), (37), (38), (39), (40), (43), (44), (45), (46),
% 251.13/59.82 | | | | | (47), (48), (49), (50), (51), (52), (53), (55), (57), (58),
% 251.13/59.82 | | | | | (59), (60), (61), (62), (63), (66), (67), (68), (69), (70),
% 251.13/59.82 | | | | | (71), (74), (76), (77), (80), (82), (84), (86), (88), (89),
% 251.13/59.82 | | | | | (90), (98), (102) are inconsistent by sub-proof #513.
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | End of split
% 251.13/59.82 | | | |
% 251.13/59.82 | | | End of split
% 251.13/59.82 | | |
% 251.13/59.82 | | Case 2:
% 251.13/59.82 | | |
% 251.13/59.82 | | | (103) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2,
% 251.13/59.82 | | | e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 251.13/59.82 | | |
% 251.13/59.82 | | | REF_CLOSE: (6), (17), (20), (22), (70), (81), (82), (103) are inconsistent
% 251.13/59.82 | | | by sub-proof #879.
% 251.13/59.82 | | |
% 251.13/59.82 | | End of split
% 251.13/59.82 | |
% 251.13/59.82 | End of split
% 251.13/59.82 |
% 251.13/59.82 End of proof
% 251.13/59.82
% 251.13/59.82 Sub-proof #513 shows that the following formulas are inconsistent:
% 251.13/59.82 ----------------------------------------------------------------
% 251.13/59.82 (1) op(e0, e3) = e2
% 251.13/59.82 (2) all_252_21 = e2
% 251.13/59.82 (3) op(e3, e0) = all_138_1
% 251.13/59.82 (4) ~ (all_10_2 = e4)
% 251.13/59.82 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.82 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.82 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.82 (6) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.82 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.82 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.82 (7) ~ (all_244_8 = e0)
% 251.13/59.82 (8) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.82 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.13/59.82 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.82 (9) ~ (all_40_2 = e3)
% 251.13/59.82 (10) all_94_2 = all_38_2
% 251.13/59.82 (11) op(all_38_2, e1) = e2
% 251.13/59.82 (12) ~ (e2 = e0)
% 251.13/59.82 (13) ~ (e1 = e0)
% 251.13/59.82 (14) ~ (all_28_2 = e3)
% 251.13/59.82 (15) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.82 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.82 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.82 (16) op(e3, e4) = e0
% 251.13/59.82 (17) ~ (all_62_2 = e2)
% 251.13/59.82 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.82 (19) op(e2, e3) = all_10_2
% 251.13/59.82 (20) ~ (e3 = e2)
% 251.13/59.82 (21) ~ (e4 = e0)
% 251.13/59.82 (22) op(e2, e2) = all_244_8
% 251.13/59.82 (23) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.13/59.82 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.13/59.82 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.13/59.82 (24) op(e2, e1) = all_38_2
% 251.13/59.82 (25) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.82 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.82 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.82 (26) op(e1, e0) = all_34_2
% 251.13/59.82 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.13/59.82 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.82 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.82 (28) ~ (all_40_2 = e4)
% 251.13/59.82 (29) ~ (all_36_2 = e2)
% 251.13/59.82 (30) op(e4, e2) = all_6_2
% 251.13/59.82 (31) ~ (all_34_2 = e2)
% 251.13/59.82 (32) ~ (e2 = e1)
% 251.13/59.82 (33) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.82 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.82 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.82 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.82 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.82 op(e0, e1) = e0)))
% 251.13/59.82 (34) op(e0, e2) = all_28_2
% 251.13/59.82 (35) ~ (e4 = e1)
% 251.13/59.82 (36) ~ (all_28_2 = e1)
% 251.13/59.82 (37) all_252_7 = e0
% 251.13/59.82 (38) ~ (all_6_2 = e1)
% 251.13/59.82 (39) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.13/59.82 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.13/59.82 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.13/59.82 (40) op(e1, e4) = all_16_2
% 251.13/59.82 (41) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.82 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.82 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.82 (42) op(e1, e3) = all_62_2
% 251.13/59.82 (43) ~ (e3 = e0)
% 251.13/59.82 (44) ~ (all_38_2 = e0)
% 251.13/59.82 (45) ~ (all_36_2 = e4)
% 251.13/59.82 (46) ~ (all_22_2 = e4)
% 251.13/59.82 (47) ~ (e3 = e1)
% 251.13/59.82 (48) op(e3, e1) = all_36_2
% 251.13/59.82 (49) ~ (all_16_2 = e2)
% 251.13/59.82 (50) ~ (all_8_2 = e1)
% 251.13/59.82 (51) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.82 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.82 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.82 (52) ~ (all_22_2 = e1)
% 251.13/59.82 (53) ~ (all_8_2 = e0)
% 251.13/59.82 (54) ~ (all_38_2 = e4)
% 251.13/59.82 (55) op(e0, e3) = all_22_2
% 251.13/59.82 (56) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.82 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.82 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.82 (57) ~ (all_36_2 = e0)
% 251.13/59.82 (58) ~ (e4 = e3)
% 251.13/59.82 (59) op(e0, e1) = all_20_2
% 251.13/59.82 (60) op(e3, e0) = all_48_2
% 251.13/59.82 (61) ~ (all_48_2 = e0)
% 251.13/59.82 (62) ~ (e4 = e2)
% 251.13/59.82 (63) ~ (all_6_2 = e0)
% 251.13/59.82 (64) op(e3, e2) = all_8_2
% 251.13/59.82 (65) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.82 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.82 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.82 (66) ~ (all_20_2 = e4)
% 251.13/59.82 (67) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.82 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.82 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.82 (68) ~ (all_244_3 = e0)
% 251.13/59.82 (69) op(e2, e0) = all_40_2
% 251.13/59.82 (70) ~ (all_20_2 = e3)
% 251.13/59.82 (71) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.82 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.82 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.82 (72) op(e3, e3) = all_244_3
% 251.13/59.82 (73) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.82 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.82 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.82 (74) all_252_20 = e3
% 251.13/59.82
% 251.13/59.82 Begin of proof
% 251.13/59.82 |
% 251.13/59.82 | GROUND_INST: instantiating (18) with all_48_2, all_138_1, e0, e3, simplifying
% 251.13/59.82 | with (3), (60) gives:
% 251.13/59.82 | (75) all_138_1 = all_48_2
% 251.13/59.82 |
% 251.13/59.82 | BETA: splitting (15) gives:
% 251.13/59.82 |
% 251.13/59.82 | Case 1:
% 251.13/59.82 | |
% 251.13/59.82 | | (76) ~ (all_94_2 = e3)
% 251.13/59.82 | |
% 251.13/59.82 | | REDUCE: (10), (76) imply:
% 251.13/59.82 | | (77) ~ (all_38_2 = e3)
% 251.13/59.82 | |
% 251.13/59.82 | | BETA: splitting (23) gives:
% 251.13/59.82 | |
% 251.13/59.82 | | Case 1:
% 251.13/59.82 | | |
% 251.13/59.82 | | | (78) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3)
% 251.13/59.82 | | | = e3)
% 251.13/59.82 | | |
% 251.13/59.82 | | | BETA: splitting (78) gives:
% 251.13/59.82 | | |
% 251.13/59.82 | | | Case 1:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | (79) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | ALPHA: (79) implies:
% 251.13/59.82 | | | | (80) all_252_6 = e3
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | BETA: splitting (65) gives:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | Case 1:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | (81) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3,
% 251.13/59.82 | | | | | e4) = e2)
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | REF_CLOSE: (6), (12), (13), (16), (18), (21), (32), (35), (47), (48),
% 251.13/59.82 | | | | | (53), (57), (58), (60), (61), (62), (64), (67), (68), (72),
% 251.13/59.82 | | | | | (73), (74), (80), (81) are inconsistent by sub-proof #535.
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | Case 2:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | (82) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 251.13/59.82 | | | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | BETA: splitting (82) gives:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | Case 1:
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | (83) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | ALPHA: (83) implies:
% 251.13/59.82 | | | | | | (84) all_252_6 = e2
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | COMBINE_EQS: (80), (84) imply:
% 251.13/59.82 | | | | | | (85) e3 = e2
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | COMBINE_EQS: (74), (85) imply:
% 251.13/59.82 | | | | | | (86) all_252_20 = e2
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | REF_CLOSE: (2), (5), (12), (13), (14), (18), (20), (21), (32), (33),
% 251.13/59.82 | | | | | | (34), (35), (41), (43), (46), (47), (51), (52), (55),
% 251.13/59.82 | | | | | | (58), (59), (62), (66), (70), (86) are inconsistent by
% 251.13/59.82 | | | | | | sub-proof #524.
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | Case 2:
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | (87) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 251.13/59.82 | | | | | | op(e0, e4) = e2)
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | REF_CLOSE: (2), (5), (12), (13), (14), (18), (20), (21), (32), (33),
% 251.13/59.82 | | | | | | (34), (35), (40), (41), (43), (46), (47), (49), (51),
% 251.13/59.82 | | | | | | (52), (55), (58), (59), (62), (66), (70), (87) are
% 251.13/59.82 | | | | | | inconsistent by sub-proof #523.
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | End of split
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | End of split
% 251.13/59.82 | | | |
% 251.13/59.82 | | | Case 2:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | (88) all_252_7 = e3 & op(e2, e3) = e3
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | REF_CLOSE: (37), (43), (88) are inconsistent by sub-proof #945.
% 251.13/59.82 | | | |
% 251.13/59.82 | | | End of split
% 251.13/59.82 | | |
% 251.13/59.82 | | Case 2:
% 251.13/59.82 | | |
% 251.13/59.82 | | | (89) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1)
% 251.13/59.82 | | | = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.13/59.82 | | |
% 251.13/59.82 | | | BETA: splitting (89) gives:
% 251.13/59.82 | | |
% 251.13/59.82 | | | Case 1:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | (90) all_252_8 = e3 & op(e2, e2) = e3
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | ALPHA: (90) implies:
% 251.13/59.82 | | | | (91) all_252_8 = e3
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | BETA: splitting (56) gives:
% 251.13/59.82 | | | |
% 251.13/59.82 | | | | Case 1:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | (92) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 251.13/59.82 | | | | | e3) = e4)
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | BETA: splitting (92) gives:
% 251.13/59.82 | | | | |
% 251.13/59.82 | | | | | Case 1:
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | (93) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | ALPHA: (93) implies:
% 251.13/59.82 | | | | | | (94) all_252_6 = e4
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | BETA: splitting (25) gives:
% 251.13/59.82 | | | | | |
% 251.13/59.82 | | | | | | Case 1:
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | | (95) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 251.13/59.82 | | | | | | | op(e3, e2) = e1)
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | | REF_CLOSE: (18), (30), (38), (50), (64), (95) are inconsistent by
% 251.13/59.82 | | | | | | | sub-proof #928.
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | Case 2:
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | | (96) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 251.13/59.82 | | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | | BETA: splitting (96) gives:
% 251.13/59.82 | | | | | | |
% 251.13/59.82 | | | | | | | Case 1:
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | | (97) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | | REF_CLOSE: (47), (91), (97) are inconsistent by sub-proof #522.
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | Case 2:
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | | (98) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 251.13/59.82 | | | | | | | | op(e0, e2) = e1)
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | | BETA: splitting (98) gives:
% 251.13/59.82 | | | | | | | |
% 251.13/59.82 | | | | | | | | Case 1:
% 251.13/59.82 | | | | | | | | |
% 251.13/59.82 | | | | | | | | | (99) all_252_14 = e1 & op(e1, e2) = e1
% 251.13/59.82 | | | | | | | | |
% 251.13/59.82 | | | | | | | | | ALPHA: (99) implies:
% 251.13/59.82 | | | | | | | | | (100) all_252_14 = e1
% 251.13/59.82 | | | | | | | | |
% 251.13/59.82 | | | | | | | | | BETA: splitting (39) gives:
% 251.13/59.82 | | | | | | | | |
% 251.13/59.82 | | | | | | | | | Case 1:
% 251.13/59.82 | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | (101) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 251.13/59.82 | | | | | | | | | | e0 & op(e3, e2) = e0)
% 251.13/59.82 | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | BETA: splitting (101) gives:
% 251.13/59.82 | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | Case 1:
% 251.13/59.82 | | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | | (102) all_252_4 = e0 & op(e4, e2) = e0
% 251.13/59.82 | | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | | REF_CLOSE: (18), (30), (63), (102) are inconsistent by
% 251.13/59.82 | | | | | | | | | | | sub-proof #875.
% 251.13/59.82 | | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | Case 2:
% 251.13/59.82 | | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | | (103) all_252_5 = e0 & op(e3, e2) = e0
% 251.13/59.82 | | | | | | | | | | |
% 251.13/59.82 | | | | | | | | | | | REF_CLOSE: (18), (53), (64), (103) are inconsistent by
% 251.13/59.82 | | | | | | | | | | | sub-proof #874.
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | (104) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.13/59.83 | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 251.13/59.83 | | | | | | | | | | e2) = e0)
% 251.13/59.83 | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | BETA: splitting (104) gives:
% 251.13/59.83 | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | (105) all_252_8 = e0 & op(e2, e2) = e0
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | ALPHA: (105) implies:
% 251.13/59.83 | | | | | | | | | | | (106) op(e2, e2) = e0
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | REF_CLOSE: (7), (18), (22), (106) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | sub-proof #880.
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | (107) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.13/59.83 | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | BETA: splitting (107) gives:
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | (108) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | REF_CLOSE: (13), (100), (108) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | #521.
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | (109) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | ALPHA: (109) implies:
% 251.13/59.83 | | | | | | | | | | | | (110) all_252_22 = e0
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | BETA: splitting (65) gives:
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | (111) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 251.13/59.83 | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | (112) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | ALPHA: (112) implies:
% 251.13/59.83 | | | | | | | | | | | | | | (113) all_252_0 = e2
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | (114) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 251.13/59.83 | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | (115) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | (116) all_252_20 = e4
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (116) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | (117) e4 = e3
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | SIMP: (117) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | (118) e4 = e3
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (118) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | (119) all_252_6 = e3
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (16), (18), (21), (32), (35), (47),
% 251.13/59.83 | | | | | | | | | | | | | | | | (48), (53), (57), (58), (60), (61), (62), (64),
% 251.13/59.83 | | | | | | | | | | | | | | | | (67), (68), (72), (73), (74), (113), (119) are
% 251.13/59.83 | | | | | | | | | | | | | | | | inconsistent by sub-proof #536.
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | (120) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (46), (55), (120) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | sub-proof #805.
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | (121) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 251.13/59.83 | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.13/59.83 | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | (122) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | (123) all_252_22 = e4
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (123) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | (124) e4 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | (125) e4 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (125) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | (126) all_252_6 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (16), (18), (21), (32), (35), (47),
% 251.13/59.83 | | | | | | | | | | | | | | | | (48), (53), (57), (58), (60), (61), (62), (64),
% 251.13/59.83 | | | | | | | | | | | | | | | | (67), (68), (72), (73), (74), (113), (126) are
% 251.13/59.83 | | | | | | | | | | | | | | | | inconsistent by sub-proof #550.
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | (127) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 251.13/59.83 | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | (128) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (59), (66), (128) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | (129) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | (130) all_252_24 = e4
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | (131) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 =
% 251.13/59.83 | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (13), (16), (18), (20), (32), (40),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | (48), (49), (53), (57), (60), (61), (62), (64),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | (65), (68), (72), (74), (94), (131) are
% 251.13/59.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517.
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | (132) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 =
% 251.13/59.83 | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 251.13/59.83 | | | | | | | | | | | | | | | | | | op(e0, e4) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | (133) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (94), (133) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | #903.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | (134) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | (135) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | (136) all_252_12 = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | (137) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (138) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (74), (138) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | #565.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (139) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (140) op(e0, e3) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (32), (140) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | sub-proof #941.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | (141) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (142) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (143) op(e0, e2) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (34), (36), (143) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | (144) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | (145) all_252_23 = e1 & op(e0, e1) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | (146) all_252_23 = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | (147) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (40), (42), (49), (147) are
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | (148) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (149) all_252_14 = e2 & op(e1, e2) = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (150) all_252_14 = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (150) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (151) e2 = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (151) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (152) all_252_0 = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (18), (20), (32), (40), (48), (49),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (53), (57), (60), (61), (62), (64), (65), (68),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (72), (74), (94), (152) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | (153) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (155) all_252_15 = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 =
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_9 = e0 & op(e4, e1) = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_9 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (21), (35), (48), (53), (57), (58),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (61), (62), (64), (67), (68), (72), (74),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (94), (113), (136), (158), (160) are inconsistent
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #516.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_10 = e4 & op(e3, e1) = e4
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (45), (48), (161) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (24), (54), (59), (62), (66), (155), (162)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #911.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_10 = e0 & op(e3, e1) = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (48), (57), (163) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #726.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 &
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_252_11 = e0 & op(e2, e1) = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (24), (44), (165) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #904.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_15 = e0 & op(e1, e1) = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_15 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (168) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) e2 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (169) imply:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_0 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (13), (18), (20), (21), (32), (35),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (53), (57), (58), (60), (61), (62),
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (67), (68), (72), (73), (74), (170)
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #559.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_252_23 = e0 & op(e0, e1) = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_23 = e0
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (146), (172) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #515.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_19 = e2 & op(e1, e0) = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (174) op(e1, e0) = e2
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (26), (31), (174) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #909.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | (176) all_252_24 = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (130), (176) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | | #514.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | (177) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (74), (177) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | | #565.
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | (178) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | ALPHA: (178) implies:
% 251.13/59.83 | | | | | | | | | | | | | | (179) all_252_2 = e2
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (18), (48), (53), (57), (60), (61),
% 251.13/59.83 | | | | | | | | | | | | | | (64), (68), (72), (179) are inconsistent by
% 251.13/59.83 | | | | | | | | | | | | | | sub-proof #571.
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | (180) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 251.13/59.83 | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 251.13/59.83 | | | | | | | | | | | | | op(e0, e4) = e2)
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | BETA: splitting (180) gives:
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | Case 1:
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | (181) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | REF_CLOSE: (62), (94), (181) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | #921.
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | (182) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 251.13/59.83 | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (12), (13), (14), (18), (20), (21),
% 251.13/59.83 | | | | | | | | | | | | | | (32), (33), (34), (35), (40), (41), (43), (46),
% 251.13/59.83 | | | | | | | | | | | | | | (47), (49), (51), (52), (55), (58), (59), (62),
% 251.13/59.83 | | | | | | | | | | | | | | (66), (70), (182) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | | | | | | | | | #523.
% 251.13/59.83 | | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | | |
% 251.13/59.83 | | | | | | | | | End of split
% 251.13/59.83 | | | | | | | | |
% 251.13/59.83 | | | | | | | | Case 2:
% 251.13/59.83 | | | | | | | | |
% 251.13/59.83 | | | | | | | | | (183) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.83 | | | | | | | | |
% 251.13/59.83 | | | | | | | | | ALPHA: (183) implies:
% 251.13/59.83 | | | | | | | | | (184) op(e0, e2) = e1
% 251.13/59.83 | | | | | | | | |
% 251.13/59.83 | | | | | | | | | REF_CLOSE: (18), (34), (36), (184) are inconsistent by
% 251.13/59.83 | | | | | | | | | sub-proof #907.
% 251.13/59.83 | | | | | | | | |
% 251.13/59.83 | | | | | | | | End of split
% 251.13/59.83 | | | | | | | |
% 251.13/59.83 | | | | | | | End of split
% 251.13/59.83 | | | | | | |
% 251.13/59.83 | | | | | | End of split
% 251.13/59.83 | | | | | |
% 251.13/59.83 | | | | | Case 2:
% 251.13/59.83 | | | | | |
% 251.13/59.83 | | | | | | (185) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.83 | | | | | |
% 251.13/59.83 | | | | | | ALPHA: (185) implies:
% 251.13/59.83 | | | | | | (186) op(e2, e3) = e4
% 251.13/59.83 | | | | | |
% 251.13/59.83 | | | | | | REF_CLOSE: (4), (18), (19), (186) are inconsistent by sub-proof
% 251.13/59.83 | | | | | | #953.
% 251.13/59.83 | | | | | |
% 251.13/59.83 | | | | | End of split
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | Case 2:
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | (187) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 251.13/59.83 | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | REF_CLOSE: (18), (24), (28), (54), (58), (69), (91), (187) are
% 251.13/59.83 | | | | | inconsistent by sub-proof #932.
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | End of split
% 251.13/59.83 | | | |
% 251.13/59.83 | | | Case 2:
% 251.13/59.83 | | | |
% 251.13/59.83 | | | | (188) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2,
% 251.13/59.83 | | | | e0) = e3)
% 251.13/59.83 | | | |
% 251.13/59.83 | | | | BETA: splitting (188) gives:
% 251.13/59.83 | | | |
% 251.13/59.83 | | | | Case 1:
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | (189) all_252_11 = e3 & op(e2, e1) = e3
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | REF_CLOSE: (18), (24), (77), (189) are inconsistent by sub-proof #900.
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | Case 2:
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | (190) all_252_18 = e3 & op(e2, e0) = e3
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | | REF_CLOSE: (9), (18), (69), (190) are inconsistent by sub-proof #899.
% 251.13/59.83 | | | | |
% 251.13/59.83 | | | | End of split
% 251.13/59.83 | | | |
% 251.13/59.83 | | | End of split
% 251.13/59.83 | | |
% 251.13/59.83 | | End of split
% 251.13/59.83 | |
% 251.13/59.83 | Case 2:
% 251.13/59.83 | |
% 251.13/59.83 | | (191) all_94_2 = e3
% 251.13/59.83 | |
% 251.13/59.83 | | REF_CLOSE: (10), (11), (18), (29), (48), (191) are inconsistent by sub-proof
% 251.13/59.83 | | #983.
% 251.13/59.83 | |
% 251.13/59.83 | End of split
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #514 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_24 = e4
% 251.13/59.83 (2) all_252_24 = e1
% 251.13/59.83 (3) ~ (e4 = e1)
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.83 | (4) e4 = e1
% 251.13/59.83 |
% 251.13/59.83 | SIMP: (4) implies:
% 251.13/59.83 | (5) e4 = e1
% 251.13/59.83 |
% 251.13/59.83 | REDUCE: (3), (5) imply:
% 251.13/59.83 | (6) $false
% 251.13/59.83 |
% 251.13/59.83 | CLOSE: (6) is inconsistent.
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #515 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_23 = e1
% 251.13/59.83 (2) all_252_23 = e0
% 251.13/59.83 (3) ~ (e1 = e0)
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.83 | (4) e1 = e0
% 251.13/59.83 |
% 251.13/59.83 | SIMP: (4) implies:
% 251.13/59.83 | (5) e1 = e0
% 251.13/59.83 |
% 251.13/59.83 | REDUCE: (3), (5) imply:
% 251.13/59.83 | (6) $false
% 251.13/59.83 |
% 251.13/59.83 | CLOSE: (6) is inconsistent.
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #516 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_6 = e4
% 251.13/59.83 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.83 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.83 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.83 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.83 (4) ~ (e4 = e0)
% 251.13/59.83 (5) all_252_0 = e2
% 251.13/59.83 (6) ~ (e4 = e1)
% 251.13/59.83 (7) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.83 (8) op(e3, e1) = all_36_2
% 251.13/59.83 (9) all_252_9 = e0
% 251.13/59.83 (10) ~ (all_8_2 = e0)
% 251.13/59.83 (11) ~ (all_36_2 = e0)
% 251.13/59.83 (12) ~ (e4 = e3)
% 251.13/59.83 (13) op(e3, e0) = all_48_2
% 251.13/59.83 (14) ~ (all_48_2 = e0)
% 251.13/59.83 (15) ~ (e4 = e2)
% 251.13/59.83 (16) op(e3, e2) = all_8_2
% 251.13/59.83 (17) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.83 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.83 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.83 (18) ~ (all_244_3 = e0)
% 251.13/59.83 (19) op(e3, e3) = all_244_3
% 251.13/59.83 (20) all_252_12 = e1
% 251.13/59.83 (21) all_252_20 = e3
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | ALPHA: (7) implies:
% 251.13/59.83 | (22) all_252_9 = e4
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (9), (22) imply:
% 251.13/59.83 | (23) e4 = e0
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (1), (23) imply:
% 251.13/59.83 | (24) all_252_6 = e0
% 251.13/59.83 |
% 251.13/59.83 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 251.13/59.83 | (16), (17), (18), (19), (20), (21), (24) are inconsistent by
% 251.13/59.83 | sub-proof #551.
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #517 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_6 = e4
% 251.13/59.83 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.83 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.83 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.83 (3) ~ (e2 = e0)
% 251.13/59.83 (4) ~ (e1 = e0)
% 251.13/59.83 (5) op(e3, e4) = e0
% 251.13/59.83 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.83 (7) ~ (e3 = e2)
% 251.13/59.83 (8) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.83 (9) ~ (e2 = e1)
% 251.13/59.83 (10) op(e1, e4) = all_16_2
% 251.13/59.83 (11) op(e3, e1) = all_36_2
% 251.13/59.83 (12) ~ (all_16_2 = e2)
% 251.13/59.83 (13) ~ (all_8_2 = e0)
% 251.13/59.83 (14) ~ (all_36_2 = e0)
% 251.13/59.83 (15) op(e3, e0) = all_48_2
% 251.13/59.83 (16) ~ (all_48_2 = e0)
% 251.13/59.83 (17) ~ (e4 = e2)
% 251.13/59.83 (18) op(e3, e2) = all_8_2
% 251.13/59.83 (19) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.83 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.83 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.83 (20) ~ (all_244_3 = e0)
% 251.13/59.83 (21) op(e3, e3) = all_244_3
% 251.13/59.83 (22) all_252_20 = e3
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | BETA: splitting (8) gives:
% 251.13/59.83 |
% 251.13/59.83 | Case 1:
% 251.13/59.83 | |
% 251.13/59.83 | | (23) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.83 | |
% 251.13/59.83 | | ALPHA: (23) implies:
% 251.13/59.83 | | (24) all_252_0 = e1
% 251.13/59.83 | |
% 251.13/59.83 | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 251.13/59.83 | | (16), (17), (18), (19), (20), (21), (22), (24) are inconsistent
% 251.13/59.83 | | by sub-proof #518.
% 251.13/59.83 | |
% 251.13/59.83 | Case 2:
% 251.13/59.83 | |
% 251.13/59.83 | | (25) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.83 | |
% 251.13/59.83 | | ALPHA: (25) implies:
% 251.13/59.83 | | (26) op(e3, e4) = e1
% 251.13/59.83 | |
% 251.13/59.83 | | REF_CLOSE: (4), (5), (6), (26) are inconsistent by sub-proof #607.
% 251.13/59.83 | |
% 251.13/59.83 | End of split
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #518 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_6 = e4
% 251.13/59.83 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.83 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.83 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.83 (3) ~ (e2 = e0)
% 251.13/59.83 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.83 (5) ~ (e3 = e2)
% 251.13/59.83 (6) ~ (e2 = e1)
% 251.13/59.83 (7) op(e1, e4) = all_16_2
% 251.13/59.83 (8) op(e3, e1) = all_36_2
% 251.13/59.83 (9) ~ (all_16_2 = e2)
% 251.13/59.83 (10) ~ (all_8_2 = e0)
% 251.13/59.83 (11) all_252_0 = e1
% 251.13/59.83 (12) ~ (all_36_2 = e0)
% 251.13/59.83 (13) op(e3, e0) = all_48_2
% 251.13/59.83 (14) ~ (all_48_2 = e0)
% 251.13/59.83 (15) ~ (e4 = e2)
% 251.13/59.83 (16) op(e3, e2) = all_8_2
% 251.13/59.83 (17) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.83 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.83 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.83 (18) ~ (all_244_3 = e0)
% 251.13/59.83 (19) op(e3, e3) = all_244_3
% 251.13/59.83 (20) all_252_20 = e3
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | BETA: splitting (17) gives:
% 251.13/59.83 |
% 251.13/59.83 | Case 1:
% 251.13/59.83 | |
% 251.13/59.83 | | (21) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.13/59.83 | | e2)
% 251.13/59.83 | |
% 251.13/59.83 | | BETA: splitting (21) gives:
% 251.13/59.83 | |
% 251.13/59.83 | | Case 1:
% 251.13/59.83 | | |
% 251.13/59.83 | | | (22) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | ALPHA: (22) implies:
% 251.13/59.83 | | | (23) all_252_0 = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | COMBINE_EQS: (11), (23) imply:
% 251.13/59.83 | | | (24) e2 = e1
% 251.13/59.83 | | |
% 251.13/59.83 | | | SIMP: (24) implies:
% 251.13/59.83 | | | (25) e2 = e1
% 251.13/59.83 | | |
% 251.13/59.83 | | | REDUCE: (6), (25) imply:
% 251.13/59.83 | | | (26) $false
% 251.13/59.83 | | |
% 251.13/59.83 | | | CLOSE: (26) is inconsistent.
% 251.13/59.83 | | |
% 251.13/59.83 | | Case 2:
% 251.13/59.83 | | |
% 251.13/59.83 | | | (27) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | ALPHA: (27) implies:
% 251.13/59.83 | | | (28) all_252_2 = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | REF_CLOSE: (2), (3), (4), (8), (10), (12), (13), (14), (16), (18), (19),
% 251.13/59.83 | | | (28) are inconsistent by sub-proof #571.
% 251.13/59.83 | | |
% 251.13/59.83 | | End of split
% 251.13/59.83 | |
% 251.13/59.83 | Case 2:
% 251.13/59.83 | |
% 251.13/59.83 | | (29) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.83 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.83 | |
% 251.13/59.83 | | BETA: splitting (29) gives:
% 251.13/59.83 | |
% 251.13/59.83 | | Case 1:
% 251.13/59.83 | | |
% 251.13/59.83 | | | (30) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | ALPHA: (30) implies:
% 251.13/59.83 | | | (31) all_252_6 = e2
% 251.13/59.83 | | |
% 251.13/59.83 | | | REF_CLOSE: (1), (15), (31) are inconsistent by sub-proof #833.
% 251.13/59.83 | | |
% 251.13/59.83 | | Case 2:
% 251.13/59.83 | | |
% 251.13/59.83 | | | (32) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 251.13/59.83 | | | e4) = e2)
% 251.13/59.83 | | |
% 251.13/59.83 | | | REF_CLOSE: (4), (5), (7), (9), (20), (32) are inconsistent by sub-proof
% 251.13/59.83 | | | #519.
% 251.13/59.83 | | |
% 251.13/59.83 | | End of split
% 251.13/59.83 | |
% 251.13/59.83 | End of split
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #519 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.83 (2) ~ (e3 = e2)
% 251.13/59.83 (3) op(e1, e4) = all_16_2
% 251.13/59.83 (4) ~ (all_16_2 = e2)
% 251.13/59.83 (5) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.83 (6) all_252_20 = e3
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | BETA: splitting (5) gives:
% 251.13/59.83 |
% 251.13/59.83 | Case 1:
% 251.13/59.83 | |
% 251.13/59.83 | | (7) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.83 | |
% 251.13/59.83 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #926.
% 251.13/59.83 | |
% 251.13/59.83 | Case 2:
% 251.13/59.83 | |
% 251.13/59.83 | | (8) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.83 | |
% 251.13/59.83 | | ALPHA: (8) implies:
% 251.13/59.83 | | (9) all_252_20 = e2
% 251.13/59.83 | |
% 251.13/59.83 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #520.
% 251.13/59.83 | |
% 251.13/59.83 | End of split
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #520 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_20 = e3
% 251.13/59.83 (2) all_252_20 = e2
% 251.13/59.83 (3) ~ (e3 = e2)
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.83 | (4) e3 = e2
% 251.13/59.83 |
% 251.13/59.83 | SIMP: (4) implies:
% 251.13/59.83 | (5) e3 = e2
% 251.13/59.83 |
% 251.13/59.83 | REDUCE: (3), (5) imply:
% 251.13/59.83 | (6) $false
% 251.13/59.83 |
% 251.13/59.83 | CLOSE: (6) is inconsistent.
% 251.13/59.83 |
% 251.13/59.83 End of proof
% 251.13/59.83
% 251.13/59.83 Sub-proof #521 shows that the following formulas are inconsistent:
% 251.13/59.83 ----------------------------------------------------------------
% 251.13/59.83 (1) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.83 (2) all_252_14 = e1
% 251.13/59.83 (3) ~ (e1 = e0)
% 251.13/59.83
% 251.13/59.83 Begin of proof
% 251.13/59.83 |
% 251.13/59.83 | ALPHA: (1) implies:
% 251.13/59.83 | (4) all_252_14 = e0
% 251.13/59.83 |
% 251.13/59.83 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.83 | (5) e1 = e0
% 251.13/59.83 |
% 251.13/59.83 | REDUCE: (3), (5) imply:
% 251.13/59.83 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #522 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.84 (2) all_252_8 = e3
% 251.13/59.84 (3) ~ (e3 = e1)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_8 = e1
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e3 = e1
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #523 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_21 = e2
% 251.13/59.84 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.84 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.84 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.84 (3) ~ (e2 = e0)
% 251.13/59.84 (4) ~ (e1 = e0)
% 251.13/59.84 (5) ~ (all_28_2 = e3)
% 251.13/59.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.84 (7) ~ (e3 = e2)
% 251.13/59.84 (8) ~ (e4 = e0)
% 251.13/59.84 (9) ~ (e2 = e1)
% 251.13/59.84 (10) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.84 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.84 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.84 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.84 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.84 op(e0, e1) = e0)))
% 251.13/59.84 (11) op(e0, e2) = all_28_2
% 251.13/59.84 (12) ~ (e4 = e1)
% 251.13/59.84 (13) op(e1, e4) = all_16_2
% 251.13/59.84 (14) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.84 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.84 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.84 (15) ~ (e3 = e0)
% 251.13/59.84 (16) ~ (all_22_2 = e4)
% 251.13/59.84 (17) ~ (e3 = e1)
% 251.13/59.84 (18) ~ (all_16_2 = e2)
% 251.13/59.84 (19) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.84 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.84 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.84 (20) ~ (all_22_2 = e1)
% 251.13/59.84 (21) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) =
% 251.13/59.84 e2)
% 251.13/59.84 (22) op(e0, e3) = all_22_2
% 251.13/59.84 (23) ~ (e4 = e3)
% 251.13/59.84 (24) op(e0, e1) = all_20_2
% 251.13/59.84 (25) ~ (e4 = e2)
% 251.13/59.84 (26) ~ (all_20_2 = e4)
% 251.13/59.84 (27) ~ (all_20_2 = e3)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | BETA: splitting (21) gives:
% 251.13/59.84 |
% 251.13/59.84 | Case 1:
% 251.13/59.84 | |
% 251.13/59.84 | | (28) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (6), (13), (18), (28) are inconsistent by sub-proof #926.
% 251.13/59.84 | |
% 251.13/59.84 | Case 2:
% 251.13/59.84 | |
% 251.13/59.84 | | (29) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.84 | |
% 251.13/59.84 | | ALPHA: (29) implies:
% 251.13/59.84 | | (30) all_252_20 = e2
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.13/59.84 | | (14), (15), (16), (17), (19), (20), (22), (23), (24), (25), (26),
% 251.13/59.84 | | (27), (30) are inconsistent by sub-proof #524.
% 251.13/59.84 | |
% 251.13/59.84 | End of split
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #524 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_21 = e2
% 251.13/59.84 (2) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.84 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.13/59.84 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.84 (3) ~ (e2 = e0)
% 251.13/59.84 (4) ~ (e1 = e0)
% 251.13/59.84 (5) ~ (all_28_2 = e3)
% 251.13/59.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.84 (7) ~ (e3 = e2)
% 251.13/59.84 (8) ~ (e4 = e0)
% 251.13/59.84 (9) ~ (e2 = e1)
% 251.13/59.84 (10) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.84 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.84 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.84 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.84 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.84 op(e0, e1) = e0)))
% 251.13/59.84 (11) op(e0, e2) = all_28_2
% 251.13/59.84 (12) ~ (e4 = e1)
% 251.13/59.84 (13) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.84 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.84 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.84 (14) ~ (e3 = e0)
% 251.13/59.84 (15) ~ (all_22_2 = e4)
% 251.13/59.84 (16) ~ (e3 = e1)
% 251.13/59.84 (17) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.84 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.84 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.84 (18) ~ (all_22_2 = e1)
% 251.13/59.84 (19) op(e0, e3) = all_22_2
% 251.13/59.84 (20) all_252_20 = e2
% 251.13/59.84 (21) ~ (e4 = e3)
% 251.13/59.84 (22) op(e0, e1) = all_20_2
% 251.13/59.84 (23) ~ (e4 = e2)
% 251.13/59.84 (24) ~ (all_20_2 = e4)
% 251.13/59.84 (25) ~ (all_20_2 = e3)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | BETA: splitting (13) gives:
% 251.13/59.84 |
% 251.13/59.84 | Case 1:
% 251.13/59.84 | |
% 251.13/59.84 | | (26) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 251.13/59.84 | | = e3)
% 251.13/59.84 | |
% 251.13/59.84 | | BETA: splitting (26) gives:
% 251.13/59.84 | |
% 251.13/59.84 | | Case 1:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (27) all_252_20 = e3 & op(e0, e4) = e3
% 251.13/59.84 | | |
% 251.13/59.84 | | | REF_CLOSE: (7), (20), (27) are inconsistent by sub-proof #539.
% 251.13/59.84 | | |
% 251.13/59.84 | | Case 2:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (28) all_252_21 = e3 & op(e0, e3) = e3
% 251.13/59.84 | | |
% 251.13/59.84 | | | ALPHA: (28) implies:
% 251.13/59.84 | | | (29) all_252_21 = e3
% 251.13/59.84 | | |
% 251.13/59.84 | | | COMBINE_EQS: (1), (29) imply:
% 251.13/59.84 | | | (30) e3 = e2
% 251.13/59.84 | | |
% 251.13/59.84 | | | REDUCE: (7), (30) imply:
% 251.13/59.84 | | | (31) $false
% 251.13/59.84 | | |
% 251.13/59.84 | | | CLOSE: (31) is inconsistent.
% 251.13/59.84 | | |
% 251.13/59.84 | | End of split
% 251.13/59.84 | |
% 251.13/59.84 | Case 2:
% 251.13/59.84 | |
% 251.13/59.84 | | (32) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 251.13/59.84 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.84 | |
% 251.13/59.84 | | BETA: splitting (32) gives:
% 251.13/59.84 | |
% 251.13/59.84 | | Case 1:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (33) all_252_22 = e3 & op(e0, e2) = e3
% 251.13/59.84 | | |
% 251.13/59.84 | | | ALPHA: (33) implies:
% 251.13/59.84 | | | (34) op(e0, e2) = e3
% 251.13/59.84 | | |
% 251.13/59.84 | | | REF_CLOSE: (5), (6), (11), (34) are inconsistent by sub-proof #975.
% 251.13/59.84 | | |
% 251.13/59.84 | | Case 2:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (35) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 251.13/59.84 | | | e0) = e3)
% 251.13/59.84 | | |
% 251.13/59.84 | | | BETA: splitting (35) gives:
% 251.13/59.84 | | |
% 251.13/59.84 | | | Case 1:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | (36) all_252_23 = e3 & op(e0, e1) = e3
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | ALPHA: (36) implies:
% 251.13/59.84 | | | | (37) op(e0, e1) = e3
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | GROUND_INST: instantiating (6) with all_20_2, e3, e1, e0, simplifying
% 251.13/59.84 | | | | with (22), (37) gives:
% 251.13/59.84 | | | | (38) all_20_2 = e3
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | REDUCE: (25), (38) imply:
% 251.13/59.84 | | | | (39) $false
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | CLOSE: (39) is inconsistent.
% 251.13/59.84 | | | |
% 251.13/59.84 | | | Case 2:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | (40) all_252_24 = e3 & op(e0, e0) = e3
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | ALPHA: (40) implies:
% 251.13/59.84 | | | | (41) all_252_24 = e3
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | BETA: splitting (2) gives:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | Case 1:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | (42) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 &
% 251.13/59.84 | | | | | op(e0, e3) = e4)
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | BETA: splitting (42) gives:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | Case 1:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (43) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | REF_CLOSE: (20), (23), (43) are inconsistent by sub-proof #534.
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | Case 2:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (44) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | REF_CLOSE: (6), (15), (19), (44) are inconsistent by sub-proof #805.
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | End of split
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | Case 2:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | (45) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 &
% 251.13/59.84 | | | | | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | BETA: splitting (45) gives:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | Case 1:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (46) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | ALPHA: (46) implies:
% 251.13/59.84 | | | | | | (47) all_252_22 = e4
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | BETA: splitting (10) gives:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | Case 1:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (48) all_252_24 = e0 & op(e0, e0) = e0
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | REF_CLOSE: (14), (41), (48) are inconsistent by sub-proof #533.
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | Case 2:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (49) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 &
% 251.13/59.84 | | | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 251.13/59.84 | | | | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 =
% 251.13/59.84 | | | | | | | e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3)
% 251.13/59.84 | | | | | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 251.13/59.84 | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | ALPHA: (49) implies:
% 251.13/59.84 | | | | | | | (50) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 &
% 251.13/59.84 | | | | | | | op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) |
% 251.13/59.84 | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | BETA: splitting (17) gives:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | | (51) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 &
% 251.13/59.84 | | | | | | | | op(e0, e3) = e1)
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | | REF_CLOSE: (6), (9), (18), (19), (20), (51) are inconsistent by
% 251.13/59.84 | | | | | | | | sub-proof #531.
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | | (52) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 &
% 251.13/59.84 | | | | | | | | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | | BETA: splitting (52) gives:
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | (53) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | ALPHA: (53) implies:
% 251.13/59.84 | | | | | | | | | (54) all_252_22 = e1
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | REF_CLOSE: (12), (47), (54) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | | | #530.
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | (55) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1
% 251.13/59.84 | | | | | | | | | & op(e0, e0) = e1)
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | BETA: splitting (55) gives:
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | (56) all_252_23 = e1 & op(e0, e1) = e1
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | ALPHA: (56) implies:
% 251.13/59.84 | | | | | | | | | | (57) all_252_23 = e1
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | BETA: splitting (50) gives:
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | (58) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21
% 251.13/59.84 | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | BETA: splitting (58) gives:
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | (59) all_252_20 = e0 & op(e0, e4) = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | REF_CLOSE: (3), (20), (59) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | | | | | | #529.
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | (60) all_252_21 = e0 & op(e0, e3) = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | ALPHA: (60) implies:
% 251.13/59.84 | | | | | | | | | | | | (61) all_252_21 = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | REF_CLOSE: (1), (3), (61) are inconsistent by sub-proof #942.
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | End of split
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | (62) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23
% 251.13/59.84 | | | | | | | | | | | = e0 & op(e0, e1) = e0)
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | BETA: splitting (62) gives:
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | Case 1:
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | (63) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | ALPHA: (63) implies:
% 251.13/59.84 | | | | | | | | | | | | (64) all_252_22 = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | REF_CLOSE: (8), (47), (64) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | | | | | | #528.
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | (65) all_252_23 = e0 & op(e0, e1) = e0
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | | REF_CLOSE: (4), (57), (65) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | | | | | | #527.
% 251.13/59.84 | | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | | End of split
% 251.13/59.84 | | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | End of split
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | Case 2:
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | (66) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | | REF_CLOSE: (16), (41), (66) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | | | | #526.
% 251.13/59.84 | | | | | | | | | |
% 251.13/59.84 | | | | | | | | | End of split
% 251.13/59.84 | | | | | | | | |
% 251.13/59.84 | | | | | | | | End of split
% 251.13/59.84 | | | | | | | |
% 251.13/59.84 | | | | | | | End of split
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | End of split
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | Case 2:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (67) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.13/59.84 | | | | | | op(e0, e0) = e4)
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | BETA: splitting (67) gives:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | Case 1:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (68) all_252_23 = e4 & op(e0, e1) = e4
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | REF_CLOSE: (6), (22), (24), (68) are inconsistent by sub-proof
% 251.13/59.84 | | | | | | | #912.
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | Case 2:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (69) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | REF_CLOSE: (21), (41), (69) are inconsistent by sub-proof #525.
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | End of split
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | End of split
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | End of split
% 251.13/59.84 | | | |
% 251.13/59.84 | | | End of split
% 251.13/59.84 | | |
% 251.13/59.84 | | End of split
% 251.13/59.84 | |
% 251.13/59.84 | End of split
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #525 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_24 = e4 & op(e0, e0) = e4
% 251.13/59.84 (2) all_252_24 = e3
% 251.13/59.84 (3) ~ (e4 = e3)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_24 = e4
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e4 = e3
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #526 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.84 (2) all_252_24 = e3
% 251.13/59.84 (3) ~ (e3 = e1)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_24 = e1
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e3 = e1
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #527 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_23 = e0 & op(e0, e1) = e0
% 251.13/59.84 (2) all_252_23 = e1
% 251.13/59.84 (3) ~ (e1 = e0)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_23 = e0
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e1 = e0
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #528 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_22 = e4
% 251.13/59.84 (2) all_252_22 = e0
% 251.13/59.84 (3) ~ (e4 = e0)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.84 | (4) e4 = e0
% 251.13/59.84 |
% 251.13/59.84 | SIMP: (4) implies:
% 251.13/59.84 | (5) e4 = e0
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #529 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_20 = e0 & op(e0, e4) = e0
% 251.13/59.84 (2) all_252_20 = e2
% 251.13/59.84 (3) ~ (e2 = e0)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_20 = e0
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e2 = e0
% 251.13/59.84 |
% 251.13/59.84 | SIMP: (5) implies:
% 251.13/59.84 | (6) e2 = e0
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (6) imply:
% 251.13/59.84 | (7) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (7) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #530 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_22 = e4
% 251.13/59.84 (2) all_252_22 = e1
% 251.13/59.84 (3) ~ (e4 = e1)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.84 | (4) e4 = e1
% 251.13/59.84 |
% 251.13/59.84 | SIMP: (4) implies:
% 251.13/59.84 | (5) e4 = e1
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #531 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.84 (2) ~ (e2 = e1)
% 251.13/59.84 (3) ~ (all_22_2 = e1)
% 251.13/59.84 (4) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 251.13/59.84 (5) op(e0, e3) = all_22_2
% 251.13/59.84 (6) all_252_20 = e2
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | BETA: splitting (4) gives:
% 251.13/59.84 |
% 251.13/59.84 | Case 1:
% 251.13/59.84 | |
% 251.13/59.84 | | (7) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #532.
% 251.13/59.84 | |
% 251.13/59.84 | Case 2:
% 251.13/59.84 | |
% 251.13/59.84 | | (8) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.84 | |
% 251.13/59.84 | | ALPHA: (8) implies:
% 251.13/59.84 | | (9) op(e0, e3) = e1
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #714.
% 251.13/59.84 | |
% 251.13/59.84 | End of split
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #532 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.84 (2) all_252_20 = e2
% 251.13/59.84 (3) ~ (e2 = e1)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_20 = e1
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e2 = e1
% 251.13/59.84 |
% 251.13/59.84 | SIMP: (5) implies:
% 251.13/59.84 | (6) e2 = e1
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (6) imply:
% 251.13/59.84 | (7) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (7) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #533 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_24 = e0 & op(e0, e0) = e0
% 251.13/59.84 (2) all_252_24 = e3
% 251.13/59.84 (3) ~ (e3 = e0)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_24 = e0
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e3 = e0
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #534 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.84 (2) all_252_20 = e2
% 251.13/59.84 (3) ~ (e4 = e2)
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | ALPHA: (1) implies:
% 251.13/59.84 | (4) all_252_20 = e4
% 251.13/59.84 |
% 251.13/59.84 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.84 | (5) e4 = e2
% 251.13/59.84 |
% 251.13/59.84 | REDUCE: (3), (5) imply:
% 251.13/59.84 | (6) $false
% 251.13/59.84 |
% 251.13/59.84 | CLOSE: (6) is inconsistent.
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #535 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.84 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.84 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.84 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.84 (3) ~ (e2 = e0)
% 251.13/59.84 (4) ~ (e1 = e0)
% 251.13/59.84 (5) op(e3, e4) = e0
% 251.13/59.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.84 (7) ~ (e4 = e0)
% 251.13/59.84 (8) ~ (e2 = e1)
% 251.13/59.84 (9) ~ (e4 = e1)
% 251.13/59.84 (10) ~ (e3 = e1)
% 251.13/59.84 (11) op(e3, e1) = all_36_2
% 251.13/59.84 (12) ~ (all_8_2 = e0)
% 251.13/59.84 (13) ~ (all_36_2 = e0)
% 251.13/59.84 (14) ~ (e4 = e3)
% 251.13/59.84 (15) op(e3, e0) = all_48_2
% 251.13/59.84 (16) ~ (all_48_2 = e0)
% 251.13/59.84 (17) ~ (e4 = e2)
% 251.13/59.84 (18) op(e3, e2) = all_8_2
% 251.13/59.84 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.84 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.84 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.84 (20) ~ (all_244_3 = e0)
% 251.13/59.84 (21) all_252_6 = e3
% 251.13/59.84 (22) op(e3, e3) = all_244_3
% 251.13/59.84 (23) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.84 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.84 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.84 (24) all_252_20 = e3
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | BETA: splitting (1) gives:
% 251.13/59.84 |
% 251.13/59.84 | Case 1:
% 251.13/59.84 | |
% 251.13/59.84 | | (25) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.84 | |
% 251.13/59.84 | | ALPHA: (25) implies:
% 251.13/59.84 | | (26) all_252_0 = e2
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 251.13/59.84 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26)
% 251.13/59.84 | | are inconsistent by sub-proof #536.
% 251.13/59.84 | |
% 251.13/59.84 | Case 2:
% 251.13/59.84 | |
% 251.13/59.84 | | (27) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.84 | |
% 251.13/59.84 | | ALPHA: (27) implies:
% 251.13/59.84 | | (28) all_252_2 = e2
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (2), (3), (6), (11), (12), (13), (15), (16), (18), (20), (22),
% 251.13/59.84 | | (28) are inconsistent by sub-proof #571.
% 251.13/59.84 | |
% 251.13/59.84 | End of split
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #536 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.84 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.84 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.84 (2) ~ (e1 = e0)
% 251.13/59.84 (3) op(e3, e4) = e0
% 251.13/59.84 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.84 (5) ~ (e4 = e0)
% 251.13/59.84 (6) all_252_0 = e2
% 251.13/59.84 (7) ~ (e2 = e1)
% 251.13/59.84 (8) ~ (e4 = e1)
% 251.13/59.84 (9) ~ (e3 = e1)
% 251.13/59.84 (10) op(e3, e1) = all_36_2
% 251.13/59.84 (11) ~ (all_8_2 = e0)
% 251.13/59.84 (12) ~ (all_36_2 = e0)
% 251.13/59.84 (13) ~ (e4 = e3)
% 251.13/59.84 (14) op(e3, e0) = all_48_2
% 251.13/59.84 (15) ~ (all_48_2 = e0)
% 251.13/59.84 (16) ~ (e4 = e2)
% 251.13/59.84 (17) op(e3, e2) = all_8_2
% 251.13/59.84 (18) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.84 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.84 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.84 (19) ~ (all_244_3 = e0)
% 251.13/59.84 (20) all_252_6 = e3
% 251.13/59.84 (21) op(e3, e3) = all_244_3
% 251.13/59.84 (22) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.84 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.84 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.84 (23) all_252_20 = e3
% 251.13/59.84
% 251.13/59.84 Begin of proof
% 251.13/59.84 |
% 251.13/59.84 | BETA: splitting (18) gives:
% 251.13/59.84 |
% 251.13/59.84 | Case 1:
% 251.13/59.84 | |
% 251.13/59.84 | | (24) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 251.13/59.84 | | e4)
% 251.13/59.84 | |
% 251.13/59.84 | | REF_CLOSE: (1), (4), (5), (6), (10), (11), (12), (14), (15), (16), (17),
% 251.13/59.84 | | (19), (21), (24) are inconsistent by sub-proof #555.
% 251.13/59.84 | |
% 251.13/59.84 | Case 2:
% 251.13/59.84 | |
% 251.13/59.84 | | (25) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.84 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.84 | |
% 251.13/59.84 | | BETA: splitting (25) gives:
% 251.13/59.84 | |
% 251.13/59.84 | | Case 1:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (26) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.84 | | |
% 251.13/59.84 | | | REF_CLOSE: (13), (20), (26) are inconsistent by sub-proof #811.
% 251.13/59.84 | | |
% 251.13/59.84 | | Case 2:
% 251.13/59.84 | | |
% 251.13/59.84 | | | (27) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 251.13/59.84 | | | e4) = e4)
% 251.13/59.84 | | |
% 251.13/59.84 | | | BETA: splitting (27) gives:
% 251.13/59.84 | | |
% 251.13/59.84 | | | Case 1:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | (28) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | ALPHA: (28) implies:
% 251.13/59.84 | | | | (29) all_252_12 = e4
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | BETA: splitting (22) gives:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | Case 1:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | (30) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3,
% 251.13/59.84 | | | | | e4) = e1)
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (30) are inconsistent by sub-proof
% 251.13/59.84 | | | | | #557.
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | Case 2:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | (31) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1,
% 251.13/59.84 | | | | | e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | BETA: splitting (31) gives:
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | | Case 1:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (32) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | ALPHA: (32) implies:
% 251.13/59.84 | | | | | | (33) all_252_6 = e1
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | COMBINE_EQS: (20), (33) imply:
% 251.13/59.84 | | | | | | (34) e3 = e1
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | SIMP: (34) implies:
% 251.13/59.84 | | | | | | (35) e3 = e1
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | REDUCE: (9), (35) imply:
% 251.13/59.84 | | | | | | (36) $false
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | CLOSE: (36) is inconsistent.
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | Case 2:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | (37) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 251.13/59.84 | | | | | | op(e0, e4) = e1)
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | BETA: splitting (37) gives:
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | | Case 1:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (38) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | ALPHA: (38) implies:
% 251.13/59.84 | | | | | | | (39) all_252_12 = e1
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | REF_CLOSE: (8), (29), (39) are inconsistent by sub-proof #554.
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | Case 2:
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | (40) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | | REF_CLOSE: (9), (23), (40) are inconsistent by sub-proof #565.
% 251.13/59.84 | | | | | | |
% 251.13/59.84 | | | | | | End of split
% 251.13/59.84 | | | | | |
% 251.13/59.84 | | | | | End of split
% 251.13/59.84 | | | | |
% 251.13/59.84 | | | | End of split
% 251.13/59.84 | | | |
% 251.13/59.84 | | | Case 2:
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | (41) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.84 | | | |
% 251.13/59.84 | | | | REF_CLOSE: (13), (23), (41) are inconsistent by sub-proof #563.
% 251.13/59.84 | | | |
% 251.13/59.84 | | | End of split
% 251.13/59.84 | | |
% 251.13/59.84 | | End of split
% 251.13/59.84 | |
% 251.13/59.84 | End of split
% 251.13/59.84 |
% 251.13/59.84 End of proof
% 251.13/59.84
% 251.13/59.84 Sub-proof #537 shows that the following formulas are inconsistent:
% 251.13/59.84 ----------------------------------------------------------------
% 251.13/59.84 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.84 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.84 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.84 (2) all_252_6 = e0
% 251.13/59.84 (3) ~ (e2 = e0)
% 251.13/59.84 (4) ~ (e1 = e0)
% 251.13/59.84 (5) op(e3, e4) = e0
% 251.13/59.85 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.85 (7) ~ (e3 = e2)
% 251.13/59.85 (8) ~ (e4 = e0)
% 251.13/59.85 (9) ~ (e2 = e1)
% 251.13/59.85 (10) ~ (e4 = e1)
% 251.13/59.85 (11) op(e1, e4) = all_16_2
% 251.13/59.85 (12) ~ (e3 = e0)
% 251.13/59.85 (13) all_252_2 = e0
% 251.13/59.85 (14) ~ (e3 = e1)
% 251.13/59.85 (15) op(e3, e1) = all_36_2
% 251.13/59.85 (16) ~ (all_16_2 = e2)
% 251.13/59.85 (17) ~ (all_8_2 = e0)
% 251.13/59.85 (18) ~ (all_36_2 = e0)
% 251.13/59.85 (19) ~ (e4 = e3)
% 251.13/59.85 (20) op(e3, e0) = all_48_2
% 251.13/59.85 (21) ~ (all_48_2 = e0)
% 251.13/59.85 (22) ~ (e4 = e2)
% 251.13/59.85 (23) op(e3, e2) = all_8_2
% 251.13/59.85 (24) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.85 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.85 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.85 (25) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.85 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.85 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.85 (26) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (27) ~ (all_244_3 = e0)
% 251.13/59.85 (28) ~ (all_16_2 = e3)
% 251.13/59.85 (29) op(e3, e3) = all_244_3
% 251.13/59.85 (30) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.85 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85 (31) all_252_20 = e3
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (25) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (32) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.13/59.85 | | e2)
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (14), (15), (17),
% 251.13/59.85 | | (18), (19), (20), (21), (22), (23), (26), (27), (29), (30), (31),
% 251.13/59.85 | | (32) are inconsistent by sub-proof #549.
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (33) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.85 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (33) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (34) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (2), (3), (34) are inconsistent by sub-proof #548.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (35) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 251.13/59.85 | | | e4) = e2)
% 251.13/59.85 | | |
% 251.13/59.85 | | | BETA: splitting (35) gives:
% 251.13/59.85 | | |
% 251.13/59.85 | | | Case 1:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (36) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (6), (11), (16), (36) are inconsistent by sub-proof #926.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | Case 2:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (37) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | ALPHA: (37) implies:
% 251.13/59.85 | | | | (38) all_252_20 = e2
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 251.13/59.85 | | | | (19), (22), (24), (26), (28), (30), (38) are inconsistent by
% 251.13/59.85 | | | | sub-proof #538.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | End of split
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #538 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e0
% 251.13/59.85 (2) ~ (e1 = e0)
% 251.13/59.85 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.85 (4) ~ (e3 = e2)
% 251.13/59.85 (5) ~ (e4 = e0)
% 251.13/59.85 (6) ~ (e2 = e1)
% 251.13/59.85 (7) ~ (e4 = e1)
% 251.13/59.85 (8) op(e1, e4) = all_16_2
% 251.13/59.85 (9) ~ (e3 = e0)
% 251.13/59.85 (10) all_252_2 = e0
% 251.13/59.85 (11) ~ (e3 = e1)
% 251.13/59.85 (12) all_252_20 = e2
% 251.13/59.85 (13) ~ (e4 = e3)
% 251.13/59.85 (14) ~ (e4 = e2)
% 251.13/59.85 (15) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.85 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.85 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.85 (16) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (17) ~ (all_16_2 = e3)
% 251.13/59.85 (18) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.85 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (15) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (19) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 251.13/59.85 | | e3)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (19) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (20) all_252_0 = e3 & op(e4, e4) = e3
% 251.13/59.85 | | |
% 251.13/59.85 | | | ALPHA: (20) implies:
% 251.13/59.85 | | | (21) all_252_0 = e3
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13), (14), (16),
% 251.13/59.85 | | | (18), (21) are inconsistent by sub-proof #542.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (22) all_252_2 = e3 & op(e3, e4) = e3
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (9), (10), (22) are inconsistent by sub-proof #541.
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (23) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.85 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (23) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (24) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (1), (9), (24) are inconsistent by sub-proof #540.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (25) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 251.13/59.85 | | | e4) = e3)
% 251.13/59.85 | | |
% 251.13/59.85 | | | BETA: splitting (25) gives:
% 251.13/59.85 | | |
% 251.13/59.85 | | | Case 1:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (26) all_252_12 = e3 & op(e1, e4) = e3
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (3), (8), (17), (26) are inconsistent by sub-proof #895.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | Case 2:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (27) all_252_20 = e3 & op(e0, e4) = e3
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (4), (12), (27) are inconsistent by sub-proof #539.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | End of split
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #539 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_20 = e3 & op(e0, e4) = e3
% 251.13/59.85 (2) all_252_20 = e2
% 251.13/59.85 (3) ~ (e3 = e2)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_20 = e3
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e3 = e2
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #540 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.85 (2) all_252_6 = e0
% 251.13/59.85 (3) ~ (e3 = e0)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_6 = e3
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e3 = e0
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #541 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_2 = e3 & op(e3, e4) = e3
% 251.13/59.85 (2) all_252_2 = e0
% 251.13/59.85 (3) ~ (e3 = e0)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_2 = e3
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e3 = e0
% 251.13/59.85 |
% 251.13/59.85 | SIMP: (5) implies:
% 251.13/59.85 | (6) e3 = e0
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (6) imply:
% 251.13/59.85 | (7) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (7) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #542 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e0
% 251.13/59.85 (2) ~ (e1 = e0)
% 251.13/59.85 (3) ~ (e4 = e0)
% 251.13/59.85 (4) ~ (e2 = e1)
% 251.13/59.85 (5) ~ (e4 = e1)
% 251.13/59.85 (6) all_252_0 = e3
% 251.13/59.85 (7) all_252_2 = e0
% 251.13/59.85 (8) ~ (e3 = e1)
% 251.13/59.85 (9) all_252_20 = e2
% 251.13/59.85 (10) ~ (e4 = e3)
% 251.13/59.85 (11) ~ (e4 = e2)
% 251.13/59.85 (12) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (13) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.85 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (12) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (14) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 251.13/59.85 | | e4)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (14) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (15) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (6), (10), (15) are inconsistent by sub-proof #547.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (16) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | ALPHA: (16) implies:
% 251.13/59.85 | | | (17) all_252_2 = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | COMBINE_EQS: (7), (17) imply:
% 251.13/59.85 | | | (18) e4 = e0
% 251.13/59.85 | | |
% 251.13/59.85 | | | SIMP: (18) implies:
% 251.13/59.85 | | | (19) e4 = e0
% 251.13/59.85 | | |
% 251.13/59.85 | | | REDUCE: (3), (19) imply:
% 251.13/59.85 | | | (20) $false
% 251.13/59.85 | | |
% 251.13/59.85 | | | CLOSE: (20) is inconsistent.
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (21) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (21) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (22) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (1), (3), (22) are inconsistent by sub-proof #938.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (23) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0,
% 251.13/59.85 | | | e4) = e4)
% 251.13/59.85 | | |
% 251.13/59.85 | | | BETA: splitting (23) gives:
% 251.13/59.85 | | |
% 251.13/59.85 | | | Case 1:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (24) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | ALPHA: (24) implies:
% 251.13/59.85 | | | | (25) all_252_12 = e4
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | BETA: splitting (13) gives:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | Case 1:
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | (26) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3,
% 251.13/59.85 | | | | | e4) = e1)
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | BETA: splitting (26) gives:
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | Case 1:
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | (27) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | REF_CLOSE: (6), (8), (27) are inconsistent by sub-proof #546.
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | Case 2:
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | (28) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | REF_CLOSE: (2), (7), (28) are inconsistent by sub-proof #568.
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | End of split
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | Case 2:
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | (29) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1,
% 251.13/59.85 | | | | | e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | BETA: splitting (29) gives:
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | | Case 1:
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | (30) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | REF_CLOSE: (1), (2), (30) are inconsistent by sub-proof #545.
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | Case 2:
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | (31) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 &
% 251.13/59.85 | | | | | | op(e0, e4) = e1)
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | BETA: splitting (31) gives:
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | | Case 1:
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | | (32) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | | ALPHA: (32) implies:
% 251.13/59.85 | | | | | | | (33) all_252_12 = e1
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | | REF_CLOSE: (5), (25), (33) are inconsistent by sub-proof #554.
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | Case 2:
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | | (34) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | | REF_CLOSE: (4), (9), (34) are inconsistent by sub-proof #544.
% 251.13/59.85 | | | | | | |
% 251.13/59.85 | | | | | | End of split
% 251.13/59.85 | | | | | |
% 251.13/59.85 | | | | | End of split
% 251.13/59.85 | | | | |
% 251.13/59.85 | | | | End of split
% 251.13/59.85 | | | |
% 251.13/59.85 | | | Case 2:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (35) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (9), (11), (35) are inconsistent by sub-proof #543.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | End of split
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #543 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.85 (2) all_252_20 = e2
% 251.13/59.85 (3) ~ (e4 = e2)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_20 = e4
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e4 = e2
% 251.13/59.85 |
% 251.13/59.85 | SIMP: (5) implies:
% 251.13/59.85 | (6) e4 = e2
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (6) imply:
% 251.13/59.85 | (7) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (7) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #544 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.85 (2) all_252_20 = e2
% 251.13/59.85 (3) ~ (e2 = e1)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_20 = e1
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e2 = e1
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #545 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.85 (2) all_252_6 = e0
% 251.13/59.85 (3) ~ (e1 = e0)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_6 = e1
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e1 = e0
% 251.13/59.85 |
% 251.13/59.85 | SIMP: (5) implies:
% 251.13/59.85 | (6) e1 = e0
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (6) imply:
% 251.13/59.85 | (7) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (7) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #546 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.85 (2) all_252_0 = e3
% 251.13/59.85 (3) ~ (e3 = e1)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_0 = e1
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e3 = e1
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #547 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.85 (2) all_252_0 = e3
% 251.13/59.85 (3) ~ (e4 = e3)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_0 = e4
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e4 = e3
% 251.13/59.85 |
% 251.13/59.85 | SIMP: (5) implies:
% 251.13/59.85 | (6) e4 = e3
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (6) imply:
% 251.13/59.85 | (7) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (7) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #548 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.85 (2) all_252_6 = e0
% 251.13/59.85 (3) ~ (e2 = e0)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_6 = e2
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e2 = e0
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #549 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.85 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.85 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.85 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.85 (3) all_252_6 = e0
% 251.13/59.85 (4) ~ (e2 = e0)
% 251.13/59.85 (5) ~ (e1 = e0)
% 251.13/59.85 (6) op(e3, e4) = e0
% 251.13/59.85 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.85 (8) ~ (e4 = e0)
% 251.13/59.85 (9) ~ (e2 = e1)
% 251.13/59.85 (10) ~ (e4 = e1)
% 251.13/59.85 (11) ~ (e3 = e1)
% 251.13/59.85 (12) op(e3, e1) = all_36_2
% 251.13/59.85 (13) ~ (all_8_2 = e0)
% 251.13/59.85 (14) ~ (all_36_2 = e0)
% 251.13/59.85 (15) ~ (e4 = e3)
% 251.13/59.85 (16) op(e3, e0) = all_48_2
% 251.13/59.85 (17) ~ (all_48_2 = e0)
% 251.13/59.85 (18) ~ (e4 = e2)
% 251.13/59.85 (19) op(e3, e2) = all_8_2
% 251.13/59.85 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (21) ~ (all_244_3 = e0)
% 251.13/59.85 (22) op(e3, e3) = all_244_3
% 251.13/59.85 (23) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.85 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85 (24) all_252_20 = e3
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (1) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (25) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.85 | |
% 251.13/59.85 | | ALPHA: (25) implies:
% 251.13/59.85 | | (26) all_252_0 = e2
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 251.13/59.85 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26)
% 251.13/59.85 | | are inconsistent by sub-proof #550.
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (27) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.85 | |
% 251.13/59.85 | | ALPHA: (27) implies:
% 251.13/59.85 | | (28) all_252_2 = e2
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (2), (4), (7), (12), (13), (14), (16), (17), (19), (21), (22),
% 251.13/59.85 | | (28) are inconsistent by sub-proof #571.
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #550 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.85 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.85 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.85 (2) all_252_6 = e0
% 251.13/59.85 (3) ~ (e1 = e0)
% 251.13/59.85 (4) op(e3, e4) = e0
% 251.13/59.85 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.85 (6) ~ (e4 = e0)
% 251.13/59.85 (7) all_252_0 = e2
% 251.13/59.85 (8) ~ (e2 = e1)
% 251.13/59.85 (9) ~ (e4 = e1)
% 251.13/59.85 (10) ~ (e3 = e1)
% 251.13/59.85 (11) op(e3, e1) = all_36_2
% 251.13/59.85 (12) ~ (all_8_2 = e0)
% 251.13/59.85 (13) ~ (all_36_2 = e0)
% 251.13/59.85 (14) ~ (e4 = e3)
% 251.13/59.85 (15) op(e3, e0) = all_48_2
% 251.13/59.85 (16) ~ (all_48_2 = e0)
% 251.13/59.85 (17) ~ (e4 = e2)
% 251.13/59.85 (18) op(e3, e2) = all_8_2
% 251.13/59.85 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (20) ~ (all_244_3 = e0)
% 251.13/59.85 (21) op(e3, e3) = all_244_3
% 251.13/59.85 (22) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.85 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85 (23) all_252_20 = e3
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (22) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (24) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 251.13/59.85 | | e1)
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (3), (4), (5), (7), (8), (24) are inconsistent by sub-proof #557.
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (25) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.85 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (25) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (26) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (2), (3), (26) are inconsistent by sub-proof #556.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (27) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 251.13/59.85 | | | e4) = e1)
% 251.13/59.85 | | |
% 251.13/59.85 | | | BETA: splitting (27) gives:
% 251.13/59.85 | | |
% 251.13/59.85 | | | Case 1:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (28) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | ALPHA: (28) implies:
% 251.13/59.85 | | | | (29) all_252_12 = e1
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 251.13/59.85 | | | | (16), (17), (18), (19), (20), (21), (23), (29) are
% 251.13/59.85 | | | | inconsistent by sub-proof #551.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | Case 2:
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | (30) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.85 | | | |
% 251.13/59.85 | | | | REF_CLOSE: (10), (23), (30) are inconsistent by sub-proof #565.
% 251.13/59.85 | | | |
% 251.13/59.85 | | | End of split
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #551 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.85 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.85 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.85 (2) all_252_6 = e0
% 251.13/59.85 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.85 (4) ~ (e4 = e0)
% 251.13/59.85 (5) all_252_0 = e2
% 251.13/59.85 (6) ~ (e4 = e1)
% 251.13/59.85 (7) op(e3, e1) = all_36_2
% 251.13/59.85 (8) ~ (all_8_2 = e0)
% 251.13/59.85 (9) ~ (all_36_2 = e0)
% 251.13/59.85 (10) ~ (e4 = e3)
% 251.13/59.85 (11) op(e3, e0) = all_48_2
% 251.13/59.85 (12) ~ (all_48_2 = e0)
% 251.13/59.85 (13) ~ (e4 = e2)
% 251.13/59.85 (14) op(e3, e2) = all_8_2
% 251.13/59.85 (15) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.85 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (16) ~ (all_244_3 = e0)
% 251.13/59.85 (17) op(e3, e3) = all_244_3
% 251.13/59.85 (18) all_252_12 = e1
% 251.13/59.85 (19) all_252_20 = e3
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (15) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) =
% 251.13/59.85 | | e4)
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), (16),
% 251.13/59.85 | | (17), (20) are inconsistent by sub-proof #555.
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (21) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.85 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (2), (4), (6), (10), (18), (19), (21) are inconsistent by
% 251.13/59.85 | | sub-proof #552.
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #552 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_6 = e0
% 251.13/59.85 (2) ~ (e4 = e0)
% 251.13/59.85 (3) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4)
% 251.13/59.85 | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.85 (4) ~ (e4 = e1)
% 251.13/59.85 (5) ~ (e4 = e3)
% 251.13/59.85 (6) all_252_12 = e1
% 251.13/59.85 (7) all_252_20 = e3
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | BETA: splitting (3) gives:
% 251.13/59.85 |
% 251.13/59.85 | Case 1:
% 251.13/59.85 | |
% 251.13/59.85 | | (8) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.85 | |
% 251.13/59.85 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #938.
% 251.13/59.85 | |
% 251.13/59.85 | Case 2:
% 251.13/59.85 | |
% 251.13/59.85 | | (9) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) =
% 251.13/59.85 | | e4)
% 251.13/59.85 | |
% 251.13/59.85 | | BETA: splitting (9) gives:
% 251.13/59.85 | |
% 251.13/59.85 | | Case 1:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (10) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | ALPHA: (10) implies:
% 251.13/59.85 | | | (11) all_252_12 = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #554.
% 251.13/59.85 | | |
% 251.13/59.85 | | Case 2:
% 251.13/59.85 | | |
% 251.13/59.85 | | | (12) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.85 | | |
% 251.13/59.85 | | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #553.
% 251.13/59.85 | | |
% 251.13/59.85 | | End of split
% 251.13/59.85 | |
% 251.13/59.85 | End of split
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #553 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.85 (2) all_252_20 = e3
% 251.13/59.85 (3) ~ (e4 = e3)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | ALPHA: (1) implies:
% 251.13/59.85 | (4) all_252_20 = e4
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.85 | (5) e4 = e3
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #554 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) all_252_12 = e4
% 251.13/59.85 (2) all_252_12 = e1
% 251.13/59.85 (3) ~ (e4 = e1)
% 251.13/59.85
% 251.13/59.85 Begin of proof
% 251.13/59.85 |
% 251.13/59.85 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.85 | (4) e4 = e1
% 251.13/59.85 |
% 251.13/59.85 | SIMP: (4) implies:
% 251.13/59.85 | (5) e4 = e1
% 251.13/59.85 |
% 251.13/59.85 | REDUCE: (3), (5) imply:
% 251.13/59.85 | (6) $false
% 251.13/59.85 |
% 251.13/59.85 | CLOSE: (6) is inconsistent.
% 251.13/59.85 |
% 251.13/59.85 End of proof
% 251.13/59.85
% 251.13/59.85 Sub-proof #555 shows that the following formulas are inconsistent:
% 251.13/59.85 ----------------------------------------------------------------
% 251.13/59.85 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.85 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.85 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (3) ~ (e4 = e0)
% 251.13/59.86 (4) all_252_0 = e2
% 251.13/59.86 (5) op(e3, e1) = all_36_2
% 251.13/59.86 (6) ~ (all_8_2 = e0)
% 251.13/59.86 (7) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.86 (8) ~ (all_36_2 = e0)
% 251.13/59.86 (9) op(e3, e0) = all_48_2
% 251.13/59.86 (10) ~ (all_48_2 = e0)
% 251.13/59.86 (11) ~ (e4 = e2)
% 251.13/59.86 (12) op(e3, e2) = all_8_2
% 251.13/59.86 (13) ~ (all_244_3 = e0)
% 251.13/59.86 (14) op(e3, e3) = all_244_3
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (7) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (15) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (4), (11), (15) are inconsistent by sub-proof #606.
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (16) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.86 | |
% 251.13/59.86 | | ALPHA: (16) implies:
% 251.13/59.86 | | (17) all_252_2 = e4
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (12), (13), (14), (17)
% 251.13/59.86 | | are inconsistent by sub-proof #569.
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #556 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.86 (2) all_252_6 = e0
% 251.13/59.86 (3) ~ (e1 = e0)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_6 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e1 = e0
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #557 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) ~ (e1 = e0)
% 251.13/59.86 (2) op(e3, e4) = e0
% 251.13/59.86 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (4) all_252_0 = e2
% 251.13/59.86 (5) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.86 (6) ~ (e2 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (5) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (7) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #558.
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (8) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.86 | |
% 251.13/59.86 | | ALPHA: (8) implies:
% 251.13/59.86 | | (9) op(e3, e4) = e1
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #607.
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #558 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.86 (2) all_252_0 = e2
% 251.13/59.86 (3) ~ (e2 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_0 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e2 = e1
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #559 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_0 = e0
% 251.13/59.86 (2) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.86 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.86 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 (3) ~ (e2 = e0)
% 251.13/59.86 (4) ~ (e1 = e0)
% 251.13/59.86 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (6) ~ (e3 = e2)
% 251.13/59.86 (7) ~ (e4 = e0)
% 251.13/59.86 (8) ~ (e2 = e1)
% 251.13/59.86 (9) ~ (e4 = e1)
% 251.13/59.86 (10) ~ (e3 = e1)
% 251.13/59.86 (11) op(e3, e1) = all_36_2
% 251.13/59.86 (12) ~ (all_8_2 = e0)
% 251.13/59.86 (13) ~ (all_36_2 = e0)
% 251.13/59.86 (14) ~ (e4 = e3)
% 251.13/59.86 (15) op(e3, e0) = all_48_2
% 251.13/59.86 (16) ~ (all_48_2 = e0)
% 251.13/59.86 (17) ~ (e4 = e2)
% 251.13/59.86 (18) op(e3, e2) = all_8_2
% 251.13/59.86 (19) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.86 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.86 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.86 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.86 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.86 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.86 (21) ~ (all_244_3 = e0)
% 251.13/59.86 (22) op(e3, e3) = all_244_3
% 251.13/59.86 (23) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1)
% 251.13/59.86 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.86 e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.86 (24) all_252_20 = e3
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (19) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (25) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.13/59.86 | | e2)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (25) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (26) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (1), (3), (26) are inconsistent by sub-proof #610.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (27) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.86 | | |
% 251.13/59.86 | | | ALPHA: (27) implies:
% 251.13/59.86 | | | (28) all_252_2 = e2
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (2), (3), (5), (11), (12), (13), (15), (16), (18), (21), (22),
% 251.13/59.86 | | | (28) are inconsistent by sub-proof #571.
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (29) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.86 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (29) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (30) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.86 | | |
% 251.13/59.86 | | | ALPHA: (30) implies:
% 251.13/59.86 | | | (31) all_252_6 = e2
% 251.13/59.86 | | |
% 251.13/59.86 | | | BETA: splitting (20) gives:
% 251.13/59.86 | | |
% 251.13/59.86 | | | Case 1:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (32) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 251.13/59.86 | | | | e4) = e4)
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | BETA: splitting (32) gives:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | Case 1:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (33) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | REF_CLOSE: (1), (7), (33) are inconsistent by sub-proof #570.
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | Case 2:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (34) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | ALPHA: (34) implies:
% 251.13/59.86 | | | | | (35) all_252_2 = e4
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | REF_CLOSE: (2), (5), (7), (11), (12), (13), (15), (16), (18), (21),
% 251.13/59.86 | | | | | (22), (35) are inconsistent by sub-proof #569.
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | End of split
% 251.13/59.86 | | | |
% 251.13/59.86 | | | Case 2:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (36) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 251.13/59.86 | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | BETA: splitting (36) gives:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | Case 1:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (37) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | ALPHA: (37) implies:
% 251.13/59.86 | | | | | (38) all_252_6 = e4
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | REF_CLOSE: (17), (31), (38) are inconsistent by sub-proof #833.
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | Case 2:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (39) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 251.13/59.86 | | | | | op(e0, e4) = e4)
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | BETA: splitting (39) gives:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | Case 1:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (40) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | ALPHA: (40) implies:
% 251.13/59.86 | | | | | | (41) all_252_12 = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | BETA: splitting (2) gives:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | Case 1:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (42) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 &
% 251.13/59.86 | | | | | | | op(e3, e3) = e0)
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | BETA: splitting (42) gives:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | (43) all_252_2 = e0 & op(e3, e4) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | ALPHA: (43) implies:
% 251.13/59.86 | | | | | | | | (44) all_252_2 = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (10), (23), (24), (31), (41),
% 251.13/59.86 | | | | | | | | (44) are inconsistent by sub-proof #564.
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | (45) all_252_3 = e0 & op(e3, e3) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | ALPHA: (45) implies:
% 251.13/59.86 | | | | | | | | (46) op(e3, e3) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | REF_CLOSE: (5), (21), (22), (46) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | #973.
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | End of split
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | Case 2:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (47) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 &
% 251.13/59.86 | | | | | | | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | REF_CLOSE: (5), (11), (12), (13), (15), (16), (18), (47) are
% 251.13/59.86 | | | | | | | inconsistent by sub-proof #572.
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | End of split
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | Case 2:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (48) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | REF_CLOSE: (14), (24), (48) are inconsistent by sub-proof #563.
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | End of split
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | End of split
% 251.13/59.86 | | | |
% 251.13/59.86 | | | End of split
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (49) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 251.13/59.86 | | | e4) = e2)
% 251.13/59.86 | | |
% 251.13/59.86 | | | BETA: splitting (49) gives:
% 251.13/59.86 | | |
% 251.13/59.86 | | | Case 1:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (50) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | ALPHA: (50) implies:
% 251.13/59.86 | | | | (51) all_252_12 = e2
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | BETA: splitting (20) gives:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | Case 1:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (52) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3,
% 251.13/59.86 | | | | | e4) = e4)
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | BETA: splitting (52) gives:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | Case 1:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (53) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | REF_CLOSE: (1), (7), (53) are inconsistent by sub-proof #570.
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | Case 2:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (54) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | ALPHA: (54) implies:
% 251.13/59.86 | | | | | | (55) all_252_2 = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | REF_CLOSE: (2), (5), (7), (11), (12), (13), (15), (16), (18), (21),
% 251.13/59.86 | | | | | | (22), (55) are inconsistent by sub-proof #569.
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | End of split
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | Case 2:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | (56) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1,
% 251.13/59.86 | | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | BETA: splitting (56) gives:
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | | Case 1:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (57) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | ALPHA: (57) implies:
% 251.13/59.86 | | | | | | (58) all_252_6 = e4
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | BETA: splitting (2) gives:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | Case 1:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (59) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 &
% 251.13/59.86 | | | | | | | op(e3, e3) = e0)
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | BETA: splitting (59) gives:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | (60) all_252_2 = e0 & op(e3, e4) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | ALPHA: (60) implies:
% 251.13/59.86 | | | | | | | | (61) all_252_2 = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | BETA: splitting (23) gives:
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | (62) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 &
% 251.13/59.86 | | | | | | | | | op(e3, e4) = e1)
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | BETA: splitting (62) gives:
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | (63) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | REF_CLOSE: (1), (4), (63) are inconsistent by sub-proof #843.
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | (64) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | REF_CLOSE: (4), (61), (64) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | | | #568.
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | End of split
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | (65) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1
% 251.13/59.86 | | | | | | | | | & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) =
% 251.13/59.86 | | | | | | | | | e1)
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | BETA: splitting (65) gives:
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | (66) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | REF_CLOSE: (9), (58), (66) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | | | #903.
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | (67) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 =
% 251.13/59.86 | | | | | | | | | | e1 & op(e0, e4) = e1)
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | BETA: splitting (67) gives:
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | Case 1:
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | | (68) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | | REF_CLOSE: (8), (51), (68) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | | | | #562.
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | | (69) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | | REF_CLOSE: (10), (24), (69) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | | | | #565.
% 251.13/59.86 | | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | | End of split
% 251.13/59.86 | | | | | | | | | |
% 251.13/59.86 | | | | | | | | | End of split
% 251.13/59.86 | | | | | | | | |
% 251.13/59.86 | | | | | | | | End of split
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | Case 2:
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | (70) all_252_3 = e0 & op(e3, e3) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | ALPHA: (70) implies:
% 251.13/59.86 | | | | | | | | (71) op(e3, e3) = e0
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | | REF_CLOSE: (5), (21), (22), (71) are inconsistent by sub-proof
% 251.13/59.86 | | | | | | | | #973.
% 251.13/59.86 | | | | | | | |
% 251.13/59.86 | | | | | | | End of split
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | Case 2:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (72) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 &
% 251.13/59.86 | | | | | | | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | REF_CLOSE: (5), (11), (12), (13), (15), (16), (18), (72) are
% 251.13/59.86 | | | | | | | inconsistent by sub-proof #572.
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | End of split
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | Case 2:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | (73) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 251.13/59.86 | | | | | | op(e0, e4) = e4)
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | BETA: splitting (73) gives:
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | | Case 1:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (74) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | REF_CLOSE: (17), (51), (74) are inconsistent by sub-proof #561.
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | Case 2:
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | (75) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | | REF_CLOSE: (14), (24), (75) are inconsistent by sub-proof #563.
% 251.13/59.86 | | | | | | |
% 251.13/59.86 | | | | | | End of split
% 251.13/59.86 | | | | | |
% 251.13/59.86 | | | | | End of split
% 251.13/59.86 | | | | |
% 251.13/59.86 | | | | End of split
% 251.13/59.86 | | | |
% 251.13/59.86 | | | Case 2:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (76) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | REF_CLOSE: (6), (24), (76) are inconsistent by sub-proof #560.
% 251.13/59.86 | | | |
% 251.13/59.86 | | | End of split
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #560 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.86 (2) all_252_20 = e3
% 251.13/59.86 (3) ~ (e3 = e2)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_20 = e2
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e3 = e2
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #561 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.86 (2) all_252_12 = e2
% 251.13/59.86 (3) ~ (e4 = e2)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_12 = e4
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e4 = e2
% 251.13/59.86 |
% 251.13/59.86 | SIMP: (5) implies:
% 251.13/59.86 | (6) e4 = e2
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (6) imply:
% 251.13/59.86 | (7) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (7) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #562 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.86 (2) all_252_12 = e2
% 251.13/59.86 (3) ~ (e2 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_12 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e2 = e1
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #563 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.86 (2) all_252_20 = e3
% 251.13/59.86 (3) ~ (e4 = e3)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_20 = e4
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e4 = e3
% 251.13/59.86 |
% 251.13/59.86 | SIMP: (5) implies:
% 251.13/59.86 | (6) e4 = e3
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (6) imply:
% 251.13/59.86 | (7) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (7) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #564 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_0 = e0
% 251.13/59.86 (2) all_252_6 = e2
% 251.13/59.86 (3) ~ (e1 = e0)
% 251.13/59.86 (4) all_252_12 = e4
% 251.13/59.86 (5) ~ (e2 = e1)
% 251.13/59.86 (6) ~ (e4 = e1)
% 251.13/59.86 (7) all_252_2 = e0
% 251.13/59.86 (8) ~ (e3 = e1)
% 251.13/59.86 (9) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) |
% 251.13/59.86 (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = e1)
% 251.13/59.86 | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.86 (10) all_252_20 = e3
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (9) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (11) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) =
% 251.13/59.86 | | e1)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (11) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (12) all_252_0 = e1 & op(e4, e4) = e1
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #843.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (13) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #568.
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (14) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) =
% 251.13/59.86 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (14) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (15) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #567.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (16) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0,
% 251.13/59.86 | | | e4) = e1)
% 251.13/59.86 | | |
% 251.13/59.86 | | | BETA: splitting (16) gives:
% 251.13/59.86 | | |
% 251.13/59.86 | | | Case 1:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (17) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #566.
% 251.13/59.86 | | | |
% 251.13/59.86 | | | Case 2:
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | (18) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.86 | | | |
% 251.13/59.86 | | | | REF_CLOSE: (8), (10), (18) are inconsistent by sub-proof #565.
% 251.13/59.86 | | | |
% 251.13/59.86 | | | End of split
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #565 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.86 (2) all_252_20 = e3
% 251.13/59.86 (3) ~ (e3 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_20 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e3 = e1
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #566 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.86 (2) all_252_12 = e4
% 251.13/59.86 (3) ~ (e4 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_12 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e4 = e1
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #567 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_6 = e1 & op(e2, e4) = e1
% 251.13/59.86 (2) all_252_6 = e2
% 251.13/59.86 (3) ~ (e2 = e1)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_6 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e2 = e1
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (5) imply:
% 251.13/59.86 | (6) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (6) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #568 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.86 (2) all_252_2 = e0
% 251.13/59.86 (3) ~ (e1 = e0)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_2 = e1
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e1 = e0
% 251.13/59.86 |
% 251.13/59.86 | SIMP: (5) implies:
% 251.13/59.86 | (6) e1 = e0
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (6) imply:
% 251.13/59.86 | (7) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (7) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #569 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.86 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.86 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (3) ~ (e4 = e0)
% 251.13/59.86 (4) all_252_2 = e4
% 251.13/59.86 (5) op(e3, e1) = all_36_2
% 251.13/59.86 (6) ~ (all_8_2 = e0)
% 251.13/59.86 (7) ~ (all_36_2 = e0)
% 251.13/59.86 (8) op(e3, e0) = all_48_2
% 251.13/59.86 (9) ~ (all_48_2 = e0)
% 251.13/59.86 (10) op(e3, e2) = all_8_2
% 251.13/59.86 (11) ~ (all_244_3 = e0)
% 251.13/59.86 (12) op(e3, e3) = all_244_3
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (1) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (13) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 251.13/59.86 | | e0)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (13) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (14) all_252_2 = e0 & op(e3, e4) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | ALPHA: (14) implies:
% 251.13/59.86 | | | (15) all_252_2 = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | COMBINE_EQS: (4), (15) imply:
% 251.13/59.86 | | | (16) e4 = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REDUCE: (3), (16) imply:
% 251.13/59.86 | | | (17) $false
% 251.13/59.86 | | |
% 251.13/59.86 | | | CLOSE: (17) is inconsistent.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (18) all_252_3 = e0 & op(e3, e3) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | ALPHA: (18) implies:
% 251.13/59.86 | | | (19) op(e3, e3) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (2), (11), (12), (19) are inconsistent by sub-proof #973.
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (20) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 251.13/59.86 | | e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (20) are inconsistent by
% 251.13/59.86 | | sub-proof #572.
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #570 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.86 (2) all_252_0 = e0
% 251.13/59.86 (3) ~ (e4 = e0)
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | ALPHA: (1) implies:
% 251.13/59.86 | (4) all_252_0 = e4
% 251.13/59.86 |
% 251.13/59.86 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.86 | (5) e4 = e0
% 251.13/59.86 |
% 251.13/59.86 | SIMP: (5) implies:
% 251.13/59.86 | (6) e4 = e0
% 251.13/59.86 |
% 251.13/59.86 | REDUCE: (3), (6) imply:
% 251.13/59.86 | (7) $false
% 251.13/59.86 |
% 251.13/59.86 | CLOSE: (7) is inconsistent.
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #571 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) |
% 251.13/59.86 (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.86 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 (2) ~ (e2 = e0)
% 251.13/59.86 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (4) op(e3, e1) = all_36_2
% 251.13/59.86 (5) ~ (all_8_2 = e0)
% 251.13/59.86 (6) ~ (all_36_2 = e0)
% 251.13/59.86 (7) op(e3, e0) = all_48_2
% 251.13/59.86 (8) ~ (all_48_2 = e0)
% 251.13/59.86 (9) all_252_2 = e2
% 251.13/59.86 (10) op(e3, e2) = all_8_2
% 251.13/59.86 (11) ~ (all_244_3 = e0)
% 251.13/59.86 (12) op(e3, e3) = all_244_3
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (1) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (13) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) =
% 251.13/59.86 | | e0)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (13) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (14) all_252_2 = e0 & op(e3, e4) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #692.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (15) all_252_3 = e0 & op(e3, e3) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | ALPHA: (15) implies:
% 251.13/59.86 | | | (16) op(e3, e3) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (3), (11), (12), (16) are inconsistent by sub-proof #973.
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (17) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 251.13/59.86 | | e0) | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (17) are inconsistent by
% 251.13/59.86 | | sub-proof #572.
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #572 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.86 (2) op(e3, e1) = all_36_2
% 251.13/59.86 (3) ~ (all_8_2 = e0)
% 251.13/59.86 (4) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.13/59.86 | (all_252_17 = e0 & op(e3, e0) = e0)
% 251.13/59.86 (5) ~ (all_36_2 = e0)
% 251.13/59.86 (6) op(e3, e0) = all_48_2
% 251.13/59.86 (7) ~ (all_48_2 = e0)
% 251.13/59.86 (8) op(e3, e2) = all_8_2
% 251.13/59.86
% 251.13/59.86 Begin of proof
% 251.13/59.86 |
% 251.13/59.86 | BETA: splitting (4) gives:
% 251.13/59.86 |
% 251.13/59.86 | Case 1:
% 251.13/59.86 | |
% 251.13/59.86 | | (9) all_252_5 = e0 & op(e3, e2) = e0
% 251.13/59.86 | |
% 251.13/59.86 | | REF_CLOSE: (1), (3), (8), (9) are inconsistent by sub-proof #874.
% 251.13/59.86 | |
% 251.13/59.86 | Case 2:
% 251.13/59.86 | |
% 251.13/59.86 | | (10) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0)
% 251.13/59.86 | | = e0)
% 251.13/59.86 | |
% 251.13/59.86 | | BETA: splitting (10) gives:
% 251.13/59.86 | |
% 251.13/59.86 | | Case 1:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (11) all_252_10 = e0 & op(e3, e1) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #726.
% 251.13/59.86 | | |
% 251.13/59.86 | | Case 2:
% 251.13/59.86 | | |
% 251.13/59.86 | | | (12) all_252_17 = e0 & op(e3, e0) = e0
% 251.13/59.86 | | |
% 251.13/59.86 | | | REF_CLOSE: (1), (6), (7), (12) are inconsistent by sub-proof #573.
% 251.13/59.86 | | |
% 251.13/59.86 | | End of split
% 251.13/59.86 | |
% 251.13/59.86 | End of split
% 251.13/59.86 |
% 251.13/59.86 End of proof
% 251.13/59.86
% 251.13/59.86 Sub-proof #573 shows that the following formulas are inconsistent:
% 251.13/59.86 ----------------------------------------------------------------
% 251.13/59.86 (1) all_252_17 = e0 & op(e3, e0) = e0
% 251.13/59.87 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.87 (3) op(e3, e0) = all_48_2
% 251.13/59.87 (4) ~ (all_48_2 = e0)
% 251.13/59.87
% 251.13/59.87 Begin of proof
% 251.13/59.87 |
% 251.13/59.87 | ALPHA: (1) implies:
% 251.13/59.87 | (5) op(e3, e0) = e0
% 251.13/59.87 |
% 251.13/59.87 | GROUND_INST: instantiating (2) with all_48_2, e0, e0, e3, simplifying with
% 251.13/59.87 | (3), (5) gives:
% 251.13/59.87 | (6) all_48_2 = e0
% 251.13/59.87 |
% 251.13/59.87 | REDUCE: (4), (6) imply:
% 251.13/59.87 | (7) $false
% 251.13/59.87 |
% 251.13/59.87 | CLOSE: (7) is inconsistent.
% 251.13/59.87 |
% 251.13/59.87 End of proof
% 251.13/59.87
% 251.13/59.87 Sub-proof #574 shows that the following formulas are inconsistent:
% 251.13/59.87 ----------------------------------------------------------------
% 251.13/59.87 (1) all_32_2 = all_20_2
% 251.13/59.87 (2) ~ (all_4_2 = e4)
% 251.13/59.87 (3) ~ (all_10_2 = e4)
% 251.13/59.87 (4) op(all_4_2, e2) = e1
% 251.13/59.87 (5) ~ (all_84_2 = all_10_2)
% 251.13/59.87 (6) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.13/59.87 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.13/59.87 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.13/59.87 (7) all_94_2 = all_38_2
% 251.13/59.87 (8) op(all_62_2, all_36_2) = e3
% 251.13/59.87 (9) op(all_38_2, e1) = e2
% 251.13/59.87 (10) all_250_13 = all_38_2
% 251.13/59.87 (11) ~ (all_28_2 = all_6_2)
% 251.13/59.87 (12) ~ (e2 = e0)
% 251.13/59.87 (13) op(all_38_2, all_4_2) = e1
% 251.13/59.87 (14) op(all_64_2, e4) = e2
% 251.13/59.87 (15) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.87 all_250_20 = e0
% 251.13/59.87 (16) ~ (all_62_2 = all_22_2)
% 251.13/59.87 (17) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.87 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.87 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.87 (18) op(e4, all_34_2) = e1
% 251.13/59.87 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.87 (20) op(e2, e3) = all_10_2
% 251.13/59.87 (21) ~ (e3 = e2)
% 251.13/59.87 (22) op(e0, e0) = all_244_24
% 251.13/59.87 (23) ~ (e4 = e0)
% 251.13/59.87 (24) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.87 all_250_17 = e0
% 251.13/59.87 (25) ~ (all_12_2 = e3)
% 251.13/59.87 (26) op(e2, e2) = all_244_8
% 251.13/59.87 (27) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.87 all_250_11 = e0
% 251.13/59.87 (28) all_20_1 = all_16_2
% 251.13/59.87 (29) op(e2, e1) = all_38_2
% 251.13/59.87 (30) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.87 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.87 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.87 (31) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.87 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.87 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.87 (32) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.87 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.87 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.87 (33) op(e1, e0) = all_34_2
% 251.13/59.87 (34) op(all_28_2, e2) = e0
% 251.13/59.87 (35) op(e4, e2) = all_6_2
% 251.13/59.87 (36) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.13/59.87 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.13/59.87 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.13/59.87 (37) all_78_2 = all_10_2
% 251.13/59.87 (38) ~ (all_8_2 = all_4_2)
% 251.13/59.87 (39) ~ (e2 = e1)
% 251.13/59.87 (40) op(e0, e2) = all_28_2
% 251.13/59.87 (41) ~ (e4 = e1)
% 251.13/59.87 (42) ~ (all_6_2 = e1)
% 251.13/59.87 (43) op(e1, e4) = all_20_1
% 251.13/59.87 (44) all_106_2 = all_38_2
% 251.13/59.87 (45) ~ (all_244_8 = all_38_2)
% 251.13/59.87 (46) op(all_244_15, all_244_15) = e1
% 251.13/59.87 (47) all_250_21 = all_22_2
% 251.13/59.87 (48) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.87 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.87 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.87 (49) op(e1, e3) = all_62_2
% 251.13/59.87 (50) ~ (e3 = e0)
% 251.13/59.87 (51) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.87 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.87 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.87 (52) ~ (all_38_2 = e0)
% 251.13/59.87 (53) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 251.13/59.87 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 251.13/59.87 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.87 (54) op(all_20_2, e1) = e0
% 251.13/59.87 (55) ~ (all_22_2 = e4)
% 251.13/59.87 (56) all_70_2 = all_62_2
% 251.13/59.87 (57) ~ (e3 = e1)
% 251.13/59.87 (58) op(all_48_2, all_22_2) = e0
% 251.13/59.87 (59) ~ (all_12_2 = e2)
% 251.13/59.87 (60) op(e3, e1) = all_36_2
% 251.13/59.87 (61) ~ (all_28_2 = all_12_2)
% 251.13/59.87 (62) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.87 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.87 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.87 (63) ~ (all_16_2 = e2)
% 251.13/59.87 (64) ~ (all_8_2 = e1)
% 251.13/59.87 (65) op(all_40_2, e0) = e2
% 251.13/59.87 (66) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 251.13/59.87 all_250_22 = e0
% 251.13/59.87 (67) ~ (all_28_2 = all_4_2)
% 251.13/59.87 (68) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.87 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.87 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.87 (69) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.87 all_250_13 = e0
% 251.13/59.87 (70) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.87 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.87 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.87 (71) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 251.13/59.87 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 251.13/59.87 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 251.13/59.87 (72) all_60_2 = e4
% 251.13/59.87 (73) ~ (all_38_2 = e4)
% 251.13/59.87 (74) ~ (all_28_2 = e4)
% 251.13/59.87 (75) ~ (all_26_2 = all_6_2)
% 251.13/59.87 (76) op(all_22_2, e3) = e0
% 251.13/59.87 (77) all_68_2 = all_22_2
% 251.13/59.87 (78) ~ (all_60_2 = e4) | ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 &
% 251.13/59.87 op(e1, e4) = all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 =
% 251.13/59.87 e3) & op(e1, e4) = all_60_1 & $i(all_60_1))
% 251.13/59.87 (79) op(e0, e3) = all_22_2
% 251.13/59.87 (80) ~ (all_28_2 = all_22_2)
% 251.13/59.87 (81) op(all_62_2, e3) = e1
% 251.13/59.87 (82) op(e4, e1) = all_26_2
% 251.13/59.87 (83) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.87 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.87 (84) op(all_10_2, e3) = e2
% 251.13/59.87 (85) op(all_30_2, all_12_2) = e0
% 251.13/59.87 (86) ~ (all_12_2 = e4)
% 251.13/59.87 (87) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.87 all_250_21 = e0
% 251.13/59.87 (88) ~ (all_244_15 = all_62_2)
% 251.13/59.87 (89) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.13/59.87 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.13/59.87 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.13/59.87 (90) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.87 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.87 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.87 (91) all_250_11 = all_10_2
% 251.13/59.87 (92) ~ (all_22_2 = all_12_2)
% 251.13/59.87 (93) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.87 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.87 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.87 (94) op(e1, e1) = all_244_15
% 251.13/59.87 (95) op(e0, e1) = all_20_2
% 251.13/59.87 (96) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.87 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.87 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.87 (97) op(all_48_2, e0) = e3
% 251.13/59.87 (98) all_82_2 = all_28_2
% 251.13/59.87 (99) ~ (all_84_2 = all_22_2)
% 251.13/59.87 (100) op(e1, e2) = all_4_2
% 251.13/59.87 (101) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.87 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.87 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.87 (102) op(all_4_2, all_38_2) = e2
% 251.13/59.87 (103) op(e4, e3) = all_84_2
% 251.13/59.87 (104) all_118_2 = all_22_2
% 251.13/59.87 (105) ~ (all_62_2 = all_10_2)
% 251.13/59.87 (106) ~ (all_22_2 = all_10_2)
% 251.13/59.87 (107) all_250_17 = all_4_2
% 251.13/59.87 (108) ~ (all_38_2 = all_26_2)
% 251.13/59.87 (109) op(all_40_2, all_28_2) = e0
% 251.13/59.87 (110) ~ (e4 = e2)
% 251.13/59.87 (111) ~ (all_244_8 = all_8_2)
% 251.13/59.87 (112) op(e3, e2) = all_8_2
% 251.13/59.87 (113) op(all_36_2, e1) = e3
% 251.13/59.87 (114) ~ (all_38_2 = all_10_2)
% 251.13/59.87 (115) ~ (all_244_15 = all_36_2)
% 251.13/59.87 (116) ~ (all_244_24 = all_22_2)
% 251.13/59.87 (117) op(all_8_2, all_10_2) = e2
% 251.13/59.87 (118) op(all_8_2, e2) = e3
% 251.13/59.87 (119) ~ (all_244_8 = all_28_2)
% 251.13/59.87 (120) all_252_23 = e4
% 251.13/59.87 (121) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.87 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.87 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.87 (122) all_250_22 = all_28_2
% 251.13/59.87 (123) all_250_20 = all_12_2
% 251.13/59.87 (124) all_26_2 = e0
% 251.13/59.87 (125) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.87 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.87 (126) all_90_2 = all_22_2
% 251.13/59.87 (127) all_46_2 = all_36_2
% 251.13/59.87 (128) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(e3, e1) = all_22_1 &
% 251.13/59.87 op(e1, all_22_1) = all_22_0 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 251.13/59.87 (all_22_1 = e4) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 251.13/59.87 (129) op(all_30_2, e0) = e4
% 251.13/59.87 (130) op(all_244_24, all_244_24) = e0
% 251.13/59.87 (131) op(e0, e4) = all_12_2
% 251.13/59.87 (132) ~ (all_34_2 = all_4_2)
% 251.13/59.87 (133) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.87 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.87 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.87 (134) op(all_64_2, all_6_2) = e4
% 251.13/59.87 (135) all_124_2 = all_10_2
% 251.13/59.87
% 251.13/59.87 Begin of proof
% 251.13/59.87 |
% 251.13/59.87 | REDUCE: (82), (124) imply:
% 251.13/59.87 | (136) op(e4, e1) = e0
% 251.13/59.87 |
% 251.13/59.87 | REDUCE: (28), (43) imply:
% 251.13/59.87 | (137) op(e1, e4) = all_16_2
% 251.13/59.87 |
% 251.13/59.87 | BETA: splitting (128) gives:
% 251.13/59.87 |
% 251.13/59.87 | Case 1:
% 251.13/59.87 | |
% 251.13/59.87 | | (138) ~ (all_22_2 = e1)
% 251.13/59.87 | |
% 251.13/59.87 | | BETA: splitting (78) gives:
% 251.13/59.87 | |
% 251.13/59.87 | | Case 1:
% 251.13/59.87 | | |
% 251.13/59.87 | | | (139) ~ (all_60_2 = e4)
% 251.13/59.87 | | |
% 251.13/59.87 | | | REDUCE: (72), (139) imply:
% 251.13/59.87 | | | (140) $false
% 251.13/59.87 | | |
% 251.13/59.87 | | | CLOSE: (140) is inconsistent.
% 251.13/59.87 | | |
% 251.13/59.87 | | Case 2:
% 251.13/59.87 | | |
% 251.13/59.87 | | | (141) ( ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 251.13/59.87 | | | all_60_1 & $i(all_60_0) & $i(all_60_1)) | ( ~ (all_60_1 = e3) &
% 251.13/59.87 | | | op(e1, e4) = all_60_1 & $i(all_60_1))
% 251.13/59.87 | | |
% 251.13/59.87 | | | BETA: splitting (141) gives:
% 251.13/59.87 | | |
% 251.13/59.87 | | | Case 1:
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | (142) ~ (all_60_0 = e2) & op(e4, all_60_1) = all_60_0 & op(e1, e4) =
% 251.13/59.87 | | | | all_60_1 & $i(all_60_0) & $i(all_60_1)
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | ALPHA: (142) implies:
% 251.13/59.87 | | | | (143) op(e1, e4) = all_60_1
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.13/59.87 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 251.13/59.87 | | | | (22), (23), (24), (25), (26), (27), (29), (30), (31), (32),
% 251.13/59.87 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 251.13/59.87 | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 251.13/59.87 | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 251.13/59.87 | | | | (64), (65), (66), (67), (68), (69), (70), (71), (73), (74),
% 251.13/59.87 | | | | (75), (76), (77), (79), (80), (81), (82), (83), (84), (85),
% 251.13/59.87 | | | | (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 251.13/59.87 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 251.13/59.87 | | | | (106), (107), (108), (109), (110), (111), (112), (113),
% 251.13/59.87 | | | | (114), (115), (116), (117), (118), (119), (120), (121),
% 251.13/59.87 | | | | (122), (123), (125), (126), (127), (129), (130), (131),
% 251.13/59.87 | | | | (132), (133), (134), (135), (136), (137), (138), (143) are
% 251.13/59.87 | | | | inconsistent by sub-proof #575.
% 251.13/59.87 | | | |
% 251.13/59.87 | | | Case 2:
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | (144) ~ (all_60_1 = e3) & op(e1, e4) = all_60_1 & $i(all_60_1)
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | ALPHA: (144) implies:
% 251.13/59.87 | | | | (145) op(e1, e4) = all_60_1
% 251.13/59.87 | | | |
% 251.13/59.87 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.13/59.87 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 251.13/59.87 | | | | (22), (23), (24), (25), (26), (27), (29), (30), (31), (32),
% 251.13/59.87 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 251.13/59.87 | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 251.13/59.87 | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 251.13/59.87 | | | | (64), (65), (66), (67), (68), (69), (70), (71), (73), (74),
% 251.13/59.87 | | | | (75), (76), (77), (79), (80), (81), (82), (83), (84), (85),
% 251.13/59.87 | | | | (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 251.13/59.87 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 251.13/59.87 | | | | (106), (107), (108), (109), (110), (111), (112), (113),
% 251.13/59.87 | | | | (114), (115), (116), (117), (118), (119), (120), (121),
% 251.13/59.87 | | | | (122), (123), (125), (126), (127), (129), (130), (131),
% 251.13/59.87 | | | | (132), (133), (134), (135), (136), (137), (138), (145) are
% 251.13/59.87 | | | | inconsistent by sub-proof #575.
% 251.13/59.87 | | | |
% 251.13/59.87 | | | End of split
% 251.13/59.87 | | |
% 251.13/59.87 | | End of split
% 251.13/59.87 | |
% 251.13/59.87 | Case 2:
% 251.13/59.87 | |
% 251.13/59.87 | | (146) all_22_2 = e1
% 251.13/59.87 | |
% 251.13/59.87 | | REDUCE: (92), (146) imply:
% 251.13/59.87 | | (147) ~ (all_12_2 = e1)
% 251.13/59.87 | |
% 251.13/59.87 | | SIMP: (147) implies:
% 251.13/59.87 | | (148) ~ (all_12_2 = e1)
% 251.13/59.87 | |
% 251.13/59.87 | | REF_CLOSE: (15), (19), (25), (59), (85), (86), (123), (129), (148) are
% 251.13/59.87 | | inconsistent by sub-proof #582.
% 251.13/59.87 | |
% 251.13/59.87 | End of split
% 251.13/59.87 |
% 251.13/59.87 End of proof
% 251.13/59.87
% 251.13/59.87 Sub-proof #575 shows that the following formulas are inconsistent:
% 251.13/59.87 ----------------------------------------------------------------
% 251.13/59.87 (1) all_32_2 = all_20_2
% 251.13/59.87 (2) ~ (all_4_2 = e4)
% 251.13/59.87 (3) ~ (all_10_2 = e4)
% 251.13/59.87 (4) op(all_4_2, e2) = e1
% 251.13/59.87 (5) op(e4, e1) = e0
% 251.13/59.87 (6) ~ (all_84_2 = all_10_2)
% 251.13/59.87 (7) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.13/59.87 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.13/59.87 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.13/59.87 (8) all_94_2 = all_38_2
% 251.13/59.87 (9) op(all_62_2, all_36_2) = e3
% 251.13/59.87 (10) op(all_38_2, e1) = e2
% 251.13/59.87 (11) all_250_13 = all_38_2
% 251.13/59.87 (12) ~ (all_28_2 = all_6_2)
% 251.13/59.87 (13) ~ (e2 = e0)
% 251.13/59.87 (14) op(all_38_2, all_4_2) = e1
% 251.13/59.87 (15) op(all_64_2, e4) = e2
% 251.13/59.87 (16) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.87 all_250_20 = e0
% 251.13/59.87 (17) ~ (all_62_2 = all_22_2)
% 251.13/59.87 (18) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.87 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.87 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.87 (19) op(e4, all_34_2) = e1
% 251.13/59.87 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.87 (21) op(e2, e3) = all_10_2
% 251.13/59.87 (22) ~ (e3 = e2)
% 251.13/59.87 (23) op(e0, e0) = all_244_24
% 251.13/59.87 (24) ~ (e4 = e0)
% 251.13/59.87 (25) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.87 all_250_17 = e0
% 251.13/59.87 (26) ~ (all_12_2 = e3)
% 251.13/59.87 (27) op(e2, e2) = all_244_8
% 251.13/59.87 (28) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.87 all_250_11 = e0
% 251.13/59.87 (29) op(e2, e1) = all_38_2
% 251.13/59.87 (30) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.87 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.87 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.87 (31) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.87 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.87 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.87 (32) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.87 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.87 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.87 (33) op(e1, e0) = all_34_2
% 251.13/59.87 (34) op(all_28_2, e2) = e0
% 251.13/59.87 (35) op(e4, e2) = all_6_2
% 251.13/59.87 (36) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.13/59.87 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.13/59.87 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.13/59.87 (37) all_78_2 = all_10_2
% 251.13/59.87 (38) ~ (all_8_2 = all_4_2)
% 251.13/59.87 (39) ~ (e2 = e1)
% 251.13/59.87 (40) op(e0, e2) = all_28_2
% 251.13/59.87 (41) ~ (e4 = e1)
% 251.13/59.87 (42) ~ (all_6_2 = e1)
% 251.13/59.87 (43) all_106_2 = all_38_2
% 251.13/59.87 (44) ~ (all_244_8 = all_38_2)
% 251.13/59.87 (45) op(all_244_15, all_244_15) = e1
% 251.13/59.87 (46) all_250_21 = all_22_2
% 251.13/59.87 (47) op(e1, e4) = all_16_2
% 251.13/59.87 (48) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.87 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.87 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.87 (49) op(e1, e3) = all_62_2
% 251.13/59.87 (50) ~ (e3 = e0)
% 251.13/59.87 (51) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.87 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.87 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.87 (52) ~ (all_38_2 = e0)
% 251.13/59.87 (53) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 251.13/59.87 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 251.13/59.87 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.87 (54) op(all_20_2, e1) = e0
% 251.13/59.87 (55) ~ (all_22_2 = e4)
% 251.13/59.87 (56) all_70_2 = all_62_2
% 251.13/59.87 (57) ~ (e3 = e1)
% 251.13/59.87 (58) op(all_48_2, all_22_2) = e0
% 251.13/59.87 (59) ~ (all_12_2 = e2)
% 251.13/59.87 (60) op(e3, e1) = all_36_2
% 251.13/59.87 (61) ~ (all_28_2 = all_12_2)
% 251.13/59.87 (62) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.87 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.87 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.87 (63) ~ (all_16_2 = e2)
% 251.13/59.87 (64) ~ (all_8_2 = e1)
% 251.13/59.87 (65) op(all_40_2, e0) = e2
% 251.13/59.87 (66) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 251.13/59.87 all_250_22 = e0
% 251.13/59.87 (67) ~ (all_22_2 = e1)
% 251.13/59.87 (68) ~ (all_28_2 = all_4_2)
% 251.13/59.87 (69) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.87 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.87 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.87 (70) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.87 all_250_13 = e0
% 251.13/59.87 (71) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.87 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.87 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.87 (72) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 251.13/59.87 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 251.13/59.87 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 251.13/59.87 (73) ~ (all_38_2 = e4)
% 251.13/59.87 (74) op(e1, e4) = all_60_1
% 251.13/59.87 (75) ~ (all_28_2 = e4)
% 251.13/59.87 (76) ~ (all_26_2 = all_6_2)
% 251.13/59.87 (77) op(all_22_2, e3) = e0
% 251.13/59.87 (78) all_68_2 = all_22_2
% 251.13/59.87 (79) op(e0, e3) = all_22_2
% 251.13/59.87 (80) ~ (all_28_2 = all_22_2)
% 251.13/59.87 (81) op(all_62_2, e3) = e1
% 251.13/59.87 (82) op(e4, e1) = all_26_2
% 251.13/59.87 (83) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.87 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.87 (84) op(all_10_2, e3) = e2
% 251.13/59.87 (85) op(all_30_2, all_12_2) = e0
% 251.13/59.87 (86) ~ (all_12_2 = e4)
% 251.13/59.87 (87) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.87 all_250_21 = e0
% 251.13/59.87 (88) ~ (all_244_15 = all_62_2)
% 251.13/59.87 (89) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.13/59.87 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.13/59.87 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.13/59.87 (90) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.87 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.87 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.87 (91) all_250_11 = all_10_2
% 251.13/59.87 (92) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.87 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.87 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.87 (93) op(e1, e1) = all_244_15
% 251.13/59.87 (94) op(e0, e1) = all_20_2
% 251.13/59.87 (95) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.87 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.87 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.87 (96) op(all_48_2, e0) = e3
% 251.13/59.87 (97) all_82_2 = all_28_2
% 251.13/59.87 (98) ~ (all_84_2 = all_22_2)
% 251.13/59.87 (99) op(e1, e2) = all_4_2
% 251.13/59.87 (100) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.87 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.87 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.87 (101) op(all_4_2, all_38_2) = e2
% 251.13/59.87 (102) op(e4, e3) = all_84_2
% 251.13/59.87 (103) all_118_2 = all_22_2
% 251.13/59.87 (104) ~ (all_62_2 = all_10_2)
% 251.13/59.87 (105) ~ (all_22_2 = all_10_2)
% 251.13/59.87 (106) all_250_17 = all_4_2
% 251.13/59.87 (107) ~ (all_38_2 = all_26_2)
% 251.13/59.87 (108) op(all_40_2, all_28_2) = e0
% 251.13/59.87 (109) ~ (e4 = e2)
% 251.13/59.87 (110) ~ (all_244_8 = all_8_2)
% 251.13/59.87 (111) op(e3, e2) = all_8_2
% 251.13/59.87 (112) op(all_36_2, e1) = e3
% 251.13/59.87 (113) ~ (all_38_2 = all_10_2)
% 251.13/59.87 (114) ~ (all_244_15 = all_36_2)
% 251.13/59.87 (115) ~ (all_244_24 = all_22_2)
% 251.13/59.87 (116) op(all_8_2, all_10_2) = e2
% 251.13/59.87 (117) op(all_8_2, e2) = e3
% 251.13/59.87 (118) ~ (all_244_8 = all_28_2)
% 251.13/59.87 (119) all_252_23 = e4
% 251.13/59.87 (120) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.87 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.87 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.87 (121) all_250_22 = all_28_2
% 251.13/59.88 (122) all_250_20 = all_12_2
% 251.13/59.88 (123) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.88 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.88 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.88 (124) all_90_2 = all_22_2
% 251.13/59.88 (125) all_46_2 = all_36_2
% 251.13/59.88 (126) op(all_30_2, e0) = e4
% 251.13/59.88 (127) op(all_244_24, all_244_24) = e0
% 251.13/59.88 (128) op(e0, e4) = all_12_2
% 251.13/59.88 (129) ~ (all_34_2 = all_4_2)
% 251.13/59.88 (130) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.88 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.88 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.88 (131) op(all_64_2, all_6_2) = e4
% 251.13/59.88 (132) all_124_2 = all_10_2
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | GROUND_INST: instantiating (20) with all_16_2, all_60_1, e4, e1, simplifying
% 251.13/59.88 | with (47), (74) gives:
% 251.13/59.88 | (133) all_60_1 = all_16_2
% 251.13/59.88 |
% 251.13/59.88 | BETA: splitting (72) gives:
% 251.13/59.88 |
% 251.13/59.88 | Case 1:
% 251.13/59.88 | |
% 251.13/59.88 | | (134) ~ (all_28_2 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | BETA: splitting (36) gives:
% 251.13/59.88 | |
% 251.13/59.88 | | Case 1:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (135) ~ (all_34_2 = e2)
% 251.13/59.88 | | |
% 251.13/59.88 | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 251.13/59.88 | | | (16), (17), (18), (20), (21), (26), (27), (28), (29), (33),
% 251.13/59.88 | | | (37), (44), (45), (46), (47), (48), (49), (52), (55), (56),
% 251.13/59.88 | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 251.13/59.88 | | | (69), (70), (71), (73), (75), (79), (80), (81), (84), (85),
% 251.13/59.88 | | | (86), (87), (88), (90), (91), (92), (93), (95), (96), (97),
% 251.13/59.88 | | | (98), (99), (101), (102), (104), (105), (108), (111), (112),
% 251.13/59.88 | | | (113), (114), (119), (120), (121), (122), (124), (125), (126),
% 251.13/59.88 | | | (132), (134), (135) are inconsistent by sub-proof #578.
% 251.13/59.88 | | |
% 251.13/59.88 | | Case 2:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (136) all_34_2 = e2
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (19), (136) imply:
% 251.13/59.88 | | | (137) op(e4, e2) = e1
% 251.13/59.88 | | |
% 251.13/59.88 | | | REF_CLOSE: (20), (35), (42), (137) are inconsistent by sub-proof #930.
% 251.13/59.88 | | |
% 251.13/59.88 | | End of split
% 251.13/59.88 | |
% 251.13/59.88 | Case 2:
% 251.13/59.88 | |
% 251.13/59.88 | | (138) all_28_2 = e3
% 251.13/59.88 | | (139) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 251.13/59.88 | | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) &
% 251.13/59.88 | | op(e2, e3) = all_28_1 & $i(all_28_1))
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (118), (138) imply:
% 251.13/59.88 | | (140) ~ (all_244_8 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (12), (138) imply:
% 251.13/59.88 | | (141) ~ (all_6_2 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | SIMP: (141) implies:
% 251.13/59.88 | | (142) ~ (all_6_2 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (68), (138) imply:
% 251.13/59.88 | | (143) ~ (all_4_2 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | SIMP: (143) implies:
% 251.13/59.88 | | (144) ~ (all_4_2 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (75), (138) imply:
% 251.13/59.88 | | (145) ~ (e4 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | SIMP: (145) implies:
% 251.13/59.88 | | (146) ~ (e4 = e3)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (34), (138) imply:
% 251.13/59.88 | | (147) op(e3, e2) = e0
% 251.13/59.88 | |
% 251.13/59.88 | | BETA: splitting (100) gives:
% 251.13/59.88 | |
% 251.13/59.88 | | Case 1:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (148) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2)
% 251.13/59.88 | | | = e3)
% 251.13/59.88 | | |
% 251.13/59.88 | | | BETA: splitting (148) gives:
% 251.13/59.88 | | |
% 251.13/59.88 | | | Case 1:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (149) all_252_4 = e3 & op(e4, e2) = e3
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REF_CLOSE: (20), (35), (142), (149) are inconsistent by sub-proof #577.
% 251.13/59.88 | | | |
% 251.13/59.88 | | | Case 2:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (150) all_252_5 = e3 & op(e3, e2) = e3
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REF_CLOSE: (20), (50), (111), (147), (150) are inconsistent by sub-proof
% 251.13/59.88 | | | | #576.
% 251.13/59.88 | | | |
% 251.13/59.88 | | | End of split
% 251.13/59.88 | | |
% 251.13/59.88 | | Case 2:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (151) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1,
% 251.13/59.88 | | | e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.88 | | |
% 251.13/59.88 | | | BETA: splitting (151) gives:
% 251.13/59.88 | | |
% 251.13/59.88 | | | Case 1:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (152) all_252_8 = e3 & op(e2, e2) = e3
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | ALPHA: (152) implies:
% 251.13/59.88 | | | | (153) op(e2, e2) = e3
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REF_CLOSE: (20), (27), (140), (153) are inconsistent by sub-proof #877.
% 251.13/59.88 | | | |
% 251.13/59.88 | | | Case 2:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (154) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0,
% 251.13/59.88 | | | | e2) = e3)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | BETA: splitting (154) gives:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | Case 1:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (155) all_252_14 = e3 & op(e1, e2) = e3
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REF_CLOSE: (20), (99), (144), (155) are inconsistent by sub-proof
% 251.13/59.88 | | | | | #858.
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | Case 2:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (156) all_252_22 = e3 & op(e0, e2) = e3
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | ALPHA: (156) implies:
% 251.13/59.88 | | | | | (157) all_252_22 = e3
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (11), (13), (14), (15),
% 251.13/59.88 | | | | | (18), (20), (21), (22), (23), (24), (25), (27), (28), (29),
% 251.13/59.88 | | | | | (30), (31), (32), (33), (35), (36), (37), (38), (39), (40),
% 251.13/59.88 | | | | | (41), (42), (43), (44), (45), (46), (47), (48), (49), (51),
% 251.13/59.88 | | | | | (53), (54), (56), (57), (58), (59), (60), (62), (63), (64),
% 251.13/59.88 | | | | | (67), (69), (70), (71), (76), (77), (78), (79), (82), (83),
% 251.13/59.88 | | | | | (84), (87), (89), (90), (91), (93), (94), (96), (99),
% 251.13/59.88 | | | | | (103), (105), (106), (107), (109), (110), (111), (112),
% 251.13/59.88 | | | | | (113), (114), (115), (116), (117), (120), (123), (124),
% 251.13/59.88 | | | | | (125), (127), (128), (129), (130), (131), (132), (139),
% 251.13/59.88 | | | | | (144), (146), (147), (157) are inconsistent by sub-proof
% 251.13/59.88 | | | | | #635.
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | End of split
% 251.13/59.88 | | | |
% 251.13/59.88 | | | End of split
% 251.13/59.88 | | |
% 251.13/59.88 | | End of split
% 251.13/59.88 | |
% 251.13/59.88 | End of split
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #576 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.88 (2) op(e3, e2) = e0
% 251.13/59.88 (3) all_252_5 = e3 & op(e3, e2) = e3
% 251.13/59.88 (4) ~ (e3 = e0)
% 251.13/59.88 (5) op(e3, e2) = all_8_2
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | ALPHA: (3) implies:
% 251.13/59.88 | (6) op(e3, e2) = e3
% 251.13/59.88 |
% 251.13/59.88 | GROUND_INST: instantiating (1) with all_8_2, e0, e2, e3, simplifying with (2),
% 251.13/59.88 | (5) gives:
% 251.13/59.88 | (7) all_8_2 = e0
% 251.13/59.88 |
% 251.13/59.88 | GROUND_INST: instantiating (1) with all_8_2, e3, e2, e3, simplifying with (5),
% 251.13/59.88 | (6) gives:
% 251.13/59.88 | (8) all_8_2 = e3
% 251.13/59.88 |
% 251.13/59.88 | COMBINE_EQS: (7), (8) imply:
% 251.13/59.88 | (9) e3 = e0
% 251.13/59.88 |
% 251.13/59.88 | SIMP: (9) implies:
% 251.13/59.88 | (10) e3 = e0
% 251.13/59.88 |
% 251.13/59.88 | REDUCE: (4), (10) imply:
% 251.13/59.88 | (11) $false
% 251.13/59.88 |
% 251.13/59.88 | CLOSE: (11) is inconsistent.
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #577 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) all_252_4 = e3 & op(e4, e2) = e3
% 251.13/59.88 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.88 (3) op(e4, e2) = all_6_2
% 251.13/59.88 (4) ~ (all_6_2 = e3)
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | ALPHA: (1) implies:
% 251.13/59.88 | (5) op(e4, e2) = e3
% 251.13/59.88 |
% 251.13/59.88 | GROUND_INST: instantiating (2) with all_6_2, e3, e2, e4, simplifying with (3),
% 251.13/59.88 | (5) gives:
% 251.13/59.88 | (6) all_6_2 = e3
% 251.13/59.88 |
% 251.13/59.88 | REDUCE: (4), (6) imply:
% 251.13/59.88 | (7) $false
% 251.13/59.88 |
% 251.13/59.88 | CLOSE: (7) is inconsistent.
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #578 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) ~ (all_10_2 = e4)
% 251.13/59.88 (2) op(all_4_2, e2) = e1
% 251.13/59.88 (3) op(e4, e1) = e0
% 251.13/59.88 (4) ~ (all_84_2 = all_10_2)
% 251.13/59.88 (5) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.13/59.88 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.13/59.88 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.13/59.88 (6) all_94_2 = all_38_2
% 251.13/59.88 (7) op(all_62_2, all_36_2) = e3
% 251.13/59.88 (8) op(all_38_2, e1) = e2
% 251.13/59.88 (9) all_250_13 = all_38_2
% 251.13/59.88 (10) ~ (e2 = e0)
% 251.13/59.88 (11) op(all_38_2, all_4_2) = e1
% 251.13/59.88 (12) ~ (all_28_2 = e3)
% 251.13/59.88 (13) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.88 all_250_20 = e0
% 251.13/59.88 (14) ~ (all_62_2 = all_22_2)
% 251.13/59.88 (15) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.88 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.88 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.88 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.88 (17) op(e2, e3) = all_10_2
% 251.13/59.88 (18) ~ (all_12_2 = e3)
% 251.13/59.88 (19) op(e2, e2) = all_244_8
% 251.13/59.88 (20) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.88 all_250_11 = e0
% 251.13/59.88 (21) op(e2, e1) = all_38_2
% 251.13/59.88 (22) op(e1, e0) = all_34_2
% 251.13/59.88 (23) all_78_2 = all_10_2
% 251.13/59.88 (24) ~ (all_34_2 = e2)
% 251.13/59.88 (25) ~ (all_244_8 = all_38_2)
% 251.13/59.88 (26) op(all_244_15, all_244_15) = e1
% 251.13/59.88 (27) all_250_21 = all_22_2
% 251.13/59.88 (28) op(e1, e4) = all_16_2
% 251.13/59.88 (29) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.88 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.88 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.88 (30) op(e1, e3) = all_62_2
% 251.13/59.88 (31) ~ (all_38_2 = e0)
% 251.13/59.88 (32) ~ (all_22_2 = e4)
% 251.13/59.88 (33) all_70_2 = all_62_2
% 251.13/59.88 (34) op(all_48_2, all_22_2) = e0
% 251.13/59.88 (35) ~ (all_12_2 = e2)
% 251.13/59.88 (36) op(e3, e1) = all_36_2
% 251.13/59.88 (37) ~ (all_28_2 = all_12_2)
% 251.13/59.88 (38) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.88 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.88 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.88 (39) ~ (all_16_2 = e2)
% 251.13/59.88 (40) ~ (all_8_2 = e1)
% 251.13/59.88 (41) op(all_40_2, e0) = e2
% 251.13/59.88 (42) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 251.13/59.88 all_250_22 = e0
% 251.13/59.88 (43) ~ (all_22_2 = e1)
% 251.13/59.88 (44) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.88 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.88 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.88 (45) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.88 all_250_13 = e0
% 251.13/59.88 (46) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.88 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.88 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.88 (47) ~ (all_38_2 = e4)
% 251.13/59.88 (48) ~ (all_28_2 = e4)
% 251.13/59.88 (49) op(e0, e3) = all_22_2
% 251.13/59.88 (50) ~ (all_28_2 = all_22_2)
% 251.13/59.88 (51) op(all_62_2, e3) = e1
% 251.13/59.88 (52) op(all_10_2, e3) = e2
% 251.13/59.88 (53) op(all_30_2, all_12_2) = e0
% 251.13/59.88 (54) ~ (all_12_2 = e4)
% 251.13/59.88 (55) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.88 all_250_21 = e0
% 251.13/59.88 (56) ~ (all_244_15 = all_62_2)
% 251.13/59.88 (57) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.88 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.88 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.88 (58) all_250_11 = all_10_2
% 251.13/59.88 (59) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.88 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.88 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.88 (60) op(e1, e1) = all_244_15
% 251.13/59.88 (61) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.88 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.88 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.88 (62) op(all_48_2, e0) = e3
% 251.13/59.88 (63) all_82_2 = all_28_2
% 251.13/59.88 (64) ~ (all_84_2 = all_22_2)
% 251.13/59.88 (65) op(e1, e2) = all_4_2
% 251.13/59.88 (66) op(all_4_2, all_38_2) = e2
% 251.13/59.88 (67) op(e4, e3) = all_84_2
% 251.13/59.88 (68) ~ (all_62_2 = all_10_2)
% 251.13/59.88 (69) ~ (all_22_2 = all_10_2)
% 251.13/59.88 (70) op(all_40_2, all_28_2) = e0
% 251.13/59.88 (71) op(e3, e2) = all_8_2
% 251.13/59.88 (72) op(all_36_2, e1) = e3
% 251.13/59.88 (73) ~ (all_38_2 = all_10_2)
% 251.13/59.88 (74) ~ (all_244_15 = all_36_2)
% 251.13/59.88 (75) all_252_23 = e4
% 251.13/59.88 (76) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.88 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.88 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.88 (77) all_250_22 = all_28_2
% 251.13/59.88 (78) all_250_20 = all_12_2
% 251.13/59.88 (79) all_90_2 = all_22_2
% 251.13/59.88 (80) all_46_2 = all_36_2
% 251.13/59.88 (81) op(all_30_2, e0) = e4
% 251.13/59.88 (82) all_124_2 = all_10_2
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | BETA: splitting (44) gives:
% 251.13/59.88 |
% 251.13/59.88 | Case 1:
% 251.13/59.88 | |
% 251.13/59.88 | | (83) ~ (all_46_2 = e2)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (80), (83) imply:
% 251.13/59.88 | | (84) ~ (all_36_2 = e2)
% 251.13/59.88 | |
% 251.13/59.88 | | BETA: splitting (61) gives:
% 251.13/59.88 | |
% 251.13/59.88 | | Case 1:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (85) ~ (all_62_2 = e4)
% 251.13/59.88 | | |
% 251.13/59.88 | | | BETA: splitting (46) gives:
% 251.13/59.88 | | |
% 251.13/59.88 | | | Case 1:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (86) ~ (all_70_2 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REDUCE: (33), (86) imply:
% 251.13/59.88 | | | | (87) ~ (all_62_2 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | BETA: splitting (38) gives:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | Case 1:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (88) ~ (all_78_2 = e1)
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REDUCE: (23), (88) imply:
% 251.13/59.88 | | | | | (89) ~ (all_10_2 = e1)
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (12), (13), (15), (16), (18),
% 251.13/59.88 | | | | | (19), (20), (25), (26), (27), (29), (31), (32), (34), (35),
% 251.13/59.88 | | | | | (36), (37), (41), (42), (43), (45), (47), (48), (49), (50),
% 251.13/59.88 | | | | | (52), (53), (54), (55), (57), (58), (60), (62), (63), (69),
% 251.13/59.88 | | | | | (70), (73), (77), (78), (79), (81), (82), (84), (89) are
% 251.13/59.88 | | | | | inconsistent by sub-proof #581.
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | Case 2:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (90) all_78_2 = e1
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | COMBINE_EQS: (23), (90) imply:
% 251.13/59.88 | | | | | (91) all_10_2 = e1
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REDUCE: (52), (91) imply:
% 251.13/59.88 | | | | | (92) op(e1, e3) = e2
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REF_CLOSE: (16), (30), (87), (92) are inconsistent by sub-proof #972.
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | End of split
% 251.13/59.88 | | | |
% 251.13/59.88 | | | Case 2:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | (93) all_70_2 = e2
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | COMBINE_EQS: (33), (93) imply:
% 251.13/59.88 | | | | (94) all_62_2 = e2
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REDUCE: (56), (94) imply:
% 251.13/59.88 | | | | (95) ~ (all_244_15 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REDUCE: (68), (94) imply:
% 251.13/59.88 | | | | (96) ~ (all_10_2 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | SIMP: (96) implies:
% 251.13/59.88 | | | | (97) ~ (all_10_2 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REDUCE: (85), (94) imply:
% 251.13/59.88 | | | | (98) ~ (e4 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | SIMP: (98) implies:
% 251.13/59.88 | | | | (99) ~ (e4 = e2)
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | REDUCE: (51), (94) imply:
% 251.13/59.88 | | | | (100) op(e2, e3) = e1
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | BETA: splitting (59) gives:
% 251.13/59.88 | | | |
% 251.13/59.88 | | | | Case 1:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (101) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 &
% 251.13/59.88 | | | | | op(e3, e1) = e2)
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | REF_CLOSE: (3), (10), (16), (36), (84), (101) are inconsistent by
% 251.13/59.88 | | | | | sub-proof #580.
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | Case 2:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | (102) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 &
% 251.13/59.88 | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | BETA: splitting (102) gives:
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | | Case 1:
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | | (103) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | | REF_CLOSE: (2), (16), (17), (21), (66), (97), (100), (103) are
% 251.13/59.88 | | | | | | inconsistent by sub-proof #967.
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | Case 2:
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | | (104) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 251.13/59.88 | | | | | | op(e0, e1) = e2)
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | | BETA: splitting (104) gives:
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | | Case 1:
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | | (105) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | | REF_CLOSE: (16), (60), (95), (105) are inconsistent by sub-proof
% 251.13/59.88 | | | | | | | #966.
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | Case 2:
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | | (106) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | | REF_CLOSE: (75), (99), (106) are inconsistent by sub-proof #579.
% 251.13/59.88 | | | | | | |
% 251.13/59.88 | | | | | | End of split
% 251.13/59.88 | | | | | |
% 251.13/59.88 | | | | | End of split
% 251.13/59.88 | | | | |
% 251.13/59.88 | | | | End of split
% 251.13/59.88 | | | |
% 251.13/59.88 | | | End of split
% 251.13/59.88 | | |
% 251.13/59.88 | | Case 2:
% 251.13/59.88 | | |
% 251.13/59.88 | | | (107) all_62_2 = e4
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (14), (107) imply:
% 251.13/59.88 | | | (108) ~ (all_22_2 = e4)
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (68), (107) imply:
% 251.13/59.88 | | | (109) ~ (all_10_2 = e4)
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (51), (107) imply:
% 251.13/59.88 | | | (110) op(e4, e3) = e1
% 251.13/59.88 | | |
% 251.13/59.88 | | | GROUND_INST: instantiating (16) with all_84_2, e1, e3, e4, simplifying
% 251.13/59.88 | | | with (67), (110) gives:
% 251.13/59.88 | | | (111) all_84_2 = e1
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (64), (111) imply:
% 251.13/59.88 | | | (112) ~ (all_22_2 = e1)
% 251.13/59.88 | | |
% 251.13/59.88 | | | REDUCE: (4), (111) imply:
% 251.13/59.88 | | | (113) ~ (all_10_2 = e1)
% 251.13/59.88 | | |
% 251.13/59.88 | | | SIMP: (113) implies:
% 251.13/59.88 | | | (114) ~ (all_10_2 = e1)
% 251.13/59.88 | | |
% 251.13/59.88 | | | REF_CLOSE: (1), (5), (6), (8), (9), (12), (13), (15), (16), (18), (19),
% 251.13/59.88 | | | (20), (25), (26), (27), (29), (31), (32), (34), (35), (36),
% 251.13/59.88 | | | (37), (41), (42), (43), (45), (47), (48), (49), (50), (52),
% 251.13/59.88 | | | (53), (54), (55), (57), (58), (60), (62), (63), (69), (70),
% 251.13/59.88 | | | (73), (77), (78), (79), (81), (82), (84), (114) are
% 251.13/59.88 | | | inconsistent by sub-proof #581.
% 251.13/59.88 | | |
% 251.13/59.88 | | End of split
% 251.13/59.88 | |
% 251.13/59.88 | Case 2:
% 251.13/59.88 | |
% 251.13/59.88 | | (115) all_46_2 = e2
% 251.13/59.88 | | (116) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.88 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 251.13/59.88 | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.88 | |
% 251.13/59.88 | | COMBINE_EQS: (80), (115) imply:
% 251.13/59.88 | | (117) all_36_2 = e2
% 251.13/59.88 | |
% 251.13/59.88 | | SIMP: (117) implies:
% 251.13/59.88 | | (118) all_36_2 = e2
% 251.13/59.88 | |
% 251.13/59.88 | | REF_CLOSE: (7), (11), (16), (19), (21), (22), (24), (25), (28), (30), (33),
% 251.13/59.88 | | (39), (40), (46), (60), (65), (71), (72), (74), (76), (116),
% 251.13/59.88 | | (118) are inconsistent by sub-proof #796.
% 251.13/59.88 | |
% 251.13/59.88 | End of split
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #579 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.88 (2) all_252_23 = e4
% 251.13/59.88 (3) ~ (e4 = e2)
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | ALPHA: (1) implies:
% 251.13/59.88 | (4) all_252_23 = e2
% 251.13/59.88 |
% 251.13/59.88 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.88 | (5) e4 = e2
% 251.13/59.88 |
% 251.13/59.88 | REDUCE: (3), (5) imply:
% 251.13/59.88 | (6) $false
% 251.13/59.88 |
% 251.13/59.88 | CLOSE: (6) is inconsistent.
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #580 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) op(e4, e1) = e0
% 251.13/59.88 (2) ~ (e2 = e0)
% 251.13/59.88 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.88 (4) ~ (all_36_2 = e2)
% 251.13/59.88 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.88 (6) op(e3, e1) = all_36_2
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | BETA: splitting (5) gives:
% 251.13/59.88 |
% 251.13/59.88 | Case 1:
% 251.13/59.88 | |
% 251.13/59.88 | | (7) all_252_9 = e2 & op(e4, e1) = e2
% 251.13/59.88 | |
% 251.13/59.88 | | ALPHA: (7) implies:
% 251.13/59.88 | | (8) op(e4, e1) = e2
% 251.13/59.88 | |
% 251.13/59.88 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #767.
% 251.13/59.88 | |
% 251.13/59.88 | Case 2:
% 251.13/59.88 | |
% 251.13/59.88 | | (9) all_252_10 = e2 & op(e3, e1) = e2
% 251.13/59.88 | |
% 251.13/59.88 | | ALPHA: (9) implies:
% 251.13/59.88 | | (10) op(e3, e1) = e2
% 251.13/59.88 | |
% 251.13/59.88 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #984.
% 251.13/59.88 | |
% 251.13/59.88 | End of split
% 251.13/59.88 |
% 251.13/59.88 End of proof
% 251.13/59.88
% 251.13/59.88 Sub-proof #581 shows that the following formulas are inconsistent:
% 251.13/59.88 ----------------------------------------------------------------
% 251.13/59.88 (1) ~ (all_10_2 = e1)
% 251.13/59.88 (2) ~ (all_10_2 = e4)
% 251.13/59.88 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.13/59.88 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.13/59.88 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.13/59.88 (4) all_94_2 = all_38_2
% 251.13/59.88 (5) op(all_38_2, e1) = e2
% 251.13/59.88 (6) all_250_13 = all_38_2
% 251.13/59.88 (7) ~ (all_28_2 = e3)
% 251.13/59.88 (8) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.88 all_250_20 = e0
% 251.13/59.88 (9) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.88 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.88 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.88 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.88 (11) ~ (all_12_2 = e3)
% 251.13/59.88 (12) op(e2, e2) = all_244_8
% 251.13/59.88 (13) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.88 all_250_11 = e0
% 251.13/59.88 (14) ~ (all_36_2 = e2)
% 251.13/59.88 (15) ~ (all_244_8 = all_38_2)
% 251.13/59.88 (16) op(all_244_15, all_244_15) = e1
% 251.13/59.88 (17) all_250_21 = all_22_2
% 251.13/59.88 (18) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.88 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.88 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.88 (19) ~ (all_38_2 = e0)
% 251.13/59.88 (20) ~ (all_22_2 = e4)
% 251.13/59.88 (21) op(all_48_2, all_22_2) = e0
% 251.13/59.88 (22) ~ (all_12_2 = e2)
% 251.13/59.88 (23) op(e3, e1) = all_36_2
% 251.13/59.88 (24) ~ (all_28_2 = all_12_2)
% 251.13/59.88 (25) op(all_40_2, e0) = e2
% 251.13/59.88 (26) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 251.13/59.88 all_250_22 = e0
% 251.13/59.88 (27) ~ (all_22_2 = e1)
% 251.13/59.88 (28) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.88 all_250_13 = e0
% 251.13/59.88 (29) ~ (all_38_2 = e4)
% 251.13/59.88 (30) ~ (all_28_2 = e4)
% 251.13/59.88 (31) op(e0, e3) = all_22_2
% 251.13/59.88 (32) ~ (all_28_2 = all_22_2)
% 251.13/59.88 (33) op(all_10_2, e3) = e2
% 251.13/59.88 (34) op(all_30_2, all_12_2) = e0
% 251.13/59.88 (35) ~ (all_12_2 = e4)
% 251.13/59.88 (36) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.88 all_250_21 = e0
% 251.13/59.88 (37) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.88 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.88 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.88 (38) all_250_11 = all_10_2
% 251.13/59.88 (39) op(e1, e1) = all_244_15
% 251.13/59.88 (40) op(all_48_2, e0) = e3
% 251.13/59.88 (41) all_82_2 = all_28_2
% 251.13/59.88 (42) ~ (all_22_2 = all_10_2)
% 251.13/59.88 (43) op(all_40_2, all_28_2) = e0
% 251.13/59.88 (44) ~ (all_38_2 = all_10_2)
% 251.13/59.88 (45) all_250_22 = all_28_2
% 251.13/59.88 (46) all_250_20 = all_12_2
% 251.13/59.88 (47) all_90_2 = all_22_2
% 251.13/59.88 (48) op(all_30_2, e0) = e4
% 251.13/59.88 (49) all_124_2 = all_10_2
% 251.13/59.88
% 251.13/59.88 Begin of proof
% 251.13/59.88 |
% 251.13/59.88 | BETA: splitting (3) gives:
% 251.13/59.88 |
% 251.13/59.88 | Case 1:
% 251.13/59.88 | |
% 251.13/59.88 | | (50) ~ (all_82_2 = e1)
% 251.13/59.88 | |
% 251.13/59.88 | | REDUCE: (41), (50) imply:
% 251.13/59.89 | | (51) ~ (all_28_2 = e1)
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (37) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (52) ~ (all_90_2 = e2)
% 251.13/59.89 | | |
% 251.13/59.89 | | | REDUCE: (47), (52) imply:
% 251.13/59.89 | | | (53) ~ (all_22_2 = e2)
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (9) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (54) ~ (all_94_2 = e3)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (4), (54) imply:
% 251.13/59.89 | | | | (55) ~ (all_38_2 = e3)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (1), (2), (5), (6), (10), (12), (13), (15), (16), (17), (18),
% 251.13/59.89 | | | | (19), (20), (21), (27), (28), (29), (31), (33), (36), (38),
% 251.13/59.89 | | | | (39), (40), (42), (44), (49), (53), (55) are inconsistent by
% 251.13/59.89 | | | | sub-proof #986.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | Case 2:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (56) all_94_2 = e3
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (4), (5), (10), (14), (23), (56) are inconsistent by
% 251.13/59.89 | | | | sub-proof #983.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | End of split
% 251.13/59.89 | | |
% 251.13/59.89 | | Case 2:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (57) all_90_2 = e2
% 251.13/59.89 | | |
% 251.13/59.89 | | | COMBINE_EQS: (47), (57) imply:
% 251.13/59.89 | | | (58) all_22_2 = e2
% 251.13/59.89 | | |
% 251.13/59.89 | | | SIMP: (58) implies:
% 251.13/59.89 | | | (59) all_22_2 = e2
% 251.13/59.89 | | |
% 251.13/59.89 | | | REDUCE: (32), (59) imply:
% 251.13/59.89 | | | (60) ~ (all_28_2 = e2)
% 251.13/59.89 | | |
% 251.13/59.89 | | | REF_CLOSE: (7), (10), (25), (26), (30), (43), (45), (51), (60) are
% 251.13/59.89 | | | inconsistent by sub-proof #583.
% 251.13/59.89 | | |
% 251.13/59.89 | | End of split
% 251.13/59.89 | |
% 251.13/59.89 | Case 2:
% 251.13/59.89 | |
% 251.13/59.89 | | (61) all_82_2 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (41), (61) imply:
% 251.13/59.89 | | (62) all_28_2 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (62) implies:
% 251.13/59.89 | | (63) all_28_2 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (24), (63) imply:
% 251.13/59.89 | | (64) ~ (all_12_2 = e1)
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (64) implies:
% 251.13/59.89 | | (65) ~ (all_12_2 = e1)
% 251.13/59.89 | |
% 251.13/59.89 | | REF_CLOSE: (8), (10), (11), (22), (34), (35), (46), (48), (65) are
% 251.13/59.89 | | inconsistent by sub-proof #582.
% 251.13/59.89 | |
% 251.13/59.89 | End of split
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #582 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.89 all_250_20 = e0
% 251.13/59.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (3) ~ (all_12_2 = e3)
% 251.13/59.89 (4) ~ (all_12_2 = e2)
% 251.13/59.89 (5) op(all_30_2, all_12_2) = e0
% 251.13/59.89 (6) ~ (all_12_2 = e4)
% 251.13/59.89 (7) all_250_20 = all_12_2
% 251.13/59.89 (8) op(all_30_2, e0) = e4
% 251.13/59.89 (9) ~ (all_12_2 = e1)
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | BETA: splitting (1) gives:
% 251.13/59.89 |
% 251.13/59.89 | Case 1:
% 251.13/59.89 | |
% 251.13/59.89 | | (10) all_250_20 = e4
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (7), (10) imply:
% 251.13/59.89 | | (11) all_12_2 = e4
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (6), (11) imply:
% 251.13/59.89 | | (12) $false
% 251.13/59.89 | |
% 251.13/59.89 | | CLOSE: (12) is inconsistent.
% 251.13/59.89 | |
% 251.13/59.89 | Case 2:
% 251.13/59.89 | |
% 251.13/59.89 | | (13) ~ (all_250_20 = e4)
% 251.13/59.89 | | (14) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 =
% 251.13/59.89 | | e0
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (14) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (15) all_250_20 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | COMBINE_EQS: (7), (15) imply:
% 251.13/59.89 | | | (16) all_12_2 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | REDUCE: (3), (16) imply:
% 251.13/59.89 | | | (17) $false
% 251.13/59.89 | | |
% 251.13/59.89 | | | CLOSE: (17) is inconsistent.
% 251.13/59.89 | | |
% 251.13/59.89 | | Case 2:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (18) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (18) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (19) all_250_20 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | COMBINE_EQS: (7), (19) imply:
% 251.13/59.89 | | | | (20) all_12_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (4), (20) imply:
% 251.13/59.89 | | | | (21) $false
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | CLOSE: (21) is inconsistent.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | Case 2:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (22) all_250_20 = e1 | all_250_20 = e0
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | BETA: splitting (22) gives:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | Case 1:
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | (23) all_250_20 = e1
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | COMBINE_EQS: (7), (23) imply:
% 251.13/59.89 | | | | | (24) all_12_2 = e1
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (9), (24) imply:
% 251.13/59.89 | | | | | (25) $false
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | CLOSE: (25) is inconsistent.
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | Case 2:
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | (26) all_250_20 = e0
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | COMBINE_EQS: (7), (26) imply:
% 251.13/59.89 | | | | | (27) all_12_2 = e0
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (6), (27) imply:
% 251.13/59.89 | | | | | (28) ~ (e4 = e0)
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | SIMP: (28) implies:
% 251.13/59.89 | | | | | (29) ~ (e4 = e0)
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (5), (27) imply:
% 251.13/59.89 | | | | | (30) op(all_30_2, e0) = e0
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | GROUND_INST: instantiating (2) with e4, e0, e0, all_30_2, simplifying
% 251.13/59.89 | | | | | with (8), (30) gives:
% 251.13/59.89 | | | | | (31) e4 = e0
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (29), (31) imply:
% 251.13/59.89 | | | | | (32) $false
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | CLOSE: (32) is inconsistent.
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | End of split
% 251.13/59.89 | | | |
% 251.13/59.89 | | | End of split
% 251.13/59.89 | | |
% 251.13/59.89 | | End of split
% 251.13/59.89 | |
% 251.13/59.89 | End of split
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #583 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) ~ (all_28_2 = e3)
% 251.13/59.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (3) ~ (all_28_2 = e1)
% 251.13/59.89 (4) op(all_40_2, e0) = e2
% 251.13/59.89 (5) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 |
% 251.13/59.89 all_250_22 = e0
% 251.13/59.89 (6) ~ (all_28_2 = e4)
% 251.13/59.89 (7) ~ (all_28_2 = e2)
% 251.13/59.89 (8) op(all_40_2, all_28_2) = e0
% 251.13/59.89 (9) all_250_22 = all_28_2
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | BETA: splitting (5) gives:
% 251.13/59.89 |
% 251.13/59.89 | Case 1:
% 251.13/59.89 | |
% 251.13/59.89 | | (10) all_250_22 = e4
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (9), (10) imply:
% 251.13/59.89 | | (11) all_28_2 = e4
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (11) implies:
% 251.13/59.89 | | (12) all_28_2 = e4
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (6), (12) imply:
% 251.13/59.89 | | (13) $false
% 251.13/59.89 | |
% 251.13/59.89 | | CLOSE: (13) is inconsistent.
% 251.13/59.89 | |
% 251.13/59.89 | Case 2:
% 251.13/59.89 | |
% 251.13/59.89 | | (14) all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 | all_250_22 =
% 251.13/59.89 | | e0
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (14) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (15) all_250_22 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | COMBINE_EQS: (9), (15) imply:
% 251.13/59.89 | | | (16) all_28_2 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | SIMP: (16) implies:
% 251.13/59.89 | | | (17) all_28_2 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | REDUCE: (1), (17) imply:
% 251.13/59.89 | | | (18) $false
% 251.13/59.89 | | |
% 251.13/59.89 | | | CLOSE: (18) is inconsistent.
% 251.13/59.89 | | |
% 251.13/59.89 | | Case 2:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (19) all_250_22 = e2 | all_250_22 = e1 | all_250_22 = e0
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (19) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (20) all_250_22 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | COMBINE_EQS: (9), (20) imply:
% 251.13/59.89 | | | | (21) all_28_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | SIMP: (21) implies:
% 251.13/59.89 | | | | (22) all_28_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (7), (22) imply:
% 251.13/59.89 | | | | (23) $false
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | CLOSE: (23) is inconsistent.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | Case 2:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (24) ~ (all_250_22 = e2)
% 251.13/59.89 | | | | (25) all_250_22 = e1 | all_250_22 = e0
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (25) are inconsistent by
% 251.13/59.89 | | | | sub-proof #584.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | End of split
% 251.13/59.89 | | |
% 251.13/59.89 | | End of split
% 251.13/59.89 | |
% 251.13/59.89 | End of split
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #584 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (2) ~ (all_28_2 = e1)
% 251.13/59.89 (3) op(all_40_2, e0) = e2
% 251.13/59.89 (4) ~ (all_28_2 = e2)
% 251.13/59.89 (5) all_250_22 = e1 | all_250_22 = e0
% 251.13/59.89 (6) op(all_40_2, all_28_2) = e0
% 251.13/59.89 (7) all_250_22 = all_28_2
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | BETA: splitting (5) gives:
% 251.13/59.89 |
% 251.13/59.89 | Case 1:
% 251.13/59.89 | |
% 251.13/59.89 | | (8) all_250_22 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (7), (8) imply:
% 251.13/59.89 | | (9) all_28_2 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (9) implies:
% 251.13/59.89 | | (10) all_28_2 = e1
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (2), (10) imply:
% 251.13/59.89 | | (11) $false
% 251.13/59.89 | |
% 251.13/59.89 | | CLOSE: (11) is inconsistent.
% 251.13/59.89 | |
% 251.13/59.89 | Case 2:
% 251.13/59.89 | |
% 251.13/59.89 | | (12) all_250_22 = e0
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (7), (12) imply:
% 251.13/59.89 | | (13) all_28_2 = e0
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (13) implies:
% 251.13/59.89 | | (14) all_28_2 = e0
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (4), (14) imply:
% 251.13/59.89 | | (15) ~ (e2 = e0)
% 251.13/59.89 | |
% 251.13/59.89 | | SIMP: (15) implies:
% 251.13/59.89 | | (16) ~ (e2 = e0)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (6), (14) imply:
% 251.13/59.89 | | (17) op(all_40_2, e0) = e0
% 251.13/59.89 | |
% 251.13/59.89 | | GROUND_INST: instantiating (1) with e2, e0, e0, all_40_2, simplifying with
% 251.13/59.89 | | (3), (17) gives:
% 251.13/59.89 | | (18) e2 = e0
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (16), (18) imply:
% 251.13/59.89 | | (19) $false
% 251.13/59.89 | |
% 251.13/59.89 | | CLOSE: (19) is inconsistent.
% 251.13/59.89 | |
% 251.13/59.89 | End of split
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #585 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) all_252_22 = e4 & op(e0, e2) = e4
% 251.13/59.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (3) op(e0, e2) = all_28_2
% 251.13/59.89 (4) ~ (all_28_2 = e4)
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | ALPHA: (1) implies:
% 251.13/59.89 | (5) op(e0, e2) = e4
% 251.13/59.89 |
% 251.13/59.89 | GROUND_INST: instantiating (2) with all_28_2, e4, e2, e0, simplifying with
% 251.13/59.89 | (3), (5) gives:
% 251.13/59.89 | (6) all_28_2 = e4
% 251.13/59.89 |
% 251.13/59.89 | REDUCE: (4), (6) imply:
% 251.13/59.89 | (7) $false
% 251.13/59.89 |
% 251.13/59.89 | CLOSE: (7) is inconsistent.
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #586 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.13/59.89 all_250_23 = e0
% 251.13/59.89 (2) all_32_2 = all_20_2
% 251.13/59.89 (3) ~ (all_4_2 = e4)
% 251.13/59.89 (4) op(all_4_2, e2) = e1
% 251.13/59.89 (5) ~ (all_244_24 = all_34_2)
% 251.13/59.89 (6) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.13/59.89 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.13/59.89 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.13/59.89 (7) all_250_8 = all_36_2
% 251.13/59.89 (8) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.13/59.89 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.13/59.89 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.13/59.89 (9) op(all_62_2, all_36_2) = e3
% 251.13/59.89 (10) op(all_38_2, e1) = e2
% 251.13/59.89 (11) ~ (e2 = e0)
% 251.13/59.89 (12) op(all_38_2, all_4_2) = e1
% 251.13/59.89 (13) ~ (all_244_24 = all_20_2)
% 251.13/59.89 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (15) ~ (e3 = e2)
% 251.13/59.89 (16) op(e0, e0) = all_244_24
% 251.13/59.89 (17) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.89 all_250_17 = e0
% 251.13/59.89 (18) ~ (all_12_2 = e3)
% 251.13/59.89 (19) op(e2, e1) = all_38_2
% 251.13/59.89 (20) ~ (all_36_2 = all_20_2)
% 251.13/59.89 (21) op(e1, e0) = all_34_2
% 251.13/59.89 (22) ~ (all_244_0 = all_16_2)
% 251.13/59.89 (23) all_62_2 = e0
% 251.13/59.89 (24) ~ (all_100_2 = all_36_2)
% 251.13/59.89 (25) op(e0, e2) = all_28_2
% 251.13/59.89 (26) ~ (all_28_2 = e1)
% 251.13/59.89 (27) ~ (all_20_2 = e1)
% 251.13/59.89 (28) all_50_2 = all_4_2
% 251.13/59.89 (29) op(all_34_2, e0) = e1
% 251.13/59.89 (30) op(e1, e4) = all_16_2
% 251.13/59.89 (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.89 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.89 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.89 (32) ~ (all_28_2 = all_20_2)
% 251.13/59.89 (33) op(e1, e3) = all_62_2
% 251.13/59.89 (34) ~ (e3 = e0)
% 251.13/59.89 (35) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.89 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.89 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.89 (36) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.13/59.89 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.13/59.89 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.13/59.89 (37) op(all_20_2, e1) = e0
% 251.13/59.89 (38) ~ (e3 = e1)
% 251.13/59.89 (39) op(e3, e1) = all_36_2
% 251.13/59.89 (40) ~ (all_16_2 = e2)
% 251.13/59.89 (41) ~ (all_8_2 = e1)
% 251.13/59.89 (42) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.13/59.89 all_250_8 = e0
% 251.13/59.89 (43) ~ (all_28_2 = all_4_2)
% 251.13/59.89 (44) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.89 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.89 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.89 (45) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 &
% 251.13/59.89 op(e2, e3) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 251.13/59.89 e4) & op(e2, e3) = all_28_1 & $i(all_28_1))
% 251.13/59.89 (46) op(all_34_2, all_20_2) = e0
% 251.13/59.89 (47) all_58_2 = all_20_2
% 251.13/59.89 (48) op(all_62_2, e3) = e1
% 251.13/59.89 (49) op(e4, e1) = all_26_2
% 251.13/59.89 (50) op(e3, e4) = all_100_2
% 251.13/59.89 (51) op(e4, e4) = all_244_0
% 251.13/59.89 (52) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.89 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.89 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.89 (53) op(e1, e1) = all_244_15
% 251.13/59.89 (54) ~ (all_244_15 = all_20_2)
% 251.13/59.89 (55) op(e1, e2) = all_4_2
% 251.13/59.89 (56) ~ (all_24_2 = e3) | ( ~ (all_24_0 = e2) & op(e4, e3) = all_24_1 &
% 251.13/59.89 op(e3, all_24_1) = all_24_0 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 251.13/59.89 (all_24_1 = e0) & op(e4, e3) = all_24_1 & $i(all_24_1))
% 251.13/59.89 (57) op(e2, e4) = all_64_2
% 251.13/59.89 (58) all_250_17 = all_4_2
% 251.13/59.89 (59) op(e3, e2) = all_8_2
% 251.13/59.89 (60) ~ (all_64_2 = all_16_2)
% 251.13/59.89 (61) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.89 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.89 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.89 (62) ~ (all_20_2 = e4)
% 251.13/59.89 (63) op(all_16_2, e4) = e1
% 251.13/59.89 (64) ~ (all_100_2 = all_16_2)
% 251.13/59.89 (65) ~ (all_244_3 = e0)
% 251.13/59.89 (66) all_24_2 = all_16_2
% 251.13/59.89 (67) op(e3, e3) = all_244_3
% 251.13/59.89 (68) ~ (all_16_2 = all_12_2)
% 251.13/59.89 (69) ~ (all_26_2 = all_20_2)
% 251.13/59.89 (70) all_46_2 = all_36_2
% 251.13/59.89 (71) ~ (all_4_2 = e0)
% 251.13/59.89 (72) op(all_244_24, all_244_24) = e0
% 251.13/59.89 (73) op(e0, e4) = all_12_2
% 251.13/59.89 (74) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 251.13/59.89 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 251.13/59.89 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.13/59.89 (75) all_250_23 = all_20_2
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | REDUCE: (9), (23) imply:
% 251.13/59.89 | (76) op(e0, all_36_2) = e3
% 251.13/59.89 |
% 251.13/59.89 | REDUCE: (23), (48) imply:
% 251.13/59.89 | (77) op(e0, e3) = e1
% 251.13/59.89 |
% 251.13/59.89 | REDUCE: (23), (33) imply:
% 251.13/59.89 | (78) op(e1, e3) = e0
% 251.13/59.89 |
% 251.13/59.89 | BETA: splitting (56) gives:
% 251.13/59.89 |
% 251.13/59.89 | Case 1:
% 251.13/59.89 | |
% 251.13/59.89 | | (79) ~ (all_24_2 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (66), (79) imply:
% 251.13/59.89 | | (80) ~ (all_16_2 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (45) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (81) ~ (all_28_2 = e3)
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (35) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (82) ~ (all_32_2 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (2), (82) imply:
% 251.13/59.89 | | | | (83) ~ (all_20_2 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (1), (4), (5), (6), (14), (16), (21), (27), (28), (29), (30),
% 251.13/59.89 | | | | (34), (36), (37), (39), (41), (46), (47), (53), (54), (55),
% 251.13/59.89 | | | | (59), (62), (74), (75), (76), (78), (80), (83) are
% 251.13/59.89 | | | | inconsistent by sub-proof #591.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | Case 2:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (84) all_32_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | COMBINE_EQS: (2), (84) imply:
% 251.13/59.89 | | | | (85) all_20_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | SIMP: (85) implies:
% 251.13/59.89 | | | | (86) all_20_2 = e2
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (54), (86) imply:
% 251.13/59.89 | | | | (87) ~ (all_244_15 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (20), (86) imply:
% 251.13/59.89 | | | | (88) ~ (all_36_2 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (69), (86) imply:
% 251.13/59.89 | | | | (89) ~ (all_26_2 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (37), (86) imply:
% 251.13/59.89 | | | | (90) op(e2, e1) = e0
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (11), (14), (15), (16), (18), (19), (25), (31), (38), (39),
% 251.13/59.89 | | | | (49), (52), (53), (65), (67), (72), (73), (77), (81), (87),
% 251.13/59.89 | | | | (88), (89), (90) are inconsistent by sub-proof #589.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | End of split
% 251.13/59.89 | | |
% 251.13/59.89 | | Case 2:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (91) all_28_2 = e3
% 251.13/59.89 | | |
% 251.13/59.89 | | | REF_CLOSE: (1), (2), (3), (10), (12), (14), (17), (19), (25), (26), (27),
% 251.13/59.89 | | | (29), (32), (35), (37), (43), (46), (55), (58), (62), (71),
% 251.13/59.89 | | | (75), (91) are inconsistent by sub-proof #588.
% 251.13/59.89 | | |
% 251.13/59.89 | | End of split
% 251.13/59.89 | |
% 251.13/59.89 | Case 2:
% 251.13/59.89 | |
% 251.13/59.89 | | (92) all_24_2 = e3
% 251.13/59.89 | |
% 251.13/59.89 | | COMBINE_EQS: (66), (92) imply:
% 251.13/59.89 | | (93) all_16_2 = e3
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (22), (93) imply:
% 251.13/59.89 | | (94) ~ (all_244_0 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (64), (93) imply:
% 251.13/59.89 | | (95) ~ (all_100_2 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (60), (93) imply:
% 251.13/59.89 | | (96) ~ (all_64_2 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (68), (93) imply:
% 251.13/59.89 | | (97) ~ (all_12_2 = e3)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (63), (93) imply:
% 251.13/59.89 | | (98) op(e3, e4) = e1
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (61) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (99) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4)
% 251.13/59.89 | | | = e3)
% 251.13/59.89 | | |
% 251.13/59.89 | | | REF_CLOSE: (14), (38), (50), (51), (94), (98), (99) are inconsistent by
% 251.13/59.89 | | | sub-proof #613.
% 251.13/59.89 | | |
% 251.13/59.89 | | Case 2:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (100) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1,
% 251.13/59.89 | | | e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (100) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (101) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REF_CLOSE: (14), (57), (96), (101) are inconsistent by sub-proof #940.
% 251.13/59.89 | | | |
% 251.13/59.89 | | | Case 2:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (102) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 251.13/59.89 | | | | e4) = e3)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | BETA: splitting (102) gives:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | Case 1:
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | GROUND_INST: instantiating (14) with all_100_2, e1, e4, e3,
% 251.13/59.89 | | | | | simplifying with (50), (98) gives:
% 251.13/59.89 | | | | | (103) all_100_2 = e1
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (24), (103) imply:
% 251.13/59.89 | | | | | (104) ~ (all_36_2 = e1)
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | SIMP: (104) implies:
% 251.13/59.89 | | | | | (105) ~ (all_36_2 = e1)
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REDUCE: (95), (103) imply:
% 251.13/59.89 | | | | | (106) ~ (e3 = e1)
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | BETA: splitting (45) gives:
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | Case 1:
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | | (107) ~ (all_28_2 = e3)
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | | REF_CLOSE: (1), (2), (7), (8), (11), (13), (14), (15), (16), (18),
% 251.13/59.89 | | | | | | (19), (20), (25), (27), (29), (31), (35), (36), (37),
% 251.13/59.89 | | | | | | (38), (39), (42), (44), (46), (47), (49), (52), (53),
% 251.13/59.89 | | | | | | (54), (62), (65), (67), (69), (70), (72), (73), (75),
% 251.13/59.89 | | | | | | (76), (77), (105), (107) are inconsistent by sub-proof
% 251.13/59.89 | | | | | | #587.
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | Case 2:
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | | (108) all_28_2 = e3
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | | REF_CLOSE: (1), (2), (3), (10), (12), (14), (17), (19), (25), (26),
% 251.13/59.89 | | | | | | (27), (29), (32), (35), (37), (43), (46), (55), (58),
% 251.13/59.89 | | | | | | (62), (71), (75), (108) are inconsistent by sub-proof
% 251.13/59.89 | | | | | | #588.
% 251.13/59.89 | | | | | |
% 251.13/59.89 | | | | | End of split
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | Case 2:
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | (109) all_252_20 = e3 & op(e0, e4) = e3
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | ALPHA: (109) implies:
% 251.13/59.89 | | | | | (110) op(e0, e4) = e3
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | | REF_CLOSE: (14), (18), (73), (110) are inconsistent by sub-proof #981.
% 251.13/59.89 | | | | |
% 251.13/59.89 | | | | End of split
% 251.13/59.89 | | | |
% 251.13/59.89 | | | End of split
% 251.13/59.89 | | |
% 251.13/59.89 | | End of split
% 251.13/59.89 | |
% 251.13/59.89 | End of split
% 251.13/59.89 |
% 251.13/59.89 End of proof
% 251.13/59.89
% 251.13/59.89 Sub-proof #587 shows that the following formulas are inconsistent:
% 251.13/59.89 ----------------------------------------------------------------
% 251.13/59.89 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.13/59.89 all_250_23 = e0
% 251.13/59.89 (2) all_32_2 = all_20_2
% 251.13/59.89 (3) op(e0, e3) = e1
% 251.13/59.89 (4) all_250_8 = all_36_2
% 251.13/59.89 (5) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.13/59.89 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.13/59.89 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.13/59.89 (6) op(e0, all_36_2) = e3
% 251.13/59.89 (7) ~ (e2 = e0)
% 251.13/59.89 (8) ~ (all_244_24 = all_20_2)
% 251.13/59.89 (9) ~ (all_28_2 = e3)
% 251.13/59.89 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.89 (11) ~ (e3 = e2)
% 251.13/59.89 (12) op(e0, e0) = all_244_24
% 251.13/59.89 (13) ~ (all_12_2 = e3)
% 251.13/59.89 (14) op(e2, e1) = all_38_2
% 251.13/59.89 (15) ~ (all_36_2 = all_20_2)
% 251.13/59.89 (16) op(e0, e2) = all_28_2
% 251.13/59.89 (17) ~ (all_20_2 = e1)
% 251.13/59.89 (18) op(all_34_2, e0) = e1
% 251.13/59.89 (19) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.89 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.89 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.89 (20) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.89 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.89 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.89 (21) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.13/59.89 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.13/59.89 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.13/59.89 (22) op(all_20_2, e1) = e0
% 251.13/59.89 (23) ~ (e3 = e1)
% 251.13/59.89 (24) op(e3, e1) = all_36_2
% 251.13/59.89 (25) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.13/59.89 all_250_8 = e0
% 251.13/59.89 (26) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.89 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.89 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.89 (27) op(all_34_2, all_20_2) = e0
% 251.13/59.89 (28) all_58_2 = all_20_2
% 251.13/59.89 (29) op(e4, e1) = all_26_2
% 251.13/59.89 (30) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.89 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.89 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.89 (31) op(e1, e1) = all_244_15
% 251.13/59.89 (32) ~ (all_244_15 = all_20_2)
% 251.13/59.89 (33) ~ (all_36_2 = e1)
% 251.13/59.89 (34) ~ (all_20_2 = e4)
% 251.13/59.89 (35) ~ (all_244_3 = e0)
% 251.13/59.89 (36) op(e3, e3) = all_244_3
% 251.13/59.89 (37) ~ (all_26_2 = all_20_2)
% 251.13/59.89 (38) all_46_2 = all_36_2
% 251.13/59.89 (39) op(all_244_24, all_244_24) = e0
% 251.13/59.89 (40) op(e0, e4) = all_12_2
% 251.13/59.89 (41) all_250_23 = all_20_2
% 251.13/59.89
% 251.13/59.89 Begin of proof
% 251.13/59.89 |
% 251.13/59.89 | BETA: splitting (20) gives:
% 251.13/59.89 |
% 251.13/59.89 | Case 1:
% 251.13/59.89 | |
% 251.13/59.89 | | (42) ~ (all_32_2 = e2)
% 251.13/59.89 | |
% 251.13/59.89 | | REDUCE: (2), (42) imply:
% 251.13/59.89 | | (43) ~ (all_20_2 = e2)
% 251.13/59.89 | |
% 251.13/59.89 | | BETA: splitting (5) gives:
% 251.13/59.89 | |
% 251.13/59.89 | | Case 1:
% 251.13/59.89 | | |
% 251.13/59.89 | | | (44) ~ (all_36_2 = e4)
% 251.13/59.89 | | |
% 251.13/59.89 | | | BETA: splitting (26) gives:
% 251.13/59.89 | | |
% 251.13/59.89 | | | Case 1:
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | (45) ~ (all_46_2 = e2)
% 251.13/59.89 | | | |
% 251.13/59.89 | | | | REDUCE: (38), (45) imply:
% 251.13/59.90 | | | | (46) ~ (all_36_2 = e2)
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | BETA: splitting (21) gives:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | Case 1:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (47) ~ (all_58_2 = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REDUCE: (28), (47) imply:
% 251.13/59.90 | | | | | (48) ~ (all_20_2 = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REF_CLOSE: (1), (10), (17), (18), (27), (34), (41), (43), (48) are
% 251.13/59.90 | | | | | inconsistent by sub-proof #780.
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | Case 2:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (49) all_58_2 = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | COMBINE_EQS: (28), (49) imply:
% 251.13/59.90 | | | | | (50) all_20_2 = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | SIMP: (50) implies:
% 251.13/59.90 | | | | | (51) all_20_2 = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REDUCE: (8), (51) imply:
% 251.13/59.90 | | | | | (52) ~ (all_244_24 = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REDUCE: (15), (51) imply:
% 251.13/59.90 | | | | | (53) ~ (all_36_2 = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | BETA: splitting (25) gives:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | Case 1:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (54) all_250_8 = e4
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (4), (44), (54) are inconsistent by sub-proof #661.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | Case 2:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (55) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | all_250_8
% 251.13/59.90 | | | | | | = e0
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | BETA: splitting (55) gives:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | Case 1:
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | (56) all_250_8 = e3
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | REF_CLOSE: (4), (53), (56) are inconsistent by sub-proof #612.
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | Case 2:
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | (57) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | BETA: splitting (57) gives:
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | Case 1:
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | | (58) all_250_8 = e2
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | | REF_CLOSE: (4), (46), (58) are inconsistent by sub-proof #660.
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | Case 2:
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | | (59) all_250_8 = e1 | all_250_8 = e0
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | | BETA: splitting (59) gives:
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | | Case 1:
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | (60) all_250_8 = e1
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | REF_CLOSE: (4), (33), (60) are inconsistent by sub-proof #659.
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | Case 2:
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | (61) all_250_8 = e0
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | COMBINE_EQS: (4), (61) imply:
% 251.13/59.90 | | | | | | | | | (62) all_36_2 = e0
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | SIMP: (62) implies:
% 251.13/59.90 | | | | | | | | | (63) all_36_2 = e0
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | REDUCE: (6), (63) imply:
% 251.13/59.90 | | | | | | | | | (64) op(e0, e0) = e3
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | | REF_CLOSE: (10), (12), (52), (64) are inconsistent by
% 251.13/59.90 | | | | | | | | | sub-proof #835.
% 251.13/59.90 | | | | | | | | |
% 251.13/59.90 | | | | | | | | End of split
% 251.13/59.90 | | | | | | | |
% 251.13/59.90 | | | | | | | End of split
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | End of split
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | End of split
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | End of split
% 251.13/59.90 | | | |
% 251.13/59.90 | | | Case 2:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | (65) all_46_2 = e2
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | COMBINE_EQS: (38), (65) imply:
% 251.13/59.90 | | | | (66) all_36_2 = e2
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | REDUCE: (6), (66) imply:
% 251.13/59.90 | | | | (67) op(e0, e2) = e3
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | REF_CLOSE: (9), (10), (16), (67) are inconsistent by sub-proof #975.
% 251.13/59.90 | | | |
% 251.13/59.90 | | | End of split
% 251.13/59.90 | | |
% 251.13/59.90 | | Case 2:
% 251.13/59.90 | | |
% 251.13/59.90 | | | (68) all_36_2 = e4
% 251.13/59.90 | | |
% 251.13/59.90 | | | REDUCE: (6), (68) imply:
% 251.13/59.90 | | | (69) op(e0, e4) = e3
% 251.13/59.90 | | |
% 251.13/59.90 | | | REF_CLOSE: (10), (13), (40), (69) are inconsistent by sub-proof #981.
% 251.13/59.90 | | |
% 251.13/59.90 | | End of split
% 251.13/59.90 | |
% 251.13/59.90 | Case 2:
% 251.13/59.90 | |
% 251.13/59.90 | | (70) all_32_2 = e2
% 251.13/59.90 | |
% 251.13/59.90 | | COMBINE_EQS: (2), (70) imply:
% 251.13/59.90 | | (71) all_20_2 = e2
% 251.13/59.90 | |
% 251.13/59.90 | | SIMP: (71) implies:
% 251.13/59.90 | | (72) all_20_2 = e2
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (32), (72) imply:
% 251.13/59.90 | | (73) ~ (all_244_15 = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (15), (72) imply:
% 251.13/59.90 | | (74) ~ (all_36_2 = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (37), (72) imply:
% 251.13/59.90 | | (75) ~ (all_26_2 = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (22), (72) imply:
% 251.13/59.90 | | (76) op(e2, e1) = e0
% 251.13/59.90 | |
% 251.13/59.90 | | REF_CLOSE: (3), (7), (9), (10), (11), (12), (13), (14), (16), (19), (23),
% 251.13/59.90 | | (24), (29), (30), (31), (35), (36), (39), (40), (73), (74), (75),
% 251.13/59.90 | | (76) are inconsistent by sub-proof #589.
% 251.13/59.90 | |
% 251.13/59.90 | End of split
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #588 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.13/59.90 all_250_23 = e0
% 251.13/59.90 (2) all_32_2 = all_20_2
% 251.13/59.90 (3) ~ (all_4_2 = e4)
% 251.13/59.90 (4) op(all_38_2, e1) = e2
% 251.13/59.90 (5) op(all_38_2, all_4_2) = e1
% 251.13/59.90 (6) all_28_2 = e3
% 251.13/59.90 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (8) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.90 all_250_17 = e0
% 251.13/59.90 (9) op(e2, e1) = all_38_2
% 251.13/59.90 (10) op(e0, e2) = all_28_2
% 251.13/59.90 (11) ~ (all_28_2 = e1)
% 251.13/59.90 (12) ~ (all_20_2 = e1)
% 251.13/59.90 (13) op(all_34_2, e0) = e1
% 251.13/59.90 (14) ~ (all_28_2 = all_20_2)
% 251.13/59.90 (15) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.90 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.90 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.90 (16) op(all_20_2, e1) = e0
% 251.13/59.90 (17) ~ (all_28_2 = all_4_2)
% 251.13/59.90 (18) op(all_34_2, all_20_2) = e0
% 251.13/59.90 (19) op(e1, e2) = all_4_2
% 251.13/59.90 (20) all_250_17 = all_4_2
% 251.13/59.90 (21) ~ (all_20_2 = e4)
% 251.13/59.90 (22) ~ (all_4_2 = e0)
% 251.13/59.90 (23) all_250_23 = all_20_2
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (6), (14) imply:
% 251.13/59.90 | (24) ~ (all_20_2 = e3)
% 251.13/59.90 |
% 251.13/59.90 | SIMP: (24) implies:
% 251.13/59.90 | (25) ~ (all_20_2 = e3)
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (6), (17) imply:
% 251.13/59.90 | (26) ~ (all_4_2 = e3)
% 251.13/59.90 |
% 251.13/59.90 | SIMP: (26) implies:
% 251.13/59.90 | (27) ~ (all_4_2 = e3)
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (6), (11) imply:
% 251.13/59.90 | (28) ~ (e3 = e1)
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (6), (10) imply:
% 251.13/59.90 | (29) op(e0, e2) = e3
% 251.13/59.90 |
% 251.13/59.90 | BETA: splitting (15) gives:
% 251.13/59.90 |
% 251.13/59.90 | Case 1:
% 251.13/59.90 | |
% 251.13/59.90 | | (30) ~ (all_32_2 = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (2), (30) imply:
% 251.13/59.90 | | (31) ~ (all_20_2 = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REF_CLOSE: (1), (7), (12), (13), (18), (21), (23), (25), (31) are
% 251.13/59.90 | | inconsistent by sub-proof #780.
% 251.13/59.90 | |
% 251.13/59.90 | Case 2:
% 251.13/59.90 | |
% 251.13/59.90 | | (32) all_32_2 = e2
% 251.13/59.90 | | (33) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) =
% 251.13/59.90 | | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 251.13/59.90 | | op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.90 | |
% 251.13/59.90 | | COMBINE_EQS: (2), (32) imply:
% 251.13/59.90 | | (34) all_20_2 = e2
% 251.13/59.90 | |
% 251.13/59.90 | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (16), (19), (20), (22), (27),
% 251.13/59.90 | | (28), (29), (33), (34) are inconsistent by sub-proof #637.
% 251.13/59.90 | |
% 251.13/59.90 | End of split
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #589 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) ~ (all_26_2 = e2)
% 251.13/59.90 (2) op(e0, e3) = e1
% 251.13/59.90 (3) ~ (e2 = e0)
% 251.13/59.90 (4) ~ (all_28_2 = e3)
% 251.13/59.90 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (6) ~ (e3 = e2)
% 251.13/59.90 (7) op(e0, e0) = all_244_24
% 251.13/59.90 (8) ~ (all_12_2 = e3)
% 251.13/59.90 (9) op(e2, e1) = all_38_2
% 251.13/59.90 (10) ~ (all_36_2 = e2)
% 251.13/59.90 (11) op(e0, e2) = all_28_2
% 251.13/59.90 (12) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.90 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.90 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.90 (13) ~ (e3 = e1)
% 251.13/59.90 (14) op(e3, e1) = all_36_2
% 251.13/59.90 (15) op(e4, e1) = all_26_2
% 251.13/59.90 (16) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.90 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.90 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.90 (17) op(e1, e1) = all_244_15
% 251.13/59.90 (18) ~ (all_244_15 = e2)
% 251.13/59.90 (19) ~ (all_244_3 = e0)
% 251.13/59.90 (20) op(e3, e3) = all_244_3
% 251.13/59.90 (21) op(e2, e1) = e0
% 251.13/59.90 (22) op(all_244_24, all_244_24) = e0
% 251.13/59.90 (23) op(e0, e4) = all_12_2
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | BETA: splitting (16) gives:
% 251.13/59.90 |
% 251.13/59.90 | Case 1:
% 251.13/59.90 | |
% 251.13/59.90 | | (24) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.90 | | e2)
% 251.13/59.90 | |
% 251.13/59.90 | | REF_CLOSE: (1), (5), (10), (14), (15), (24) are inconsistent by sub-proof
% 251.13/59.90 | | #969.
% 251.13/59.90 | |
% 251.13/59.90 | Case 2:
% 251.13/59.90 | |
% 251.13/59.90 | | (25) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.13/59.90 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.90 | |
% 251.13/59.90 | | BETA: splitting (25) gives:
% 251.13/59.90 | |
% 251.13/59.90 | | Case 1:
% 251.13/59.90 | | |
% 251.13/59.90 | | | (26) all_252_11 = e2 & op(e2, e1) = e2
% 251.13/59.90 | | |
% 251.13/59.90 | | | REF_CLOSE: (3), (5), (9), (21), (26) are inconsistent by sub-proof #722.
% 251.13/59.90 | | |
% 251.13/59.90 | | Case 2:
% 251.13/59.90 | | |
% 251.13/59.90 | | | (27) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.90 | | | e1) = e2)
% 251.13/59.90 | | |
% 251.13/59.90 | | | BETA: splitting (27) gives:
% 251.13/59.90 | | |
% 251.13/59.90 | | | Case 1:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | (28) all_252_15 = e2 & op(e1, e1) = e2
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | REF_CLOSE: (5), (17), (18), (28) are inconsistent by sub-proof #966.
% 251.13/59.90 | | | |
% 251.13/59.90 | | | Case 2:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | (29) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | ALPHA: (29) implies:
% 251.13/59.90 | | | | (30) all_252_23 = e2
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | BETA: splitting (12) gives:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | Case 1:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (31) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 251.13/59.90 | | | | | op(e0, e3) = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | BETA: splitting (31) gives:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | Case 1:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (32) all_252_20 = e3 & op(e0, e4) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | ALPHA: (32) implies:
% 251.13/59.90 | | | | | | (33) op(e0, e4) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (5), (8), (23), (33) are inconsistent by sub-proof #981.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | Case 2:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (34) all_252_21 = e3 & op(e0, e3) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | ALPHA: (34) implies:
% 251.13/59.90 | | | | | | (35) op(e0, e3) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (2), (5), (13), (35) are inconsistent by sub-proof #590.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | End of split
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | Case 2:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (36) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 251.13/59.90 | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | BETA: splitting (36) gives:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | Case 1:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (37) all_252_22 = e3 & op(e0, e2) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | ALPHA: (37) implies:
% 251.13/59.90 | | | | | | (38) op(e0, e2) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (4), (5), (11), (38) are inconsistent by sub-proof #975.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | Case 2:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (39) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 251.13/59.90 | | | | | | op(e0, e0) = e3)
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | BETA: splitting (39) gives:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | Case 1:
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | (40) all_252_23 = e3 & op(e0, e1) = e3
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | REF_CLOSE: (6), (30), (40) are inconsistent by sub-proof #687.
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | Case 2:
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | (41) all_252_24 = e3 & op(e0, e0) = e3
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | ALPHA: (41) implies:
% 251.13/59.90 | | | | | | | (42) op(e0, e0) = e3
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | GROUND_INST: instantiating (5) with all_244_24, e3, e0, e0,
% 251.13/59.90 | | | | | | | simplifying with (7), (42) gives:
% 251.13/59.90 | | | | | | | (43) all_244_24 = e3
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | REDUCE: (22), (43) imply:
% 251.13/59.90 | | | | | | | (44) op(e3, e3) = e0
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | | REF_CLOSE: (5), (19), (20), (44) are inconsistent by sub-proof
% 251.13/59.90 | | | | | | | #973.
% 251.13/59.90 | | | | | | |
% 251.13/59.90 | | | | | | End of split
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | End of split
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | End of split
% 251.13/59.90 | | | |
% 251.13/59.90 | | | End of split
% 251.13/59.90 | | |
% 251.13/59.90 | | End of split
% 251.13/59.90 | |
% 251.13/59.90 | End of split
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #590 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (2) op(e0, e3) = e3
% 251.13/59.90 (3) op(e0, e3) = e1
% 251.13/59.90 (4) ~ (e3 = e1)
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | GROUND_INST: instantiating (1) with e1, e3, e3, e0, simplifying with (2), (3)
% 251.13/59.90 | gives:
% 251.13/59.90 | (5) e3 = e1
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (4), (5) imply:
% 251.13/59.90 | (6) $false
% 251.13/59.90 |
% 251.13/59.90 | CLOSE: (6) is inconsistent.
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #591 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) op(e1, e3) = e0
% 251.13/59.90 (2) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.13/59.90 all_250_23 = e0
% 251.13/59.90 (3) op(all_4_2, e2) = e1
% 251.13/59.90 (4) ~ (all_244_24 = all_34_2)
% 251.13/59.90 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.13/59.90 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.13/59.90 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.13/59.90 (6) op(e0, all_36_2) = e3
% 251.13/59.90 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (8) op(e0, e0) = all_244_24
% 251.13/59.90 (9) op(e1, e0) = all_34_2
% 251.13/59.90 (10) ~ (all_20_2 = e1)
% 251.13/59.90 (11) all_50_2 = all_4_2
% 251.13/59.90 (12) op(all_34_2, e0) = e1
% 251.13/59.90 (13) op(e1, e4) = all_16_2
% 251.13/59.90 (14) ~ (e3 = e0)
% 251.13/59.90 (15) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.13/59.90 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.13/59.90 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.13/59.90 (16) op(all_20_2, e1) = e0
% 251.13/59.90 (17) op(e3, e1) = all_36_2
% 251.13/59.90 (18) ~ (all_8_2 = e1)
% 251.13/59.90 (19) op(all_34_2, all_20_2) = e0
% 251.13/59.90 (20) all_58_2 = all_20_2
% 251.13/59.90 (21) op(e1, e1) = all_244_15
% 251.13/59.90 (22) ~ (all_244_15 = all_20_2)
% 251.13/59.90 (23) op(e1, e2) = all_4_2
% 251.13/59.90 (24) op(e3, e2) = all_8_2
% 251.13/59.90 (25) ~ (all_20_2 = e4)
% 251.13/59.90 (26) ~ (all_16_2 = e3)
% 251.13/59.90 (27) ~ (all_20_2 = e2)
% 251.13/59.90 (28) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 251.13/59.90 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 251.13/59.90 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.13/59.90 (29) all_250_23 = all_20_2
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | BETA: splitting (28) gives:
% 251.13/59.90 |
% 251.13/59.90 | Case 1:
% 251.13/59.90 | |
% 251.13/59.90 | | (30) ~ (all_50_2 = e3)
% 251.13/59.90 | |
% 251.13/59.90 | | REDUCE: (11), (30) imply:
% 251.13/59.90 | | (31) ~ (all_4_2 = e3)
% 251.13/59.90 | |
% 251.13/59.90 | | BETA: splitting (15) gives:
% 251.13/59.90 | |
% 251.13/59.90 | | Case 1:
% 251.13/59.90 | | |
% 251.13/59.90 | | | (32) ~ (all_58_2 = e3)
% 251.13/59.90 | | |
% 251.13/59.90 | | | REDUCE: (20), (32) imply:
% 251.13/59.90 | | | (33) ~ (all_20_2 = e3)
% 251.13/59.90 | | |
% 251.13/59.90 | | | REF_CLOSE: (2), (7), (10), (12), (19), (25), (27), (29), (33) are
% 251.13/59.90 | | | inconsistent by sub-proof #780.
% 251.13/59.90 | | |
% 251.13/59.90 | | Case 2:
% 251.13/59.90 | | |
% 251.13/59.90 | | | (34) all_58_2 = e3
% 251.13/59.90 | | |
% 251.13/59.90 | | | COMBINE_EQS: (20), (34) imply:
% 251.13/59.90 | | | (35) all_20_2 = e3
% 251.13/59.90 | | |
% 251.13/59.90 | | | REDUCE: (22), (35) imply:
% 251.13/59.90 | | | (36) ~ (all_244_15 = e3)
% 251.13/59.90 | | |
% 251.13/59.90 | | | REDUCE: (16), (35) imply:
% 251.13/59.90 | | | (37) op(e3, e1) = e0
% 251.13/59.90 | | |
% 251.13/59.90 | | | BETA: splitting (5) gives:
% 251.13/59.90 | | |
% 251.13/59.90 | | | Case 1:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | (38) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1,
% 251.13/59.90 | | | | e3) = e3)
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | BETA: splitting (38) gives:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | Case 1:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (39) all_252_12 = e3 & op(e1, e4) = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REF_CLOSE: (7), (13), (26), (39) are inconsistent by sub-proof #895.
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | Case 2:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (40) all_252_13 = e3 & op(e1, e3) = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | ALPHA: (40) implies:
% 251.13/59.90 | | | | | (41) op(e1, e3) = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REF_CLOSE: (1), (7), (14), (41) are inconsistent by sub-proof #592.
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | End of split
% 251.13/59.90 | | | |
% 251.13/59.90 | | | Case 2:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | (42) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 251.13/59.90 | | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | BETA: splitting (42) gives:
% 251.13/59.90 | | | |
% 251.13/59.90 | | | | Case 1:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (43) all_252_14 = e3 & op(e1, e2) = e3
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | REF_CLOSE: (7), (23), (31), (43) are inconsistent by sub-proof #858.
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | Case 2:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | (44) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 251.13/59.90 | | | | | op(e1, e0) = e3)
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | BETA: splitting (44) gives:
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | | Case 1:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (45) all_252_15 = e3 & op(e1, e1) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | ALPHA: (45) implies:
% 251.13/59.90 | | | | | | (46) op(e1, e1) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (7), (21), (36), (46) are inconsistent by sub-proof #822.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | Case 2:
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | (47) all_252_19 = e3 & op(e1, e0) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | ALPHA: (47) implies:
% 251.13/59.90 | | | | | | (48) op(e1, e0) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | GROUND_INST: instantiating (7) with all_34_2, e3, e0, e1,
% 251.13/59.90 | | | | | | simplifying with (9), (48) gives:
% 251.13/59.90 | | | | | | (49) all_34_2 = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | GROUND_INST: instantiating (7) with all_36_2, e0, e1, e3,
% 251.13/59.90 | | | | | | simplifying with (17), (37) gives:
% 251.13/59.90 | | | | | | (50) all_36_2 = e0
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REDUCE: (4), (49) imply:
% 251.13/59.90 | | | | | | (51) ~ (all_244_24 = e3)
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REDUCE: (6), (50) imply:
% 251.13/59.90 | | | | | | (52) op(e0, e0) = e3
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | | REF_CLOSE: (7), (8), (51), (52) are inconsistent by sub-proof #835.
% 251.13/59.90 | | | | | |
% 251.13/59.90 | | | | | End of split
% 251.13/59.90 | | | | |
% 251.13/59.90 | | | | End of split
% 251.13/59.90 | | | |
% 251.13/59.90 | | | End of split
% 251.13/59.90 | | |
% 251.13/59.90 | | End of split
% 251.13/59.90 | |
% 251.13/59.90 | Case 2:
% 251.13/59.90 | |
% 251.13/59.90 | | (53) all_50_2 = e3
% 251.13/59.90 | |
% 251.13/59.90 | | REF_CLOSE: (3), (7), (11), (18), (24), (53) are inconsistent by sub-proof
% 251.13/59.90 | | #802.
% 251.13/59.90 | |
% 251.13/59.90 | End of split
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #592 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (2) op(e1, e3) = e3
% 251.13/59.90 (3) op(e1, e3) = e0
% 251.13/59.90 (4) ~ (e3 = e0)
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | GROUND_INST: instantiating (1) with e0, e3, e3, e1, simplifying with (2), (3)
% 251.13/59.90 | gives:
% 251.13/59.90 | (5) e3 = e0
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (4), (5) imply:
% 251.13/59.90 | (6) $false
% 251.13/59.90 |
% 251.13/59.90 | CLOSE: (6) is inconsistent.
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #593 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (3) op(e0, e4) = all_12_2
% 251.13/59.90 (4) ~ (all_12_2 = e1)
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | ALPHA: (1) implies:
% 251.13/59.90 | (5) op(e0, e4) = e1
% 251.13/59.90 |
% 251.13/59.90 | GROUND_INST: instantiating (2) with all_12_2, e1, e4, e0, simplifying with
% 251.13/59.90 | (3), (5) gives:
% 251.13/59.90 | (6) all_12_2 = e1
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (4), (6) imply:
% 251.13/59.90 | (7) $false
% 251.13/59.90 |
% 251.13/59.90 | CLOSE: (7) is inconsistent.
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #594 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) all_252_12 = e1 & op(e1, e4) = e1
% 251.13/59.90 (2) all_252_12 = e3
% 251.13/59.90 (3) ~ (e3 = e1)
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | ALPHA: (1) implies:
% 251.13/59.90 | (4) all_252_12 = e1
% 251.13/59.90 |
% 251.13/59.90 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.90 | (5) e3 = e1
% 251.13/59.90 |
% 251.13/59.90 | REDUCE: (3), (5) imply:
% 251.13/59.90 | (6) $false
% 251.13/59.90 |
% 251.13/59.90 | CLOSE: (6) is inconsistent.
% 251.13/59.90 |
% 251.13/59.90 End of proof
% 251.13/59.90
% 251.13/59.90 Sub-proof #595 shows that the following formulas are inconsistent:
% 251.13/59.90 ----------------------------------------------------------------
% 251.13/59.90 (1) ~ (all_10_2 = e1)
% 251.13/59.90 (2) ~ (all_4_2 = e4)
% 251.13/59.90 (3) op(all_4_2, e2) = e1
% 251.13/59.90 (4) ~ (all_38_2 = e1)
% 251.13/59.90 (5) op(all_36_2, all_62_2) = e1
% 251.13/59.90 (6) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(e2, all_44_1) = all_44_0 &
% 251.13/59.90 op(e1, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 251.13/59.90 e3) & op(e1, e2) = all_44_1 & $i(all_44_1))
% 251.13/59.90 (7) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.13/59.90 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.13/59.90 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.13/59.90 (8) all_208_2 = e1
% 251.13/59.90 (9) op(e0, e1) = all_174_1
% 251.13/59.90 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.90 (11) op(e2, e3) = all_10_2
% 251.13/59.90 (12) op(e2, e2) = all_244_8
% 251.13/59.90 (13) ~ (all_244_3 = e1)
% 251.13/59.90 (14) op(e2, e1) = all_38_2
% 251.13/59.90 (15) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.90 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.90 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.90 (16) op(all_26_2, e1) = e4
% 251.13/59.90 (17) op(e3, e4) = e1
% 251.13/59.90 (18) op(all_244_15, all_244_15) = e1
% 251.13/59.90 (19) op(e1, e3) = all_62_2
% 251.13/59.90 (20) ~ (all_208_2 = e1) | ( ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 &
% 251.13/59.90 op(e1, all_208_1) = all_208_0 & $i(all_208_0) & $i(all_208_1)) | ( ~
% 251.13/59.90 (all_208_1 = e2) & op(e4, e1) = all_208_1 & $i(all_208_1))
% 251.13/59.90 (21) op(e3, e1) = all_36_2
% 251.13/59.90 (22) ~ (all_22_2 = e1)
% 251.13/59.90 (23) op(e1, all_84_2) = e4
% 251.13/59.90 (24) ~ (all_64_2 = e1)
% 251.13/59.90 (25) op(e1, e0) = e2
% 251.13/59.90 (26) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.90 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.90 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.90 (27) ~ (all_244_15 = all_38_2)
% 251.13/59.90 (28) all_44_2 = all_26_2
% 251.13/59.90 (29) op(e1, e4) = e3
% 251.13/59.90 (30) op(e0, e3) = all_22_2
% 251.13/59.90 (31) ~ (all_244_0 = all_100_2)
% 251.13/59.90 (32) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.13/59.90 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.90 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.90 (33) op(e4, e1) = all_26_2
% 251.13/59.90 (34) ~ (all_244_15 = all_62_2)
% 251.13/59.90 (35) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 251.13/59.90 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 251.13/59.90 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 251.13/59.90 (36) op(e3, e4) = all_100_2
% 251.13/59.90 (37) ~ (all_244_8 = e1)
% 251.13/59.90 (38) op(e4, e4) = all_244_0
% 251.13/59.90 (39) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.90 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.90 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.90 (40) ~ (e4 = e3)
% 251.13/59.90 (41) op(e1, e1) = all_244_15
% 251.13/59.90 (42) op(e0, e1) = all_20_2
% 251.13/59.90 (43) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.90 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.90 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.90 (44) ~ (all_26_2 = e3)
% 251.13/59.90 (45) op(e1, e2) = all_4_2
% 251.13/59.90 (46) op(all_4_2, all_38_2) = e2
% 251.13/59.90 (47) op(e4, e3) = all_84_2
% 251.13/59.90 (48) op(e2, e4) = all_64_2
% 251.13/59.90 (49) ~ (e4 = e2)
% 251.13/59.90 (50) op(all_36_2, e1) = e3
% 251.13/59.90 (51) op(e3, e3) = all_244_3
% 251.13/59.90 (52) all_188_2 = all_38_2
% 251.13/59.90 (53) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.13/59.90 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 251.13/59.90 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 251.13/59.90 (54) all_46_2 = all_36_2
% 251.13/59.90 (55) ~ (all_20_2 = e2)
% 251.13/59.90
% 251.13/59.90 Begin of proof
% 251.13/59.90 |
% 251.13/59.90 | GROUND_INST: instantiating (10) with all_20_2, all_174_1, e1, e0, simplifying
% 251.13/59.90 | with (9), (42) gives:
% 251.13/59.90 | (56) all_174_1 = all_20_2
% 251.13/59.90 |
% 251.13/59.90 | BETA: splitting (7) gives:
% 251.13/59.90 |
% 251.13/59.90 | Case 1:
% 251.13/59.90 | |
% 251.13/59.90 | | (57) ~ (all_36_2 = e4)
% 251.13/59.90 | |
% 251.13/59.91 | | BETA: splitting (15) gives:
% 251.13/59.91 | |
% 251.13/59.91 | | Case 1:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (58) ~ (all_38_2 = e4)
% 251.13/59.91 | | |
% 251.13/59.91 | | | BETA: splitting (6) gives:
% 251.13/59.91 | | |
% 251.13/59.91 | | | Case 1:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (59) ~ (all_44_2 = e2)
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REDUCE: (28), (59) imply:
% 251.13/59.91 | | | | (60) ~ (all_26_2 = e2)
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | BETA: splitting (20) gives:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | Case 1:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (61) ~ (all_208_2 = e1)
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | REDUCE: (8), (61) imply:
% 251.13/59.91 | | | | | (62) $false
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | CLOSE: (62) is inconsistent.
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | Case 2:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (63) ( ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 & op(e1,
% 251.13/59.91 | | | | | all_208_1) = all_208_0 & $i(all_208_0) & $i(all_208_1)) |
% 251.13/59.91 | | | | | ( ~ (all_208_1 = e2) & op(e4, e1) = all_208_1 & $i(all_208_1))
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | BETA: splitting (63) gives:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | Case 1:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | (64) ~ (all_208_0 = e0) & op(e4, e1) = all_208_1 & op(e1,
% 251.13/59.91 | | | | | | all_208_1) = all_208_0 & $i(all_208_0) & $i(all_208_1)
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | ALPHA: (64) implies:
% 251.13/59.91 | | | | | | (65) op(e4, e1) = all_208_1
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | REF_CLOSE: (2), (3), (4), (5), (10), (12), (14), (17), (18), (19),
% 251.13/59.91 | | | | | | (21), (24), (25), (26), (29), (31), (32), (33), (35),
% 251.13/59.91 | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (45),
% 251.13/59.91 | | | | | | (46), (48), (50), (52), (54), (55), (57), (58), (60),
% 251.13/59.91 | | | | | | (65) are inconsistent by sub-proof #596.
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | Case 2:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | (66) ~ (all_208_1 = e2) & op(e4, e1) = all_208_1 & $i(all_208_1)
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | ALPHA: (66) implies:
% 251.13/59.91 | | | | | | (67) op(e4, e1) = all_208_1
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | REF_CLOSE: (2), (3), (4), (5), (10), (12), (14), (17), (18), (19),
% 251.13/59.91 | | | | | | (21), (24), (25), (26), (29), (31), (32), (33), (35),
% 251.13/59.91 | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (45),
% 251.13/59.91 | | | | | | (46), (48), (50), (52), (54), (55), (57), (58), (60),
% 251.13/59.91 | | | | | | (67) are inconsistent by sub-proof #596.
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | End of split
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | End of split
% 251.13/59.91 | | | |
% 251.13/59.91 | | | Case 2:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (68) all_44_2 = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | COMBINE_EQS: (28), (68) imply:
% 251.13/59.91 | | | | (69) all_26_2 = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REDUCE: (16), (69) imply:
% 251.13/59.91 | | | | (70) op(e2, e1) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (10), (14), (58), (70) are inconsistent by sub-proof #935.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | End of split
% 251.13/59.91 | | |
% 251.13/59.91 | | Case 2:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (71) all_38_2 = e4
% 251.13/59.91 | | |
% 251.13/59.91 | | | REDUCE: (27), (71) imply:
% 251.13/59.91 | | | (72) ~ (all_244_15 = e4)
% 251.13/59.91 | | |
% 251.13/59.91 | | | REDUCE: (4), (71) imply:
% 251.13/59.91 | | | (73) ~ (e4 = e1)
% 251.13/59.91 | | |
% 251.13/59.91 | | | BETA: splitting (32) gives:
% 251.13/59.91 | | |
% 251.13/59.91 | | | Case 1:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (74) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 251.13/59.91 | | | | e3) = e4)
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | BETA: splitting (74) gives:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | Case 1:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (75) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | ALPHA: (75) implies:
% 251.13/59.91 | | | | | (76) op(e1, e4) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | REF_CLOSE: (10), (29), (40), (76) are inconsistent by sub-proof #603.
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | Case 2:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (77) all_252_13 = e4 & op(e1, e3) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | ALPHA: (77) implies:
% 251.13/59.91 | | | | | (78) all_252_13 = e4
% 251.13/59.91 | | | | | (79) op(e1, e3) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | BETA: splitting (53) gives:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | Case 1:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | (80) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 &
% 251.13/59.91 | | | | | | op(e3, e3) = e1)
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | BETA: splitting (80) gives:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | Case 1:
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | (81) all_252_1 = e1 & op(e4, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | ALPHA: (81) implies:
% 251.13/59.91 | | | | | | | (82) op(e4, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | GROUND_INST: instantiating (10) with all_62_2, e4, e3, e1,
% 251.13/59.91 | | | | | | | simplifying with (19), (79) gives:
% 251.13/59.91 | | | | | | | (83) all_62_2 = e4
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | GROUND_INST: instantiating (10) with all_84_2, e1, e3, e4,
% 251.13/59.91 | | | | | | | simplifying with (47), (82) gives:
% 251.13/59.91 | | | | | | | (84) all_84_2 = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | REDUCE: (23), (84) imply:
% 251.13/59.91 | | | | | | | (85) op(e1, e1) = e4
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | REF_CLOSE: (10), (41), (72), (85) are inconsistent by sub-proof
% 251.13/59.91 | | | | | | | #756.
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | Case 2:
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | (86) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | ALPHA: (86) implies:
% 251.13/59.91 | | | | | | | (87) op(e3, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | REF_CLOSE: (10), (13), (51), (87) are inconsistent by sub-proof
% 251.13/59.91 | | | | | | | #801.
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | End of split
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | Case 2:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | (88) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 &
% 251.13/59.91 | | | | | | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | BETA: splitting (88) gives:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | Case 1:
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | (89) all_252_7 = e1 & op(e2, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | ALPHA: (89) implies:
% 251.13/59.91 | | | | | | | (90) op(e2, e3) = e1
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | REF_CLOSE: (1), (10), (11), (90) are inconsistent by sub-proof
% 251.13/59.91 | | | | | | | #948.
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | Case 2:
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | (91) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 251.13/59.91 | | | | | | | op(e0, e3) = e1)
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | BETA: splitting (91) gives:
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | | Case 1:
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | | (92) all_252_13 = e1 & op(e1, e3) = e1
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | | REF_CLOSE: (73), (78), (92) are inconsistent by sub-proof #754.
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | Case 2:
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | | (93) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | | ALPHA: (93) implies:
% 251.13/59.91 | | | | | | | | (94) op(e0, e3) = e1
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | | REF_CLOSE: (10), (22), (30), (94) are inconsistent by sub-proof
% 251.13/59.91 | | | | | | | | #714.
% 251.13/59.91 | | | | | | | |
% 251.13/59.91 | | | | | | | End of split
% 251.13/59.91 | | | | | | |
% 251.13/59.91 | | | | | | End of split
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | End of split
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | End of split
% 251.13/59.91 | | | |
% 251.13/59.91 | | | Case 2:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (95) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.91 | | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (2), (10), (25), (41), (45), (49), (72), (95) are
% 251.13/59.91 | | | | inconsistent by sub-proof #730.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | End of split
% 251.13/59.91 | | |
% 251.13/59.91 | | End of split
% 251.13/59.91 | |
% 251.13/59.91 | Case 2:
% 251.13/59.91 | |
% 251.13/59.91 | | (96) all_36_2 = e4
% 251.13/59.91 | |
% 251.13/59.91 | | REDUCE: (50), (96) imply:
% 251.13/59.91 | | (97) op(e4, e1) = e3
% 251.13/59.91 | |
% 251.13/59.91 | | REF_CLOSE: (10), (33), (44), (97) are inconsistent by sub-proof #834.
% 251.13/59.91 | |
% 251.13/59.91 | End of split
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #596 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) ~ (all_26_2 = e2)
% 251.13/59.91 (2) ~ (all_4_2 = e4)
% 251.13/59.91 (3) op(all_4_2, e2) = e1
% 251.13/59.91 (4) ~ (all_38_2 = e1)
% 251.13/59.91 (5) op(all_36_2, all_62_2) = e1
% 251.13/59.91 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.91 (7) op(e2, e2) = all_244_8
% 251.13/59.91 (8) op(e2, e1) = all_38_2
% 251.13/59.91 (9) op(e3, e4) = e1
% 251.13/59.91 (10) op(all_244_15, all_244_15) = e1
% 251.13/59.91 (11) op(e1, e3) = all_62_2
% 251.13/59.91 (12) ~ (all_36_2 = e4)
% 251.13/59.91 (13) op(e3, e1) = all_36_2
% 251.13/59.91 (14) ~ (all_64_2 = e1)
% 251.13/59.91 (15) op(e1, e0) = e2
% 251.13/59.91 (16) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.91 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.91 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.91 (17) ~ (all_38_2 = e4)
% 251.13/59.91 (18) op(e1, e4) = e3
% 251.13/59.91 (19) ~ (all_244_0 = all_100_2)
% 251.13/59.91 (20) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.13/59.91 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.91 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.91 (21) op(e4, e1) = all_26_2
% 251.13/59.91 (22) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 251.13/59.91 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 251.13/59.91 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 251.13/59.91 (23) op(e4, e1) = all_208_1
% 251.13/59.91 (24) op(e3, e4) = all_100_2
% 251.13/59.91 (25) ~ (all_244_8 = e1)
% 251.13/59.91 (26) op(e4, e4) = all_244_0
% 251.13/59.91 (27) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.91 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.91 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.91 (28) ~ (e4 = e3)
% 251.13/59.91 (29) op(e1, e1) = all_244_15
% 251.13/59.91 (30) op(e0, e1) = all_20_2
% 251.13/59.91 (31) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.91 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.91 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.91 (32) op(e1, e2) = all_4_2
% 251.13/59.91 (33) op(all_4_2, all_38_2) = e2
% 251.13/59.91 (34) op(e2, e4) = all_64_2
% 251.13/59.91 (35) op(all_36_2, e1) = e3
% 251.13/59.91 (36) all_188_2 = all_38_2
% 251.13/59.91 (37) all_46_2 = all_36_2
% 251.13/59.91 (38) ~ (all_20_2 = e2)
% 251.13/59.91
% 251.13/59.91 Begin of proof
% 251.13/59.91 |
% 251.13/59.91 | GROUND_INST: instantiating (6) with all_26_2, all_208_1, e1, e4, simplifying
% 251.13/59.91 | with (21), (23) gives:
% 251.13/59.91 | (39) all_208_1 = all_26_2
% 251.13/59.91 |
% 251.13/59.91 | BETA: splitting (16) gives:
% 251.13/59.91 |
% 251.13/59.91 | Case 1:
% 251.13/59.91 | |
% 251.13/59.91 | | (40) ~ (all_46_2 = e2)
% 251.13/59.91 | |
% 251.13/59.91 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (13), (21), (25), (27), (29),
% 251.13/59.91 | | (30), (33), (37), (38), (40) are inconsistent by sub-proof #598.
% 251.13/59.91 | |
% 251.13/59.91 | Case 2:
% 251.13/59.91 | |
% 251.13/59.91 | | (41) all_46_2 = e2
% 251.13/59.91 | | (42) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.91 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 251.13/59.91 | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.91 | |
% 251.13/59.91 | | COMBINE_EQS: (37), (41) imply:
% 251.13/59.91 | | (43) all_36_2 = e2
% 251.13/59.91 | |
% 251.13/59.91 | | SIMP: (43) implies:
% 251.13/59.91 | | (44) all_36_2 = e2
% 251.13/59.91 | |
% 251.13/59.91 | | REDUCE: (12), (44) imply:
% 251.13/59.91 | | (45) ~ (e4 = e2)
% 251.13/59.91 | |
% 251.13/59.91 | | SIMP: (45) implies:
% 251.13/59.91 | | (46) ~ (e4 = e2)
% 251.13/59.91 | |
% 251.13/59.91 | | REDUCE: (5), (44) imply:
% 251.13/59.91 | | (47) op(e2, all_62_2) = e1
% 251.13/59.91 | |
% 251.13/59.91 | | REDUCE: (35), (44) imply:
% 251.13/59.91 | | (48) op(e2, e1) = e3
% 251.13/59.91 | |
% 251.13/59.91 | | BETA: splitting (42) gives:
% 251.13/59.91 | |
% 251.13/59.91 | | Case 1:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (49) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.91 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 251.13/59.91 | | |
% 251.13/59.91 | | | ALPHA: (49) implies:
% 251.13/59.91 | | | (50) op(e1, e2) = all_46_1
% 251.13/59.91 | | |
% 251.13/59.91 | | | GROUND_INST: instantiating (6) with all_4_2, all_46_1, e2, e1, simplifying
% 251.13/59.91 | | | with (32), (50) gives:
% 251.13/59.91 | | | (51) all_46_1 = all_4_2
% 251.13/59.91 | | |
% 251.13/59.91 | | | GROUND_INST: instantiating (6) with all_38_2, e3, e1, e2, simplifying with
% 251.13/59.91 | | | (8), (48) gives:
% 251.13/59.91 | | | (52) all_38_2 = e3
% 251.13/59.91 | | |
% 251.13/59.91 | | | COMBINE_EQS: (36), (52) imply:
% 251.13/59.91 | | | (53) all_188_2 = e3
% 251.13/59.91 | | |
% 251.13/59.91 | | | REDUCE: (17), (52) imply:
% 251.13/59.91 | | | (54) ~ (e4 = e3)
% 251.13/59.91 | | |
% 251.13/59.91 | | | REF_CLOSE: (2), (6), (9), (10), (11), (14), (15), (18), (19), (20), (22),
% 251.13/59.91 | | | (24), (26), (28), (29), (31), (32), (34), (46), (47), (53) are
% 251.13/59.91 | | | inconsistent by sub-proof #597.
% 251.13/59.91 | | |
% 251.13/59.91 | | Case 2:
% 251.13/59.91 | | |
% 251.13/59.91 | | |
% 251.13/59.91 | | | GROUND_INST: instantiating (6) with all_38_2, e3, e1, e2, simplifying with
% 251.13/59.91 | | | (8), (48) gives:
% 251.13/59.91 | | | (55) all_38_2 = e3
% 251.13/59.91 | | |
% 251.13/59.91 | | | COMBINE_EQS: (36), (55) imply:
% 251.13/59.91 | | | (56) all_188_2 = e3
% 251.13/59.91 | | |
% 251.13/59.91 | | | REF_CLOSE: (2), (6), (9), (10), (11), (14), (15), (18), (19), (20), (22),
% 251.13/59.91 | | | (24), (26), (28), (29), (31), (32), (34), (46), (47), (56) are
% 251.13/59.91 | | | inconsistent by sub-proof #597.
% 251.13/59.91 | | |
% 251.13/59.91 | | End of split
% 251.13/59.91 | |
% 251.13/59.91 | End of split
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #597 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) ~ (all_4_2 = e4)
% 251.13/59.91 (2) op(e2, all_62_2) = e1
% 251.13/59.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.91 (4) all_188_2 = e3
% 251.13/59.91 (5) op(e3, e4) = e1
% 251.13/59.91 (6) op(all_244_15, all_244_15) = e1
% 251.13/59.91 (7) op(e1, e3) = all_62_2
% 251.13/59.91 (8) ~ (all_64_2 = e1)
% 251.13/59.91 (9) op(e1, e0) = e2
% 251.13/59.91 (10) op(e1, e4) = e3
% 251.13/59.91 (11) ~ (all_244_0 = all_100_2)
% 251.13/59.91 (12) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.13/59.91 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.91 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.91 (13) ~ (all_188_2 = e3) | ( ~ (all_188_0 = e0) & op(e3, all_188_1) =
% 251.13/59.91 all_188_0 & op(e1, e3) = all_188_1 & $i(all_188_0) & $i(all_188_1)) |
% 251.13/59.91 ( ~ (all_188_1 = e4) & op(e1, e3) = all_188_1 & $i(all_188_1))
% 251.13/59.91 (14) op(e3, e4) = all_100_2
% 251.13/59.91 (15) op(e4, e4) = all_244_0
% 251.13/59.91 (16) ~ (e4 = e3)
% 251.13/59.91 (17) op(e1, e1) = all_244_15
% 251.13/59.91 (18) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.91 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.91 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.91 (19) op(e1, e2) = all_4_2
% 251.13/59.91 (20) op(e2, e4) = all_64_2
% 251.13/59.91 (21) ~ (e4 = e2)
% 251.13/59.91
% 251.13/59.91 Begin of proof
% 251.13/59.91 |
% 251.13/59.91 | BETA: splitting (18) gives:
% 251.13/59.91 |
% 251.13/59.91 | Case 1:
% 251.13/59.91 | |
% 251.13/59.91 | | (22) ~ (all_62_2 = e4)
% 251.13/59.91 | |
% 251.13/59.91 | | BETA: splitting (12) gives:
% 251.13/59.91 | |
% 251.13/59.91 | | Case 1:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (23) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 251.13/59.91 | | | e3) = e4)
% 251.13/59.91 | | |
% 251.13/59.91 | | | BETA: splitting (23) gives:
% 251.13/59.91 | | |
% 251.13/59.91 | | | Case 1:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (24) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | ALPHA: (24) implies:
% 251.13/59.91 | | | | (25) op(e1, e4) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (3), (10), (16), (25) are inconsistent by sub-proof #603.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | Case 2:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (26) all_252_13 = e4 & op(e1, e3) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (3), (7), (22), (26) are inconsistent by sub-proof #952.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | End of split
% 251.13/59.91 | | |
% 251.13/59.91 | | Case 2:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (27) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.91 | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.91 | | |
% 251.13/59.91 | | | BETA: splitting (27) gives:
% 251.13/59.91 | | |
% 251.13/59.91 | | | Case 1:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (28) all_252_14 = e4 & op(e1, e2) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | ALPHA: (28) implies:
% 251.13/59.91 | | | | (29) op(e1, e2) = e4
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (1), (3), (19), (29) are inconsistent by sub-proof #831.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | Case 2:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (30) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1,
% 251.13/59.91 | | | | e0) = e4)
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | BETA: splitting (30) gives:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | Case 1:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (31) all_252_15 = e4 & op(e1, e1) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | ALPHA: (31) implies:
% 251.13/59.91 | | | | | (32) op(e1, e1) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | BETA: splitting (13) gives:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | Case 1:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | (33) ~ (all_188_2 = e3)
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | REDUCE: (4), (33) imply:
% 251.13/59.91 | | | | | | (34) $false
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | CLOSE: (34) is inconsistent.
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | Case 2:
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | GROUND_INST: instantiating (3) with all_244_15, e4, e1, e1,
% 251.13/59.91 | | | | | | simplifying with (17), (32) gives:
% 251.13/59.91 | | | | | | (35) all_244_15 = e4
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | REDUCE: (6), (35) imply:
% 251.13/59.91 | | | | | | (36) op(e4, e4) = e1
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | | REF_CLOSE: (3), (5), (11), (14), (15), (36) are inconsistent by
% 251.13/59.91 | | | | | | sub-proof #625.
% 251.13/59.91 | | | | | |
% 251.13/59.91 | | | | | End of split
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | Case 2:
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | (37) all_252_19 = e4 & op(e1, e0) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | ALPHA: (37) implies:
% 251.13/59.91 | | | | | (38) op(e1, e0) = e4
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | | REF_CLOSE: (3), (9), (21), (38) are inconsistent by sub-proof #829.
% 251.13/59.91 | | | | |
% 251.13/59.91 | | | | End of split
% 251.13/59.91 | | | |
% 251.13/59.91 | | | End of split
% 251.13/59.91 | | |
% 251.13/59.91 | | End of split
% 251.13/59.91 | |
% 251.13/59.91 | Case 2:
% 251.13/59.91 | |
% 251.13/59.91 | | (39) all_62_2 = e4
% 251.13/59.91 | |
% 251.13/59.91 | | REDUCE: (2), (39) imply:
% 251.13/59.91 | | (40) op(e2, e4) = e1
% 251.13/59.91 | |
% 251.13/59.91 | | REF_CLOSE: (3), (8), (20), (40) are inconsistent by sub-proof #731.
% 251.13/59.91 | |
% 251.13/59.91 | End of split
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #598 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) ~ (all_26_2 = e2)
% 251.13/59.91 (2) op(all_4_2, e2) = e1
% 251.13/59.91 (3) ~ (all_38_2 = e1)
% 251.13/59.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.91 (5) op(e2, e2) = all_244_8
% 251.13/59.91 (6) op(e2, e1) = all_38_2
% 251.13/59.91 (7) op(all_244_15, all_244_15) = e1
% 251.13/59.91 (8) ~ (all_46_2 = e2)
% 251.13/59.91 (9) op(e3, e1) = all_36_2
% 251.13/59.91 (10) op(e4, e1) = all_26_2
% 251.13/59.91 (11) ~ (all_244_8 = e1)
% 251.13/59.91 (12) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.13/59.91 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.13/59.91 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.91 (13) op(e1, e1) = all_244_15
% 251.13/59.91 (14) op(e0, e1) = all_20_2
% 251.13/59.91 (15) op(all_4_2, all_38_2) = e2
% 251.13/59.91 (16) all_46_2 = all_36_2
% 251.13/59.91 (17) ~ (all_20_2 = e2)
% 251.13/59.91
% 251.13/59.91 Begin of proof
% 251.13/59.91 |
% 251.13/59.91 | REDUCE: (8), (16) imply:
% 251.13/59.91 | (18) ~ (all_36_2 = e2)
% 251.13/59.91 |
% 251.13/59.91 | BETA: splitting (12) gives:
% 251.13/59.91 |
% 251.13/59.91 | Case 1:
% 251.13/59.91 | |
% 251.13/59.91 | | (19) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.91 | | e2)
% 251.13/59.91 | |
% 251.13/59.91 | | REF_CLOSE: (1), (4), (9), (10), (18), (19) are inconsistent by sub-proof
% 251.13/59.91 | | #969.
% 251.13/59.91 | |
% 251.13/59.91 | Case 2:
% 251.13/59.91 | |
% 251.13/59.91 | | (20) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.13/59.91 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.91 | |
% 251.13/59.91 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (13), (14), (15), (17), (20)
% 251.13/59.91 | | are inconsistent by sub-proof #737.
% 251.13/59.91 | |
% 251.13/59.91 | End of split
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #599 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) op(all_6_2, e2) = e4
% 251.13/59.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.91 (3) all_252_2 = e1
% 251.13/59.91 (4) ~ (e2 = e1)
% 251.13/59.91 (5) ~ (all_244_0 = e2)
% 251.13/59.91 (6) op(all_6_2, all_64_2) = e2
% 251.13/59.91 (7) op(e1, e4) = all_16_2
% 251.13/59.91 (8) ~ (all_12_2 = e2)
% 251.13/59.91 (9) ~ (all_16_2 = e2)
% 251.13/59.91 (10) op(e1, e4) = all_242_1
% 251.13/59.91 (11) op(e4, e4) = all_244_0
% 251.13/59.91 (12) op(e2, e4) = all_64_2
% 251.13/59.91 (13) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.91 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.91 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.91 (14) ~ (all_64_2 = e4)
% 251.13/59.91 (15) op(e0, e4) = all_12_2
% 251.13/59.91
% 251.13/59.91 Begin of proof
% 251.13/59.91 |
% 251.13/59.91 | BETA: splitting (13) gives:
% 251.13/59.91 |
% 251.13/59.91 | Case 1:
% 251.13/59.91 | |
% 251.13/59.91 | | (16) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.13/59.91 | | e2)
% 251.13/59.91 | |
% 251.13/59.91 | | BETA: splitting (16) gives:
% 251.13/59.91 | |
% 251.13/59.91 | | Case 1:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (17) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.91 | | |
% 251.13/59.91 | | | ALPHA: (17) implies:
% 251.13/59.91 | | | (18) op(e4, e4) = e2
% 251.13/59.91 | | |
% 251.13/59.91 | | | REF_CLOSE: (2), (5), (11), (18) are inconsistent by sub-proof #809.
% 251.13/59.91 | | |
% 251.13/59.91 | | Case 2:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (19) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.91 | | |
% 251.13/59.91 | | | REF_CLOSE: (3), (4), (19) are inconsistent by sub-proof #893.
% 251.13/59.91 | | |
% 251.13/59.91 | | End of split
% 251.13/59.91 | |
% 251.13/59.91 | Case 2:
% 251.13/59.91 | |
% 251.13/59.91 | | (20) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.91 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.91 | |
% 251.13/59.91 | | BETA: splitting (20) gives:
% 251.13/59.91 | |
% 251.13/59.91 | | Case 1:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (21) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.91 | | |
% 251.13/59.91 | | | ALPHA: (21) implies:
% 251.13/59.91 | | | (22) op(e2, e4) = e2
% 251.13/59.91 | | |
% 251.13/59.91 | | | REF_CLOSE: (1), (2), (6), (12), (14), (22) are inconsistent by sub-proof
% 251.13/59.91 | | | #790.
% 251.13/59.91 | | |
% 251.13/59.91 | | Case 2:
% 251.13/59.91 | | |
% 251.13/59.91 | | | (23) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0,
% 251.13/59.91 | | | e4) = e2)
% 251.13/59.91 | | |
% 251.13/59.91 | | | BETA: splitting (23) gives:
% 251.13/59.91 | | |
% 251.13/59.91 | | | Case 1:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (24) all_252_12 = e2 & op(e1, e4) = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | ALPHA: (24) implies:
% 251.13/59.91 | | | | (25) op(e1, e4) = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (2), (7), (9), (10), (25) are inconsistent by sub-proof #600.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | Case 2:
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | (26) all_252_20 = e2 & op(e0, e4) = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | ALPHA: (26) implies:
% 251.13/59.91 | | | | (27) op(e0, e4) = e2
% 251.13/59.91 | | | |
% 251.13/59.91 | | | | REF_CLOSE: (2), (8), (15), (27) are inconsistent by sub-proof #980.
% 251.13/59.91 | | | |
% 251.13/59.91 | | | End of split
% 251.13/59.91 | | |
% 251.13/59.91 | | End of split
% 251.13/59.91 | |
% 251.13/59.91 | End of split
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #600 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.91 (2) op(e1, e4) = all_16_2
% 251.13/59.91 (3) ~ (all_16_2 = e2)
% 251.13/59.91 (4) op(e1, e4) = all_242_1
% 251.13/59.91 (5) op(e1, e4) = e2
% 251.13/59.91
% 251.13/59.91 Begin of proof
% 251.13/59.91 |
% 251.13/59.91 | GROUND_INST: instantiating (1) with all_16_2, all_242_1, e4, e1, simplifying
% 251.13/59.91 | with (2), (4) gives:
% 251.13/59.91 | (6) all_242_1 = all_16_2
% 251.13/59.91 |
% 251.13/59.91 | GROUND_INST: instantiating (1) with e2, all_242_1, e4, e1, simplifying with
% 251.13/59.91 | (4), (5) gives:
% 251.13/59.91 | (7) all_242_1 = e2
% 251.13/59.91 |
% 251.13/59.91 | COMBINE_EQS: (6), (7) imply:
% 251.13/59.91 | (8) all_16_2 = e2
% 251.13/59.91 |
% 251.13/59.91 | REDUCE: (3), (8) imply:
% 251.13/59.91 | (9) $false
% 251.13/59.91 |
% 251.13/59.91 | CLOSE: (9) is inconsistent.
% 251.13/59.91 |
% 251.13/59.91 End of proof
% 251.13/59.91
% 251.13/59.91 Sub-proof #601 shows that the following formulas are inconsistent:
% 251.13/59.91 ----------------------------------------------------------------
% 251.13/59.91 (1) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) |
% 251.13/59.91 (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = e2) |
% 251.13/59.91 (all_252_16 = e2 & op(e4, e0) = e2)
% 251.13/59.91 (2) ~ (all_244_8 = all_4_2)
% 251.13/59.91 (3) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.13/59.91 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.13/59.91 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.13/59.91 (4) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 251.13/59.91 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 251.13/59.91 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.13/59.91 (5) ~ (all_26_2 = e2)
% 251.13/59.91 (6) ~ (all_10_2 = e4)
% 251.13/59.91 (7) op(all_4_2, e2) = e1
% 251.13/59.91 (8) op(all_6_2, e2) = e4
% 251.13/59.91 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.13/59.91 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.13/59.91 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.13/59.91 (10) op(e4, e0) = all_30_2
% 251.13/59.91 (11) all_250_8 = all_36_2
% 251.13/59.91 (12) ~ (all_244_8 = all_6_2)
% 251.13/59.91 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 251.13/59.91 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 251.13/59.91 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.13/59.91 (14) all_94_2 = all_38_2
% 251.13/59.91 (15) all_162_2 = all_28_2
% 251.13/59.92 (16) op(all_62_2, all_36_2) = e3
% 251.13/59.92 (17) op(all_38_2, e1) = e2
% 251.13/59.92 (18) all_250_13 = all_38_2
% 251.13/59.92 (19) ~ (all_28_2 = all_6_2)
% 251.13/59.92 (20) op(all_38_2, all_4_2) = e1
% 251.13/59.92 (21) ~ (all_28_2 = e3)
% 251.13/59.92 (22) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.92 all_250_20 = e0
% 251.13/59.92 (23) ~ (all_62_2 = all_22_2)
% 251.13/59.92 (24) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.92 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.92 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.92 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.92 (26) op(e2, e3) = all_10_2
% 251.13/59.92 (27) ~ (e3 = e2)
% 251.13/59.92 (28) op(e0, e0) = all_244_24
% 251.13/59.92 (29) ~ (all_12_2 = e3)
% 251.13/59.92 (30) op(e2, e2) = all_244_8
% 251.13/59.92 (31) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.92 all_250_11 = e0
% 251.13/59.92 (32) op(e2, e1) = all_38_2
% 251.13/59.92 (33) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.92 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.92 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.92 (34) ~ (all_36_2 = all_20_2)
% 251.13/59.92 (35) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.92 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.92 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.92 (36) all_252_2 = e1
% 251.13/59.92 (37) ~ (all_244_3 = all_22_2)
% 251.13/59.92 (38) op(e1, e0) = all_34_2
% 251.13/59.92 (39) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 251.13/59.92 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 251.13/59.92 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 251.13/59.92 (40) ~ (all_40_2 = e4)
% 251.13/59.92 (41) op(all_28_2, e2) = e0
% 251.13/59.92 (42) op(e4, e2) = all_6_2
% 251.13/59.92 (43) all_78_2 = all_10_2
% 251.13/59.92 (44) ~ (all_8_2 = all_4_2)
% 251.13/59.92 (45) ~ (all_20_2 = all_12_2)
% 251.13/59.92 (46) ~ (all_34_2 = e2)
% 251.13/59.92 (47) ~ (e2 = e1)
% 251.13/59.92 (48) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.92 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.92 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.92 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.92 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.92 op(e0, e1) = e0)))
% 251.13/59.92 (49) op(e0, e2) = all_28_2
% 251.13/59.92 (50) op(e3, e4) = e1
% 251.13/59.92 (51) ~ (e4 = e1)
% 251.13/59.92 (52) op(all_6_2, all_64_2) = e2
% 251.13/59.92 (53) ~ (all_6_2 = e1)
% 251.13/59.92 (54) all_106_2 = all_38_2
% 251.13/59.92 (55) ~ (all_244_8 = all_38_2)
% 251.13/59.92 (56) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.13/59.92 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.13/59.92 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.13/59.92 (57) op(all_244_15, all_244_15) = e1
% 251.13/59.92 (58) all_80_2 = all_6_2
% 251.13/59.92 (59) all_250_21 = all_22_2
% 251.13/59.92 (60) ~ (all_244_3 = all_84_2)
% 251.13/59.92 (61) op(e1, e4) = all_16_2
% 251.13/59.92 (62) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.92 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.92 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.92 (63) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.92 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.92 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.92 (64) ~ (all_28_2 = all_20_2)
% 251.13/59.92 (65) op(e1, e3) = all_62_2
% 251.13/59.92 (66) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.13/59.92 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.13/59.92 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.13/59.92 (67) ~ (all_244_3 = all_10_2)
% 251.13/59.92 (68) ~ (all_30_2 = e2)
% 251.13/59.92 (69) ~ (all_36_2 = e4)
% 251.13/59.92 (70) all_70_2 = all_62_2
% 251.13/59.92 (71) ~ (all_36_2 = all_8_2)
% 251.13/59.92 (72) ~ (e3 = e1)
% 251.13/59.92 (73) op(all_48_2, all_22_2) = e0
% 251.13/59.92 (74) ~ (all_12_2 = e2)
% 251.13/59.92 (75) op(e3, e1) = all_36_2
% 251.13/59.92 (76) all_252_12 = e3
% 251.13/59.92 (77) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.92 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.92 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.92 (78) ~ (all_16_2 = e2)
% 251.13/59.92 (79) ~ (all_8_2 = e1)
% 251.13/59.92 (80) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.13/59.92 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.13/59.92 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.92 (81) ~ (all_22_2 = e1)
% 251.13/59.92 (82) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.13/59.92 all_250_8 = e0
% 251.13/59.92 (83) ~ (all_28_2 = all_4_2)
% 251.13/59.92 (84) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.92 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.92 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.92 (85) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.92 all_250_13 = e0
% 251.13/59.92 (86) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.92 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.92 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.92 (87) ~ (all_38_2 = e4)
% 251.13/59.92 (88) op(e1, e4) = e3
% 251.13/59.92 (89) op(all_22_2, e3) = e0
% 251.13/59.92 (90) all_68_2 = all_22_2
% 251.13/59.92 (91) op(e0, e3) = all_22_2
% 251.13/59.92 (92) ~ (all_28_2 = all_22_2)
% 251.13/59.92 (93) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.92 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.92 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.92 (94) all_58_2 = all_20_2
% 251.13/59.92 (95) op(all_62_2, e3) = e1
% 251.13/59.92 (96) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.92 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.92 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.92 (97) op(all_10_2, e3) = e2
% 251.13/59.92 (98) op(all_30_2, all_12_2) = e0
% 251.13/59.92 (99) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.92 all_250_21 = e0
% 251.13/59.92 (100) ~ (all_244_15 = all_62_2)
% 251.13/59.92 (101) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.92 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.92 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.92 (102) op(e4, e1) = all_208_1
% 251.13/59.92 (103) ~ (all_8_2 = all_6_2)
% 251.13/59.92 (104) all_250_11 = all_10_2
% 251.13/59.92 (105) ~ (all_22_2 = all_12_2)
% 251.13/59.92 (106) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.13/59.92 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.92 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.13/59.92 (107) ~ (e4 = e3)
% 251.13/59.92 (108) op(e1, e1) = all_244_15
% 251.13/59.92 (109) op(e0, e1) = all_20_2
% 251.13/59.92 (110) op(all_48_2, e0) = e3
% 251.13/59.92 (111) all_82_2 = all_28_2
% 251.13/59.92 (112) ~ (all_84_2 = all_22_2)
% 251.13/59.92 (113) op(e1, e2) = all_4_2
% 251.13/59.92 (114) all_208_1 = all_26_2
% 251.13/59.92 (115) ~ (all_28_2 = all_8_2)
% 251.13/59.92 (116) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.13/59.92 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.13/59.92 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.13/59.92 (117) op(all_4_2, all_38_2) = e2
% 251.13/59.92 (118) op(e4, e3) = all_84_2
% 251.13/59.92 (119) ~ (all_62_2 = all_10_2)
% 251.13/59.92 (120) op(e2, e4) = all_64_2
% 251.13/59.92 (121) ~ (all_22_2 = all_10_2)
% 251.13/59.92 (122) ~ (all_36_2 = e1)
% 251.13/59.92 (123) ~ (all_6_2 = all_4_2)
% 251.13/59.92 (124) ~ (e4 = e2)
% 251.13/59.92 (125) ~ (all_22_2 = all_20_2)
% 251.13/59.92 (126) op(e3, e2) = all_8_2
% 251.13/59.92 (127) op(all_36_2, e1) = e3
% 251.13/59.92 (128) ~ (all_38_2 = all_10_2)
% 251.13/59.92 (129) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.92 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.92 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.92 (130) ~ (all_244_15 = all_36_2)
% 251.13/59.92 (131) ~ (all_244_24 = all_22_2)
% 251.13/59.92 (132) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.92 | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) =
% 251.13/59.92 e4) | (all_252_20 = e4 & op(e0, e4) = e4)
% 251.13/59.92 (133) op(e2, e0) = all_40_2
% 251.13/59.92 (134) ~ (all_244_8 = all_28_2)
% 251.13/59.92 (135) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.92 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.92 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.92 (136) all_250_20 = all_12_2
% 251.13/59.92 (137) op(e3, e3) = all_244_3
% 251.13/59.92 (138) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.92 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.92 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.92 (139) ~ (all_4_2 = e3)
% 251.13/59.92 (140) all_90_2 = all_22_2
% 251.13/59.92 (141) all_46_2 = all_36_2
% 251.13/59.92 (142) op(all_30_2, e0) = e4
% 251.13/59.92 (143) op(all_244_24, all_244_24) = e0
% 251.13/59.92 (144) op(e0, e4) = all_12_2
% 251.13/59.92 (145) ~ (all_20_2 = e2)
% 251.13/59.92 (146) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.92 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.92 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.92 (147) ~ (all_12_2 = e1)
% 251.13/59.92 (148) all_124_2 = all_10_2
% 251.13/59.92
% 251.13/59.92 Begin of proof
% 251.13/59.92 |
% 251.13/59.92 | REDUCE: (102), (114) imply:
% 251.13/59.92 | (149) op(e4, e1) = all_26_2
% 251.13/59.92 |
% 251.13/59.92 | BETA: splitting (84) gives:
% 251.13/59.92 |
% 251.13/59.92 | Case 1:
% 251.13/59.92 | |
% 251.13/59.92 | | (150) ~ (all_46_2 = e2)
% 251.13/59.92 | |
% 251.13/59.92 | | REDUCE: (141), (150) imply:
% 251.13/59.92 | | (151) ~ (all_36_2 = e2)
% 251.13/59.92 | |
% 251.13/59.92 | | BETA: splitting (66) gives:
% 251.13/59.92 | |
% 251.13/59.92 | | Case 1:
% 251.13/59.92 | | |
% 251.13/59.92 | | | (152) ~ (all_58_2 = e3)
% 251.13/59.92 | | |
% 251.13/59.92 | | | REF_CLOSE: (5), (6), (7), (14), (17), (18), (21), (24), (25), (26), (27),
% 251.13/59.92 | | | (28), (29), (30), (31), (32), (35), (43), (49), (54), (55),
% 251.13/59.92 | | | (57), (59), (60), (62), (63), (65), (67), (70), (73), (75),
% 251.13/59.92 | | | (77), (81), (85), (86), (87), (89), (90), (91), (92), (94),
% 251.13/59.92 | | | (95), (96), (97), (99), (100), (101), (104), (105), (106),
% 251.13/59.92 | | | (107), (108), (109), (110), (117), (118), (119), (121), (125),
% 251.13/59.92 | | | (128), (131), (137), (140), (143), (144), (145), (146), (148),
% 251.13/59.92 | | | (149), (151), (152) are inconsistent by sub-proof #960.
% 251.13/59.92 | | |
% 251.13/59.92 | | Case 2:
% 251.13/59.92 | | |
% 251.13/59.92 | | | (153) all_58_2 = e3
% 251.13/59.92 | | |
% 251.13/59.92 | | | COMBINE_EQS: (94), (153) imply:
% 251.13/59.92 | | | (154) all_20_2 = e3
% 251.13/59.92 | | |
% 251.13/59.92 | | | REDUCE: (34), (154) imply:
% 251.13/59.92 | | | (155) ~ (all_36_2 = e3)
% 251.13/59.92 | | |
% 251.13/59.92 | | | REDUCE: (125), (154) imply:
% 251.13/59.92 | | | (156) ~ (all_22_2 = e3)
% 251.13/59.92 | | |
% 251.13/59.92 | | | REDUCE: (45), (154) imply:
% 251.13/59.92 | | | (157) ~ (all_12_2 = e3)
% 251.13/59.92 | | |
% 251.13/59.92 | | | BETA: splitting (82) gives:
% 251.13/59.92 | | |
% 251.13/59.92 | | | Case 1:
% 251.13/59.92 | | | |
% 251.13/59.92 | | | | (158) all_250_8 = e4
% 251.13/59.92 | | | |
% 251.13/59.92 | | | | REF_CLOSE: (11), (69), (158) are inconsistent by sub-proof #661.
% 251.13/59.92 | | | |
% 251.13/59.92 | | | Case 2:
% 251.13/59.92 | | | |
% 251.13/59.92 | | | | (159) ~ (all_250_8 = e4)
% 251.13/59.92 | | | | (160) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | all_250_8 =
% 251.13/59.92 | | | | e0
% 251.13/59.92 | | | |
% 251.13/59.92 | | | | BETA: splitting (160) gives:
% 251.13/59.92 | | | |
% 251.13/59.92 | | | | Case 1:
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | | (161) all_250_8 = e3
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | | REF_CLOSE: (11), (155), (161) are inconsistent by sub-proof #612.
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | Case 2:
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | | (162) ~ (all_250_8 = e3)
% 251.13/59.92 | | | | | (163) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | | BETA: splitting (163) gives:
% 251.13/59.92 | | | | |
% 251.13/59.92 | | | | | Case 1:
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | | (164) all_250_8 = e2
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | | REF_CLOSE: (11), (151), (164) are inconsistent by sub-proof #660.
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | Case 2:
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | | (165) ~ (all_250_8 = e2)
% 251.13/59.92 | | | | | | (166) all_250_8 = e1 | all_250_8 = e0
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | | BETA: splitting (166) gives:
% 251.13/59.92 | | | | | |
% 251.13/59.92 | | | | | | Case 1:
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | (167) all_250_8 = e1
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REF_CLOSE: (11), (122), (167) are inconsistent by sub-proof #659.
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | Case 2:
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | (168) all_250_8 = e0
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | COMBINE_EQS: (11), (168) imply:
% 251.13/59.92 | | | | | | | (169) all_36_2 = e0
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (169) implies:
% 251.13/59.92 | | | | | | | (170) all_36_2 = e0
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (130), (170) imply:
% 251.13/59.92 | | | | | | | (171) ~ (all_244_15 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (71), (170) imply:
% 251.13/59.92 | | | | | | | (172) ~ (all_8_2 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (172) implies:
% 251.13/59.92 | | | | | | | (173) ~ (all_8_2 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (69), (170) imply:
% 251.13/59.92 | | | | | | | (174) ~ (e4 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (174) implies:
% 251.13/59.92 | | | | | | | (175) ~ (e4 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (155), (170) imply:
% 251.13/59.92 | | | | | | | (176) ~ (e3 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (176) implies:
% 251.13/59.92 | | | | | | | (177) ~ (e3 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (151), (170) imply:
% 251.13/59.92 | | | | | | | (178) ~ (e2 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (178) implies:
% 251.13/59.92 | | | | | | | (179) ~ (e2 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (122), (170) imply:
% 251.13/59.92 | | | | | | | (180) ~ (e1 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | SIMP: (180) implies:
% 251.13/59.92 | | | | | | | (181) ~ (e1 = e0)
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | REDUCE: (127), (170) imply:
% 251.13/59.92 | | | | | | | (182) op(e0, e1) = e3
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | BETA: splitting (35) gives:
% 251.13/59.92 | | | | | | |
% 251.13/59.92 | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | (183) ~ (all_68_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (90), (183) imply:
% 251.13/59.92 | | | | | | | | (184) ~ (all_22_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | BETA: splitting (86) gives:
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | (185) ~ (all_70_2 = e2)
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | REDUCE: (70), (185) imply:
% 251.13/59.92 | | | | | | | | | (186) ~ (all_62_2 = e2)
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | BETA: splitting (39) gives:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | (187) ~ (all_80_2 = e0)
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (58), (187) imply:
% 251.13/59.92 | | | | | | | | | | (188) ~ (all_6_2 = e0)
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | BETA: splitting (13) gives:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | (189) ~ (all_82_2 = e1)
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | REDUCE: (111), (189) imply:
% 251.13/59.92 | | | | | | | | | | | (190) ~ (all_28_2 = e1)
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | BETA: splitting (80) gives:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (191) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 251.13/59.92 | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | BETA: splitting (191) gives:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (192) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | ALPHA: (192) implies:
% 251.13/59.92 | | | | | | | | | | | | | (193) op(e0, e4) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_12_2, e1, e4, e0,
% 251.13/59.92 | | | | | | | | | | | | | simplifying with (144), (193) gives:
% 251.13/59.92 | | | | | | | | | | | | | (194) all_12_2 = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | REDUCE: (147), (194) imply:
% 251.13/59.92 | | | | | | | | | | | | | (195) $false
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (196) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | ALPHA: (196) implies:
% 251.13/59.92 | | | | | | | | | | | | | (197) op(e0, e3) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | REF_CLOSE: (25), (81), (91), (197) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | | sub-proof #714.
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (198) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 251.13/59.92 | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 251.13/59.92 | | | | | | | | | | | | op(e0, e0) = e1)
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | BETA: splitting (198) gives:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (199) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | ALPHA: (199) implies:
% 251.13/59.92 | | | | | | | | | | | | | (200) op(e0, e2) = e1
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | REF_CLOSE: (25), (49), (190), (200) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | | sub-proof #907.
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (201) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 251.13/59.92 | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | BETA: splitting (201) gives:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | (202) all_252_23 = e1 & op(e0, e1) = e1
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | ALPHA: (202) implies:
% 251.13/59.92 | | | | | | | | | | | | | | (203) op(e0, e1) = e1
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | REF_CLOSE: (25), (72), (182), (203) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | | | sub-proof #915.
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | (204) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | REF_CLOSE: (25), (28), (108), (143), (171), (204) are
% 251.13/59.92 | | | | | | | | | | | | | | inconsistent by sub-proof #611.
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | (205) all_82_2 = e1
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | COMBINE_EQS: (111), (205) imply:
% 251.13/59.92 | | | | | | | | | | | (206) all_28_2 = e1
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | REF_CLOSE: (2), (19), (25), (30), (33), (38), (41), (42),
% 251.13/59.92 | | | | | | | | | | | (44), (46), (49), (56), (57), (61), (65), (78),
% 251.13/59.92 | | | | | | | | | | | (83), (108), (113), (115), (123), (126), (134),
% 251.13/59.92 | | | | | | | | | | | (135), (173), (179), (181), (186), (188), (206)
% 251.13/59.92 | | | | | | | | | | | are inconsistent by sub-proof #867.
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | (207) all_80_2 = e0
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | COMBINE_EQS: (58), (207) imply:
% 251.13/59.92 | | | | | | | | | | (208) all_6_2 = e0
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | SIMP: (208) implies:
% 251.13/59.92 | | | | | | | | | | (209) all_6_2 = e0
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (12), (209) imply:
% 251.13/59.92 | | | | | | | | | | (210) ~ (all_244_8 = e0)
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (123), (209) imply:
% 251.13/59.92 | | | | | | | | | | (211) ~ (all_4_2 = e0)
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | SIMP: (211) implies:
% 251.13/59.92 | | | | | | | | | | (212) ~ (all_4_2 = e0)
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (52), (209) imply:
% 251.13/59.92 | | | | | | | | | | (213) op(e0, all_64_2) = e2
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (8), (209) imply:
% 251.13/59.92 | | | | | | | | | | (214) op(e0, e2) = e4
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REF_CLOSE: (4), (6), (15), (21), (25), (26), (27), (30),
% 251.13/59.92 | | | | | | | | | | (32), (33), (40), (42), (47), (49), (51), (53),
% 251.13/59.92 | | | | | | | | | | (56), (74), (79), (87), (93), (113), (116), (120),
% 251.13/59.92 | | | | | | | | | | (124), (126), (133), (138), (139), (144), (173),
% 251.13/59.92 | | | | | | | | | | (175), (177), (179), (210), (212), (213), (214)
% 251.13/59.92 | | | | | | | | | | are inconsistent by sub-proof #853.
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | (215) all_70_2 = e2
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | COMBINE_EQS: (70), (215) imply:
% 251.13/59.92 | | | | | | | | | (216) all_62_2 = e2
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | REF_CLOSE: (23), (25), (59), (73), (81), (99), (110), (156),
% 251.13/59.92 | | | | | | | | | (184), (216) are inconsistent by sub-proof #852.
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | End of split
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | (217) all_68_2 = e4
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | COMBINE_EQS: (90), (217) imply:
% 251.13/59.92 | | | | | | | | (218) all_22_2 = e4
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | SIMP: (218) implies:
% 251.13/59.92 | | | | | | | | (219) all_22_2 = e4
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (37), (219) imply:
% 251.13/59.92 | | | | | | | | (220) ~ (all_244_3 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (112), (219) imply:
% 251.13/59.92 | | | | | | | | (221) ~ (all_84_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (23), (219) imply:
% 251.13/59.92 | | | | | | | | (222) ~ (all_62_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (105), (219) imply:
% 251.13/59.92 | | | | | | | | (223) ~ (all_12_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | SIMP: (223) implies:
% 251.13/59.92 | | | | | | | | (224) ~ (all_12_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (121), (219) imply:
% 251.13/59.92 | | | | | | | | (225) ~ (all_10_2 = e4)
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | REDUCE: (89), (219) imply:
% 251.13/59.92 | | | | | | | | (226) op(e4, e3) = e0
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | BETA: splitting (22) gives:
% 251.13/59.92 | | | | | | | |
% 251.13/59.92 | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | (227) all_250_20 = e4
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | COMBINE_EQS: (136), (227) imply:
% 251.13/59.92 | | | | | | | | | (228) all_12_2 = e4
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | SIMP: (228) implies:
% 251.13/59.92 | | | | | | | | | (229) all_12_2 = e4
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | REDUCE: (224), (229) imply:
% 251.13/59.92 | | | | | | | | | (230) $false
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | CLOSE: (230) is inconsistent.
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | (231) ~ (all_250_20 = e4)
% 251.13/59.92 | | | | | | | | | (232) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 |
% 251.13/59.92 | | | | | | | | | all_250_20 = e0
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | BETA: splitting (232) gives:
% 251.13/59.92 | | | | | | | | |
% 251.13/59.92 | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | (233) all_250_20 = e3
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | COMBINE_EQS: (136), (233) imply:
% 251.13/59.92 | | | | | | | | | | (234) all_12_2 = e3
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | SIMP: (234) implies:
% 251.13/59.92 | | | | | | | | | | (235) all_12_2 = e3
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | REDUCE: (29), (235) imply:
% 251.13/59.92 | | | | | | | | | | (236) $false
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | CLOSE: (236) is inconsistent.
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | (237) ~ (all_250_20 = e3)
% 251.13/59.92 | | | | | | | | | | (238) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | BETA: splitting (9) gives:
% 251.13/59.92 | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | (239) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.13/59.92 | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | BETA: splitting (239) gives:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (240) all_252_1 = e4 & op(e4, e3) = e4
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | REF_CLOSE: (25), (118), (221), (240) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | sub-proof #815.
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (241) all_252_3 = e4 & op(e3, e3) = e4
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | REF_CLOSE: (25), (137), (220), (241) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | sub-proof #846.
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | End of split
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | (242) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.13/59.92 | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.13/59.92 | | | | | | | | | | | op(e0, e3) = e4)
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | BETA: splitting (242) gives:
% 251.13/59.92 | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (243) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | ALPHA: (243) implies:
% 251.13/59.92 | | | | | | | | | | | | (244) op(e2, e3) = e4
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | REF_CLOSE: (6), (25), (26), (244) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | sub-proof #953.
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | (245) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 251.13/59.92 | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | BETA: splitting (245) gives:
% 251.13/59.92 | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (246) all_252_13 = e4 & op(e1, e3) = e4
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | REF_CLOSE: (25), (65), (222), (246) are inconsistent by
% 251.13/59.92 | | | | | | | | | | | | | sub-proof #952.
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | (247) all_252_21 = e4 & op(e0, e3) = e4
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | ALPHA: (247) implies:
% 251.13/59.92 | | | | | | | | | | | | | (248) all_252_21 = e4
% 251.13/59.92 | | | | | | | | | | | | | (249) op(e0, e3) = e4
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | BETA: splitting (238) gives:
% 251.13/59.92 | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | (250) all_250_20 = e2
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | COMBINE_EQS: (136), (250) imply:
% 251.13/59.92 | | | | | | | | | | | | | | (251) all_12_2 = e2
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | SIMP: (251) implies:
% 251.13/59.92 | | | | | | | | | | | | | | (252) all_12_2 = e2
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | REDUCE: (74), (252) imply:
% 251.13/59.92 | | | | | | | | | | | | | | (253) $false
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | (254) ~ (all_250_20 = e2)
% 251.13/59.92 | | | | | | | | | | | | | | (255) all_250_20 = e1 | all_250_20 = e0
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 251.13/59.92 | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | Case 1:
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | (256) all_250_20 = e1
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | COMBINE_EQS: (136), (256) imply:
% 251.13/59.92 | | | | | | | | | | | | | | | (257) all_12_2 = e1
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | SIMP: (257) implies:
% 251.13/59.92 | | | | | | | | | | | | | | | (258) all_12_2 = e1
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | REDUCE: (147), (258) imply:
% 251.13/59.92 | | | | | | | | | | | | | | | (259) $false
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent.
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | Case 2:
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | (260) all_250_20 = e0
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | COMBINE_EQS: (136), (260) imply:
% 251.13/59.92 | | | | | | | | | | | | | | | (261) all_12_2 = e0
% 251.13/59.92 | | | | | | | | | | | | | | |
% 251.13/59.92 | | | | | | | | | | | | | | | SIMP: (261) implies:
% 251.13/59.92 | | | | | | | | | | | | | | | (262) all_12_2 = e0
% 251.13/59.93 | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | REDUCE: (98), (262) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | (263) op(all_30_2, e0) = e0
% 251.13/59.93 | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 251.13/59.93 | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | (264) all_252_24 = e0 & op(e0, e0) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | (265) all_252_24 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | (266) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (267) all_252_0 = e0 & op(e4, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (268) all_252_0 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (269) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (270) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (268), (270) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | #610.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (271) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (47), (271) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | #893.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (272) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (273) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (274) all_252_6 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (275) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (74), (91), (124), (144), (249), (275) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #650.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (276) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (277) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (278) all_252_22 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (279) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (280) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_6 = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (281) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (282) e4 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (282) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (283) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (284) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (285) op(e2, e3) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (25), (26), (285) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (286) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (287) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (288) all_252_8 = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | (289) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (42), (53), (79), (126), (289) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #928.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | (290) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (288), (291) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | #644.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_252_14 = e1 & op(e1, e2) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) op(e1, e2) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_252_4 = e0 & op(e4, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_252_4 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (268), (299) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_252_1 = e2 & op(e4, e3) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) op(e4, e3) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (118), (179), (226), (301) are inconsistent
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #850.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_252_4 = e2 & op(e4, e2) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_252_4 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (304) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e2 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (305) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (306) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (25), (68), (149), (307) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_252_5 = e0 & op(e3, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (126), (173), (308) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #874.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_252_8 = e0 & op(e2, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_252_8 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (311) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) e4 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (312) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_252_21 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (25), (26), (65), (118), (137), (175),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (313) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #814.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_252_14 = e0 & op(e1, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) op(e1, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (113), (181), (294), (316) are inconsistent
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #870.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (278), (317) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #608.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_252_22 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (319) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) e2 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (320) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (32), (40), (87), (133), (322) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #933.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (323) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (324) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (325) all_252_23 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (25), (27), (28), (29), (49), (60), (63),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (107), (118), (137), (143), (144), (226), (249),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (325) are inconsistent by sub-proof #847.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (326) all_252_24 = e2 & op(e0, e0) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_24 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (327) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (328) e2 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (328) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (329) e2 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (329) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (330) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (331) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (61), (74), (78), (144), (331) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #891.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (332) all_252_2 = e0 & op(e3, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (333) op(e3, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (50), (181), (333) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | sub-proof #607.
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | (334) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | op(e0, e4) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (335) all_252_6 = e0 & op(e2, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (336) all_252_6 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (337) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (338) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (339) all_252_0 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (340) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e4) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (51), (124), (339), (340) are inconsistent
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | by sub-proof #604.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (341) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e4) = e4) | (all_252_20 = e4 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (342) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (343) all_252_6 = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (343) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (344) e4 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (345) e4 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (345) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (346) all_252_21 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (25), (26), (65), (118), (137), (175),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (346) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | sub-proof #814.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (347) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e4) = e4)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (348) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (349) op(e1, e4) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (88), (107), (349) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #603.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (350) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (144), (224), (350) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #602.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (351) all_252_2 = e2 & op(e3, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (47), (351) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | #893.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (352) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (353) all_252_6 = e2 & op(e2, e4) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (179), (336), (353) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | #892.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (354) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (61), (74), (78), (144), (354) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #891.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | (355) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20
% 251.13/59.93 | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0)
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (356) all_252_12 = e0 & op(e1, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (357) all_252_12 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (357) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (358) e3 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | SIMP: (358) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (359) e3 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | REDUCE: (177), (359) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (360) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (361) all_252_20 = e0 & op(e0, e4) = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | (362) all_252_20 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (363) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (74), (91), (124), (144), (249), (363) are
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #650.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | (364) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (365) all_252_22 = e2 & op(e0, e2) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (366) all_252_22 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (367) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (368) all_252_20 = e1 & op(e0, e4) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (369) all_252_20 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (362), (369) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | #824.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (370) all_252_21 = e1 & op(e0, e3) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (371) op(e0, e3) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (51), (249), (371) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #828.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (372) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (373) all_252_22 = e1 & op(e0, e2) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (374) all_252_22 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (374) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (375) e2 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (375) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (376) e2 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (376) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (377) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | (378) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (379) all_252_23 = e1 & op(e0, e1) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (380) op(e0, e1) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (72), (182), (380) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #915.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (381) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (381) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | (382) all_252_24 = e1
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (181), (265), (382) are inconsistent by sub-proof
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | | #623.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | (383) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (383) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (384) all_252_23 = e2 & op(e0, e1) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (384) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (385) all_252_23 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (25), (27), (28), (29), (49), (60), (63),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (107), (118), (137), (143), (144), (226), (249),
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (385) are inconsistent by sub-proof #847.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (386) all_252_24 = e2 & op(e0, e0) = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (387) all_252_24 = e2
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (387) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (388) e2 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (388) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | (389) $false
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (389) is inconsistent.
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | Case 2:
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with e4, e0, e0, all_30_2,
% 251.13/59.93 | | | | | | | | | | | | | | | | simplifying with (142), (263) gives:
% 251.13/59.93 | | | | | | | | | | | | | | | | (390) e4 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (390) imply:
% 251.13/59.93 | | | | | | | | | | | | | | | | (391) all_252_21 = e0
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (25), (26), (65), (118), (137), (175),
% 251.13/59.93 | | | | | | | | | | | | | | | | (220), (221), (222), (391) are inconsistent by
% 251.13/59.93 | | | | | | | | | | | | | | | | sub-proof #814.
% 251.13/59.93 | | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | | |
% 251.13/59.93 | | | | | | | | | End of split
% 251.13/59.93 | | | | | | | | |
% 251.13/59.93 | | | | | | | | End of split
% 251.13/59.93 | | | | | | | |
% 251.13/59.93 | | | | | | | End of split
% 251.13/59.93 | | | | | | |
% 251.13/59.93 | | | | | | End of split
% 251.13/59.93 | | | | | |
% 251.13/59.93 | | | | | End of split
% 251.13/59.93 | | | | |
% 251.13/59.93 | | | | End of split
% 251.13/59.93 | | | |
% 251.13/59.93 | | | End of split
% 251.13/59.93 | | |
% 251.13/59.93 | | End of split
% 251.13/59.93 | |
% 251.13/59.93 | Case 2:
% 251.13/59.93 | |
% 251.13/59.93 | | (392) all_46_2 = e2
% 251.13/59.93 | | (393) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.13/59.93 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 251.13/59.93 | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.93 | |
% 251.13/59.93 | | COMBINE_EQS: (141), (392) imply:
% 251.13/59.93 | | (394) all_36_2 = e2
% 251.13/59.93 | |
% 251.13/59.93 | | SIMP: (394) implies:
% 251.13/59.93 | | (395) all_36_2 = e2
% 251.13/59.93 | |
% 251.13/59.93 | | REF_CLOSE: (16), (20), (25), (30), (32), (38), (46), (55), (61), (65), (70),
% 251.13/59.93 | | (78), (79), (86), (108), (113), (126), (127), (130), (135),
% 251.13/59.93 | | (393), (395) are inconsistent by sub-proof #796.
% 251.13/59.93 | |
% 251.13/59.93 | End of split
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #602 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) all_252_20 = e4 & op(e0, e4) = e4
% 251.13/59.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.93 (3) op(e0, e4) = all_12_2
% 251.13/59.93 (4) ~ (all_12_2 = e4)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | ALPHA: (1) implies:
% 251.13/59.93 | (5) op(e0, e4) = e4
% 251.13/59.93 |
% 251.13/59.93 | GROUND_INST: instantiating (2) with all_12_2, e4, e4, e0, simplifying with
% 251.13/59.93 | (3), (5) gives:
% 251.13/59.93 | (6) all_12_2 = e4
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (4), (6) imply:
% 251.13/59.93 | (7) $false
% 251.13/59.93 |
% 251.13/59.93 | CLOSE: (7) is inconsistent.
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #603 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.93 (2) op(e1, e4) = e4
% 251.13/59.93 (3) op(e1, e4) = e3
% 251.13/59.93 (4) ~ (e4 = e3)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | GROUND_INST: instantiating (1) with e3, e4, e4, e1, simplifying with (2), (3)
% 251.13/59.93 | gives:
% 251.13/59.93 | (5) e4 = e3
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (4), (5) imply:
% 251.13/59.93 | (6) $false
% 251.13/59.93 |
% 251.13/59.93 | CLOSE: (6) is inconsistent.
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #604 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) all_252_0 = e2
% 251.13/59.93 (2) all_252_2 = e1
% 251.13/59.93 (3) ~ (e4 = e1)
% 251.13/59.93 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4)
% 251.13/59.93 (5) ~ (e4 = e2)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | BETA: splitting (4) gives:
% 251.13/59.93 |
% 251.13/59.93 | Case 1:
% 251.13/59.93 | |
% 251.13/59.93 | | (6) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.93 | |
% 251.13/59.93 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #606.
% 251.13/59.93 | |
% 251.13/59.93 | Case 2:
% 251.13/59.93 | |
% 251.13/59.93 | | (7) all_252_2 = e4 & op(e3, e4) = e4
% 251.13/59.93 | |
% 251.13/59.93 | | ALPHA: (7) implies:
% 251.13/59.93 | | (8) all_252_2 = e4
% 251.13/59.93 | |
% 251.13/59.93 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #605.
% 251.13/59.93 | |
% 251.13/59.93 | End of split
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #605 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) all_252_2 = e4
% 251.13/59.93 (2) all_252_2 = e1
% 251.13/59.93 (3) ~ (e4 = e1)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.93 | (4) e4 = e1
% 251.13/59.93 |
% 251.13/59.93 | SIMP: (4) implies:
% 251.13/59.93 | (5) e4 = e1
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (3), (5) imply:
% 251.13/59.93 | (6) $false
% 251.13/59.93 |
% 251.13/59.93 | CLOSE: (6) is inconsistent.
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #606 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) all_252_0 = e4 & op(e4, e4) = e4
% 251.13/59.93 (2) all_252_0 = e2
% 251.13/59.93 (3) ~ (e4 = e2)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | ALPHA: (1) implies:
% 251.13/59.93 | (4) all_252_0 = e4
% 251.13/59.93 |
% 251.13/59.93 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.93 | (5) e4 = e2
% 251.13/59.93 |
% 251.13/59.93 | SIMP: (5) implies:
% 251.13/59.93 | (6) e4 = e2
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (3), (6) imply:
% 251.13/59.93 | (7) $false
% 251.13/59.93 |
% 251.13/59.93 | CLOSE: (7) is inconsistent.
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #607 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.93 (2) op(e3, e4) = e1
% 251.13/59.93 (3) op(e3, e4) = e0
% 251.13/59.93 (4) ~ (e1 = e0)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | GROUND_INST: instantiating (1) with e0, e1, e4, e3, simplifying with (2), (3)
% 251.13/59.93 | gives:
% 251.13/59.93 | (5) e1 = e0
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (4), (5) imply:
% 251.13/59.93 | (6) $false
% 251.13/59.93 |
% 251.13/59.93 | CLOSE: (6) is inconsistent.
% 251.13/59.93 |
% 251.13/59.93 End of proof
% 251.13/59.93
% 251.13/59.93 Sub-proof #608 shows that the following formulas are inconsistent:
% 251.13/59.93 ----------------------------------------------------------------
% 251.13/59.93 (1) all_252_22 = e0 & op(e0, e2) = e0
% 251.13/59.93 (2) all_252_22 = e2
% 251.13/59.93 (3) ~ (e2 = e0)
% 251.13/59.93
% 251.13/59.93 Begin of proof
% 251.13/59.93 |
% 251.13/59.93 | ALPHA: (1) implies:
% 251.13/59.93 | (4) all_252_22 = e0
% 251.13/59.93 |
% 251.13/59.93 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.93 | (5) e2 = e0
% 251.13/59.93 |
% 251.13/59.93 | SIMP: (5) implies:
% 251.13/59.93 | (6) e2 = e0
% 251.13/59.93 |
% 251.13/59.93 | REDUCE: (3), (6) imply:
% 251.13/59.94 | (7) $false
% 251.13/59.94 |
% 251.13/59.94 | CLOSE: (7) is inconsistent.
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #609 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) ~ (all_26_2 = e2)
% 251.13/59.94 (2) op(e4, e0) = all_30_2
% 251.13/59.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (4) ~ (all_30_2 = e2)
% 251.13/59.94 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2)
% 251.13/59.94 (6) op(e4, e1) = all_26_2
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | BETA: splitting (5) gives:
% 251.13/59.94 |
% 251.13/59.94 | Case 1:
% 251.13/59.94 | |
% 251.13/59.94 | | (7) all_252_9 = e2 & op(e4, e1) = e2
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (1), (3), (6), (7) are inconsistent by sub-proof #970.
% 251.13/59.94 | |
% 251.13/59.94 | Case 2:
% 251.13/59.94 | |
% 251.13/59.94 | | (8) all_252_16 = e2 & op(e4, e0) = e2
% 251.13/59.94 | |
% 251.13/59.94 | | ALPHA: (8) implies:
% 251.13/59.94 | | (9) op(e4, e0) = e2
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #830.
% 251.13/59.94 | |
% 251.13/59.94 | End of split
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #610 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) all_252_0 = e2 & op(e4, e4) = e2
% 251.13/59.94 (2) all_252_0 = e0
% 251.13/59.94 (3) ~ (e2 = e0)
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | ALPHA: (1) implies:
% 251.13/59.94 | (4) all_252_0 = e2
% 251.13/59.94 |
% 251.13/59.94 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.94 | (5) e2 = e0
% 251.13/59.94 |
% 251.13/59.94 | SIMP: (5) implies:
% 251.13/59.94 | (6) e2 = e0
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (3), (6) imply:
% 251.13/59.94 | (7) $false
% 251.13/59.94 |
% 251.13/59.94 | CLOSE: (7) is inconsistent.
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #611 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (2) op(e0, e0) = all_244_24
% 251.13/59.94 (3) ~ (all_244_15 = e0)
% 251.13/59.94 (4) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.94 (5) op(e1, e1) = all_244_15
% 251.13/59.94 (6) op(all_244_24, all_244_24) = e0
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | ALPHA: (4) implies:
% 251.13/59.94 | (7) op(e0, e0) = e1
% 251.13/59.94 |
% 251.13/59.94 | GROUND_INST: instantiating (1) with all_244_24, e1, e0, e0, simplifying with
% 251.13/59.94 | (2), (7) gives:
% 251.13/59.94 | (8) all_244_24 = e1
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (6), (8) imply:
% 251.13/59.94 | (9) op(e1, e1) = e0
% 251.13/59.94 |
% 251.13/59.94 | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #712.
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #612 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) all_250_8 = all_36_2
% 251.13/59.94 (2) all_250_8 = e3
% 251.13/59.94 (3) ~ (all_36_2 = e3)
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.94 | (4) all_36_2 = e3
% 251.13/59.94 |
% 251.13/59.94 | SIMP: (4) implies:
% 251.13/59.94 | (5) all_36_2 = e3
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (3), (5) imply:
% 251.13/59.94 | (6) $false
% 251.13/59.94 |
% 251.13/59.94 | CLOSE: (6) is inconsistent.
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #613 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (2) op(e3, e4) = e1
% 251.13/59.94 (3) ~ (e3 = e1)
% 251.13/59.94 (4) op(e3, e4) = all_100_2
% 251.13/59.94 (5) op(e4, e4) = all_244_0
% 251.13/59.94 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.94 (7) ~ (all_244_0 = e3)
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | BETA: splitting (6) gives:
% 251.13/59.94 |
% 251.13/59.94 | Case 1:
% 251.13/59.94 | |
% 251.13/59.94 | | (8) all_252_0 = e3 & op(e4, e4) = e3
% 251.13/59.94 | |
% 251.13/59.94 | | ALPHA: (8) implies:
% 251.13/59.94 | | (9) op(e4, e4) = e3
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (1), (5), (7), (9) are inconsistent by sub-proof #813.
% 251.13/59.94 | |
% 251.13/59.94 | Case 2:
% 251.13/59.94 | |
% 251.13/59.94 | | (10) all_252_2 = e3 & op(e3, e4) = e3
% 251.13/59.94 | |
% 251.13/59.94 | | ALPHA: (10) implies:
% 251.13/59.94 | | (11) op(e3, e4) = e3
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (1), (2), (3), (4), (11) are inconsistent by sub-proof #896.
% 251.13/59.94 | |
% 251.13/59.94 | End of split
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #614 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (2) op(e3, e1) = e3
% 251.13/59.94 (3) op(e3, e1) = all_36_2
% 251.13/59.94 (4) op(e3, e1) = e4
% 251.13/59.94 (5) ~ (e4 = e3)
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | GROUND_INST: instantiating (1) with all_36_2, e3, e1, e3, simplifying with
% 251.13/59.94 | (2), (3) gives:
% 251.13/59.94 | (6) all_36_2 = e3
% 251.13/59.94 |
% 251.13/59.94 | GROUND_INST: instantiating (1) with all_36_2, e4, e1, e3, simplifying with
% 251.13/59.94 | (3), (4) gives:
% 251.13/59.94 | (7) all_36_2 = e4
% 251.13/59.94 |
% 251.13/59.94 | COMBINE_EQS: (6), (7) imply:
% 251.13/59.94 | (8) e4 = e3
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (5), (8) imply:
% 251.13/59.94 | (9) $false
% 251.13/59.94 |
% 251.13/59.94 | CLOSE: (9) is inconsistent.
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #615 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (2) op(e2, e1) = all_38_2
% 251.13/59.94 (3) ~ (all_244_15 = e4)
% 251.13/59.94 (4) ~ (all_38_2 = e4)
% 251.13/59.94 (5) op(e1, e1) = all_244_15
% 251.13/59.94 (6) op(e0, e1) = all_20_2
% 251.13/59.94 (7) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 251.13/59.94 | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.13/59.94 (8) ~ (all_20_2 = e4)
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | BETA: splitting (7) gives:
% 251.13/59.94 |
% 251.13/59.94 | Case 1:
% 251.13/59.94 | |
% 251.13/59.94 | | (9) all_252_11 = e4 & op(e2, e1) = e4
% 251.13/59.94 | |
% 251.13/59.94 | | ALPHA: (9) implies:
% 251.13/59.94 | | (10) op(e2, e1) = e4
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #935.
% 251.13/59.94 | |
% 251.13/59.94 | Case 2:
% 251.13/59.94 | |
% 251.13/59.94 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1)
% 251.13/59.94 | | = e4)
% 251.13/59.94 | |
% 251.13/59.94 | | REF_CLOSE: (1), (3), (5), (6), (8), (11) are inconsistent by sub-proof #750.
% 251.13/59.94 | |
% 251.13/59.94 | End of split
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #616 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) op(all_62_2, e4) = e3
% 251.13/59.94 (2) ~ (all_4_2 = e4)
% 251.13/59.94 (3) ~ (all_244_0 = all_30_2)
% 251.13/59.94 (4) op(e3, all_16_2) = e1
% 251.13/59.94 (5) ~ (all_40_2 = all_38_2)
% 251.13/59.94 (6) op(all_6_2, e2) = e4
% 251.13/59.94 (7) op(e4, e0) = all_30_2
% 251.13/59.94 (8) ~ (all_30_2 = e3)
% 251.13/59.94 (9) ~ (e2 = e0)
% 251.13/59.94 (10) ~ (e1 = e0)
% 251.13/59.94 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (12) op(e2, e3) = all_10_2
% 251.13/59.94 (13) op(e0, e0) = all_244_24
% 251.13/59.94 (14) ~ (e4 = e0)
% 251.13/59.94 (15) ~ (all_12_2 = e3)
% 251.13/59.94 (16) op(all_244_8, all_244_8) = e2
% 251.13/59.94 (17) op(e2, e2) = all_244_8
% 251.13/59.94 (18) op(e2, e1) = all_38_2
% 251.13/59.94 (19) ~ (all_64_2 = all_40_2)
% 251.13/59.94 (20) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 251.13/59.94 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 251.13/59.94 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.94 (21) op(e1, e0) = all_34_2
% 251.13/59.94 (22) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 251.13/59.94 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 251.13/59.94 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.94 (23) ~ (all_244_15 = e4)
% 251.13/59.94 (24) ~ (e2 = e1)
% 251.13/59.94 (25) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.94 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.94 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.94 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.94 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.94 op(e0, e1) = e0)))
% 251.13/59.94 (26) ~ (e4 = e1)
% 251.13/59.94 (27) op(all_6_2, all_64_2) = e2
% 251.13/59.94 (28) op(e1, e4) = all_16_2
% 251.13/59.94 (29) ~ (all_48_2 = all_30_2)
% 251.13/59.94 (30) op(e1, e3) = all_62_2
% 251.13/59.94 (31) ~ (e3 = e0)
% 251.13/59.94 (32) ~ (all_40_2 = all_10_2)
% 251.13/59.94 (33) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 251.13/59.94 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 251.13/59.94 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.13/59.94 (34) all_30_2 = e2
% 251.13/59.94 (35) ~ (e3 = e1)
% 251.13/59.94 (36) ~ (all_12_2 = e2)
% 251.13/59.94 (37) ~ (all_16_2 = e2)
% 251.13/59.94 (38) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.13/59.94 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.13/59.94 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.13/59.94 (39) ~ (all_244_0 = all_100_2)
% 251.13/59.94 (40) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 251.13/59.94 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 251.13/59.94 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.94 (41) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.13/59.94 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.94 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.94 (42) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.94 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.94 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.94 (43) op(e3, e4) = all_100_2
% 251.13/59.94 (44) op(e4, e4) = all_244_0
% 251.13/59.94 (45) ~ (e4 = e3)
% 251.13/59.94 (46) op(e1, e1) = all_244_15
% 251.13/59.94 (47) ~ (all_34_2 = all_30_2)
% 251.13/59.94 (48) op(e3, e0) = all_48_2
% 251.13/59.94 (49) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.94 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.94 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.94 (50) op(all_48_2, e0) = e3
% 251.13/59.94 (51) op(e1, e2) = all_4_2
% 251.13/59.94 (52) ~ (all_100_2 = all_48_2)
% 251.13/59.94 (53) op(e2, e4) = all_64_2
% 251.13/59.94 (54) ~ (e4 = e2)
% 251.13/59.94 (55) ~ (all_244_24 = all_30_2)
% 251.13/59.94 (56) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.94 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.94 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.94 (57) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.94 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.94 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.94 (58) op(all_16_2, e4) = e1
% 251.13/59.94 (59) op(e2, e0) = all_40_2
% 251.13/59.94 (60) ~ (all_16_2 = e3)
% 251.13/59.94 (61) ~ (all_244_0 = e3)
% 251.13/59.94 (62) op(all_30_2, e0) = e4
% 251.13/59.94 (63) op(e0, e4) = all_12_2
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (3), (34) imply:
% 251.13/59.94 | (64) ~ (all_244_0 = e2)
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (34), (55) imply:
% 251.13/59.94 | (65) ~ (all_244_24 = e2)
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (29), (34) imply:
% 251.13/59.94 | (66) ~ (all_48_2 = e2)
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (34), (47) imply:
% 251.13/59.94 | (67) ~ (all_34_2 = e2)
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (8), (34) imply:
% 251.13/59.94 | (68) ~ (e3 = e2)
% 251.13/59.94 |
% 251.13/59.94 | SIMP: (68) implies:
% 251.13/59.94 | (69) ~ (e3 = e2)
% 251.13/59.94 |
% 251.13/59.94 | REDUCE: (34), (62) imply:
% 251.13/59.94 | (70) op(e2, e0) = e4
% 251.13/59.94 |
% 251.13/59.94 | BETA: splitting (20) gives:
% 251.13/59.94 |
% 251.13/59.94 | Case 1:
% 251.13/59.94 | |
% 251.13/59.94 | | (71) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0)
% 251.13/59.94 | | = e2)
% 251.13/59.94 | |
% 251.13/59.94 | | BETA: splitting (71) gives:
% 251.13/59.94 | |
% 251.13/59.94 | | Case 1:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (72) all_252_16 = e2 & op(e4, e0) = e2
% 251.13/59.94 | | |
% 251.13/59.94 | | | ALPHA: (72) implies:
% 251.13/59.94 | | | (73) all_252_16 = e2
% 251.13/59.94 | | |
% 251.13/59.94 | | | GROUND_INST: instantiating (11) with all_40_2, e4, e0, e2, simplifying
% 251.13/59.94 | | | with (59), (70) gives:
% 251.13/59.94 | | | (74) all_40_2 = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | REDUCE: (19), (74) imply:
% 251.13/59.94 | | | (75) ~ (all_64_2 = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | REDUCE: (5), (74) imply:
% 251.13/59.94 | | | (76) ~ (all_38_2 = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | SIMP: (76) implies:
% 251.13/59.94 | | | (77) ~ (all_38_2 = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | REDUCE: (32), (74) imply:
% 251.13/59.94 | | | (78) ~ (all_10_2 = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | SIMP: (78) implies:
% 251.13/59.94 | | | (79) ~ (all_10_2 = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | BETA: splitting (33) gives:
% 251.13/59.94 | | |
% 251.13/59.94 | | | Case 1:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (80) ~ (all_40_2 = e4)
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | REF_CLOSE: (11), (59), (70), (80) are inconsistent by sub-proof #707.
% 251.13/59.94 | | | |
% 251.13/59.94 | | | Case 2:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (81) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 251.13/59.94 | | | | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3)
% 251.13/59.94 | | | | & op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | BETA: splitting (81) gives:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | Case 1:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (82) ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4)
% 251.13/59.94 | | | | | = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | ALPHA: (82) implies:
% 251.13/59.94 | | | | | (83) op(e0, e4) = all_40_1
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 251.13/59.94 | | | | | (15), (16), (17), (18), (22), (23), (24), (25), (26), (27),
% 251.13/59.94 | | | | | (28), (30), (31), (35), (36), (37), (38), (39), (40), (41),
% 251.13/59.94 | | | | | (42), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 251.13/59.94 | | | | | (53), (56), (57), (58), (60), (61), (63), (64), (69), (73),
% 251.13/59.94 | | | | | (75), (77), (79), (83) are inconsistent by sub-proof #617.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | Case 2:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (84) ~ (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1)
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | ALPHA: (84) implies:
% 251.13/59.94 | | | | | (85) op(e0, e4) = all_40_1
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 251.13/59.94 | | | | | (15), (16), (17), (18), (22), (23), (24), (25), (26), (27),
% 251.13/59.94 | | | | | (28), (30), (31), (35), (36), (37), (38), (39), (40), (41),
% 251.13/59.94 | | | | | (42), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 251.13/59.94 | | | | | (53), (56), (57), (58), (60), (61), (63), (64), (69), (73),
% 251.13/59.94 | | | | | (75), (77), (79), (85) are inconsistent by sub-proof #617.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | End of split
% 251.13/59.94 | | | |
% 251.13/59.94 | | | End of split
% 251.13/59.94 | | |
% 251.13/59.94 | | Case 2:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (86) all_252_17 = e2 & op(e3, e0) = e2
% 251.13/59.94 | | |
% 251.13/59.94 | | | REF_CLOSE: (11), (48), (66), (86) are inconsistent by sub-proof #653.
% 251.13/59.94 | | |
% 251.13/59.94 | | End of split
% 251.13/59.94 | |
% 251.13/59.94 | Case 2:
% 251.13/59.94 | |
% 251.13/59.94 | | (87) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1, e0)
% 251.13/59.94 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.94 | |
% 251.13/59.94 | | BETA: splitting (87) gives:
% 251.13/59.94 | |
% 251.13/59.94 | | Case 1:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (88) all_252_18 = e2 & op(e2, e0) = e2
% 251.13/59.94 | | |
% 251.13/59.94 | | | REF_CLOSE: (11), (54), (59), (70), (88) are inconsistent by sub-proof
% 251.13/59.94 | | | #702.
% 251.13/59.94 | | |
% 251.13/59.94 | | Case 2:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (89) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0,
% 251.13/59.94 | | | e0) = e2)
% 251.13/59.94 | | |
% 251.13/59.94 | | | REF_CLOSE: (11), (13), (21), (65), (67), (89) are inconsistent by
% 251.13/59.94 | | | sub-proof #652.
% 251.13/59.94 | | |
% 251.13/59.94 | | End of split
% 251.13/59.94 | |
% 251.13/59.94 | End of split
% 251.13/59.94 |
% 251.13/59.94 End of proof
% 251.13/59.94
% 251.13/59.94 Sub-proof #617 shows that the following formulas are inconsistent:
% 251.13/59.94 ----------------------------------------------------------------
% 251.13/59.94 (1) op(all_62_2, e4) = e3
% 251.13/59.94 (2) ~ (all_4_2 = e4)
% 251.13/59.94 (3) ~ (all_10_2 = e4)
% 251.13/59.94 (4) op(e3, all_16_2) = e1
% 251.13/59.94 (5) op(all_6_2, e2) = e4
% 251.13/59.94 (6) op(e4, e0) = all_30_2
% 251.13/59.94 (7) ~ (all_30_2 = e3)
% 251.13/59.94 (8) ~ (e2 = e0)
% 251.13/59.94 (9) ~ (e1 = e0)
% 251.13/59.94 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.94 (11) op(e2, e3) = all_10_2
% 251.13/59.94 (12) ~ (e3 = e2)
% 251.13/59.94 (13) ~ (e4 = e0)
% 251.13/59.94 (14) ~ (all_12_2 = e3)
% 251.13/59.94 (15) op(all_244_8, all_244_8) = e2
% 251.13/59.94 (16) op(e2, e2) = all_244_8
% 251.13/59.94 (17) op(e2, e1) = all_38_2
% 251.13/59.94 (18) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 251.13/59.94 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 251.13/59.94 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.94 (19) ~ (all_244_15 = e4)
% 251.13/59.94 (20) ~ (e2 = e1)
% 251.13/59.94 (21) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) =
% 251.13/59.94 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.94 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) &
% 251.13/59.94 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) =
% 251.13/59.94 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 &
% 251.13/59.94 op(e0, e1) = e0)))
% 251.13/59.94 (22) ~ (e4 = e1)
% 251.13/59.94 (23) ~ (all_244_0 = e2)
% 251.13/59.94 (24) op(all_6_2, all_64_2) = e2
% 251.13/59.94 (25) all_252_16 = e2
% 251.13/59.94 (26) op(e1, e4) = all_16_2
% 251.13/59.94 (27) op(e1, e3) = all_62_2
% 251.13/59.94 (28) ~ (e3 = e0)
% 251.13/59.94 (29) ~ (e3 = e1)
% 251.13/59.94 (30) ~ (all_12_2 = e2)
% 251.13/59.94 (31) ~ (all_16_2 = e2)
% 251.13/59.94 (32) ~ (all_38_2 = e4)
% 251.13/59.94 (33) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.13/59.94 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.13/59.94 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.13/59.94 (34) ~ (all_244_0 = all_100_2)
% 251.13/59.94 (35) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 251.13/59.94 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 251.13/59.94 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.13/59.94 (36) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.13/59.94 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.94 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.94 (37) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.13/59.94 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.94 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.94 (38) op(e3, e4) = all_100_2
% 251.13/59.94 (39) op(e4, e4) = all_244_0
% 251.13/59.94 (40) ~ (e4 = e3)
% 251.13/59.94 (41) op(e1, e1) = all_244_15
% 251.13/59.94 (42) op(e3, e0) = all_48_2
% 251.13/59.94 (43) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.94 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.94 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.94 (44) op(all_48_2, e0) = e3
% 251.13/59.94 (45) op(e1, e2) = all_4_2
% 251.13/59.94 (46) ~ (all_100_2 = all_48_2)
% 251.13/59.94 (47) op(e2, e4) = all_64_2
% 251.13/59.94 (48) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.13/59.94 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.13/59.94 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.94 (49) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.13/59.94 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.13/59.94 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.13/59.94 (50) op(all_16_2, e4) = e1
% 251.13/59.94 (51) op(e0, e4) = all_40_1
% 251.13/59.94 (52) ~ (all_16_2 = e3)
% 251.13/59.94 (53) ~ (all_244_0 = e3)
% 251.13/59.94 (54) ~ (all_64_2 = e4)
% 251.13/59.94 (55) op(e0, e4) = all_12_2
% 251.13/59.94
% 251.13/59.94 Begin of proof
% 251.13/59.94 |
% 251.13/59.94 | BETA: splitting (37) gives:
% 251.13/59.94 |
% 251.13/59.94 | Case 1:
% 251.13/59.94 | |
% 251.13/59.94 | | (56) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 251.13/59.94 | | e4)
% 251.13/59.94 | |
% 251.13/59.94 | | BETA: splitting (56) gives:
% 251.13/59.94 | |
% 251.13/59.94 | | Case 1:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (57) all_252_6 = e4 & op(e2, e4) = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | ALPHA: (57) implies:
% 251.13/59.94 | | | (58) all_252_6 = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | BETA: splitting (48) gives:
% 251.13/59.94 | | |
% 251.13/59.94 | | | Case 1:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (59) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3,
% 251.13/59.94 | | | | e4) = e3)
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | BETA: splitting (59) gives:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | Case 1:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (60) all_252_0 = e3 & op(e4, e4) = e3
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | ALPHA: (60) implies:
% 251.13/59.94 | | | | | (61) op(e4, e4) = e3
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (10), (39), (53), (61) are inconsistent by sub-proof #813.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | Case 2:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (62) all_252_2 = e3 & op(e3, e4) = e3
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | ALPHA: (62) implies:
% 251.13/59.94 | | | | | (63) all_252_2 = e3
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (5), (10), (12), (23), (24), (26), (30), (31), (39), (47),
% 251.13/59.94 | | | | | (49), (51), (54), (55), (63) are inconsistent by sub-proof
% 251.13/59.94 | | | | | #696.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | End of split
% 251.13/59.94 | | | |
% 251.13/59.94 | | | Case 2:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (64) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1,
% 251.13/59.94 | | | | e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | BETA: splitting (64) gives:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | Case 1:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (65) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (40), (58), (65) are inconsistent by sub-proof #629.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | Case 2:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (66) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 251.13/59.94 | | | | | op(e0, e4) = e3)
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | REF_CLOSE: (10), (14), (26), (52), (55), (66) are inconsistent by
% 251.13/59.94 | | | | | sub-proof #894.
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | End of split
% 251.13/59.94 | | | |
% 251.13/59.94 | | | End of split
% 251.13/59.94 | | |
% 251.13/59.94 | | Case 2:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (67) all_252_7 = e4 & op(e2, e3) = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | ALPHA: (67) implies:
% 251.13/59.94 | | | (68) op(e2, e3) = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | REF_CLOSE: (3), (10), (11), (68) are inconsistent by sub-proof #953.
% 251.13/59.94 | | |
% 251.13/59.94 | | End of split
% 251.13/59.94 | |
% 251.13/59.94 | Case 2:
% 251.13/59.94 | |
% 251.13/59.94 | | (69) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.13/59.94 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.13/59.94 | |
% 251.13/59.94 | | BETA: splitting (69) gives:
% 251.13/59.94 | |
% 251.13/59.94 | | Case 1:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (70) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | ALPHA: (70) implies:
% 251.13/59.94 | | | (71) op(e2, e2) = e4
% 251.13/59.94 | | |
% 251.13/59.94 | | | REF_CLOSE: (10), (15), (16), (23), (39), (71) are inconsistent by
% 251.13/59.94 | | | sub-proof #626.
% 251.13/59.94 | | |
% 251.13/59.94 | | Case 2:
% 251.13/59.94 | | |
% 251.13/59.94 | | | (72) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 251.13/59.94 | | | e0) = e4)
% 251.13/59.94 | | |
% 251.13/59.94 | | | BETA: splitting (72) gives:
% 251.13/59.94 | | |
% 251.13/59.94 | | | Case 1:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (73) all_252_11 = e4 & op(e2, e1) = e4
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | ALPHA: (73) implies:
% 251.13/59.94 | | | | (74) op(e2, e1) = e4
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | REF_CLOSE: (10), (17), (32), (74) are inconsistent by sub-proof #935.
% 251.13/59.94 | | | |
% 251.13/59.94 | | | Case 2:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | (75) all_252_18 = e4 & op(e2, e0) = e4
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | ALPHA: (75) implies:
% 251.13/59.94 | | | | (76) all_252_18 = e4
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | BETA: splitting (33) gives:
% 251.13/59.94 | | | |
% 251.13/59.94 | | | | Case 1:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | (77) ~ (all_48_2 = e1)
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | BETA: splitting (43) gives:
% 251.13/59.94 | | | | |
% 251.13/59.94 | | | | | Case 1:
% 251.13/59.94 | | | | | |
% 251.13/59.94 | | | | | | (78) ~ (all_62_2 = e4)
% 251.13/59.94 | | | | | |
% 251.13/59.94 | | | | | | BETA: splitting (36) gives:
% 251.13/59.94 | | | | | |
% 251.13/59.94 | | | | | | Case 1:
% 251.13/59.94 | | | | | | |
% 251.13/59.94 | | | | | | | (79) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 &
% 251.13/59.94 | | | | | | | op(e1, e3) = e4)
% 251.13/59.94 | | | | | | |
% 251.13/59.94 | | | | | | | BETA: splitting (79) gives:
% 251.13/59.94 | | | | | | |
% 251.13/59.94 | | | | | | | Case 1:
% 251.13/59.94 | | | | | | | |
% 251.13/59.94 | | | | | | | | (80) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | ALPHA: (80) implies:
% 251.13/59.95 | | | | | | | | (81) op(e1, e4) = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | GROUND_INST: instantiating (10) with all_16_2, e4, e4, e1,
% 251.13/59.95 | | | | | | | | simplifying with (26), (81) gives:
% 251.13/59.95 | | | | | | | | (82) all_16_2 = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | REDUCE: (50), (82) imply:
% 251.13/59.95 | | | | | | | | (83) op(e4, e4) = e1
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | REDUCE: (4), (82) imply:
% 251.13/59.95 | | | | | | | | (84) op(e3, e4) = e1
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | REF_CLOSE: (10), (34), (38), (39), (83), (84) are inconsistent
% 251.13/59.95 | | | | | | | | by sub-proof #625.
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | (85) all_252_13 = e4 & op(e1, e3) = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | REF_CLOSE: (10), (27), (78), (85) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | #952.
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | End of split
% 251.13/59.95 | | | | | | |
% 251.13/59.95 | | | | | | Case 2:
% 251.13/59.95 | | | | | | |
% 251.13/59.95 | | | | | | | (86) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 &
% 251.13/59.95 | | | | | | | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.95 | | | | | | |
% 251.13/59.95 | | | | | | | BETA: splitting (86) gives:
% 251.13/59.95 | | | | | | |
% 251.13/59.95 | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | (87) all_252_14 = e4 & op(e1, e2) = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | ALPHA: (87) implies:
% 251.13/59.95 | | | | | | | | (88) op(e1, e2) = e4
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | REF_CLOSE: (2), (10), (45), (88) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | #831.
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | (89) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 251.13/59.95 | | | | | | | | op(e1, e0) = e4)
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | BETA: splitting (89) gives:
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | (90) all_252_15 = e4 & op(e1, e1) = e4
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | ALPHA: (90) implies:
% 251.13/59.95 | | | | | | | | | (91) op(e1, e1) = e4
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | REF_CLOSE: (10), (19), (41), (91) are inconsistent by
% 251.13/59.95 | | | | | | | | | sub-proof #756.
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | (92) all_252_19 = e4 & op(e1, e0) = e4
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | ALPHA: (92) implies:
% 251.13/59.95 | | | | | | | | | (93) all_252_19 = e4
% 251.13/59.95 | | | | | | | | | (94) op(e1, e0) = e4
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | BETA: splitting (35) gives:
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | (95) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 =
% 251.13/59.95 | | | | | | | | | | e1 & op(e3, e0) = e1)
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | BETA: splitting (95) gives:
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | (96) all_252_16 = e1 & op(e4, e0) = e1
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | REF_CLOSE: (20), (25), (96) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | #676.
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | (97) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | ALPHA: (97) implies:
% 251.13/59.95 | | | | | | | | | | | (98) op(e3, e0) = e1
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | REF_CLOSE: (10), (42), (77), (98) are inconsistent by
% 251.13/59.95 | | | | | | | | | | | sub-proof #889.
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | (99) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 =
% 251.13/59.95 | | | | | | | | | | e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0,
% 251.13/59.95 | | | | | | | | | | e0) = e1)
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | BETA: splitting (99) gives:
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | (100) all_252_18 = e1 & op(e2, e0) = e1
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | REF_CLOSE: (22), (76), (100) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | #624.
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | (101) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 251.13/59.95 | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | BETA: splitting (101) gives:
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | (102) all_252_19 = e1 & op(e1, e0) = e1
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | REF_CLOSE: (22), (93), (102) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | | #826.
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | (103) all_252_24 = e1 & op(e0, e0) = e1
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | ALPHA: (103) implies:
% 251.13/59.95 | | | | | | | | | | | | (104) all_252_24 = e1
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | BETA: splitting (21) gives:
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | (105) all_252_24 = e0 & op(e0, e0) = e0
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | ALPHA: (105) implies:
% 251.13/59.95 | | | | | | | | | | | | | (106) all_252_24 = e0
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | REF_CLOSE: (9), (104), (106) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | | | #623.
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | (107) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 251.13/59.95 | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.95 | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1,
% 251.13/59.95 | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4)
% 251.13/59.95 | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) |
% 251.13/59.95 | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) |
% 251.13/59.95 | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0))
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | ALPHA: (107) implies:
% 251.13/59.95 | | | | | | | | | | | | | (108) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 251.13/59.95 | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 &
% 251.13/59.95 | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0)
% 251.13/59.95 | | | | | | | | | | | | | = e0)
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | BETA: splitting (108) gives:
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | (109) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17
% 251.13/59.95 | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0)
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | (110) all_252_16 = e0 & op(e4, e0) = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | (111) all_252_16 = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (111) imply:
% 251.13/59.95 | | | | | | | | | | | | | | | (112) e2 = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | SIMP: (112) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | (113) e2 = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | REDUCE: (8), (113) imply:
% 251.13/59.95 | | | | | | | | | | | | | | | (114) $false
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | (115) all_252_17 = e0 & op(e3, e0) = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | (116) all_252_17 = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | (117) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 251.13/59.95 | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | (118) all_252_16 = e3 & op(e4, e0) = e3
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | | | (119) op(e4, e0) = e3
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (119) are inconsistent by
% 251.13/59.95 | | | | | | | | | | | | | | | | | sub-proof #622.
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | (120) all_252_17 = e3 & op(e3, e0) = e3
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | | | (121) all_252_17 = e3
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (121) imply:
% 251.13/59.95 | | | | | | | | | | | | | | | | | (122) e3 = e0
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | REDUCE: (28), (122) imply:
% 251.13/59.95 | | | | | | | | | | | | | | | | | (123) $false
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | CLOSE: (123) is inconsistent.
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | (124) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 251.13/59.95 | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 251.13/59.95 | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | (125) all_252_18 = e3 & op(e2, e0) = e3
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (76), (125) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | | | | | | | #663.
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | (126) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 251.13/59.95 | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (40), (94), (104), (126) are
% 251.13/59.95 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #620.
% 251.13/59.95 | | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | (127) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19
% 251.13/59.95 | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | Case 1:
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | (128) all_252_18 = e0 & op(e2, e0) = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | REF_CLOSE: (13), (76), (128) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | | | | | #619.
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | Case 2:
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | (129) all_252_19 = e0 & op(e1, e0) = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 251.13/59.95 | | | | | | | | | | | | | | | (130) all_252_19 = e0
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | | REF_CLOSE: (13), (93), (130) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | | | | | | | | | | #618.
% 251.13/59.95 | | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | | |
% 251.13/59.95 | | | | | | | | | End of split
% 251.13/59.95 | | | | | | | | |
% 251.13/59.95 | | | | | | | | End of split
% 251.13/59.95 | | | | | | | |
% 251.13/59.95 | | | | | | | End of split
% 251.13/59.95 | | | | | | |
% 251.13/59.95 | | | | | | End of split
% 251.13/59.95 | | | | | |
% 251.13/59.95 | | | | | Case 2:
% 251.13/59.95 | | | | | |
% 251.13/59.95 | | | | | | (131) all_62_2 = e4
% 251.13/59.95 | | | | | |
% 251.13/59.95 | | | | | | REDUCE: (1), (131) imply:
% 251.13/59.95 | | | | | | (132) op(e4, e4) = e3
% 251.13/59.95 | | | | | |
% 251.13/59.95 | | | | | | REF_CLOSE: (10), (39), (53), (132) are inconsistent by sub-proof
% 251.13/59.95 | | | | | | #813.
% 251.13/59.95 | | | | | |
% 251.13/59.95 | | | | | End of split
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | Case 2:
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | (133) all_48_2 = e1
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | REF_CLOSE: (1), (2), (4), (10), (19), (26), (27), (36), (38), (39),
% 251.13/59.95 | | | | | (40), (41), (43), (44), (45), (46), (53), (133) are
% 251.13/59.95 | | | | | inconsistent by sub-proof #627.
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | End of split
% 251.13/59.95 | | | |
% 251.13/59.95 | | | End of split
% 251.13/59.95 | | |
% 251.13/59.95 | | End of split
% 251.13/59.95 | |
% 251.13/59.95 | End of split
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #618 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_19 = e4
% 251.13/59.95 (2) all_252_19 = e0
% 251.13/59.95 (3) ~ (e4 = e0)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.95 | (4) e4 = e0
% 251.13/59.95 |
% 251.13/59.95 | SIMP: (4) implies:
% 251.13/59.95 | (5) e4 = e0
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #619 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_18 = e0 & op(e2, e0) = e0
% 251.13/59.95 (2) all_252_18 = e4
% 251.13/59.95 (3) ~ (e4 = e0)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | ALPHA: (1) implies:
% 251.13/59.95 | (4) all_252_18 = e0
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.95 | (5) e4 = e0
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #620 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) op(e1, e0) = e4
% 251.13/59.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (3) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.95 (4) ~ (e3 = e1)
% 251.13/59.95 (5) ~ (e4 = e3)
% 251.13/59.95 (6) all_252_24 = e1
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | BETA: splitting (3) gives:
% 251.13/59.95 |
% 251.13/59.95 | Case 1:
% 251.13/59.95 | |
% 251.13/59.95 | | (7) all_252_19 = e3 & op(e1, e0) = e3
% 251.13/59.95 | |
% 251.13/59.95 | | ALPHA: (7) implies:
% 251.13/59.95 | | (8) op(e1, e0) = e3
% 251.13/59.95 | |
% 251.13/59.95 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #827.
% 251.13/59.95 | |
% 251.13/59.95 | Case 2:
% 251.13/59.95 | |
% 251.13/59.95 | | (9) all_252_24 = e3 & op(e0, e0) = e3
% 251.13/59.95 | |
% 251.13/59.95 | | ALPHA: (9) implies:
% 251.13/59.95 | | (10) all_252_24 = e3
% 251.13/59.95 | |
% 251.13/59.95 | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #621.
% 251.13/59.95 | |
% 251.13/59.95 | End of split
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #621 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_24 = e3
% 251.13/59.95 (2) all_252_24 = e1
% 251.13/59.95 (3) ~ (e3 = e1)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.95 | (4) e3 = e1
% 251.13/59.95 |
% 251.13/59.95 | SIMP: (4) implies:
% 251.13/59.95 | (5) e3 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #622 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) op(e4, e0) = all_30_2
% 251.13/59.95 (3) op(e4, e0) = e3
% 251.13/59.95 (4) ~ (all_30_2 = e3)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_30_2, e3, e0, e4, simplifying with
% 251.13/59.95 | (2), (3) gives:
% 251.13/59.95 | (5) all_30_2 = e3
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (4), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #623 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_24 = e1
% 251.13/59.95 (2) all_252_24 = e0
% 251.13/59.95 (3) ~ (e1 = e0)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (1), (2) imply:
% 251.13/59.95 | (4) e1 = e0
% 251.13/59.95 |
% 251.13/59.95 | SIMP: (4) implies:
% 251.13/59.95 | (5) e1 = e0
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #624 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_18 = e1 & op(e2, e0) = e1
% 251.13/59.95 (2) all_252_18 = e4
% 251.13/59.95 (3) ~ (e4 = e1)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | ALPHA: (1) implies:
% 251.13/59.95 | (4) all_252_18 = e1
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.95 | (5) e4 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #625 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) op(e3, e4) = e1
% 251.13/59.95 (3) ~ (all_244_0 = all_100_2)
% 251.13/59.95 (4) op(e3, e4) = all_100_2
% 251.13/59.95 (5) op(e4, e4) = all_244_0
% 251.13/59.95 (6) op(e4, e4) = e1
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_100_2, e1, e4, e3, simplifying with
% 251.13/59.95 | (2), (4) gives:
% 251.13/59.95 | (7) all_100_2 = e1
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_244_0, e1, e4, e4, simplifying with
% 251.13/59.95 | (5), (6) gives:
% 251.13/59.95 | (8) all_244_0 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (7), (8) imply:
% 251.13/59.95 | (9) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (9) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #626 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) op(all_244_8, all_244_8) = e2
% 251.13/59.95 (3) op(e2, e2) = all_244_8
% 251.13/59.95 (4) ~ (all_244_0 = e2)
% 251.13/59.95 (5) op(e4, e4) = all_244_0
% 251.13/59.95 (6) op(e2, e2) = e4
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_244_8, e4, e2, e2, simplifying with
% 251.13/59.95 | (3), (6) gives:
% 251.13/59.95 | (7) all_244_8 = e4
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (2), (7) imply:
% 251.13/59.95 | (8) op(e4, e4) = e2
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_244_0, e2, e4, e4, simplifying with
% 251.13/59.95 | (5), (8) gives:
% 251.13/59.95 | (9) all_244_0 = e2
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (4), (9) imply:
% 251.13/59.95 | (10) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (10) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #627 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) op(all_62_2, e4) = e3
% 251.13/59.95 (2) ~ (all_4_2 = e4)
% 251.13/59.95 (3) op(e3, all_16_2) = e1
% 251.13/59.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (5) ~ (all_244_15 = e4)
% 251.13/59.95 (6) op(e1, e4) = all_16_2
% 251.13/59.95 (7) op(e1, e3) = all_62_2
% 251.13/59.95 (8) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.13/59.95 | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.13/59.95 e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.95 (9) op(e3, e4) = all_100_2
% 251.13/59.95 (10) op(e4, e4) = all_244_0
% 251.13/59.95 (11) ~ (e4 = e3)
% 251.13/59.95 (12) op(e1, e1) = all_244_15
% 251.13/59.95 (13) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.13/59.95 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.13/59.95 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.13/59.95 (14) op(all_48_2, e0) = e3
% 251.13/59.95 (15) op(e1, e2) = all_4_2
% 251.13/59.95 (16) ~ (all_100_2 = all_48_2)
% 251.13/59.95 (17) all_48_2 = e1
% 251.13/59.95 (18) ~ (all_244_0 = e3)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (16), (17) imply:
% 251.13/59.95 | (19) ~ (all_100_2 = e1)
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (14), (17) imply:
% 251.13/59.95 | (20) op(e1, e0) = e3
% 251.13/59.95 |
% 251.13/59.95 | BETA: splitting (13) gives:
% 251.13/59.95 |
% 251.13/59.95 | Case 1:
% 251.13/59.95 | |
% 251.13/59.95 | | (21) ~ (all_62_2 = e4)
% 251.13/59.95 | |
% 251.13/59.95 | | BETA: splitting (8) gives:
% 251.13/59.95 | |
% 251.13/59.95 | | Case 1:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (22) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1,
% 251.13/59.95 | | | e3) = e4)
% 251.13/59.95 | | |
% 251.13/59.95 | | | BETA: splitting (22) gives:
% 251.13/59.95 | | |
% 251.13/59.95 | | | Case 1:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (23) all_252_12 = e4 & op(e1, e4) = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | ALPHA: (23) implies:
% 251.13/59.95 | | | | (24) op(e1, e4) = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | GROUND_INST: instantiating (4) with all_16_2, e4, e4, e1, simplifying
% 251.13/59.95 | | | | with (6), (24) gives:
% 251.13/59.95 | | | | (25) all_16_2 = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REDUCE: (3), (25) imply:
% 251.13/59.95 | | | | (26) op(e3, e4) = e1
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REF_CLOSE: (4), (9), (19), (26) are inconsistent by sub-proof #628.
% 251.13/59.95 | | | |
% 251.13/59.95 | | | Case 2:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (27) all_252_13 = e4 & op(e1, e3) = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REF_CLOSE: (4), (7), (21), (27) are inconsistent by sub-proof #952.
% 251.13/59.95 | | | |
% 251.13/59.95 | | | End of split
% 251.13/59.95 | | |
% 251.13/59.95 | | Case 2:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (28) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.13/59.95 | | | e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.13/59.95 | | |
% 251.13/59.95 | | | BETA: splitting (28) gives:
% 251.13/59.95 | | |
% 251.13/59.95 | | | Case 1:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (29) all_252_14 = e4 & op(e1, e2) = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | ALPHA: (29) implies:
% 251.13/59.95 | | | | (30) op(e1, e2) = e4
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REF_CLOSE: (2), (4), (15), (30) are inconsistent by sub-proof #831.
% 251.13/59.95 | | | |
% 251.13/59.95 | | | Case 2:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (31) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1,
% 251.13/59.95 | | | | e0) = e4)
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | BETA: splitting (31) gives:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | Case 1:
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | (32) all_252_15 = e4 & op(e1, e1) = e4
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | ALPHA: (32) implies:
% 251.13/59.95 | | | | | (33) op(e1, e1) = e4
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | REF_CLOSE: (4), (5), (12), (33) are inconsistent by sub-proof #756.
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | Case 2:
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | (34) all_252_19 = e4 & op(e1, e0) = e4
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | ALPHA: (34) implies:
% 251.13/59.95 | | | | | (35) op(e1, e0) = e4
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | | REF_CLOSE: (4), (11), (20), (35) are inconsistent by sub-proof #827.
% 251.13/59.95 | | | | |
% 251.13/59.95 | | | | End of split
% 251.13/59.95 | | | |
% 251.13/59.95 | | | End of split
% 251.13/59.95 | | |
% 251.13/59.95 | | End of split
% 251.13/59.95 | |
% 251.13/59.95 | Case 2:
% 251.13/59.95 | |
% 251.13/59.95 | | (36) all_62_2 = e4
% 251.13/59.95 | |
% 251.13/59.95 | | REDUCE: (1), (36) imply:
% 251.13/59.95 | | (37) op(e4, e4) = e3
% 251.13/59.95 | |
% 251.13/59.95 | | REF_CLOSE: (4), (10), (18), (37) are inconsistent by sub-proof #813.
% 251.13/59.95 | |
% 251.13/59.95 | End of split
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #628 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) op(e3, e4) = all_100_2
% 251.13/59.95 (3) op(e3, e4) = e1
% 251.13/59.95 (4) ~ (all_100_2 = e1)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_100_2, e1, e4, e3, simplifying with
% 251.13/59.95 | (2), (3) gives:
% 251.13/59.95 | (5) all_100_2 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (4), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #629 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_6 = e3 & op(e2, e4) = e3
% 251.13/59.95 (2) all_252_6 = e4
% 251.13/59.95 (3) ~ (e4 = e3)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | ALPHA: (1) implies:
% 251.13/59.95 | (4) all_252_6 = e3
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.95 | (5) e4 = e3
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #630 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 251.13/59.95 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 251.13/59.95 | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.95 (3) ~ (e4 = e1)
% 251.13/59.95 (4) op(e3, e4) = e3
% 251.13/59.95 (5) all_252_10 = e4
% 251.13/59.95 (6) ~ (e3 = e1)
% 251.13/59.95 (7) ~ (all_8_2 = e1)
% 251.13/59.95 (8) ~ (all_244_15 = e3)
% 251.13/59.95 (9) op(e3, e4) = all_100_2
% 251.13/59.95 (10) op(e1, e1) = all_244_15
% 251.13/59.95 (11) op(e3, e0) = all_48_2
% 251.13/59.95 (12) ~ (all_48_2 = e1)
% 251.13/59.95 (13) op(all_244_3, all_244_3) = e3
% 251.13/59.95 (14) op(e3, e2) = all_8_2
% 251.13/59.95 (15) op(e3, e3) = all_244_3
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | BETA: splitting (2) gives:
% 251.13/59.95 |
% 251.13/59.95 | Case 1:
% 251.13/59.95 | |
% 251.13/59.95 | | (16) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 251.13/59.95 | | e1)
% 251.13/59.95 | |
% 251.13/59.95 | | BETA: splitting (16) gives:
% 251.13/59.95 | |
% 251.13/59.95 | | Case 1:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (17) all_252_2 = e1 & op(e3, e4) = e1
% 251.13/59.95 | | |
% 251.13/59.95 | | | ALPHA: (17) implies:
% 251.13/59.95 | | | (18) op(e3, e4) = e1
% 251.13/59.95 | | |
% 251.13/59.95 | | | REF_CLOSE: (1), (4), (6), (9), (18) are inconsistent by sub-proof #896.
% 251.13/59.95 | | |
% 251.13/59.95 | | Case 2:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (19) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.95 | | |
% 251.13/59.95 | | | REF_CLOSE: (1), (8), (10), (13), (15), (19) are inconsistent by sub-proof
% 251.13/59.95 | | | #632.
% 251.13/59.95 | | |
% 251.13/59.95 | | End of split
% 251.13/59.95 | |
% 251.13/59.95 | Case 2:
% 251.13/59.95 | |
% 251.13/59.95 | | (20) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.13/59.95 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.13/59.95 | |
% 251.13/59.95 | | BETA: splitting (20) gives:
% 251.13/59.95 | |
% 251.13/59.95 | | Case 1:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (21) all_252_5 = e1 & op(e3, e2) = e1
% 251.13/59.95 | | |
% 251.13/59.95 | | | ALPHA: (21) implies:
% 251.13/59.95 | | | (22) op(e3, e2) = e1
% 251.13/59.95 | | |
% 251.13/59.95 | | | REF_CLOSE: (1), (7), (14), (22) are inconsistent by sub-proof #929.
% 251.13/59.95 | | |
% 251.13/59.95 | | Case 2:
% 251.13/59.95 | | |
% 251.13/59.95 | | | (23) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 251.13/59.95 | | | e0) = e1)
% 251.13/59.95 | | |
% 251.13/59.95 | | | BETA: splitting (23) gives:
% 251.13/59.95 | | |
% 251.13/59.95 | | | Case 1:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (24) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REF_CLOSE: (3), (5), (24) are inconsistent by sub-proof #631.
% 251.13/59.95 | | | |
% 251.13/59.95 | | | Case 2:
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | (25) all_252_17 = e1 & op(e3, e0) = e1
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | ALPHA: (25) implies:
% 251.13/59.95 | | | | (26) op(e3, e0) = e1
% 251.13/59.95 | | | |
% 251.13/59.95 | | | | REF_CLOSE: (1), (11), (12), (26) are inconsistent by sub-proof #889.
% 251.13/59.95 | | | |
% 251.13/59.95 | | | End of split
% 251.13/59.95 | | |
% 251.13/59.95 | | End of split
% 251.13/59.95 | |
% 251.13/59.95 | End of split
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #631 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) all_252_10 = e1 & op(e3, e1) = e1
% 251.13/59.95 (2) all_252_10 = e4
% 251.13/59.95 (3) ~ (e4 = e1)
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | ALPHA: (1) implies:
% 251.13/59.95 | (4) all_252_10 = e1
% 251.13/59.95 |
% 251.13/59.95 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.95 | (5) e4 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (3), (5) imply:
% 251.13/59.95 | (6) $false
% 251.13/59.95 |
% 251.13/59.95 | CLOSE: (6) is inconsistent.
% 251.13/59.95 |
% 251.13/59.95 End of proof
% 251.13/59.95
% 251.13/59.95 Sub-proof #632 shows that the following formulas are inconsistent:
% 251.13/59.95 ----------------------------------------------------------------
% 251.13/59.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.95 (2) all_252_3 = e1 & op(e3, e3) = e1
% 251.13/59.95 (3) ~ (all_244_15 = e3)
% 251.13/59.95 (4) op(e1, e1) = all_244_15
% 251.13/59.95 (5) op(all_244_3, all_244_3) = e3
% 251.13/59.95 (6) op(e3, e3) = all_244_3
% 251.13/59.95
% 251.13/59.95 Begin of proof
% 251.13/59.95 |
% 251.13/59.95 | ALPHA: (2) implies:
% 251.13/59.95 | (7) op(e3, e3) = e1
% 251.13/59.95 |
% 251.13/59.95 | GROUND_INST: instantiating (1) with all_244_3, e1, e3, e3, simplifying with
% 251.13/59.95 | (6), (7) gives:
% 251.13/59.95 | (8) all_244_3 = e1
% 251.13/59.95 |
% 251.13/59.95 | REDUCE: (5), (8) imply:
% 251.13/59.95 | (9) op(e1, e1) = e3
% 251.13/59.95 |
% 251.13/59.96 | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #822.
% 251.13/59.96 |
% 251.13/59.96 End of proof
% 251.13/59.96
% 251.13/59.96 Sub-proof #633 shows that the following formulas are inconsistent:
% 251.13/59.96 ----------------------------------------------------------------
% 251.13/59.96 (1) all_252_9 = e4 & op(e4, e1) = e4
% 251.13/59.96 (2) all_252_9 = e3
% 251.13/59.96 (3) ~ (e4 = e3)
% 251.13/59.96
% 251.13/59.96 Begin of proof
% 251.13/59.96 |
% 251.13/59.96 | ALPHA: (1) implies:
% 251.13/59.96 | (4) all_252_9 = e4
% 251.13/59.96 |
% 251.13/59.96 | COMBINE_EQS: (2), (4) imply:
% 251.13/59.96 | (5) e4 = e3
% 251.13/59.96 |
% 251.13/59.96 | SIMP: (5) implies:
% 251.13/59.96 | (6) e4 = e3
% 251.13/59.96 |
% 251.13/59.96 | REDUCE: (3), (6) imply:
% 251.13/59.96 | (7) $false
% 251.13/59.96 |
% 251.13/59.96 | CLOSE: (7) is inconsistent.
% 251.13/59.96 |
% 251.13/59.96 End of proof
% 251.13/59.96
% 251.13/59.96 Sub-proof #634 shows that the following formulas are inconsistent:
% 251.13/59.96 ----------------------------------------------------------------
% 251.13/59.96 (1) all_32_2 = all_20_2
% 251.13/59.96 (2) ~ (all_4_2 = e4)
% 251.13/59.96 (3) ~ (all_10_2 = e4)
% 251.13/59.96 (4) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) = all_28_1
% 251.13/59.96 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3) =
% 251.13/59.96 all_28_1 & $i(all_28_1))
% 251.13/59.96 (5) all_94_2 = all_38_2
% 251.13/59.96 (6) op(all_62_2, all_36_2) = e3
% 251.13/59.96 (7) op(all_38_2, e1) = e2
% 251.13/59.96 (8) all_250_13 = all_38_2
% 251.13/59.96 (9) ~ (e2 = e0)
% 251.13/59.96 (10) op(all_38_2, all_4_2) = e1
% 251.13/59.96 (11) op(all_64_2, e4) = e2
% 251.13/59.96 (12) ~ (all_22_2 = e3)
% 251.13/59.96 (13) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.96 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.96 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.96 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.96 (15) op(e2, e3) = all_10_2
% 251.13/59.96 (16) ~ (e3 = e2)
% 251.13/59.96 (17) op(e0, e0) = all_244_24
% 251.13/59.96 (18) ~ (e4 = e0)
% 251.13/59.96 (19) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.96 all_250_17 = e0
% 251.13/59.96 (20) ~ (all_12_2 = e3)
% 251.13/59.96 (21) op(e2, e2) = all_244_8
% 251.13/59.96 (22) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.96 all_250_11 = e0
% 251.13/59.96 (23) op(e2, e1) = all_38_2
% 251.13/59.96 (24) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.96 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.96 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.96 (25) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.96 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.96 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.96 (26) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.96 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.96 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.96 (27) op(e1, e0) = all_34_2
% 251.13/59.96 (28) op(e4, e2) = all_6_2
% 251.13/59.96 (29) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.13/59.96 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.13/59.96 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.13/59.96 (30) all_78_2 = all_10_2
% 251.13/59.96 (31) ~ (all_8_2 = all_4_2)
% 251.13/59.96 (32) ~ (e2 = e1)
% 251.13/59.96 (33) op(e3, e2) = e0
% 251.13/59.96 (34) op(e0, e2) = all_28_2
% 251.13/59.96 (35) ~ (e4 = e1)
% 251.13/59.96 (36) ~ (all_6_2 = e1)
% 251.13/59.96 (37) all_106_2 = all_38_2
% 251.13/59.96 (38) ~ (all_244_8 = all_38_2)
% 251.13/59.96 (39) op(all_244_15, all_244_15) = e1
% 251.13/59.96 (40) all_250_21 = all_22_2
% 251.13/59.96 (41) op(e1, e4) = all_16_2
% 251.13/59.96 (42) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.96 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.96 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.96 (43) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.13/59.96 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.13/59.96 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.96 (44) op(e1, e3) = all_62_2
% 251.13/59.96 (45) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.96 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.96 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.96 (46) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 251.13/59.96 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 251.13/59.96 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.96 (47) op(all_20_2, e1) = e0
% 251.13/59.96 (48) all_70_2 = all_62_2
% 251.13/59.96 (49) ~ (all_244_24 = e3)
% 251.13/59.96 (50) ~ (e3 = e1)
% 251.13/59.96 (51) op(all_48_2, all_22_2) = e0
% 251.13/59.96 (52) ~ (all_12_2 = e2)
% 251.13/59.96 (53) op(e3, e1) = all_36_2
% 251.13/59.96 (54) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.96 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.96 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.96 (55) ~ (all_16_2 = e2)
% 251.13/59.96 (56) ~ (all_8_2 = e1)
% 251.13/59.96 (57) ~ (all_22_2 = e1)
% 251.13/59.96 (58) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.96 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.96 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.96 (59) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.96 all_250_13 = e0
% 251.13/59.96 (60) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.96 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.96 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.96 (61) ~ (all_26_2 = all_6_2)
% 251.13/59.96 (62) op(all_22_2, e3) = e0
% 251.13/59.96 (63) all_68_2 = all_22_2
% 251.13/59.96 (64) op(e0, e3) = all_22_2
% 251.13/59.96 (65) op(e4, e1) = all_26_2
% 251.13/59.96 (66) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.96 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.96 (67) op(all_10_2, e3) = e2
% 251.13/59.96 (68) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.96 all_250_21 = e0
% 251.13/59.96 (69) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.13/59.96 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.13/59.96 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.13/59.96 (70) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.96 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.96 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.96 (71) all_250_11 = all_10_2
% 251.13/59.96 (72) ~ (e4 = e3)
% 251.13/59.96 (73) op(e1, e1) = all_244_15
% 251.13/59.96 (74) op(e0, e1) = all_20_2
% 251.13/59.96 (75) op(all_48_2, e0) = e3
% 251.13/59.96 (76) op(e1, e2) = all_4_2
% 251.13/59.96 (77) all_118_2 = all_22_2
% 251.13/59.96 (78) ~ (all_22_2 = all_10_2)
% 251.13/59.96 (79) all_250_17 = all_4_2
% 251.13/59.96 (80) ~ (all_38_2 = all_26_2)
% 251.13/59.96 (81) ~ (e4 = e2)
% 251.13/59.96 (82) ~ (all_244_8 = all_8_2)
% 251.13/59.96 (83) op(e3, e2) = all_8_2
% 251.13/59.96 (84) op(all_36_2, e1) = e3
% 251.13/59.96 (85) ~ (all_38_2 = all_10_2)
% 251.13/59.96 (86) ~ (all_244_15 = all_36_2)
% 251.13/59.96 (87) ~ (all_244_24 = all_22_2)
% 251.13/59.96 (88) op(all_8_2, all_10_2) = e2
% 251.13/59.96 (89) ~ (all_20_2 = e3)
% 251.13/59.96 (90) op(all_8_2, e2) = e3
% 251.13/59.96 (91) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.96 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.96 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.96 (92) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.96 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.96 (93) ~ (all_4_2 = e3)
% 251.13/59.96 (94) all_90_2 = all_22_2
% 251.13/59.96 (95) all_46_2 = all_36_2
% 251.13/59.96 (96) op(all_244_24, all_244_24) = e0
% 251.13/59.96 (97) op(e0, e4) = all_12_2
% 251.13/59.96 (98) ~ (all_34_2 = all_4_2)
% 251.13/59.96 (99) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.96 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.96 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.96 (100) op(all_64_2, all_6_2) = e4
% 251.13/59.96 (101) all_124_2 = all_10_2
% 251.13/59.96
% 251.13/59.96 Begin of proof
% 251.13/59.96 |
% 251.13/59.96 | BETA: splitting (43) gives:
% 251.13/59.96 |
% 251.13/59.96 | Case 1:
% 251.13/59.96 | |
% 251.13/59.96 | | (102) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 251.13/59.96 | | = e3)
% 251.13/59.96 | |
% 251.13/59.96 | | REF_CLOSE: (12), (14), (20), (64), (97), (102) are inconsistent by sub-proof
% 251.13/59.96 | | #958.
% 251.13/59.96 | |
% 251.13/59.96 | Case 2:
% 251.13/59.96 | |
% 251.13/59.96 | | (103) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 251.13/59.96 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.13/59.96 | |
% 251.13/59.96 | | BETA: splitting (103) gives:
% 251.13/59.96 | |
% 251.13/59.96 | | Case 1:
% 251.13/59.96 | | |
% 251.13/59.96 | | | (104) all_252_22 = e3 & op(e0, e2) = e3
% 251.13/59.96 | | |
% 251.13/59.96 | | | ALPHA: (104) implies:
% 251.13/59.96 | | | (105) all_252_22 = e3
% 251.13/59.96 | | |
% 251.13/59.96 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 251.13/59.96 | | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 251.13/59.96 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 251.13/59.96 | | | (35), (36), (37), (38), (39), (40), (41), (42), (44), (45),
% 251.13/59.96 | | | (46), (47), (48), (50), (51), (52), (53), (54), (55), (56),
% 251.13/59.96 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 251.13/59.96 | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 251.13/59.96 | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 251.13/59.96 | | | (87), (88), (90), (91), (92), (93), (94), (95), (96), (97),
% 251.13/59.96 | | | (98), (99), (100), (101), (105) are inconsistent by sub-proof
% 251.13/59.96 | | | #635.
% 251.13/59.96 | | |
% 251.13/59.96 | | Case 2:
% 251.13/59.96 | | |
% 251.13/59.96 | | | (106) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 251.13/59.96 | | | e0) = e3)
% 251.13/59.96 | | |
% 251.13/59.96 | | | REF_CLOSE: (14), (17), (49), (74), (89), (106) are inconsistent by
% 251.13/59.96 | | | sub-proof #744.
% 251.13/59.96 | | |
% 251.13/59.96 | | End of split
% 251.13/59.96 | |
% 251.13/59.96 | End of split
% 251.13/59.96 |
% 251.13/59.96 End of proof
% 251.13/59.96
% 251.13/59.96 Sub-proof #635 shows that the following formulas are inconsistent:
% 251.13/59.96 ----------------------------------------------------------------
% 251.13/59.96 (1) all_32_2 = all_20_2
% 251.13/59.96 (2) ~ (all_4_2 = e4)
% 251.13/59.96 (3) ~ (all_10_2 = e4)
% 251.13/59.96 (4) ( ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) = all_28_1
% 251.13/59.96 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e4) & op(e2, e3) =
% 251.13/59.96 all_28_1 & $i(all_28_1))
% 251.13/59.96 (5) all_94_2 = all_38_2
% 251.13/59.96 (6) op(all_62_2, all_36_2) = e3
% 251.13/59.96 (7) op(all_38_2, e1) = e2
% 251.13/59.96 (8) all_250_13 = all_38_2
% 251.13/59.96 (9) ~ (e2 = e0)
% 251.13/59.96 (10) op(all_38_2, all_4_2) = e1
% 251.13/59.96 (11) op(all_64_2, e4) = e2
% 251.13/59.96 (12) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.96 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.96 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.96 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.96 (14) op(e2, e3) = all_10_2
% 251.13/59.96 (15) ~ (e3 = e2)
% 251.13/59.96 (16) op(e0, e0) = all_244_24
% 251.13/59.96 (17) ~ (e4 = e0)
% 251.13/59.96 (18) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.96 all_250_17 = e0
% 251.13/59.96 (19) op(e2, e2) = all_244_8
% 251.13/59.96 (20) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.96 all_250_11 = e0
% 251.13/59.96 (21) op(e2, e1) = all_38_2
% 251.13/59.96 (22) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.96 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.96 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.96 (23) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.96 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.96 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.96 (24) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.96 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.96 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.96 (25) op(e1, e0) = all_34_2
% 251.13/59.96 (26) op(e4, e2) = all_6_2
% 251.13/59.96 (27) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.13/59.96 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.13/59.96 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.13/59.96 (28) all_78_2 = all_10_2
% 251.13/59.96 (29) ~ (all_8_2 = all_4_2)
% 251.13/59.96 (30) ~ (e2 = e1)
% 251.13/59.96 (31) op(e3, e2) = e0
% 251.13/59.96 (32) op(e0, e2) = all_28_2
% 251.13/59.96 (33) ~ (e4 = e1)
% 251.13/59.96 (34) ~ (all_6_2 = e1)
% 251.13/59.96 (35) all_106_2 = all_38_2
% 251.13/59.96 (36) ~ (all_244_8 = all_38_2)
% 251.13/59.96 (37) op(all_244_15, all_244_15) = e1
% 251.13/59.96 (38) all_252_22 = e3
% 251.13/59.96 (39) all_250_21 = all_22_2
% 251.13/59.96 (40) op(e1, e4) = all_16_2
% 251.13/59.96 (41) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.96 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.96 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.96 (42) op(e1, e3) = all_62_2
% 251.13/59.96 (43) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.96 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.96 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.96 (44) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 251.13/59.96 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 251.13/59.96 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.96 (45) op(all_20_2, e1) = e0
% 251.13/59.96 (46) all_70_2 = all_62_2
% 251.13/59.96 (47) ~ (e3 = e1)
% 251.13/59.96 (48) op(all_48_2, all_22_2) = e0
% 251.13/59.96 (49) ~ (all_12_2 = e2)
% 251.13/59.96 (50) op(e3, e1) = all_36_2
% 251.13/59.96 (51) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.96 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.96 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.96 (52) ~ (all_16_2 = e2)
% 251.13/59.96 (53) ~ (all_8_2 = e1)
% 251.13/59.96 (54) ~ (all_22_2 = e1)
% 251.13/59.96 (55) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.96 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.96 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.96 (56) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.96 all_250_13 = e0
% 251.13/59.96 (57) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.96 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.96 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.96 (58) ~ (all_26_2 = all_6_2)
% 251.13/59.96 (59) op(all_22_2, e3) = e0
% 251.13/59.96 (60) all_68_2 = all_22_2
% 251.13/59.96 (61) op(e0, e3) = all_22_2
% 251.13/59.96 (62) op(e4, e1) = all_26_2
% 251.13/59.96 (63) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.96 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.96 (64) op(all_10_2, e3) = e2
% 251.13/59.96 (65) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.96 all_250_21 = e0
% 251.13/59.96 (66) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.13/59.96 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.13/59.96 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.13/59.96 (67) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.96 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.96 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.96 (68) all_250_11 = all_10_2
% 251.13/59.96 (69) ~ (e4 = e3)
% 251.13/59.96 (70) op(e1, e1) = all_244_15
% 251.13/59.96 (71) op(e0, e1) = all_20_2
% 251.13/59.96 (72) op(all_48_2, e0) = e3
% 251.13/59.96 (73) op(e1, e2) = all_4_2
% 251.13/59.96 (74) all_118_2 = all_22_2
% 251.13/59.96 (75) ~ (all_22_2 = all_10_2)
% 251.13/59.96 (76) all_250_17 = all_4_2
% 251.13/59.96 (77) ~ (all_38_2 = all_26_2)
% 251.13/59.96 (78) ~ (e4 = e2)
% 251.13/59.96 (79) ~ (all_244_8 = all_8_2)
% 251.13/59.96 (80) op(e3, e2) = all_8_2
% 251.13/59.96 (81) op(all_36_2, e1) = e3
% 251.13/59.96 (82) ~ (all_38_2 = all_10_2)
% 251.13/59.96 (83) ~ (all_244_15 = all_36_2)
% 251.13/59.96 (84) ~ (all_244_24 = all_22_2)
% 251.13/59.96 (85) op(all_8_2, all_10_2) = e2
% 251.13/59.96 (86) op(all_8_2, e2) = e3
% 251.13/59.96 (87) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.96 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.96 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.96 (88) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.96 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.96 (89) ~ (all_4_2 = e3)
% 251.13/59.96 (90) all_90_2 = all_22_2
% 251.13/59.96 (91) all_46_2 = all_36_2
% 251.13/59.96 (92) op(all_244_24, all_244_24) = e0
% 251.13/59.96 (93) op(e0, e4) = all_12_2
% 251.13/59.96 (94) ~ (all_34_2 = all_4_2)
% 251.13/59.96 (95) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.96 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.96 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.96 (96) op(all_64_2, all_6_2) = e4
% 251.13/59.96 (97) all_124_2 = all_10_2
% 251.13/59.96
% 251.13/59.96 Begin of proof
% 251.13/59.96 |
% 251.13/59.96 | BETA: splitting (4) gives:
% 251.13/59.96 |
% 251.13/59.96 | Case 1:
% 251.13/59.96 | |
% 251.13/59.96 | | (98) ~ (all_28_0 = e1) & op(e3, all_28_1) = all_28_0 & op(e2, e3) =
% 251.13/59.96 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 251.13/59.96 | |
% 251.13/59.96 | | ALPHA: (98) implies:
% 251.13/59.96 | | (99) op(e2, e3) = all_28_1
% 251.13/59.96 | |
% 251.13/59.96 | | GROUND_INST: instantiating (13) with all_10_2, all_28_1, e3, e2, simplifying
% 251.13/59.96 | | with (14), (99) gives:
% 251.13/59.96 | | (100) all_28_1 = all_10_2
% 251.13/59.96 | |
% 251.13/59.96 | | GROUND_INST: instantiating (13) with all_8_2, e0, e2, e3, simplifying with
% 251.13/59.96 | | (31), (80) gives:
% 251.13/59.96 | | (101) all_8_2 = e0
% 251.13/59.96 | |
% 251.13/59.96 | | REDUCE: (79), (101) imply:
% 251.13/59.96 | | (102) ~ (all_244_8 = e0)
% 251.13/59.96 | |
% 251.13/59.96 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 251.13/59.96 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 251.13/59.96 | | (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 251.13/59.96 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 251.13/59.96 | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 251.13/59.96 | | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 251.13/59.96 | | (71), (72), (73), (74), (75), (76), (77), (78), (80), (81), (82),
% 251.13/59.96 | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 251.13/59.96 | | (94), (95), (96), (97), (99), (100), (101), (102) are
% 251.13/59.96 | | inconsistent by sub-proof #636.
% 251.13/59.96 | |
% 251.13/59.96 | Case 2:
% 251.13/59.96 | |
% 251.13/59.96 | | (103) ~ (all_28_1 = e4) & op(e2, e3) = all_28_1 & $i(all_28_1)
% 251.13/59.96 | |
% 251.13/59.96 | | ALPHA: (103) implies:
% 251.13/59.96 | | (104) ~ (all_28_1 = e4)
% 251.13/59.96 | | (105) op(e2, e3) = all_28_1
% 251.13/59.96 | |
% 251.13/59.96 | | GROUND_INST: instantiating (13) with all_10_2, all_28_1, e3, e2, simplifying
% 251.13/59.96 | | with (14), (105) gives:
% 251.13/59.96 | | (106) all_28_1 = all_10_2
% 251.13/59.96 | |
% 251.13/59.96 | | GROUND_INST: instantiating (13) with all_8_2, e0, e2, e3, simplifying with
% 251.13/59.96 | | (31), (80) gives:
% 251.13/59.96 | | (107) all_8_2 = e0
% 251.13/59.96 | |
% 251.13/59.96 | | REDUCE: (79), (107) imply:
% 251.13/59.96 | | (108) ~ (all_244_8 = e0)
% 251.13/59.96 | |
% 251.13/59.96 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 251.13/59.96 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 251.13/59.96 | | (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 251.13/59.96 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 251.13/59.96 | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 251.13/59.96 | | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 251.13/59.96 | | (71), (72), (73), (74), (75), (76), (77), (78), (80), (81), (82),
% 251.13/59.96 | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 251.13/59.96 | | (94), (95), (96), (97), (105), (106), (107), (108) are
% 251.13/59.96 | | inconsistent by sub-proof #636.
% 251.13/59.96 | |
% 251.13/59.96 | End of split
% 251.13/59.96 |
% 251.13/59.96 End of proof
% 251.13/59.96
% 251.13/59.96 Sub-proof #636 shows that the following formulas are inconsistent:
% 251.13/59.96 ----------------------------------------------------------------
% 251.13/59.96 (1) all_32_2 = all_20_2
% 251.13/59.96 (2) ~ (all_4_2 = e4)
% 251.13/59.96 (3) ~ (all_10_2 = e4)
% 251.13/59.96 (4) ~ (all_244_8 = e0)
% 251.13/59.96 (5) all_94_2 = all_38_2
% 251.13/59.96 (6) op(all_62_2, all_36_2) = e3
% 251.13/59.96 (7) op(all_38_2, e1) = e2
% 251.13/59.96 (8) all_250_13 = all_38_2
% 251.13/59.96 (9) ~ (e2 = e0)
% 251.13/59.96 (10) op(all_38_2, all_4_2) = e1
% 251.13/59.96 (11) op(all_64_2, e4) = e2
% 251.13/59.96 (12) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.13/59.96 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.13/59.96 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.13/59.96 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.13/59.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.13/59.96 (14) ~ (e3 = e2)
% 251.13/59.96 (15) op(e0, e0) = all_244_24
% 251.13/59.96 (16) ~ (e4 = e0)
% 251.13/59.96 (17) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.13/59.96 all_250_17 = e0
% 251.13/59.96 (18) op(e2, e2) = all_244_8
% 251.13/59.96 (19) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.13/59.96 all_250_11 = e0
% 251.13/59.96 (20) op(e2, e1) = all_38_2
% 251.13/59.96 (21) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.13/59.96 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.13/59.96 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.96 (22) ~ (all_38_2 = e4) | ( ~ (all_38_0 = e0) & op(e4, all_38_1) = all_38_0 &
% 251.13/59.96 op(e1, e4) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 251.13/59.96 e3) & op(e1, e4) = all_38_1 & $i(all_38_1))
% 251.13/59.96 (23) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.13/59.96 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.13/59.96 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.13/59.96 (24) op(e1, e0) = all_34_2
% 251.13/59.96 (25) op(e4, e2) = all_6_2
% 251.13/59.96 (26) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.13/59.96 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.13/59.96 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.13/59.96 (27) all_78_2 = all_10_2
% 251.13/59.96 (28) ~ (all_8_2 = all_4_2)
% 251.13/59.96 (29) ~ (e2 = e1)
% 251.13/59.96 (30) op(e0, e2) = all_28_2
% 251.13/59.96 (31) ~ (e4 = e1)
% 251.13/59.96 (32) ~ (all_6_2 = e1)
% 251.13/59.96 (33) all_106_2 = all_38_2
% 251.13/59.96 (34) ~ (all_244_8 = all_38_2)
% 251.13/59.96 (35) op(all_244_15, all_244_15) = e1
% 251.13/59.96 (36) all_252_22 = e3
% 251.13/59.96 (37) all_250_21 = all_22_2
% 251.13/59.96 (38) op(e1, e4) = all_16_2
% 251.13/59.96 (39) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.13/59.96 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.13/59.96 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.13/59.96 (40) op(e1, e3) = all_62_2
% 251.13/59.96 (41) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.13/59.96 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.13/59.97 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.13/59.97 (42) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4)
% 251.13/59.97 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) =
% 251.13/59.97 e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.97 (43) op(all_20_2, e1) = e0
% 251.13/59.97 (44) all_70_2 = all_62_2
% 251.13/59.97 (45) ~ (e3 = e1)
% 251.13/59.97 (46) op(all_48_2, all_22_2) = e0
% 251.13/59.97 (47) ~ (all_12_2 = e2)
% 251.13/59.97 (48) op(e3, e1) = all_36_2
% 251.13/59.97 (49) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.13/59.97 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.13/59.97 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.13/59.97 (50) ~ (all_16_2 = e2)
% 251.13/59.97 (51) ~ (all_8_2 = e1)
% 251.13/59.97 (52) ~ (all_22_2 = e1)
% 251.13/59.97 (53) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.13/59.97 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.13/59.97 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.13/59.97 (54) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.13/59.97 all_250_13 = e0
% 251.13/59.97 (55) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.13/59.97 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.13/59.97 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.13/59.97 (56) all_8_2 = e0
% 251.13/59.97 (57) ~ (all_26_2 = all_6_2)
% 251.13/59.97 (58) op(all_22_2, e3) = e0
% 251.13/59.97 (59) all_68_2 = all_22_2
% 251.13/59.97 (60) op(e0, e3) = all_22_2
% 251.13/59.97 (61) op(e4, e1) = all_26_2
% 251.13/59.97 (62) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.13/59.97 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.13/59.97 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.13/59.97 (63) op(all_10_2, e3) = e2
% 251.13/59.97 (64) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.13/59.97 all_250_21 = e0
% 251.13/59.97 (65) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.13/59.97 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.13/59.97 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.13/59.97 (66) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.13/59.97 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.13/59.97 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.13/59.97 (67) all_250_11 = all_10_2
% 251.13/59.97 (68) ~ (e4 = e3)
% 251.13/59.97 (69) op(e1, e1) = all_244_15
% 251.13/59.97 (70) op(e0, e1) = all_20_2
% 251.13/59.97 (71) op(all_48_2, e0) = e3
% 251.13/59.97 (72) op(e2, e3) = all_28_1
% 251.13/59.97 (73) op(e1, e2) = all_4_2
% 251.13/59.97 (74) all_118_2 = all_22_2
% 251.13/59.97 (75) ~ (all_22_2 = all_10_2)
% 251.13/59.97 (76) all_28_1 = all_10_2
% 251.13/59.97 (77) all_250_17 = all_4_2
% 251.13/59.97 (78) ~ (all_38_2 = all_26_2)
% 251.13/59.97 (79) ~ (e4 = e2)
% 251.13/59.97 (80) op(e3, e2) = all_8_2
% 251.13/59.97 (81) op(all_36_2, e1) = e3
% 251.13/59.97 (82) ~ (all_38_2 = all_10_2)
% 251.13/59.97 (83) ~ (all_244_15 = all_36_2)
% 251.13/59.97 (84) ~ (all_244_24 = all_22_2)
% 251.13/59.97 (85) op(all_8_2, all_10_2) = e2
% 251.13/59.97 (86) op(all_8_2, e2) = e3
% 251.13/59.97 (87) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.13/59.97 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.13/59.97 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.13/59.97 (88) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.13/59.97 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.13/59.97 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.13/59.97 (89) ~ (all_4_2 = e3)
% 251.13/59.97 (90) all_90_2 = all_22_2
% 251.13/59.97 (91) all_46_2 = all_36_2
% 251.13/59.97 (92) op(all_244_24, all_244_24) = e0
% 251.13/59.97 (93) op(e0, e4) = all_12_2
% 251.13/59.97 (94) ~ (all_34_2 = all_4_2)
% 251.13/59.97 (95) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.13/59.97 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.13/59.97 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.13/59.97 (96) op(all_64_2, all_6_2) = e4
% 251.13/59.97 (97) all_124_2 = all_10_2
% 251.13/59.97
% 251.13/59.97 Begin of proof
% 251.13/59.97 |
% 251.13/59.97 | REDUCE: (28), (56) imply:
% 251.13/59.97 | (98) ~ (all_4_2 = e0)
% 251.13/59.97 |
% 251.13/59.97 | SIMP: (98) implies:
% 251.13/59.97 | (99) ~ (all_4_2 = e0)
% 251.13/59.97 |
% 251.13/59.97 | REDUCE: (56), (85) imply:
% 251.13/59.97 | (100) op(e0, all_10_2) = e2
% 251.13/59.97 |
% 251.13/59.97 | REDUCE: (56), (86) imply:
% 251.13/59.97 | (101) op(e0, e2) = e3
% 251.13/59.97 |
% 251.13/59.97 | REDUCE: (56), (80) imply:
% 251.13/59.97 | (102) op(e3, e2) = e0
% 251.13/59.97 |
% 251.13/59.97 | REDUCE: (72), (76) imply:
% 251.13/59.97 | (103) op(e2, e3) = all_10_2
% 251.13/59.97 |
% 251.13/59.97 | BETA: splitting (41) gives:
% 251.13/59.97 |
% 251.13/59.97 | Case 1:
% 251.13/59.97 | |
% 251.13/59.97 | | (104) ~ (all_32_2 = e2)
% 251.13/59.97 | |
% 251.13/59.97 | | REDUCE: (1), (104) imply:
% 251.13/59.97 | | (105) ~ (all_20_2 = e2)
% 251.13/59.97 | |
% 251.13/59.97 | | BETA: splitting (26) gives:
% 251.13/59.97 | |
% 251.13/59.97 | | Case 1:
% 251.13/59.97 | | |
% 251.13/59.97 | | | (106) ~ (all_34_2 = e2)
% 251.13/59.97 | | |
% 251.13/59.97 | | | BETA: splitting (22) gives:
% 251.13/59.97 | | |
% 251.13/59.97 | | | Case 1:
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | (107) ~ (all_38_2 = e4)
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 251.13/59.97 | | | | (18), (19), (20), (23), (24), (27), (33), (34), (35), (36),
% 251.13/59.97 | | | | (37), (38), (39), (40), (44), (46), (47), (48), (49), (50),
% 251.13/59.97 | | | | (51), (52), (53), (54), (55), (58), (59), (60), (62), (63),
% 251.13/59.97 | | | | (64), (65), (66), (67), (69), (70), (71), (73), (74), (75),
% 251.13/59.97 | | | | (79), (80), (81), (82), (83), (84), (87), (90), (91), (92),
% 251.13/59.97 | | | | (93), (95), (97), (100), (103), (105), (106), (107) are
% 251.13/59.97 | | | | inconsistent by sub-proof #647.
% 251.13/59.97 | | | |
% 251.13/59.97 | | | Case 2:
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | (108) all_38_2 = e4
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | REDUCE: (78), (108) imply:
% 251.13/59.97 | | | | (109) ~ (all_26_2 = e4)
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | SIMP: (109) implies:
% 251.13/59.97 | | | | (110) ~ (all_26_2 = e4)
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | REDUCE: (7), (108) imply:
% 251.13/59.97 | | | | (111) op(e4, e1) = e2
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | BETA: splitting (42) gives:
% 251.13/59.97 | | | |
% 251.13/59.97 | | | | Case 1:
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | (112) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3,
% 251.13/59.97 | | | | | e2) = e4)
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | BETA: splitting (112) gives:
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | Case 1:
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | (113) all_252_4 = e4 & op(e4, e2) = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | ALPHA: (113) implies:
% 251.13/59.97 | | | | | | (114) op(e4, e2) = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | GROUND_INST: instantiating (13) with all_26_2, e2, e1, e4,
% 251.13/59.97 | | | | | | simplifying with (61), (111) gives:
% 251.13/59.97 | | | | | | (115) all_26_2 = e2
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | GROUND_INST: instantiating (13) with all_6_2, e4, e2, e4,
% 251.13/59.97 | | | | | | simplifying with (25), (114) gives:
% 251.13/59.97 | | | | | | (116) all_6_2 = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | REDUCE: (110), (115) imply:
% 251.13/59.97 | | | | | | (117) ~ (e4 = e2)
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | REF_CLOSE: (11), (13), (79), (96), (116) are inconsistent by
% 251.13/59.97 | | | | | | sub-proof #646.
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | Case 2:
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | (118) all_252_5 = e4 & op(e3, e2) = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | ALPHA: (118) implies:
% 251.13/59.97 | | | | | | (119) op(e3, e2) = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | REF_CLOSE: (13), (16), (102), (119) are inconsistent by sub-proof
% 251.13/59.97 | | | | | | #645.
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | End of split
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | Case 2:
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | (120) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 &
% 251.13/59.97 | | | | | op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | BETA: splitting (120) gives:
% 251.13/59.97 | | | | |
% 251.13/59.97 | | | | | Case 1:
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | (121) all_252_8 = e4 & op(e2, e2) = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | ALPHA: (121) implies:
% 251.13/59.97 | | | | | | (122) all_252_8 = e4
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | BETA: splitting (21) gives:
% 251.13/59.97 | | | | | |
% 251.13/59.97 | | | | | | Case 1:
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | | (123) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 251.13/59.97 | | | | | | | op(e3, e2) = e1)
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | | REF_CLOSE: (13), (25), (32), (51), (80), (123) are inconsistent by
% 251.13/59.97 | | | | | | | sub-proof #928.
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | Case 2:
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | | (124) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 251.13/59.97 | | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | | BETA: splitting (124) gives:
% 251.13/59.97 | | | | | | |
% 251.13/59.97 | | | | | | | Case 1:
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | | (125) all_252_8 = e1 & op(e2, e2) = e1
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | | REF_CLOSE: (31), (122), (125) are inconsistent by sub-proof
% 251.13/59.97 | | | | | | | | #644.
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | Case 2:
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | | (126) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1
% 251.13/59.97 | | | | | | | | & op(e0, e2) = e1)
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | | BETA: splitting (126) gives:
% 251.13/59.97 | | | | | | | |
% 251.13/59.97 | | | | | | | | Case 1:
% 251.13/59.97 | | | | | | | | |
% 251.13/59.97 | | | | | | | | | (127) all_252_14 = e1 & op(e1, e2) = e1
% 251.13/59.97 | | | | | | | | |
% 251.13/59.97 | | | | | | | | | ALPHA: (127) implies:
% 251.13/59.97 | | | | | | | | | (128) all_252_14 = e1
% 251.13/59.97 | | | | | | | | |
% 251.13/59.97 | | | | | | | | | BETA: splitting (88) gives:
% 251.13/59.97 | | | | | | | | |
% 251.13/59.97 | | | | | | | | | Case 1:
% 251.13/59.97 | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | (129) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 251.13/59.97 | | | | | | | | | | e2 & op(e3, e2) = e2)
% 251.13/59.97 | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | BETA: splitting (129) gives:
% 251.13/59.97 | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | Case 1:
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | (130) all_252_4 = e2 & op(e4, e2) = e2
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | ALPHA: (130) implies:
% 251.13/59.97 | | | | | | | | | | | (131) op(e4, e2) = e2
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_26_2, e2, e1, e4,
% 251.13/59.97 | | | | | | | | | | | simplifying with (61), (111) gives:
% 251.13/59.97 | | | | | | | | | | | (132) all_26_2 = e2
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | GROUND_INST: instantiating (13) with all_6_2, e2, e2, e4,
% 251.13/59.97 | | | | | | | | | | | simplifying with (25), (131) gives:
% 251.13/59.97 | | | | | | | | | | | (133) all_6_2 = e2
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | REDUCE: (57), (132), (133) imply:
% 251.13/59.97 | | | | | | | | | | | (134) $false
% 251.13/59.97 | | | | | | | | | | |
% 251.13/59.97 | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 251.13/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | Case 2:
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | (135) all_252_5 = e2 & op(e3, e2) = e2
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | ALPHA: (135) implies:
% 251.28/59.97 | | | | | | | | | | | (136) op(e3, e2) = e2
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | REF_CLOSE: (9), (13), (102), (136) are inconsistent by
% 251.28/59.97 | | | | | | | | | | | sub-proof #643.
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | End of split
% 251.28/59.97 | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | Case 2:
% 251.28/59.97 | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | (137) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 251.28/59.97 | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 & op(e0,
% 251.28/59.97 | | | | | | | | | | e2) = e2)
% 251.28/59.97 | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | BETA: splitting (137) gives:
% 251.28/59.97 | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | Case 1:
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | (138) all_252_8 = e2 & op(e2, e2) = e2
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | REF_CLOSE: (79), (122), (138) are inconsistent by sub-proof
% 251.28/59.97 | | | | | | | | | | | #642.
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | Case 2:
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | (139) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 251.28/59.97 | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | BETA: splitting (139) gives:
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | Case 1:
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | | (140) all_252_14 = e2 & op(e1, e2) = e2
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | | REF_CLOSE: (29), (128), (140) are inconsistent by sub-proof
% 251.28/59.97 | | | | | | | | | | | | #924.
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | Case 2:
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | | (141) all_252_22 = e2 & op(e0, e2) = e2
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | | REF_CLOSE: (14), (36), (141) are inconsistent by sub-proof
% 251.28/59.97 | | | | | | | | | | | | #649.
% 251.28/59.97 | | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | | End of split
% 251.28/59.97 | | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | | End of split
% 251.28/59.97 | | | | | | | | | |
% 251.28/59.97 | | | | | | | | | End of split
% 251.28/59.97 | | | | | | | | |
% 251.28/59.97 | | | | | | | | Case 2:
% 251.28/59.97 | | | | | | | | |
% 251.28/59.97 | | | | | | | | | (142) all_252_22 = e1 & op(e0, e2) = e1
% 251.28/59.97 | | | | | | | | |
% 251.28/59.97 | | | | | | | | | ALPHA: (142) implies:
% 251.28/59.97 | | | | | | | | | (143) op(e0, e2) = e1
% 251.28/59.97 | | | | | | | | |
% 251.28/59.97 | | | | | | | | | REF_CLOSE: (13), (30), (45), (101), (143) are inconsistent by
% 251.28/59.97 | | | | | | | | | sub-proof #641.
% 251.28/59.97 | | | | | | | | |
% 251.28/59.97 | | | | | | | | End of split
% 251.28/59.97 | | | | | | | |
% 251.28/59.97 | | | | | | | End of split
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | End of split
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | Case 2:
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | (144) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 = e4 &
% 251.28/59.97 | | | | | | op(e0, e2) = e4)
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | BETA: splitting (144) gives:
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | Case 1:
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | (145) all_252_14 = e4 & op(e1, e2) = e4
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | ALPHA: (145) implies:
% 251.28/59.97 | | | | | | | (146) op(e1, e2) = e4
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | REF_CLOSE: (2), (13), (73), (146) are inconsistent by sub-proof
% 251.28/59.97 | | | | | | | #831.
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | Case 2:
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | (147) all_252_22 = e4 & op(e0, e2) = e4
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | ALPHA: (147) implies:
% 251.28/59.97 | | | | | | | (148) op(e0, e2) = e4
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | | REF_CLOSE: (13), (68), (101), (148) are inconsistent by sub-proof
% 251.28/59.97 | | | | | | | #857.
% 251.28/59.97 | | | | | | |
% 251.28/59.97 | | | | | | End of split
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | End of split
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | End of split
% 251.28/59.97 | | | |
% 251.28/59.97 | | | End of split
% 251.28/59.97 | | |
% 251.28/59.97 | | Case 2:
% 251.28/59.97 | | |
% 251.28/59.97 | | | (149) all_34_2 = e2
% 251.28/59.97 | | |
% 251.28/59.97 | | | REDUCE: (94), (149) imply:
% 251.28/59.97 | | | (150) ~ (all_4_2 = e2)
% 251.28/59.97 | | |
% 251.28/59.97 | | | SIMP: (150) implies:
% 251.28/59.97 | | | (151) ~ (all_4_2 = e2)
% 251.28/59.97 | | |
% 251.28/59.97 | | | BETA: splitting (17) gives:
% 251.28/59.97 | | |
% 251.28/59.97 | | | Case 1:
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | (152) all_250_17 = e4
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | REF_CLOSE: (2), (77), (152) are inconsistent by sub-proof #721.
% 251.28/59.97 | | | |
% 251.28/59.97 | | | Case 2:
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | (153) all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.28/59.97 | | | | all_250_17 = e0
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | BETA: splitting (153) gives:
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | Case 1:
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | | (154) all_250_17 = e3
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | | REF_CLOSE: (77), (89), (154) are inconsistent by sub-proof #720.
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | Case 2:
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | | (155) all_250_17 = e2 | all_250_17 = e1 | all_250_17 = e0
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | | BETA: splitting (155) gives:
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | | Case 1:
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | (156) all_250_17 = e2
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | REF_CLOSE: (77), (151), (156) are inconsistent by sub-proof #719.
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | Case 2:
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | (157) ~ (all_250_17 = e2)
% 251.28/59.97 | | | | | | (158) all_250_17 = e1 | all_250_17 = e0
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | | REF_CLOSE: (7), (10), (13), (77), (99), (151), (158) are
% 251.28/59.97 | | | | | | inconsistent by sub-proof #639.
% 251.28/59.97 | | | | | |
% 251.28/59.97 | | | | | End of split
% 251.28/59.97 | | | | |
% 251.28/59.97 | | | | End of split
% 251.28/59.97 | | | |
% 251.28/59.97 | | | End of split
% 251.28/59.97 | | |
% 251.28/59.97 | | End of split
% 251.28/59.97 | |
% 251.28/59.97 | Case 2:
% 251.28/59.97 | |
% 251.28/59.97 | | (159) all_32_2 = e2
% 251.28/59.97 | | (160) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) =
% 251.28/59.97 | | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 251.28/59.97 | | op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.28/59.97 | |
% 251.28/59.97 | | COMBINE_EQS: (1), (159) imply:
% 251.28/59.97 | | (161) all_20_2 = e2
% 251.28/59.97 | |
% 251.28/59.97 | | SIMP: (161) implies:
% 251.28/59.97 | | (162) all_20_2 = e2
% 251.28/59.97 | |
% 251.28/59.97 | | REF_CLOSE: (2), (7), (10), (13), (17), (20), (30), (43), (45), (73), (77),
% 251.28/59.97 | | (89), (99), (101), (160), (162) are inconsistent by sub-proof
% 251.28/59.97 | | #637.
% 251.28/59.97 | |
% 251.28/59.97 | End of split
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #637 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) = all_32_1
% 251.28/59.97 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 251.28/59.97 all_32_1 & $i(all_32_1))
% 251.28/59.97 (2) ~ (all_4_2 = e4)
% 251.28/59.97 (3) op(e0, e2) = e3
% 251.28/59.97 (4) op(all_38_2, e1) = e2
% 251.28/59.97 (5) op(all_38_2, all_4_2) = e1
% 251.28/59.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (7) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.28/59.97 all_250_17 = e0
% 251.28/59.97 (8) op(e2, e1) = all_38_2
% 251.28/59.97 (9) op(e0, e2) = all_28_2
% 251.28/59.97 (10) op(all_20_2, e1) = e0
% 251.28/59.97 (11) ~ (e3 = e1)
% 251.28/59.97 (12) op(e1, e2) = all_4_2
% 251.28/59.97 (13) all_250_17 = all_4_2
% 251.28/59.97 (14) ~ (all_4_2 = e3)
% 251.28/59.97 (15) ~ (all_4_2 = e0)
% 251.28/59.97 (16) all_20_2 = e2
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (10), (16) imply:
% 251.28/59.97 | (17) op(e2, e1) = e0
% 251.28/59.97 |
% 251.28/59.97 | BETA: splitting (1) gives:
% 251.28/59.97 |
% 251.28/59.97 | Case 1:
% 251.28/59.97 | |
% 251.28/59.97 | |
% 251.28/59.97 | | GROUND_INST: instantiating (6) with all_38_2, e0, e1, e2, simplifying with
% 251.28/59.97 | | (8), (17) gives:
% 251.28/59.97 | | (18) all_38_2 = e0
% 251.28/59.97 | |
% 251.28/59.97 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (15), (18)
% 251.28/59.97 | | are inconsistent by sub-proof #638.
% 251.28/59.97 | |
% 251.28/59.97 | Case 2:
% 251.28/59.97 | |
% 251.28/59.97 | | (19) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 251.28/59.97 | |
% 251.28/59.97 | | ALPHA: (19) implies:
% 251.28/59.97 | | (20) ~ (all_32_1 = e3)
% 251.28/59.97 | | (21) op(e1, e2) = all_32_1
% 251.28/59.97 | |
% 251.28/59.97 | | GROUND_INST: instantiating (6) with all_4_2, all_32_1, e2, e1, simplifying
% 251.28/59.97 | | with (12), (21) gives:
% 251.28/59.97 | | (22) all_32_1 = all_4_2
% 251.28/59.97 | |
% 251.28/59.97 | | GROUND_INST: instantiating (6) with all_38_2, e0, e1, e2, simplifying with
% 251.28/59.97 | | (8), (17) gives:
% 251.28/59.97 | | (23) all_38_2 = e0
% 251.28/59.97 | |
% 251.28/59.97 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (15), (23)
% 251.28/59.97 | | are inconsistent by sub-proof #638.
% 251.28/59.97 | |
% 251.28/59.97 | End of split
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #638 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) ~ (all_4_2 = e4)
% 251.28/59.97 (2) op(e0, e2) = e3
% 251.28/59.97 (3) op(all_38_2, e1) = e2
% 251.28/59.97 (4) op(all_38_2, all_4_2) = e1
% 251.28/59.97 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (6) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.28/59.97 all_250_17 = e0
% 251.28/59.97 (7) op(e0, e2) = all_28_2
% 251.28/59.97 (8) all_38_2 = e0
% 251.28/59.97 (9) ~ (e3 = e1)
% 251.28/59.97 (10) all_250_17 = all_4_2
% 251.28/59.97 (11) ~ (all_4_2 = e3)
% 251.28/59.97 (12) ~ (all_4_2 = e0)
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (4), (8) imply:
% 251.28/59.97 | (13) op(e0, all_4_2) = e1
% 251.28/59.97 |
% 251.28/59.97 | BETA: splitting (6) gives:
% 251.28/59.97 |
% 251.28/59.97 | Case 1:
% 251.28/59.97 | |
% 251.28/59.97 | | (14) all_250_17 = e4
% 251.28/59.97 | |
% 251.28/59.97 | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #721.
% 251.28/59.97 | |
% 251.28/59.97 | Case 2:
% 251.28/59.97 | |
% 251.28/59.97 | | (15) all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | all_250_17 =
% 251.28/59.97 | | e0
% 251.28/59.97 | |
% 251.28/59.97 | | BETA: splitting (15) gives:
% 251.28/59.97 | |
% 251.28/59.97 | | Case 1:
% 251.28/59.97 | | |
% 251.28/59.97 | | | (16) all_250_17 = e3
% 251.28/59.97 | | |
% 251.28/59.97 | | | REF_CLOSE: (10), (11), (16) are inconsistent by sub-proof #720.
% 251.28/59.97 | | |
% 251.28/59.97 | | Case 2:
% 251.28/59.97 | | |
% 251.28/59.97 | | | (17) all_250_17 = e2 | all_250_17 = e1 | all_250_17 = e0
% 251.28/59.97 | | |
% 251.28/59.97 | | | BETA: splitting (17) gives:
% 251.28/59.97 | | |
% 251.28/59.97 | | | Case 1:
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | (18) all_250_17 = e2
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | COMBINE_EQS: (10), (18) imply:
% 251.28/59.97 | | | | (19) all_4_2 = e2
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | SIMP: (19) implies:
% 251.28/59.97 | | | | (20) all_4_2 = e2
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | REDUCE: (13), (20) imply:
% 251.28/59.97 | | | | (21) op(e0, e2) = e1
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | REF_CLOSE: (2), (5), (7), (9), (21) are inconsistent by sub-proof #641.
% 251.28/59.97 | | | |
% 251.28/59.97 | | | Case 2:
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | (22) ~ (all_250_17 = e2)
% 251.28/59.97 | | | | (23) all_250_17 = e1 | all_250_17 = e0
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | REDUCE: (10), (22) imply:
% 251.28/59.97 | | | | (24) ~ (all_4_2 = e2)
% 251.28/59.97 | | | |
% 251.28/59.97 | | | | REF_CLOSE: (3), (4), (5), (10), (12), (23), (24) are inconsistent by
% 251.28/59.97 | | | | sub-proof #639.
% 251.28/59.97 | | | |
% 251.28/59.97 | | | End of split
% 251.28/59.97 | | |
% 251.28/59.97 | | End of split
% 251.28/59.97 | |
% 251.28/59.97 | End of split
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #639 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) op(all_38_2, e1) = e2
% 251.28/59.97 (2) op(all_38_2, all_4_2) = e1
% 251.28/59.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (4) all_250_17 = e1 | all_250_17 = e0
% 251.28/59.97 (5) all_250_17 = all_4_2
% 251.28/59.97 (6) ~ (all_4_2 = e0)
% 251.28/59.97 (7) ~ (all_4_2 = e2)
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | BETA: splitting (4) gives:
% 251.28/59.97 |
% 251.28/59.97 | Case 1:
% 251.28/59.97 | |
% 251.28/59.97 | | (8) all_250_17 = e1
% 251.28/59.97 | |
% 251.28/59.97 | | COMBINE_EQS: (5), (8) imply:
% 251.28/59.97 | | (9) all_4_2 = e1
% 251.28/59.97 | |
% 251.28/59.97 | | SIMP: (9) implies:
% 251.28/59.97 | | (10) all_4_2 = e1
% 251.28/59.97 | |
% 251.28/59.97 | | REDUCE: (7), (10) imply:
% 251.28/59.97 | | (11) ~ (e2 = e1)
% 251.28/59.97 | |
% 251.28/59.97 | | SIMP: (11) implies:
% 251.28/59.97 | | (12) ~ (e2 = e1)
% 251.28/59.97 | |
% 251.28/59.97 | | REF_CLOSE: (1), (2), (3), (10), (12) are inconsistent by sub-proof #640.
% 251.28/59.97 | |
% 251.28/59.97 | Case 2:
% 251.28/59.97 | |
% 251.28/59.97 | | (13) all_250_17 = e0
% 251.28/59.97 | |
% 251.28/59.97 | | COMBINE_EQS: (5), (13) imply:
% 251.28/59.97 | | (14) all_4_2 = e0
% 251.28/59.97 | |
% 251.28/59.97 | | SIMP: (14) implies:
% 251.28/59.97 | | (15) all_4_2 = e0
% 251.28/59.97 | |
% 251.28/59.97 | | REDUCE: (6), (15) imply:
% 251.28/59.97 | | (16) $false
% 251.28/59.97 | |
% 251.28/59.97 | | CLOSE: (16) is inconsistent.
% 251.28/59.97 | |
% 251.28/59.97 | End of split
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #640 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) op(all_38_2, e1) = e2
% 251.28/59.97 (2) op(all_38_2, all_4_2) = e1
% 251.28/59.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (4) ~ (e2 = e1)
% 251.28/59.97 (5) all_4_2 = e1
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (2), (5) imply:
% 251.28/59.97 | (6) op(all_38_2, e1) = e1
% 251.28/59.97 |
% 251.28/59.97 | GROUND_INST: instantiating (3) with e2, e1, e1, all_38_2, simplifying with
% 251.28/59.97 | (1), (6) gives:
% 251.28/59.97 | (7) e2 = e1
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (4), (7) imply:
% 251.28/59.97 | (8) $false
% 251.28/59.97 |
% 251.28/59.97 | CLOSE: (8) is inconsistent.
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #641 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) op(e0, e2) = e3
% 251.28/59.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (3) op(e0, e2) = all_28_2
% 251.28/59.97 (4) ~ (e3 = e1)
% 251.28/59.97 (5) op(e0, e2) = e1
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | GROUND_INST: instantiating (2) with all_28_2, e1, e2, e0, simplifying with
% 251.28/59.97 | (3), (5) gives:
% 251.28/59.97 | (6) all_28_2 = e1
% 251.28/59.97 |
% 251.28/59.97 | GROUND_INST: instantiating (2) with all_28_2, e3, e2, e0, simplifying with
% 251.28/59.97 | (1), (3) gives:
% 251.28/59.97 | (7) all_28_2 = e3
% 251.28/59.97 |
% 251.28/59.97 | COMBINE_EQS: (6), (7) imply:
% 251.28/59.97 | (8) e3 = e1
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (4), (8) imply:
% 251.28/59.97 | (9) $false
% 251.28/59.97 |
% 251.28/59.97 | CLOSE: (9) is inconsistent.
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #642 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) all_252_8 = e2 & op(e2, e2) = e2
% 251.28/59.97 (2) all_252_8 = e4
% 251.28/59.97 (3) ~ (e4 = e2)
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | ALPHA: (1) implies:
% 251.28/59.97 | (4) all_252_8 = e2
% 251.28/59.97 |
% 251.28/59.97 | COMBINE_EQS: (2), (4) imply:
% 251.28/59.97 | (5) e4 = e2
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (3), (5) imply:
% 251.28/59.97 | (6) $false
% 251.28/59.97 |
% 251.28/59.97 | CLOSE: (6) is inconsistent.
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #643 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.97 (2) op(e3, e2) = e2
% 251.28/59.97 (3) op(e3, e2) = e0
% 251.28/59.97 (4) ~ (e2 = e0)
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | GROUND_INST: instantiating (1) with e0, e2, e2, e3, simplifying with (2), (3)
% 251.28/59.97 | gives:
% 251.28/59.97 | (5) e2 = e0
% 251.28/59.97 |
% 251.28/59.97 | REDUCE: (4), (5) imply:
% 251.28/59.97 | (6) $false
% 251.28/59.97 |
% 251.28/59.97 | CLOSE: (6) is inconsistent.
% 251.28/59.97 |
% 251.28/59.97 End of proof
% 251.28/59.97
% 251.28/59.97 Sub-proof #644 shows that the following formulas are inconsistent:
% 251.28/59.97 ----------------------------------------------------------------
% 251.28/59.97 (1) all_252_8 = e1 & op(e2, e2) = e1
% 251.28/59.97 (2) all_252_8 = e4
% 251.28/59.97 (3) ~ (e4 = e1)
% 251.28/59.97
% 251.28/59.97 Begin of proof
% 251.28/59.97 |
% 251.28/59.97 | ALPHA: (1) implies:
% 251.28/59.98 | (4) all_252_8 = e1
% 251.28/59.98 |
% 251.28/59.98 | COMBINE_EQS: (2), (4) imply:
% 251.28/59.98 | (5) e4 = e1
% 251.28/59.98 |
% 251.28/59.98 | REDUCE: (3), (5) imply:
% 251.28/59.98 | (6) $false
% 251.28/59.98 |
% 251.28/59.98 | CLOSE: (6) is inconsistent.
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #645 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (2) op(e3, e2) = e4
% 251.28/59.98 (3) op(e3, e2) = e0
% 251.28/59.98 (4) ~ (e4 = e0)
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | GROUND_INST: instantiating (1) with e0, e4, e2, e3, simplifying with (2), (3)
% 251.28/59.98 | gives:
% 251.28/59.98 | (5) e4 = e0
% 251.28/59.98 |
% 251.28/59.98 | REDUCE: (4), (5) imply:
% 251.28/59.98 | (6) $false
% 251.28/59.98 |
% 251.28/59.98 | CLOSE: (6) is inconsistent.
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #646 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) op(all_64_2, e4) = e2
% 251.28/59.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (3) all_6_2 = e4
% 251.28/59.98 (4) ~ (e4 = e2)
% 251.28/59.98 (5) op(all_64_2, all_6_2) = e4
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | REDUCE: (3), (5) imply:
% 251.28/59.98 | (6) op(all_64_2, e4) = e4
% 251.28/59.98 |
% 251.28/59.98 | GROUND_INST: instantiating (2) with e2, e4, e4, all_64_2, simplifying with
% 251.28/59.98 | (1), (6) gives:
% 251.28/59.98 | (7) e4 = e2
% 251.28/59.98 |
% 251.28/59.98 | REDUCE: (4), (7) imply:
% 251.28/59.98 | (8) $false
% 251.28/59.98 |
% 251.28/59.98 | CLOSE: (8) is inconsistent.
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #647 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) ~ (all_10_2 = e4)
% 251.28/59.98 (2) ~ (all_244_8 = e0)
% 251.28/59.98 (3) all_94_2 = all_38_2
% 251.28/59.98 (4) op(all_62_2, all_36_2) = e3
% 251.28/59.98 (5) op(all_38_2, e1) = e2
% 251.28/59.98 (6) all_250_13 = all_38_2
% 251.28/59.98 (7) op(all_38_2, all_4_2) = e1
% 251.28/59.98 (8) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.28/59.98 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.28/59.98 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.28/59.98 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (10) op(e2, e3) = all_10_2
% 251.28/59.98 (11) ~ (e3 = e2)
% 251.28/59.98 (12) op(e0, e0) = all_244_24
% 251.28/59.98 (13) op(e2, e2) = all_244_8
% 251.28/59.98 (14) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/59.98 all_250_11 = e0
% 251.28/59.98 (15) op(e2, e1) = all_38_2
% 251.28/59.98 (16) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/59.98 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/59.98 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/59.98 (17) op(e1, e0) = all_34_2
% 251.28/59.98 (18) all_78_2 = all_10_2
% 251.28/59.98 (19) ~ (all_34_2 = e2)
% 251.28/59.98 (20) all_106_2 = all_38_2
% 251.28/59.98 (21) ~ (all_244_8 = all_38_2)
% 251.28/59.98 (22) op(all_244_15, all_244_15) = e1
% 251.28/59.98 (23) all_252_22 = e3
% 251.28/59.98 (24) all_250_21 = all_22_2
% 251.28/59.98 (25) op(e1, e4) = all_16_2
% 251.28/59.98 (26) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.28/59.98 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.28/59.98 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.28/59.98 (27) op(e1, e3) = all_62_2
% 251.28/59.98 (28) all_70_2 = all_62_2
% 251.28/59.98 (29) op(e0, all_10_2) = e2
% 251.28/59.98 (30) op(all_48_2, all_22_2) = e0
% 251.28/59.98 (31) ~ (all_12_2 = e2)
% 251.28/59.98 (32) op(e3, e1) = all_36_2
% 251.28/59.98 (33) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.28/59.98 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.28/59.98 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.28/59.98 (34) ~ (all_16_2 = e2)
% 251.28/59.98 (35) ~ (all_8_2 = e1)
% 251.28/59.98 (36) ~ (all_22_2 = e1)
% 251.28/59.98 (37) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 &
% 251.28/59.98 op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 251.28/59.98 e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/59.98 (38) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.28/59.98 all_250_13 = e0
% 251.28/59.98 (39) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/59.98 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/59.98 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/59.98 (40) ~ (all_38_2 = e4)
% 251.28/59.98 (41) op(all_22_2, e3) = e0
% 251.28/59.98 (42) all_68_2 = all_22_2
% 251.28/59.98 (43) op(e0, e3) = all_22_2
% 251.28/59.98 (44) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.28/59.98 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/59.98 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.98 (45) op(all_10_2, e3) = e2
% 251.28/59.98 (46) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.28/59.98 all_250_21 = e0
% 251.28/59.98 (47) ~ (all_118_2 = e2) | ( ~ (all_118_0 = e1) & op(e3, e2) = all_118_1 &
% 251.28/59.98 op(e2, all_118_1) = all_118_0 & $i(all_118_0) & $i(all_118_1)) | ( ~
% 251.28/59.98 (all_118_1 = e4) & op(e3, e2) = all_118_1 & $i(all_118_1))
% 251.28/59.98 (48) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.28/59.98 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.28/59.98 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.28/59.98 (49) all_250_11 = all_10_2
% 251.28/59.98 (50) op(e1, e1) = all_244_15
% 251.28/59.98 (51) op(e0, e1) = all_20_2
% 251.28/59.98 (52) op(all_48_2, e0) = e3
% 251.28/59.98 (53) op(e1, e2) = all_4_2
% 251.28/59.98 (54) all_118_2 = all_22_2
% 251.28/59.98 (55) ~ (all_22_2 = all_10_2)
% 251.28/59.98 (56) ~ (e4 = e2)
% 251.28/59.98 (57) op(e3, e2) = all_8_2
% 251.28/59.98 (58) op(all_36_2, e1) = e3
% 251.28/59.98 (59) ~ (all_38_2 = all_10_2)
% 251.28/59.98 (60) ~ (all_244_15 = all_36_2)
% 251.28/59.98 (61) ~ (all_244_24 = all_22_2)
% 251.28/59.98 (62) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/59.98 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/59.98 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/59.98 (63) all_90_2 = all_22_2
% 251.28/59.98 (64) all_46_2 = all_36_2
% 251.28/59.98 (65) op(all_244_24, all_244_24) = e0
% 251.28/59.98 (66) op(e0, e4) = all_12_2
% 251.28/59.98 (67) ~ (all_20_2 = e2)
% 251.28/59.98 (68) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.28/59.98 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.28/59.98 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.28/59.98 (69) all_124_2 = all_10_2
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | BETA: splitting (37) gives:
% 251.28/59.98 |
% 251.28/59.98 | Case 1:
% 251.28/59.98 | |
% 251.28/59.98 | | (70) ~ (all_46_2 = e2)
% 251.28/59.98 | |
% 251.28/59.98 | | REDUCE: (64), (70) imply:
% 251.28/59.98 | | (71) ~ (all_36_2 = e2)
% 251.28/59.98 | |
% 251.28/59.98 | | BETA: splitting (16) gives:
% 251.28/59.98 | |
% 251.28/59.98 | | Case 1:
% 251.28/59.98 | | |
% 251.28/59.98 | | | (72) ~ (all_68_2 = e4)
% 251.28/59.98 | | |
% 251.28/59.98 | | | REDUCE: (42), (72) imply:
% 251.28/59.98 | | | (73) ~ (all_22_2 = e4)
% 251.28/59.98 | | |
% 251.28/59.98 | | | BETA: splitting (33) gives:
% 251.28/59.98 | | |
% 251.28/59.98 | | | Case 1:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | (74) ~ (all_78_2 = e1)
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | REDUCE: (18), (74) imply:
% 251.28/59.98 | | | | (75) ~ (all_10_2 = e1)
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | BETA: splitting (48) gives:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | Case 1:
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | (76) ~ (all_90_2 = e2)
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REDUCE: (63), (76) imply:
% 251.28/59.98 | | | | | (77) ~ (all_22_2 = e2)
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (13), (14), (20), (21), (22),
% 251.28/59.98 | | | | | (24), (26), (30), (32), (36), (38), (40), (43), (45), (46),
% 251.28/59.98 | | | | | (49), (50), (51), (52), (55), (59), (67), (68), (69), (71),
% 251.28/59.98 | | | | | (73), (75), (77) are inconsistent by sub-proof #982.
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | Case 2:
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | (78) all_90_2 = e2
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | COMBINE_EQS: (63), (78) imply:
% 251.28/59.98 | | | | | (79) all_22_2 = e2
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | SIMP: (79) implies:
% 251.28/59.98 | | | | | (80) all_22_2 = e2
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | COMBINE_EQS: (54), (80) imply:
% 251.28/59.98 | | | | | (81) all_118_2 = e2
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REDUCE: (61), (80) imply:
% 251.28/59.98 | | | | | (82) ~ (all_244_24 = e2)
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REDUCE: (41), (80) imply:
% 251.28/59.98 | | | | | (83) op(e2, e3) = e0
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | BETA: splitting (47) gives:
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | Case 1:
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | (84) ~ (all_118_2 = e2)
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | REDUCE: (81), (84) imply:
% 251.28/59.98 | | | | | | (85) $false
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | CLOSE: (85) is inconsistent.
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | Case 2:
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | GROUND_INST: instantiating (9) with all_10_2, e0, e3, e2,
% 251.28/59.98 | | | | | | simplifying with (10), (83) gives:
% 251.28/59.98 | | | | | | (86) all_10_2 = e0
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | REDUCE: (29), (86) imply:
% 251.28/59.98 | | | | | | (87) op(e0, e0) = e2
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | | REF_CLOSE: (9), (12), (82), (87) are inconsistent by sub-proof #978.
% 251.28/59.98 | | | | | |
% 251.28/59.98 | | | | | End of split
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | End of split
% 251.28/59.98 | | | |
% 251.28/59.98 | | | Case 2:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | (88) all_78_2 = e1
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | COMBINE_EQS: (18), (88) imply:
% 251.28/59.98 | | | | (89) all_10_2 = e1
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | SIMP: (89) implies:
% 251.28/59.98 | | | | (90) all_10_2 = e1
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | REDUCE: (29), (90) imply:
% 251.28/59.98 | | | | (91) op(e0, e1) = e2
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | REF_CLOSE: (9), (51), (67), (91) are inconsistent by sub-proof #985.
% 251.28/59.98 | | | |
% 251.28/59.98 | | | End of split
% 251.28/59.98 | | |
% 251.28/59.98 | | Case 2:
% 251.28/59.98 | | |
% 251.28/59.98 | | | (92) all_68_2 = e4
% 251.28/59.98 | | |
% 251.28/59.98 | | | COMBINE_EQS: (42), (92) imply:
% 251.28/59.98 | | | (93) all_22_2 = e4
% 251.28/59.98 | | |
% 251.28/59.98 | | | SIMP: (93) implies:
% 251.28/59.98 | | | (94) all_22_2 = e4
% 251.28/59.98 | | |
% 251.28/59.98 | | | REDUCE: (43), (94) imply:
% 251.28/59.98 | | | (95) op(e0, e3) = e4
% 251.28/59.98 | | |
% 251.28/59.98 | | | BETA: splitting (44) gives:
% 251.28/59.98 | | |
% 251.28/59.98 | | | Case 1:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | (96) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0,
% 251.28/59.98 | | | | e3) = e2)
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | REF_CLOSE: (9), (31), (43), (56), (66), (95), (96) are inconsistent by
% 251.28/59.98 | | | | sub-proof #650.
% 251.28/59.98 | | | |
% 251.28/59.98 | | | Case 2:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | (97) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/59.98 | | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | BETA: splitting (97) gives:
% 251.28/59.98 | | | |
% 251.28/59.98 | | | | Case 1:
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | (98) all_252_22 = e2 & op(e0, e2) = e2
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REF_CLOSE: (11), (23), (98) are inconsistent by sub-proof #649.
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | Case 2:
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | (99) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.28/59.98 | | | | | op(e0, e0) = e2)
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | | REF_CLOSE: (2), (9), (12), (13), (51), (65), (67), (99) are
% 251.28/59.98 | | | | | inconsistent by sub-proof #648.
% 251.28/59.98 | | | | |
% 251.28/59.98 | | | | End of split
% 251.28/59.98 | | | |
% 251.28/59.98 | | | End of split
% 251.28/59.98 | | |
% 251.28/59.98 | | End of split
% 251.28/59.98 | |
% 251.28/59.98 | Case 2:
% 251.28/59.98 | |
% 251.28/59.98 | | (100) all_46_2 = e2
% 251.28/59.98 | | (101) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.28/59.98 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 251.28/59.98 | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/59.98 | |
% 251.28/59.98 | | COMBINE_EQS: (64), (100) imply:
% 251.28/59.98 | | (102) all_36_2 = e2
% 251.28/59.98 | |
% 251.28/59.98 | | REF_CLOSE: (4), (7), (9), (13), (15), (17), (19), (21), (25), (27), (28),
% 251.28/59.98 | | (34), (35), (39), (50), (53), (57), (58), (60), (62), (101),
% 251.28/59.98 | | (102) are inconsistent by sub-proof #796.
% 251.28/59.98 | |
% 251.28/59.98 | End of split
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #648 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) ~ (all_244_8 = e0)
% 251.28/59.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (3) op(e0, e0) = all_244_24
% 251.28/59.98 (4) op(e2, e2) = all_244_8
% 251.28/59.98 (5) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.98 (6) op(e0, e1) = all_20_2
% 251.28/59.98 (7) op(all_244_24, all_244_24) = e0
% 251.28/59.98 (8) ~ (all_20_2 = e2)
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | BETA: splitting (5) gives:
% 251.28/59.98 |
% 251.28/59.98 | Case 1:
% 251.28/59.98 | |
% 251.28/59.98 | | (9) all_252_23 = e2 & op(e0, e1) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | ALPHA: (9) implies:
% 251.28/59.98 | | (10) op(e0, e1) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | REF_CLOSE: (2), (6), (8), (10) are inconsistent by sub-proof #985.
% 251.28/59.98 | |
% 251.28/59.98 | Case 2:
% 251.28/59.98 | |
% 251.28/59.98 | | (11) all_252_24 = e2 & op(e0, e0) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | ALPHA: (11) implies:
% 251.28/59.98 | | (12) op(e0, e0) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | GROUND_INST: instantiating (2) with all_244_24, e2, e0, e0, simplifying with
% 251.28/59.98 | | (3), (12) gives:
% 251.28/59.98 | | (13) all_244_24 = e2
% 251.28/59.98 | |
% 251.28/59.98 | | REDUCE: (7), (13) imply:
% 251.28/59.98 | | (14) op(e2, e2) = e0
% 251.28/59.98 | |
% 251.28/59.98 | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #880.
% 251.28/59.98 | |
% 251.28/59.98 | End of split
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #649 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) all_252_22 = e2 & op(e0, e2) = e2
% 251.28/59.98 (2) all_252_22 = e3
% 251.28/59.98 (3) ~ (e3 = e2)
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | ALPHA: (1) implies:
% 251.28/59.98 | (4) all_252_22 = e2
% 251.28/59.98 |
% 251.28/59.98 | COMBINE_EQS: (2), (4) imply:
% 251.28/59.98 | (5) e3 = e2
% 251.28/59.98 |
% 251.28/59.98 | REDUCE: (3), (5) imply:
% 251.28/59.98 | (6) $false
% 251.28/59.98 |
% 251.28/59.98 | CLOSE: (6) is inconsistent.
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #650 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (2) ~ (all_12_2 = e2)
% 251.28/59.98 (3) op(e0, e3) = all_22_2
% 251.28/59.98 (4) op(e0, e3) = e4
% 251.28/59.98 (5) ~ (e4 = e2)
% 251.28/59.98 (6) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/59.98 (7) op(e0, e4) = all_12_2
% 251.28/59.98
% 251.28/59.98 Begin of proof
% 251.28/59.98 |
% 251.28/59.98 | BETA: splitting (6) gives:
% 251.28/59.98 |
% 251.28/59.98 | Case 1:
% 251.28/59.98 | |
% 251.28/59.98 | | (8) all_252_20 = e2 & op(e0, e4) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | ALPHA: (8) implies:
% 251.28/59.98 | | (9) op(e0, e4) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | REF_CLOSE: (1), (2), (7), (9) are inconsistent by sub-proof #980.
% 251.28/59.98 | |
% 251.28/59.98 | Case 2:
% 251.28/59.98 | |
% 251.28/59.98 | | (10) all_252_21 = e2 & op(e0, e3) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | ALPHA: (10) implies:
% 251.28/59.98 | | (11) op(e0, e3) = e2
% 251.28/59.98 | |
% 251.28/59.98 | | REF_CLOSE: (1), (3), (4), (5), (11) are inconsistent by sub-proof #951.
% 251.28/59.98 | |
% 251.28/59.98 | End of split
% 251.28/59.98 |
% 251.28/59.98 End of proof
% 251.28/59.98
% 251.28/59.98 Sub-proof #651 shows that the following formulas are inconsistent:
% 251.28/59.98 ----------------------------------------------------------------
% 251.28/59.98 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/59.98 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/59.98 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/59.98 (2) all_32_2 = all_20_2
% 251.28/59.98 (3) ~ (all_26_2 = e2)
% 251.28/59.98 (4) ~ (all_4_2 = e4)
% 251.28/59.98 (5) all_250_9 = all_48_2
% 251.28/59.98 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/59.98 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/59.98 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/59.98 (7) op(all_4_2, e2) = e1
% 251.28/59.98 (8) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/59.98 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/59.98 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/59.98 (9) ~ (all_244_24 = all_40_2)
% 251.28/59.98 (10) ~ (all_40_2 = all_38_2)
% 251.28/59.98 (11) op(all_6_2, e2) = e4
% 251.28/59.98 (12) ~ (all_48_2 = e2)
% 251.28/59.98 (13) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.28/59.98 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.28/59.98 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/59.98 (14) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/59.98 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/59.98 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/59.98 (15) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/59.98 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/59.98 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/59.98 (16) all_250_8 = all_36_2
% 251.28/59.98 (17) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.28/59.98 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.28/59.98 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.28/59.98 (18) op(e2, e0) = e4
% 251.28/59.98 (19) all_94_2 = all_38_2
% 251.28/59.98 (20) op(all_62_2, all_36_2) = e3
% 251.28/59.98 (21) op(all_38_2, e1) = e2
% 251.28/59.98 (22) all_250_13 = all_38_2
% 251.28/59.98 (23) ~ (e2 = e0)
% 251.28/59.98 (24) op(all_38_2, all_4_2) = e1
% 251.28/59.98 (25) ~ (e1 = e0)
% 251.28/59.98 (26) ~ (all_28_2 = e3)
% 251.28/59.98 (27) ~ (all_62_2 = all_22_2)
% 251.28/59.98 (28) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.28/59.98 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.28/59.98 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.28/59.98 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.98 (30) op(e2, e3) = all_10_2
% 251.28/59.98 (31) ~ (e3 = e2)
% 251.28/59.98 (32) op(e0, e0) = all_244_24
% 251.28/59.98 (33) ~ (all_12_2 = e3)
% 251.28/59.98 (34) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/59.98 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/59.98 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/59.98 (35) ~ (all_244_8 = all_64_2)
% 251.28/59.98 (36) op(e2, e2) = all_244_8
% 251.28/59.98 (37) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/59.98 all_250_11 = e0
% 251.28/59.98 (38) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/59.98 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/59.98 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/59.98 (39) op(e2, e1) = all_38_2
% 251.28/59.98 (40) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/59.98 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/59.98 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/59.98 (41) ~ (all_36_2 = all_20_2)
% 251.28/59.98 (42) ~ (all_64_2 = all_40_2)
% 251.28/59.98 (43) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 251.28/59.98 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 251.28/59.98 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 251.28/59.98 (44) ~ (all_84_2 = all_62_2)
% 251.28/59.98 (45) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 251.28/59.98 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 251.28/59.98 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.98 (46) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/59.98 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/59.98 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/59.98 (47) ~ (all_48_2 = all_40_2)
% 251.28/59.98 (48) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/59.98 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/59.98 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/59.98 (49) all_168_2 = all_100_2
% 251.28/59.98 (50) op(e1, e0) = all_34_2
% 251.28/59.98 (51) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/59.98 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/59.98 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/59.98 (52) op(e4, e2) = all_6_2
% 251.28/59.98 (53) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/59.98 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/59.98 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/59.98 (54) all_78_2 = all_10_2
% 251.28/59.98 (55) ~ (all_20_2 = all_12_2)
% 251.28/59.98 (56) ~ (all_34_2 = e2)
% 251.28/59.98 (57) ~ (e2 = e1)
% 251.28/59.98 (58) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 |
% 251.28/59.98 all_250_9 = e0
% 251.28/59.98 (59) ~ (all_100_2 = all_64_2)
% 251.28/59.98 (60) all_56_2 = all_8_2
% 251.28/59.98 (61) op(e0, e2) = all_28_2
% 251.28/59.98 (62) ~ (e4 = e1)
% 251.28/59.98 (63) ~ (all_244_0 = e2)
% 251.28/59.98 (64) op(all_6_2, all_64_2) = e2
% 251.28/59.98 (65) ~ (all_64_2 = all_10_2)
% 251.28/59.98 (66) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/59.98 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/59.98 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/59.98 (67) ~ (all_244_8 = all_10_2)
% 251.28/59.98 (68) ~ (all_6_2 = e1)
% 251.28/59.98 (69) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/59.98 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/59.98 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/59.98 (70) all_106_2 = all_38_2
% 251.28/59.98 (71) ~ (all_244_8 = all_38_2)
% 251.28/59.98 (72) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/59.98 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/59.98 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/59.98 (73) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 251.28/59.98 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 251.28/59.98 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/59.98 (74) op(all_244_15, all_244_15) = e1
% 251.28/59.98 (75) all_250_21 = all_22_2
% 251.28/59.98 (76) all_50_2 = all_4_2
% 251.28/59.98 (77) ~ (all_244_3 = all_84_2)
% 251.28/59.98 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/59.98 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/59.98 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/59.98 (79) op(e1, e4) = all_16_2
% 251.28/59.98 (80) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.28/59.98 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.28/59.98 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.28/59.98 (81) ~ (all_244_0 = all_64_2)
% 251.28/59.98 (82) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/59.98 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/59.98 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/59.98 (83) op(e1, e3) = all_62_2
% 251.28/59.98 (84) op(all_16_2, all_26_2) = e4
% 251.28/59.98 (85) ~ (e3 = e0)
% 251.28/59.98 (86) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.28/59.98 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.28/59.98 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.28/59.98 (87) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 251.28/59.98 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 251.28/59.98 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 251.28/59.98 (88) ~ (all_40_2 = all_10_2)
% 251.28/59.98 (89) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.28/59.98 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.28/59.98 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.28/59.99 (90) op(all_20_2, e1) = e0
% 251.28/59.99 (91) ~ (all_244_3 = all_10_2)
% 251.28/59.99 (92) ~ (all_48_2 = all_36_2)
% 251.28/59.99 (93) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 251.28/59.99 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 251.28/59.99 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.28/59.99 (94) all_70_2 = all_62_2
% 251.28/59.99 (95) ~ (e3 = e1)
% 251.28/59.99 (96) op(all_48_2, all_22_2) = e0
% 251.28/59.99 (97) op(e3, e1) = all_36_2
% 251.28/59.99 (98) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.28/59.99 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.28/59.99 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.28/59.99 (99) ~ (all_16_2 = e2)
% 251.28/59.99 (100) ~ (all_8_2 = e1)
% 251.28/59.99 (101) ~ (all_54_2 = e2) | ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0
% 251.28/59.99 & op(e0, e2) = all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~
% 251.28/59.99 (all_54_1 = e3) & op(e0, e2) = all_54_1 & $i(all_54_1))
% 251.28/59.99 (102) ~ (all_244_3 = all_62_2)
% 251.28/59.99 (103) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/59.99 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/59.99 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/59.99 (104) ~ (all_22_2 = e1)
% 251.28/59.99 (105) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/59.99 all_250_8 = e0
% 251.28/59.99 (106) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/59.99 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/59.99 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/59.99 (107) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 251.28/59.99 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 251.28/59.99 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/59.99 (108) ~ (all_40_2 = all_34_2)
% 251.28/59.99 (109) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.28/59.99 all_250_13 = e0
% 251.28/59.99 (110) ~ (all_244_15 = all_38_2)
% 251.28/59.99 (111) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/59.99 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/59.99 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/59.99 (112) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/59.99 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/59.99 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/59.99 (113) all_190_2 = all_38_2
% 251.28/59.99 (114) ~ (all_64_2 = all_12_2)
% 251.28/59.99 (115) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 251.28/59.99 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 251.28/59.99 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/59.99 (116) op(all_22_2, e3) = e0
% 251.28/59.99 (117) all_68_2 = all_22_2
% 251.28/59.99 (118) op(all_20_2, all_34_2) = e1
% 251.28/59.99 (119) op(e0, e3) = all_22_2
% 251.28/59.99 (120) ~ (all_28_2 = all_22_2)
% 251.28/59.99 (121) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/59.99 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/59.99 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/59.99 (122) all_58_2 = all_20_2
% 251.28/59.99 (123) op(all_62_2, e3) = e1
% 251.28/59.99 (124) op(e4, e1) = all_26_2
% 251.28/59.99 (125) ~ (all_40_2 = e2)
% 251.28/59.99 (126) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.28/59.99 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/59.99 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.99 (127) ~ (all_64_2 = all_38_2)
% 251.28/59.99 (128) op(all_10_2, e3) = e2
% 251.28/59.99 (129) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.28/59.99 all_250_21 = e0
% 251.28/59.99 (130) ~ (all_244_15 = all_62_2)
% 251.28/59.99 (131) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.28/59.99 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.28/59.99 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.28/59.99 (132) op(e3, e4) = all_100_2
% 251.28/59.99 (133) all_250_11 = all_10_2
% 251.28/59.99 (134) op(e4, e4) = all_244_0
% 251.28/59.99 (135) all_126_2 = all_48_2
% 251.28/59.99 (136) ~ (all_22_2 = all_12_2)
% 251.28/59.99 (137) all_230_2 = all_20_2
% 251.28/59.99 (138) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.28/59.99 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/59.99 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.28/59.99 (139) ~ (e4 = e3)
% 251.28/59.99 (140) op(e1, e1) = all_244_15
% 251.28/59.99 (141) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/59.99 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/59.99 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/59.99 (142) op(e0, e1) = all_20_2
% 251.28/59.99 (143) ~ (all_244_15 = all_20_2)
% 251.28/59.99 (144) op(e3, e0) = all_48_2
% 251.28/59.99 (145) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.28/59.99 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.28/59.99 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.28/59.99 (146) op(all_48_2, e0) = e3
% 251.28/59.99 (147) ~ (all_38_2 = all_36_2)
% 251.28/59.99 (148) ~ (all_26_2 = e3)
% 251.28/59.99 (149) ~ (all_244_24 = e2)
% 251.28/59.99 (150) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.28/59.99 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.28/59.99 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.28/59.99 (151) op(e1, e2) = all_4_2
% 251.28/59.99 (152) all_54_2 = e2
% 251.28/59.99 (153) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.28/59.99 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.28/59.99 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.28/59.99 (154) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.28/59.99 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.28/59.99 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.28/59.99 (155) op(all_4_2, all_38_2) = e2
% 251.28/59.99 (156) op(e4, e3) = all_84_2
% 251.28/59.99 (157) ~ (all_62_2 = all_10_2)
% 251.28/59.99 (158) op(e2, e4) = all_64_2
% 251.28/59.99 (159) ~ (all_22_2 = all_10_2)
% 251.28/59.99 (160) ~ (all_38_2 = all_26_2)
% 251.28/59.99 (161) ~ (e4 = e2)
% 251.28/59.99 (162) ~ (all_22_2 = all_20_2)
% 251.28/59.99 (163) op(e3, e2) = all_8_2
% 251.28/59.99 (164) ~ (all_64_2 = all_16_2)
% 251.28/59.99 (165) op(all_36_2, e1) = e3
% 251.28/59.99 (166) ~ (all_38_2 = all_20_2)
% 251.28/59.99 (167) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.28/59.99 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.28/59.99 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.28/59.99 (168) ~ (all_38_2 = all_10_2)
% 251.28/59.99 (169) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.28/59.99 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.28/59.99 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.28/59.99 (170) ~ (all_244_15 = all_36_2)
% 251.28/59.99 (171) ~ (all_20_2 = e4)
% 251.28/59.99 (172) ~ (all_244_24 = all_22_2)
% 251.28/59.99 (173) op(all_16_2, e4) = e1
% 251.28/59.99 (174) ~ (all_100_2 = all_16_2)
% 251.28/59.99 (175) op(e2, e0) = all_40_2
% 251.28/59.99 (176) op(all_8_2, e2) = e3
% 251.28/59.99 (177) ~ (all_244_8 = all_28_2)
% 251.28/59.99 (178) ~ (all_244_3 = all_48_2)
% 251.28/59.99 (179) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/59.99 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/59.99 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/59.99 (180) op(e3, e3) = all_244_3
% 251.28/59.99 (181) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.28/59.99 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.28/59.99 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.28/59.99 (182) ~ (all_26_2 = all_20_2)
% 251.28/59.99 (183) all_90_2 = all_22_2
% 251.28/59.99 (184) all_46_2 = all_36_2
% 251.28/59.99 (185) op(all_244_24, all_244_24) = e0
% 251.28/59.99 (186) op(e0, e4) = all_12_2
% 251.28/59.99 (187) op(all_22_2, all_48_2) = e3
% 251.28/59.99 (188) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.28/59.99 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.28/59.99 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.28/59.99 (189) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.28/59.99 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.28/59.99 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.28/59.99 (190) all_124_2 = all_10_2
% 251.28/59.99
% 251.28/59.99 Begin of proof
% 251.28/59.99 |
% 251.28/59.99 | BETA: splitting (101) gives:
% 251.28/59.99 |
% 251.28/59.99 | Case 1:
% 251.28/59.99 | |
% 251.28/59.99 | | (191) ~ (all_54_2 = e2)
% 251.28/59.99 | |
% 251.28/59.99 | | REDUCE: (152), (191) imply:
% 251.28/59.99 | | (192) $false
% 251.28/59.99 | |
% 251.28/59.99 | | CLOSE: (192) is inconsistent.
% 251.28/59.99 | |
% 251.28/59.99 | Case 2:
% 251.28/59.99 | |
% 251.28/59.99 | | (193) ( ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0, e2) =
% 251.28/59.99 | | all_54_1 & $i(all_54_0) & $i(all_54_1)) | ( ~ (all_54_1 = e3) &
% 251.28/59.99 | | op(e0, e2) = all_54_1 & $i(all_54_1))
% 251.28/59.99 | |
% 251.28/59.99 | | BETA: splitting (45) gives:
% 251.28/59.99 | |
% 251.28/59.99 | | Case 1:
% 251.28/59.99 | | |
% 251.28/59.99 | | | (194) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3,
% 251.28/59.99 | | | e0) = e2)
% 251.28/59.99 | | |
% 251.28/59.99 | | | BETA: splitting (194) gives:
% 251.28/59.99 | | |
% 251.28/59.99 | | | Case 1:
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | (195) all_252_16 = e2 & op(e4, e0) = e2
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | ALPHA: (195) implies:
% 251.28/59.99 | | | | (196) all_252_16 = e2
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | BETA: splitting (193) gives:
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | Case 1:
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | (197) ~ (all_54_0 = e1) & op(e2, all_54_1) = all_54_0 & op(e0, e2)
% 251.28/59.99 | | | | | = all_54_1 & $i(all_54_0) & $i(all_54_1)
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | ALPHA: (197) implies:
% 251.28/59.99 | | | | | (198) op(e0, e2) = all_54_1
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.28/59.99 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 251.28/59.99 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 251.28/59.99 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 251.28/59.99 | | | | | (42), (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 251.28/59.99 | | | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 251.28/59.99 | | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 251.28/59.99 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 251.28/59.99 | | | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 251.28/59.99 | | | | | (93), (94), (95), (96), (97), (98), (99), (100), (102),
% 251.28/59.99 | | | | | (103), (104), (105), (106), (107), (108), (109), (110),
% 251.28/59.99 | | | | | (111), (112), (113), (114), (115), (116), (117), (118),
% 251.28/59.99 | | | | | (119), (120), (121), (122), (123), (124), (125), (126),
% 251.28/59.99 | | | | | (127), (128), (129), (130), (131), (132), (133), (134),
% 251.28/59.99 | | | | | (135), (136), (137), (138), (139), (140), (141), (142),
% 251.28/59.99 | | | | | (143), (144), (145), (146), (147), (148), (150), (151),
% 251.28/59.99 | | | | | (153), (154), (155), (156), (157), (158), (159), (160),
% 251.28/59.99 | | | | | (162), (163), (164), (165), (166), (167), (168), (169),
% 251.28/59.99 | | | | | (170), (171), (172), (173), (174), (175), (176), (177),
% 251.28/59.99 | | | | | (178), (179), (180), (181), (182), (183), (184), (185),
% 251.28/59.99 | | | | | (186), (187), (188), (189), (190), (196), (198) are
% 251.28/59.99 | | | | | inconsistent by sub-proof #654.
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | Case 2:
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | (199) ~ (all_54_1 = e3) & op(e0, e2) = all_54_1 & $i(all_54_1)
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | ALPHA: (199) implies:
% 251.28/59.99 | | | | | (200) op(e0, e2) = all_54_1
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.28/59.99 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 251.28/59.99 | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 251.28/59.99 | | | | | (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 251.28/59.99 | | | | | (42), (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 251.28/59.99 | | | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 251.28/59.99 | | | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 251.28/59.99 | | | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 251.28/59.99 | | | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 251.28/59.99 | | | | | (93), (94), (95), (96), (97), (98), (99), (100), (102),
% 251.28/59.99 | | | | | (103), (104), (105), (106), (107), (108), (109), (110),
% 251.28/59.99 | | | | | (111), (112), (113), (114), (115), (116), (117), (118),
% 251.28/59.99 | | | | | (119), (120), (121), (122), (123), (124), (125), (126),
% 251.28/59.99 | | | | | (127), (128), (129), (130), (131), (132), (133), (134),
% 251.28/59.99 | | | | | (135), (136), (137), (138), (139), (140), (141), (142),
% 251.28/59.99 | | | | | (143), (144), (145), (146), (147), (148), (150), (151),
% 251.28/59.99 | | | | | (153), (154), (155), (156), (157), (158), (159), (160),
% 251.28/59.99 | | | | | (162), (163), (164), (165), (166), (167), (168), (169),
% 251.28/59.99 | | | | | (170), (171), (172), (173), (174), (175), (176), (177),
% 251.28/59.99 | | | | | (178), (179), (180), (181), (182), (183), (184), (185),
% 251.28/59.99 | | | | | (186), (187), (188), (189), (190), (196), (200) are
% 251.28/59.99 | | | | | inconsistent by sub-proof #654.
% 251.28/59.99 | | | | |
% 251.28/59.99 | | | | End of split
% 251.28/59.99 | | | |
% 251.28/59.99 | | | Case 2:
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | (201) all_252_17 = e2 & op(e3, e0) = e2
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | REF_CLOSE: (12), (29), (144), (201) are inconsistent by sub-proof #653.
% 251.28/59.99 | | | |
% 251.28/59.99 | | | End of split
% 251.28/59.99 | | |
% 251.28/59.99 | | Case 2:
% 251.28/59.99 | | |
% 251.28/59.99 | | | (202) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 251.28/59.99 | | | e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.99 | | |
% 251.28/59.99 | | | BETA: splitting (202) gives:
% 251.28/59.99 | | |
% 251.28/59.99 | | | Case 1:
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | (203) all_252_18 = e2 & op(e2, e0) = e2
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | REF_CLOSE: (18), (29), (161), (175), (203) are inconsistent by sub-proof
% 251.28/59.99 | | | | #702.
% 251.28/59.99 | | | |
% 251.28/59.99 | | | Case 2:
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | (204) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0,
% 251.28/59.99 | | | | e0) = e2)
% 251.28/59.99 | | | |
% 251.28/59.99 | | | | REF_CLOSE: (29), (32), (50), (56), (149), (204) are inconsistent by
% 251.28/59.99 | | | | sub-proof #652.
% 251.28/59.99 | | | |
% 251.28/59.99 | | | End of split
% 251.28/59.99 | | |
% 251.28/59.99 | | End of split
% 251.28/59.99 | |
% 251.28/59.99 | End of split
% 251.28/59.99 |
% 251.28/59.99 End of proof
% 251.28/59.99
% 251.28/59.99 Sub-proof #652 shows that the following formulas are inconsistent:
% 251.28/59.99 ----------------------------------------------------------------
% 251.28/59.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.99 (2) op(e0, e0) = all_244_24
% 251.28/59.99 (3) op(e1, e0) = all_34_2
% 251.28/59.99 (4) ~ (all_34_2 = e2)
% 251.28/59.99 (5) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/59.99 (6) ~ (all_244_24 = e2)
% 251.28/59.99
% 251.28/59.99 Begin of proof
% 251.28/59.99 |
% 251.28/59.99 | BETA: splitting (5) gives:
% 251.28/59.99 |
% 251.28/59.99 | Case 1:
% 251.28/59.99 | |
% 251.28/59.99 | | (7) all_252_19 = e2 & op(e1, e0) = e2
% 251.28/59.99 | |
% 251.28/59.99 | | ALPHA: (7) implies:
% 251.28/59.99 | | (8) op(e1, e0) = e2
% 251.28/59.99 | |
% 251.28/59.99 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #909.
% 251.28/59.99 | |
% 251.28/59.99 | Case 2:
% 251.28/59.99 | |
% 251.28/59.99 | | (9) all_252_24 = e2 & op(e0, e0) = e2
% 251.28/59.99 | |
% 251.28/59.99 | | ALPHA: (9) implies:
% 251.28/59.99 | | (10) op(e0, e0) = e2
% 251.28/59.99 | |
% 251.28/59.99 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #978.
% 251.28/59.99 | |
% 251.28/59.99 | End of split
% 251.28/59.99 |
% 251.28/59.99 End of proof
% 251.28/59.99
% 251.28/59.99 Sub-proof #653 shows that the following formulas are inconsistent:
% 251.28/59.99 ----------------------------------------------------------------
% 251.28/59.99 (1) all_252_17 = e2 & op(e3, e0) = e2
% 251.28/59.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.99 (3) op(e3, e0) = all_48_2
% 251.28/59.99 (4) ~ (all_48_2 = e2)
% 251.28/59.99
% 251.28/59.99 Begin of proof
% 251.28/59.99 |
% 251.28/59.99 | ALPHA: (1) implies:
% 251.28/59.99 | (5) op(e3, e0) = e2
% 251.28/59.99 |
% 251.28/59.99 | GROUND_INST: instantiating (2) with all_48_2, e2, e0, e3, simplifying with
% 251.28/59.99 | (3), (5) gives:
% 251.28/59.99 | (6) all_48_2 = e2
% 251.28/59.99 |
% 251.28/59.99 | REDUCE: (4), (6) imply:
% 251.28/59.99 | (7) $false
% 251.28/59.99 |
% 251.28/59.99 | CLOSE: (7) is inconsistent.
% 251.28/59.99 |
% 251.28/59.99 End of proof
% 251.28/59.99
% 251.28/59.99 Sub-proof #654 shows that the following formulas are inconsistent:
% 251.28/59.99 ----------------------------------------------------------------
% 251.28/59.99 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/59.99 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/59.99 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/59.99 (2) all_32_2 = all_20_2
% 251.28/59.99 (3) ~ (all_26_2 = e2)
% 251.28/59.99 (4) ~ (all_4_2 = e4)
% 251.28/59.99 (5) all_250_9 = all_48_2
% 251.28/59.99 (6) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/59.99 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/59.99 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/59.99 (7) op(all_4_2, e2) = e1
% 251.28/59.99 (8) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/59.99 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/59.99 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/59.99 (9) ~ (all_244_24 = all_40_2)
% 251.28/59.99 (10) ~ (all_40_2 = all_38_2)
% 251.28/59.99 (11) op(all_6_2, e2) = e4
% 251.28/59.99 (12) ~ (all_48_2 = e2)
% 251.28/59.99 (13) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.28/59.99 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.28/59.99 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/59.99 (14) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/59.99 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/59.99 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/59.99 (15) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/59.99 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/59.99 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/59.99 (16) all_250_8 = all_36_2
% 251.28/59.99 (17) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.28/59.99 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.28/59.99 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.28/59.99 (18) op(e2, e0) = e4
% 251.28/59.99 (19) all_94_2 = all_38_2
% 251.28/59.99 (20) op(all_62_2, all_36_2) = e3
% 251.28/59.99 (21) op(all_38_2, e1) = e2
% 251.28/59.99 (22) all_250_13 = all_38_2
% 251.28/59.99 (23) ~ (e2 = e0)
% 251.28/59.99 (24) op(all_38_2, all_4_2) = e1
% 251.28/59.99 (25) ~ (e1 = e0)
% 251.28/59.99 (26) ~ (all_28_2 = e3)
% 251.28/59.99 (27) ~ (all_62_2 = all_22_2)
% 251.28/59.99 (28) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.28/59.99 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.28/59.99 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.28/59.99 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/59.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/59.99 (30) op(e2, e3) = all_10_2
% 251.28/59.99 (31) ~ (e3 = e2)
% 251.28/59.99 (32) op(e0, e0) = all_244_24
% 251.28/59.99 (33) ~ (all_12_2 = e3)
% 251.28/59.99 (34) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/59.99 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/59.99 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/59.99 (35) ~ (all_244_8 = all_64_2)
% 251.28/59.99 (36) op(e2, e2) = all_244_8
% 251.28/59.99 (37) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/59.99 all_250_11 = e0
% 251.28/59.99 (38) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/59.99 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/59.99 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/59.99 (39) op(e2, e1) = all_38_2
% 251.28/59.99 (40) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/59.99 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/59.99 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/59.99 (41) ~ (all_36_2 = all_20_2)
% 251.28/59.99 (42) ~ (all_64_2 = all_40_2)
% 251.28/59.99 (43) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 251.28/59.99 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 251.28/59.99 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 251.28/59.99 (44) ~ (all_84_2 = all_62_2)
% 251.28/59.99 (45) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/59.99 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/59.99 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/59.99 (46) ~ (all_48_2 = all_40_2)
% 251.28/59.99 (47) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/59.99 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/59.99 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/59.99 (48) all_168_2 = all_100_2
% 251.28/59.99 (49) op(e1, e0) = all_34_2
% 251.28/59.99 (50) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/59.99 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/59.99 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/59.99 (51) op(e4, e2) = all_6_2
% 251.28/59.99 (52) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/59.99 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/59.99 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/59.99 (53) all_78_2 = all_10_2
% 251.28/59.99 (54) ~ (all_20_2 = all_12_2)
% 251.28/59.99 (55) ~ (all_34_2 = e2)
% 251.28/59.99 (56) ~ (e2 = e1)
% 251.28/59.99 (57) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 |
% 251.28/59.99 all_250_9 = e0
% 251.28/59.99 (58) ~ (all_100_2 = all_64_2)
% 251.28/59.99 (59) all_56_2 = all_8_2
% 251.28/59.99 (60) op(e0, e2) = all_28_2
% 251.28/59.99 (61) ~ (e4 = e1)
% 251.28/59.99 (62) ~ (all_244_0 = e2)
% 251.28/59.99 (63) op(all_6_2, all_64_2) = e2
% 251.28/59.99 (64) ~ (all_64_2 = all_10_2)
% 251.28/59.99 (65) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/59.99 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/59.99 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/59.99 (66) ~ (all_244_8 = all_10_2)
% 251.28/59.99 (67) ~ (all_6_2 = e1)
% 251.28/59.99 (68) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/59.99 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/59.99 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/59.99 (69) all_106_2 = all_38_2
% 251.28/59.99 (70) all_252_16 = e2
% 251.28/59.99 (71) ~ (all_244_8 = all_38_2)
% 251.28/59.99 (72) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/59.99 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/59.99 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/59.99 (73) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) =
% 251.28/59.99 e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 251.28/59.99 e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/59.99 (74) op(all_244_15, all_244_15) = e1
% 251.28/59.99 (75) all_250_21 = all_22_2
% 251.28/59.99 (76) all_50_2 = all_4_2
% 251.28/59.99 (77) ~ (all_244_3 = all_84_2)
% 251.28/59.99 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/59.99 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/59.99 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/59.99 (79) op(e1, e4) = all_16_2
% 251.28/59.99 (80) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.28/59.99 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.28/59.99 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.28/59.99 (81) ~ (all_244_0 = all_64_2)
% 251.28/59.99 (82) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/59.99 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/59.99 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/59.99 (83) op(e1, e3) = all_62_2
% 251.28/59.99 (84) op(all_16_2, all_26_2) = e4
% 251.28/59.99 (85) ~ (e3 = e0)
% 251.28/59.99 (86) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.28/59.99 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.28/59.99 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.28/59.99 (87) op(e0, e2) = all_54_1
% 251.28/59.99 (88) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 251.28/59.99 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 251.28/59.99 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 251.28/59.99 (89) ~ (all_40_2 = all_10_2)
% 251.28/59.99 (90) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.28/59.99 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.28/59.99 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.28/60.00 (91) op(all_20_2, e1) = e0
% 251.28/60.00 (92) ~ (all_244_3 = all_10_2)
% 251.28/60.00 (93) ~ (all_48_2 = all_36_2)
% 251.28/60.00 (94) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 251.28/60.00 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 251.28/60.00 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.28/60.00 (95) all_70_2 = all_62_2
% 251.28/60.00 (96) ~ (e3 = e1)
% 251.28/60.00 (97) op(all_48_2, all_22_2) = e0
% 251.28/60.00 (98) op(e3, e1) = all_36_2
% 251.28/60.00 (99) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.28/60.00 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.28/60.00 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.28/60.00 (100) ~ (all_16_2 = e2)
% 251.28/60.00 (101) ~ (all_8_2 = e1)
% 251.28/60.00 (102) ~ (all_244_3 = all_62_2)
% 251.28/60.00 (103) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/60.00 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/60.00 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/60.00 (104) ~ (all_22_2 = e1)
% 251.28/60.00 (105) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/60.00 all_250_8 = e0
% 251.28/60.00 (106) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/60.00 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/60.00 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/60.00 (107) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 251.28/60.00 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 251.28/60.00 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/60.00 (108) ~ (all_40_2 = all_34_2)
% 251.28/60.00 (109) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.28/60.00 all_250_13 = e0
% 251.28/60.00 (110) ~ (all_244_15 = all_38_2)
% 251.28/60.00 (111) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/60.00 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/60.00 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/60.00 (112) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/60.00 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/60.00 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/60.00 (113) all_190_2 = all_38_2
% 251.28/60.00 (114) ~ (all_64_2 = all_12_2)
% 251.28/60.00 (115) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 251.28/60.00 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 251.28/60.00 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/60.00 (116) op(all_22_2, e3) = e0
% 251.28/60.00 (117) all_68_2 = all_22_2
% 251.28/60.00 (118) op(all_20_2, all_34_2) = e1
% 251.28/60.00 (119) op(e0, e3) = all_22_2
% 251.28/60.00 (120) ~ (all_28_2 = all_22_2)
% 251.28/60.00 (121) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.00 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/60.00 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/60.00 (122) all_58_2 = all_20_2
% 251.28/60.00 (123) op(all_62_2, e3) = e1
% 251.28/60.00 (124) op(e4, e1) = all_26_2
% 251.28/60.00 (125) ~ (all_40_2 = e2)
% 251.28/60.00 (126) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.28/60.00 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/60.00 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/60.00 (127) ~ (all_64_2 = all_38_2)
% 251.28/60.00 (128) op(all_10_2, e3) = e2
% 251.28/60.00 (129) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.28/60.00 all_250_21 = e0
% 251.28/60.00 (130) ~ (all_244_15 = all_62_2)
% 251.28/60.00 (131) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.28/60.00 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.28/60.00 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.28/60.00 (132) op(e3, e4) = all_100_2
% 251.28/60.00 (133) all_250_11 = all_10_2
% 251.28/60.00 (134) op(e4, e4) = all_244_0
% 251.28/60.00 (135) all_126_2 = all_48_2
% 251.28/60.00 (136) ~ (all_22_2 = all_12_2)
% 251.28/60.00 (137) all_230_2 = all_20_2
% 251.28/60.00 (138) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.28/60.00 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.00 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.28/60.00 (139) ~ (e4 = e3)
% 251.28/60.00 (140) op(e1, e1) = all_244_15
% 251.28/60.00 (141) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.00 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/60.00 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/60.00 (142) op(e0, e1) = all_20_2
% 251.28/60.00 (143) ~ (all_244_15 = all_20_2)
% 251.28/60.00 (144) op(e3, e0) = all_48_2
% 251.28/60.00 (145) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.28/60.00 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.28/60.00 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.28/60.00 (146) op(all_48_2, e0) = e3
% 251.28/60.00 (147) ~ (all_38_2 = all_36_2)
% 251.28/60.00 (148) ~ (all_26_2 = e3)
% 251.28/60.00 (149) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.28/60.00 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.28/60.00 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.28/60.00 (150) op(e1, e2) = all_4_2
% 251.28/60.00 (151) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.28/60.00 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.28/60.00 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.28/60.00 (152) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.28/60.00 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.28/60.00 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.28/60.00 (153) op(all_4_2, all_38_2) = e2
% 251.28/60.00 (154) op(e4, e3) = all_84_2
% 251.28/60.00 (155) ~ (all_62_2 = all_10_2)
% 251.28/60.00 (156) op(e2, e4) = all_64_2
% 251.28/60.00 (157) ~ (all_22_2 = all_10_2)
% 251.28/60.00 (158) ~ (all_38_2 = all_26_2)
% 251.28/60.00 (159) ~ (all_22_2 = all_20_2)
% 251.28/60.00 (160) op(e3, e2) = all_8_2
% 251.28/60.00 (161) ~ (all_64_2 = all_16_2)
% 251.28/60.00 (162) op(all_36_2, e1) = e3
% 251.28/60.00 (163) ~ (all_38_2 = all_20_2)
% 251.28/60.00 (164) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.28/60.00 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.28/60.00 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.28/60.00 (165) ~ (all_38_2 = all_10_2)
% 251.28/60.00 (166) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.28/60.00 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.28/60.00 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.28/60.00 (167) ~ (all_244_15 = all_36_2)
% 251.28/60.00 (168) ~ (all_20_2 = e4)
% 251.28/60.00 (169) ~ (all_244_24 = all_22_2)
% 251.28/60.00 (170) op(all_16_2, e4) = e1
% 251.28/60.00 (171) ~ (all_100_2 = all_16_2)
% 251.28/60.00 (172) op(e2, e0) = all_40_2
% 251.28/60.00 (173) op(all_8_2, e2) = e3
% 251.28/60.00 (174) ~ (all_244_8 = all_28_2)
% 251.28/60.00 (175) ~ (all_244_3 = all_48_2)
% 251.28/60.00 (176) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.00 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.00 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/60.00 (177) op(e3, e3) = all_244_3
% 251.28/60.00 (178) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.28/60.00 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.28/60.00 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.28/60.00 (179) ~ (all_26_2 = all_20_2)
% 251.28/60.00 (180) all_90_2 = all_22_2
% 251.28/60.00 (181) all_46_2 = all_36_2
% 251.28/60.00 (182) op(all_244_24, all_244_24) = e0
% 251.28/60.00 (183) op(e0, e4) = all_12_2
% 251.28/60.00 (184) op(all_22_2, all_48_2) = e3
% 251.28/60.00 (185) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.28/60.00 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.28/60.00 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.28/60.00 (186) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.28/60.00 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.28/60.00 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.28/60.00 (187) all_124_2 = all_10_2
% 251.28/60.00
% 251.28/60.00 Begin of proof
% 251.28/60.00 |
% 251.28/60.00 | GROUND_INST: instantiating (29) with all_28_2, all_54_1, e2, e0, simplifying
% 251.28/60.00 | with (60), (87) gives:
% 251.28/60.00 | (188) all_54_1 = all_28_2
% 251.28/60.00 |
% 251.28/60.00 | GROUND_INST: instantiating (29) with all_40_2, e4, e0, e2, simplifying with
% 251.28/60.00 | (18), (172) gives:
% 251.28/60.00 | (189) all_40_2 = e4
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (9), (189) imply:
% 251.28/60.00 | (190) ~ (all_244_24 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (42), (189) imply:
% 251.28/60.00 | (191) ~ (all_64_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (46), (189) imply:
% 251.28/60.00 | (192) ~ (all_48_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (10), (189) imply:
% 251.28/60.00 | (193) ~ (all_38_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | SIMP: (193) implies:
% 251.28/60.00 | (194) ~ (all_38_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (108), (189) imply:
% 251.28/60.00 | (195) ~ (all_34_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | SIMP: (195) implies:
% 251.28/60.00 | (196) ~ (all_34_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (89), (189) imply:
% 251.28/60.00 | (197) ~ (all_10_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | SIMP: (197) implies:
% 251.28/60.00 | (198) ~ (all_10_2 = e4)
% 251.28/60.00 |
% 251.28/60.00 | REDUCE: (125), (189) imply:
% 251.28/60.00 | (199) ~ (e4 = e2)
% 251.28/60.00 |
% 251.28/60.00 | BETA: splitting (94) gives:
% 251.28/60.00 |
% 251.28/60.00 | Case 1:
% 251.28/60.00 | |
% 251.28/60.00 | | (200) ~ (all_40_2 = e4)
% 251.28/60.00 | |
% 251.28/60.00 | | REF_CLOSE: (18), (29), (172), (200) are inconsistent by sub-proof #707.
% 251.28/60.00 | |
% 251.28/60.00 | Case 2:
% 251.28/60.00 | |
% 251.28/60.00 | | (201) ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4) =
% 251.28/60.00 | | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 251.28/60.00 | | op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.28/60.00 | |
% 251.28/60.00 | | BETA: splitting (73) gives:
% 251.28/60.00 | |
% 251.28/60.00 | | Case 1:
% 251.28/60.00 | | |
% 251.28/60.00 | | | (202) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3,
% 251.28/60.00 | | | e0) = e4)
% 251.28/60.00 | | |
% 251.28/60.00 | | | REF_CLOSE: (29), (70), (144), (192), (199), (202) are inconsistent by
% 251.28/60.00 | | | sub-proof #705.
% 251.28/60.00 | | |
% 251.28/60.00 | | Case 2:
% 251.28/60.00 | | |
% 251.28/60.00 | | | (203) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & op(e1,
% 251.28/60.00 | | | e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/60.00 | | |
% 251.28/60.00 | | | BETA: splitting (203) gives:
% 251.28/60.00 | | |
% 251.28/60.00 | | | Case 1:
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | (204) all_252_18 = e4 & op(e2, e0) = e4
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | ALPHA: (204) implies:
% 251.28/60.00 | | | | (205) all_252_18 = e4
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | BETA: splitting (201) gives:
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | Case 1:
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | (206) ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 & op(e0, e4)
% 251.28/60.00 | | | | | = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | ALPHA: (206) implies:
% 251.28/60.00 | | | | | (207) op(e0, e4) = all_40_1
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13),
% 251.28/60.00 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.28/60.00 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 251.28/60.00 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 251.28/60.00 | | | | | (45), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 251.28/60.00 | | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 251.28/60.00 | | | | | (66), (67), (68), (69), (70), (71), (72), (74), (75), (76),
% 251.28/60.00 | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 251.28/60.00 | | | | | (88), (90), (91), (92), (93), (95), (96), (97), (98), (99),
% 251.28/60.00 | | | | | (100), (101), (102), (103), (104), (105), (106), (107),
% 251.28/60.00 | | | | | (109), (110), (111), (112), (113), (114), (115), (116),
% 251.28/60.00 | | | | | (117), (118), (119), (120), (121), (122), (123), (124),
% 251.28/60.00 | | | | | (126), (127), (128), (129), (130), (131), (132), (133),
% 251.28/60.00 | | | | | (134), (135), (136), (137), (138), (139), (140), (141),
% 251.28/60.00 | | | | | (142), (143), (144), (145), (146), (147), (148), (149),
% 251.28/60.00 | | | | | (150), (151), (152), (153), (154), (155), (156), (157),
% 251.28/60.00 | | | | | (158), (159), (160), (161), (162), (163), (164), (165),
% 251.28/60.00 | | | | | (166), (167), (168), (169), (170), (171), (172), (173),
% 251.28/60.00 | | | | | (174), (175), (176), (177), (178), (179), (180), (181),
% 251.28/60.00 | | | | | (182), (183), (184), (185), (186), (187), (190), (191),
% 251.28/60.00 | | | | | (192), (194), (196), (198), (205), (207) are inconsistent
% 251.28/60.00 | | | | | by sub-proof #655.
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | Case 2:
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | (208) ~ (all_40_1 = e3) & op(e0, e4) = all_40_1 & $i(all_40_1)
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | ALPHA: (208) implies:
% 251.28/60.00 | | | | | (209) op(e0, e4) = all_40_1
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13),
% 251.28/60.00 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.28/60.00 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 251.28/60.00 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 251.28/60.00 | | | | | (45), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 251.28/60.00 | | | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 251.28/60.00 | | | | | (66), (67), (68), (69), (70), (71), (72), (74), (75), (76),
% 251.28/60.00 | | | | | (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 251.28/60.00 | | | | | (88), (90), (91), (92), (93), (95), (96), (97), (98), (99),
% 251.28/60.00 | | | | | (100), (101), (102), (103), (104), (105), (106), (107),
% 251.28/60.00 | | | | | (109), (110), (111), (112), (113), (114), (115), (116),
% 251.28/60.00 | | | | | (117), (118), (119), (120), (121), (122), (123), (124),
% 251.28/60.00 | | | | | (126), (127), (128), (129), (130), (131), (132), (133),
% 251.28/60.00 | | | | | (134), (135), (136), (137), (138), (139), (140), (141),
% 251.28/60.00 | | | | | (142), (143), (144), (145), (146), (147), (148), (149),
% 251.28/60.00 | | | | | (150), (151), (152), (153), (154), (155), (156), (157),
% 251.28/60.00 | | | | | (158), (159), (160), (161), (162), (163), (164), (165),
% 251.28/60.00 | | | | | (166), (167), (168), (169), (170), (171), (172), (173),
% 251.28/60.00 | | | | | (174), (175), (176), (177), (178), (179), (180), (181),
% 251.28/60.00 | | | | | (182), (183), (184), (185), (186), (187), (190), (191),
% 251.28/60.00 | | | | | (192), (194), (196), (198), (205), (209) are inconsistent
% 251.28/60.00 | | | | | by sub-proof #655.
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | End of split
% 251.28/60.00 | | | |
% 251.28/60.00 | | | Case 2:
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | (210) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & op(e0,
% 251.28/60.00 | | | | e0) = e4)
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | BETA: splitting (210) gives:
% 251.28/60.00 | | | |
% 251.28/60.00 | | | | Case 1:
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | (211) all_252_19 = e4 & op(e1, e0) = e4
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | REF_CLOSE: (29), (49), (196), (211) are inconsistent by sub-proof
% 251.28/60.00 | | | | | #677.
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | Case 2:
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | (212) all_252_24 = e4 & op(e0, e0) = e4
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | | REF_CLOSE: (29), (32), (190), (212) are inconsistent by sub-proof
% 251.28/60.00 | | | | | #679.
% 251.28/60.00 | | | | |
% 251.28/60.00 | | | | End of split
% 251.28/60.00 | | | |
% 251.28/60.00 | | | End of split
% 251.28/60.00 | | |
% 251.28/60.00 | | End of split
% 251.28/60.00 | |
% 251.28/60.00 | End of split
% 251.28/60.00 |
% 251.28/60.00 End of proof
% 251.28/60.00
% 251.28/60.00 Sub-proof #655 shows that the following formulas are inconsistent:
% 251.28/60.00 ----------------------------------------------------------------
% 251.28/60.00 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/60.00 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/60.00 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/60.00 (2) all_32_2 = all_20_2
% 251.28/60.00 (3) ~ (all_26_2 = e2)
% 251.28/60.00 (4) ~ (all_4_2 = e4)
% 251.28/60.00 (5) all_250_9 = all_48_2
% 251.28/60.00 (6) ~ (all_10_2 = e4)
% 251.28/60.00 (7) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.00 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/60.00 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/60.00 (8) op(all_4_2, e2) = e1
% 251.28/60.00 (9) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/60.00 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/60.00 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/60.00 (10) op(all_6_2, e2) = e4
% 251.28/60.00 (11) ~ (all_48_2 = e2)
% 251.28/60.00 (12) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.28/60.00 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.28/60.00 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/60.00 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.00 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.00 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.00 (14) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/60.00 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.00 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/60.00 (15) all_250_8 = all_36_2
% 251.28/60.00 (16) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.28/60.00 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.28/60.00 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.28/60.00 (17) op(e2, e0) = e4
% 251.28/60.00 (18) all_94_2 = all_38_2
% 251.28/60.00 (19) op(all_62_2, all_36_2) = e3
% 251.28/60.00 (20) op(all_38_2, e1) = e2
% 251.28/60.00 (21) all_250_13 = all_38_2
% 251.28/60.00 (22) ~ (e2 = e0)
% 251.28/60.00 (23) op(all_38_2, all_4_2) = e1
% 251.28/60.00 (24) ~ (e1 = e0)
% 251.28/60.00 (25) ~ (all_28_2 = e3)
% 251.28/60.00 (26) ~ (all_62_2 = all_22_2)
% 251.28/60.00 (27) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.28/60.00 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.28/60.00 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.28/60.00 (28) all_252_18 = e4
% 251.28/60.00 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/60.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/60.00 (30) op(e2, e3) = all_10_2
% 251.28/60.00 (31) ~ (e3 = e2)
% 251.28/60.00 (32) op(e0, e0) = all_244_24
% 251.28/60.00 (33) ~ (all_12_2 = e3)
% 251.28/60.00 (34) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/60.00 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/60.00 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/60.00 (35) ~ (all_244_8 = all_64_2)
% 251.28/60.00 (36) op(e2, e2) = all_244_8
% 251.28/60.00 (37) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/60.00 all_250_11 = e0
% 251.28/60.00 (38) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/60.00 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/60.00 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/60.00 (39) op(e2, e1) = all_38_2
% 251.28/60.00 (40) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/60.00 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/60.00 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/60.00 (41) ~ (all_36_2 = all_20_2)
% 251.28/60.00 (42) ~ (all_190_2 = e0) | ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 &
% 251.28/60.00 op(e0, all_190_1) = all_190_0 & $i(all_190_0) & $i(all_190_1)) | ( ~
% 251.28/60.00 (all_190_1 = e4) & op(e1, e0) = all_190_1 & $i(all_190_1))
% 251.28/60.00 (43) ~ (all_84_2 = all_62_2)
% 251.28/60.00 (44) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/60.00 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/60.00 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/60.00 (45) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/60.00 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/60.00 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/60.00 (46) all_168_2 = all_100_2
% 251.28/60.00 (47) op(e1, e0) = all_34_2
% 251.28/60.00 (48) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/60.00 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/60.00 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/60.00 (49) op(e4, e2) = all_6_2
% 251.28/60.00 (50) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/60.00 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/60.00 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/60.00 (51) all_78_2 = all_10_2
% 251.28/60.00 (52) ~ (all_20_2 = all_12_2)
% 251.28/60.00 (53) ~ (all_34_2 = e2)
% 251.28/60.00 (54) ~ (e2 = e1)
% 251.28/60.00 (55) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 |
% 251.28/60.00 all_250_9 = e0
% 251.28/60.00 (56) ~ (all_100_2 = all_64_2)
% 251.28/60.00 (57) all_56_2 = all_8_2
% 251.28/60.00 (58) ~ (all_34_2 = e4)
% 251.28/60.00 (59) op(e0, e2) = all_28_2
% 251.28/60.00 (60) ~ (e4 = e1)
% 251.28/60.00 (61) ~ (all_244_0 = e2)
% 251.28/60.00 (62) op(all_6_2, all_64_2) = e2
% 251.28/60.00 (63) ~ (all_64_2 = all_10_2)
% 251.28/60.00 (64) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/60.00 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/60.00 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/60.00 (65) ~ (all_244_8 = all_10_2)
% 251.28/60.00 (66) ~ (all_6_2 = e1)
% 251.28/60.00 (67) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/60.00 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/60.00 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/60.00 (68) all_106_2 = all_38_2
% 251.28/60.00 (69) all_252_16 = e2
% 251.28/60.00 (70) ~ (all_244_8 = all_38_2)
% 251.28/60.00 (71) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/60.00 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/60.00 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/60.00 (72) op(all_244_15, all_244_15) = e1
% 251.28/60.00 (73) all_250_21 = all_22_2
% 251.28/60.00 (74) all_50_2 = all_4_2
% 251.28/60.00 (75) ~ (all_244_3 = all_84_2)
% 251.28/60.00 (76) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/60.00 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/60.00 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/60.00 (77) op(e1, e4) = all_16_2
% 251.28/60.00 (78) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.28/60.00 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.28/60.00 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.28/60.00 (79) ~ (all_244_0 = all_64_2)
% 251.28/60.00 (80) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/60.00 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/60.00 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/60.00 (81) op(e1, e3) = all_62_2
% 251.28/60.00 (82) op(all_16_2, all_26_2) = e4
% 251.28/60.00 (83) ~ (e3 = e0)
% 251.28/60.01 (84) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 &
% 251.28/60.01 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 251.28/60.01 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.28/60.01 (85) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 251.28/60.01 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 251.28/60.01 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 251.28/60.01 (86) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.28/60.01 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.28/60.01 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.28/60.01 (87) op(all_20_2, e1) = e0
% 251.28/60.01 (88) ~ (all_244_3 = all_10_2)
% 251.28/60.01 (89) ~ (all_48_2 = all_36_2)
% 251.28/60.01 (90) all_70_2 = all_62_2
% 251.28/60.01 (91) ~ (e3 = e1)
% 251.28/60.01 (92) op(all_48_2, all_22_2) = e0
% 251.28/60.01 (93) op(e3, e1) = all_36_2
% 251.28/60.01 (94) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.28/60.01 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.28/60.01 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.28/60.01 (95) ~ (all_16_2 = e2)
% 251.28/60.01 (96) ~ (all_8_2 = e1)
% 251.28/60.01 (97) ~ (all_244_3 = all_62_2)
% 251.28/60.01 (98) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/60.01 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/60.01 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/60.01 (99) ~ (all_22_2 = e1)
% 251.28/60.01 (100) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/60.01 all_250_8 = e0
% 251.28/60.01 (101) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/60.01 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/60.01 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/60.01 (102) ~ (all_46_2 = e2) | ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0
% 251.28/60.01 & op(e1, e2) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 251.28/60.01 (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/60.01 (103) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.28/60.01 all_250_13 = e0
% 251.28/60.01 (104) ~ (all_244_15 = all_38_2)
% 251.28/60.01 (105) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/60.01 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/60.01 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/60.01 (106) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/60.01 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/60.01 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/60.01 (107) ~ (all_38_2 = e4)
% 251.28/60.01 (108) all_190_2 = all_38_2
% 251.28/60.01 (109) ~ (all_64_2 = all_12_2)
% 251.28/60.01 (110) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0
% 251.28/60.01 & op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~
% 251.28/60.01 (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/60.01 (111) op(all_22_2, e3) = e0
% 251.28/60.01 (112) all_68_2 = all_22_2
% 251.28/60.01 (113) op(all_20_2, all_34_2) = e1
% 251.28/60.01 (114) op(e0, e3) = all_22_2
% 251.28/60.01 (115) ~ (all_244_24 = e4)
% 251.28/60.01 (116) ~ (all_28_2 = all_22_2)
% 251.28/60.01 (117) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.01 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/60.01 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/60.01 (118) all_58_2 = all_20_2
% 251.28/60.01 (119) op(all_62_2, e3) = e1
% 251.28/60.01 (120) op(e4, e1) = all_26_2
% 251.28/60.01 (121) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.28/60.01 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/60.01 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.28/60.01 (122) ~ (all_64_2 = all_38_2)
% 251.28/60.01 (123) op(all_10_2, e3) = e2
% 251.28/60.01 (124) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.28/60.01 all_250_21 = e0
% 251.28/60.01 (125) ~ (all_244_15 = all_62_2)
% 251.28/60.01 (126) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.28/60.01 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.28/60.01 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.28/60.01 (127) op(e3, e4) = all_100_2
% 251.28/60.01 (128) all_250_11 = all_10_2
% 251.28/60.01 (129) op(e4, e4) = all_244_0
% 251.28/60.01 (130) all_126_2 = all_48_2
% 251.28/60.01 (131) ~ (all_22_2 = all_12_2)
% 251.28/60.01 (132) all_230_2 = all_20_2
% 251.28/60.01 (133) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.28/60.01 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.01 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.28/60.01 (134) ~ (all_48_2 = e4)
% 251.28/60.01 (135) ~ (e4 = e3)
% 251.28/60.01 (136) op(e1, e1) = all_244_15
% 251.28/60.01 (137) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.01 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/60.01 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/60.01 (138) op(e0, e1) = all_20_2
% 251.28/60.01 (139) ~ (all_244_15 = all_20_2)
% 251.28/60.01 (140) op(e3, e0) = all_48_2
% 251.28/60.01 (141) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.28/60.01 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.28/60.01 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.28/60.01 (142) op(all_48_2, e0) = e3
% 251.28/60.01 (143) ~ (all_38_2 = all_36_2)
% 251.28/60.01 (144) ~ (all_26_2 = e3)
% 251.28/60.01 (145) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.28/60.01 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.28/60.01 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.28/60.01 (146) op(e1, e2) = all_4_2
% 251.28/60.01 (147) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.28/60.01 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.28/60.01 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.28/60.01 (148) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.28/60.01 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.28/60.01 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.28/60.01 (149) op(all_4_2, all_38_2) = e2
% 251.28/60.01 (150) op(e4, e3) = all_84_2
% 251.28/60.01 (151) ~ (all_62_2 = all_10_2)
% 251.28/60.01 (152) op(e2, e4) = all_64_2
% 251.28/60.01 (153) ~ (all_22_2 = all_10_2)
% 251.28/60.01 (154) ~ (all_38_2 = all_26_2)
% 251.28/60.01 (155) ~ (all_22_2 = all_20_2)
% 251.28/60.01 (156) op(e3, e2) = all_8_2
% 251.28/60.01 (157) ~ (all_64_2 = all_16_2)
% 251.28/60.01 (158) op(all_36_2, e1) = e3
% 251.28/60.01 (159) ~ (all_38_2 = all_20_2)
% 251.28/60.01 (160) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.28/60.01 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.28/60.01 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.28/60.01 (161) ~ (all_38_2 = all_10_2)
% 251.28/60.01 (162) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.28/60.01 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.28/60.01 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.28/60.01 (163) ~ (all_244_15 = all_36_2)
% 251.28/60.01 (164) ~ (all_20_2 = e4)
% 251.28/60.01 (165) ~ (all_244_24 = all_22_2)
% 251.28/60.01 (166) op(all_16_2, e4) = e1
% 251.28/60.01 (167) ~ (all_100_2 = all_16_2)
% 251.28/60.01 (168) op(e2, e0) = all_40_2
% 251.28/60.01 (169) op(e0, e4) = all_40_1
% 251.28/60.01 (170) op(all_8_2, e2) = e3
% 251.28/60.01 (171) ~ (all_244_8 = all_28_2)
% 251.28/60.01 (172) ~ (all_244_3 = all_48_2)
% 251.28/60.01 (173) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.01 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.01 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/60.01 (174) op(e3, e3) = all_244_3
% 251.28/60.01 (175) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.28/60.01 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.28/60.01 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.28/60.01 (176) ~ (all_26_2 = all_20_2)
% 251.28/60.01 (177) all_90_2 = all_22_2
% 251.28/60.01 (178) all_46_2 = all_36_2
% 251.28/60.01 (179) ~ (all_64_2 = e4)
% 251.28/60.01 (180) op(all_244_24, all_244_24) = e0
% 251.28/60.01 (181) op(e0, e4) = all_12_2
% 251.28/60.01 (182) op(all_22_2, all_48_2) = e3
% 251.28/60.01 (183) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.28/60.01 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.28/60.01 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.28/60.01 (184) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.28/60.01 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.28/60.01 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.28/60.01 (185) all_124_2 = all_10_2
% 251.28/60.01
% 251.28/60.01 Begin of proof
% 251.28/60.01 |
% 251.28/60.01 | GROUND_INST: instantiating (29) with all_12_2, all_40_1, e4, e0, simplifying
% 251.28/60.01 | with (169), (181) gives:
% 251.28/60.01 | (186) all_40_1 = all_12_2
% 251.28/60.01 |
% 251.28/60.01 | BETA: splitting (84) gives:
% 251.28/60.01 |
% 251.28/60.01 | Case 1:
% 251.28/60.01 | |
% 251.28/60.01 | | (187) ~ (all_32_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (2), (187) imply:
% 251.28/60.01 | | (188) ~ (all_20_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | BETA: splitting (102) gives:
% 251.28/60.01 | |
% 251.28/60.01 | | Case 1:
% 251.28/60.01 | | |
% 251.28/60.01 | | | (189) ~ (all_46_2 = e2)
% 251.28/60.01 | | |
% 251.28/60.01 | | | REDUCE: (178), (189) imply:
% 251.28/60.01 | | | (190) ~ (all_36_2 = e2)
% 251.28/60.01 | | |
% 251.28/60.01 | | | BETA: splitting (110) gives:
% 251.28/60.01 | | |
% 251.28/60.01 | | | Case 1:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | (191) ~ (all_48_2 = e1)
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | BETA: splitting (86) gives:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | Case 1:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | (192) ~ (all_58_2 = e3)
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | REF_CLOSE: (3), (6), (8), (18), (20), (21), (25), (27), (29), (30),
% 251.28/60.01 | | | | | (31), (32), (33), (36), (37), (39), (44), (51), (59), (68),
% 251.28/60.01 | | | | | (70), (72), (73), (75), (78), (80), (81), (88), (90), (92),
% 251.28/60.01 | | | | | (93), (94), (99), (103), (105), (107), (111), (112), (114),
% 251.28/60.01 | | | | | (116), (118), (119), (120), (121), (123), (124), (125),
% 251.28/60.01 | | | | | (126), (128), (131), (133), (135), (136), (138), (142),
% 251.28/60.01 | | | | | (149), (150), (151), (153), (155), (161), (165), (174),
% 251.28/60.01 | | | | | (177), (180), (181), (183), (185), (188), (190), (192) are
% 251.28/60.01 | | | | | inconsistent by sub-proof #960.
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | Case 2:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | (193) all_58_2 = e3
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | COMBINE_EQS: (118), (193) imply:
% 251.28/60.01 | | | | | (194) all_20_2 = e3
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | REDUCE: (87), (194) imply:
% 251.28/60.01 | | | | | (195) op(e3, e1) = e0
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | GROUND_INST: instantiating (29) with all_36_2, e0, e1, e3, simplifying
% 251.28/60.01 | | | | | with (93), (195) gives:
% 251.28/60.01 | | | | | (196) all_36_2 = e0
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | REDUCE: (89), (196) imply:
% 251.28/60.01 | | | | | (197) ~ (all_48_2 = e0)
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | BETA: splitting (55) gives:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | Case 1:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | (198) all_250_9 = e4
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | COMBINE_EQS: (5), (198) imply:
% 251.28/60.01 | | | | | | (199) all_48_2 = e4
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | SIMP: (199) implies:
% 251.28/60.01 | | | | | | (200) all_48_2 = e4
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | REDUCE: (134), (200) imply:
% 251.28/60.01 | | | | | | (201) $false
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | CLOSE: (201) is inconsistent.
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | Case 2:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | (202) all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 |
% 251.28/60.01 | | | | | | all_250_9 = e0
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | BETA: splitting (202) gives:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | Case 1:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | (203) all_250_9 = e3
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | COMBINE_EQS: (5), (203) imply:
% 251.28/60.01 | | | | | | | (204) all_48_2 = e3
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | SIMP: (204) implies:
% 251.28/60.01 | | | | | | | (205) all_48_2 = e3
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (182), (205) imply:
% 251.28/60.01 | | | | | | | (206) op(all_22_2, e3) = e3
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | GROUND_INST: instantiating (29) with e0, e3, e3, all_22_2,
% 251.28/60.01 | | | | | | | simplifying with (111), (206) gives:
% 251.28/60.01 | | | | | | | (207) e3 = e0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (83), (207) imply:
% 251.28/60.01 | | | | | | | (208) $false
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | CLOSE: (208) is inconsistent.
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | Case 2:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | (209) all_250_9 = e2 | all_250_9 = e1 | all_250_9 = e0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | BETA: splitting (209) gives:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | Case 1:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | (210) all_250_9 = e2
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | COMBINE_EQS: (5), (210) imply:
% 251.28/60.01 | | | | | | | | (211) all_48_2 = e2
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | REDUCE: (11), (211) imply:
% 251.28/60.01 | | | | | | | | (212) $false
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | CLOSE: (212) is inconsistent.
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | Case 2:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | (213) all_250_9 = e1 | all_250_9 = e0
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | BETA: splitting (213) gives:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | Case 1:
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | (214) all_250_9 = e1
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | COMBINE_EQS: (5), (214) imply:
% 251.28/60.01 | | | | | | | | | (215) all_48_2 = e1
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | REDUCE: (191), (215) imply:
% 251.28/60.01 | | | | | | | | | (216) $false
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | CLOSE: (216) is inconsistent.
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | Case 2:
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | (217) all_250_9 = e0
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | COMBINE_EQS: (5), (217) imply:
% 251.28/60.01 | | | | | | | | | (218) all_48_2 = e0
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | REDUCE: (197), (218) imply:
% 251.28/60.01 | | | | | | | | | (219) $false
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | CLOSE: (219) is inconsistent.
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | End of split
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | End of split
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | End of split
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | End of split
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | End of split
% 251.28/60.01 | | | |
% 251.28/60.01 | | | Case 2:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | (220) all_48_2 = e1
% 251.28/60.01 | | | | (221) ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 & op(e0, e1)
% 251.28/60.01 | | | | = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.28/60.01 | | | | e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | REF_CLOSE: (3), (6), (8), (18), (20), (21), (25), (27), (29), (30),
% 251.28/60.01 | | | | (32), (33), (36), (37), (39), (44), (47), (51), (53), (59),
% 251.28/60.01 | | | | (68), (70), (72), (73), (75), (78), (80), (81), (86), (88),
% 251.28/60.01 | | | | (90), (92), (93), (94), (99), (103), (105), (107), (111),
% 251.28/60.01 | | | | (112), (113), (114), (116), (118), (119), (120), (121),
% 251.28/60.01 | | | | (123), (124), (125), (126), (128), (130), (131), (133),
% 251.28/60.01 | | | | (135), (136), (138), (142), (145), (149), (150), (151),
% 251.28/60.01 | | | | (153), (155), (161), (165), (172), (174), (177), (180),
% 251.28/60.01 | | | | (181), (183), (185), (188), (190), (220), (221) are
% 251.28/60.01 | | | | inconsistent by sub-proof #799.
% 251.28/60.01 | | | |
% 251.28/60.01 | | | End of split
% 251.28/60.01 | | |
% 251.28/60.01 | | Case 2:
% 251.28/60.01 | | |
% 251.28/60.01 | | | (222) all_46_2 = e2
% 251.28/60.01 | | | (223) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.28/60.01 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) &
% 251.28/60.01 | | | op(e1, e2) = all_46_1 & $i(all_46_1))
% 251.28/60.01 | | |
% 251.28/60.01 | | | COMBINE_EQS: (178), (222) imply:
% 251.28/60.01 | | | (224) all_36_2 = e2
% 251.28/60.01 | | |
% 251.28/60.01 | | | SIMP: (224) implies:
% 251.28/60.01 | | | (225) all_36_2 = e2
% 251.28/60.01 | | |
% 251.28/60.01 | | | REF_CLOSE: (19), (23), (29), (36), (39), (47), (53), (70), (77), (81),
% 251.28/60.01 | | | (90), (95), (96), (105), (136), (146), (156), (158), (163),
% 251.28/60.01 | | | (173), (223), (225) are inconsistent by sub-proof #796.
% 251.28/60.01 | | |
% 251.28/60.01 | | End of split
% 251.28/60.01 | |
% 251.28/60.01 | Case 2:
% 251.28/60.01 | |
% 251.28/60.01 | | (226) all_32_2 = e2
% 251.28/60.01 | | (227) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) =
% 251.28/60.01 | | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 251.28/60.01 | | op(e1, e2) = all_32_1 & $i(all_32_1))
% 251.28/60.01 | |
% 251.28/60.01 | | COMBINE_EQS: (2), (226) imply:
% 251.28/60.01 | | (228) all_20_2 = e2
% 251.28/60.01 | |
% 251.28/60.01 | | SIMP: (228) implies:
% 251.28/60.01 | | (229) all_20_2 = e2
% 251.28/60.01 | |
% 251.28/60.01 | | COMBINE_EQS: (132), (229) imply:
% 251.28/60.01 | | (230) all_230_2 = e2
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (139), (229) imply:
% 251.28/60.01 | | (231) ~ (all_244_15 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (159), (229) imply:
% 251.28/60.01 | | (232) ~ (all_38_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (41), (229) imply:
% 251.28/60.01 | | (233) ~ (all_36_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (52), (229) imply:
% 251.28/60.01 | | (234) ~ (all_12_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | SIMP: (234) implies:
% 251.28/60.01 | | (235) ~ (all_12_2 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (164), (229) imply:
% 251.28/60.01 | | (236) ~ (e4 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | SIMP: (236) implies:
% 251.28/60.01 | | (237) ~ (e4 = e2)
% 251.28/60.01 | |
% 251.28/60.01 | | REDUCE: (87), (229) imply:
% 251.28/60.01 | | (238) op(e2, e1) = e0
% 251.28/60.01 | |
% 251.28/60.01 | | BETA: splitting (133) gives:
% 251.28/60.01 | |
% 251.28/60.01 | | Case 1:
% 251.28/60.01 | | |
% 251.28/60.01 | | | (239) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3,
% 251.28/60.01 | | | e1) = e2)
% 251.28/60.01 | | |
% 251.28/60.01 | | | REF_CLOSE: (3), (29), (93), (120), (233), (239) are inconsistent by
% 251.28/60.01 | | | sub-proof #969.
% 251.28/60.01 | | |
% 251.28/60.01 | | Case 2:
% 251.28/60.01 | | |
% 251.28/60.01 | | | (240) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.01 | | | e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.28/60.01 | | |
% 251.28/60.01 | | | BETA: splitting (240) gives:
% 251.28/60.01 | | |
% 251.28/60.01 | | | Case 1:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | (241) all_252_11 = e2 & op(e2, e1) = e2
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | REF_CLOSE: (22), (29), (39), (238), (241) are inconsistent by sub-proof
% 251.28/60.01 | | | | #722.
% 251.28/60.01 | | | |
% 251.28/60.01 | | | Case 2:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | (242) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0,
% 251.28/60.01 | | | | e1) = e2)
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | BETA: splitting (242) gives:
% 251.28/60.01 | | | |
% 251.28/60.01 | | | | Case 1:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | (243) all_252_15 = e2 & op(e1, e1) = e2
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | REF_CLOSE: (29), (136), (231), (243) are inconsistent by sub-proof
% 251.28/60.01 | | | | | #966.
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | Case 2:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | (244) all_252_23 = e2 & op(e0, e1) = e2
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | ALPHA: (244) implies:
% 251.28/60.01 | | | | | (245) all_252_23 = e2
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | BETA: splitting (85) gives:
% 251.28/60.01 | | | | |
% 251.28/60.01 | | | | | Case 1:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | (246) ~ (all_230_2 = e2)
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | REDUCE: (230), (246) imply:
% 251.28/60.01 | | | | | | (247) $false
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | CLOSE: (247) is inconsistent.
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | Case 2:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | (248) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 &
% 251.28/60.01 | | | | | | op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 251.28/60.01 | | | | | | ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 &
% 251.28/60.01 | | | | | | $i(all_230_1))
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | BETA: splitting (248) gives:
% 251.28/60.01 | | | | | |
% 251.28/60.01 | | | | | | Case 1:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | (249) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 &
% 251.28/60.01 | | | | | | | op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | ALPHA: (249) implies:
% 251.28/60.01 | | | | | | | (250) op(e1, e2) = all_230_1
% 251.28/60.01 | | | | | | | (251) op(e2, all_230_1) = all_230_0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | GROUND_INST: instantiating (29) with all_4_2, all_230_1, e2, e1,
% 251.28/60.01 | | | | | | | simplifying with (146), (250) gives:
% 251.28/60.01 | | | | | | | (252) all_230_1 = all_4_2
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | GROUND_INST: instantiating (29) with all_38_2, e0, e1, e2,
% 251.28/60.01 | | | | | | | simplifying with (39), (238) gives:
% 251.28/60.01 | | | | | | | (253) all_38_2 = e0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | COMBINE_EQS: (108), (253) imply:
% 251.28/60.01 | | | | | | | (254) all_190_2 = e0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (70), (253) imply:
% 251.28/60.01 | | | | | | | (255) ~ (all_244_8 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (104), (253) imply:
% 251.28/60.01 | | | | | | | (256) ~ (all_244_15 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (122), (253) imply:
% 251.28/60.01 | | | | | | | (257) ~ (all_64_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (143), (253) imply:
% 251.28/60.01 | | | | | | | (258) ~ (all_36_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | SIMP: (258) implies:
% 251.28/60.01 | | | | | | | (259) ~ (all_36_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (154), (253) imply:
% 251.28/60.01 | | | | | | | (260) ~ (all_26_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | SIMP: (260) implies:
% 251.28/60.01 | | | | | | | (261) ~ (all_26_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (161), (253) imply:
% 251.28/60.01 | | | | | | | (262) ~ (all_10_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | SIMP: (262) implies:
% 251.28/60.01 | | | | | | | (263) ~ (all_10_2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (107), (253) imply:
% 251.28/60.01 | | | | | | | (264) ~ (e4 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | SIMP: (264) implies:
% 251.28/60.01 | | | | | | | (265) ~ (e4 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (232), (253) imply:
% 251.28/60.01 | | | | | | | (266) ~ (e2 = e0)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (23), (253) imply:
% 251.28/60.01 | | | | | | | (267) op(e0, all_4_2) = e1
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | REDUCE: (251), (252) imply:
% 251.28/60.01 | | | | | | | (268) op(e2, all_4_2) = all_230_0
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | BETA: splitting (42) gives:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | Case 1:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | (269) ~ (all_190_2 = e0)
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | REDUCE: (254), (269) imply:
% 251.28/60.01 | | | | | | | | (270) $false
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | CLOSE: (270) is inconsistent.
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | Case 2:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | (271) ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 251.28/60.01 | | | | | | | | all_190_1) = all_190_0 & $i(all_190_0) &
% 251.28/60.01 | | | | | | | | $i(all_190_1)) | ( ~ (all_190_1 = e4) & op(e1, e0) =
% 251.28/60.01 | | | | | | | | all_190_1 & $i(all_190_1))
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | BETA: splitting (271) gives:
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | | Case 1:
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | (272) ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 251.28/60.01 | | | | | | | | | all_190_1) = all_190_0 & $i(all_190_0) &
% 251.28/60.01 | | | | | | | | | $i(all_190_1)
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | ALPHA: (272) implies:
% 251.28/60.01 | | | | | | | | | (273) op(e1, e0) = all_190_1
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13),
% 251.28/60.01 | | | | | | | | | (14), (15), (16), (17), (19), (22), (24), (25),
% 251.28/60.01 | | | | | | | | | (26), (28), (29), (30), (31), (32), (34), (35),
% 251.28/60.01 | | | | | | | | | (36), (37), (38), (39), (40), (43), (44), (45),
% 251.28/60.01 | | | | | | | | | (46), (47), (48), (49), (50), (53), (54), (56),
% 251.28/60.01 | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 251.28/60.01 | | | | | | | | | (65), (66), (67), (69), (71), (74), (75), (76),
% 251.28/60.01 | | | | | | | | | (77), (79), (80), (81), (82), (83), (89), (90),
% 251.28/60.01 | | | | | | | | | (91), (93), (95), (96), (97), (98), (99), (100),
% 251.28/60.01 | | | | | | | | | (101), (105), (106), (107), (109), (110), (111),
% 251.28/60.01 | | | | | | | | | (112), (114), (115), (117), (119), (120), (123),
% 251.28/60.01 | | | | | | | | | (125), (127), (128), (129), (134), (135), (136),
% 251.28/60.01 | | | | | | | | | (137), (138), (140), (141), (144), (146), (147),
% 251.28/60.01 | | | | | | | | | (148), (150), (151), (152), (153), (156), (157),
% 251.28/60.01 | | | | | | | | | (158), (160), (162), (164), (166), (167), (168),
% 251.28/60.01 | | | | | | | | | (169), (170), (171), (173), (174), (175), (179),
% 251.28/60.01 | | | | | | | | | (180), (181), (184), (227), (231), (233), (235),
% 251.28/60.01 | | | | | | | | | (237), (245), (255), (256), (257), (259), (261),
% 251.28/60.01 | | | | | | | | | (263), (265), (267), (268), (273) are inconsistent
% 251.28/60.01 | | | | | | | | | by sub-proof #657.
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | Case 2:
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | (274) ~ (all_190_1 = e4) & op(e1, e0) = all_190_1 &
% 251.28/60.01 | | | | | | | | | $i(all_190_1)
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | ALPHA: (274) implies:
% 251.28/60.01 | | | | | | | | | (275) op(e1, e0) = all_190_1
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13),
% 251.28/60.01 | | | | | | | | | (14), (15), (16), (17), (19), (22), (24), (25),
% 251.28/60.01 | | | | | | | | | (26), (28), (29), (30), (31), (32), (34), (35),
% 251.28/60.01 | | | | | | | | | (36), (37), (38), (39), (40), (43), (44), (45),
% 251.28/60.01 | | | | | | | | | (46), (47), (48), (49), (50), (53), (54), (56),
% 251.28/60.01 | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 251.28/60.01 | | | | | | | | | (65), (66), (67), (69), (71), (74), (75), (76),
% 251.28/60.01 | | | | | | | | | (77), (79), (80), (81), (82), (83), (89), (90),
% 251.28/60.01 | | | | | | | | | (91), (93), (95), (96), (97), (98), (99), (100),
% 251.28/60.01 | | | | | | | | | (101), (105), (106), (107), (109), (110), (111),
% 251.28/60.01 | | | | | | | | | (112), (114), (115), (117), (119), (120), (123),
% 251.28/60.01 | | | | | | | | | (125), (127), (128), (129), (134), (135), (136),
% 251.28/60.01 | | | | | | | | | (137), (138), (140), (141), (144), (146), (147),
% 251.28/60.01 | | | | | | | | | (148), (150), (151), (152), (153), (156), (157),
% 251.28/60.01 | | | | | | | | | (158), (160), (162), (164), (166), (167), (168),
% 251.28/60.01 | | | | | | | | | (169), (170), (171), (173), (174), (175), (179),
% 251.28/60.01 | | | | | | | | | (180), (181), (184), (227), (231), (233), (235),
% 251.28/60.01 | | | | | | | | | (237), (245), (255), (256), (257), (259), (261),
% 251.28/60.01 | | | | | | | | | (263), (265), (267), (268), (275) are inconsistent
% 251.28/60.01 | | | | | | | | | by sub-proof #657.
% 251.28/60.01 | | | | | | | | |
% 251.28/60.01 | | | | | | | | End of split
% 251.28/60.01 | | | | | | | |
% 251.28/60.01 | | | | | | | End of split
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | Case 2:
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | (276) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 &
% 251.28/60.01 | | | | | | | $i(all_230_1)
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | ALPHA: (276) implies:
% 251.28/60.01 | | | | | | | (277) ~ (all_230_1 = e4)
% 251.28/60.01 | | | | | | | (278) op(e1, e2) = all_230_1
% 251.28/60.01 | | | | | | |
% 251.28/60.01 | | | | | | | GROUND_INST: instantiating (29) with all_4_2, all_230_1, e2, e1,
% 251.28/60.01 | | | | | | | simplifying with (146), (278) gives:
% 251.28/60.01 | | | | | | | (279) all_230_1 = all_4_2
% 251.28/60.01 | | | | | | |
% 251.28/60.02 | | | | | | | GROUND_INST: instantiating (29) with all_38_2, e0, e1, e2,
% 251.28/60.02 | | | | | | | simplifying with (39), (238) gives:
% 251.28/60.02 | | | | | | | (280) all_38_2 = e0
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | COMBINE_EQS: (108), (280) imply:
% 251.28/60.02 | | | | | | | (281) all_190_2 = e0
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (70), (280) imply:
% 251.28/60.02 | | | | | | | (282) ~ (all_244_8 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (104), (280) imply:
% 251.28/60.02 | | | | | | | (283) ~ (all_244_15 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (122), (280) imply:
% 251.28/60.02 | | | | | | | (284) ~ (all_64_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (143), (280) imply:
% 251.28/60.02 | | | | | | | (285) ~ (all_36_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | SIMP: (285) implies:
% 251.28/60.02 | | | | | | | (286) ~ (all_36_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (154), (280) imply:
% 251.28/60.02 | | | | | | | (287) ~ (all_26_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | SIMP: (287) implies:
% 251.28/60.02 | | | | | | | (288) ~ (all_26_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (161), (280) imply:
% 251.28/60.02 | | | | | | | (289) ~ (all_10_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | SIMP: (289) implies:
% 251.28/60.02 | | | | | | | (290) ~ (all_10_2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (107), (280) imply:
% 251.28/60.02 | | | | | | | (291) ~ (e4 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | SIMP: (291) implies:
% 251.28/60.02 | | | | | | | (292) ~ (e4 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (232), (280) imply:
% 251.28/60.02 | | | | | | | (293) ~ (e2 = e0)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (23), (280) imply:
% 251.28/60.02 | | | | | | | (294) op(e0, all_4_2) = e1
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | BETA: splitting (42) gives:
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | Case 1:
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | (295) ~ (all_190_2 = e0)
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | REDUCE: (281), (295) imply:
% 251.28/60.02 | | | | | | | | (296) $false
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | CLOSE: (296) is inconsistent.
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | Case 2:
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | (297) ( ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 251.28/60.02 | | | | | | | | all_190_1) = all_190_0 & $i(all_190_0) &
% 251.28/60.02 | | | | | | | | $i(all_190_1)) | ( ~ (all_190_1 = e4) & op(e1, e0) =
% 251.28/60.02 | | | | | | | | all_190_1 & $i(all_190_1))
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | BETA: splitting (297) gives:
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | Case 1:
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | (298) ~ (all_190_0 = e3) & op(e1, e0) = all_190_1 & op(e0,
% 251.28/60.02 | | | | | | | | | all_190_1) = all_190_0 & $i(all_190_0) &
% 251.28/60.02 | | | | | | | | | $i(all_190_1)
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | ALPHA: (298) implies:
% 251.28/60.02 | | | | | | | | | (299) op(e1, e0) = all_190_1
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13),
% 251.28/60.02 | | | | | | | | | (14), (15), (16), (17), (19), (22), (24), (25),
% 251.28/60.02 | | | | | | | | | (26), (28), (29), (30), (31), (32), (34), (35),
% 251.28/60.02 | | | | | | | | | (36), (37), (38), (39), (40), (43), (44), (45),
% 251.28/60.02 | | | | | | | | | (46), (47), (48), (49), (50), (53), (54), (56),
% 251.28/60.02 | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 251.28/60.02 | | | | | | | | | (65), (66), (67), (69), (71), (74), (75), (76),
% 251.28/60.02 | | | | | | | | | (77), (79), (80), (81), (82), (83), (89), (90),
% 251.28/60.02 | | | | | | | | | (91), (93), (95), (96), (97), (98), (99), (100),
% 251.28/60.02 | | | | | | | | | (101), (105), (106), (107), (109), (110), (111),
% 251.28/60.02 | | | | | | | | | (112), (114), (115), (117), (119), (120), (123),
% 251.28/60.02 | | | | | | | | | (125), (127), (128), (129), (134), (135), (136),
% 251.28/60.02 | | | | | | | | | (137), (138), (140), (141), (144), (146), (147),
% 251.28/60.02 | | | | | | | | | (148), (150), (151), (152), (153), (156), (157),
% 251.28/60.02 | | | | | | | | | (158), (160), (162), (164), (166), (167), (168),
% 251.28/60.02 | | | | | | | | | (169), (170), (171), (173), (174), (175), (179),
% 251.28/60.02 | | | | | | | | | (180), (181), (184), (227), (231), (233), (235),
% 251.28/60.02 | | | | | | | | | (237), (245), (282), (283), (284), (286), (288),
% 251.28/60.02 | | | | | | | | | (290), (292), (294), (299) are inconsistent by
% 251.28/60.02 | | | | | | | | | sub-proof #656.
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | Case 2:
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | (300) ~ (all_190_1 = e4) & op(e1, e0) = all_190_1 &
% 251.28/60.02 | | | | | | | | | $i(all_190_1)
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | ALPHA: (300) implies:
% 251.28/60.02 | | | | | | | | | (301) op(e1, e0) = all_190_1
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (12), (13),
% 251.28/60.02 | | | | | | | | | (14), (15), (16), (17), (19), (22), (24), (25),
% 251.28/60.02 | | | | | | | | | (26), (28), (29), (30), (31), (32), (34), (35),
% 251.28/60.02 | | | | | | | | | (36), (37), (38), (39), (40), (43), (44), (45),
% 251.28/60.02 | | | | | | | | | (46), (47), (48), (49), (50), (53), (54), (56),
% 251.28/60.02 | | | | | | | | | (57), (58), (59), (60), (61), (62), (63), (64),
% 251.28/60.02 | | | | | | | | | (65), (66), (67), (69), (71), (74), (75), (76),
% 251.28/60.02 | | | | | | | | | (77), (79), (80), (81), (82), (83), (89), (90),
% 251.28/60.02 | | | | | | | | | (91), (93), (95), (96), (97), (98), (99), (100),
% 251.28/60.02 | | | | | | | | | (101), (105), (106), (107), (109), (110), (111),
% 251.28/60.02 | | | | | | | | | (112), (114), (115), (117), (119), (120), (123),
% 251.28/60.02 | | | | | | | | | (125), (127), (128), (129), (134), (135), (136),
% 251.28/60.02 | | | | | | | | | (137), (138), (140), (141), (144), (146), (147),
% 251.28/60.02 | | | | | | | | | (148), (150), (151), (152), (153), (156), (157),
% 251.28/60.02 | | | | | | | | | (158), (160), (162), (164), (166), (167), (168),
% 251.28/60.02 | | | | | | | | | (169), (170), (171), (173), (174), (175), (179),
% 251.28/60.02 | | | | | | | | | (180), (181), (184), (227), (231), (233), (235),
% 251.28/60.02 | | | | | | | | | (237), (245), (282), (283), (284), (286), (288),
% 251.28/60.02 | | | | | | | | | (290), (292), (294), (301) are inconsistent by
% 251.28/60.02 | | | | | | | | | sub-proof #656.
% 251.28/60.02 | | | | | | | | |
% 251.28/60.02 | | | | | | | | End of split
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | End of split
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | End of split
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | End of split
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | End of split
% 251.28/60.02 | | | |
% 251.28/60.02 | | | End of split
% 251.28/60.02 | | |
% 251.28/60.02 | | End of split
% 251.28/60.02 | |
% 251.28/60.02 | End of split
% 251.28/60.02 |
% 251.28/60.02 End of proof
% 251.28/60.02
% 251.28/60.02 Sub-proof #656 shows that the following formulas are inconsistent:
% 251.28/60.02 ----------------------------------------------------------------
% 251.28/60.02 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/60.02 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/60.02 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/60.02 (2) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) = all_32_1
% 251.28/60.02 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 251.28/60.02 all_32_1 & $i(all_32_1))
% 251.28/60.02 (3) ~ (all_4_2 = e4)
% 251.28/60.02 (4) ~ (all_10_2 = e4)
% 251.28/60.02 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.02 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/60.02 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/60.02 (6) op(all_4_2, e2) = e1
% 251.28/60.02 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/60.02 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/60.02 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/60.02 (8) ~ (all_244_8 = e0)
% 251.28/60.02 (9) op(all_6_2, e2) = e4
% 251.28/60.02 (10) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.28/60.02 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.28/60.02 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/60.02 (11) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.02 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.02 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.02 (12) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/60.02 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.02 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/60.02 (13) all_250_8 = all_36_2
% 251.28/60.02 (14) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.28/60.02 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.28/60.02 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.28/60.02 (15) op(e2, e0) = e4
% 251.28/60.02 (16) op(all_62_2, all_36_2) = e3
% 251.28/60.02 (17) ~ (e2 = e0)
% 251.28/60.02 (18) ~ (e1 = e0)
% 251.28/60.02 (19) ~ (all_28_2 = e3)
% 251.28/60.02 (20) ~ (all_62_2 = all_22_2)
% 251.28/60.02 (21) all_252_18 = e4
% 251.28/60.02 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/60.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/60.02 (23) op(e2, e3) = all_10_2
% 251.28/60.02 (24) ~ (e3 = e2)
% 251.28/60.02 (25) op(e0, e0) = all_244_24
% 251.28/60.02 (26) ~ (e4 = e0)
% 251.28/60.02 (27) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/60.02 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/60.02 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/60.02 (28) ~ (all_244_8 = all_64_2)
% 251.28/60.02 (29) op(e2, e2) = all_244_8
% 251.28/60.02 (30) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/60.02 all_250_11 = e0
% 251.28/60.02 (31) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/60.02 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/60.02 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/60.02 (32) op(e2, e1) = all_38_2
% 251.28/60.02 (33) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/60.02 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/60.02 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/60.02 (34) ~ (all_84_2 = all_62_2)
% 251.28/60.02 (35) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/60.02 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/60.02 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/60.02 (36) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/60.02 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/60.02 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/60.02 (37) all_168_2 = all_100_2
% 251.28/60.02 (38) op(e1, e0) = all_34_2
% 251.28/60.02 (39) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/60.02 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/60.02 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/60.02 (40) ~ (all_36_2 = e2)
% 251.28/60.02 (41) op(e4, e2) = all_6_2
% 251.28/60.02 (42) ~ (all_244_15 = e0)
% 251.28/60.02 (43) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/60.02 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/60.02 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/60.02 (44) ~ (all_34_2 = e2)
% 251.28/60.02 (45) ~ (e2 = e1)
% 251.28/60.02 (46) ~ (all_100_2 = all_64_2)
% 251.28/60.02 (47) all_56_2 = all_8_2
% 251.28/60.02 (48) ~ (all_34_2 = e4)
% 251.28/60.02 (49) op(e0, e2) = all_28_2
% 251.28/60.02 (50) ~ (e4 = e1)
% 251.28/60.02 (51) ~ (all_244_0 = e2)
% 251.28/60.02 (52) op(all_6_2, all_64_2) = e2
% 251.28/60.02 (53) ~ (all_64_2 = all_10_2)
% 251.28/60.02 (54) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/60.02 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/60.02 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/60.02 (55) ~ (all_244_8 = all_10_2)
% 251.28/60.02 (56) ~ (all_6_2 = e1)
% 251.28/60.02 (57) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/60.02 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/60.02 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/60.02 (58) all_252_16 = e2
% 251.28/60.02 (59) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/60.02 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/60.02 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/60.02 (60) all_50_2 = all_4_2
% 251.28/60.02 (61) ~ (all_244_3 = all_84_2)
% 251.28/60.02 (62) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/60.02 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/60.02 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/60.02 (63) op(e1, e4) = all_16_2
% 251.28/60.02 (64) ~ (all_244_0 = all_64_2)
% 251.28/60.02 (65) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/60.02 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/60.02 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/60.02 (66) op(e1, e3) = all_62_2
% 251.28/60.02 (67) op(all_16_2, all_26_2) = e4
% 251.28/60.02 (68) ~ (e3 = e0)
% 251.28/60.02 (69) ~ (all_48_2 = all_36_2)
% 251.28/60.02 (70) all_70_2 = all_62_2
% 251.28/60.02 (71) ~ (e3 = e1)
% 251.28/60.02 (72) ~ (all_12_2 = e2)
% 251.28/60.02 (73) op(e3, e1) = all_36_2
% 251.28/60.02 (74) op(e1, e0) = all_190_1
% 251.28/60.02 (75) ~ (all_16_2 = e2)
% 251.28/60.02 (76) ~ (all_8_2 = e1)
% 251.28/60.02 (77) ~ (all_244_3 = all_62_2)
% 251.28/60.02 (78) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/60.02 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/60.02 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/60.02 (79) ~ (all_22_2 = e1)
% 251.28/60.02 (80) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/60.02 all_250_8 = e0
% 251.28/60.02 (81) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/60.02 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/60.02 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/60.02 (82) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/60.02 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/60.02 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/60.02 (83) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/60.02 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/60.02 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/60.02 (84) ~ (all_38_2 = e4)
% 251.28/60.02 (85) ~ (all_64_2 = all_12_2)
% 251.28/60.02 (86) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.28/60.02 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.28/60.02 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/60.02 (87) op(all_22_2, e3) = e0
% 251.28/60.02 (88) all_68_2 = all_22_2
% 251.28/60.02 (89) op(e0, e3) = all_22_2
% 251.28/60.02 (90) ~ (all_244_24 = e4)
% 251.28/60.02 (91) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.02 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/60.02 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/60.02 (92) op(all_62_2, e3) = e1
% 251.28/60.02 (93) op(e4, e1) = all_26_2
% 251.28/60.02 (94) op(all_10_2, e3) = e2
% 251.28/60.02 (95) ~ (all_244_15 = all_62_2)
% 251.28/60.02 (96) op(e3, e4) = all_100_2
% 251.28/60.02 (97) all_250_11 = all_10_2
% 251.28/60.02 (98) ~ (all_36_2 = e0)
% 251.28/60.02 (99) op(e4, e4) = all_244_0
% 251.28/60.02 (100) ~ (all_48_2 = e4)
% 251.28/60.02 (101) ~ (e4 = e3)
% 251.28/60.02 (102) op(e1, e1) = all_244_15
% 251.28/60.02 (103) ~ (all_64_2 = e0)
% 251.28/60.02 (104) all_252_23 = e2
% 251.28/60.02 (105) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.02 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/60.02 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/60.02 (106) op(e0, e1) = all_20_2
% 251.28/60.02 (107) op(e3, e0) = all_48_2
% 251.28/60.02 (108) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.28/60.02 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.28/60.02 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.28/60.02 (109) ~ (all_26_2 = e3)
% 251.28/60.02 (110) op(e1, e2) = all_4_2
% 251.28/60.02 (111) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.28/60.02 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.28/60.02 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.28/60.02 (112) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.28/60.02 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.28/60.02 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.28/60.02 (113) op(e4, e3) = all_84_2
% 251.28/60.02 (114) ~ (all_62_2 = all_10_2)
% 251.28/60.02 (115) op(e2, e4) = all_64_2
% 251.28/60.02 (116) ~ (all_22_2 = all_10_2)
% 251.28/60.02 (117) ~ (all_244_15 = e2)
% 251.28/60.02 (118) ~ (e4 = e2)
% 251.28/60.02 (119) op(e0, all_4_2) = e1
% 251.28/60.02 (120) op(e3, e2) = all_8_2
% 251.28/60.02 (121) ~ (all_64_2 = all_16_2)
% 251.28/60.02 (122) op(all_36_2, e1) = e3
% 251.28/60.02 (123) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.28/60.02 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.28/60.02 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.28/60.02 (124) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.28/60.02 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.28/60.02 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.28/60.02 (125) ~ (all_20_2 = e4)
% 251.28/60.02 (126) op(all_16_2, e4) = e1
% 251.28/60.02 (127) ~ (all_100_2 = all_16_2)
% 251.28/60.02 (128) op(e2, e0) = all_40_2
% 251.28/60.02 (129) op(e0, e4) = all_40_1
% 251.28/60.02 (130) op(all_8_2, e2) = e3
% 251.28/60.02 (131) ~ (all_244_8 = all_28_2)
% 251.28/60.02 (132) ~ (all_10_2 = e0)
% 251.28/60.02 (133) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.02 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.02 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/60.02 (134) op(e3, e3) = all_244_3
% 251.28/60.02 (135) ~ (all_26_2 = e0)
% 251.28/60.02 (136) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.28/60.02 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.28/60.02 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.28/60.02 (137) ~ (all_64_2 = e4)
% 251.28/60.02 (138) op(all_244_24, all_244_24) = e0
% 251.28/60.02 (139) op(e0, e4) = all_12_2
% 251.28/60.02 (140) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.28/60.02 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.28/60.02 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.28/60.02
% 251.28/60.02 Begin of proof
% 251.28/60.02 |
% 251.28/60.02 | BETA: splitting (10) gives:
% 251.28/60.02 |
% 251.28/60.02 | Case 1:
% 251.28/60.02 | |
% 251.28/60.02 | | (141) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1)
% 251.28/60.02 | | = e0)
% 251.28/60.02 | |
% 251.28/60.02 | | REF_CLOSE: (22), (73), (93), (98), (135), (141) are inconsistent by
% 251.28/60.02 | | sub-proof #710.
% 251.28/60.02 | |
% 251.28/60.02 | Case 2:
% 251.28/60.02 | |
% 251.28/60.02 | | (142) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1)
% 251.28/60.02 | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/60.02 | |
% 251.28/60.02 | | BETA: splitting (142) gives:
% 251.28/60.02 | |
% 251.28/60.02 | | Case 1:
% 251.28/60.02 | | |
% 251.28/60.02 | | | (143) all_252_11 = e0 & op(e2, e1) = e0
% 251.28/60.02 | | |
% 251.28/60.02 | | | ALPHA: (143) implies:
% 251.28/60.02 | | | (144) all_252_11 = e0
% 251.28/60.02 | | | (145) op(e2, e1) = e0
% 251.28/60.02 | | |
% 251.28/60.02 | | | GROUND_INST: instantiating (22) with all_34_2, all_190_1, e0, e1,
% 251.28/60.02 | | | simplifying with (38), (74) gives:
% 251.28/60.02 | | | (146) all_190_1 = all_34_2
% 251.28/60.02 | | |
% 251.28/60.02 | | | BETA: splitting (14) gives:
% 251.28/60.02 | | |
% 251.28/60.02 | | | Case 1:
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | (147) ~ (all_36_2 = e4)
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | BETA: splitting (86) gives:
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | Case 1:
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | (148) ~ (all_48_2 = e1)
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | BETA: splitting (140) gives:
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | Case 1:
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | (149) ~ (all_50_2 = e3)
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | REDUCE: (60), (149) imply:
% 251.28/60.02 | | | | | | (150) ~ (all_4_2 = e3)
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | BETA: splitting (2) gives:
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | Case 1:
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | (151) ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1,
% 251.28/60.02 | | | | | | | e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | ALPHA: (151) implies:
% 251.28/60.02 | | | | | | | (152) op(e1, e2) = all_32_1
% 251.28/60.02 | | | | | | | (153) op(e2, all_32_1) = all_32_0
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | GROUND_INST: instantiating (22) with all_4_2, all_32_1, e2, e1,
% 251.28/60.02 | | | | | | | simplifying with (110), (152) gives:
% 251.28/60.02 | | | | | | | (154) all_32_1 = all_4_2
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REDUCE: (153), (154) imply:
% 251.28/60.02 | | | | | | | (155) op(e2, all_4_2) = all_32_0
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | BETA: splitting (36) gives:
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | Case 1:
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | (156) ~ (all_56_2 = e0)
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | REDUCE: (47), (156) imply:
% 251.28/60.02 | | | | | | | | (157) ~ (all_8_2 = e0)
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 251.28/60.02 | | | | | | | | (15), (17), (19), (20), (21), (22), (23), (24), (25),
% 251.28/60.02 | | | | | | | | (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 251.28/60.02 | | | | | | | | (37), (38), (39), (41), (43), (44), (45), (46), (48),
% 251.28/60.02 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 251.28/60.02 | | | | | | | | (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 251.28/60.02 | | | | | | | | (70), (71), (72), (73), (75), (76), (77), (78), (81),
% 251.28/60.02 | | | | | | | | (82), (83), (84), (85), (87), (88), (89), (90), (91),
% 251.28/60.02 | | | | | | | | (92), (93), (94), (95), (96), (97), (99), (100),
% 251.28/60.02 | | | | | | | | (101), (102), (103), (104), (105), (106), (107),
% 251.28/60.02 | | | | | | | | (108), (109), (110), (111), (112), (113), (114),
% 251.28/60.02 | | | | | | | | (115), (116), (117), (119), (120), (121), (123),
% 251.28/60.02 | | | | | | | | (124), (125), (126), (127), (128), (129), (131),
% 251.28/60.02 | | | | | | | | (132), (133), (134), (136), (137), (138), (139),
% 251.28/60.02 | | | | | | | | (144), (145), (147), (148), (150), (155), (157) are
% 251.28/60.02 | | | | | | | | inconsistent by sub-proof #669.
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | Case 2:
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | (158) all_56_2 = e0
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | | REF_CLOSE: (19), (22), (47), (49), (130), (158) are inconsistent
% 251.28/60.02 | | | | | | | | by sub-proof #668.
% 251.28/60.02 | | | | | | | |
% 251.28/60.02 | | | | | | | End of split
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | Case 2:
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | (159) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | ALPHA: (159) implies:
% 251.28/60.02 | | | | | | | (160) ~ (all_32_1 = e3)
% 251.28/60.02 | | | | | | | (161) op(e1, e2) = all_32_1
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 251.28/60.02 | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.28/60.02 | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 251.28/60.02 | | | | | | | (34), (35), (36), (37), (38), (39), (41), (43), (44),
% 251.28/60.02 | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 251.28/60.02 | | | | | | | (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 251.28/60.02 | | | | | | | (64), (65), (66), (67), (68), (70), (71), (72), (73),
% 251.28/60.02 | | | | | | | (75), (76), (77), (78), (81), (82), (83), (84), (85),
% 251.28/60.02 | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 251.28/60.02 | | | | | | | (96), (97), (99), (100), (101), (102), (103), (104),
% 251.28/60.02 | | | | | | | (105), (106), (107), (108), (109), (110), (111), (112),
% 251.28/60.02 | | | | | | | (113), (114), (115), (116), (117), (118), (119), (120),
% 251.28/60.02 | | | | | | | (121), (123), (124), (125), (126), (127), (128), (129),
% 251.28/60.02 | | | | | | | (130), (131), (132), (133), (134), (136), (137), (138),
% 251.28/60.02 | | | | | | | (139), (144), (145), (147), (148), (160), (161) are
% 251.28/60.02 | | | | | | | inconsistent by sub-proof #662.
% 251.28/60.02 | | | | | | |
% 251.28/60.02 | | | | | | End of split
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | Case 2:
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | (162) all_50_2 = e3
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | | REF_CLOSE: (22), (60), (79), (89), (119), (162) are inconsistent by
% 251.28/60.02 | | | | | | sub-proof #713.
% 251.28/60.02 | | | | | |
% 251.28/60.02 | | | | | End of split
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | Case 2:
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | (163) all_48_2 = e1
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | REDUCE: (69), (163) imply:
% 251.28/60.02 | | | | | (164) ~ (all_36_2 = e1)
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | SIMP: (164) implies:
% 251.28/60.02 | | | | | (165) ~ (all_36_2 = e1)
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | | REF_CLOSE: (13), (16), (22), (40), (80), (92), (98), (147), (165) are
% 251.28/60.02 | | | | | inconsistent by sub-proof #658.
% 251.28/60.02 | | | | |
% 251.28/60.02 | | | | End of split
% 251.28/60.02 | | | |
% 251.28/60.02 | | | Case 2:
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | (166) all_36_2 = e4
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | REDUCE: (122), (166) imply:
% 251.28/60.02 | | | | (167) op(e4, e1) = e3
% 251.28/60.02 | | | |
% 251.28/60.02 | | | | REF_CLOSE: (22), (93), (109), (167) are inconsistent by sub-proof #834.
% 251.28/60.02 | | | |
% 251.28/60.02 | | | End of split
% 251.28/60.02 | | |
% 251.28/60.02 | | Case 2:
% 251.28/60.02 | | |
% 251.28/60.02 | | | (168) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0,
% 251.28/60.02 | | | e1) = e0)
% 251.28/60.02 | | |
% 251.28/60.02 | | | REF_CLOSE: (17), (22), (42), (102), (104), (168) are inconsistent by
% 251.28/60.02 | | | sub-proof #711.
% 251.28/60.02 | | |
% 251.28/60.02 | | End of split
% 251.28/60.02 | |
% 251.28/60.02 | End of split
% 251.28/60.02 |
% 251.28/60.02 End of proof
% 251.28/60.02
% 251.28/60.02 Sub-proof #657 shows that the following formulas are inconsistent:
% 251.28/60.02 ----------------------------------------------------------------
% 251.28/60.02 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/60.02 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/60.02 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/60.02 (2) ( ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1, e2) = all_32_1
% 251.28/60.02 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 251.28/60.02 all_32_1 & $i(all_32_1))
% 251.28/60.02 (3) ~ (all_4_2 = e4)
% 251.28/60.02 (4) ~ (all_10_2 = e4)
% 251.28/60.03 (5) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.03 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/60.03 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/60.03 (6) op(all_4_2, e2) = e1
% 251.28/60.03 (7) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/60.03 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/60.03 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/60.03 (8) ~ (all_244_8 = e0)
% 251.28/60.03 (9) op(all_6_2, e2) = e4
% 251.28/60.03 (10) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.28/60.03 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.28/60.03 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/60.03 (11) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.03 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.03 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.03 (12) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/60.03 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.03 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/60.03 (13) all_250_8 = all_36_2
% 251.28/60.03 (14) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.28/60.03 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.28/60.03 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.28/60.03 (15) op(e2, e0) = e4
% 251.28/60.03 (16) op(all_62_2, all_36_2) = e3
% 251.28/60.03 (17) ~ (e2 = e0)
% 251.28/60.03 (18) ~ (e1 = e0)
% 251.28/60.03 (19) ~ (all_28_2 = e3)
% 251.28/60.03 (20) ~ (all_62_2 = all_22_2)
% 251.28/60.03 (21) all_252_18 = e4
% 251.28/60.03 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/60.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/60.03 (23) op(e2, e3) = all_10_2
% 251.28/60.03 (24) ~ (e3 = e2)
% 251.28/60.03 (25) op(e0, e0) = all_244_24
% 251.28/60.03 (26) ~ (e4 = e0)
% 251.28/60.03 (27) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/60.03 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/60.03 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/60.03 (28) ~ (all_244_8 = all_64_2)
% 251.28/60.03 (29) op(e2, e2) = all_244_8
% 251.28/60.03 (30) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/60.03 all_250_11 = e0
% 251.28/60.03 (31) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/60.03 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/60.03 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/60.03 (32) op(e2, e1) = all_38_2
% 251.28/60.03 (33) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/60.03 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/60.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/60.03 (34) ~ (all_84_2 = all_62_2)
% 251.28/60.03 (35) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/60.03 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/60.03 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/60.03 (36) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/60.03 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/60.03 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/60.03 (37) all_168_2 = all_100_2
% 251.28/60.03 (38) op(e1, e0) = all_34_2
% 251.28/60.03 (39) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/60.03 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/60.03 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/60.03 (40) ~ (all_36_2 = e2)
% 251.28/60.03 (41) op(e4, e2) = all_6_2
% 251.28/60.03 (42) ~ (all_244_15 = e0)
% 251.28/60.03 (43) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/60.03 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/60.03 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/60.03 (44) ~ (all_34_2 = e2)
% 251.28/60.03 (45) ~ (e2 = e1)
% 251.28/60.03 (46) ~ (all_100_2 = all_64_2)
% 251.28/60.03 (47) all_56_2 = all_8_2
% 251.28/60.03 (48) ~ (all_34_2 = e4)
% 251.28/60.03 (49) op(e0, e2) = all_28_2
% 251.28/60.03 (50) ~ (e4 = e1)
% 251.28/60.03 (51) ~ (all_244_0 = e2)
% 251.28/60.03 (52) op(all_6_2, all_64_2) = e2
% 251.28/60.03 (53) ~ (all_64_2 = all_10_2)
% 251.28/60.03 (54) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/60.03 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/60.03 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/60.03 (55) ~ (all_244_8 = all_10_2)
% 251.28/60.03 (56) ~ (all_6_2 = e1)
% 251.28/60.03 (57) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/60.03 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/60.03 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/60.03 (58) op(e2, all_4_2) = all_230_0
% 251.28/60.03 (59) all_252_16 = e2
% 251.28/60.03 (60) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/60.03 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/60.03 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/60.03 (61) all_50_2 = all_4_2
% 251.28/60.03 (62) ~ (all_244_3 = all_84_2)
% 251.28/60.03 (63) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/60.03 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/60.03 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/60.03 (64) op(e1, e4) = all_16_2
% 251.28/60.03 (65) ~ (all_244_0 = all_64_2)
% 251.28/60.03 (66) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/60.03 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/60.03 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/60.03 (67) op(e1, e3) = all_62_2
% 251.28/60.03 (68) op(all_16_2, all_26_2) = e4
% 251.28/60.03 (69) ~ (e3 = e0)
% 251.28/60.03 (70) ~ (all_48_2 = all_36_2)
% 251.28/60.03 (71) all_70_2 = all_62_2
% 251.28/60.03 (72) ~ (e3 = e1)
% 251.28/60.03 (73) ~ (all_12_2 = e2)
% 251.28/60.03 (74) op(e3, e1) = all_36_2
% 251.28/60.03 (75) op(e1, e0) = all_190_1
% 251.28/60.03 (76) ~ (all_16_2 = e2)
% 251.28/60.03 (77) ~ (all_8_2 = e1)
% 251.28/60.03 (78) ~ (all_244_3 = all_62_2)
% 251.28/60.03 (79) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/60.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/60.03 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/60.03 (80) ~ (all_22_2 = e1)
% 251.28/60.03 (81) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/60.03 all_250_8 = e0
% 251.28/60.03 (82) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/60.03 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/60.03 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/60.03 (83) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/60.03 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/60.03 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/60.03 (84) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/60.03 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/60.03 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/60.03 (85) ~ (all_38_2 = e4)
% 251.28/60.03 (86) ~ (all_64_2 = all_12_2)
% 251.28/60.03 (87) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.28/60.03 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.28/60.03 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.28/60.03 (88) op(all_22_2, e3) = e0
% 251.28/60.03 (89) all_68_2 = all_22_2
% 251.28/60.03 (90) op(e0, e3) = all_22_2
% 251.28/60.03 (91) ~ (all_244_24 = e4)
% 251.28/60.03 (92) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.03 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/60.03 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/60.03 (93) op(all_62_2, e3) = e1
% 251.28/60.03 (94) op(e4, e1) = all_26_2
% 251.28/60.03 (95) op(all_10_2, e3) = e2
% 251.28/60.03 (96) ~ (all_244_15 = all_62_2)
% 251.28/60.03 (97) op(e3, e4) = all_100_2
% 251.28/60.03 (98) all_250_11 = all_10_2
% 251.28/60.03 (99) ~ (all_36_2 = e0)
% 251.28/60.03 (100) op(e4, e4) = all_244_0
% 251.28/60.03 (101) ~ (all_48_2 = e4)
% 251.28/60.03 (102) ~ (e4 = e3)
% 251.28/60.03 (103) op(e1, e1) = all_244_15
% 251.28/60.03 (104) ~ (all_64_2 = e0)
% 251.28/60.03 (105) all_252_23 = e2
% 251.28/60.03 (106) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.03 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/60.03 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/60.03 (107) op(e0, e1) = all_20_2
% 251.28/60.03 (108) op(e3, e0) = all_48_2
% 251.28/60.03 (109) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.28/60.03 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.28/60.03 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.28/60.03 (110) ~ (all_26_2 = e3)
% 251.28/60.03 (111) op(e1, e2) = all_4_2
% 251.28/60.03 (112) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.28/60.03 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.28/60.03 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.28/60.03 (113) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.28/60.03 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.28/60.03 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.28/60.03 (114) op(e4, e3) = all_84_2
% 251.28/60.03 (115) ~ (all_62_2 = all_10_2)
% 251.28/60.03 (116) op(e2, e4) = all_64_2
% 251.28/60.03 (117) ~ (all_22_2 = all_10_2)
% 251.28/60.03 (118) ~ (all_244_15 = e2)
% 251.28/60.03 (119) ~ (e4 = e2)
% 251.28/60.03 (120) op(e0, all_4_2) = e1
% 251.28/60.03 (121) op(e3, e2) = all_8_2
% 251.28/60.03 (122) ~ (all_64_2 = all_16_2)
% 251.28/60.03 (123) op(all_36_2, e1) = e3
% 251.28/60.03 (124) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.28/60.03 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.28/60.03 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.28/60.03 (125) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.28/60.03 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.28/60.03 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.28/60.03 (126) ~ (all_20_2 = e4)
% 251.28/60.03 (127) op(all_16_2, e4) = e1
% 251.28/60.03 (128) ~ (all_100_2 = all_16_2)
% 251.28/60.03 (129) op(e2, e0) = all_40_2
% 251.28/60.03 (130) op(e0, e4) = all_40_1
% 251.28/60.03 (131) op(all_8_2, e2) = e3
% 251.28/60.03 (132) ~ (all_244_8 = all_28_2)
% 251.28/60.03 (133) ~ (all_10_2 = e0)
% 251.28/60.03 (134) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.03 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.28/60.03 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.28/60.03 (135) op(e3, e3) = all_244_3
% 251.28/60.03 (136) ~ (all_26_2 = e0)
% 251.28/60.03 (137) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.28/60.03 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.28/60.03 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.28/60.03 (138) ~ (all_64_2 = e4)
% 251.28/60.03 (139) op(all_244_24, all_244_24) = e0
% 251.28/60.03 (140) op(e0, e4) = all_12_2
% 251.28/60.03 (141) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.28/60.03 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.28/60.03 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.28/60.03
% 251.28/60.03 Begin of proof
% 251.28/60.03 |
% 251.28/60.03 | BETA: splitting (10) gives:
% 251.28/60.03 |
% 251.28/60.03 | Case 1:
% 251.28/60.03 | |
% 251.28/60.03 | | (142) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1)
% 251.28/60.03 | | = e0)
% 251.28/60.03 | |
% 251.28/60.03 | | REF_CLOSE: (22), (74), (94), (99), (136), (142) are inconsistent by
% 251.28/60.03 | | sub-proof #710.
% 251.28/60.03 | |
% 251.28/60.03 | Case 2:
% 251.28/60.03 | |
% 251.28/60.03 | | (143) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1)
% 251.28/60.03 | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.28/60.03 | |
% 251.28/60.03 | | BETA: splitting (143) gives:
% 251.28/60.03 | |
% 251.28/60.03 | | Case 1:
% 251.28/60.03 | | |
% 251.28/60.03 | | | (144) all_252_11 = e0 & op(e2, e1) = e0
% 251.28/60.03 | | |
% 251.28/60.03 | | | ALPHA: (144) implies:
% 251.28/60.03 | | | (145) all_252_11 = e0
% 251.28/60.03 | | | (146) op(e2, e1) = e0
% 251.28/60.03 | | |
% 251.28/60.03 | | | GROUND_INST: instantiating (22) with all_34_2, all_190_1, e0, e1,
% 251.28/60.03 | | | simplifying with (38), (75) gives:
% 251.28/60.03 | | | (147) all_190_1 = all_34_2
% 251.28/60.03 | | |
% 251.28/60.03 | | | BETA: splitting (14) gives:
% 251.28/60.03 | | |
% 251.28/60.03 | | | Case 1:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | (148) ~ (all_36_2 = e4)
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | BETA: splitting (87) gives:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | Case 1:
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | (149) ~ (all_48_2 = e1)
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | BETA: splitting (141) gives:
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | Case 1:
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | (150) ~ (all_50_2 = e3)
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | REDUCE: (61), (150) imply:
% 251.28/60.03 | | | | | | (151) ~ (all_4_2 = e3)
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | BETA: splitting (2) gives:
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | Case 1:
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | (152) ~ (all_32_0 = e4) & op(e2, all_32_1) = all_32_0 & op(e1,
% 251.28/60.03 | | | | | | | e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | ALPHA: (152) implies:
% 251.28/60.03 | | | | | | | (153) op(e1, e2) = all_32_1
% 251.28/60.03 | | | | | | | (154) op(e2, all_32_1) = all_32_0
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | GROUND_INST: instantiating (22) with all_4_2, all_32_1, e2, e1,
% 251.28/60.03 | | | | | | | simplifying with (111), (153) gives:
% 251.28/60.03 | | | | | | | (155) all_32_1 = all_4_2
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | REDUCE: (154), (155) imply:
% 251.28/60.03 | | | | | | | (156) op(e2, all_4_2) = all_32_0
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | GROUND_INST: instantiating (22) with all_230_0, all_32_0, all_4_2,
% 251.28/60.03 | | | | | | | e2, simplifying with (58), (156) gives:
% 251.28/60.03 | | | | | | | (157) all_230_0 = all_32_0
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | BETA: splitting (36) gives:
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | Case 1:
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | | (158) ~ (all_56_2 = e0)
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | | REDUCE: (47), (158) imply:
% 251.28/60.03 | | | | | | | | (159) ~ (all_8_2 = e0)
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 251.28/60.03 | | | | | | | | (15), (17), (19), (20), (21), (22), (23), (24), (25),
% 251.28/60.03 | | | | | | | | (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 251.28/60.03 | | | | | | | | (37), (38), (39), (41), (43), (44), (45), (46), (48),
% 251.28/60.03 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (59),
% 251.28/60.03 | | | | | | | | (60), (62), (63), (64), (65), (66), (67), (68), (69),
% 251.28/60.03 | | | | | | | | (71), (72), (73), (74), (76), (77), (78), (79), (82),
% 251.28/60.03 | | | | | | | | (83), (84), (85), (86), (88), (89), (90), (91), (92),
% 251.28/60.03 | | | | | | | | (93), (94), (95), (96), (97), (98), (100), (101),
% 251.28/60.03 | | | | | | | | (102), (103), (104), (105), (106), (107), (108),
% 251.28/60.03 | | | | | | | | (109), (110), (111), (112), (113), (114), (115),
% 251.28/60.03 | | | | | | | | (116), (117), (118), (120), (121), (122), (124),
% 251.28/60.03 | | | | | | | | (125), (126), (127), (128), (129), (130), (132),
% 251.28/60.03 | | | | | | | | (133), (134), (135), (137), (138), (139), (140),
% 251.28/60.03 | | | | | | | | (145), (146), (148), (149), (151), (156), (159) are
% 251.28/60.03 | | | | | | | | inconsistent by sub-proof #669.
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | Case 2:
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | | (160) all_56_2 = e0
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | | REF_CLOSE: (19), (22), (47), (49), (131), (160) are inconsistent
% 251.28/60.03 | | | | | | | | by sub-proof #668.
% 251.28/60.03 | | | | | | | |
% 251.28/60.03 | | | | | | | End of split
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | Case 2:
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | (161) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | ALPHA: (161) implies:
% 251.28/60.03 | | | | | | | (162) ~ (all_32_1 = e3)
% 251.28/60.03 | | | | | | | (163) op(e1, e2) = all_32_1
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 251.28/60.03 | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 251.28/60.03 | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 251.28/60.03 | | | | | | | (34), (35), (36), (37), (38), (39), (41), (43), (44),
% 251.28/60.03 | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 251.28/60.03 | | | | | | | (54), (55), (56), (57), (59), (60), (62), (63), (64),
% 251.28/60.03 | | | | | | | (65), (66), (67), (68), (69), (71), (72), (73), (74),
% 251.28/60.03 | | | | | | | (76), (77), (78), (79), (82), (83), (84), (85), (86),
% 251.28/60.03 | | | | | | | (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 251.28/60.03 | | | | | | | (97), (98), (100), (101), (102), (103), (104), (105),
% 251.28/60.03 | | | | | | | (106), (107), (108), (109), (110), (111), (112), (113),
% 251.28/60.03 | | | | | | | (114), (115), (116), (117), (118), (119), (120), (121),
% 251.28/60.03 | | | | | | | (122), (124), (125), (126), (127), (128), (129), (130),
% 251.28/60.03 | | | | | | | (131), (132), (133), (134), (135), (137), (138), (139),
% 251.28/60.03 | | | | | | | (140), (145), (146), (148), (149), (162), (163) are
% 251.28/60.03 | | | | | | | inconsistent by sub-proof #662.
% 251.28/60.03 | | | | | | |
% 251.28/60.03 | | | | | | End of split
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | Case 2:
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | (164) all_50_2 = e3
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | | REF_CLOSE: (22), (61), (80), (90), (120), (164) are inconsistent by
% 251.28/60.03 | | | | | | sub-proof #713.
% 251.28/60.03 | | | | | |
% 251.28/60.03 | | | | | End of split
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | Case 2:
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | (165) all_48_2 = e1
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | REDUCE: (70), (165) imply:
% 251.28/60.03 | | | | | (166) ~ (all_36_2 = e1)
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | SIMP: (166) implies:
% 251.28/60.03 | | | | | (167) ~ (all_36_2 = e1)
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | REF_CLOSE: (13), (16), (22), (40), (81), (93), (99), (148), (167) are
% 251.28/60.03 | | | | | inconsistent by sub-proof #658.
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | End of split
% 251.28/60.03 | | | |
% 251.28/60.03 | | | Case 2:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | (168) all_36_2 = e4
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | REDUCE: (123), (168) imply:
% 251.28/60.03 | | | | (169) op(e4, e1) = e3
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | REF_CLOSE: (22), (94), (110), (169) are inconsistent by sub-proof #834.
% 251.28/60.03 | | | |
% 251.28/60.03 | | | End of split
% 251.28/60.03 | | |
% 251.28/60.03 | | Case 2:
% 251.28/60.03 | | |
% 251.28/60.03 | | | (170) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0,
% 251.28/60.03 | | | e1) = e0)
% 251.28/60.03 | | |
% 251.28/60.03 | | | REF_CLOSE: (17), (22), (42), (103), (105), (170) are inconsistent by
% 251.28/60.03 | | | sub-proof #711.
% 251.28/60.03 | | |
% 251.28/60.03 | | End of split
% 251.28/60.03 | |
% 251.28/60.03 | End of split
% 251.28/60.03 |
% 251.28/60.03 End of proof
% 251.28/60.03
% 251.28/60.03 Sub-proof #658 shows that the following formulas are inconsistent:
% 251.28/60.03 ----------------------------------------------------------------
% 251.28/60.03 (1) all_250_8 = all_36_2
% 251.28/60.03 (2) op(all_62_2, all_36_2) = e3
% 251.28/60.03 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/60.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/60.03 (4) ~ (all_36_2 = e2)
% 251.28/60.03 (5) ~ (all_36_2 = e4)
% 251.28/60.03 (6) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 |
% 251.28/60.03 all_250_8 = e0
% 251.28/60.03 (7) op(all_62_2, e3) = e1
% 251.28/60.03 (8) ~ (all_36_2 = e0)
% 251.28/60.03 (9) ~ (all_36_2 = e1)
% 251.28/60.03
% 251.28/60.03 Begin of proof
% 251.28/60.03 |
% 251.28/60.03 | BETA: splitting (6) gives:
% 251.28/60.03 |
% 251.28/60.03 | Case 1:
% 251.28/60.03 | |
% 251.28/60.03 | | (10) all_250_8 = e4
% 251.28/60.03 | |
% 251.28/60.03 | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #661.
% 251.28/60.03 | |
% 251.28/60.03 | Case 2:
% 251.28/60.03 | |
% 251.28/60.03 | | (11) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0
% 251.28/60.03 | |
% 251.28/60.03 | | BETA: splitting (11) gives:
% 251.28/60.03 | |
% 251.28/60.03 | | Case 1:
% 251.28/60.03 | | |
% 251.28/60.03 | | | (12) all_250_8 = e3
% 251.28/60.03 | | |
% 251.28/60.03 | | | COMBINE_EQS: (1), (12) imply:
% 251.28/60.03 | | | (13) all_36_2 = e3
% 251.28/60.03 | | |
% 251.28/60.03 | | | SIMP: (13) implies:
% 251.28/60.03 | | | (14) all_36_2 = e3
% 251.28/60.03 | | |
% 251.28/60.03 | | | REDUCE: (9), (14) imply:
% 251.28/60.03 | | | (15) ~ (e3 = e1)
% 251.28/60.03 | | |
% 251.28/60.03 | | | REF_CLOSE: (2), (3), (7), (14), (15) are inconsistent by sub-proof #745.
% 251.28/60.03 | | |
% 251.28/60.03 | | Case 2:
% 251.28/60.03 | | |
% 251.28/60.03 | | | (16) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0
% 251.28/60.03 | | |
% 251.28/60.03 | | | BETA: splitting (16) gives:
% 251.28/60.03 | | |
% 251.28/60.03 | | | Case 1:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | (17) all_250_8 = e2
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | REF_CLOSE: (1), (4), (17) are inconsistent by sub-proof #660.
% 251.28/60.03 | | | |
% 251.28/60.03 | | | Case 2:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | (18) all_250_8 = e1 | all_250_8 = e0
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | BETA: splitting (18) gives:
% 251.28/60.03 | | | |
% 251.28/60.03 | | | | Case 1:
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | (19) all_250_8 = e1
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | REF_CLOSE: (1), (9), (19) are inconsistent by sub-proof #659.
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | Case 2:
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | (20) all_250_8 = e0
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | COMBINE_EQS: (1), (20) imply:
% 251.28/60.03 | | | | | (21) all_36_2 = e0
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | SIMP: (21) implies:
% 251.28/60.03 | | | | | (22) all_36_2 = e0
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | REDUCE: (8), (22) imply:
% 251.28/60.03 | | | | | (23) $false
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | | CLOSE: (23) is inconsistent.
% 251.28/60.03 | | | | |
% 251.28/60.03 | | | | End of split
% 251.28/60.03 | | | |
% 251.28/60.03 | | | End of split
% 251.28/60.03 | | |
% 251.28/60.03 | | End of split
% 251.28/60.03 | |
% 251.28/60.03 | End of split
% 251.28/60.03 |
% 251.28/60.03 End of proof
% 251.28/60.03
% 251.28/60.03 Sub-proof #659 shows that the following formulas are inconsistent:
% 251.28/60.03 ----------------------------------------------------------------
% 251.28/60.03 (1) all_250_8 = all_36_2
% 251.28/60.03 (2) all_250_8 = e1
% 251.28/60.03 (3) ~ (all_36_2 = e1)
% 251.28/60.03
% 251.28/60.03 Begin of proof
% 251.28/60.03 |
% 251.28/60.03 | COMBINE_EQS: (1), (2) imply:
% 251.28/60.03 | (4) all_36_2 = e1
% 251.28/60.03 |
% 251.28/60.03 | SIMP: (4) implies:
% 251.28/60.03 | (5) all_36_2 = e1
% 251.28/60.03 |
% 251.28/60.03 | REDUCE: (3), (5) imply:
% 251.28/60.03 | (6) $false
% 251.28/60.03 |
% 251.28/60.03 | CLOSE: (6) is inconsistent.
% 251.28/60.03 |
% 251.28/60.03 End of proof
% 251.28/60.03
% 251.28/60.03 Sub-proof #660 shows that the following formulas are inconsistent:
% 251.28/60.03 ----------------------------------------------------------------
% 251.28/60.03 (1) all_250_8 = all_36_2
% 251.28/60.03 (2) all_250_8 = e2
% 251.28/60.03 (3) ~ (all_36_2 = e2)
% 251.28/60.03
% 251.28/60.03 Begin of proof
% 251.28/60.03 |
% 251.28/60.03 | COMBINE_EQS: (1), (2) imply:
% 251.28/60.03 | (4) all_36_2 = e2
% 251.28/60.03 |
% 251.28/60.03 | SIMP: (4) implies:
% 251.28/60.03 | (5) all_36_2 = e2
% 251.28/60.03 |
% 251.28/60.03 | REDUCE: (3), (5) imply:
% 251.28/60.03 | (6) $false
% 251.28/60.03 |
% 251.28/60.03 | CLOSE: (6) is inconsistent.
% 251.28/60.03 |
% 251.28/60.03 End of proof
% 251.28/60.03
% 251.28/60.03 Sub-proof #661 shows that the following formulas are inconsistent:
% 251.28/60.03 ----------------------------------------------------------------
% 251.28/60.03 (1) all_250_8 = all_36_2
% 251.28/60.03 (2) all_250_8 = e4
% 251.28/60.03 (3) ~ (all_36_2 = e4)
% 251.28/60.03
% 251.28/60.03 Begin of proof
% 251.28/60.03 |
% 251.28/60.03 | COMBINE_EQS: (1), (2) imply:
% 251.28/60.03 | (4) all_36_2 = e4
% 251.28/60.03 |
% 251.28/60.03 | SIMP: (4) implies:
% 251.28/60.03 | (5) all_36_2 = e4
% 251.28/60.03 |
% 251.28/60.03 | REDUCE: (3), (5) imply:
% 251.28/60.03 | (6) $false
% 251.28/60.03 |
% 251.28/60.03 | CLOSE: (6) is inconsistent.
% 251.28/60.03 |
% 251.28/60.03 End of proof
% 251.28/60.03
% 251.28/60.03 Sub-proof #662 shows that the following formulas are inconsistent:
% 251.28/60.03 ----------------------------------------------------------------
% 251.28/60.03 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.28/60.03 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.28/60.03 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.28/60.03 (2) ~ (all_4_2 = e4)
% 251.28/60.03 (3) ~ (all_10_2 = e4)
% 251.28/60.03 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.03 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.28/60.03 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.28/60.03 (5) op(all_4_2, e2) = e1
% 251.28/60.03 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.28/60.03 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.28/60.03 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.28/60.03 (7) ~ (all_244_8 = e0)
% 251.28/60.03 (8) op(all_6_2, e2) = e4
% 251.28/60.03 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.28/60.03 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.28/60.03 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.28/60.03 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.28/60.03 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.28/60.03 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.28/60.03 (11) op(e2, e0) = e4
% 251.28/60.03 (12) ~ (e2 = e0)
% 251.28/60.03 (13) ~ (e1 = e0)
% 251.28/60.03 (14) ~ (all_28_2 = e3)
% 251.28/60.03 (15) ~ (all_62_2 = all_22_2)
% 251.28/60.03 (16) all_252_18 = e4
% 251.28/60.03 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.28/60.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.28/60.03 (18) op(e2, e3) = all_10_2
% 251.28/60.03 (19) ~ (e3 = e2)
% 251.28/60.03 (20) op(e0, e0) = all_244_24
% 251.28/60.03 (21) ~ (e4 = e0)
% 251.28/60.03 (22) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.28/60.03 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.28/60.03 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.28/60.03 (23) ~ (all_244_8 = all_64_2)
% 251.28/60.03 (24) op(e2, e2) = all_244_8
% 251.28/60.03 (25) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.28/60.03 all_250_11 = e0
% 251.28/60.03 (26) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.28/60.03 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.28/60.03 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.28/60.03 (27) op(e2, e1) = all_38_2
% 251.28/60.03 (28) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.28/60.03 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.28/60.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.28/60.03 (29) ~ (all_84_2 = all_62_2)
% 251.28/60.03 (30) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.28/60.03 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.28/60.03 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.28/60.03 (31) ~ (all_56_2 = e0) | ( ~ (all_56_0 = e4) & op(e2, e0) = all_56_1 &
% 251.28/60.03 op(e0, all_56_1) = all_56_0 & $i(all_56_0) & $i(all_56_1)) | ( ~
% 251.28/60.03 (all_56_1 = e1) & op(e2, e0) = all_56_1 & $i(all_56_1))
% 251.28/60.03 (32) all_168_2 = all_100_2
% 251.28/60.03 (33) op(e1, e0) = all_34_2
% 251.28/60.04 (34) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.28/60.04 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.28/60.04 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.28/60.04 (35) op(e4, e2) = all_6_2
% 251.28/60.04 (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.28/60.04 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.28/60.04 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.28/60.04 (37) ~ (all_34_2 = e2)
% 251.28/60.04 (38) ~ (e2 = e1)
% 251.28/60.04 (39) ~ (all_100_2 = all_64_2)
% 251.28/60.04 (40) all_56_2 = all_8_2
% 251.28/60.04 (41) ~ (all_34_2 = e4)
% 251.28/60.04 (42) op(e0, e2) = all_28_2
% 251.28/60.04 (43) ~ (e4 = e1)
% 251.28/60.04 (44) ~ (all_244_0 = e2)
% 251.28/60.04 (45) op(all_6_2, all_64_2) = e2
% 251.28/60.04 (46) ~ (all_64_2 = all_10_2)
% 251.28/60.04 (47) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.28/60.04 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.28/60.04 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.28/60.04 (48) ~ (all_244_8 = all_10_2)
% 251.28/60.04 (49) ~ (all_6_2 = e1)
% 251.28/60.04 (50) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.28/60.04 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.28/60.04 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.28/60.04 (51) all_252_16 = e2
% 251.28/60.04 (52) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.28/60.04 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.28/60.04 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.28/60.04 (53) ~ (all_32_1 = e3)
% 251.28/60.04 (54) ~ (all_244_3 = all_84_2)
% 251.28/60.04 (55) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.28/60.04 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.28/60.04 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.28/60.04 (56) op(e1, e4) = all_16_2
% 251.28/60.04 (57) ~ (all_244_0 = all_64_2)
% 251.28/60.04 (58) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.28/60.04 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.28/60.04 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.28/60.04 (59) op(e1, e3) = all_62_2
% 251.28/60.04 (60) op(all_16_2, all_26_2) = e4
% 251.28/60.04 (61) ~ (e3 = e0)
% 251.28/60.04 (62) ~ (all_36_2 = e4)
% 251.28/60.04 (63) all_70_2 = all_62_2
% 251.28/60.04 (64) ~ (e3 = e1)
% 251.28/60.04 (65) ~ (all_12_2 = e2)
% 251.28/60.04 (66) op(e3, e1) = all_36_2
% 251.28/60.04 (67) ~ (all_16_2 = e2)
% 251.28/60.04 (68) ~ (all_8_2 = e1)
% 251.28/60.04 (69) ~ (all_244_3 = all_62_2)
% 251.28/60.04 (70) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.28/60.04 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.28/60.04 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.28/60.04 (71) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.28/60.04 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.28/60.04 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.28/60.04 (72) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.28/60.04 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.28/60.04 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.28/60.04 (73) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.28/60.04 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.28/60.04 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.28/60.04 (74) ~ (all_38_2 = e4)
% 251.28/60.04 (75) ~ (all_64_2 = all_12_2)
% 251.28/60.04 (76) op(all_22_2, e3) = e0
% 251.28/60.04 (77) all_68_2 = all_22_2
% 251.28/60.04 (78) op(e0, e3) = all_22_2
% 251.28/60.04 (79) ~ (all_244_24 = e4)
% 251.28/60.04 (80) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.28/60.04 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.28/60.04 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.28/60.04 (81) op(all_62_2, e3) = e1
% 251.28/60.04 (82) op(e4, e1) = all_26_2
% 251.28/60.04 (83) op(all_10_2, e3) = e2
% 251.28/60.04 (84) ~ (all_244_15 = all_62_2)
% 251.28/60.04 (85) op(e3, e4) = all_100_2
% 251.28/60.04 (86) all_250_11 = all_10_2
% 251.28/60.04 (87) op(e4, e4) = all_244_0
% 251.28/60.04 (88) ~ (all_48_2 = e4)
% 251.28/60.04 (89) ~ (e4 = e3)
% 251.28/60.04 (90) op(e1, e1) = all_244_15
% 251.28/60.04 (91) ~ (all_64_2 = e0)
% 251.28/60.04 (92) all_252_23 = e2
% 251.28/60.04 (93) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.28/60.04 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.28/60.04 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.28/60.04 (94) op(e0, e1) = all_20_2
% 251.53/60.04 (95) all_252_11 = e0
% 251.53/60.04 (96) op(e3, e0) = all_48_2
% 251.53/60.04 (97) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.53/60.04 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.53/60.04 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.53/60.04 (98) ~ (all_26_2 = e3)
% 251.53/60.04 (99) op(e1, e2) = all_4_2
% 251.53/60.04 (100) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.53/60.04 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.53/60.04 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.53/60.04 (101) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.53/60.04 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.53/60.04 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.53/60.04 (102) ~ (all_48_2 = e1)
% 251.53/60.04 (103) op(e4, e3) = all_84_2
% 251.53/60.04 (104) ~ (all_62_2 = all_10_2)
% 251.53/60.04 (105) op(e2, e4) = all_64_2
% 251.53/60.04 (106) ~ (all_22_2 = all_10_2)
% 251.53/60.04 (107) ~ (all_244_15 = e2)
% 251.53/60.04 (108) ~ (e4 = e2)
% 251.53/60.04 (109) op(e0, all_4_2) = e1
% 251.53/60.04 (110) op(e3, e2) = all_8_2
% 251.53/60.04 (111) ~ (all_64_2 = all_16_2)
% 251.53/60.04 (112) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.53/60.04 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.53/60.04 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.53/60.04 (113) op(e1, e2) = all_32_1
% 251.53/60.04 (114) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.53/60.04 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.53/60.04 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.53/60.04 (115) ~ (all_20_2 = e4)
% 251.53/60.04 (116) op(all_16_2, e4) = e1
% 251.53/60.04 (117) ~ (all_100_2 = all_16_2)
% 251.53/60.04 (118) op(e2, e0) = all_40_2
% 251.53/60.04 (119) op(e0, e4) = all_40_1
% 251.53/60.04 (120) op(all_8_2, e2) = e3
% 251.53/60.04 (121) ~ (all_244_8 = all_28_2)
% 251.53/60.04 (122) ~ (all_10_2 = e0)
% 251.53/60.04 (123) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.53/60.04 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.53/60.04 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.53/60.04 (124) op(e3, e3) = all_244_3
% 251.53/60.04 (125) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.53/60.04 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.53/60.04 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.53/60.04 (126) op(e2, e1) = e0
% 251.53/60.04 (127) ~ (all_64_2 = e4)
% 251.53/60.04 (128) op(all_244_24, all_244_24) = e0
% 251.53/60.04 (129) op(e0, e4) = all_12_2
% 251.53/60.04
% 251.53/60.04 Begin of proof
% 251.53/60.04 |
% 251.53/60.04 | GROUND_INST: instantiating (17) with all_4_2, all_32_1, e2, e1, simplifying
% 251.53/60.04 | with (99), (113) gives:
% 251.53/60.04 | (130) all_32_1 = all_4_2
% 251.53/60.04 |
% 251.53/60.04 | REDUCE: (53), (130) imply:
% 251.53/60.04 | (131) ~ (all_4_2 = e3)
% 251.53/60.04 |
% 251.53/60.04 | BETA: splitting (31) gives:
% 251.53/60.04 |
% 251.53/60.04 | Case 1:
% 251.53/60.04 | |
% 251.53/60.04 | | (132) ~ (all_56_2 = e0)
% 251.53/60.04 | |
% 251.53/60.04 | | REDUCE: (40), (132) imply:
% 251.53/60.04 | | (133) ~ (all_8_2 = e0)
% 251.53/60.04 | |
% 251.53/60.04 | | BETA: splitting (97) gives:
% 251.53/60.04 | |
% 251.53/60.04 | | Case 1:
% 251.53/60.04 | | |
% 251.53/60.04 | | | (134) ~ (all_62_2 = e4)
% 251.53/60.04 | | |
% 251.53/60.04 | | | BETA: splitting (50) gives:
% 251.53/60.04 | | |
% 251.53/60.04 | | | Case 1:
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | (135) ~ (all_64_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | BETA: splitting (72) gives:
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | Case 1:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | (136) ~ (all_70_2 = e2)
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | REDUCE: (63), (136) imply:
% 251.53/60.04 | | | | | (137) ~ (all_62_2 = e2)
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | REF_CLOSE: (5), (17), (24), (33), (37), (42), (56), (59), (67), (90),
% 251.53/60.04 | | | | | (99), (107), (109), (121), (123), (137) are inconsistent by
% 251.53/60.04 | | | | | sub-proof #709.
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | Case 2:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | (138) all_70_2 = e2
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | REF_CLOSE: (8), (11), (12), (16), (17), (18), (19), (26), (27), (38),
% 251.53/60.04 | | | | | (45), (61), (63), (64), (73), (81), (89), (95), (105),
% 251.53/60.04 | | | | | (118), (126), (127), (134), (135), (138) are inconsistent
% 251.53/60.04 | | | | | by sub-proof #699.
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | End of split
% 251.53/60.04 | | | |
% 251.53/60.04 | | | Case 2:
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | (139) all_64_2 = e3
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (57), (139) imply:
% 251.53/60.04 | | | | (140) ~ (all_244_0 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (23), (139) imply:
% 251.53/60.04 | | | | (141) ~ (all_244_8 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (39), (139) imply:
% 251.53/60.04 | | | | (142) ~ (all_100_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (111), (139) imply:
% 251.53/60.04 | | | | (143) ~ (all_16_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | SIMP: (143) implies:
% 251.53/60.04 | | | | (144) ~ (all_16_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (75), (139) imply:
% 251.53/60.04 | | | | (145) ~ (all_12_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | SIMP: (145) implies:
% 251.53/60.04 | | | | (146) ~ (all_12_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (46), (139) imply:
% 251.53/60.04 | | | | (147) ~ (all_10_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | SIMP: (147) implies:
% 251.53/60.04 | | | | (148) ~ (all_10_2 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | REDUCE: (127), (139) imply:
% 251.53/60.04 | | | | (149) ~ (e4 = e3)
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | BETA: splitting (26) gives:
% 251.53/60.04 | | | |
% 251.53/60.04 | | | | Case 1:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | (150) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 251.53/60.04 | | | | | e3) = e3)
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | BETA: splitting (150) gives:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | Case 1:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | (151) all_252_6 = e3 & op(e2, e4) = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | ALPHA: (151) implies:
% 251.53/60.04 | | | | | | (152) all_252_6 = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | BETA: splitting (114) gives:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | Case 1:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (153) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 &
% 251.53/60.04 | | | | | | | op(e3, e4) = e2)
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | BETA: splitting (153) gives:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (154) all_252_0 = e2 & op(e4, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | ALPHA: (154) implies:
% 251.53/60.04 | | | | | | | | (155) op(e4, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | REF_CLOSE: (17), (44), (87), (155) are inconsistent by sub-proof
% 251.53/60.04 | | | | | | | | #809.
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (156) all_252_2 = e2 & op(e3, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | ALPHA: (156) implies:
% 251.53/60.04 | | | | | | | | (157) all_252_2 = e2
% 251.53/60.04 | | | | | | | | (158) op(e3, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | GROUND_INST: instantiating (17) with all_100_2, e2, e4, e3,
% 251.53/60.04 | | | | | | | | simplifying with (85), (158) gives:
% 251.53/60.04 | | | | | | | | (159) all_100_2 = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | COMBINE_EQS: (32), (159) imply:
% 251.53/60.04 | | | | | | | | (160) all_168_2 = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | REDUCE: (117), (159) imply:
% 251.53/60.04 | | | | | | | | (161) ~ (all_16_2 = e2)
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | REDUCE: (142), (159) imply:
% 251.53/60.04 | | | | | | | | (162) ~ (e3 = e2)
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | BETA: splitting (125) gives:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (163) ~ (all_168_2 = e2)
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | REDUCE: (160), (163) imply:
% 251.53/60.04 | | | | | | | | | (164) $false
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | CLOSE: (164) is inconsistent.
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (165) ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.53/60.04 | | | | | | | | | op(e2, all_168_1) = all_168_0 & $i(all_168_0) &
% 251.53/60.04 | | | | | | | | | $i(all_168_1)) | ( ~ (all_168_1 = e1) & op(e4, e2)
% 251.53/60.04 | | | | | | | | | = all_168_1 & $i(all_168_1))
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | BETA: splitting (165) gives:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | (166) ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.53/60.04 | | | | | | | | | | op(e2, all_168_1) = all_168_0 & $i(all_168_0) &
% 251.53/60.04 | | | | | | | | | | $i(all_168_1)
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | ALPHA: (166) implies:
% 251.53/60.04 | | | | | | | | | | (167) op(e4, e2) = all_168_1
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 251.53/60.04 | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 251.53/60.04 | | | | | | | | | | (24), (25), (27), (28), (29), (30), (33), (34),
% 251.53/60.04 | | | | | | | | | | (35), (36), (37), (38), (41), (42), (47), (48),
% 251.53/60.04 | | | | | | | | | | (49), (51), (52), (54), (55), (56), (58), (59),
% 251.53/60.04 | | | | | | | | | | (61), (62), (63), (66), (67), (68), (69), (70),
% 251.53/60.04 | | | | | | | | | | (71), (72), (74), (76), (77), (78), (79), (80),
% 251.53/60.04 | | | | | | | | | | (81), (82), (83), (86), (87), (88), (89), (90),
% 251.53/60.04 | | | | | | | | | | (92), (93), (94), (95), (96), (98), (99), (100),
% 251.53/60.04 | | | | | | | | | | (101), (102), (103), (104), (106), (107), (109),
% 251.53/60.04 | | | | | | | | | | (110), (115), (121), (122), (123), (124), (128),
% 251.53/60.04 | | | | | | | | | | (129), (131), (133), (134), (140), (141), (146),
% 251.53/60.04 | | | | | | | | | | (148), (152), (157), (167) are inconsistent by
% 251.53/60.04 | | | | | | | | | | sub-proof #667.
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | (168) ~ (all_168_1 = e1) & op(e4, e2) = all_168_1 &
% 251.53/60.04 | | | | | | | | | | $i(all_168_1)
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | ALPHA: (168) implies:
% 251.53/60.04 | | | | | | | | | | (169) op(e4, e2) = all_168_1
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 251.53/60.04 | | | | | | | | | | (12), (14), (15), (17), (18), (19), (20), (21),
% 251.53/60.04 | | | | | | | | | | (24), (25), (27), (28), (29), (30), (33), (34),
% 251.53/60.04 | | | | | | | | | | (35), (36), (37), (38), (41), (42), (47), (48),
% 251.53/60.04 | | | | | | | | | | (49), (51), (52), (54), (55), (56), (58), (59),
% 251.53/60.04 | | | | | | | | | | (61), (62), (63), (66), (67), (68), (69), (70),
% 251.53/60.04 | | | | | | | | | | (71), (72), (74), (76), (77), (78), (79), (80),
% 251.53/60.04 | | | | | | | | | | (81), (82), (83), (86), (87), (88), (89), (90),
% 251.53/60.04 | | | | | | | | | | (92), (93), (94), (95), (96), (98), (99), (100),
% 251.53/60.04 | | | | | | | | | | (101), (102), (103), (104), (106), (107), (109),
% 251.53/60.04 | | | | | | | | | | (110), (115), (121), (122), (123), (124), (128),
% 251.53/60.04 | | | | | | | | | | (129), (131), (133), (134), (140), (141), (146),
% 251.53/60.04 | | | | | | | | | | (148), (152), (157), (169) are inconsistent by
% 251.53/60.04 | | | | | | | | | | sub-proof #667.
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | End of split
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | End of split
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | Case 2:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (170) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 251.53/60.04 | | | | | | | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | REF_CLOSE: (8), (17), (45), (56), (65), (67), (105), (119), (127),
% 251.53/60.04 | | | | | | | (129), (170) are inconsistent by sub-proof #697.
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | End of split
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | Case 2:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | (171) all_252_7 = e3 & op(e2, e3) = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | ALPHA: (171) implies:
% 251.53/60.04 | | | | | | (172) all_252_7 = e3
% 251.53/60.04 | | | | | | (173) op(e2, e3) = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | BETA: splitting (73) gives:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | Case 1:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (174) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 &
% 251.53/60.04 | | | | | | | op(e2, e3) = e2)
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | BETA: splitting (174) gives:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (175) all_252_6 = e2 & op(e2, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | ALPHA: (175) implies:
% 251.53/60.04 | | | | | | | | (176) op(e2, e4) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | REF_CLOSE: (8), (17), (45), (105), (127), (176) are inconsistent
% 251.53/60.04 | | | | | | | | by sub-proof #790.
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (177) all_252_7 = e2 & op(e2, e3) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | REF_CLOSE: (19), (172), (177) are inconsistent by sub-proof
% 251.53/60.04 | | | | | | | | #666.
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | End of split
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | Case 2:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (178) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 &
% 251.53/60.04 | | | | | | | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | BETA: splitting (178) gives:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (179) all_252_8 = e2 & op(e2, e2) = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | ALPHA: (179) implies:
% 251.53/60.04 | | | | | | | | (180) all_252_8 = e2
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | BETA: splitting (112) gives:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (181) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3
% 251.53/60.04 | | | | | | | | | & op(e3, e4) = e3)
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | REF_CLOSE: (8), (17), (19), (44), (45), (56), (65), (67),
% 251.53/60.04 | | | | | | | | | (87), (105), (114), (119), (127), (129), (140),
% 251.53/60.04 | | | | | | | | | (181) are inconsistent by sub-proof #695.
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (182) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3
% 251.53/60.04 | | | | | | | | | & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4)
% 251.53/60.04 | | | | | | | | | = e3)
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | BETA: splitting (182) gives:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | (183) all_252_6 = e3 & op(e2, e4) = e3
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | ALPHA: (183) implies:
% 251.53/60.04 | | | | | | | | | | (184) all_252_6 = e3
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | BETA: splitting (22) gives:
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | (185) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 251.53/60.04 | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | BETA: splitting (185) gives:
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | (186) all_252_6 = e1 & op(e2, e4) = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | ALPHA: (186) implies:
% 251.53/60.04 | | | | | | | | | | | | (187) all_252_6 = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | COMBINE_EQS: (184), (187) imply:
% 251.53/60.04 | | | | | | | | | | | | (188) e3 = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | REDUCE: (64), (188) imply:
% 251.53/60.04 | | | | | | | | | | | | (189) $false
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | (190) all_252_7 = e1 & op(e2, e3) = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | ALPHA: (190) implies:
% 251.53/60.04 | | | | | | | | | | | | (191) op(e2, e3) = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | REF_CLOSE: (17), (64), (173), (191) are inconsistent by
% 251.53/60.04 | | | | | | | | | | | | sub-proof #881.
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | (192) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 251.53/60.04 | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 251.53/60.04 | | | | | | | | | | | op(e2, e0) = e1)
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | BETA: splitting (192) gives:
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | (193) all_252_8 = e1 & op(e2, e2) = e1
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | REF_CLOSE: (38), (180), (193) are inconsistent by sub-proof
% 251.53/60.04 | | | | | | | | | | | | #665.
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | (194) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 251.53/60.04 | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | BETA: splitting (194) gives:
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | (195) all_252_11 = e1 & op(e2, e1) = e1
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | ALPHA: (195) implies:
% 251.53/60.04 | | | | | | | | | | | | | (196) all_252_11 = e1
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | COMBINE_EQS: (95), (196) imply:
% 251.53/60.04 | | | | | | | | | | | | | (197) e1 = e0
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | REDUCE: (13), (197) imply:
% 251.53/60.04 | | | | | | | | | | | | | (198) $false
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | (199) all_252_18 = e1 & op(e2, e0) = e1
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | ALPHA: (199) implies:
% 251.53/60.04 | | | | | | | | | | | | | (200) op(e2, e0) = e1
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | | REF_CLOSE: (11), (17), (43), (200) are inconsistent by
% 251.53/60.04 | | | | | | | | | | | | | sub-proof #664.
% 251.53/60.04 | | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | (201) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 =
% 251.53/60.04 | | | | | | | | | | e3 & op(e0, e4) = e3)
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | | REF_CLOSE: (17), (56), (129), (144), (146), (201) are
% 251.53/60.04 | | | | | | | | | | inconsistent by sub-proof #894.
% 251.53/60.04 | | | | | | | | | |
% 251.53/60.04 | | | | | | | | | End of split
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | End of split
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | (202) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2
% 251.53/60.04 | | | | | | | | & op(e2, e0) = e2)
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | BETA: splitting (202) gives:
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 1:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (203) all_252_11 = e2 & op(e2, e1) = e2
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | REF_CLOSE: (12), (17), (27), (126), (203) are inconsistent by
% 251.53/60.04 | | | | | | | | | sub-proof #722.
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | Case 2:
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | (204) all_252_18 = e2 & op(e2, e0) = e2
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | | REF_CLOSE: (11), (17), (108), (118), (204) are inconsistent by
% 251.53/60.04 | | | | | | | | | sub-proof #702.
% 251.53/60.04 | | | | | | | | |
% 251.53/60.04 | | | | | | | | End of split
% 251.53/60.04 | | | | | | | |
% 251.53/60.04 | | | | | | | End of split
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | End of split
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | End of split
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | Case 2:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | (205) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 &
% 251.53/60.04 | | | | | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | BETA: splitting (205) gives:
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | | Case 1:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | (206) all_252_8 = e3 & op(e2, e2) = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | ALPHA: (206) implies:
% 251.53/60.04 | | | | | | (207) op(e2, e2) = e3
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | REF_CLOSE: (17), (24), (141), (207) are inconsistent by sub-proof
% 251.53/60.04 | | | | | | #877.
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | Case 2:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | (208) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 251.53/60.04 | | | | | | op(e2, e0) = e3)
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | BETA: splitting (208) gives:
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | | Case 1:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (209) all_252_11 = e3 & op(e2, e1) = e3
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | REF_CLOSE: (61), (95), (209) are inconsistent by sub-proof #701.
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | Case 2:
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | (210) all_252_18 = e3 & op(e2, e0) = e3
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | | REF_CLOSE: (16), (89), (210) are inconsistent by sub-proof #663.
% 251.53/60.04 | | | | | | |
% 251.53/60.04 | | | | | | End of split
% 251.53/60.04 | | | | | |
% 251.53/60.04 | | | | | End of split
% 251.53/60.04 | | | | |
% 251.53/60.04 | | | | End of split
% 251.53/60.04 | | | |
% 251.53/60.04 | | | End of split
% 251.53/60.04 | | |
% 251.53/60.04 | | Case 2:
% 251.53/60.04 | | |
% 251.53/60.04 | | | (211) all_62_2 = e4
% 251.53/60.04 | | |
% 251.53/60.04 | | | REF_CLOSE: (17), (21), (29), (34), (60), (62), (66), (81), (82), (84),
% 251.53/60.04 | | | (90), (94), (95), (103), (115), (116), (211) are inconsistent
% 251.53/60.04 | | | by sub-proof #715.
% 251.53/60.04 | | |
% 251.53/60.04 | | End of split
% 251.53/60.04 | |
% 251.53/60.04 | Case 2:
% 251.53/60.04 | |
% 251.53/60.04 | | (212) all_56_2 = e0
% 251.53/60.04 | |
% 251.53/60.04 | | REF_CLOSE: (14), (17), (40), (42), (120), (212) are inconsistent by
% 251.53/60.04 | | sub-proof #668.
% 251.53/60.04 | |
% 251.53/60.04 | End of split
% 251.53/60.04 |
% 251.53/60.04 End of proof
% 251.53/60.04
% 251.53/60.04 Sub-proof #663 shows that the following formulas are inconsistent:
% 251.53/60.04 ----------------------------------------------------------------
% 251.53/60.04 (1) all_252_18 = e3 & op(e2, e0) = e3
% 251.53/60.04 (2) all_252_18 = e4
% 251.53/60.04 (3) ~ (e4 = e3)
% 251.53/60.04
% 251.53/60.04 Begin of proof
% 251.53/60.04 |
% 251.53/60.04 | ALPHA: (1) implies:
% 251.53/60.04 | (4) all_252_18 = e3
% 251.53/60.04 |
% 251.53/60.04 | COMBINE_EQS: (2), (4) imply:
% 251.53/60.04 | (5) e4 = e3
% 251.53/60.04 |
% 251.53/60.04 | SIMP: (5) implies:
% 251.53/60.04 | (6) e4 = e3
% 251.53/60.04 |
% 251.53/60.04 | REDUCE: (3), (6) imply:
% 251.53/60.04 | (7) $false
% 251.53/60.04 |
% 251.53/60.04 | CLOSE: (7) is inconsistent.
% 251.53/60.04 |
% 251.53/60.04 End of proof
% 251.53/60.04
% 251.53/60.04 Sub-proof #664 shows that the following formulas are inconsistent:
% 251.53/60.04 ----------------------------------------------------------------
% 251.53/60.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.04 (2) op(e2, e0) = e4
% 251.53/60.04 (3) op(e2, e0) = e1
% 251.53/60.04 (4) ~ (e4 = e1)
% 251.53/60.04
% 251.53/60.04 Begin of proof
% 251.53/60.04 |
% 251.53/60.04 | GROUND_INST: instantiating (1) with e1, e4, e0, e2, simplifying with (2), (3)
% 251.53/60.04 | gives:
% 251.53/60.04 | (5) e4 = e1
% 251.53/60.04 |
% 251.53/60.04 | REDUCE: (4), (5) imply:
% 251.53/60.04 | (6) $false
% 251.53/60.04 |
% 251.53/60.04 | CLOSE: (6) is inconsistent.
% 251.53/60.04 |
% 251.53/60.04 End of proof
% 251.53/60.04
% 251.53/60.04 Sub-proof #665 shows that the following formulas are inconsistent:
% 251.53/60.04 ----------------------------------------------------------------
% 251.53/60.04 (1) all_252_8 = e1 & op(e2, e2) = e1
% 251.53/60.04 (2) all_252_8 = e2
% 251.53/60.04 (3) ~ (e2 = e1)
% 251.53/60.04
% 251.53/60.04 Begin of proof
% 251.53/60.04 |
% 251.53/60.04 | ALPHA: (1) implies:
% 251.53/60.04 | (4) all_252_8 = e1
% 251.53/60.04 |
% 251.53/60.04 | COMBINE_EQS: (2), (4) imply:
% 251.53/60.04 | (5) e2 = e1
% 251.53/60.04 |
% 251.53/60.04 | REDUCE: (3), (5) imply:
% 251.53/60.04 | (6) $false
% 251.53/60.04 |
% 251.53/60.04 | CLOSE: (6) is inconsistent.
% 251.53/60.04 |
% 251.53/60.04 End of proof
% 251.53/60.04
% 251.53/60.04 Sub-proof #666 shows that the following formulas are inconsistent:
% 251.53/60.04 ----------------------------------------------------------------
% 251.53/60.04 (1) all_252_7 = e2 & op(e2, e3) = e2
% 251.53/60.04 (2) all_252_7 = e3
% 251.53/60.04 (3) ~ (e3 = e2)
% 251.53/60.04
% 251.53/60.04 Begin of proof
% 251.53/60.04 |
% 251.53/60.04 | ALPHA: (1) implies:
% 251.53/60.04 | (4) all_252_7 = e2
% 251.53/60.04 |
% 251.53/60.04 | COMBINE_EQS: (2), (4) imply:
% 251.53/60.04 | (5) e3 = e2
% 251.53/60.04 |
% 251.53/60.04 | REDUCE: (3), (5) imply:
% 251.53/60.04 | (6) $false
% 251.53/60.04 |
% 251.53/60.04 | CLOSE: (6) is inconsistent.
% 251.53/60.04 |
% 251.53/60.04 End of proof
% 251.53/60.04
% 251.53/60.04 Sub-proof #667 shows that the following formulas are inconsistent:
% 251.53/60.04 ----------------------------------------------------------------
% 251.53/60.04 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.53/60.04 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.53/60.04 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.53/60.04 (2) ~ (all_4_2 = e4)
% 251.53/60.04 (3) ~ (all_10_2 = e4)
% 251.53/60.05 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.05 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.53/60.05 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.53/60.05 (5) op(all_4_2, e2) = e1
% 251.53/60.05 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.53/60.05 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.53/60.05 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.53/60.05 (7) ~ (all_244_8 = e0)
% 251.53/60.05 (8) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.53/60.05 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.53/60.05 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.05 (9) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 251.53/60.05 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 251.53/60.05 | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.53/60.05 (10) ~ (e2 = e0)
% 251.53/60.05 (11) ~ (all_28_2 = e3)
% 251.53/60.05 (12) ~ (all_62_2 = all_22_2)
% 251.53/60.05 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.05 (14) op(e2, e3) = all_10_2
% 251.53/60.05 (15) ~ (e3 = e2)
% 251.53/60.05 (16) ~ (all_10_2 = e3)
% 251.53/60.05 (17) op(e0, e0) = all_244_24
% 251.53/60.05 (18) ~ (e4 = e0)
% 251.53/60.05 (19) ~ (all_12_2 = e3)
% 251.53/60.05 (20) op(e2, e2) = all_244_8
% 251.53/60.05 (21) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.53/60.05 all_250_11 = e0
% 251.53/60.05 (22) op(e2, e1) = all_38_2
% 251.53/60.05 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.53/60.05 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.53/60.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.53/60.05 (24) ~ (all_84_2 = all_62_2)
% 251.53/60.05 (25) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.53/60.05 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.53/60.05 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.53/60.05 (26) op(e1, e0) = all_34_2
% 251.53/60.05 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.53/60.05 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.53/60.05 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.53/60.05 (28) op(e4, e2) = all_6_2
% 251.53/60.05 (29) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.53/60.05 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.53/60.05 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.53/60.05 (30) ~ (all_34_2 = e2)
% 251.53/60.05 (31) ~ (e2 = e1)
% 251.53/60.05 (32) ~ (all_34_2 = e4)
% 251.53/60.05 (33) op(e0, e2) = all_28_2
% 251.53/60.05 (34) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.53/60.05 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.53/60.05 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.53/60.05 (35) ~ (all_244_8 = all_10_2)
% 251.53/60.05 (36) ~ (all_6_2 = e1)
% 251.53/60.05 (37) all_252_16 = e2
% 251.53/60.05 (38) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.53/60.05 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.53/60.05 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.53/60.05 (39) ~ (all_244_3 = all_84_2)
% 251.53/60.05 (40) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.53/60.05 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.53/60.05 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.53/60.05 (41) op(e1, e4) = all_16_2
% 251.53/60.05 (42) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.53/60.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.53/60.05 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.53/60.05 (43) op(e1, e3) = all_62_2
% 251.53/60.05 (44) ~ (e3 = e0)
% 251.53/60.05 (45) ~ (all_36_2 = e4)
% 251.53/60.05 (46) all_70_2 = all_62_2
% 251.53/60.05 (47) op(e3, e1) = all_36_2
% 251.53/60.05 (48) ~ (all_16_2 = e2)
% 251.53/60.05 (49) op(e4, e2) = all_168_1
% 251.53/60.05 (50) ~ (all_8_2 = e1)
% 251.53/60.05 (51) ~ (all_244_3 = all_62_2)
% 251.53/60.05 (52) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.53/60.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.53/60.05 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.53/60.05 (53) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.53/60.05 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.53/60.05 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.53/60.05 (54) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.53/60.05 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.53/60.05 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.53/60.05 (55) ~ (all_8_2 = e0)
% 251.53/60.05 (56) ~ (all_38_2 = e4)
% 251.53/60.05 (57) op(all_22_2, e3) = e0
% 251.53/60.05 (58) all_68_2 = all_22_2
% 251.53/60.05 (59) op(e0, e3) = all_22_2
% 251.53/60.05 (60) ~ (all_244_24 = e4)
% 251.53/60.05 (61) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.53/60.05 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.53/60.05 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.53/60.05 (62) ~ (all_244_8 = e3)
% 251.53/60.05 (63) op(all_62_2, e3) = e1
% 251.53/60.05 (64) op(e4, e1) = all_26_2
% 251.53/60.05 (65) op(all_10_2, e3) = e2
% 251.53/60.05 (66) all_250_11 = all_10_2
% 251.53/60.05 (67) op(e4, e4) = all_244_0
% 251.53/60.05 (68) ~ (all_48_2 = e4)
% 251.53/60.05 (69) ~ (e4 = e3)
% 251.53/60.05 (70) op(e1, e1) = all_244_15
% 251.53/60.05 (71) all_252_23 = e2
% 251.53/60.05 (72) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.53/60.05 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.53/60.05 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.53/60.05 (73) op(e0, e1) = all_20_2
% 251.53/60.05 (74) all_252_11 = e0
% 251.53/60.05 (75) op(e3, e0) = all_48_2
% 251.53/60.05 (76) ~ (all_26_2 = e3)
% 251.53/60.05 (77) op(e1, e2) = all_4_2
% 251.53/60.05 (78) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.53/60.05 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.53/60.05 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.53/60.05 (79) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.53/60.05 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.53/60.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.53/60.05 (80) all_252_2 = e2
% 251.53/60.05 (81) ~ (all_48_2 = e1)
% 251.53/60.05 (82) op(e4, e3) = all_84_2
% 251.53/60.05 (83) ~ (all_62_2 = all_10_2)
% 251.53/60.05 (84) ~ (all_22_2 = all_10_2)
% 251.53/60.05 (85) ~ (all_244_15 = e2)
% 251.53/60.05 (86) op(e0, all_4_2) = e1
% 251.53/60.05 (87) op(e3, e2) = all_8_2
% 251.53/60.05 (88) ~ (all_20_2 = e4)
% 251.53/60.05 (89) ~ (all_244_8 = all_28_2)
% 251.53/60.05 (90) ~ (all_10_2 = e0)
% 251.53/60.05 (91) all_252_6 = e3
% 251.53/60.05 (92) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.53/60.05 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.53/60.05 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.53/60.05 (93) ~ (all_244_0 = e3)
% 251.53/60.05 (94) op(e3, e3) = all_244_3
% 251.53/60.05 (95) ~ (all_4_2 = e3)
% 251.53/60.05 (96) ~ (all_62_2 = e4)
% 251.53/60.05 (97) op(all_244_24, all_244_24) = e0
% 251.53/60.05 (98) op(e0, e4) = all_12_2
% 251.53/60.05
% 251.53/60.05 Begin of proof
% 251.53/60.05 |
% 251.53/60.05 | GROUND_INST: instantiating (13) with all_6_2, all_168_1, e2, e4, simplifying
% 251.53/60.05 | with (28), (49) gives:
% 251.53/60.05 | (99) all_168_1 = all_6_2
% 251.53/60.05 |
% 251.53/60.05 | BETA: splitting (25) gives:
% 251.53/60.05 |
% 251.53/60.05 | Case 1:
% 251.53/60.05 | |
% 251.53/60.05 | | (100) ~ (all_68_2 = e4)
% 251.53/60.05 | |
% 251.53/60.05 | | REDUCE: (58), (100) imply:
% 251.53/60.05 | | (101) ~ (all_22_2 = e4)
% 251.53/60.05 | |
% 251.53/60.05 | | BETA: splitting (54) gives:
% 251.53/60.05 | |
% 251.53/60.05 | | Case 1:
% 251.53/60.05 | | |
% 251.53/60.05 | | | (102) ~ (all_70_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (46), (102) imply:
% 251.53/60.05 | | | (103) ~ (all_62_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REF_CLOSE: (5), (13), (20), (26), (30), (33), (41), (43), (48), (70),
% 251.53/60.05 | | | (77), (85), (86), (89), (92), (103) are inconsistent by
% 251.53/60.05 | | | sub-proof #709.
% 251.53/60.05 | | |
% 251.53/60.05 | | Case 2:
% 251.53/60.05 | | |
% 251.53/60.05 | | | (104) all_70_2 = e2
% 251.53/60.05 | | |
% 251.53/60.05 | | | COMBINE_EQS: (46), (104) imply:
% 251.53/60.05 | | | (105) all_62_2 = e2
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (105) implies:
% 251.53/60.05 | | | (106) all_62_2 = e2
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (51), (106) imply:
% 251.53/60.05 | | | (107) ~ (all_244_3 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (24), (106) imply:
% 251.53/60.05 | | | (108) ~ (all_84_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (12), (106) imply:
% 251.53/60.05 | | | (109) ~ (all_22_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (109) implies:
% 251.53/60.05 | | | (110) ~ (all_22_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (83), (106) imply:
% 251.53/60.05 | | | (111) ~ (all_10_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (111) implies:
% 251.53/60.05 | | | (112) ~ (all_10_2 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (96), (106) imply:
% 251.53/60.05 | | | (113) ~ (e4 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (113) implies:
% 251.53/60.05 | | | (114) ~ (e4 = e2)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (63), (106) imply:
% 251.53/60.05 | | | (115) op(e2, e3) = e1
% 251.53/60.05 | | |
% 251.53/60.05 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (13), (14), (15),
% 251.53/60.05 | | | (16), (17), (18), (19), (20), (21), (22), (23), (26), (27),
% 251.53/60.05 | | | (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 251.53/60.05 | | | (40), (42), (43), (44), (45), (47), (50), (52), (53), (55),
% 251.53/60.05 | | | (56), (59), (60), (61), (62), (64), (65), (66), (67), (68),
% 251.53/60.05 | | | (69), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 251.53/60.05 | | | (80), (81), (82), (84), (87), (88), (90), (91), (93), (94),
% 251.53/60.05 | | | (95), (96), (98), (101), (107), (108), (110), (112), (114),
% 251.53/60.05 | | | (115) are inconsistent by sub-proof #672.
% 251.53/60.05 | | |
% 251.53/60.05 | | End of split
% 251.53/60.05 | |
% 251.53/60.05 | Case 2:
% 251.53/60.05 | |
% 251.53/60.05 | | (116) all_68_2 = e4
% 251.53/60.05 | |
% 251.53/60.05 | | REF_CLOSE: (11), (13), (15), (17), (19), (33), (39), (42), (57), (58), (59),
% 251.53/60.05 | | (69), (71), (82), (94), (97), (98), (116) are inconsistent by
% 251.53/60.05 | | sub-proof #670.
% 251.53/60.05 | |
% 251.53/60.05 | End of split
% 251.53/60.05 |
% 251.53/60.05 End of proof
% 251.53/60.05
% 251.53/60.05 Sub-proof #668 shows that the following formulas are inconsistent:
% 251.53/60.05 ----------------------------------------------------------------
% 251.53/60.05 (1) ~ (all_28_2 = e3)
% 251.53/60.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.05 (3) all_56_2 = e0
% 251.53/60.05 (4) all_56_2 = all_8_2
% 251.53/60.05 (5) op(e0, e2) = all_28_2
% 251.53/60.05 (6) op(all_8_2, e2) = e3
% 251.53/60.05
% 251.53/60.05 Begin of proof
% 251.53/60.05 |
% 251.53/60.05 | COMBINE_EQS: (3), (4) imply:
% 251.53/60.05 | (7) all_8_2 = e0
% 251.53/60.05 |
% 251.53/60.05 | SIMP: (7) implies:
% 251.53/60.05 | (8) all_8_2 = e0
% 251.53/60.05 |
% 251.53/60.05 | REDUCE: (6), (8) imply:
% 251.53/60.05 | (9) op(e0, e2) = e3
% 251.53/60.05 |
% 251.53/60.05 | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #975.
% 251.53/60.05 |
% 251.53/60.05 End of proof
% 251.53/60.05
% 251.53/60.05 Sub-proof #669 shows that the following formulas are inconsistent:
% 251.53/60.05 ----------------------------------------------------------------
% 251.53/60.05 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.53/60.05 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.53/60.05 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.53/60.05 (2) ~ (all_4_2 = e4)
% 251.53/60.05 (3) ~ (all_10_2 = e4)
% 251.53/60.05 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.05 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.53/60.05 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.53/60.05 (5) op(all_4_2, e2) = e1
% 251.53/60.05 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.53/60.05 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.53/60.05 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.53/60.05 (7) ~ (all_244_8 = e0)
% 251.53/60.05 (8) op(all_6_2, e2) = e4
% 251.53/60.05 (9) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.53/60.05 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.53/60.05 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.05 (10) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.53/60.05 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.53/60.05 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.53/60.05 (11) op(e2, e0) = e4
% 251.53/60.05 (12) op(e2, all_4_2) = all_32_0
% 251.53/60.05 (13) ~ (e2 = e0)
% 251.53/60.05 (14) ~ (all_28_2 = e3)
% 251.53/60.05 (15) ~ (all_62_2 = all_22_2)
% 251.53/60.05 (16) all_252_18 = e4
% 251.53/60.05 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.05 (18) op(e2, e3) = all_10_2
% 251.53/60.05 (19) ~ (e3 = e2)
% 251.53/60.05 (20) op(e0, e0) = all_244_24
% 251.53/60.05 (21) ~ (e4 = e0)
% 251.53/60.05 (22) ~ (all_244_8 = all_64_2)
% 251.53/60.05 (23) op(e2, e2) = all_244_8
% 251.53/60.05 (24) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.53/60.05 all_250_11 = e0
% 251.53/60.05 (25) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.53/60.05 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.53/60.05 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.53/60.05 (26) op(e2, e1) = all_38_2
% 251.53/60.05 (27) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.53/60.05 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.53/60.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.53/60.05 (28) ~ (all_84_2 = all_62_2)
% 251.53/60.05 (29) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.53/60.05 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.53/60.05 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.53/60.05 (30) all_168_2 = all_100_2
% 251.53/60.05 (31) op(e1, e0) = all_34_2
% 251.53/60.05 (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.53/60.05 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.53/60.05 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.53/60.05 (33) op(e4, e2) = all_6_2
% 251.53/60.05 (34) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.53/60.05 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.53/60.05 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.53/60.05 (35) ~ (all_34_2 = e2)
% 251.53/60.05 (36) ~ (e2 = e1)
% 251.53/60.05 (37) ~ (all_100_2 = all_64_2)
% 251.53/60.05 (38) ~ (all_34_2 = e4)
% 251.53/60.05 (39) op(e0, e2) = all_28_2
% 251.53/60.05 (40) ~ (all_244_0 = e2)
% 251.53/60.05 (41) op(all_6_2, all_64_2) = e2
% 251.53/60.05 (42) ~ (all_64_2 = all_10_2)
% 251.53/60.05 (43) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.53/60.05 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.53/60.05 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.53/60.05 (44) ~ (all_244_8 = all_10_2)
% 251.53/60.05 (45) ~ (all_6_2 = e1)
% 251.53/60.05 (46) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.53/60.05 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.53/60.05 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.53/60.05 (47) all_252_16 = e2
% 251.53/60.05 (48) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.53/60.05 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.53/60.05 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.53/60.05 (49) ~ (all_244_3 = all_84_2)
% 251.53/60.05 (50) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.53/60.05 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.53/60.05 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.53/60.05 (51) op(e1, e4) = all_16_2
% 251.53/60.05 (52) ~ (all_244_0 = all_64_2)
% 251.53/60.05 (53) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.53/60.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.53/60.05 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.53/60.05 (54) op(e1, e3) = all_62_2
% 251.53/60.05 (55) op(all_16_2, all_26_2) = e4
% 251.53/60.05 (56) ~ (e3 = e0)
% 251.53/60.05 (57) ~ (all_36_2 = e4)
% 251.53/60.05 (58) all_70_2 = all_62_2
% 251.53/60.05 (59) ~ (e3 = e1)
% 251.53/60.05 (60) ~ (all_12_2 = e2)
% 251.53/60.05 (61) op(e3, e1) = all_36_2
% 251.53/60.05 (62) ~ (all_16_2 = e2)
% 251.53/60.05 (63) ~ (all_8_2 = e1)
% 251.53/60.05 (64) ~ (all_244_3 = all_62_2)
% 251.53/60.05 (65) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.53/60.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.53/60.05 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.53/60.05 (66) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.53/60.05 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.53/60.05 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.53/60.05 (67) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.53/60.05 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.53/60.05 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.53/60.05 (68) ~ (all_8_2 = e0)
% 251.53/60.05 (69) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.53/60.05 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.53/60.05 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.53/60.05 (70) ~ (all_38_2 = e4)
% 251.53/60.05 (71) ~ (all_64_2 = all_12_2)
% 251.53/60.05 (72) op(all_22_2, e3) = e0
% 251.53/60.05 (73) all_68_2 = all_22_2
% 251.53/60.05 (74) op(e0, e3) = all_22_2
% 251.53/60.05 (75) ~ (all_244_24 = e4)
% 251.53/60.05 (76) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.53/60.05 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.53/60.05 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.53/60.05 (77) op(all_62_2, e3) = e1
% 251.53/60.05 (78) op(e4, e1) = all_26_2
% 251.53/60.05 (79) op(all_10_2, e3) = e2
% 251.53/60.05 (80) ~ (all_244_15 = all_62_2)
% 251.53/60.05 (81) op(e3, e4) = all_100_2
% 251.53/60.05 (82) all_250_11 = all_10_2
% 251.53/60.05 (83) op(e4, e4) = all_244_0
% 251.53/60.05 (84) ~ (all_48_2 = e4)
% 251.53/60.05 (85) ~ (e4 = e3)
% 251.53/60.05 (86) op(e1, e1) = all_244_15
% 251.53/60.05 (87) ~ (all_64_2 = e0)
% 251.53/60.05 (88) all_252_23 = e2
% 251.53/60.05 (89) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.53/60.05 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.53/60.05 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.53/60.05 (90) op(e0, e1) = all_20_2
% 251.53/60.05 (91) all_252_11 = e0
% 251.53/60.05 (92) op(e3, e0) = all_48_2
% 251.53/60.05 (93) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.53/60.05 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.53/60.05 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.53/60.05 (94) ~ (all_26_2 = e3)
% 251.53/60.05 (95) op(e1, e2) = all_4_2
% 251.53/60.05 (96) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.53/60.05 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.53/60.05 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.53/60.05 (97) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.53/60.05 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.53/60.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.53/60.05 (98) ~ (all_48_2 = e1)
% 251.53/60.05 (99) op(e4, e3) = all_84_2
% 251.53/60.05 (100) ~ (all_62_2 = all_10_2)
% 251.53/60.05 (101) op(e2, e4) = all_64_2
% 251.53/60.05 (102) ~ (all_22_2 = all_10_2)
% 251.53/60.05 (103) ~ (all_244_15 = e2)
% 251.53/60.05 (104) op(e0, all_4_2) = e1
% 251.53/60.05 (105) op(e3, e2) = all_8_2
% 251.53/60.05 (106) ~ (all_64_2 = all_16_2)
% 251.53/60.05 (107) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.53/60.05 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.53/60.05 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.53/60.05 (108) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.53/60.05 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.53/60.05 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.53/60.05 (109) ~ (all_20_2 = e4)
% 251.53/60.05 (110) op(all_16_2, e4) = e1
% 251.53/60.05 (111) ~ (all_100_2 = all_16_2)
% 251.53/60.05 (112) op(e2, e0) = all_40_2
% 251.53/60.05 (113) op(e0, e4) = all_40_1
% 251.53/60.05 (114) ~ (all_244_8 = all_28_2)
% 251.53/60.05 (115) ~ (all_10_2 = e0)
% 251.53/60.05 (116) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.53/60.05 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.53/60.05 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.53/60.05 (117) op(e3, e3) = all_244_3
% 251.53/60.05 (118) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.53/60.05 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.53/60.05 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.53/60.05 (119) ~ (all_4_2 = e3)
% 251.53/60.05 (120) op(e2, e1) = e0
% 251.53/60.05 (121) ~ (all_64_2 = e4)
% 251.53/60.05 (122) op(all_244_24, all_244_24) = e0
% 251.53/60.05 (123) op(e0, e4) = all_12_2
% 251.53/60.05
% 251.53/60.05 Begin of proof
% 251.53/60.05 |
% 251.53/60.05 | BETA: splitting (93) gives:
% 251.53/60.05 |
% 251.53/60.05 | Case 1:
% 251.53/60.05 | |
% 251.53/60.05 | | (124) ~ (all_62_2 = e4)
% 251.53/60.05 | |
% 251.53/60.05 | | BETA: splitting (46) gives:
% 251.53/60.05 | |
% 251.53/60.05 | | Case 1:
% 251.53/60.05 | | |
% 251.53/60.05 | | | (125) ~ (all_64_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | BETA: splitting (67) gives:
% 251.53/60.05 | | |
% 251.53/60.05 | | | Case 1:
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | (126) ~ (all_70_2 = e2)
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | REF_CLOSE: (5), (12), (17), (23), (31), (35), (39), (51), (54), (58),
% 251.53/60.05 | | | | (62), (86), (95), (103), (104), (114), (116), (126) are
% 251.53/60.05 | | | | inconsistent by sub-proof #704.
% 251.53/60.05 | | | |
% 251.53/60.05 | | | Case 2:
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | (127) all_70_2 = e2
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | REF_CLOSE: (8), (11), (13), (16), (17), (18), (19), (25), (26), (36),
% 251.53/60.05 | | | | (41), (56), (58), (59), (69), (77), (85), (91), (101), (112),
% 251.53/60.05 | | | | (120), (121), (124), (125), (127) are inconsistent by
% 251.53/60.05 | | | | sub-proof #699.
% 251.53/60.05 | | | |
% 251.53/60.05 | | | End of split
% 251.53/60.05 | | |
% 251.53/60.05 | | Case 2:
% 251.53/60.05 | | |
% 251.53/60.05 | | | (128) all_64_2 = e3
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (52), (128) imply:
% 251.53/60.05 | | | (129) ~ (all_244_0 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (22), (128) imply:
% 251.53/60.05 | | | (130) ~ (all_244_8 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (37), (128) imply:
% 251.53/60.05 | | | (131) ~ (all_100_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (106), (128) imply:
% 251.53/60.05 | | | (132) ~ (all_16_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (132) implies:
% 251.53/60.05 | | | (133) ~ (all_16_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (71), (128) imply:
% 251.53/60.05 | | | (134) ~ (all_12_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (134) implies:
% 251.53/60.05 | | | (135) ~ (all_12_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (42), (128) imply:
% 251.53/60.05 | | | (136) ~ (all_10_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | SIMP: (136) implies:
% 251.53/60.05 | | | (137) ~ (all_10_2 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | REDUCE: (121), (128) imply:
% 251.53/60.05 | | | (138) ~ (e4 = e3)
% 251.53/60.05 | | |
% 251.53/60.05 | | | BETA: splitting (108) gives:
% 251.53/60.05 | | |
% 251.53/60.05 | | | Case 1:
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | (139) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3,
% 251.53/60.05 | | | | e4) = e2)
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | BETA: splitting (139) gives:
% 251.53/60.05 | | | |
% 251.53/60.05 | | | | Case 1:
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | (140) all_252_0 = e2 & op(e4, e4) = e2
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | ALPHA: (140) implies:
% 251.53/60.05 | | | | | (141) op(e4, e4) = e2
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | REF_CLOSE: (17), (40), (83), (141) are inconsistent by sub-proof #809.
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | Case 2:
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | (142) all_252_2 = e2 & op(e3, e4) = e2
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | ALPHA: (142) implies:
% 251.53/60.05 | | | | | (143) all_252_2 = e2
% 251.53/60.05 | | | | | (144) op(e3, e4) = e2
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | BETA: splitting (107) gives:
% 251.53/60.05 | | | | |
% 251.53/60.05 | | | | | Case 1:
% 251.53/60.05 | | | | | |
% 251.53/60.06 | | | | | | (145) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 &
% 251.53/60.06 | | | | | | op(e3, e4) = e3)
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | | REF_CLOSE: (8), (17), (19), (40), (41), (51), (60), (62), (83),
% 251.53/60.06 | | | | | | (101), (108), (113), (121), (123), (129), (145) are
% 251.53/60.06 | | | | | | inconsistent by sub-proof #695.
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | Case 2:
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | | (146) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 251.53/60.06 | | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | | BETA: splitting (146) gives:
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | | Case 1:
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | (147) all_252_6 = e3 & op(e2, e4) = e3
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | ALPHA: (147) implies:
% 251.53/60.06 | | | | | | | (148) all_252_6 = e3
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | GROUND_INST: instantiating (17) with all_100_2, e2, e4, e3,
% 251.53/60.06 | | | | | | | simplifying with (81), (144) gives:
% 251.53/60.06 | | | | | | | (149) all_100_2 = e2
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | COMBINE_EQS: (30), (149) imply:
% 251.53/60.06 | | | | | | | (150) all_168_2 = e2
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | REDUCE: (111), (149) imply:
% 251.53/60.06 | | | | | | | (151) ~ (all_16_2 = e2)
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | REDUCE: (131), (149) imply:
% 251.53/60.06 | | | | | | | (152) ~ (e3 = e2)
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | BETA: splitting (118) gives:
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | Case 1:
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | (153) ~ (all_168_2 = e2)
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | REDUCE: (150), (153) imply:
% 251.53/60.06 | | | | | | | | (154) $false
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | CLOSE: (154) is inconsistent.
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | Case 2:
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | (155) ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 & op(e2,
% 251.53/60.06 | | | | | | | | all_168_1) = all_168_0 & $i(all_168_0) &
% 251.53/60.06 | | | | | | | | $i(all_168_1)) | ( ~ (all_168_1 = e1) & op(e4, e2) =
% 251.53/60.06 | | | | | | | | all_168_1 & $i(all_168_1))
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | BETA: splitting (155) gives:
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | | Case 1:
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | (156) ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 & op(e2,
% 251.53/60.06 | | | | | | | | | all_168_1) = all_168_0 & $i(all_168_0) &
% 251.53/60.06 | | | | | | | | | $i(all_168_1)
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | ALPHA: (156) implies:
% 251.53/60.06 | | | | | | | | | (157) op(e4, e2) = all_168_1
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | GROUND_INST: instantiating (17) with all_6_2, all_168_1, e2,
% 251.53/60.06 | | | | | | | | | e4, simplifying with (33), (157) gives:
% 251.53/60.06 | | | | | | | | | (158) all_168_1 = all_6_2
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | BETA: splitting (29) gives:
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | Case 1:
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | (159) ~ (all_68_2 = e4)
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REDUCE: (73), (159) imply:
% 251.53/60.06 | | | | | | | | | | (160) ~ (all_22_2 = e4)
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 251.53/60.06 | | | | | | | | | | (12), (13), (15), (17), (18), (19), (20), (21),
% 251.53/60.06 | | | | | | | | | | (23), (24), (26), (27), (28), (31), (32), (33),
% 251.53/60.06 | | | | | | | | | | (34), (35), (36), (38), (39), (43), (44), (45),
% 251.53/60.06 | | | | | | | | | | (47), (48), (50), (51), (53), (54), (56), (57),
% 251.53/60.06 | | | | | | | | | | (58), (61), (62), (63), (64), (65), (66), (67),
% 251.53/60.06 | | | | | | | | | | (68), (70), (74), (75), (76), (77), (78), (79),
% 251.53/60.06 | | | | | | | | | | (82), (83), (84), (85), (86), (88), (89), (90),
% 251.53/60.06 | | | | | | | | | | (91), (92), (94), (95), (96), (97), (98), (99),
% 251.53/60.06 | | | | | | | | | | (100), (102), (103), (104), (105), (109), (114),
% 251.53/60.06 | | | | | | | | | | (115), (116), (117), (119), (123), (124), (129),
% 251.53/60.06 | | | | | | | | | | (130), (135), (137), (143), (148), (160) are
% 251.53/60.06 | | | | | | | | | | inconsistent by sub-proof #671.
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | Case 2:
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | (161) all_68_2 = e4
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REF_CLOSE: (14), (17), (19), (20), (39), (49), (53), (72),
% 251.53/60.06 | | | | | | | | | | (73), (74), (85), (88), (99), (117), (122), (123),
% 251.53/60.06 | | | | | | | | | | (135), (161) are inconsistent by sub-proof #670.
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | End of split
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | Case 2:
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | (162) ~ (all_168_1 = e1) & op(e4, e2) = all_168_1 &
% 251.53/60.06 | | | | | | | | | $i(all_168_1)
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | ALPHA: (162) implies:
% 251.53/60.06 | | | | | | | | | (163) ~ (all_168_1 = e1)
% 251.53/60.06 | | | | | | | | | (164) op(e4, e2) = all_168_1
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | GROUND_INST: instantiating (17) with all_6_2, all_168_1, e2,
% 251.53/60.06 | | | | | | | | | e4, simplifying with (33), (164) gives:
% 251.53/60.06 | | | | | | | | | (165) all_168_1 = all_6_2
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | BETA: splitting (29) gives:
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | | Case 1:
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | (166) ~ (all_68_2 = e4)
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REDUCE: (73), (166) imply:
% 251.53/60.06 | | | | | | | | | | (167) ~ (all_22_2 = e4)
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 251.53/60.06 | | | | | | | | | | (12), (13), (15), (17), (18), (19), (20), (21),
% 251.53/60.06 | | | | | | | | | | (23), (24), (26), (27), (28), (31), (32), (33),
% 251.53/60.06 | | | | | | | | | | (34), (35), (36), (38), (39), (43), (44), (45),
% 251.53/60.06 | | | | | | | | | | (47), (48), (50), (51), (53), (54), (56), (57),
% 251.53/60.06 | | | | | | | | | | (58), (61), (62), (63), (64), (65), (66), (67),
% 251.53/60.06 | | | | | | | | | | (68), (70), (74), (75), (76), (77), (78), (79),
% 251.53/60.06 | | | | | | | | | | (82), (83), (84), (85), (86), (88), (89), (90),
% 251.53/60.06 | | | | | | | | | | (91), (92), (94), (95), (96), (97), (98), (99),
% 251.53/60.06 | | | | | | | | | | (100), (102), (103), (104), (105), (109), (114),
% 251.53/60.06 | | | | | | | | | | (115), (116), (117), (119), (123), (124), (129),
% 251.53/60.06 | | | | | | | | | | (130), (135), (137), (143), (148), (167) are
% 251.53/60.06 | | | | | | | | | | inconsistent by sub-proof #671.
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | Case 2:
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | (168) all_68_2 = e4
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | | REF_CLOSE: (14), (17), (19), (20), (39), (49), (53), (72),
% 251.53/60.06 | | | | | | | | | | (73), (74), (85), (88), (99), (117), (122), (123),
% 251.53/60.06 | | | | | | | | | | (135), (168) are inconsistent by sub-proof #670.
% 251.53/60.06 | | | | | | | | | |
% 251.53/60.06 | | | | | | | | | End of split
% 251.53/60.06 | | | | | | | | |
% 251.53/60.06 | | | | | | | | End of split
% 251.53/60.06 | | | | | | | |
% 251.53/60.06 | | | | | | | End of split
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | Case 2:
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | (169) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 251.53/60.06 | | | | | | | op(e0, e4) = e3)
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | | REF_CLOSE: (17), (51), (123), (133), (135), (169) are inconsistent
% 251.53/60.06 | | | | | | | by sub-proof #894.
% 251.53/60.06 | | | | | | |
% 251.53/60.06 | | | | | | End of split
% 251.53/60.06 | | | | | |
% 251.53/60.06 | | | | | End of split
% 251.53/60.06 | | | | |
% 251.53/60.06 | | | | End of split
% 251.53/60.06 | | | |
% 251.53/60.06 | | | Case 2:
% 251.53/60.06 | | | |
% 251.53/60.06 | | | | (170) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 251.53/60.06 | | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.53/60.06 | | | |
% 251.53/60.06 | | | | REF_CLOSE: (8), (17), (41), (51), (60), (62), (101), (113), (121),
% 251.53/60.06 | | | | (123), (170) are inconsistent by sub-proof #697.
% 251.53/60.06 | | | |
% 251.53/60.06 | | | End of split
% 251.53/60.06 | | |
% 251.53/60.06 | | End of split
% 251.53/60.06 | |
% 251.53/60.06 | Case 2:
% 251.53/60.06 | |
% 251.53/60.06 | | (171) all_62_2 = e4
% 251.53/60.06 | |
% 251.53/60.06 | | REF_CLOSE: (17), (21), (28), (32), (55), (57), (61), (77), (78), (80), (86),
% 251.53/60.06 | | (90), (91), (99), (109), (110), (171) are inconsistent by
% 251.53/60.06 | | sub-proof #715.
% 251.53/60.06 | |
% 251.53/60.06 | End of split
% 251.53/60.06 |
% 251.53/60.06 End of proof
% 251.53/60.06
% 251.53/60.06 Sub-proof #670 shows that the following formulas are inconsistent:
% 251.53/60.06 ----------------------------------------------------------------
% 251.53/60.06 (1) ~ (all_28_2 = e3)
% 251.53/60.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.06 (3) ~ (e3 = e2)
% 251.53/60.06 (4) op(e0, e0) = all_244_24
% 251.53/60.06 (5) ~ (all_12_2 = e3)
% 251.53/60.06 (6) op(e0, e2) = all_28_2
% 251.53/60.06 (7) ~ (all_244_3 = all_84_2)
% 251.53/60.06 (8) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.53/60.06 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 251.53/60.06 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.53/60.06 (9) op(all_22_2, e3) = e0
% 251.53/60.06 (10) all_68_2 = all_22_2
% 251.53/60.06 (11) op(e0, e3) = all_22_2
% 251.53/60.06 (12) ~ (e4 = e3)
% 251.53/60.06 (13) all_252_23 = e2
% 251.53/60.06 (14) op(e4, e3) = all_84_2
% 251.53/60.06 (15) all_68_2 = e4
% 251.53/60.06 (16) op(e3, e3) = all_244_3
% 251.53/60.06 (17) op(all_244_24, all_244_24) = e0
% 251.53/60.06 (18) op(e0, e4) = all_12_2
% 251.53/60.06
% 251.53/60.06 Begin of proof
% 251.53/60.06 |
% 251.53/60.06 | COMBINE_EQS: (10), (15) imply:
% 251.53/60.06 | (19) all_22_2 = e4
% 251.53/60.06 |
% 251.53/60.06 | SIMP: (19) implies:
% 251.53/60.06 | (20) all_22_2 = e4
% 251.53/60.06 |
% 251.53/60.06 | REDUCE: (9), (20) imply:
% 251.53/60.06 | (21) op(e4, e3) = e0
% 251.53/60.06 |
% 251.53/60.06 | REDUCE: (11), (20) imply:
% 251.53/60.06 | (22) op(e0, e3) = e4
% 251.53/60.06 |
% 251.53/60.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (13), (14), (16),
% 251.53/60.06 | (17), (18), (21), (22) are inconsistent by sub-proof #847.
% 251.53/60.06 |
% 251.53/60.06 End of proof
% 251.53/60.06
% 251.53/60.06 Sub-proof #671 shows that the following formulas are inconsistent:
% 251.53/60.06 ----------------------------------------------------------------
% 251.53/60.06 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.53/60.06 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.53/60.06 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.53/60.06 (2) ~ (all_4_2 = e4)
% 251.53/60.06 (3) ~ (all_10_2 = e4)
% 251.53/60.06 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.06 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.53/60.06 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.53/60.06 (5) op(all_4_2, e2) = e1
% 251.53/60.06 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.53/60.06 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.53/60.06 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.53/60.06 (7) ~ (all_244_8 = e0)
% 251.53/60.06 (8) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.53/60.06 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.53/60.06 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.06 (9) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 251.53/60.06 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 251.53/60.06 | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.53/60.06 (10) op(e2, all_4_2) = all_32_0
% 251.53/60.06 (11) ~ (e2 = e0)
% 251.53/60.06 (12) ~ (all_62_2 = all_22_2)
% 251.53/60.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.06 (14) op(e2, e3) = all_10_2
% 251.53/60.06 (15) ~ (e3 = e2)
% 251.53/60.06 (16) ~ (all_10_2 = e3)
% 251.53/60.06 (17) op(e0, e0) = all_244_24
% 251.53/60.06 (18) ~ (e4 = e0)
% 251.53/60.06 (19) ~ (all_12_2 = e3)
% 251.53/60.06 (20) op(e2, e2) = all_244_8
% 251.53/60.06 (21) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.53/60.06 all_250_11 = e0
% 251.53/60.06 (22) op(e2, e1) = all_38_2
% 251.53/60.06 (23) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.53/60.06 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.53/60.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.53/60.06 (24) ~ (all_84_2 = all_62_2)
% 251.53/60.06 (25) op(e1, e0) = all_34_2
% 251.53/60.06 (26) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.53/60.06 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.53/60.06 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.53/60.06 (27) op(e4, e2) = all_6_2
% 251.53/60.06 (28) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.53/60.06 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.53/60.06 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.53/60.06 (29) ~ (all_34_2 = e2)
% 251.53/60.06 (30) ~ (e2 = e1)
% 251.53/60.06 (31) ~ (all_34_2 = e4)
% 251.53/60.06 (32) op(e0, e2) = all_28_2
% 251.53/60.06 (33) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.53/60.06 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.53/60.06 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.53/60.06 (34) ~ (all_244_8 = all_10_2)
% 251.53/60.06 (35) ~ (all_6_2 = e1)
% 251.53/60.06 (36) all_252_16 = e2
% 251.53/60.06 (37) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.53/60.06 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.53/60.06 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.53/60.06 (38) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.53/60.06 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.53/60.06 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.53/60.06 (39) op(e1, e4) = all_16_2
% 251.53/60.06 (40) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.53/60.06 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.53/60.06 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.53/60.06 (41) op(e1, e3) = all_62_2
% 251.53/60.06 (42) ~ (e3 = e0)
% 251.53/60.06 (43) ~ (all_36_2 = e4)
% 251.53/60.06 (44) ~ (all_22_2 = e4)
% 251.53/60.06 (45) all_70_2 = all_62_2
% 251.53/60.06 (46) op(e3, e1) = all_36_2
% 251.53/60.06 (47) ~ (all_16_2 = e2)
% 251.53/60.06 (48) ~ (all_8_2 = e1)
% 251.53/60.06 (49) ~ (all_244_3 = all_62_2)
% 251.53/60.06 (50) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.53/60.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.53/60.06 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.53/60.06 (51) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.53/60.06 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.53/60.06 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.53/60.06 (52) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.53/60.06 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.53/60.06 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.53/60.06 (53) ~ (all_8_2 = e0)
% 251.53/60.06 (54) ~ (all_38_2 = e4)
% 251.53/60.06 (55) op(e0, e3) = all_22_2
% 251.53/60.06 (56) ~ (all_244_24 = e4)
% 251.53/60.06 (57) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.53/60.06 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.53/60.06 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.53/60.06 (58) ~ (all_244_8 = e3)
% 251.53/60.06 (59) op(all_62_2, e3) = e1
% 251.53/60.06 (60) op(e4, e1) = all_26_2
% 251.53/60.06 (61) op(all_10_2, e3) = e2
% 251.53/60.06 (62) all_250_11 = all_10_2
% 251.53/60.06 (63) op(e4, e4) = all_244_0
% 251.53/60.06 (64) ~ (all_48_2 = e4)
% 251.53/60.06 (65) ~ (e4 = e3)
% 251.53/60.06 (66) op(e1, e1) = all_244_15
% 251.53/60.06 (67) all_252_23 = e2
% 251.53/60.06 (68) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.53/60.06 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.53/60.06 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.53/60.06 (69) op(e0, e1) = all_20_2
% 251.53/60.06 (70) all_252_11 = e0
% 251.53/60.06 (71) op(e3, e0) = all_48_2
% 251.53/60.06 (72) ~ (all_26_2 = e3)
% 251.53/60.06 (73) op(e1, e2) = all_4_2
% 251.53/60.06 (74) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.53/60.06 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.53/60.06 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.53/60.06 (75) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.53/60.06 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.53/60.06 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.53/60.06 (76) all_252_2 = e2
% 251.53/60.06 (77) ~ (all_48_2 = e1)
% 251.53/60.06 (78) op(e4, e3) = all_84_2
% 251.53/60.06 (79) ~ (all_62_2 = all_10_2)
% 251.53/60.06 (80) ~ (all_22_2 = all_10_2)
% 251.53/60.06 (81) ~ (all_244_15 = e2)
% 251.53/60.06 (82) op(e0, all_4_2) = e1
% 251.53/60.06 (83) op(e3, e2) = all_8_2
% 251.53/60.06 (84) ~ (all_20_2 = e4)
% 251.53/60.06 (85) ~ (all_244_8 = all_28_2)
% 251.53/60.06 (86) ~ (all_10_2 = e0)
% 251.53/60.06 (87) all_252_6 = e3
% 251.53/60.06 (88) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.53/60.06 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.53/60.06 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.53/60.06 (89) ~ (all_244_0 = e3)
% 251.53/60.06 (90) op(e3, e3) = all_244_3
% 251.53/60.06 (91) ~ (all_4_2 = e3)
% 251.53/60.06 (92) ~ (all_62_2 = e4)
% 251.53/60.06 (93) op(e0, e4) = all_12_2
% 251.53/60.06
% 251.53/60.06 Begin of proof
% 251.53/60.06 |
% 251.53/60.06 | BETA: splitting (52) gives:
% 251.53/60.06 |
% 251.53/60.06 | Case 1:
% 251.53/60.06 | |
% 251.53/60.06 | | (94) ~ (all_70_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REF_CLOSE: (5), (10), (13), (20), (25), (29), (32), (39), (41), (45), (47),
% 251.53/60.06 | | (66), (73), (81), (82), (85), (88), (94) are inconsistent by
% 251.53/60.06 | | sub-proof #704.
% 251.53/60.06 | |
% 251.53/60.06 | Case 2:
% 251.53/60.06 | |
% 251.53/60.06 | | (95) all_70_2 = e2
% 251.53/60.06 | |
% 251.53/60.06 | | COMBINE_EQS: (45), (95) imply:
% 251.53/60.06 | | (96) all_62_2 = e2
% 251.53/60.06 | |
% 251.53/60.06 | | SIMP: (96) implies:
% 251.53/60.06 | | (97) all_62_2 = e2
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (49), (97) imply:
% 251.53/60.06 | | (98) ~ (all_244_3 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (24), (97) imply:
% 251.53/60.06 | | (99) ~ (all_84_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (12), (97) imply:
% 251.53/60.06 | | (100) ~ (all_22_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | SIMP: (100) implies:
% 251.53/60.06 | | (101) ~ (all_22_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (79), (97) imply:
% 251.53/60.06 | | (102) ~ (all_10_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | SIMP: (102) implies:
% 251.53/60.06 | | (103) ~ (all_10_2 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (92), (97) imply:
% 251.53/60.06 | | (104) ~ (e4 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | SIMP: (104) implies:
% 251.53/60.06 | | (105) ~ (e4 = e2)
% 251.53/60.06 | |
% 251.53/60.06 | | REDUCE: (59), (97) imply:
% 251.53/60.06 | | (106) op(e2, e3) = e1
% 251.53/60.06 | |
% 251.53/60.06 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (13), (14), (15),
% 251.53/60.06 | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (26), (27),
% 251.53/60.06 | | (28), (30), (31), (32), (33), (34), (35), (36), (37), (38), (40),
% 251.53/60.06 | | (41), (42), (43), (44), (46), (48), (50), (51), (53), (54), (55),
% 251.53/60.06 | | (56), (57), (58), (60), (61), (62), (63), (64), (65), (67), (68),
% 251.53/60.06 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (80),
% 251.53/60.06 | | (83), (84), (86), (87), (89), (90), (91), (92), (93), (98), (99),
% 251.53/60.06 | | (101), (103), (105), (106) are inconsistent by sub-proof #672.
% 251.53/60.06 | |
% 251.53/60.06 | End of split
% 251.53/60.06 |
% 251.53/60.06 End of proof
% 251.53/60.06
% 251.53/60.06 Sub-proof #672 shows that the following formulas are inconsistent:
% 251.53/60.06 ----------------------------------------------------------------
% 251.53/60.06 (1) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.53/60.06 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.53/60.06 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.53/60.06 (2) ~ (all_4_2 = e4)
% 251.53/60.06 (3) ~ (all_10_2 = e4)
% 251.53/60.06 (4) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.06 | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) =
% 251.53/60.06 e4) | (all_252_24 = e4 & op(e0, e0) = e4)
% 251.53/60.06 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.53/60.06 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.53/60.06 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.53/60.06 (6) ~ (all_244_8 = e0)
% 251.53/60.06 (7) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.53/60.06 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.53/60.06 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.53/60.06 (8) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 251.53/60.06 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 251.53/60.06 | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.53/60.06 (9) ~ (all_22_2 = e2)
% 251.53/60.06 (10) ~ (all_244_3 = e2)
% 251.53/60.06 (11) ~ (e2 = e0)
% 251.53/60.06 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.53/60.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.53/60.06 (13) op(e2, e3) = all_10_2
% 251.53/60.06 (14) ~ (e3 = e2)
% 251.53/60.06 (15) ~ (all_10_2 = e3)
% 251.53/60.06 (16) op(e0, e0) = all_244_24
% 251.53/60.06 (17) ~ (e4 = e0)
% 251.53/60.06 (18) ~ (all_12_2 = e3)
% 251.53/60.06 (19) op(e2, e2) = all_244_8
% 251.57/60.06 (20) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.57/60.06 all_250_11 = e0
% 251.57/60.06 (21) op(e2, e1) = all_38_2
% 251.57/60.06 (22) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.57/60.06 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.57/60.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.57/60.06 (23) op(e1, e0) = all_34_2
% 251.57/60.06 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.57/60.06 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.57/60.06 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.57/60.06 (25) op(e4, e2) = all_6_2
% 251.57/60.06 (26) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.57/60.06 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.57/60.06 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.57/60.06 (27) ~ (e2 = e1)
% 251.57/60.06 (28) ~ (all_34_2 = e4)
% 251.57/60.06 (29) op(e0, e2) = all_28_2
% 251.57/60.06 (30) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.57/60.06 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.57/60.06 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.57/60.06 (31) ~ (all_244_8 = all_10_2)
% 251.57/60.06 (32) ~ (all_6_2 = e1)
% 251.57/60.06 (33) all_252_16 = e2
% 251.57/60.06 (34) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.57/60.06 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.57/60.06 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.57/60.06 (35) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.57/60.06 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.57/60.06 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.57/60.06 (36) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.57/60.06 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.57/60.06 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.57/60.06 (37) op(e1, e3) = all_62_2
% 251.57/60.06 (38) ~ (e3 = e0)
% 251.57/60.06 (39) op(e2, e3) = e1
% 251.57/60.06 (40) ~ (all_36_2 = e4)
% 251.57/60.06 (41) ~ (all_22_2 = e4)
% 251.57/60.06 (42) op(e3, e1) = all_36_2
% 251.57/60.06 (43) ~ (all_8_2 = e1)
% 251.57/60.06 (44) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.57/60.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.57/60.06 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.57/60.06 (45) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.57/60.06 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.57/60.06 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.57/60.06 (46) ~ (all_8_2 = e0)
% 251.57/60.06 (47) ~ (all_38_2 = e4)
% 251.57/60.06 (48) op(e0, e3) = all_22_2
% 251.57/60.06 (49) ~ (all_244_24 = e4)
% 251.57/60.06 (50) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.57/60.06 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.57/60.06 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.57/60.06 (51) ~ (all_244_8 = e3)
% 251.57/60.06 (52) op(e4, e1) = all_26_2
% 251.57/60.06 (53) op(all_10_2, e3) = e2
% 251.57/60.06 (54) all_250_11 = all_10_2
% 251.57/60.06 (55) op(e4, e4) = all_244_0
% 251.57/60.06 (56) ~ (all_48_2 = e4)
% 251.57/60.06 (57) ~ (e4 = e3)
% 251.57/60.06 (58) all_252_23 = e2
% 251.57/60.07 (59) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.57/60.07 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.57/60.07 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.57/60.07 (60) op(e0, e1) = all_20_2
% 251.57/60.07 (61) all_252_11 = e0
% 251.57/60.07 (62) op(e3, e0) = all_48_2
% 251.57/60.07 (63) ~ (all_26_2 = e3)
% 251.57/60.07 (64) op(e1, e2) = all_4_2
% 251.57/60.07 (65) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.57/60.07 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.57/60.07 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.57/60.07 (66) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.57/60.07 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.57/60.07 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.57/60.07 (67) all_252_2 = e2
% 251.57/60.07 (68) ~ (all_48_2 = e1)
% 251.57/60.07 (69) op(e4, e3) = all_84_2
% 251.57/60.07 (70) ~ (all_22_2 = all_10_2)
% 251.57/60.07 (71) ~ (e4 = e2)
% 251.57/60.07 (72) ~ (all_84_2 = e2)
% 251.57/60.07 (73) op(e3, e2) = all_8_2
% 251.57/60.07 (74) ~ (all_20_2 = e4)
% 251.57/60.07 (75) ~ (all_10_2 = e0)
% 251.57/60.07 (76) all_252_6 = e3
% 251.57/60.07 (77) ~ (all_244_0 = e3)
% 251.57/60.07 (78) op(e3, e3) = all_244_3
% 251.57/60.07 (79) ~ (all_4_2 = e3)
% 251.57/60.07 (80) ~ (all_62_2 = e4)
% 251.57/60.07 (81) op(e0, e4) = all_12_2
% 251.57/60.07 (82) ~ (all_10_2 = e2)
% 251.57/60.07
% 251.57/60.07 Begin of proof
% 251.57/60.07 |
% 251.57/60.07 | BETA: splitting (8) gives:
% 251.57/60.07 |
% 251.57/60.07 | Case 1:
% 251.57/60.07 | |
% 251.57/60.07 | | (83) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) =
% 251.57/60.07 | | e2)
% 251.57/60.07 | |
% 251.57/60.07 | | BETA: splitting (83) gives:
% 251.57/60.07 | |
% 251.57/60.07 | | Case 1:
% 251.57/60.07 | | |
% 251.57/60.07 | | | (84) all_252_1 = e2 & op(e4, e3) = e2
% 251.57/60.07 | | |
% 251.57/60.07 | | | REF_CLOSE: (12), (69), (72), (84) are inconsistent by sub-proof #956.
% 251.57/60.07 | | |
% 251.57/60.07 | | Case 2:
% 251.57/60.07 | | |
% 251.57/60.07 | | | (85) all_252_3 = e2 & op(e3, e3) = e2
% 251.57/60.07 | | |
% 251.57/60.07 | | | ALPHA: (85) implies:
% 251.57/60.07 | | | (86) op(e3, e3) = e2
% 251.57/60.07 | | |
% 251.57/60.07 | | | REF_CLOSE: (10), (12), (78), (86) are inconsistent by sub-proof #694.
% 251.57/60.07 | | |
% 251.57/60.07 | | End of split
% 251.57/60.07 | |
% 251.57/60.07 | Case 2:
% 251.57/60.07 | |
% 251.57/60.07 | | (87) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.57/60.07 | | e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.57/60.07 | |
% 251.57/60.07 | | BETA: splitting (87) gives:
% 251.57/60.07 | |
% 251.57/60.07 | | Case 1:
% 251.57/60.07 | | |
% 251.57/60.07 | | | (88) all_252_7 = e2 & op(e2, e3) = e2
% 251.57/60.07 | | |
% 251.57/60.07 | | | ALPHA: (88) implies:
% 251.57/60.07 | | | (89) op(e2, e3) = e2
% 251.57/60.07 | | |
% 251.57/60.07 | | | REF_CLOSE: (12), (13), (27), (39), (89) are inconsistent by sub-proof
% 251.57/60.07 | | | #902.
% 251.57/60.07 | | |
% 251.57/60.07 | | Case 2:
% 251.57/60.07 | | |
% 251.57/60.07 | | | (90) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0,
% 251.57/60.07 | | | e3) = e2)
% 251.57/60.07 | | |
% 251.57/60.07 | | | BETA: splitting (90) gives:
% 251.57/60.07 | | |
% 251.57/60.07 | | | Case 1:
% 251.57/60.07 | | | |
% 251.57/60.07 | | | | (91) all_252_13 = e2 & op(e1, e3) = e2
% 251.57/60.07 | | | |
% 251.57/60.07 | | | | ALPHA: (91) implies:
% 251.57/60.07 | | | | (92) all_252_13 = e2
% 251.57/60.07 | | | |
% 251.57/60.07 | | | | BETA: splitting (20) gives:
% 251.57/60.07 | | | |
% 251.57/60.07 | | | | Case 1:
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | (93) all_250_11 = e4
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | COMBINE_EQS: (54), (93) imply:
% 251.57/60.07 | | | | | (94) all_10_2 = e4
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | REDUCE: (3), (94) imply:
% 251.57/60.07 | | | | | (95) $false
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | CLOSE: (95) is inconsistent.
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | Case 2:
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | (96) ~ (all_250_11 = e4)
% 251.57/60.07 | | | | | (97) all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.57/60.07 | | | | | all_250_11 = e0
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | BETA: splitting (97) gives:
% 251.57/60.07 | | | | |
% 251.57/60.07 | | | | | Case 1:
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | (98) all_250_11 = e3
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | COMBINE_EQS: (54), (98) imply:
% 251.57/60.07 | | | | | | (99) all_10_2 = e3
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | REDUCE: (15), (99) imply:
% 251.57/60.07 | | | | | | (100) $false
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | CLOSE: (100) is inconsistent.
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | Case 2:
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | (101) ~ (all_250_11 = e3)
% 251.57/60.07 | | | | | | (102) all_250_11 = e2 | all_250_11 = e1 | all_250_11 = e0
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | BETA: splitting (102) gives:
% 251.57/60.07 | | | | | |
% 251.57/60.07 | | | | | | Case 1:
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | (103) all_250_11 = e2
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | COMBINE_EQS: (54), (103) imply:
% 251.57/60.07 | | | | | | | (104) all_10_2 = e2
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | REDUCE: (82), (104) imply:
% 251.57/60.07 | | | | | | | (105) $false
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | CLOSE: (105) is inconsistent.
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | Case 2:
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | (106) ~ (all_250_11 = e2)
% 251.57/60.07 | | | | | | | (107) all_250_11 = e1 | all_250_11 = e0
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | BETA: splitting (107) gives:
% 251.57/60.07 | | | | | | |
% 251.57/60.07 | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | (108) all_250_11 = e1
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | COMBINE_EQS: (54), (108) imply:
% 251.57/60.07 | | | | | | | | (109) all_10_2 = e1
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (31), (109) imply:
% 251.57/60.07 | | | | | | | | (110) ~ (all_244_8 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (70), (109) imply:
% 251.57/60.07 | | | | | | | | (111) ~ (all_22_2 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (3), (109) imply:
% 251.57/60.07 | | | | | | | | (112) ~ (e4 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | SIMP: (112) implies:
% 251.57/60.07 | | | | | | | | (113) ~ (e4 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (15), (109) imply:
% 251.57/60.07 | | | | | | | | (114) ~ (e3 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | SIMP: (114) implies:
% 251.57/60.07 | | | | | | | | (115) ~ (e3 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (82), (109) imply:
% 251.57/60.07 | | | | | | | | (116) ~ (e2 = e1)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (75), (109) imply:
% 251.57/60.07 | | | | | | | | (117) ~ (e1 = e0)
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | REDUCE: (53), (109) imply:
% 251.57/60.07 | | | | | | | | (118) op(e1, e3) = e2
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | BETA: splitting (26) gives:
% 251.57/60.07 | | | | | | | |
% 251.57/60.07 | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | | (119) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1
% 251.57/60.07 | | | | | | | | | & op(e3, e3) = e1)
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | | REF_CLOSE: (3), (7), (11), (12), (13), (14), (17), (27), (37),
% 251.57/60.07 | | | | | | | | | (38), (39), (41), (45), (48), (57), (65), (67),
% 251.57/60.07 | | | | | | | | | (80), (92), (113), (115), (117), (118), (119) are
% 251.57/60.07 | | | | | | | | | inconsistent by sub-proof #770.
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | | (120) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1
% 251.57/60.07 | | | | | | | | | & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0)
% 251.57/60.07 | | | | | | | | | = e1)
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | | BETA: splitting (120) gives:
% 251.57/60.07 | | | | | | | | |
% 251.57/60.07 | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | (121) all_252_5 = e1 & op(e3, e2) = e1
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | ALPHA: (121) implies:
% 251.57/60.07 | | | | | | | | | | (122) op(e3, e2) = e1
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | REF_CLOSE: (12), (43), (73), (122) are inconsistent by
% 251.57/60.07 | | | | | | | | | | sub-proof #929.
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | (123) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 =
% 251.57/60.07 | | | | | | | | | | e1 & op(e3, e0) = e1)
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | BETA: splitting (123) gives:
% 251.57/60.07 | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | (124) all_252_10 = e1 & op(e3, e1) = e1
% 251.57/60.07 | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | ALPHA: (124) implies:
% 251.57/60.07 | | | | | | | | | | | (125) all_252_10 = e1
% 251.57/60.07 | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | BETA: splitting (30) gives:
% 251.57/60.07 | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | (126) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 =
% 251.57/60.07 | | | | | | | | | | | | e3 & op(e3, e1) = e3)
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | BETA: splitting (126) gives:
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | (127) all_252_9 = e3 & op(e4, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | ALPHA: (127) implies:
% 251.57/60.07 | | | | | | | | | | | | | (128) op(e4, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | REF_CLOSE: (12), (52), (63), (128) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | sub-proof #834.
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | (129) all_252_10 = e3 & op(e3, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | ALPHA: (129) implies:
% 251.57/60.07 | | | | | | | | | | | | | (130) all_252_10 = e3
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | REF_CLOSE: (115), (125), (130) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | #693.
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | (131) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15
% 251.57/60.07 | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.57/60.07 | | | | | | | | | | | | op(e0, e1) = e3)
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | BETA: splitting (131) gives:
% 251.57/60.07 | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | (132) all_252_11 = e3 & op(e2, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | REF_CLOSE: (38), (61), (132) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | #701.
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | (133) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23
% 251.57/60.07 | | | | | | | | | | | | | = e3 & op(e0, e1) = e3)
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | BETA: splitting (133) gives:
% 251.57/60.07 | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | (134) all_252_15 = e3 & op(e1, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | ALPHA: (134) implies:
% 251.57/60.07 | | | | | | | | | | | | | | (135) all_252_15 = e3
% 251.57/60.07 | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 251.57/60.07 | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | (136) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 251.57/60.07 | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 251.57/60.07 | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 251.57/60.07 | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | (137) all_252_9 = e4 & op(e4, e1) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | (138) all_252_9 = e4
% 251.57/60.07 | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | (139) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | (140) all_252_0 = e1 & op(e4, e4) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | (141) all_252_0 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | (142) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | (143) all_252_12 = e4 & op(e1, e4) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | (144) all_252_12 = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | (145) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (146) all_252_0 = e0 & op(e4, e4) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (147) all_252_0 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (147) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (148) e1 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (148) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (149) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (150) all_252_2 = e0 & op(e3, e4) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (67), (150) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | #692.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | (151) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (152) all_252_6 = e0 & op(e2, e4) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (153) all_252_6 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (76), (153) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | #691.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | (154) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (155) all_252_12 = e0 & op(e1, e4) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_12 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (156) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (157) e4 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (157) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (158) e4 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (158) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (159) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_20 = e0 & op(e0, e4) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_20 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | (162) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_20 = e4 & op(e0, e4) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_20 = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (164) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (165) e4 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (165) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (166) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_21 = e4 & op(e0, e3) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (41), (48), (167) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #805.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_252_22 = e4 & op(e0, e2) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | (170) op(e0, e2) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (32), (43), (73), (171) are
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #928.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (172) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_8 = e1 & op(e2, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) op(e2, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (110), (174) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_252_14 = e1 & op(e1, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) op(e1, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_252_4 = e0 & op(e4, e2) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_252_4 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_4 = e3 & op(e4, e2) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (180), (182) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_252_5 = e3 & op(e3, e2) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_252_5 = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_2 = e4 & op(e3, e4) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_2 = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (187) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) e4 = e2
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) e4 = e2
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (189) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_252_3 = e4 & op(e3, e3) = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_252_3 = e4
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_0 = e3 & op(e4, e4) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) op(e4, e4) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (55), (77), (195) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #813.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_1 = e3 & op(e4, e3) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_1 = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_252_20 = e1 & op(e0, e4) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_20 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (200) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) e1 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (201) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_21 = e1 & op(e0, e3) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) op(e0, e3) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (48), (111), (204) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #714.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_22 = e1 & op(e0, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) op(e0, e2) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (113), (170), (207) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #859.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_252_23 = e1 & op(e0, e1) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_23 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (210) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e2 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (212) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_24 = e1 & op(e0, e0) = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_24 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_1 = e0 & op(e4, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_1 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (218) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) e3 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (219) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_3 = e0 & op(e3, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (192), (221) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #688.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_7 = e0 & op(e2, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (75), (223) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #816.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_13 = e0 & op(e1, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) op(e1, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (118), (226) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #776.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_21 = e0 & op(e0, e3) = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_252_21 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_20 = e3 & op(e0, e4) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) op(e0, e4) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (18), (81), (231) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #981.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_252_21 = e3 & op(e0, e3) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_21 = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (233) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) e3 = e0
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (234) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) $false
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_22 = e3 & op(e0, e2) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) op(e0, e2) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (57), (170), (238) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #857.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_252_23 = e3 & op(e0, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (58), (240) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_252_24 = e3 & op(e0, e0) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_24 = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (242) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) e3 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (243) imply:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_252_1 = e1
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (14), (17), (38), (39), (45),
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (65), (75), (92), (115), (117), (118),
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (244) are inconsistent by sub-proof #682.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_252_4 = e3 & op(e4, e2) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (180), (246) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #865.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_9 = e3 & op(e4, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) op(e4, e1) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (52), (63), (249) are inconsistent by
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_252_16 = e3 & op(e4, e0) = e3
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (33), (250) are inconsistent by sub-proof
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_252_5 = e4 & op(e3, e2) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (184), (252) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #680.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_252_10 = e4 & op(e3, e1) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (40), (42), (254) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_252_17 = e4 & op(e3, e0) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (56), (62), (255) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #706.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_252_8 = e3 & op(e2, e2) = e3
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) op(e2, e2) = e3
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (51), (258) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #877.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (57), (64), (79), (170), (259) are
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #856.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_252_5 = e0 & op(e3, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (46), (73), (260) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #874.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_252_8 = e0 & op(e2, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) op(e2, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (19), (263) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_252_14 = e0 & op(e1, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) op(e1, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (64), (117), (177), (266) are inconsistent
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #870.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_252_22 = e0 & op(e0, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) op(e0, e2) = e0
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (29), (170), (268) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #854.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_252_22 = e1 & op(e0, e2) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) op(e0, e2) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (113), (170), (270) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #859.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | (271) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_252_23 = e4 & op(e0, e1) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (60), (74), (272) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #912.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_252_24 = e4 & op(e0, e0) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (16), (49), (273) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #679.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (274) all_252_13 = e4 & op(e1, e3) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (37), (80), (274) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | sub-proof #952.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (275) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (276) all_252_14 = e4 & op(e1, e2) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (277) op(e1, e2) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (64), (277) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (278) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | (279) all_252_15 = e4 & op(e1, e1) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (135), (279) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | #678.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | (280) all_252_19 = e4 & op(e1, e0) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (23), (28), (280) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | | sub-proof #677.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | (281) all_252_1 = e1 & op(e4, e3) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | (282) all_252_1 = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (283) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (284) all_252_1 = e4 & op(e4, e3) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (282), (284) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | #955.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (285) all_252_3 = e4 & op(e3, e3) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (286) all_252_3 = e4
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (14), (17), (38), (39), (45),
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (57), (65), (75), (92), (115), (117), (118),
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | | (282), (286) are inconsistent by sub-proof #682.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (287) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (37), (41), (48), (80), (287) are
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | (288) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 251.57/60.08 | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 251.57/60.08 | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | (289) all_252_4 = e1 & op(e4, e2) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | (290) op(e4, e2) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (32), (290) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | | | sub-proof #930.
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | (291) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 =
% 251.57/60.08 | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1)
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (292) all_252_9 = e1 & op(e4, e1) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (293) all_252_9 = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (138), (293) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | #842.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | (294) all_252_16 = e1 & op(e4, e0) = e1
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (33), (294) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | | | | | | #676.
% 251.57/60.08 | | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | (295) all_252_10 = e4 & op(e3, e1) = e4
% 251.57/60.08 | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (40), (42), (295) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | | | | | | sub-proof #914.
% 251.57/60.08 | | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | (296) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 251.57/60.08 | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 251.57/60.08 | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 251.57/60.08 | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (47), (57), (60), (74), (135), (296)
% 251.57/60.08 | | | | | | | | | | | | | | | are inconsistent by sub-proof #673.
% 251.57/60.08 | | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | (297) all_252_23 = e3 & op(e0, e1) = e3
% 251.57/60.08 | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | | REF_CLOSE: (14), (58), (297) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | | | | | | | | #848.
% 251.57/60.08 | | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | (298) all_252_17 = e1 & op(e3, e0) = e1
% 251.57/60.08 | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | ALPHA: (298) implies:
% 251.57/60.08 | | | | | | | | | | | (299) op(e3, e0) = e1
% 251.57/60.08 | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | | REF_CLOSE: (12), (62), (68), (299) are inconsistent by
% 251.57/60.08 | | | | | | | | | | | sub-proof #889.
% 251.57/60.08 | | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | | |
% 251.57/60.08 | | | | | | | | | End of split
% 251.57/60.08 | | | | | | | | |
% 251.57/60.08 | | | | | | | | End of split
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | Case 2:
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | | (300) all_250_11 = e0
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | | COMBINE_EQS: (54), (300) imply:
% 251.57/60.08 | | | | | | | | (301) all_10_2 = e0
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | | REDUCE: (75), (301) imply:
% 251.57/60.08 | | | | | | | | (302) $false
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | | CLOSE: (302) is inconsistent.
% 251.57/60.08 | | | | | | | |
% 251.57/60.08 | | | | | | | End of split
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | End of split
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | End of split
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | End of split
% 251.57/60.08 | | | |
% 251.57/60.08 | | | Case 2:
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | (303) all_252_21 = e2 & op(e0, e3) = e2
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | ALPHA: (303) implies:
% 251.57/60.08 | | | | (304) op(e0, e3) = e2
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | REF_CLOSE: (9), (12), (48), (304) are inconsistent by sub-proof #987.
% 251.57/60.08 | | | |
% 251.57/60.08 | | | End of split
% 251.57/60.08 | | |
% 251.57/60.08 | | End of split
% 251.57/60.08 | |
% 251.57/60.08 | End of split
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #673 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (2) op(e2, e1) = all_38_2
% 251.57/60.08 (3) ~ (all_38_2 = e4)
% 251.57/60.08 (4) ~ (e4 = e3)
% 251.57/60.08 (5) op(e0, e1) = all_20_2
% 251.57/60.08 (6) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 251.57/60.08 | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.57/60.08 (7) all_252_15 = e3
% 251.57/60.08 (8) ~ (all_20_2 = e4)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | BETA: splitting (6) gives:
% 251.57/60.08 |
% 251.57/60.08 | Case 1:
% 251.57/60.08 | |
% 251.57/60.08 | | (9) all_252_11 = e4 & op(e2, e1) = e4
% 251.57/60.08 | |
% 251.57/60.08 | | ALPHA: (9) implies:
% 251.57/60.08 | | (10) op(e2, e1) = e4
% 251.57/60.08 | |
% 251.57/60.08 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #935.
% 251.57/60.08 | |
% 251.57/60.08 | Case 2:
% 251.57/60.08 | |
% 251.57/60.08 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1)
% 251.57/60.08 | | = e4)
% 251.57/60.08 | |
% 251.57/60.08 | | REF_CLOSE: (1), (4), (5), (7), (8), (11) are inconsistent by sub-proof #674.
% 251.57/60.08 | |
% 251.57/60.08 | End of split
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #674 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (2) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.57/60.08 (3) ~ (e4 = e3)
% 251.57/60.08 (4) op(e0, e1) = all_20_2
% 251.57/60.08 (5) all_252_15 = e3
% 251.57/60.08 (6) ~ (all_20_2 = e4)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | BETA: splitting (2) gives:
% 251.57/60.08 |
% 251.57/60.08 | Case 1:
% 251.57/60.08 | |
% 251.57/60.08 | | (7) all_252_15 = e4 & op(e1, e1) = e4
% 251.57/60.08 | |
% 251.57/60.08 | | ALPHA: (7) implies:
% 251.57/60.08 | | (8) all_252_15 = e4
% 251.57/60.08 | |
% 251.57/60.08 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #675.
% 251.57/60.08 | |
% 251.57/60.08 | Case 2:
% 251.57/60.08 | |
% 251.57/60.08 | | (9) all_252_23 = e4 & op(e0, e1) = e4
% 251.57/60.08 | |
% 251.57/60.08 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #912.
% 251.57/60.08 | |
% 251.57/60.08 | End of split
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #675 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_15 = e4
% 251.57/60.08 (2) all_252_15 = e3
% 251.57/60.08 (3) ~ (e4 = e3)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.08 | (4) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (4) implies:
% 251.57/60.08 | (5) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #676 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_16 = e1 & op(e4, e0) = e1
% 251.57/60.08 (2) all_252_16 = e2
% 251.57/60.08 (3) ~ (e2 = e1)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_16 = e1
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e2 = e1
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (5) implies:
% 251.57/60.08 | (6) e2 = e1
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #677 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_19 = e4 & op(e1, e0) = e4
% 251.57/60.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (3) op(e1, e0) = all_34_2
% 251.57/60.08 (4) ~ (all_34_2 = e4)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (5) op(e1, e0) = e4
% 251.57/60.08 |
% 251.57/60.08 | GROUND_INST: instantiating (2) with all_34_2, e4, e0, e1, simplifying with
% 251.57/60.08 | (3), (5) gives:
% 251.57/60.08 | (6) all_34_2 = e4
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (4), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #678 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_15 = e4 & op(e1, e1) = e4
% 251.57/60.08 (2) all_252_15 = e3
% 251.57/60.08 (3) ~ (e4 = e3)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_15 = e4
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #679 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_24 = e4 & op(e0, e0) = e4
% 251.57/60.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (3) op(e0, e0) = all_244_24
% 251.57/60.08 (4) ~ (all_244_24 = e4)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (5) op(e0, e0) = e4
% 251.57/60.08 |
% 251.57/60.08 | GROUND_INST: instantiating (2) with all_244_24, e4, e0, e0, simplifying with
% 251.57/60.08 | (3), (5) gives:
% 251.57/60.08 | (6) all_244_24 = e4
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (4), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #680 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_5 = e4 & op(e3, e2) = e4
% 251.57/60.08 (2) all_252_5 = e3
% 251.57/60.08 (3) ~ (e4 = e3)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_5 = e4
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (5) implies:
% 251.57/60.08 | (6) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #681 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_16 = e3 & op(e4, e0) = e3
% 251.57/60.08 (2) all_252_16 = e2
% 251.57/60.08 (3) ~ (e3 = e2)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_16 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e3 = e2
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (5) implies:
% 251.57/60.08 | (6) e3 = e2
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #682 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_3 = e4
% 251.57/60.08 (2) ~ (e2 = e0)
% 251.57/60.08 (3) ~ (e1 = e0)
% 251.57/60.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (5) op(e2, e3) = all_10_2
% 251.57/60.08 (6) ~ (e3 = e2)
% 251.57/60.08 (7) ~ (e4 = e0)
% 251.57/60.08 (8) all_252_1 = e1
% 251.57/60.08 (9) all_252_13 = e2
% 251.57/60.08 (10) ~ (e3 = e0)
% 251.57/60.08 (11) op(e2, e3) = e1
% 251.57/60.08 (12) ~ (e3 = e1)
% 251.57/60.08 (13) op(e1, e3) = e2
% 251.57/60.08 (14) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.57/60.08 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.57/60.08 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.57/60.08 (15) ~ (e4 = e3)
% 251.57/60.08 (16) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.57/60.08 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.57/60.08 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.57/60.08 (17) ~ (all_10_2 = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | BETA: splitting (16) gives:
% 251.57/60.08 |
% 251.57/60.08 | Case 1:
% 251.57/60.08 | |
% 251.57/60.08 | | (18) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) =
% 251.57/60.08 | | e3)
% 251.57/60.08 | |
% 251.57/60.08 | | BETA: splitting (18) gives:
% 251.57/60.08 | |
% 251.57/60.08 | | Case 1:
% 251.57/60.08 | | |
% 251.57/60.08 | | | (19) all_252_1 = e3 & op(e4, e3) = e3
% 251.57/60.08 | | |
% 251.57/60.08 | | | REF_CLOSE: (8), (12), (19) are inconsistent by sub-proof #686.
% 251.57/60.08 | | |
% 251.57/60.08 | | Case 2:
% 251.57/60.08 | | |
% 251.57/60.08 | | | (20) all_252_3 = e3 & op(e3, e3) = e3
% 251.57/60.08 | | |
% 251.57/60.08 | | | REF_CLOSE: (1), (15), (20) are inconsistent by sub-proof #685.
% 251.57/60.08 | | |
% 251.57/60.08 | | End of split
% 251.57/60.08 | |
% 251.57/60.08 | Case 2:
% 251.57/60.08 | |
% 251.57/60.08 | | (21) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.57/60.08 | | e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.57/60.08 | |
% 251.57/60.08 | | BETA: splitting (21) gives:
% 251.57/60.08 | |
% 251.57/60.08 | | Case 1:
% 251.57/60.08 | | |
% 251.57/60.08 | | | (22) all_252_7 = e3 & op(e2, e3) = e3
% 251.57/60.08 | | |
% 251.57/60.08 | | | ALPHA: (22) implies:
% 251.57/60.08 | | | (23) op(e2, e3) = e3
% 251.57/60.08 | | |
% 251.57/60.08 | | | REF_CLOSE: (4), (11), (12), (23) are inconsistent by sub-proof #881.
% 251.57/60.08 | | |
% 251.57/60.08 | | Case 2:
% 251.57/60.08 | | |
% 251.57/60.08 | | | (24) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0,
% 251.57/60.08 | | | e3) = e3)
% 251.57/60.08 | | |
% 251.57/60.08 | | | BETA: splitting (24) gives:
% 251.57/60.08 | | |
% 251.57/60.08 | | | Case 1:
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | (25) all_252_13 = e3 & op(e1, e3) = e3
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | REF_CLOSE: (6), (9), (25) are inconsistent by sub-proof #684.
% 251.57/60.08 | | | |
% 251.57/60.08 | | | Case 2:
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | (26) all_252_21 = e3 & op(e0, e3) = e3
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | ALPHA: (26) implies:
% 251.57/60.08 | | | | (27) all_252_21 = e3
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | BETA: splitting (14) gives:
% 251.57/60.08 | | | |
% 251.57/60.08 | | | | Case 1:
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | | (28) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 251.57/60.08 | | | | | e3) = e0)
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | | REF_CLOSE: (1), (3), (7), (8), (28) are inconsistent by sub-proof
% 251.57/60.08 | | | | | #683.
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | Case 2:
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | | (29) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1,
% 251.57/60.08 | | | | | e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | | BETA: splitting (29) gives:
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | | Case 1:
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | | (30) all_252_7 = e0 & op(e2, e3) = e0
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | | REF_CLOSE: (4), (5), (17), (30) are inconsistent by sub-proof #816.
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | Case 2:
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | | (31) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.57/60.08 | | | | | | op(e0, e3) = e0)
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | | BETA: splitting (31) gives:
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | | Case 1:
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | (32) all_252_13 = e0 & op(e1, e3) = e0
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | ALPHA: (32) implies:
% 251.57/60.08 | | | | | | | (33) op(e1, e3) = e0
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | REF_CLOSE: (2), (4), (13), (33) are inconsistent by sub-proof
% 251.57/60.08 | | | | | | | #776.
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | Case 2:
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | (34) all_252_21 = e0 & op(e0, e3) = e0
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | ALPHA: (34) implies:
% 251.57/60.08 | | | | | | | (35) all_252_21 = e0
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | | REF_CLOSE: (10), (27), (35) are inconsistent by sub-proof #773.
% 251.57/60.08 | | | | | | |
% 251.57/60.08 | | | | | | End of split
% 251.57/60.08 | | | | | |
% 251.57/60.08 | | | | | End of split
% 251.57/60.08 | | | | |
% 251.57/60.08 | | | | End of split
% 251.57/60.08 | | | |
% 251.57/60.08 | | | End of split
% 251.57/60.08 | | |
% 251.57/60.08 | | End of split
% 251.57/60.08 | |
% 251.57/60.08 | End of split
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #683 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_3 = e4
% 251.57/60.08 (2) ~ (e1 = e0)
% 251.57/60.08 (3) ~ (e4 = e0)
% 251.57/60.08 (4) all_252_1 = e1
% 251.57/60.08 (5) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | BETA: splitting (5) gives:
% 251.57/60.08 |
% 251.57/60.08 | Case 1:
% 251.57/60.08 | |
% 251.57/60.08 | | (6) all_252_1 = e0 & op(e4, e3) = e0
% 251.57/60.08 | |
% 251.57/60.08 | | ALPHA: (6) implies:
% 251.57/60.08 | | (7) all_252_1 = e0
% 251.57/60.08 | |
% 251.57/60.08 | | COMBINE_EQS: (4), (7) imply:
% 251.57/60.08 | | (8) e1 = e0
% 251.57/60.08 | |
% 251.57/60.08 | | REDUCE: (2), (8) imply:
% 251.57/60.08 | | (9) $false
% 251.57/60.08 | |
% 251.57/60.08 | | CLOSE: (9) is inconsistent.
% 251.57/60.08 | |
% 251.57/60.08 | Case 2:
% 251.57/60.08 | |
% 251.57/60.08 | | (10) all_252_3 = e0 & op(e3, e3) = e0
% 251.57/60.08 | |
% 251.57/60.08 | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #688.
% 251.57/60.08 | |
% 251.57/60.08 | End of split
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #684 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_13 = e3 & op(e1, e3) = e3
% 251.57/60.08 (2) all_252_13 = e2
% 251.57/60.08 (3) ~ (e3 = e2)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_13 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e3 = e2
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #685 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_3 = e3 & op(e3, e3) = e3
% 251.57/60.08 (2) all_252_3 = e4
% 251.57/60.08 (3) ~ (e4 = e3)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_3 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e4 = e3
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #686 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_1 = e3 & op(e4, e3) = e3
% 251.57/60.08 (2) all_252_1 = e1
% 251.57/60.08 (3) ~ (e3 = e1)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_1 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e3 = e1
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (5) implies:
% 251.57/60.08 | (6) e3 = e1
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (6) imply:
% 251.57/60.08 | (7) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (7) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #687 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_23 = e3 & op(e0, e1) = e3
% 251.57/60.08 (2) all_252_23 = e2
% 251.57/60.08 (3) ~ (e3 = e2)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_23 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e3 = e2
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #688 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_3 = e0 & op(e3, e3) = e0
% 251.57/60.08 (2) all_252_3 = e4
% 251.57/60.08 (3) ~ (e4 = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_3 = e0
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e4 = e0
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #689 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_4 = e3 & op(e4, e2) = e3
% 251.57/60.08 (2) all_252_4 = e0
% 251.57/60.08 (3) ~ (e3 = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_4 = e3
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e3 = e0
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #690 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.08 (2) op(e2, e2) = all_244_8
% 251.57/60.08 (3) op(e2, e2) = e1
% 251.57/60.08 (4) ~ (all_244_8 = e1)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | GROUND_INST: instantiating (1) with all_244_8, e1, e2, e2, simplifying with
% 251.57/60.08 | (2), (3) gives:
% 251.57/60.08 | (5) all_244_8 = e1
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (4), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #691 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_6 = e3
% 251.57/60.08 (2) all_252_6 = e0
% 251.57/60.08 (3) ~ (e3 = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.08 | (4) e3 = e0
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (4) implies:
% 251.57/60.08 | (5) e3 = e0
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #692 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_2 = e0 & op(e3, e4) = e0
% 251.57/60.08 (2) all_252_2 = e2
% 251.57/60.08 (3) ~ (e2 = e0)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | ALPHA: (1) implies:
% 251.57/60.08 | (4) all_252_2 = e0
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.08 | (5) e2 = e0
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.08 |
% 251.57/60.08 | CLOSE: (6) is inconsistent.
% 251.57/60.08 |
% 251.57/60.08 End of proof
% 251.57/60.08
% 251.57/60.08 Sub-proof #693 shows that the following formulas are inconsistent:
% 251.57/60.08 ----------------------------------------------------------------
% 251.57/60.08 (1) all_252_10 = e3
% 251.57/60.08 (2) all_252_10 = e1
% 251.57/60.08 (3) ~ (e3 = e1)
% 251.57/60.08
% 251.57/60.08 Begin of proof
% 251.57/60.08 |
% 251.57/60.08 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.08 | (4) e3 = e1
% 251.57/60.08 |
% 251.57/60.08 | SIMP: (4) implies:
% 251.57/60.08 | (5) e3 = e1
% 251.57/60.08 |
% 251.57/60.08 | REDUCE: (3), (5) imply:
% 251.57/60.08 | (6) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (6) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #694 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (2) op(e3, e3) = all_244_3
% 251.57/60.09 (3) op(e3, e3) = e2
% 251.57/60.09 (4) ~ (all_244_3 = e2)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (1) with all_244_3, e2, e3, e3, simplifying with
% 251.57/60.09 | (2), (3) gives:
% 251.57/60.09 | (5) all_244_3 = e2
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (4), (5) imply:
% 251.57/60.09 | (6) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (6) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #695 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) op(all_6_2, e2) = e4
% 251.57/60.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (3) ~ (e3 = e2)
% 251.57/60.09 (4) ~ (all_244_0 = e2)
% 251.57/60.09 (5) op(all_6_2, all_64_2) = e2
% 251.57/60.09 (6) op(e1, e4) = all_16_2
% 251.57/60.09 (7) ~ (all_12_2 = e2)
% 251.57/60.09 (8) ~ (all_16_2 = e2)
% 251.57/60.09 (9) op(e4, e4) = all_244_0
% 251.57/60.09 (10) op(e2, e4) = all_64_2
% 251.57/60.09 (11) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.57/60.09 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.57/60.09 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.57/60.09 (12) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.57/60.09 (13) op(e0, e4) = all_40_1
% 251.57/60.09 (14) ~ (all_244_0 = e3)
% 251.57/60.09 (15) ~ (all_64_2 = e4)
% 251.57/60.09 (16) op(e0, e4) = all_12_2
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (12) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (17) all_252_0 = e3 & op(e4, e4) = e3
% 251.57/60.09 | |
% 251.57/60.09 | | ALPHA: (17) implies:
% 251.57/60.09 | | (18) op(e4, e4) = e3
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (2), (9), (14), (18) are inconsistent by sub-proof #813.
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (19) all_252_2 = e3 & op(e3, e4) = e3
% 251.57/60.09 | |
% 251.57/60.09 | | ALPHA: (19) implies:
% 251.57/60.09 | | (20) all_252_2 = e3
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 251.57/60.09 | | (15), (16), (20) are inconsistent by sub-proof #696.
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #696 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) op(all_6_2, e2) = e4
% 251.57/60.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (3) ~ (e3 = e2)
% 251.57/60.09 (4) ~ (all_244_0 = e2)
% 251.57/60.09 (5) op(all_6_2, all_64_2) = e2
% 251.57/60.09 (6) op(e1, e4) = all_16_2
% 251.57/60.09 (7) ~ (all_12_2 = e2)
% 251.57/60.09 (8) ~ (all_16_2 = e2)
% 251.57/60.09 (9) all_252_2 = e3
% 251.57/60.09 (10) op(e4, e4) = all_244_0
% 251.57/60.09 (11) op(e2, e4) = all_64_2
% 251.57/60.09 (12) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.57/60.09 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.57/60.09 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.57/60.09 (13) op(e0, e4) = all_40_1
% 251.57/60.09 (14) ~ (all_64_2 = e4)
% 251.57/60.09 (15) op(e0, e4) = all_12_2
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (12) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (16) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) =
% 251.57/60.09 | | e2)
% 251.57/60.09 | |
% 251.57/60.09 | | BETA: splitting (16) gives:
% 251.57/60.09 | |
% 251.57/60.09 | | Case 1:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (17) all_252_0 = e2 & op(e4, e4) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | ALPHA: (17) implies:
% 251.57/60.09 | | | (18) op(e4, e4) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | REF_CLOSE: (2), (4), (10), (18) are inconsistent by sub-proof #809.
% 251.57/60.09 | | |
% 251.57/60.09 | | Case 2:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (19) all_252_2 = e2 & op(e3, e4) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | ALPHA: (19) implies:
% 251.57/60.09 | | | (20) all_252_2 = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | COMBINE_EQS: (9), (20) imply:
% 251.57/60.09 | | | (21) e3 = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | REDUCE: (3), (21) imply:
% 251.57/60.09 | | | (22) $false
% 251.57/60.09 | | |
% 251.57/60.09 | | | CLOSE: (22) is inconsistent.
% 251.57/60.09 | | |
% 251.57/60.09 | | End of split
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (23) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.57/60.09 | | e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (13), (14), (15), (23) are
% 251.57/60.09 | | inconsistent by sub-proof #697.
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #697 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = e2)
% 251.57/60.09 | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.57/60.09 (2) op(all_6_2, e2) = e4
% 251.57/60.09 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (4) op(all_6_2, all_64_2) = e2
% 251.57/60.09 (5) op(e1, e4) = all_16_2
% 251.57/60.09 (6) ~ (all_12_2 = e2)
% 251.57/60.09 (7) ~ (all_16_2 = e2)
% 251.57/60.09 (8) op(e2, e4) = all_64_2
% 251.57/60.09 (9) op(e0, e4) = all_40_1
% 251.57/60.09 (10) ~ (all_64_2 = e4)
% 251.57/60.09 (11) op(e0, e4) = all_12_2
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (1) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (12) all_252_6 = e2 & op(e2, e4) = e2
% 251.57/60.09 | |
% 251.57/60.09 | | ALPHA: (12) implies:
% 251.57/60.09 | | (13) op(e2, e4) = e2
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (2), (3), (4), (8), (10), (13) are inconsistent by sub-proof
% 251.57/60.09 | | #790.
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4)
% 251.57/60.09 | | = e2)
% 251.57/60.09 | |
% 251.57/60.09 | | BETA: splitting (14) gives:
% 251.57/60.09 | |
% 251.57/60.09 | | Case 1:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (15) all_252_12 = e2 & op(e1, e4) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | REF_CLOSE: (3), (5), (7), (15) are inconsistent by sub-proof #926.
% 251.57/60.09 | | |
% 251.57/60.09 | | Case 2:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (16) all_252_20 = e2 & op(e0, e4) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | REF_CLOSE: (3), (6), (9), (11), (16) are inconsistent by sub-proof #698.
% 251.57/60.09 | | |
% 251.57/60.09 | | End of split
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #698 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (2) ~ (all_12_2 = e2)
% 251.57/60.09 (3) all_252_20 = e2 & op(e0, e4) = e2
% 251.57/60.09 (4) op(e0, e4) = all_40_1
% 251.57/60.09 (5) op(e0, e4) = all_12_2
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (3) implies:
% 251.57/60.09 | (6) op(e0, e4) = e2
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (1) with all_12_2, all_40_1, e4, e0, simplifying
% 251.57/60.09 | with (4), (5) gives:
% 251.57/60.09 | (7) all_40_1 = all_12_2
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (1) with e2, all_40_1, e4, e0, simplifying with
% 251.57/60.09 | (4), (6) gives:
% 251.57/60.09 | (8) all_40_1 = e2
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (7), (8) imply:
% 251.57/60.09 | (9) all_12_2 = e2
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (2), (9) imply:
% 251.57/60.09 | (10) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (10) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #699 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) op(all_6_2, e2) = e4
% 251.57/60.09 (2) op(e2, e0) = e4
% 251.57/60.09 (3) ~ (all_64_2 = e3)
% 251.57/60.09 (4) ~ (e2 = e0)
% 251.57/60.09 (5) all_252_18 = e4
% 251.57/60.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (7) op(e2, e3) = all_10_2
% 251.57/60.09 (8) ~ (e3 = e2)
% 251.57/60.09 (9) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) |
% 251.57/60.09 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3)
% 251.57/60.09 | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.57/60.09 (10) op(e2, e1) = all_38_2
% 251.57/60.09 (11) ~ (e2 = e1)
% 251.57/60.09 (12) op(all_6_2, all_64_2) = e2
% 251.57/60.09 (13) ~ (e3 = e0)
% 251.57/60.09 (14) all_70_2 = all_62_2
% 251.57/60.09 (15) ~ (e3 = e1)
% 251.57/60.09 (16) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.57/60.09 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.57/60.09 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.57/60.09 (17) all_70_2 = e2
% 251.57/60.09 (18) op(all_62_2, e3) = e1
% 251.57/60.09 (19) ~ (e4 = e3)
% 251.57/60.09 (20) all_252_11 = e0
% 251.57/60.09 (21) op(e2, e4) = all_64_2
% 251.57/60.09 (22) op(e2, e0) = all_40_2
% 251.57/60.09 (23) ~ (all_62_2 = e4)
% 251.57/60.09 (24) op(e2, e1) = e0
% 251.57/60.09 (25) ~ (all_64_2 = e4)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (14), (17) imply:
% 251.57/60.09 | (26) all_62_2 = e2
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (23), (26) imply:
% 251.57/60.09 | (27) ~ (e4 = e2)
% 251.57/60.09 |
% 251.57/60.09 | SIMP: (27) implies:
% 251.57/60.09 | (28) ~ (e4 = e2)
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (18), (26) imply:
% 251.57/60.09 | (29) op(e2, e3) = e1
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (9) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (30) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) =
% 251.57/60.09 | | e3)
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (3), (6), (15), (21), (29), (30) are inconsistent by sub-proof
% 251.57/60.09 | | #792.
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (31) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.57/60.09 | | e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.57/60.09 | |
% 251.57/60.09 | | BETA: splitting (31) gives:
% 251.57/60.09 | |
% 251.57/60.09 | | Case 1:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (32) all_252_8 = e3 & op(e2, e2) = e3
% 251.57/60.09 | | |
% 251.57/60.09 | | | ALPHA: (32) implies:
% 251.57/60.09 | | | (33) all_252_8 = e3
% 251.57/60.09 | | |
% 251.57/60.09 | | | BETA: splitting (16) gives:
% 251.57/60.09 | | |
% 251.57/60.09 | | | Case 1:
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | (34) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2,
% 251.57/60.09 | | | | e3) = e2)
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | REF_CLOSE: (1), (6), (7), (11), (12), (21), (25), (29), (34) are
% 251.57/60.09 | | | | inconsistent by sub-proof #789.
% 251.57/60.09 | | | |
% 251.57/60.09 | | | Case 2:
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | (35) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2,
% 251.57/60.09 | | | | e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | BETA: splitting (35) gives:
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | Case 1:
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | | (36) all_252_8 = e2 & op(e2, e2) = e2
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | | REF_CLOSE: (8), (33), (36) are inconsistent by sub-proof #703.
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | Case 2:
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | | (37) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 251.57/60.09 | | | | | op(e2, e0) = e2)
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | | BETA: splitting (37) gives:
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | | Case 1:
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | | (38) all_252_11 = e2 & op(e2, e1) = e2
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | | REF_CLOSE: (4), (6), (10), (24), (38) are inconsistent by sub-proof
% 251.57/60.09 | | | | | | #722.
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | Case 2:
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | | (39) all_252_18 = e2 & op(e2, e0) = e2
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | | REF_CLOSE: (2), (6), (22), (28), (39) are inconsistent by sub-proof
% 251.57/60.09 | | | | | | #702.
% 251.57/60.09 | | | | | |
% 251.57/60.09 | | | | | End of split
% 251.57/60.09 | | | | |
% 251.57/60.09 | | | | End of split
% 251.57/60.09 | | | |
% 251.57/60.09 | | | End of split
% 251.57/60.09 | | |
% 251.57/60.09 | | Case 2:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (40) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2,
% 251.57/60.09 | | | e0) = e3)
% 251.57/60.09 | | |
% 251.57/60.09 | | | BETA: splitting (40) gives:
% 251.57/60.09 | | |
% 251.57/60.09 | | | Case 1:
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | (41) all_252_11 = e3 & op(e2, e1) = e3
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | REF_CLOSE: (13), (20), (41) are inconsistent by sub-proof #701.
% 251.57/60.09 | | | |
% 251.57/60.09 | | | Case 2:
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | (42) all_252_18 = e3 & op(e2, e0) = e3
% 251.57/60.09 | | | |
% 251.57/60.09 | | | | REF_CLOSE: (5), (19), (42) are inconsistent by sub-proof #700.
% 251.57/60.09 | | | |
% 251.57/60.09 | | | End of split
% 251.57/60.09 | | |
% 251.57/60.09 | | End of split
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #700 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) all_252_18 = e3 & op(e2, e0) = e3
% 251.57/60.09 (2) all_252_18 = e4
% 251.57/60.09 (3) ~ (e4 = e3)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (1) implies:
% 251.57/60.09 | (4) all_252_18 = e3
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.09 | (5) e4 = e3
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (3), (5) imply:
% 251.57/60.09 | (6) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (6) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #701 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) all_252_11 = e3 & op(e2, e1) = e3
% 251.57/60.09 (2) all_252_11 = e0
% 251.57/60.09 (3) ~ (e3 = e0)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (1) implies:
% 251.57/60.09 | (4) all_252_11 = e3
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.09 | (5) e3 = e0
% 251.57/60.09 |
% 251.57/60.09 | SIMP: (5) implies:
% 251.57/60.09 | (6) e3 = e0
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (3), (6) imply:
% 251.57/60.09 | (7) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (7) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #702 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) op(e2, e0) = e4
% 251.57/60.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (3) ~ (e4 = e2)
% 251.57/60.09 (4) op(e2, e0) = all_40_2
% 251.57/60.09 (5) all_252_18 = e2 & op(e2, e0) = e2
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (5) implies:
% 251.57/60.09 | (6) op(e2, e0) = e2
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (2) with all_40_2, e2, e0, e2, simplifying with
% 251.57/60.09 | (4), (6) gives:
% 251.57/60.09 | (7) all_40_2 = e2
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (2) with all_40_2, e4, e0, e2, simplifying with
% 251.57/60.09 | (1), (4) gives:
% 251.57/60.09 | (8) all_40_2 = e4
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (7), (8) imply:
% 251.57/60.09 | (9) e4 = e2
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (3), (9) imply:
% 251.57/60.09 | (10) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (10) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #703 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) all_252_8 = e2 & op(e2, e2) = e2
% 251.57/60.09 (2) all_252_8 = e3
% 251.57/60.09 (3) ~ (e3 = e2)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (1) implies:
% 251.57/60.09 | (4) all_252_8 = e2
% 251.57/60.09 |
% 251.57/60.09 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.09 | (5) e3 = e2
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (3), (5) imply:
% 251.57/60.09 | (6) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (6) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #704 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) op(all_4_2, e2) = e1
% 251.57/60.09 (2) op(e2, all_4_2) = all_32_0
% 251.57/60.09 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (4) op(e2, e2) = all_244_8
% 251.57/60.09 (5) op(e1, e0) = all_34_2
% 251.57/60.09 (6) ~ (all_34_2 = e2)
% 251.57/60.09 (7) op(e0, e2) = all_28_2
% 251.57/60.09 (8) op(e1, e4) = all_16_2
% 251.57/60.09 (9) op(e1, e3) = all_62_2
% 251.57/60.09 (10) all_70_2 = all_62_2
% 251.57/60.09 (11) ~ (all_16_2 = e2)
% 251.57/60.09 (12) ~ (all_70_2 = e2)
% 251.57/60.09 (13) op(e1, e1) = all_244_15
% 251.57/60.09 (14) op(e1, e2) = all_4_2
% 251.57/60.09 (15) ~ (all_244_15 = e2)
% 251.57/60.09 (16) op(e0, all_4_2) = e1
% 251.57/60.09 (17) ~ (all_244_8 = all_28_2)
% 251.57/60.09 (18) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.57/60.09 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.57/60.09 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (10), (12) imply:
% 251.57/60.09 | (19) ~ (all_62_2 = e2)
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (18) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (20) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 251.57/60.09 | | = e2)
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (3), (8), (9), (11), (19), (20) are inconsistent by sub-proof
% 251.57/60.09 | | #925.
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (21) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.57/60.09 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.09 | |
% 251.57/60.09 | | BETA: splitting (21) gives:
% 251.57/60.09 | |
% 251.57/60.09 | | Case 1:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (22) all_252_14 = e2 & op(e1, e2) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | ALPHA: (22) implies:
% 251.57/60.09 | | | (23) op(e1, e2) = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | GROUND_INST: instantiating (3) with all_4_2, e2, e2, e1, simplifying with
% 251.57/60.09 | | | (14), (23) gives:
% 251.57/60.09 | | | (24) all_4_2 = e2
% 251.57/60.09 | | |
% 251.57/60.09 | | | REDUCE: (1), (24) imply:
% 251.57/60.09 | | | (25) op(e2, e2) = e1
% 251.57/60.09 | | |
% 251.57/60.09 | | | REDUCE: (2), (24) imply:
% 251.57/60.09 | | | (26) op(e2, e2) = all_32_0
% 251.57/60.09 | | |
% 251.57/60.09 | | | REDUCE: (16), (24) imply:
% 251.57/60.09 | | | (27) op(e0, e2) = e1
% 251.57/60.09 | | |
% 251.57/60.09 | | | GROUND_INST: instantiating (3) with all_28_2, e1, e2, e0, simplifying with
% 251.57/60.09 | | | (7), (27) gives:
% 251.57/60.09 | | | (28) all_28_2 = e1
% 251.57/60.09 | | |
% 251.57/60.09 | | | GROUND_INST: instantiating (3) with all_244_8, e1, e2, e2, simplifying
% 251.57/60.09 | | | with (4), (25) gives:
% 251.57/60.09 | | | (29) all_244_8 = e1
% 251.57/60.09 | | |
% 251.57/60.09 | | | GROUND_INST: instantiating (3) with all_244_8, all_32_0, e2, e2,
% 251.57/60.09 | | | simplifying with (4), (26) gives:
% 251.57/60.09 | | | (30) all_244_8 = all_32_0
% 251.57/60.09 | | |
% 251.57/60.09 | | | COMBINE_EQS: (29), (30) imply:
% 251.57/60.09 | | | (31) all_32_0 = e1
% 251.57/60.09 | | |
% 251.57/60.09 | | | REDUCE: (17), (28), (29) imply:
% 251.57/60.09 | | | (32) $false
% 251.57/60.09 | | |
% 251.57/60.09 | | | CLOSE: (32) is inconsistent.
% 251.57/60.09 | | |
% 251.57/60.09 | | Case 2:
% 251.57/60.09 | | |
% 251.57/60.09 | | | (33) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.57/60.09 | | | e0) = e2)
% 251.57/60.09 | | |
% 251.57/60.09 | | | REF_CLOSE: (3), (5), (6), (13), (15), (33) are inconsistent by sub-proof
% 251.57/60.09 | | | #819.
% 251.57/60.09 | | |
% 251.57/60.09 | | End of split
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #705 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.57/60.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (3) all_252_16 = e2
% 251.57/60.09 (4) ~ (all_48_2 = e4)
% 251.57/60.09 (5) op(e3, e0) = all_48_2
% 251.57/60.09 (6) ~ (e4 = e2)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | BETA: splitting (1) gives:
% 251.57/60.09 |
% 251.57/60.09 | Case 1:
% 251.57/60.09 | |
% 251.57/60.09 | | (7) all_252_16 = e4 & op(e4, e0) = e4
% 251.57/60.09 | |
% 251.57/60.09 | | ALPHA: (7) implies:
% 251.57/60.09 | | (8) all_252_16 = e4
% 251.57/60.09 | |
% 251.57/60.09 | | COMBINE_EQS: (3), (8) imply:
% 251.57/60.09 | | (9) e4 = e2
% 251.57/60.09 | |
% 251.57/60.09 | | SIMP: (9) implies:
% 251.57/60.09 | | (10) e4 = e2
% 251.57/60.09 | |
% 251.57/60.09 | | REDUCE: (6), (10) imply:
% 251.57/60.09 | | (11) $false
% 251.57/60.09 | |
% 251.57/60.09 | | CLOSE: (11) is inconsistent.
% 251.57/60.09 | |
% 251.57/60.09 | Case 2:
% 251.57/60.09 | |
% 251.57/60.09 | | (12) all_252_17 = e4 & op(e3, e0) = e4
% 251.57/60.09 | |
% 251.57/60.09 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #706.
% 251.57/60.09 | |
% 251.57/60.09 | End of split
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #706 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) all_252_17 = e4 & op(e3, e0) = e4
% 251.57/60.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (3) op(e3, e0) = all_48_2
% 251.57/60.09 (4) ~ (all_48_2 = e4)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | ALPHA: (1) implies:
% 251.57/60.09 | (5) op(e3, e0) = e4
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (2) with all_48_2, e4, e0, e3, simplifying with
% 251.57/60.09 | (3), (5) gives:
% 251.57/60.09 | (6) all_48_2 = e4
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (4), (6) imply:
% 251.57/60.09 | (7) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (7) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #707 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (2) op(e2, e0) = all_40_2
% 251.57/60.09 (3) op(e2, e0) = e4
% 251.57/60.09 (4) ~ (all_40_2 = e4)
% 251.57/60.09
% 251.57/60.09 Begin of proof
% 251.57/60.09 |
% 251.57/60.09 | GROUND_INST: instantiating (1) with all_40_2, e4, e0, e2, simplifying with
% 251.57/60.09 | (2), (3) gives:
% 251.57/60.09 | (5) all_40_2 = e4
% 251.57/60.09 |
% 251.57/60.09 | REDUCE: (4), (5) imply:
% 251.57/60.09 | (6) $false
% 251.57/60.09 |
% 251.57/60.09 | CLOSE: (6) is inconsistent.
% 251.57/60.09 |
% 251.57/60.09 End of proof
% 251.57/60.09
% 251.57/60.09 Sub-proof #708 shows that the following formulas are inconsistent:
% 251.57/60.09 ----------------------------------------------------------------
% 251.57/60.09 (1) ~ (all_4_2 = e4)
% 251.57/60.09 (2) ~ (all_10_2 = e4)
% 251.57/60.09 (3) op(all_4_2, e2) = e1
% 251.57/60.09 (4) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.57/60.09 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.57/60.09 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.57/60.09 (5) op(e4, e0) = all_30_2
% 251.57/60.09 (6) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.57/60.09 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.57/60.09 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.57/60.09 (7) ~ (all_36_2 = e4) | ( ~ (all_36_0 = e0) & op(e4, all_36_1) = all_36_0 &
% 251.57/60.09 op(e1, e4) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 251.57/60.09 e2) & op(e1, e4) = all_36_1 & $i(all_36_1))
% 251.57/60.09 (8) ~ (all_22_2 = e2)
% 251.57/60.09 (9) op(all_38_2, all_4_2) = e1
% 251.57/60.09 (10) op(all_64_2, e4) = e2
% 251.57/60.09 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.09 (12) all_230_2 = e2
% 251.57/60.09 (13) op(e2, e3) = all_10_2
% 251.57/60.09 (14) ~ (e3 = e2)
% 251.57/60.09 (15) op(e0, e0) = all_244_24
% 251.57/60.09 (16) ~ (e4 = e0)
% 251.57/60.09 (17) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.57/60.09 all_250_17 = e0
% 251.57/60.09 (18) op(all_244_8, all_244_8) = e2
% 251.57/60.09 (19) op(e2, e2) = all_244_8
% 251.57/60.09 (20) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.57/60.09 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.57/60.09 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.57/60.09 (21) op(e2, e1) = all_38_2
% 251.57/60.09 (22) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.57/60.09 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.57/60.09 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.57/60.09 (23) ~ (all_84_2 = all_62_2)
% 251.57/60.09 (24) op(e1, e0) = all_34_2
% 251.57/60.09 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.57/60.09 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.57/60.09 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.57/60.09 (26) op(e4, e2) = all_6_2
% 251.57/60.09 (27) ~ (all_34_2 = e2) | ( ~ (all_34_0 = e4) & op(e2, all_34_1) = all_34_0 &
% 251.57/60.09 op(e0, e2) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 251.57/60.09 e3) & op(e0, e2) = all_34_1 & $i(all_34_1))
% 251.57/60.09 (28) ~ (e2 = e1)
% 251.57/60.09 (29) op(e0, e2) = all_28_2
% 251.57/60.09 (30) ~ (e4 = e1)
% 251.57/60.09 (31) ~ (all_6_2 = e1)
% 251.57/60.09 (32) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.57/60.09 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.57/60.09 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.57/60.09 (33) ~ (all_62_2 = all_34_2)
% 251.57/60.09 (34) ~ (all_244_8 = all_38_2)
% 251.57/60.09 (35) all_50_2 = all_4_2
% 251.57/60.09 (36) op(e1, e4) = all_16_2
% 251.57/60.09 (37) ~ (all_244_0 = all_64_2)
% 251.57/60.09 (38) op(e1, e3) = all_62_2
% 251.57/60.09 (39) op(all_16_2, all_26_2) = e4
% 251.57/60.09 (40) ~ (e3 = e0)
% 251.57/60.09 (41) ~ (all_230_2 = e2) | ( ~ (all_230_0 = e3) & op(e2, all_230_1) =
% 251.57/60.09 all_230_0 & op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)) |
% 251.57/60.09 ( ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 & $i(all_230_1))
% 251.57/60.09 (42) ~ (all_40_2 = e4) | ( ~ (all_40_0 = e1) & op(e4, all_40_1) = all_40_0 &
% 251.57/60.09 op(e0, e4) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 251.57/60.09 e3) & op(e0, e4) = all_40_1 & $i(all_40_1))
% 251.57/60.10 (43) ~ (all_30_2 = e2)
% 251.57/60.10 (44) all_70_2 = all_62_2
% 251.57/60.10 (45) ~ (e3 = e1)
% 251.57/60.10 (46) ~ (all_12_2 = e2)
% 251.57/60.10 (47) op(e3, e1) = all_36_2
% 251.57/60.10 (48) ~ (all_16_2 = e2)
% 251.57/60.10 (49) ~ (all_8_2 = e1)
% 251.57/60.10 (50) op(all_40_2, e0) = e2
% 251.57/60.10 (51) ~ (all_22_2 = e1)
% 251.57/60.10 (52) ~ (all_28_2 = all_4_2)
% 251.57/60.10 (53) ~ (all_38_2 = e2)
% 251.57/60.10 (54) ~ (all_244_15 = all_38_2)
% 251.57/60.10 (55) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.57/60.10 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.57/60.10 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.57/60.10 (56) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.57/60.10 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.57/60.10 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.57/60.10 (57) ~ (all_64_2 = all_12_2)
% 251.57/60.10 (58) ~ (all_28_2 = e2)
% 251.57/60.10 (59) op(e0, e3) = all_22_2
% 251.57/60.10 (60) ~ (all_244_0 = all_100_2)
% 251.57/60.10 (61) op(all_34_2, e2) = e0
% 251.57/60.10 (62) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.57/60.10 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.57/60.10 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.57/60.10 (63) op(all_62_2, e3) = e1
% 251.57/60.10 (64) op(e4, e1) = all_26_2
% 251.57/60.10 (65) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.57/60.10 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.57/60.10 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.57/60.10 (66) ~ (all_244_15 = all_62_2)
% 251.57/60.10 (67) op(e3, e4) = all_100_2
% 251.57/60.10 (68) op(e4, e4) = all_244_0
% 251.57/60.10 (69) ~ (e4 = e3)
% 251.57/60.10 (70) op(e1, e1) = all_244_15
% 251.57/60.10 (71) op(e0, e1) = all_20_2
% 251.57/60.10 (72) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.57/60.10 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.57/60.10 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.57/60.10 (73) ~ (all_38_2 = all_36_2)
% 251.57/60.10 (74) ~ (all_26_2 = e3)
% 251.57/60.10 (75) all_82_2 = all_28_2
% 251.57/60.10 (76) ~ (all_244_24 = e2)
% 251.57/60.10 (77) op(e1, e2) = all_4_2
% 251.57/60.10 (78) op(all_4_2, all_38_2) = e2
% 251.57/60.10 (79) op(e4, e3) = all_84_2
% 251.57/60.10 (80) op(e2, e4) = all_64_2
% 251.57/60.10 (81) ~ (all_244_15 = e2)
% 251.57/60.10 (82) all_250_17 = all_4_2
% 251.57/60.10 (83) ~ (all_38_2 = all_26_2)
% 251.57/60.10 (84) op(e3, e2) = all_8_2
% 251.57/60.10 (85) ~ (all_64_2 = all_16_2)
% 251.57/60.10 (86) op(all_36_2, e1) = e3
% 251.57/60.10 (87) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.57/60.10 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.57/60.10 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.57/60.10 (88) ~ (all_20_2 = e4)
% 251.57/60.10 (89) op(all_16_2, e4) = e1
% 251.57/60.10 (90) op(e2, e0) = all_40_2
% 251.57/60.10 (91) ~ (all_244_8 = all_28_2)
% 251.57/60.10 (92) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.57/60.10 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.57/60.10 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.10 (93) ~ (all_62_2 = all_4_2)
% 251.57/60.10 (94) op(e2, e1) = e0
% 251.57/60.10 (95) op(e0, e4) = all_12_2
% 251.57/60.10 (96) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 251.57/60.10 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 251.57/60.10 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.57/60.10
% 251.57/60.10 Begin of proof
% 251.57/60.10 |
% 251.57/60.10 | BETA: splitting (41) gives:
% 251.57/60.10 |
% 251.57/60.10 | Case 1:
% 251.57/60.10 | |
% 251.57/60.10 | | (97) ~ (all_230_2 = e2)
% 251.57/60.10 | |
% 251.57/60.10 | | REDUCE: (12), (97) imply:
% 251.57/60.10 | | (98) $false
% 251.57/60.10 | |
% 251.57/60.10 | | CLOSE: (98) is inconsistent.
% 251.57/60.10 | |
% 251.57/60.10 | Case 2:
% 251.57/60.10 | |
% 251.57/60.10 | | (99) ( ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 & op(e1, e2) =
% 251.57/60.10 | | all_230_1 & $i(all_230_0) & $i(all_230_1)) | ( ~ (all_230_1 = e4)
% 251.57/60.10 | | & op(e1, e2) = all_230_1 & $i(all_230_1))
% 251.57/60.10 | |
% 251.57/60.10 | | BETA: splitting (65) gives:
% 251.57/60.10 | |
% 251.57/60.10 | | Case 1:
% 251.57/60.10 | | |
% 251.57/60.10 | | | (100) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0,
% 251.57/60.10 | | | e3) = e2)
% 251.57/60.10 | | |
% 251.57/60.10 | | | REF_CLOSE: (8), (11), (46), (59), (95), (100) are inconsistent by
% 251.57/60.10 | | | sub-proof #727.
% 251.57/60.10 | | |
% 251.57/60.10 | | Case 2:
% 251.57/60.10 | | |
% 251.57/60.10 | | | (101) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.57/60.10 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.57/60.10 | | |
% 251.57/60.10 | | | BETA: splitting (101) gives:
% 251.57/60.10 | | |
% 251.57/60.10 | | | Case 1:
% 251.57/60.10 | | | |
% 251.57/60.10 | | | | (102) all_252_22 = e2 & op(e0, e2) = e2
% 251.57/60.10 | | | |
% 251.57/60.10 | | | | REF_CLOSE: (11), (29), (58), (102) are inconsistent by sub-proof #979.
% 251.57/60.10 | | | |
% 251.57/60.10 | | | Case 2:
% 251.57/60.10 | | | |
% 251.57/60.10 | | | | (103) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 251.57/60.10 | | | | e0) = e2)
% 251.57/60.10 | | | |
% 251.57/60.10 | | | | BETA: splitting (103) gives:
% 251.57/60.10 | | | |
% 251.57/60.10 | | | | Case 1:
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | (104) all_252_23 = e2 & op(e0, e1) = e2
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | ALPHA: (104) implies:
% 251.57/60.10 | | | | | (105) all_252_23 = e2
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | BETA: splitting (99) gives:
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | Case 1:
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | (106) ~ (all_230_0 = e3) & op(e2, all_230_1) = all_230_0 &
% 251.57/60.10 | | | | | | op(e1, e2) = all_230_1 & $i(all_230_0) & $i(all_230_1)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | ALPHA: (106) implies:
% 251.57/60.10 | | | | | | (107) op(e1, e2) = all_230_1
% 251.57/60.10 | | | | | | (108) op(e2, all_230_1) = all_230_0
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | GROUND_INST: instantiating (11) with all_4_2, all_230_1, e2, e1,
% 251.57/60.10 | | | | | | simplifying with (77), (107) gives:
% 251.57/60.10 | | | | | | (109) all_230_1 = all_4_2
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | GROUND_INST: instantiating (11) with all_38_2, e0, e1, e2,
% 251.57/60.10 | | | | | | simplifying with (21), (94) gives:
% 251.57/60.10 | | | | | | (110) all_38_2 = e0
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (34), (110) imply:
% 251.57/60.10 | | | | | | (111) ~ (all_244_8 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (54), (110) imply:
% 251.57/60.10 | | | | | | (112) ~ (all_244_15 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (73), (110) imply:
% 251.57/60.10 | | | | | | (113) ~ (all_36_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (113) implies:
% 251.57/60.10 | | | | | | (114) ~ (all_36_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (83), (110) imply:
% 251.57/60.10 | | | | | | (115) ~ (all_26_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (115) implies:
% 251.57/60.10 | | | | | | (116) ~ (all_26_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (53), (110) imply:
% 251.57/60.10 | | | | | | (117) ~ (e2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (117) implies:
% 251.57/60.10 | | | | | | (118) ~ (e2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (9), (110) imply:
% 251.57/60.10 | | | | | | (119) op(e0, all_4_2) = e1
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (78), (110) imply:
% 251.57/60.10 | | | | | | (120) op(all_4_2, e0) = e2
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (108), (109) imply:
% 251.57/60.10 | | | | | | (121) op(e2, all_4_2) = all_230_0
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | BETA: splitting (4) gives:
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | Case 1:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | (122) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 &
% 251.57/60.10 | | | | | | | op(e3, e1) = e0)
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | BETA: splitting (122) gives:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (123) all_252_9 = e0 & op(e4, e1) = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | ALPHA: (123) implies:
% 251.57/60.10 | | | | | | | | (124) op(e4, e1) = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | GROUND_INST: instantiating (11) with all_26_2, e0, e1, e4,
% 251.57/60.10 | | | | | | | | simplifying with (64), (124) gives:
% 251.57/60.10 | | | | | | | | (125) all_26_2 = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | REDUCE: (116), (125) imply:
% 251.57/60.10 | | | | | | | | (126) $false
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | CLOSE: (126) is inconsistent.
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (127) all_252_10 = e0 & op(e3, e1) = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | REF_CLOSE: (11), (47), (114), (127) are inconsistent by
% 251.57/60.10 | | | | | | | | sub-proof #726.
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | End of split
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | Case 2:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | (128) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 &
% 251.57/60.10 | | | | | | | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | BETA: splitting (128) gives:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (129) all_252_11 = e0 & op(e2, e1) = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | ALPHA: (129) implies:
% 251.57/60.10 | | | | | | | | (130) all_252_11 = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | BETA: splitting (27) gives:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | (131) ~ (all_34_2 = e2)
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | BETA: splitting (7) gives:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | (132) ~ (all_36_2 = e4)
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | BETA: splitting (42) gives:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | (133) ~ (all_40_2 = e4)
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | BETA: splitting (96) gives:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | (134) ~ (all_50_2 = e3)
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | REDUCE: (35), (134) imply:
% 251.57/60.10 | | | | | | | | | | | | (135) ~ (all_4_2 = e3)
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | BETA: splitting (72) gives:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | (136) ~ (all_62_2 = e4)
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | (137) ~ (all_64_2 = e3)
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | (138) ~ (all_70_2 = e2)
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | REDUCE: (44), (138) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | (139) ~ (all_62_2 = e2)
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | (140) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 251.57/60.10 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (36), (38), (48), (139), (140) are
% 251.57/60.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | (141) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 251.57/60.10 | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 251.57/60.10 | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | (142) all_252_14 = e2 & op(e1, e2) = e2
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (143) op(e1, e2) = e2
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_4_2, e2, e2, e1,
% 251.57/60.10 | | | | | | | | | | | | | | | | | simplifying with (77), (143) gives:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (144) all_4_2 = e2
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | REDUCE: (3), (144) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (145) op(e2, e2) = e1
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | REDUCE: (121), (144) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (146) op(e2, e2) = all_230_0
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | REDUCE: (119), (144) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (147) op(e0, e2) = e1
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_28_2, e1, e2, e0,
% 251.57/60.10 | | | | | | | | | | | | | | | | | simplifying with (29), (147) gives:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (148) all_28_2 = e1
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_244_8, e1, e2, e2,
% 251.57/60.10 | | | | | | | | | | | | | | | | | simplifying with (19), (145) gives:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (149) all_244_8 = e1
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_244_8, all_230_0, e2,
% 251.57/60.10 | | | | | | | | | | | | | | | | | e2, simplifying with (19), (146) gives:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (150) all_244_8 = all_230_0
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (150) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (151) all_230_0 = e1
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | REDUCE: (91), (148), (149) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | | | (152) $false
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | CLOSE: (152) is inconsistent.
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | (153) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 251.57/60.10 | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (24), (70), (81), (131), (153) are
% 251.57/60.10 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #819.
% 251.57/60.10 | | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | (154) all_70_2 = e2
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (6), (11), (13), (14), (15), (16), (17),
% 251.57/60.10 | | | | | | | | | | | | | | | (20), (21), (22), (24), (26), (28), (29), (30),
% 251.57/60.10 | | | | | | | | | | | | | | | (31), (33), (40), (44), (45), (49), (52), (56),
% 251.57/60.10 | | | | | | | | | | | | | | | (62), (63), (75), (76), (77), (80), (82), (84),
% 251.57/60.10 | | | | | | | | | | | | | | | (90), (93), (94), (118), (120), (130), (133),
% 251.57/60.10 | | | | | | | | | | | | | | | (135), (136), (137), (154) are inconsistent by
% 251.57/60.10 | | | | | | | | | | | | | | | sub-proof #717.
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | (155) all_64_2 = e3
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (11), (13), (14), (16), (18), (19),
% 251.57/60.10 | | | | | | | | | | | | | | (36), (37), (57), (60), (62), (67), (68), (69),
% 251.57/60.10 | | | | | | | | | | | | | | (85), (87), (90), (95), (130), (133), (155) are
% 251.57/60.10 | | | | | | | | | | | | | | inconsistent by sub-proof #716.
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | (156) all_62_2 = e4
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | REF_CLOSE: (11), (16), (23), (25), (39), (47), (63), (64),
% 251.57/60.10 | | | | | | | | | | | | | (66), (70), (71), (79), (88), (89), (130), (132),
% 251.57/60.10 | | | | | | | | | | | | | (156) are inconsistent by sub-proof #715.
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | (157) all_50_2 = e3
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | REF_CLOSE: (11), (35), (51), (59), (119), (157) are
% 251.57/60.10 | | | | | | | | | | | | inconsistent by sub-proof #713.
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | (158) all_40_2 = e4
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | REDUCE: (50), (158) imply:
% 251.57/60.10 | | | | | | | | | | | (159) op(e4, e0) = e2
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | REF_CLOSE: (5), (11), (43), (159) are inconsistent by
% 251.57/60.10 | | | | | | | | | | | sub-proof #830.
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | (160) all_36_2 = e4
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | REDUCE: (86), (160) imply:
% 251.57/60.10 | | | | | | | | | | (161) op(e4, e1) = e3
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | REF_CLOSE: (11), (64), (74), (161) are inconsistent by
% 251.57/60.10 | | | | | | | | | | sub-proof #834.
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | (162) all_34_2 = e2
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | REDUCE: (61), (162) imply:
% 251.57/60.10 | | | | | | | | | (163) op(e2, e2) = e0
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | REF_CLOSE: (11), (19), (111), (163) are inconsistent by
% 251.57/60.10 | | | | | | | | | sub-proof #880.
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | End of split
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (164) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0
% 251.57/60.10 | | | | | | | | & op(e0, e1) = e0)
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | REF_CLOSE: (11), (70), (105), (112), (118), (164) are
% 251.57/60.10 | | | | | | | | inconsistent by sub-proof #711.
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | End of split
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | End of split
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | Case 2:
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | (165) ~ (all_230_1 = e4) & op(e1, e2) = all_230_1 &
% 251.57/60.10 | | | | | | $i(all_230_1)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | ALPHA: (165) implies:
% 251.57/60.10 | | | | | | (166) ~ (all_230_1 = e4)
% 251.57/60.10 | | | | | | (167) op(e1, e2) = all_230_1
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | GROUND_INST: instantiating (11) with all_4_2, all_230_1, e2, e1,
% 251.57/60.10 | | | | | | simplifying with (77), (167) gives:
% 251.57/60.10 | | | | | | (168) all_230_1 = all_4_2
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | GROUND_INST: instantiating (11) with all_38_2, e0, e1, e2,
% 251.57/60.10 | | | | | | simplifying with (21), (94) gives:
% 251.57/60.10 | | | | | | (169) all_38_2 = e0
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (34), (169) imply:
% 251.57/60.10 | | | | | | (170) ~ (all_244_8 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (54), (169) imply:
% 251.57/60.10 | | | | | | (171) ~ (all_244_15 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (73), (169) imply:
% 251.57/60.10 | | | | | | (172) ~ (all_36_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (172) implies:
% 251.57/60.10 | | | | | | (173) ~ (all_36_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (83), (169) imply:
% 251.57/60.10 | | | | | | (174) ~ (all_26_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (174) implies:
% 251.57/60.10 | | | | | | (175) ~ (all_26_2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (53), (169) imply:
% 251.57/60.10 | | | | | | (176) ~ (e2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | SIMP: (176) implies:
% 251.57/60.10 | | | | | | (177) ~ (e2 = e0)
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (9), (169) imply:
% 251.57/60.10 | | | | | | (178) op(e0, all_4_2) = e1
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | REDUCE: (78), (169) imply:
% 251.57/60.10 | | | | | | (179) op(all_4_2, e0) = e2
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | BETA: splitting (4) gives:
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | | Case 1:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | (180) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 &
% 251.57/60.10 | | | | | | | op(e3, e1) = e0)
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | REF_CLOSE: (11), (47), (64), (173), (175), (180) are inconsistent
% 251.57/60.10 | | | | | | | by sub-proof #710.
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | Case 2:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | (181) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 &
% 251.57/60.10 | | | | | | | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | BETA: splitting (181) gives:
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (182) all_252_11 = e0 & op(e2, e1) = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | ALPHA: (182) implies:
% 251.57/60.10 | | | | | | | | (183) all_252_11 = e0
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | BETA: splitting (27) gives:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | (184) ~ (all_34_2 = e2)
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | BETA: splitting (7) gives:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | (185) ~ (all_36_2 = e4)
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | BETA: splitting (42) gives:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | (186) ~ (all_40_2 = e4)
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | BETA: splitting (96) gives:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | (187) ~ (all_50_2 = e3)
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | REDUCE: (35), (187) imply:
% 251.57/60.10 | | | | | | | | | | | | (188) ~ (all_4_2 = e3)
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | BETA: splitting (72) gives:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | (189) ~ (all_62_2 = e4)
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | (190) ~ (all_64_2 = e3)
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | Case 1:
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | (191) ~ (all_70_2 = e2)
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | REDUCE: (44), (191) imply:
% 251.57/60.10 | | | | | | | | | | | | | | | (192) ~ (all_62_2 = e2)
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (19), (24), (29), (36), (38), (48),
% 251.57/60.10 | | | | | | | | | | | | | | | (70), (77), (81), (91), (92), (178), (184), (192)
% 251.57/60.10 | | | | | | | | | | | | | | | are inconsistent by sub-proof #709.
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | (193) all_70_2 = e2
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (6), (11), (13), (14), (15), (16), (17),
% 251.57/60.10 | | | | | | | | | | | | | | | (20), (21), (22), (24), (26), (28), (29), (30),
% 251.57/60.10 | | | | | | | | | | | | | | | (31), (33), (40), (44), (45), (49), (52), (56),
% 251.57/60.10 | | | | | | | | | | | | | | | (62), (63), (75), (76), (77), (80), (82), (84),
% 251.57/60.10 | | | | | | | | | | | | | | | (90), (93), (94), (177), (179), (183), (186),
% 251.57/60.10 | | | | | | | | | | | | | | | (188), (189), (190), (193) are inconsistent by
% 251.57/60.10 | | | | | | | | | | | | | | | sub-proof #717.
% 251.57/60.10 | | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | (194) all_64_2 = e3
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (11), (13), (14), (16), (18), (19),
% 251.57/60.10 | | | | | | | | | | | | | | (36), (37), (57), (60), (62), (67), (68), (69),
% 251.57/60.10 | | | | | | | | | | | | | | (85), (87), (90), (95), (183), (186), (194) are
% 251.57/60.10 | | | | | | | | | | | | | | inconsistent by sub-proof #716.
% 251.57/60.10 | | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | (195) all_62_2 = e4
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | | REF_CLOSE: (11), (16), (23), (25), (39), (47), (63), (64),
% 251.57/60.10 | | | | | | | | | | | | | (66), (70), (71), (79), (88), (89), (183), (185),
% 251.57/60.10 | | | | | | | | | | | | | (195) are inconsistent by sub-proof #715.
% 251.57/60.10 | | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | (196) all_50_2 = e3
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | | REF_CLOSE: (11), (35), (51), (59), (178), (196) are
% 251.57/60.10 | | | | | | | | | | | | inconsistent by sub-proof #713.
% 251.57/60.10 | | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | (197) all_40_2 = e4
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | REDUCE: (50), (197) imply:
% 251.57/60.10 | | | | | | | | | | | (198) op(e4, e0) = e2
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | | REF_CLOSE: (5), (11), (43), (198) are inconsistent by
% 251.57/60.10 | | | | | | | | | | | sub-proof #830.
% 251.57/60.10 | | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | (199) all_36_2 = e4
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | REDUCE: (86), (199) imply:
% 251.57/60.10 | | | | | | | | | | (200) op(e4, e1) = e3
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | | REF_CLOSE: (11), (64), (74), (200) are inconsistent by
% 251.57/60.10 | | | | | | | | | | sub-proof #834.
% 251.57/60.10 | | | | | | | | | |
% 251.57/60.10 | | | | | | | | | End of split
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | (201) all_34_2 = e2
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | REDUCE: (61), (201) imply:
% 251.57/60.10 | | | | | | | | | (202) op(e2, e2) = e0
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | | REF_CLOSE: (11), (19), (170), (202) are inconsistent by
% 251.57/60.10 | | | | | | | | | sub-proof #880.
% 251.57/60.10 | | | | | | | | |
% 251.57/60.10 | | | | | | | | End of split
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | Case 2:
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | (203) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0
% 251.57/60.10 | | | | | | | | & op(e0, e1) = e0)
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | | REF_CLOSE: (11), (70), (105), (171), (177), (203) are
% 251.57/60.10 | | | | | | | | inconsistent by sub-proof #711.
% 251.57/60.10 | | | | | | | |
% 251.57/60.10 | | | | | | | End of split
% 251.57/60.10 | | | | | | |
% 251.57/60.10 | | | | | | End of split
% 251.57/60.10 | | | | | |
% 251.57/60.10 | | | | | End of split
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | Case 2:
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | (204) all_252_24 = e2 & op(e0, e0) = e2
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | ALPHA: (204) implies:
% 251.57/60.10 | | | | | (205) op(e0, e0) = e2
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | | REF_CLOSE: (11), (15), (76), (205) are inconsistent by sub-proof #978.
% 251.57/60.10 | | | | |
% 251.57/60.10 | | | | End of split
% 251.57/60.10 | | | |
% 251.57/60.10 | | | End of split
% 251.57/60.10 | | |
% 251.57/60.10 | | End of split
% 251.57/60.10 | |
% 251.57/60.10 | End of split
% 251.57/60.10 |
% 251.57/60.10 End of proof
% 251.57/60.10
% 251.57/60.10 Sub-proof #709 shows that the following formulas are inconsistent:
% 251.57/60.10 ----------------------------------------------------------------
% 251.57/60.10 (1) op(all_4_2, e2) = e1
% 251.57/60.10 (2) ~ (all_62_2 = e2)
% 251.57/60.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.10 (4) op(e2, e2) = all_244_8
% 251.57/60.10 (5) op(e1, e0) = all_34_2
% 251.57/60.10 (6) ~ (all_34_2 = e2)
% 251.57/60.10 (7) op(e0, e2) = all_28_2
% 251.57/60.10 (8) op(e1, e4) = all_16_2
% 251.57/60.10 (9) op(e1, e3) = all_62_2
% 251.57/60.10 (10) ~ (all_16_2 = e2)
% 251.57/60.10 (11) op(e1, e1) = all_244_15
% 251.57/60.10 (12) op(e1, e2) = all_4_2
% 251.57/60.10 (13) ~ (all_244_15 = e2)
% 251.57/60.10 (14) op(e0, all_4_2) = e1
% 251.57/60.10 (15) ~ (all_244_8 = all_28_2)
% 251.57/60.10 (16) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.57/60.10 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.57/60.10 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.10
% 251.57/60.10 Begin of proof
% 251.57/60.10 |
% 251.57/60.10 | BETA: splitting (16) gives:
% 251.57/60.10 |
% 251.57/60.10 | Case 1:
% 251.57/60.10 | |
% 251.57/60.10 | | (17) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 251.57/60.10 | | = e2)
% 251.57/60.10 | |
% 251.57/60.10 | | REF_CLOSE: (2), (3), (8), (9), (10), (17) are inconsistent by sub-proof
% 251.57/60.10 | | #925.
% 251.57/60.10 | |
% 251.57/60.10 | Case 2:
% 251.57/60.10 | |
% 251.57/60.10 | | (18) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.57/60.10 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.10 | |
% 251.57/60.10 | | BETA: splitting (18) gives:
% 251.57/60.10 | |
% 251.57/60.10 | | Case 1:
% 251.57/60.10 | | |
% 251.57/60.10 | | | (19) all_252_14 = e2 & op(e1, e2) = e2
% 251.57/60.10 | | |
% 251.57/60.10 | | | ALPHA: (19) implies:
% 251.57/60.10 | | | (20) op(e1, e2) = e2
% 251.57/60.10 | | |
% 251.57/60.10 | | | GROUND_INST: instantiating (3) with all_4_2, e2, e2, e1, simplifying with
% 251.57/60.10 | | | (12), (20) gives:
% 251.57/60.10 | | | (21) all_4_2 = e2
% 251.57/60.10 | | |
% 251.57/60.10 | | | REDUCE: (1), (21) imply:
% 251.57/60.10 | | | (22) op(e2, e2) = e1
% 251.57/60.10 | | |
% 251.57/60.10 | | | REDUCE: (14), (21) imply:
% 251.57/60.10 | | | (23) op(e0, e2) = e1
% 251.57/60.10 | | |
% 251.57/60.10 | | | GROUND_INST: instantiating (3) with all_28_2, e1, e2, e0, simplifying with
% 251.57/60.10 | | | (7), (23) gives:
% 251.57/60.10 | | | (24) all_28_2 = e1
% 251.57/60.10 | | |
% 251.57/60.10 | | | GROUND_INST: instantiating (3) with all_244_8, e1, e2, e2, simplifying
% 251.57/60.10 | | | with (4), (22) gives:
% 251.57/60.10 | | | (25) all_244_8 = e1
% 251.57/60.10 | | |
% 251.57/60.10 | | | REDUCE: (15), (24), (25) imply:
% 251.57/60.10 | | | (26) $false
% 251.57/60.10 | | |
% 251.57/60.10 | | | CLOSE: (26) is inconsistent.
% 251.57/60.10 | | |
% 251.57/60.10 | | Case 2:
% 251.57/60.10 | | |
% 251.57/60.10 | | | (27) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.57/60.10 | | | e0) = e2)
% 251.57/60.10 | | |
% 251.57/60.10 | | | REF_CLOSE: (3), (5), (6), (11), (13), (27) are inconsistent by sub-proof
% 251.57/60.10 | | | #819.
% 251.57/60.10 | | |
% 251.57/60.10 | | End of split
% 251.57/60.10 | |
% 251.57/60.10 | End of split
% 251.57/60.10 |
% 251.57/60.10 End of proof
% 251.57/60.10
% 251.57/60.10 Sub-proof #710 shows that the following formulas are inconsistent:
% 251.57/60.10 ----------------------------------------------------------------
% 251.57/60.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.10 (2) op(e3, e1) = all_36_2
% 251.57/60.10 (3) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.57/60.10 (4) op(e4, e1) = all_26_2
% 251.57/60.10 (5) ~ (all_36_2 = e0)
% 251.57/60.10 (6) ~ (all_26_2 = e0)
% 251.57/60.10
% 251.57/60.10 Begin of proof
% 251.57/60.10 |
% 251.57/60.10 | BETA: splitting (3) gives:
% 251.57/60.10 |
% 251.57/60.10 | Case 1:
% 251.57/60.10 | |
% 251.57/60.10 | | (7) all_252_9 = e0 & op(e4, e1) = e0
% 251.57/60.10 | |
% 251.57/60.10 | | ALPHA: (7) implies:
% 251.57/60.11 | | (8) op(e4, e1) = e0
% 251.57/60.11 | |
% 251.57/60.11 | | GROUND_INST: instantiating (1) with all_26_2, e0, e1, e4, simplifying with
% 251.57/60.11 | | (4), (8) gives:
% 251.57/60.11 | | (9) all_26_2 = e0
% 251.57/60.11 | |
% 251.57/60.11 | | REDUCE: (6), (9) imply:
% 251.57/60.11 | | (10) $false
% 251.57/60.11 | |
% 251.57/60.11 | | CLOSE: (10) is inconsistent.
% 251.57/60.11 | |
% 251.57/60.11 | Case 2:
% 251.57/60.11 | |
% 251.57/60.11 | | (11) all_252_10 = e0 & op(e3, e1) = e0
% 251.57/60.11 | |
% 251.57/60.11 | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #726.
% 251.57/60.11 | |
% 251.57/60.11 | End of split
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #711 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ~ (e2 = e0)
% 251.57/60.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (3) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.57/60.11 (4) ~ (all_244_15 = e0)
% 251.57/60.11 (5) op(e1, e1) = all_244_15
% 251.57/60.11 (6) all_252_23 = e2
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | BETA: splitting (3) gives:
% 251.57/60.11 |
% 251.57/60.11 | Case 1:
% 251.57/60.11 | |
% 251.57/60.11 | | (7) all_252_15 = e0 & op(e1, e1) = e0
% 251.57/60.11 | |
% 251.57/60.11 | | ALPHA: (7) implies:
% 251.57/60.11 | | (8) op(e1, e1) = e0
% 251.57/60.11 | |
% 251.57/60.11 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #712.
% 251.57/60.11 | |
% 251.57/60.11 | Case 2:
% 251.57/60.11 | |
% 251.57/60.11 | | (9) all_252_23 = e0 & op(e0, e1) = e0
% 251.57/60.11 | |
% 251.57/60.11 | | ALPHA: (9) implies:
% 251.57/60.11 | | (10) all_252_23 = e0
% 251.57/60.11 | |
% 251.57/60.11 | | COMBINE_EQS: (6), (10) imply:
% 251.57/60.11 | | (11) e2 = e0
% 251.57/60.11 | |
% 251.57/60.11 | | REDUCE: (1), (11) imply:
% 251.57/60.11 | | (12) $false
% 251.57/60.11 | |
% 251.57/60.11 | | CLOSE: (12) is inconsistent.
% 251.57/60.11 | |
% 251.57/60.11 | End of split
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #712 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (2) op(e1, e1) = all_244_15
% 251.57/60.11 (3) op(e1, e1) = e0
% 251.57/60.11 (4) ~ (all_244_15 = e0)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | GROUND_INST: instantiating (1) with all_244_15, e0, e1, e1, simplifying with
% 251.57/60.11 | (2), (3) gives:
% 251.57/60.11 | (5) all_244_15 = e0
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (4), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #713 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (2) all_50_2 = all_4_2
% 251.57/60.11 (3) all_50_2 = e3
% 251.57/60.11 (4) ~ (all_22_2 = e1)
% 251.57/60.11 (5) op(e0, e3) = all_22_2
% 251.57/60.11 (6) op(e0, all_4_2) = e1
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (2), (3) imply:
% 251.57/60.11 | (7) all_4_2 = e3
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (7) implies:
% 251.57/60.11 | (8) all_4_2 = e3
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (6), (8) imply:
% 251.57/60.11 | (9) op(e0, e3) = e1
% 251.57/60.11 |
% 251.57/60.11 | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #714.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #714 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (2) op(e0, e3) = all_22_2
% 251.57/60.11 (3) op(e0, e3) = e1
% 251.57/60.11 (4) ~ (all_22_2 = e1)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | GROUND_INST: instantiating (1) with all_22_2, e1, e3, e0, simplifying with
% 251.57/60.11 | (2), (3) gives:
% 251.57/60.11 | (5) all_22_2 = e1
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (4), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #715 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (2) ~ (e4 = e0)
% 251.57/60.11 (3) ~ (all_84_2 = all_62_2)
% 251.57/60.11 (4) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.57/60.11 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.57/60.11 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.57/60.11 (5) op(all_16_2, all_26_2) = e4
% 251.57/60.11 (6) ~ (all_36_2 = e4)
% 251.57/60.11 (7) op(e3, e1) = all_36_2
% 251.57/60.11 (8) op(all_62_2, e3) = e1
% 251.57/60.11 (9) op(e4, e1) = all_26_2
% 251.57/60.11 (10) ~ (all_244_15 = all_62_2)
% 251.57/60.11 (11) op(e1, e1) = all_244_15
% 251.57/60.11 (12) op(e0, e1) = all_20_2
% 251.57/60.11 (13) all_252_11 = e0
% 251.57/60.11 (14) op(e4, e3) = all_84_2
% 251.57/60.11 (15) ~ (all_20_2 = e4)
% 251.57/60.11 (16) op(all_16_2, e4) = e1
% 251.57/60.11 (17) all_62_2 = e4
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (10), (17) imply:
% 251.57/60.11 | (18) ~ (all_244_15 = e4)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (3), (17) imply:
% 251.57/60.11 | (19) ~ (all_84_2 = e4)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (8), (17) imply:
% 251.57/60.11 | (20) op(e4, e3) = e1
% 251.57/60.11 |
% 251.57/60.11 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 251.57/60.11 | (16), (18), (19), (20) are inconsistent by sub-proof #749.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #716 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ~ (all_10_2 = e4)
% 251.57/60.11 (2) all_64_2 = e3
% 251.57/60.11 (3) op(all_64_2, e4) = e2
% 251.57/60.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (5) op(e2, e3) = all_10_2
% 251.57/60.11 (6) ~ (e3 = e2)
% 251.57/60.11 (7) ~ (e4 = e0)
% 251.57/60.11 (8) op(all_244_8, all_244_8) = e2
% 251.57/60.11 (9) op(e2, e2) = all_244_8
% 251.57/60.11 (10) ~ (all_40_2 = e4)
% 251.57/60.11 (11) op(e1, e4) = all_16_2
% 251.57/60.11 (12) ~ (all_244_0 = all_64_2)
% 251.57/60.11 (13) ~ (all_64_2 = all_12_2)
% 251.57/60.11 (14) ~ (all_244_0 = all_100_2)
% 251.57/60.11 (15) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.57/60.11 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.57/60.11 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.57/60.11 (16) op(e3, e4) = all_100_2
% 251.57/60.11 (17) op(e4, e4) = all_244_0
% 251.57/60.11 (18) ~ (e4 = e3)
% 251.57/60.11 (19) all_252_11 = e0
% 251.57/60.11 (20) ~ (all_64_2 = all_16_2)
% 251.57/60.11 (21) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.57/60.11 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.57/60.11 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.57/60.11 (22) op(e2, e0) = all_40_2
% 251.57/60.11 (23) op(e0, e4) = all_12_2
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (2), (12) imply:
% 251.57/60.11 | (24) ~ (all_244_0 = e3)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (2), (20) imply:
% 251.57/60.11 | (25) ~ (all_16_2 = e3)
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (25) implies:
% 251.57/60.11 | (26) ~ (all_16_2 = e3)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (2), (13) imply:
% 251.57/60.11 | (27) ~ (all_12_2 = e3)
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (27) implies:
% 251.57/60.11 | (28) ~ (all_12_2 = e3)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (2), (3) imply:
% 251.57/60.11 | (29) op(e3, e4) = e2
% 251.57/60.11 |
% 251.57/60.11 | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15), (16),
% 251.57/60.11 | (17), (18), (19), (21), (22), (23), (24), (26), (28), (29) are
% 251.57/60.11 | inconsistent by sub-proof #764.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #717 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ~ (all_4_2 = e4)
% 251.57/60.11 (2) ~ (all_10_2 = e4)
% 251.57/60.11 (3) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 & op(e1,
% 251.57/60.11 all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~ (all_82_1 =
% 251.57/60.11 e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.57/60.11 (4) ~ (all_64_2 = e3)
% 251.57/60.11 (5) ~ (e2 = e0)
% 251.57/60.11 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (7) op(e2, e3) = all_10_2
% 251.57/60.11 (8) ~ (e3 = e2)
% 251.57/60.11 (9) op(e0, e0) = all_244_24
% 251.57/60.11 (10) ~ (e4 = e0)
% 251.57/60.11 (11) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.57/60.11 all_250_17 = e0
% 251.57/60.11 (12) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.57/60.11 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.57/60.11 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.57/60.11 (13) op(e2, e1) = all_38_2
% 251.57/60.11 (14) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.57/60.11 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.57/60.11 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.57/60.11 (15) op(e1, e0) = all_34_2
% 251.57/60.11 (16) ~ (all_40_2 = e4)
% 251.57/60.11 (17) op(e4, e2) = all_6_2
% 251.57/60.11 (18) ~ (e2 = e1)
% 251.57/60.11 (19) op(e0, e2) = all_28_2
% 251.57/60.11 (20) ~ (e4 = e1)
% 251.57/60.11 (21) ~ (all_6_2 = e1)
% 251.57/60.11 (22) ~ (all_62_2 = all_34_2)
% 251.57/60.11 (23) ~ (e3 = e0)
% 251.57/60.11 (24) all_70_2 = all_62_2
% 251.57/60.11 (25) ~ (e3 = e1)
% 251.57/60.11 (26) ~ (all_8_2 = e1)
% 251.57/60.11 (27) ~ (all_28_2 = all_4_2)
% 251.57/60.11 (28) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.57/60.11 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.57/60.11 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.57/60.11 (29) all_70_2 = e2
% 251.57/60.11 (30) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.57/60.11 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.57/60.11 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.57/60.11 (31) op(all_62_2, e3) = e1
% 251.57/60.11 (32) op(all_4_2, e0) = e2
% 251.57/60.11 (33) all_252_11 = e0
% 251.57/60.11 (34) all_82_2 = all_28_2
% 251.57/60.11 (35) ~ (all_244_24 = e2)
% 251.57/60.11 (36) op(e1, e2) = all_4_2
% 251.57/60.11 (37) op(e2, e4) = all_64_2
% 251.57/60.11 (38) all_250_17 = all_4_2
% 251.57/60.11 (39) op(e3, e2) = all_8_2
% 251.57/60.11 (40) op(e2, e0) = all_40_2
% 251.57/60.11 (41) ~ (all_4_2 = e3)
% 251.57/60.11 (42) ~ (all_62_2 = e4)
% 251.57/60.11 (43) ~ (all_62_2 = all_4_2)
% 251.57/60.11 (44) op(e2, e1) = e0
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (24), (29) imply:
% 251.57/60.11 | (45) all_62_2 = e2
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (45) implies:
% 251.57/60.11 | (46) all_62_2 = e2
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (22), (46) imply:
% 251.57/60.11 | (47) ~ (all_34_2 = e2)
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (47) implies:
% 251.57/60.11 | (48) ~ (all_34_2 = e2)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (43), (46) imply:
% 251.57/60.11 | (49) ~ (all_4_2 = e2)
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (49) implies:
% 251.57/60.11 | (50) ~ (all_4_2 = e2)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (42), (46) imply:
% 251.57/60.11 | (51) ~ (e4 = e2)
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (51) implies:
% 251.57/60.11 | (52) ~ (e4 = e2)
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (31), (46) imply:
% 251.57/60.11 | (53) op(e2, e3) = e1
% 251.57/60.11 |
% 251.57/60.11 | BETA: splitting (3) gives:
% 251.57/60.11 |
% 251.57/60.11 | Case 1:
% 251.57/60.11 | |
% 251.57/60.11 | | (54) ~ (all_82_2 = e1)
% 251.57/60.11 | |
% 251.57/60.11 | | REDUCE: (34), (54) imply:
% 251.57/60.11 | | (55) ~ (all_28_2 = e1)
% 251.57/60.11 | |
% 251.57/60.11 | | BETA: splitting (14) gives:
% 251.57/60.11 | |
% 251.57/60.11 | | Case 1:
% 251.57/60.11 | | |
% 251.57/60.11 | | | (56) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2)
% 251.57/60.11 | | | = e1)
% 251.57/60.11 | | |
% 251.57/60.11 | | | REF_CLOSE: (6), (17), (21), (26), (39), (56) are inconsistent by sub-proof
% 251.57/60.11 | | | #928.
% 251.57/60.11 | | |
% 251.57/60.11 | | Case 2:
% 251.57/60.11 | | |
% 251.57/60.11 | | | (57) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2)
% 251.57/60.11 | | | = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.57/60.11 | | |
% 251.57/60.11 | | | BETA: splitting (57) gives:
% 251.57/60.11 | | |
% 251.57/60.11 | | | Case 1:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | (58) all_252_8 = e1 & op(e2, e2) = e1
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | ALPHA: (58) implies:
% 251.57/60.11 | | | | (59) all_252_8 = e1
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | BETA: splitting (12) gives:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | Case 1:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (60) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 251.57/60.11 | | | | | e3) = e3)
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REF_CLOSE: (4), (6), (25), (37), (53), (60) are inconsistent by
% 251.57/60.11 | | | | | sub-proof #792.
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | Case 2:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (61) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2,
% 251.57/60.11 | | | | | e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | BETA: splitting (61) gives:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | Case 1:
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | (62) all_252_8 = e3 & op(e2, e2) = e3
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | ALPHA: (62) implies:
% 251.57/60.11 | | | | | | (63) all_252_8 = e3
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | REF_CLOSE: (25), (59), (63) are inconsistent by sub-proof #927.
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | Case 2:
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | (64) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 251.57/60.11 | | | | | | op(e2, e0) = e3)
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | BETA: splitting (64) gives:
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | | Case 1:
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | (65) all_252_11 = e3 & op(e2, e1) = e3
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | REF_CLOSE: (23), (33), (65) are inconsistent by sub-proof #725.
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | Case 2:
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | (66) all_252_18 = e3 & op(e2, e0) = e3
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | ALPHA: (66) implies:
% 251.57/60.11 | | | | | | | (67) all_252_18 = e3
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | BETA: splitting (28) gives:
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | (68) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 &
% 251.57/60.11 | | | | | | | | op(e2, e3) = e2)
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | BETA: splitting (68) gives:
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | (69) all_252_6 = e2 & op(e2, e4) = e2
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | ALPHA: (69) implies:
% 251.57/60.11 | | | | | | | | | (70) all_252_6 = e2
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | BETA: splitting (30) gives:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | (71) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4
% 251.57/60.11 | | | | | | | | | | & op(e2, e3) = e4)
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | REF_CLOSE: (2), (6), (7), (52), (70), (71) are inconsistent
% 251.57/60.11 | | | | | | | | | | by sub-proof #724.
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | (72) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 251.57/60.11 | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2,
% 251.57/60.11 | | | | | | | | | | e0) = e4)
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | BETA: splitting (72) gives:
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | | (73) all_252_8 = e4 & op(e2, e2) = e4
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | | REF_CLOSE: (20), (59), (73) are inconsistent by sub-proof
% 251.57/60.11 | | | | | | | | | | | #723.
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | | (74) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18
% 251.57/60.11 | | | | | | | | | | | = e4 & op(e2, e0) = e4)
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | | REF_CLOSE: (6), (10), (16), (33), (40), (74) are inconsistent
% 251.57/60.11 | | | | | | | | | | | by sub-proof #765.
% 251.57/60.11 | | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | End of split
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | End of split
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | (75) all_252_7 = e2 & op(e2, e3) = e2
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | ALPHA: (75) implies:
% 251.57/60.11 | | | | | | | | | (76) op(e2, e3) = e2
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | REF_CLOSE: (6), (7), (18), (53), (76) are inconsistent by
% 251.57/60.11 | | | | | | | | | sub-proof #902.
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | End of split
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | (77) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 &
% 251.57/60.11 | | | | | | | | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | BETA: splitting (77) gives:
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | (78) all_252_8 = e2 & op(e2, e2) = e2
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | REF_CLOSE: (18), (59), (78) are inconsistent by sub-proof
% 251.57/60.11 | | | | | | | | | #788.
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | (79) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2
% 251.57/60.11 | | | | | | | | | & op(e2, e0) = e2)
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | BETA: splitting (79) gives:
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | | Case 1:
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | (80) all_252_11 = e2 & op(e2, e1) = e2
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | REF_CLOSE: (5), (6), (13), (44), (80) are inconsistent by
% 251.57/60.11 | | | | | | | | | | sub-proof #722.
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | Case 2:
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | (81) all_252_18 = e2 & op(e2, e0) = e2
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | ALPHA: (81) implies:
% 251.57/60.11 | | | | | | | | | | (82) all_252_18 = e2
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | | REF_CLOSE: (8), (67), (82) are inconsistent by sub-proof
% 251.57/60.11 | | | | | | | | | | #786.
% 251.57/60.11 | | | | | | | | | |
% 251.57/60.11 | | | | | | | | | End of split
% 251.57/60.11 | | | | | | | | |
% 251.57/60.11 | | | | | | | | End of split
% 251.57/60.11 | | | | | | | |
% 251.57/60.11 | | | | | | | End of split
% 251.57/60.11 | | | | | | |
% 251.57/60.11 | | | | | | End of split
% 251.57/60.11 | | | | | |
% 251.57/60.11 | | | | | End of split
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | End of split
% 251.57/60.11 | | | |
% 251.57/60.11 | | | Case 2:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | (83) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 251.57/60.11 | | | | e2) = e1)
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | BETA: splitting (83) gives:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | Case 1:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (84) all_252_14 = e1 & op(e1, e2) = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | ALPHA: (84) implies:
% 251.57/60.11 | | | | | (85) op(e1, e2) = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | GROUND_INST: instantiating (6) with all_4_2, e1, e2, e1, simplifying
% 251.57/60.11 | | | | | with (36), (85) gives:
% 251.57/60.11 | | | | | (86) all_4_2 = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REDUCE: (32), (86) imply:
% 251.57/60.11 | | | | | (87) op(e1, e0) = e2
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REF_CLOSE: (6), (15), (48), (87) are inconsistent by sub-proof #909.
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | Case 2:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (88) all_252_22 = e1 & op(e0, e2) = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | ALPHA: (88) implies:
% 251.57/60.11 | | | | | (89) op(e0, e2) = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REF_CLOSE: (6), (19), (55), (89) are inconsistent by sub-proof #907.
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | End of split
% 251.57/60.11 | | | |
% 251.57/60.11 | | | End of split
% 251.57/60.11 | | |
% 251.57/60.11 | | End of split
% 251.57/60.11 | |
% 251.57/60.11 | Case 2:
% 251.57/60.11 | |
% 251.57/60.11 | | (90) all_82_2 = e1
% 251.57/60.11 | |
% 251.57/60.11 | | COMBINE_EQS: (34), (90) imply:
% 251.57/60.11 | | (91) all_28_2 = e1
% 251.57/60.11 | |
% 251.57/60.11 | | REDUCE: (27), (91) imply:
% 251.57/60.11 | | (92) ~ (all_4_2 = e1)
% 251.57/60.11 | |
% 251.57/60.11 | | SIMP: (92) implies:
% 251.57/60.11 | | (93) ~ (all_4_2 = e1)
% 251.57/60.11 | |
% 251.57/60.11 | | REF_CLOSE: (1), (6), (9), (11), (32), (35), (38), (41), (50), (93) are
% 251.57/60.11 | | inconsistent by sub-proof #718.
% 251.57/60.11 | |
% 251.57/60.11 | End of split
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #718 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) ~ (all_4_2 = e4)
% 251.57/60.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (3) op(e0, e0) = all_244_24
% 251.57/60.11 (4) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 |
% 251.57/60.11 all_250_17 = e0
% 251.57/60.11 (5) op(all_4_2, e0) = e2
% 251.57/60.11 (6) ~ (all_244_24 = e2)
% 251.57/60.11 (7) all_250_17 = all_4_2
% 251.57/60.11 (8) ~ (all_4_2 = e1)
% 251.57/60.11 (9) ~ (all_4_2 = e3)
% 251.57/60.11 (10) ~ (all_4_2 = e2)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | BETA: splitting (4) gives:
% 251.57/60.11 |
% 251.57/60.11 | Case 1:
% 251.57/60.11 | |
% 251.57/60.11 | | (11) all_250_17 = e4
% 251.57/60.11 | |
% 251.57/60.11 | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #721.
% 251.57/60.11 | |
% 251.57/60.11 | Case 2:
% 251.57/60.11 | |
% 251.57/60.11 | | (12) all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | all_250_17 =
% 251.57/60.11 | | e0
% 251.57/60.11 | |
% 251.57/60.11 | | BETA: splitting (12) gives:
% 251.57/60.11 | |
% 251.57/60.11 | | Case 1:
% 251.57/60.11 | | |
% 251.57/60.11 | | | (13) all_250_17 = e3
% 251.57/60.11 | | |
% 251.57/60.11 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #720.
% 251.57/60.11 | | |
% 251.57/60.11 | | Case 2:
% 251.57/60.11 | | |
% 251.57/60.11 | | | (14) all_250_17 = e2 | all_250_17 = e1 | all_250_17 = e0
% 251.57/60.11 | | |
% 251.57/60.11 | | | BETA: splitting (14) gives:
% 251.57/60.11 | | |
% 251.57/60.11 | | | Case 1:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | (15) all_250_17 = e2
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | REF_CLOSE: (7), (10), (15) are inconsistent by sub-proof #719.
% 251.57/60.11 | | | |
% 251.57/60.11 | | | Case 2:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | (16) all_250_17 = e1 | all_250_17 = e0
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | BETA: splitting (16) gives:
% 251.57/60.11 | | | |
% 251.57/60.11 | | | | Case 1:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (17) all_250_17 = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | COMBINE_EQS: (7), (17) imply:
% 251.57/60.11 | | | | | (18) all_4_2 = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | SIMP: (18) implies:
% 251.57/60.11 | | | | | (19) all_4_2 = e1
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REDUCE: (8), (19) imply:
% 251.57/60.11 | | | | | (20) $false
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | CLOSE: (20) is inconsistent.
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | Case 2:
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | (21) all_250_17 = e0
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | COMBINE_EQS: (7), (21) imply:
% 251.57/60.11 | | | | | (22) all_4_2 = e0
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | SIMP: (22) implies:
% 251.57/60.11 | | | | | (23) all_4_2 = e0
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REDUCE: (5), (23) imply:
% 251.57/60.11 | | | | | (24) op(e0, e0) = e2
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | | REF_CLOSE: (2), (3), (6), (24) are inconsistent by sub-proof #978.
% 251.57/60.11 | | | | |
% 251.57/60.11 | | | | End of split
% 251.57/60.11 | | | |
% 251.57/60.11 | | | End of split
% 251.57/60.11 | | |
% 251.57/60.11 | | End of split
% 251.57/60.11 | |
% 251.57/60.11 | End of split
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #719 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) all_250_17 = all_4_2
% 251.57/60.11 (2) all_250_17 = e2
% 251.57/60.11 (3) ~ (all_4_2 = e2)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.11 | (4) all_4_2 = e2
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (4) implies:
% 251.57/60.11 | (5) all_4_2 = e2
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (3), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #720 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) all_250_17 = all_4_2
% 251.57/60.11 (2) all_250_17 = e3
% 251.57/60.11 (3) ~ (all_4_2 = e3)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.11 | (4) all_4_2 = e3
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (4) implies:
% 251.57/60.11 | (5) all_4_2 = e3
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (3), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #721 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) all_250_17 = all_4_2
% 251.57/60.11 (2) all_250_17 = e4
% 251.57/60.11 (3) ~ (all_4_2 = e4)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (1), (2) imply:
% 251.57/60.11 | (4) all_4_2 = e4
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (4) implies:
% 251.57/60.11 | (5) all_4_2 = e4
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (3), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #722 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) all_252_11 = e2 & op(e2, e1) = e2
% 251.57/60.11 (2) ~ (e2 = e0)
% 251.57/60.11 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.11 (4) op(e2, e1) = all_38_2
% 251.57/60.11 (5) op(e2, e1) = e0
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | ALPHA: (1) implies:
% 251.57/60.11 | (6) op(e2, e1) = e2
% 251.57/60.11 |
% 251.57/60.11 | GROUND_INST: instantiating (3) with all_38_2, e0, e1, e2, simplifying with
% 251.57/60.11 | (4), (5) gives:
% 251.57/60.11 | (7) all_38_2 = e0
% 251.57/60.11 |
% 251.57/60.11 | GROUND_INST: instantiating (3) with all_38_2, e2, e1, e2, simplifying with
% 251.57/60.11 | (4), (6) gives:
% 251.57/60.11 | (8) all_38_2 = e2
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (7), (8) imply:
% 251.57/60.11 | (9) e2 = e0
% 251.57/60.11 |
% 251.57/60.11 | SIMP: (9) implies:
% 251.57/60.11 | (10) e2 = e0
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (2), (10) imply:
% 251.57/60.11 | (11) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (11) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.11 Sub-proof #723 shows that the following formulas are inconsistent:
% 251.57/60.11 ----------------------------------------------------------------
% 251.57/60.11 (1) all_252_8 = e4 & op(e2, e2) = e4
% 251.57/60.11 (2) all_252_8 = e1
% 251.57/60.11 (3) ~ (e4 = e1)
% 251.57/60.11
% 251.57/60.11 Begin of proof
% 251.57/60.11 |
% 251.57/60.11 | ALPHA: (1) implies:
% 251.57/60.11 | (4) all_252_8 = e4
% 251.57/60.11 |
% 251.57/60.11 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.11 | (5) e4 = e1
% 251.57/60.11 |
% 251.57/60.11 | REDUCE: (3), (5) imply:
% 251.57/60.11 | (6) $false
% 251.57/60.11 |
% 251.57/60.11 | CLOSE: (6) is inconsistent.
% 251.57/60.11 |
% 251.57/60.11 End of proof
% 251.57/60.11
% 251.57/60.12 Sub-proof #724 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ~ (all_10_2 = e4)
% 251.57/60.12 (2) all_252_6 = e2
% 251.57/60.12 (3) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.57/60.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (5) op(e2, e3) = all_10_2
% 251.57/60.12 (6) ~ (e4 = e2)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (3) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (7) all_252_6 = e4 & op(e2, e4) = e4
% 251.57/60.12 | |
% 251.57/60.12 | | ALPHA: (7) implies:
% 251.57/60.12 | | (8) all_252_6 = e4
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #833.
% 251.57/60.12 | |
% 251.57/60.12 | Case 2:
% 251.57/60.12 | |
% 251.57/60.12 | | (9) all_252_7 = e4 & op(e2, e3) = e4
% 251.57/60.12 | |
% 251.57/60.12 | | ALPHA: (9) implies:
% 251.57/60.12 | | (10) op(e2, e3) = e4
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #953.
% 251.57/60.12 | |
% 251.57/60.12 | End of split
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #725 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) all_252_11 = e3 & op(e2, e1) = e3
% 251.57/60.12 (2) all_252_11 = e0
% 251.57/60.12 (3) ~ (e3 = e0)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | ALPHA: (1) implies:
% 251.57/60.12 | (4) all_252_11 = e3
% 251.57/60.12 |
% 251.57/60.12 | COMBINE_EQS: (2), (4) imply:
% 251.57/60.12 | (5) e3 = e0
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (3), (5) imply:
% 251.57/60.12 | (6) $false
% 251.57/60.12 |
% 251.57/60.12 | CLOSE: (6) is inconsistent.
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #726 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) all_252_10 = e0 & op(e3, e1) = e0
% 251.57/60.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (3) op(e3, e1) = all_36_2
% 251.57/60.12 (4) ~ (all_36_2 = e0)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | ALPHA: (1) implies:
% 251.57/60.12 | (5) op(e3, e1) = e0
% 251.57/60.12 |
% 251.57/60.12 | GROUND_INST: instantiating (2) with all_36_2, e0, e1, e3, simplifying with
% 251.57/60.12 | (3), (5) gives:
% 251.57/60.12 | (6) all_36_2 = e0
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (4), (6) imply:
% 251.57/60.12 | (7) $false
% 251.57/60.12 |
% 251.57/60.12 | CLOSE: (7) is inconsistent.
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #727 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ~ (all_22_2 = e2)
% 251.57/60.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (3) ~ (all_12_2 = e2)
% 251.57/60.12 (4) op(e0, e3) = all_22_2
% 251.57/60.12 (5) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.57/60.12 (6) op(e0, e4) = all_12_2
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (5) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (7) all_252_20 = e2 & op(e0, e4) = e2
% 251.57/60.12 | |
% 251.57/60.12 | | ALPHA: (7) implies:
% 251.57/60.12 | | (8) op(e0, e4) = e2
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #980.
% 251.57/60.12 | |
% 251.57/60.12 | Case 2:
% 251.57/60.12 | |
% 251.57/60.12 | | (9) all_252_21 = e2 & op(e0, e3) = e2
% 251.57/60.12 | |
% 251.57/60.12 | | ALPHA: (9) implies:
% 251.57/60.12 | | (10) op(e0, e3) = e2
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #987.
% 251.57/60.12 | |
% 251.57/60.12 | End of split
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #728 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) all_26_2 = e2
% 251.57/60.12 (2) ~ (all_4_2 = e4)
% 251.57/60.12 (3) op(all_4_2, e2) = e1
% 251.57/60.12 (4) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.57/60.12 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.57/60.12 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.57/60.12 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.57/60.12 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.57/60.12 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.57/60.12 (6) ~ (all_62_2 = all_22_2)
% 251.57/60.12 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (8) op(e2, e3) = all_10_2
% 251.57/60.12 (9) ~ (all_84_2 = all_62_2)
% 251.57/60.12 (10) ~ (all_244_15 = e4)
% 251.57/60.12 (11) op(all_244_15, all_244_15) = e1
% 251.57/60.12 (12) all_50_2 = all_4_2
% 251.57/60.12 (13) ~ (all_244_3 = all_84_2)
% 251.57/60.12 (14) op(e1, e3) = all_62_2
% 251.57/60.12 (15) ~ (all_8_2 = e1)
% 251.57/60.12 (16) ~ (all_244_3 = all_62_2)
% 251.57/60.12 (17) ~ (all_64_2 = e1)
% 251.57/60.12 (18) op(e1, e0) = e2
% 251.57/60.12 (19) op(e1, e4) = all_38_1
% 251.57/60.12 (20) all_38_1 = all_16_2
% 251.57/60.12 (21) op(e0, e3) = all_22_2
% 251.57/60.12 (22) ~ (all_26_2 = e4)
% 251.57/60.12 (23) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.57/60.12 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.57/60.12 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.57/60.12 (24) op(all_62_2, e3) = e1
% 251.57/60.12 (25) ~ (e4 = e3)
% 251.57/60.12 (26) op(e1, e1) = all_244_15
% 251.57/60.12 (27) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0 &
% 251.57/60.12 op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~ (all_62_1 =
% 251.57/60.12 e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.57/60.12 (28) ~ (all_26_2 = e3)
% 251.57/60.12 (29) op(e1, e2) = all_4_2
% 251.57/60.12 (30) op(e4, e3) = all_84_2
% 251.57/60.12 (31) ~ (all_62_2 = all_10_2)
% 251.57/60.12 (32) op(e2, e4) = all_64_2
% 251.57/60.12 (33) op(e3, e2) = all_8_2
% 251.57/60.12 (34) ~ (all_16_2 = e3)
% 251.57/60.12 (35) op(e3, e3) = all_244_3
% 251.57/60.12 (36) op(all_26_2, all_16_2) = e1
% 251.57/60.12 (37) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 251.57/60.12 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 251.57/60.12 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (1), (22) imply:
% 251.57/60.12 | (38) ~ (e4 = e2)
% 251.57/60.12 |
% 251.57/60.12 | SIMP: (38) implies:
% 251.57/60.12 | (39) ~ (e4 = e2)
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (1), (28) imply:
% 251.57/60.12 | (40) ~ (e3 = e2)
% 251.57/60.12 |
% 251.57/60.12 | SIMP: (40) implies:
% 251.57/60.12 | (41) ~ (e3 = e2)
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (1), (36) imply:
% 251.57/60.12 | (42) op(e2, all_16_2) = e1
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (19), (20) imply:
% 251.57/60.12 | (43) op(e1, e4) = all_16_2
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (37) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (44) ~ (all_50_2 = e3)
% 251.57/60.12 | |
% 251.57/60.12 | | REDUCE: (12), (44) imply:
% 251.57/60.12 | | (45) ~ (all_4_2 = e3)
% 251.57/60.12 | |
% 251.57/60.12 | | BETA: splitting (27) gives:
% 251.57/60.12 | |
% 251.57/60.12 | | Case 1:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (46) ~ (all_62_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (2), (7), (10), (14), (17), (18), (23), (26), (29), (32), (39),
% 251.57/60.12 | | | (42), (43), (46) are inconsistent by sub-proof #729.
% 251.57/60.12 | | |
% 251.57/60.12 | | Case 2:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (47) all_62_2 = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (16), (47) imply:
% 251.57/60.12 | | | (48) ~ (all_244_3 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (9), (47) imply:
% 251.57/60.12 | | | (49) ~ (all_84_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (6), (47) imply:
% 251.57/60.12 | | | (50) ~ (all_22_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | SIMP: (50) implies:
% 251.57/60.12 | | | (51) ~ (all_22_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (31), (47) imply:
% 251.57/60.12 | | | (52) ~ (all_10_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | SIMP: (52) implies:
% 251.57/60.12 | | | (53) ~ (all_10_2 = e4)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (24), (47) imply:
% 251.57/60.12 | | | (54) op(e4, e3) = e1
% 251.57/60.12 | | |
% 251.57/60.12 | | | BETA: splitting (5) gives:
% 251.57/60.12 | | |
% 251.57/60.12 | | | Case 1:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | (55) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1,
% 251.57/60.12 | | | | e3) = e3)
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | BETA: splitting (55) gives:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | Case 1:
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | (56) all_252_12 = e3 & op(e1, e4) = e3
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | REF_CLOSE: (7), (34), (43), (56) are inconsistent by sub-proof #895.
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | Case 2:
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | (57) all_252_13 = e3 & op(e1, e3) = e3
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | ALPHA: (57) implies:
% 251.57/60.12 | | | | | (58) all_252_13 = e3
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | REF_CLOSE: (4), (7), (8), (21), (25), (30), (35), (48), (49), (51),
% 251.57/60.12 | | | | | (53), (58) are inconsistent by sub-proof #755.
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | End of split
% 251.57/60.12 | | | |
% 251.57/60.12 | | | Case 2:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | (59) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 251.57/60.12 | | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | BETA: splitting (59) gives:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | Case 1:
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | (60) all_252_14 = e3 & op(e1, e2) = e3
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | REF_CLOSE: (7), (29), (45), (60) are inconsistent by sub-proof #858.
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | Case 2:
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | (61) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 251.57/60.12 | | | | | op(e1, e0) = e3)
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | BETA: splitting (61) gives:
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | | Case 1:
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | (62) all_252_15 = e3 & op(e1, e1) = e3
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | ALPHA: (62) implies:
% 251.57/60.12 | | | | | | (63) op(e1, e1) = e3
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | GROUND_INST: instantiating (7) with all_244_15, e3, e1, e1,
% 251.57/60.12 | | | | | | simplifying with (26), (63) gives:
% 251.57/60.12 | | | | | | (64) all_244_15 = e3
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | GROUND_INST: instantiating (7) with all_84_2, e1, e3, e4,
% 251.57/60.12 | | | | | | simplifying with (30), (54) gives:
% 251.57/60.12 | | | | | | (65) all_84_2 = e1
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | REDUCE: (13), (65) imply:
% 251.57/60.12 | | | | | | (66) ~ (all_244_3 = e1)
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | REDUCE: (11), (64) imply:
% 251.57/60.12 | | | | | | (67) op(e3, e3) = e1
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | REF_CLOSE: (7), (35), (66), (67) are inconsistent by sub-proof #801.
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | Case 2:
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | (68) all_252_19 = e3 & op(e1, e0) = e3
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | ALPHA: (68) implies:
% 251.57/60.12 | | | | | | (69) op(e1, e0) = e3
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | | REF_CLOSE: (7), (18), (41), (69) are inconsistent by sub-proof #736.
% 251.57/60.12 | | | | | |
% 251.57/60.12 | | | | | End of split
% 251.57/60.12 | | | | |
% 251.57/60.12 | | | | End of split
% 251.57/60.12 | | | |
% 251.57/60.12 | | | End of split
% 251.57/60.12 | | |
% 251.57/60.12 | | End of split
% 251.57/60.12 | |
% 251.57/60.12 | Case 2:
% 251.57/60.12 | |
% 251.57/60.12 | | (70) all_50_2 = e3
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (3), (7), (12), (15), (33), (70) are inconsistent by sub-proof
% 251.57/60.12 | | #802.
% 251.57/60.12 | |
% 251.57/60.12 | End of split
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #729 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ~ (all_4_2 = e4)
% 251.57/60.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (3) ~ (all_244_15 = e4)
% 251.57/60.12 (4) op(e1, e4) = all_16_2
% 251.57/60.12 (5) op(e2, all_16_2) = e1
% 251.57/60.12 (6) op(e1, e3) = all_62_2
% 251.57/60.12 (7) ~ (all_64_2 = e1)
% 251.57/60.12 (8) op(e1, e0) = e2
% 251.57/60.12 (9) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.57/60.12 | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.57/60.12 e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.57/60.12 (10) op(e1, e1) = all_244_15
% 251.57/60.12 (11) op(e1, e2) = all_4_2
% 251.57/60.12 (12) op(e2, e4) = all_64_2
% 251.57/60.12 (13) ~ (e4 = e2)
% 251.57/60.12 (14) ~ (all_62_2 = e4)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (9) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (15) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3)
% 251.57/60.12 | | = e4)
% 251.57/60.12 | |
% 251.57/60.12 | | BETA: splitting (15) gives:
% 251.57/60.12 | |
% 251.57/60.12 | | Case 1:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (16) all_252_12 = e4 & op(e1, e4) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | ALPHA: (16) implies:
% 251.57/60.12 | | | (17) op(e1, e4) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | GROUND_INST: instantiating (2) with all_16_2, e4, e4, e1, simplifying with
% 251.57/60.12 | | | (4), (17) gives:
% 251.57/60.12 | | | (18) all_16_2 = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | REDUCE: (5), (18) imply:
% 251.57/60.12 | | | (19) op(e2, e4) = e1
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (2), (7), (12), (19) are inconsistent by sub-proof #731.
% 251.57/60.12 | | |
% 251.57/60.12 | | Case 2:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (20) all_252_13 = e4 & op(e1, e3) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (2), (6), (14), (20) are inconsistent by sub-proof #952.
% 251.57/60.12 | | |
% 251.57/60.12 | | End of split
% 251.57/60.12 | |
% 251.57/60.12 | Case 2:
% 251.57/60.12 | |
% 251.57/60.12 | | (21) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1)
% 251.57/60.12 | | = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (1), (2), (3), (8), (10), (11), (13), (21) are inconsistent by
% 251.57/60.12 | | sub-proof #730.
% 251.57/60.12 | |
% 251.57/60.12 | End of split
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #730 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ~ (all_4_2 = e4)
% 251.57/60.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (3) ~ (all_244_15 = e4)
% 251.57/60.12 (4) op(e1, e0) = e2
% 251.57/60.12 (5) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 251.57/60.12 | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.57/60.12 (6) op(e1, e1) = all_244_15
% 251.57/60.12 (7) op(e1, e2) = all_4_2
% 251.57/60.12 (8) ~ (e4 = e2)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (5) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (9) all_252_14 = e4 & op(e1, e2) = e4
% 251.57/60.12 | |
% 251.57/60.12 | | ALPHA: (9) implies:
% 251.57/60.12 | | (10) op(e1, e2) = e4
% 251.57/60.12 | |
% 251.57/60.12 | | REF_CLOSE: (1), (2), (7), (10) are inconsistent by sub-proof #831.
% 251.57/60.12 | |
% 251.57/60.12 | Case 2:
% 251.57/60.12 | |
% 251.57/60.12 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0)
% 251.57/60.12 | | = e4)
% 251.57/60.12 | |
% 251.57/60.12 | | BETA: splitting (11) gives:
% 251.57/60.12 | |
% 251.57/60.12 | | Case 1:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (12) all_252_15 = e4 & op(e1, e1) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | ALPHA: (12) implies:
% 251.57/60.12 | | | (13) op(e1, e1) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (2), (3), (6), (13) are inconsistent by sub-proof #756.
% 251.57/60.12 | | |
% 251.57/60.12 | | Case 2:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (14) all_252_19 = e4 & op(e1, e0) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | ALPHA: (14) implies:
% 251.57/60.12 | | | (15) op(e1, e0) = e4
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (2), (4), (8), (15) are inconsistent by sub-proof #829.
% 251.57/60.12 | | |
% 251.57/60.12 | | End of split
% 251.57/60.12 | |
% 251.57/60.12 | End of split
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #731 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (2) op(e2, e4) = all_64_2
% 251.57/60.12 (3) op(e2, e4) = e1
% 251.57/60.12 (4) ~ (all_64_2 = e1)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | GROUND_INST: instantiating (1) with all_64_2, e1, e4, e2, simplifying with
% 251.57/60.12 | (2), (3) gives:
% 251.57/60.12 | (5) all_64_2 = e1
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (4), (5) imply:
% 251.57/60.12 | (6) $false
% 251.57/60.12 |
% 251.57/60.12 | CLOSE: (6) is inconsistent.
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #732 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (2) op(e2, e1) = all_38_2
% 251.57/60.12 (3) op(all_26_2, e1) = e4
% 251.57/60.12 (4) all_44_2 = e2
% 251.57/60.12 (5) all_44_2 = all_26_2
% 251.57/60.12 (6) ~ (all_38_2 = e4)
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | COMBINE_EQS: (4), (5) imply:
% 251.57/60.12 | (7) all_26_2 = e2
% 251.57/60.12 |
% 251.57/60.12 | SIMP: (7) implies:
% 251.57/60.12 | (8) all_26_2 = e2
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (3), (8) imply:
% 251.57/60.12 | (9) op(e2, e1) = e4
% 251.57/60.12 |
% 251.57/60.12 | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #935.
% 251.57/60.12 |
% 251.57/60.12 End of proof
% 251.57/60.12
% 251.57/60.12 Sub-proof #733 shows that the following formulas are inconsistent:
% 251.57/60.12 ----------------------------------------------------------------
% 251.57/60.12 (1) ~ (all_10_2 = e1)
% 251.57/60.12 (2) op(all_4_2, e2) = e1
% 251.57/60.12 (3) op(e2, all_62_2) = e1
% 251.57/60.12 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.57/60.12 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.57/60.12 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.57/60.12 (5) op(all_38_2, all_4_2) = e1
% 251.57/60.12 (6) ~ (all_62_2 = e2)
% 251.57/60.12 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.57/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.57/60.12 (8) op(e2, e3) = all_10_2
% 251.57/60.12 (9) op(e2, e1) = all_38_2
% 251.57/60.12 (10) all_50_2 = all_4_2
% 251.57/60.12 (11) op(e1, e4) = all_16_2
% 251.57/60.12 (12) op(e1, e3) = all_62_2
% 251.57/60.12 (13) op(e2, e1) = e3
% 251.57/60.12 (14) ~ (all_16_2 = e2)
% 251.57/60.12 (15) ~ (all_8_2 = e1)
% 251.57/60.12 (16) ~ (all_38_2 = e2)
% 251.57/60.12 (17) ~ (all_244_15 = all_38_2)
% 251.57/60.12 (18) op(e1, e1) = all_244_15
% 251.57/60.12 (19) op(e1, e2) = all_46_1
% 251.57/60.12 (20) op(e1, e2) = all_4_2
% 251.57/60.12 (21) ~ (all_244_15 = e2)
% 251.57/60.12 (22) op(e3, e2) = all_8_2
% 251.57/60.12 (23) ~ (all_16_2 = e3)
% 251.57/60.12 (24) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.57/60.12 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.57/60.12 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.57/60.12 (25) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0 &
% 251.57/60.12 op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 251.57/60.12 e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.57/60.12
% 251.57/60.12 Begin of proof
% 251.57/60.12 |
% 251.57/60.12 | GROUND_INST: instantiating (7) with all_4_2, all_46_1, e2, e1, simplifying
% 251.57/60.12 | with (19), (20) gives:
% 251.57/60.12 | (26) all_46_1 = all_4_2
% 251.57/60.12 |
% 251.57/60.12 | GROUND_INST: instantiating (7) with all_38_2, e3, e1, e2, simplifying with
% 251.57/60.12 | (9), (13) gives:
% 251.57/60.12 | (27) all_38_2 = e3
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (17), (27) imply:
% 251.57/60.12 | (28) ~ (all_244_15 = e3)
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (16), (27) imply:
% 251.57/60.12 | (29) ~ (e3 = e2)
% 251.57/60.12 |
% 251.57/60.12 | REDUCE: (5), (27) imply:
% 251.57/60.12 | (30) op(e3, all_4_2) = e1
% 251.57/60.12 |
% 251.57/60.12 | BETA: splitting (25) gives:
% 251.57/60.12 |
% 251.57/60.12 | Case 1:
% 251.57/60.12 | |
% 251.57/60.12 | | (31) ~ (all_50_2 = e3)
% 251.57/60.12 | |
% 251.57/60.12 | | REDUCE: (10), (31) imply:
% 251.57/60.12 | | (32) ~ (all_4_2 = e3)
% 251.57/60.12 | |
% 251.57/60.12 | | BETA: splitting (4) gives:
% 251.57/60.12 | |
% 251.57/60.12 | | Case 1:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (33) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1,
% 251.57/60.12 | | | e3) = e3)
% 251.57/60.12 | | |
% 251.57/60.12 | | | BETA: splitting (33) gives:
% 251.57/60.12 | | |
% 251.57/60.12 | | | Case 1:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | (34) all_252_12 = e3 & op(e1, e4) = e3
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | REF_CLOSE: (7), (11), (23), (34) are inconsistent by sub-proof #895.
% 251.57/60.12 | | | |
% 251.57/60.12 | | | Case 2:
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | (35) all_252_13 = e3 & op(e1, e3) = e3
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | ALPHA: (35) implies:
% 251.57/60.12 | | | | (36) op(e1, e3) = e3
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | GROUND_INST: instantiating (7) with all_62_2, e3, e3, e1, simplifying
% 251.57/60.12 | | | | with (12), (36) gives:
% 251.57/60.12 | | | | (37) all_62_2 = e3
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | REDUCE: (3), (37) imply:
% 251.57/60.12 | | | | (38) op(e2, e3) = e1
% 251.57/60.12 | | | |
% 251.57/60.12 | | | | REF_CLOSE: (1), (7), (8), (38) are inconsistent by sub-proof #948.
% 251.57/60.12 | | | |
% 251.57/60.12 | | | End of split
% 251.57/60.12 | | |
% 251.57/60.12 | | Case 2:
% 251.57/60.12 | | |
% 251.57/60.12 | | | (39) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 251.57/60.12 | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.57/60.12 | | |
% 251.57/60.12 | | | REF_CLOSE: (6), (7), (11), (12), (14), (15), (18), (20), (21), (22), (24),
% 251.57/60.12 | | | (28), (29), (30), (32), (39) are inconsistent by sub-proof
% 251.57/60.12 | | | #734.
% 251.75/60.12 | | |
% 251.75/60.12 | | End of split
% 251.75/60.12 | |
% 251.75/60.12 | Case 2:
% 251.75/60.12 | |
% 251.75/60.12 | | (40) all_50_2 = e3
% 251.75/60.12 | |
% 251.75/60.12 | | REF_CLOSE: (2), (7), (10), (15), (22), (40) are inconsistent by sub-proof
% 251.75/60.12 | | #802.
% 251.75/60.12 | |
% 251.75/60.12 | End of split
% 251.75/60.12 |
% 251.75/60.12 End of proof
% 251.75/60.12
% 251.75/60.12 Sub-proof #734 shows that the following formulas are inconsistent:
% 251.75/60.12 ----------------------------------------------------------------
% 251.75/60.12 (1) ~ (all_62_2 = e2)
% 251.75/60.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.12 (3) ~ (e3 = e2)
% 251.75/60.12 (4) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) = e3)
% 251.75/60.12 | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.75/60.12 (5) op(e1, e4) = all_16_2
% 251.75/60.12 (6) op(e1, e3) = all_62_2
% 251.75/60.12 (7) ~ (all_16_2 = e2)
% 251.75/60.12 (8) ~ (all_8_2 = e1)
% 251.75/60.12 (9) op(e3, all_4_2) = e1
% 251.75/60.12 (10) ~ (all_244_15 = e3)
% 251.75/60.12 (11) op(e1, e1) = all_244_15
% 251.75/60.12 (12) op(e1, e2) = all_4_2
% 251.75/60.12 (13) ~ (all_244_15 = e2)
% 251.75/60.12 (14) op(e3, e2) = all_8_2
% 251.75/60.12 (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.75/60.12 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.75/60.12 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.75/60.12 (16) ~ (all_4_2 = e3)
% 251.75/60.12
% 251.75/60.12 Begin of proof
% 251.75/60.12 |
% 251.75/60.12 | BETA: splitting (4) gives:
% 251.75/60.12 |
% 251.75/60.12 | Case 1:
% 251.75/60.12 | |
% 251.75/60.12 | | (17) all_252_14 = e3 & op(e1, e2) = e3
% 251.75/60.12 | |
% 251.75/60.12 | | REF_CLOSE: (2), (12), (16), (17) are inconsistent by sub-proof #858.
% 251.75/60.12 | |
% 251.75/60.12 | Case 2:
% 251.75/60.12 | |
% 251.75/60.12 | | (18) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0)
% 251.75/60.12 | | = e3)
% 251.75/60.12 | |
% 251.75/60.12 | | BETA: splitting (18) gives:
% 251.75/60.12 | |
% 251.75/60.12 | | Case 1:
% 251.75/60.12 | | |
% 251.75/60.12 | | | (19) all_252_15 = e3 & op(e1, e1) = e3
% 251.75/60.12 | | |
% 251.75/60.12 | | | ALPHA: (19) implies:
% 251.75/60.12 | | | (20) op(e1, e1) = e3
% 251.75/60.12 | | |
% 251.75/60.12 | | | REF_CLOSE: (2), (10), (11), (20) are inconsistent by sub-proof #822.
% 251.75/60.12 | | |
% 251.75/60.12 | | Case 2:
% 251.75/60.12 | | |
% 251.75/60.12 | | | (21) all_252_19 = e3 & op(e1, e0) = e3
% 251.75/60.12 | | |
% 251.75/60.12 | | | ALPHA: (21) implies:
% 251.75/60.13 | | | (22) op(e1, e0) = e3
% 251.75/60.13 | | |
% 251.75/60.13 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 251.75/60.13 | | | (15), (22) are inconsistent by sub-proof #735.
% 251.75/60.13 | | |
% 251.75/60.13 | | End of split
% 251.75/60.13 | |
% 251.75/60.13 | End of split
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #735 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) ~ (all_62_2 = e2)
% 251.75/60.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (3) ~ (e3 = e2)
% 251.75/60.13 (4) op(e1, e4) = all_16_2
% 251.75/60.13 (5) op(e1, e3) = all_62_2
% 251.75/60.13 (6) ~ (all_16_2 = e2)
% 251.75/60.13 (7) ~ (all_8_2 = e1)
% 251.75/60.13 (8) op(e3, all_4_2) = e1
% 251.75/60.13 (9) op(e1, e1) = all_244_15
% 251.75/60.13 (10) op(e1, e2) = all_4_2
% 251.75/60.13 (11) ~ (all_244_15 = e2)
% 251.75/60.13 (12) op(e1, e0) = e3
% 251.75/60.13 (13) op(e3, e2) = all_8_2
% 251.75/60.13 (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.75/60.13 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.75/60.13 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | BETA: splitting (14) gives:
% 251.75/60.13 |
% 251.75/60.13 | Case 1:
% 251.75/60.13 | |
% 251.75/60.13 | | (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 251.75/60.13 | | = e2)
% 251.75/60.13 | |
% 251.75/60.13 | | REF_CLOSE: (1), (2), (4), (5), (6), (15) are inconsistent by sub-proof #925.
% 251.75/60.13 | |
% 251.75/60.13 | Case 2:
% 251.75/60.13 | |
% 251.75/60.13 | | (16) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.75/60.13 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.75/60.13 | |
% 251.75/60.13 | | BETA: splitting (16) gives:
% 251.75/60.13 | |
% 251.75/60.13 | | Case 1:
% 251.75/60.13 | | |
% 251.75/60.13 | | | (17) all_252_14 = e2 & op(e1, e2) = e2
% 251.75/60.13 | | |
% 251.75/60.13 | | | REF_CLOSE: (2), (7), (8), (10), (13), (17) are inconsistent by sub-proof
% 251.75/60.13 | | | #798.
% 251.75/60.13 | | |
% 251.75/60.13 | | Case 2:
% 251.75/60.13 | | |
% 251.75/60.13 | | | (18) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.75/60.13 | | | e0) = e2)
% 251.75/60.13 | | |
% 251.75/60.13 | | | BETA: splitting (18) gives:
% 251.75/60.13 | | |
% 251.75/60.13 | | | Case 1:
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | (19) all_252_15 = e2 & op(e1, e1) = e2
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | REF_CLOSE: (2), (9), (11), (19) are inconsistent by sub-proof #966.
% 251.75/60.13 | | | |
% 251.75/60.13 | | | Case 2:
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | (20) all_252_19 = e2 & op(e1, e0) = e2
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | ALPHA: (20) implies:
% 251.75/60.13 | | | | (21) op(e1, e0) = e2
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | REF_CLOSE: (2), (3), (12), (21) are inconsistent by sub-proof #736.
% 251.75/60.13 | | | |
% 251.75/60.13 | | | End of split
% 251.75/60.13 | | |
% 251.75/60.13 | | End of split
% 251.75/60.13 | |
% 251.75/60.13 | End of split
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #736 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (2) op(e1, e0) = e3
% 251.75/60.13 (3) op(e1, e0) = e2
% 251.75/60.13 (4) ~ (e3 = e2)
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | GROUND_INST: instantiating (1) with e2, e3, e0, e1, simplifying with (2), (3)
% 251.75/60.13 | gives:
% 251.75/60.13 | (5) e3 = e2
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (4), (5) imply:
% 251.75/60.13 | (6) $false
% 251.75/60.13 |
% 251.75/60.13 | CLOSE: (6) is inconsistent.
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #737 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) op(all_4_2, e2) = e1
% 251.75/60.13 (2) ~ (all_38_2 = e1)
% 251.75/60.13 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (4) op(e2, e2) = all_244_8
% 251.75/60.13 (5) op(e2, e1) = all_38_2
% 251.75/60.13 (6) op(all_244_15, all_244_15) = e1
% 251.75/60.13 (7) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = e2)
% 251.75/60.13 | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.75/60.13 (8) ~ (all_244_8 = e1)
% 251.75/60.13 (9) op(e1, e1) = all_244_15
% 251.75/60.13 (10) op(e0, e1) = all_20_2
% 251.75/60.13 (11) op(all_4_2, all_38_2) = e2
% 251.75/60.13 (12) ~ (all_20_2 = e2)
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | BETA: splitting (7) gives:
% 251.75/60.13 |
% 251.75/60.13 | Case 1:
% 251.75/60.13 | |
% 251.75/60.13 | | (13) all_252_11 = e2 & op(e2, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | ALPHA: (13) implies:
% 251.75/60.13 | | (14) op(e2, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | REF_CLOSE: (1), (2), (3), (5), (11), (14) are inconsistent by sub-proof
% 251.75/60.13 | | #739.
% 251.75/60.13 | |
% 251.75/60.13 | Case 2:
% 251.75/60.13 | |
% 251.75/60.13 | | (15) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1)
% 251.75/60.13 | | = e2)
% 251.75/60.13 | |
% 251.75/60.13 | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (12), (15) are inconsistent by
% 251.75/60.13 | | sub-proof #738.
% 251.75/60.13 | |
% 251.75/60.13 | End of split
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #738 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (2) op(e2, e2) = all_244_8
% 251.75/60.13 (3) op(all_244_15, all_244_15) = e1
% 251.75/60.13 (4) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.75/60.13 (5) ~ (all_244_8 = e1)
% 251.75/60.13 (6) op(e1, e1) = all_244_15
% 251.75/60.13 (7) op(e0, e1) = all_20_2
% 251.75/60.13 (8) ~ (all_20_2 = e2)
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | BETA: splitting (4) gives:
% 251.75/60.13 |
% 251.75/60.13 | Case 1:
% 251.75/60.13 | |
% 251.75/60.13 | | (9) all_252_15 = e2 & op(e1, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | ALPHA: (9) implies:
% 251.75/60.13 | | (10) op(e1, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | REF_CLOSE: (1), (2), (3), (5), (6), (10) are inconsistent by sub-proof #991.
% 251.75/60.13 | |
% 251.75/60.13 | Case 2:
% 251.75/60.13 | |
% 251.75/60.13 | | (11) all_252_23 = e2 & op(e0, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | ALPHA: (11) implies:
% 251.75/60.13 | | (12) op(e0, e1) = e2
% 251.75/60.13 | |
% 251.75/60.13 | | REF_CLOSE: (1), (7), (8), (12) are inconsistent by sub-proof #985.
% 251.75/60.13 | |
% 251.75/60.13 | End of split
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #739 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) op(all_4_2, e2) = e1
% 251.75/60.13 (2) ~ (all_38_2 = e1)
% 251.75/60.13 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (4) op(e2, e1) = all_38_2
% 251.75/60.13 (5) op(e2, e1) = e2
% 251.75/60.13 (6) op(all_4_2, all_38_2) = e2
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | GROUND_INST: instantiating (3) with all_38_2, e2, e1, e2, simplifying with
% 251.75/60.13 | (4), (5) gives:
% 251.75/60.13 | (7) all_38_2 = e2
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (2), (7) imply:
% 251.75/60.13 | (8) ~ (e2 = e1)
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (6), (7) imply:
% 251.75/60.13 | (9) op(all_4_2, e2) = e2
% 251.75/60.13 |
% 251.75/60.13 | GROUND_INST: instantiating (3) with e1, e2, e2, all_4_2, simplifying with (1),
% 251.75/60.13 | (9) gives:
% 251.75/60.13 | (10) e2 = e1
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (8), (10) imply:
% 251.75/60.13 | (11) $false
% 251.75/60.13 |
% 251.75/60.13 | CLOSE: (11) is inconsistent.
% 251.75/60.13 |
% 251.75/60.13 End of proof
% 251.75/60.13
% 251.75/60.13 Sub-proof #740 shows that the following formulas are inconsistent:
% 251.75/60.13 ----------------------------------------------------------------
% 251.75/60.13 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.75/60.13 all_250_23 = e0
% 251.75/60.13 (2) all_26_2 = e2
% 251.75/60.13 (3) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0)
% 251.75/60.13 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.75/60.13 e0) | (all_252_19 = e0 & op(e1, e0) = e0)
% 251.75/60.13 (4) ~ (all_10_2 = e4)
% 251.75/60.13 (5) op(all_4_2, e2) = e1
% 251.75/60.13 (6) ~ (all_244_24 = all_34_2)
% 251.75/60.13 (7) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1)
% 251.75/60.13 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 251.75/60.13 e1) | (all_252_19 = e1 & op(e1, e0) = e1)
% 251.75/60.13 (8) op(all_6_2, e2) = e4
% 251.75/60.13 (9) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.75/60.13 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.75/60.13 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.75/60.13 (10) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.75/60.13 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.75/60.13 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.75/60.13 (11) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.75/60.13 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 251.75/60.13 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.75/60.13 (12) all_172_2 = all_10_2
% 251.75/60.13 (13) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 251.75/60.13 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 251.75/60.13 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.75/60.13 (14) op(all_62_2, all_36_2) = e3
% 251.75/60.13 (15) ~ (e2 = e0)
% 251.75/60.13 (16) ~ (e1 = e0)
% 251.75/60.13 (17) ~ (all_28_2 = e3)
% 251.75/60.13 (18) ~ (all_62_2 = all_22_2)
% 251.75/60.13 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.13 (20) op(e2, e3) = all_10_2
% 251.75/60.13 (21) op(e0, e0) = all_244_24
% 251.75/60.13 (22) ~ (e4 = e0)
% 251.75/60.13 (23) ~ (all_12_2 = e3)
% 251.75/60.13 (24) op(all_244_8, all_244_8) = e2
% 251.75/60.13 (25) op(e2, e2) = all_244_8
% 251.75/60.13 (26) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.75/60.13 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.75/60.13 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.75/60.13 (27) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.75/60.13 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.75/60.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.75/60.13 (28) ~ (all_36_2 = all_20_2)
% 251.75/60.13 (29) ~ (all_84_2 = all_62_2)
% 251.75/60.13 (30) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.75/60.13 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.75/60.13 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.75/60.13 (31) all_168_2 = all_100_2
% 251.75/60.13 (32) op(e1, e0) = all_34_2
% 251.75/60.13 (33) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.75/60.13 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.75/60.13 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.75/60.13 (34) ~ (all_40_2 = e4)
% 251.75/60.13 (35) op(e4, e2) = all_6_2
% 251.75/60.13 (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.75/60.13 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.75/60.13 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.75/60.13 (37) ~ (all_20_2 = all_12_2)
% 251.75/60.13 (38) ~ (all_34_2 = e2)
% 251.75/60.13 (39) ~ (e2 = e1)
% 251.75/60.13 (40) ~ (all_100_2 = all_64_2)
% 251.75/60.13 (41) op(e0, e2) = all_28_2
% 251.75/60.13 (42) ~ (e4 = e1)
% 251.75/60.13 (43) ~ (all_244_0 = e2)
% 251.75/60.13 (44) op(all_6_2, all_64_2) = e2
% 251.75/60.13 (45) ~ (all_64_2 = all_10_2)
% 251.75/60.13 (46) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.75/60.13 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.75/60.13 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.13 (47) ~ (all_6_2 = e1)
% 251.75/60.13 (48) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.75/60.13 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.75/60.13 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.75/60.13 (49) ~ (all_62_2 = all_34_2)
% 251.75/60.13 (50) all_250_21 = all_22_2
% 251.75/60.13 (51) all_50_2 = all_4_2
% 251.75/60.13 (52) op(all_34_2, e0) = e1
% 251.75/60.13 (53) ~ (all_244_3 = all_84_2)
% 251.75/60.13 (54) ~ (all_244_0 = all_64_2)
% 251.75/60.13 (55) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.75/60.13 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.75/60.13 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.75/60.13 (56) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 251.75/60.13 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 251.75/60.13 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 251.75/60.13 (57) ~ (all_28_2 = all_20_2)
% 251.75/60.13 (58) op(e1, e3) = all_62_2
% 251.75/60.13 (59) op(all_16_2, all_26_2) = e4
% 251.75/60.13 (60) ~ (e3 = e0)
% 251.75/60.13 (61) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.75/60.13 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.75/60.13 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.75/60.13 (62) op(all_20_2, e1) = e0
% 251.75/60.13 (63) ~ (all_36_2 = e4)
% 251.75/60.13 (64) all_70_2 = all_62_2
% 251.75/60.13 (65) ~ (e3 = e1)
% 251.75/60.13 (66) op(all_48_2, all_22_2) = e0
% 251.75/60.13 (67) ~ (all_12_2 = e2)
% 251.75/60.13 (68) op(e3, e1) = all_36_2
% 251.75/60.13 (69) ~ (all_16_2 = e2)
% 251.75/60.13 (70) all_252_11 = e4
% 251.75/60.13 (71) ~ (all_8_2 = e1)
% 251.75/60.13 (72) ~ (all_244_3 = all_62_2)
% 251.75/60.13 (73) ~ (all_22_2 = e1)
% 251.75/60.13 (74) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.75/60.13 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.75/60.13 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.75/60.13 (75) ~ (all_40_2 = all_34_2)
% 251.75/60.13 (76) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.75/60.13 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.75/60.13 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.75/60.13 (77) all_130_2 = all_62_2
% 251.75/60.13 (78) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.75/60.13 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.75/60.13 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.75/60.13 (79) op(e1, e4) = all_38_1
% 251.75/60.13 (80) ~ (all_244_15 = all_34_2)
% 251.75/60.13 (81) op(e4, all_4_2) = e1
% 251.75/60.13 (82) ~ (all_64_2 = all_12_2)
% 251.75/60.13 (83) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 &
% 251.75/60.13 op(e0, e1) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 251.75/60.13 e4) & op(e0, e1) = all_48_1 & $i(all_48_1))
% 251.75/60.13 (84) all_38_1 = all_16_2
% 251.75/60.13 (85) op(all_22_2, e3) = e0
% 251.75/60.13 (86) all_68_2 = all_22_2
% 251.75/60.13 (87) op(all_20_2, all_34_2) = e1
% 251.75/60.13 (88) op(e0, e3) = all_22_2
% 251.75/60.13 (89) ~ (all_26_2 = e4)
% 251.75/60.13 (90) ~ (all_244_0 = all_100_2)
% 251.75/60.13 (91) op(all_34_2, all_20_2) = e0
% 251.75/60.13 (92) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.75/60.13 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.75/60.13 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.75/60.13 (93) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.75/60.13 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.75/60.13 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.75/60.13 (94) all_58_2 = all_20_2
% 251.75/60.13 (95) op(all_62_2, e3) = e1
% 251.75/60.13 (96) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 251.75/60.13 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 251.75/60.13 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 251.75/60.13 (97) op(e4, e1) = all_26_2
% 251.75/60.13 (98) op(all_10_2, e3) = e2
% 251.75/60.13 (99) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.75/60.13 all_250_21 = e0
% 251.75/60.13 (100) ~ (all_244_15 = all_62_2)
% 251.75/60.13 (101) ~ (all_62_2 = all_16_2)
% 251.75/60.13 (102) op(e3, e4) = all_100_2
% 251.75/60.13 (103) op(e4, e4) = all_244_0
% 251.75/60.13 (104) all_126_2 = all_48_2
% 251.75/60.13 (105) ~ (e4 = e3)
% 251.75/60.13 (106) op(e1, e1) = all_244_15
% 251.75/60.13 (107) op(e0, e1) = all_20_2
% 251.75/60.13 (108) ~ (all_244_15 = all_20_2)
% 251.75/60.13 (109) op(e3, e0) = all_48_2
% 251.75/60.13 (110) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.75/60.13 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.75/60.13 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.75/60.13 (111) op(all_48_2, e0) = e3
% 251.75/60.13 (112) ~ (all_26_2 = e3)
% 251.75/60.13 (113) all_82_2 = all_28_2
% 251.75/60.13 (114) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.75/60.13 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.75/60.13 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.75/60.13 (115) op(e1, e2) = all_4_2
% 251.75/60.13 (116) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.75/60.13 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.75/60.13 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.75/60.13 (117) op(e4, e3) = all_84_2
% 251.75/60.13 (118) ~ (all_62_2 = all_10_2)
% 251.75/60.13 (119) op(e2, e4) = all_64_2
% 251.75/60.13 (120) ~ (all_244_15 = e2)
% 251.75/60.13 (121) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.75/60.13 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 251.75/60.13 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 251.75/60.13 (122) ~ (all_22_2 = all_20_2)
% 251.75/60.13 (123) op(e3, e2) = all_8_2
% 251.75/60.13 (124) ~ (all_64_2 = all_16_2)
% 251.75/60.13 (125) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.75/60.13 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.75/60.13 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.75/60.13 (126) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.75/60.13 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.75/60.13 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.75/60.13 (127) ~ (all_20_2 = e4)
% 251.75/60.13 (128) ~ (all_84_2 = all_6_2)
% 251.75/60.13 (129) op(all_16_2, e4) = e1
% 251.75/60.13 (130) ~ (all_100_2 = all_16_2)
% 251.75/60.13 (131) op(e2, e0) = all_40_2
% 251.75/60.13 (132) ~ (all_16_2 = e3)
% 251.75/60.13 (133) ~ (all_244_3 = all_48_2)
% 251.75/60.13 (134) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.75/60.13 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.75/60.13 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.75/60.13 (135) op(e3, e3) = all_244_3
% 251.75/60.13 (136) ~ (all_168_2 = e2) | ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.75/60.13 op(e2, all_168_1) = all_168_0 & $i(all_168_0) & $i(all_168_1)) | ( ~
% 251.75/60.13 (all_168_1 = e1) & op(e4, e2) = all_168_1 & $i(all_168_1))
% 251.75/60.13 (137) ~ (all_26_2 = all_20_2)
% 251.75/60.13 (138) ~ (all_62_2 = all_4_2)
% 251.75/60.13 (139) ~ (all_64_2 = e4)
% 251.75/60.13 (140) op(all_244_24, all_244_24) = e0
% 251.75/60.13 (141) op(e0, e4) = all_12_2
% 251.75/60.13 (142) ~ (all_50_2 = e3) | ( ~ (all_50_0 = e0) & op(e3, all_50_1) = all_50_0
% 251.75/60.13 & op(e2, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~
% 251.75/60.13 (all_50_1 = e4) & op(e2, e3) = all_50_1 & $i(all_50_1))
% 251.75/60.13 (143) all_250_23 = all_20_2
% 251.75/60.13
% 251.75/60.13 Begin of proof
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (2), (137) imply:
% 251.75/60.13 | (144) ~ (all_20_2 = e2)
% 251.75/60.13 |
% 251.75/60.13 | SIMP: (144) implies:
% 251.75/60.13 | (145) ~ (all_20_2 = e2)
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (2), (89) imply:
% 251.75/60.13 | (146) ~ (e4 = e2)
% 251.75/60.13 |
% 251.75/60.13 | SIMP: (146) implies:
% 251.75/60.13 | (147) ~ (e4 = e2)
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (2), (112) imply:
% 251.75/60.13 | (148) ~ (e3 = e2)
% 251.75/60.13 |
% 251.75/60.13 | SIMP: (148) implies:
% 251.75/60.13 | (149) ~ (e3 = e2)
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (2), (97) imply:
% 251.75/60.13 | (150) op(e4, e1) = e2
% 251.75/60.13 |
% 251.75/60.13 | REDUCE: (79), (84) imply:
% 251.75/60.13 | (151) op(e1, e4) = all_16_2
% 251.75/60.13 |
% 251.75/60.13 | BETA: splitting (83) gives:
% 251.75/60.13 |
% 251.75/60.13 | Case 1:
% 251.75/60.13 | |
% 251.75/60.13 | | (152) ~ (all_48_2 = e1)
% 251.75/60.13 | |
% 251.75/60.13 | | BETA: splitting (142) gives:
% 251.75/60.13 | |
% 251.75/60.13 | | Case 1:
% 251.75/60.13 | | |
% 251.75/60.13 | | | (153) ~ (all_50_2 = e3)
% 251.75/60.13 | | |
% 251.75/60.13 | | | REDUCE: (51), (153) imply:
% 251.75/60.13 | | | (154) ~ (all_4_2 = e3)
% 251.75/60.13 | | |
% 251.75/60.13 | | | BETA: splitting (61) gives:
% 251.75/60.13 | | |
% 251.75/60.13 | | | Case 1:
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | (155) ~ (all_58_2 = e3)
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | REDUCE: (94), (155) imply:
% 251.75/60.13 | | | | (156) ~ (all_20_2 = e3)
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | BETA: splitting (110) gives:
% 251.75/60.13 | | | |
% 251.75/60.13 | | | | Case 1:
% 251.75/60.13 | | | | |
% 251.75/60.13 | | | | | (157) ~ (all_62_2 = e4)
% 251.75/60.13 | | | | |
% 251.75/60.13 | | | | | BETA: splitting (48) gives:
% 251.75/60.13 | | | | |
% 251.75/60.13 | | | | | Case 1:
% 251.75/60.13 | | | | | |
% 251.75/60.13 | | | | | | (158) ~ (all_64_2 = e3)
% 251.75/60.13 | | | | | |
% 251.75/60.13 | | | | | | BETA: splitting (76) gives:
% 251.75/60.13 | | | | | |
% 251.75/60.13 | | | | | | Case 1:
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | (159) ~ (all_70_2 = e2)
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | REDUCE: (64), (159) imply:
% 251.75/60.13 | | | | | | | (160) ~ (all_62_2 = e2)
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | REF_CLOSE: (19), (32), (35), (38), (47), (58), (69), (81), (106),
% 251.75/60.13 | | | | | | | (115), (120), (134), (151), (160) are inconsistent by
% 251.75/60.13 | | | | | | | sub-proof #793.
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | Case 2:
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | (161) all_70_2 = e2
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | COMBINE_EQS: (64), (161) imply:
% 251.75/60.13 | | | | | | | (162) all_62_2 = e2
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | REDUCE: (138), (162) imply:
% 251.75/60.13 | | | | | | | (163) ~ (all_4_2 = e2)
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | SIMP: (163) implies:
% 251.75/60.13 | | | | | | | (164) ~ (all_4_2 = e2)
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | REDUCE: (95), (162) imply:
% 251.75/60.13 | | | | | | | (165) op(e2, e3) = e1
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | BETA: splitting (13) gives:
% 251.75/60.13 | | | | | | |
% 251.75/60.13 | | | | | | | Case 1:
% 251.75/60.13 | | | | | | | |
% 251.75/60.13 | | | | | | | | (166) ~ (all_82_2 = e1)
% 251.75/60.13 | | | | | | | |
% 251.75/60.13 | | | | | | | | REDUCE: (113), (166) imply:
% 251.75/60.13 | | | | | | | | (167) ~ (all_28_2 = e1)
% 251.75/60.13 | | | | | | | |
% 251.75/60.13 | | | | | | | | BETA: splitting (27) gives:
% 251.75/60.13 | | | | | | | |
% 251.75/60.13 | | | | | | | | Case 1:
% 251.75/60.13 | | | | | | | | |
% 251.75/60.13 | | | | | | | | | (168) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1
% 251.75/60.13 | | | | | | | | | & op(e3, e2) = e1)
% 251.75/60.13 | | | | | | | | |
% 251.75/60.13 | | | | | | | | | REF_CLOSE: (19), (35), (47), (71), (123), (168) are
% 251.75/60.13 | | | | | | | | | inconsistent by sub-proof #928.
% 251.75/60.13 | | | | | | | | |
% 251.75/60.13 | | | | | | | | Case 2:
% 251.75/60.13 | | | | | | | | |
% 251.75/60.13 | | | | | | | | | (169) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1
% 251.75/60.13 | | | | | | | | | & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2)
% 251.75/60.13 | | | | | | | | | = e1)
% 251.75/60.13 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | BETA: splitting (169) gives:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (170) all_252_8 = e1 & op(e2, e2) = e1
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (170) implies:
% 251.75/60.14 | | | | | | | | | | (171) all_252_8 = e1
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | BETA: splitting (26) gives:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (172) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 251.75/60.14 | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (19), (65), (119), (158), (165), (172) are
% 251.75/60.14 | | | | | | | | | | | inconsistent by sub-proof #792.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (173) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 251.75/60.14 | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 251.75/60.14 | | | | | | | | | | | op(e2, e0) = e3)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | BETA: splitting (173) gives:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (174) all_252_8 = e3 & op(e2, e2) = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | ALPHA: (174) implies:
% 251.75/60.14 | | | | | | | | | | | | (175) all_252_8 = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | REF_CLOSE: (65), (171), (175) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | #927.
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (176) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 251.75/60.14 | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | BETA: splitting (176) gives:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | (177) all_252_11 = e3 & op(e2, e1) = e3
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | REF_CLOSE: (70), (105), (177) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | #791.
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | (178) all_252_18 = e3 & op(e2, e0) = e3
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | ALPHA: (178) implies:
% 251.75/60.14 | | | | | | | | | | | | | (179) all_252_18 = e3
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | BETA: splitting (78) gives:
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | (180) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 =
% 251.75/60.14 | | | | | | | | | | | | | | e2 & op(e2, e3) = e2)
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (20), (39), (44), (119), (139), (165),
% 251.75/60.14 | | | | | | | | | | | | | | (180) are inconsistent by sub-proof #789.
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | (181) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 =
% 251.75/60.14 | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 &
% 251.75/60.14 | | | | | | | | | | | | | | op(e2, e0) = e2)
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (182) all_252_8 = e2 & op(e2, e2) = e2
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | REF_CLOSE: (39), (171), (182) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | #788.
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (183) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18
% 251.75/60.14 | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2)
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | (184) all_252_11 = e2 & op(e2, e1) = e2
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | REF_CLOSE: (70), (147), (184) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | #787.
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | (185) all_252_18 = e2 & op(e2, e0) = e2
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | (186) all_252_18 = e2
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | REF_CLOSE: (149), (179), (186) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | #786.
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (187) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 =
% 251.75/60.14 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | BETA: splitting (187) gives:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (188) all_252_14 = e1 & op(e1, e2) = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | ALPHA: (188) implies:
% 251.75/60.14 | | | | | | | | | | | (189) op(e1, e2) = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | GROUND_INST: instantiating (19) with all_4_2, e1, e2, e1,
% 251.75/60.14 | | | | | | | | | | | simplifying with (115), (189) gives:
% 251.75/60.14 | | | | | | | | | | | (190) all_4_2 = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REDUCE: (164), (190) imply:
% 251.75/60.14 | | | | | | | | | | | (191) ~ (e2 = e1)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REDUCE: (81), (190) imply:
% 251.75/60.14 | | | | | | | | | | | (192) op(e4, e1) = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (19), (39), (150), (192) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | sub-proof #785.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (193) all_252_22 = e1 & op(e0, e2) = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | ALPHA: (193) implies:
% 251.75/60.14 | | | | | | | | | | | (194) op(e0, e2) = e1
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (19), (41), (167), (194) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | sub-proof #907.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | End of split
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (195) all_82_2 = e1
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | REF_CLOSE: (1), (19), (52), (57), (91), (113), (127), (143),
% 251.75/60.14 | | | | | | | | (145), (156), (195) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | #779.
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | End of split
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | End of split
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | Case 2:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | (196) all_64_2 = e3
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (54), (196) imply:
% 251.75/60.14 | | | | | | (197) ~ (all_244_0 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (40), (196) imply:
% 251.75/60.14 | | | | | | (198) ~ (all_100_2 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (124), (196) imply:
% 251.75/60.14 | | | | | | (199) ~ (all_16_2 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (82), (196) imply:
% 251.75/60.14 | | | | | | (200) ~ (all_12_2 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (45), (196) imply:
% 251.75/60.14 | | | | | | (201) ~ (all_10_2 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | SIMP: (201) implies:
% 251.75/60.14 | | | | | | (202) ~ (all_10_2 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | REDUCE: (139), (196) imply:
% 251.75/60.14 | | | | | | (203) ~ (e4 = e3)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | BETA: splitting (126) gives:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | Case 1:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | (204) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 &
% 251.75/60.14 | | | | | | | op(e3, e4) = e2)
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | BETA: splitting (204) gives:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (205) all_252_0 = e2 & op(e4, e4) = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | ALPHA: (205) implies:
% 251.75/60.14 | | | | | | | | (206) op(e4, e4) = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | REF_CLOSE: (19), (43), (103), (206) are inconsistent by
% 251.75/60.14 | | | | | | | | sub-proof #809.
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (207) all_252_2 = e2 & op(e3, e4) = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | ALPHA: (207) implies:
% 251.75/60.14 | | | | | | | | (208) all_252_2 = e2
% 251.75/60.14 | | | | | | | | (209) op(e3, e4) = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | GROUND_INST: instantiating (19) with all_100_2, e2, e4, e3,
% 251.75/60.14 | | | | | | | | simplifying with (102), (209) gives:
% 251.75/60.14 | | | | | | | | (210) all_100_2 = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | COMBINE_EQS: (31), (210) imply:
% 251.75/60.14 | | | | | | | | (211) all_168_2 = e2
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | REDUCE: (130), (210) imply:
% 251.75/60.14 | | | | | | | | (212) ~ (all_16_2 = e2)
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | BETA: splitting (136) gives:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (213) ~ (all_168_2 = e2)
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REDUCE: (211), (213) imply:
% 251.75/60.14 | | | | | | | | | (214) $false
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | CLOSE: (214) is inconsistent.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (215) ( ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.75/60.14 | | | | | | | | | op(e2, all_168_1) = all_168_0 & $i(all_168_0) &
% 251.75/60.14 | | | | | | | | | $i(all_168_1)) | ( ~ (all_168_1 = e1) & op(e4, e2)
% 251.75/60.14 | | | | | | | | | = all_168_1 & $i(all_168_1))
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | BETA: splitting (215) gives:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (216) ~ (all_168_0 = e0) & op(e4, e2) = all_168_1 &
% 251.75/60.14 | | | | | | | | | | op(e2, all_168_1) = all_168_0 & $i(all_168_0) &
% 251.75/60.14 | | | | | | | | | | $i(all_168_1)
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (216) implies:
% 251.75/60.14 | | | | | | | | | | (217) op(e4, e2) = all_168_1
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | GROUND_INST: instantiating (19) with all_6_2, all_168_1, e2,
% 251.75/60.14 | | | | | | | | | | e4, simplifying with (35), (217) gives:
% 251.75/60.14 | | | | | | | | | | (218) all_168_1 = all_6_2
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | BETA: splitting (30) gives:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (219) ~ (all_68_2 = e4)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REDUCE: (86), (219) imply:
% 251.75/60.14 | | | | | | | | | | | (220) ~ (all_22_2 = e4)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (12), (15), (16), (19), (20),
% 251.75/60.14 | | | | | | | | | | | (22), (23), (24), (25), (28), (32), (34), (35),
% 251.75/60.14 | | | | | | | | | | | (36), (38), (46), (47), (49), (52), (56), (58),
% 251.75/60.14 | | | | | | | | | | | (60), (64), (68), (69), (70), (71), (74), (76),
% 251.75/60.14 | | | | | | | | | | | (77), (81), (88), (90), (91), (93), (95), (96),
% 251.75/60.14 | | | | | | | | | | | (97), (98), (100), (101), (102), (103), (105),
% 251.75/60.14 | | | | | | | | | | | (106), (107), (109), (112), (115), (116), (118),
% 251.75/60.14 | | | | | | | | | | | (120), (123), (125), (131), (132), (134), (138),
% 251.75/60.14 | | | | | | | | | | | (141), (149), (150), (151), (152), (156), (157),
% 251.75/60.14 | | | | | | | | | | | (197), (202), (208), (209), (220) are inconsistent
% 251.75/60.14 | | | | | | | | | | | by sub-proof #760.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (221) all_68_2 = e4
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (17), (19), (21), (23), (41), (53), (55), (85),
% 251.75/60.14 | | | | | | | | | | | (86), (88), (105), (107), (117), (135), (140),
% 251.75/60.14 | | | | | | | | | | | (141), (156), (221) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | #759.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (222) ~ (all_168_1 = e1) & op(e4, e2) = all_168_1 &
% 251.75/60.14 | | | | | | | | | | $i(all_168_1)
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (222) implies:
% 251.75/60.14 | | | | | | | | | | (223) ~ (all_168_1 = e1)
% 251.75/60.14 | | | | | | | | | | (224) op(e4, e2) = all_168_1
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | GROUND_INST: instantiating (19) with all_6_2, all_168_1, e2,
% 251.75/60.14 | | | | | | | | | | e4, simplifying with (35), (224) gives:
% 251.75/60.14 | | | | | | | | | | (225) all_168_1 = all_6_2
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | BETA: splitting (30) gives:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (226) ~ (all_68_2 = e4)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REDUCE: (86), (226) imply:
% 251.75/60.14 | | | | | | | | | | | (227) ~ (all_22_2 = e4)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (12), (15), (16), (19), (20),
% 251.75/60.14 | | | | | | | | | | | (22), (23), (24), (25), (28), (32), (34), (35),
% 251.75/60.14 | | | | | | | | | | | (36), (38), (46), (47), (49), (52), (56), (58),
% 251.75/60.14 | | | | | | | | | | | (60), (64), (68), (69), (70), (71), (74), (76),
% 251.75/60.14 | | | | | | | | | | | (77), (81), (88), (90), (91), (93), (95), (96),
% 251.75/60.14 | | | | | | | | | | | (97), (98), (100), (101), (102), (103), (105),
% 251.75/60.14 | | | | | | | | | | | (106), (107), (109), (112), (115), (116), (118),
% 251.75/60.14 | | | | | | | | | | | (120), (123), (125), (131), (132), (134), (138),
% 251.75/60.14 | | | | | | | | | | | (141), (149), (150), (151), (152), (156), (157),
% 251.75/60.14 | | | | | | | | | | | (197), (202), (208), (209), (227) are inconsistent
% 251.75/60.14 | | | | | | | | | | | by sub-proof #760.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (228) all_68_2 = e4
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | REF_CLOSE: (17), (19), (21), (23), (41), (53), (55), (85),
% 251.75/60.14 | | | | | | | | | | | (86), (88), (105), (107), (117), (135), (140),
% 251.75/60.14 | | | | | | | | | | | (141), (156), (228) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | #759.
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | End of split
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | End of split
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | Case 2:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | (229) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 &
% 251.75/60.14 | | | | | | | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | REF_CLOSE: (8), (19), (44), (67), (69), (119), (139), (141),
% 251.75/60.14 | | | | | | | (151), (229) are inconsistent by sub-proof #758.
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | End of split
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | End of split
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | Case 2:
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | (230) all_62_2 = e4
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (72), (230) imply:
% 251.75/60.14 | | | | | (231) ~ (all_244_3 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (100), (230) imply:
% 251.75/60.14 | | | | | (232) ~ (all_244_15 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (29), (230) imply:
% 251.75/60.14 | | | | | (233) ~ (all_84_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (18), (230) imply:
% 251.75/60.14 | | | | | (234) ~ (all_22_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | SIMP: (234) implies:
% 251.75/60.14 | | | | | (235) ~ (all_22_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (101), (230) imply:
% 251.75/60.14 | | | | | (236) ~ (all_16_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | SIMP: (236) implies:
% 251.75/60.14 | | | | | (237) ~ (all_16_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (118), (230) imply:
% 251.75/60.14 | | | | | (238) ~ (all_10_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (138), (230) imply:
% 251.75/60.14 | | | | | (239) ~ (all_4_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | SIMP: (239) implies:
% 251.75/60.14 | | | | | (240) ~ (all_4_2 = e4)
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | REDUCE: (95), (230) imply:
% 251.75/60.14 | | | | | (241) op(e4, e3) = e1
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | BETA: splitting (134) gives:
% 251.75/60.14 | | | | |
% 251.75/60.14 | | | | | Case 1:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | (242) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 &
% 251.75/60.14 | | | | | | op(e1, e3) = e2)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | BETA: splitting (242) gives:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | Case 1:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | (243) all_252_12 = e2 & op(e1, e4) = e2
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | REF_CLOSE: (19), (69), (151), (243) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | #926.
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | Case 2:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | (244) all_252_13 = e2 & op(e1, e3) = e2
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | ALPHA: (244) implies:
% 251.75/60.14 | | | | | | | (245) all_252_13 = e2
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | BETA: splitting (10) gives:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (246) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 251.75/60.14 | | | | | | | | op(e3, e3) = e4)
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | BETA: splitting (246) gives:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (247) all_252_1 = e4 & op(e4, e3) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (19), (117), (233), (247) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #815.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (248) all_252_3 = e4 & op(e3, e3) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (19), (135), (231), (248) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #846.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | End of split
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (249) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 251.75/60.14 | | | | | | | | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) =
% 251.75/60.14 | | | | | | | | e4)
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | BETA: splitting (249) gives:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (250) all_252_7 = e4 & op(e2, e3) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | ALPHA: (250) implies:
% 251.75/60.14 | | | | | | | | | (251) op(e2, e3) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (4), (19), (20), (251) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #953.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (252) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 =
% 251.75/60.14 | | | | | | | | | e4 & op(e0, e3) = e4)
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | BETA: splitting (252) gives:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (253) all_252_13 = e4 & op(e1, e3) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (253) implies:
% 251.75/60.14 | | | | | | | | | | (254) all_252_13 = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | COMBINE_EQS: (245), (254) imply:
% 251.75/60.14 | | | | | | | | | | (255) e4 = e2
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | REDUCE: (147), (255) imply:
% 251.75/60.14 | | | | | | | | | | (256) $false
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | CLOSE: (256) is inconsistent.
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (257) all_252_21 = e4 & op(e0, e3) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | REF_CLOSE: (19), (88), (235), (257) are inconsistent by
% 251.75/60.14 | | | | | | | | | | sub-proof #805.
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | End of split
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | End of split
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | End of split
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | Case 2:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | (258) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 &
% 251.75/60.14 | | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | BETA: splitting (258) gives:
% 251.75/60.14 | | | | | |
% 251.75/60.14 | | | | | | Case 1:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | (259) all_252_14 = e2 & op(e1, e2) = e2
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | ALPHA: (259) implies:
% 251.75/60.14 | | | | | | | (260) all_252_14 = e2
% 251.75/60.14 | | | | | | | (261) op(e1, e2) = e2
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | BETA: splitting (92) gives:
% 251.75/60.14 | | | | | | |
% 251.75/60.14 | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (262) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4
% 251.75/60.14 | | | | | | | | & op(e1, e3) = e4)
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | BETA: splitting (262) gives:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (263) all_252_12 = e4 & op(e1, e4) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (19), (151), (237), (263) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #757.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | GROUND_INST: instantiating (19) with all_4_2, e2, e2, e1,
% 251.75/60.14 | | | | | | | | | simplifying with (115), (261) gives:
% 251.75/60.14 | | | | | | | | | (264) all_4_2 = e2
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | GROUND_INST: instantiating (19) with all_84_2, e1, e3, e4,
% 251.75/60.14 | | | | | | | | | simplifying with (117), (241) gives:
% 251.75/60.14 | | | | | | | | | (265) all_84_2 = e1
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REDUCE: (128), (265) imply:
% 251.75/60.14 | | | | | | | | | (266) ~ (all_6_2 = e1)
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REDUCE: (81), (264) imply:
% 251.75/60.14 | | | | | | | | | (267) op(e4, e2) = e1
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (19), (35), (47), (267) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #930.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | End of split
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | (268) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4
% 251.75/60.14 | | | | | | | | & op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) =
% 251.75/60.14 | | | | | | | | e4)
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | BETA: splitting (268) gives:
% 251.75/60.14 | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (269) all_252_14 = e4 & op(e1, e2) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | ALPHA: (269) implies:
% 251.75/60.14 | | | | | | | | | (270) op(e1, e2) = e4
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | REF_CLOSE: (19), (115), (240), (270) are inconsistent by
% 251.75/60.14 | | | | | | | | | sub-proof #831.
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | (271) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 =
% 251.75/60.14 | | | | | | | | | e4 & op(e1, e0) = e4)
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | BETA: splitting (271) gives:
% 251.75/60.14 | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (272) all_252_15 = e4 & op(e1, e1) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (272) implies:
% 251.75/60.14 | | | | | | | | | | (273) op(e1, e1) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | REF_CLOSE: (19), (106), (232), (273) are inconsistent by
% 251.75/60.14 | | | | | | | | | | sub-proof #756.
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | (274) all_252_19 = e4 & op(e1, e0) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | ALPHA: (274) implies:
% 251.75/60.14 | | | | | | | | | | (275) all_252_19 = e4
% 251.75/60.14 | | | | | | | | | | (276) op(e1, e0) = e4
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | BETA: splitting (11) gives:
% 251.75/60.14 | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (277) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13
% 251.75/60.14 | | | | | | | | | | | = e3 & op(e1, e3) = e3)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | BETA: splitting (277) gives:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (278) all_252_12 = e3 & op(e1, e4) = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | REF_CLOSE: (19), (132), (151), (278) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | sub-proof #895.
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (279) all_252_13 = e3 & op(e1, e3) = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | ALPHA: (279) implies:
% 251.75/60.14 | | | | | | | | | | | | (280) all_252_13 = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | REF_CLOSE: (4), (10), (19), (20), (88), (105), (117), (135),
% 251.75/60.14 | | | | | | | | | | | | (231), (233), (235), (280) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | sub-proof #755.
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | (281) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15
% 251.75/60.14 | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 251.75/60.14 | | | | | | | | | | | op(e1, e0) = e3)
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | BETA: splitting (281) gives:
% 251.75/60.14 | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (282) all_252_14 = e3 & op(e1, e2) = e3
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | REF_CLOSE: (19), (115), (154), (282) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | sub-proof #858.
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | (283) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19
% 251.75/60.14 | | | | | | | | | | | | = e3 & op(e1, e0) = e3)
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | BETA: splitting (283) gives:
% 251.75/60.14 | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | (284) all_252_15 = e3 & op(e1, e1) = e3
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | ALPHA: (284) implies:
% 251.75/60.14 | | | | | | | | | | | | | (285) all_252_15 = e3
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | BETA: splitting (10) gives:
% 251.75/60.14 | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | (286) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.75/60.14 | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (287) all_252_1 = e4 & op(e4, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | REF_CLOSE: (19), (117), (233), (287) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | | | | sub-proof #815.
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (288) all_252_3 = e4 & op(e3, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | REF_CLOSE: (19), (135), (231), (288) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | | | | sub-proof #846.
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | (289) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.75/60.14 | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.75/60.14 | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 251.75/60.14 | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (290) all_252_7 = e4 & op(e2, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | (291) op(e2, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (20), (291) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | | | | sub-proof #953.
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | (292) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21
% 251.75/60.14 | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4)
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 251.75/60.14 | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | (293) all_252_13 = e4 & op(e1, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | (294) all_252_13 = e4
% 251.75/60.14 | | | | | | | | | | | | | | | | (295) op(e1, e3) = e4
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | (296) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13
% 251.75/60.14 | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0)
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (297) all_252_12 = e0 & op(e1, e4) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (298) all_252_12 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (299) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1)
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (300) all_252_12 = e1 & op(e1, e4) = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (301) all_252_12 = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (301) imply:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (302) e1 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (302) imply:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (303) $false
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (304) all_252_13 = e1 & op(e1, e3) = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (294), (304) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | #754.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (305) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 &
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1)
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (306) all_252_14 = e1 & op(e1, e2) = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (260), (306) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | #753.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | (307) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1)
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | (308) all_252_15 = e1 & op(e1, e1) = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (285), (308) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | #752.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | (309) all_252_19 = e1 & op(e1, e0) = e1
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (275), (309) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | | #826.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (310) all_252_13 = e0 & op(e1, e3) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (311) op(e1, e3) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (295), (311) are inconsistent by
% 251.75/60.14 | | | | | | | | | | | | | | | | | | sub-proof #886.
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | End of split
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | (312) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15
% 251.75/60.14 | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 &
% 251.75/60.14 | | | | | | | | | | | | | | | | | op(e1, e0) = e0)
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (313) all_252_14 = e0 & op(e1, e2) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (260), (313) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | #751.
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | (314) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19
% 251.75/60.14 | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0)
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 251.75/60.14 | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | Case 1:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (315) all_252_15 = e0 & op(e1, e1) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (285), (315) are inconsistent by sub-proof
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | #763.
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | Case 2:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (316) all_252_19 = e0 & op(e1, e0) = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (317) all_252_19 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (317) imply:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (318) e4 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (319) e4 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (319) imply:
% 251.75/60.14 | | | | | | | | | | | | | | | | | | | (320) all_252_11 = e0
% 251.75/60.14 | | | | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (33), (59), (63), (68), (97), (106),
% 251.75/60.15 | | | | | | | | | | | | | | | | | | | (107), (117), (127), (129), (232), (233), (241),
% 251.75/60.15 | | | | | | | | | | | | | | | | | | | (320) are inconsistent by sub-proof #749.
% 251.75/60.15 | | | | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | Case 2:
% 251.75/60.15 | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | (321) all_252_21 = e4 & op(e0, e3) = e4
% 251.75/60.15 | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | | REF_CLOSE: (19), (88), (235), (321) are inconsistent by
% 251.75/60.15 | | | | | | | | | | | | | | | | sub-proof #805.
% 251.75/60.15 | | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | Case 2:
% 251.75/60.15 | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | (322) all_252_19 = e3 & op(e1, e0) = e3
% 251.75/60.15 | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | ALPHA: (322) implies:
% 251.75/60.15 | | | | | | | | | | | | | (323) op(e1, e0) = e3
% 251.75/60.15 | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | | REF_CLOSE: (19), (105), (276), (323) are inconsistent by
% 251.75/60.15 | | | | | | | | | | | | | sub-proof #827.
% 251.75/60.15 | | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | | |
% 251.75/60.15 | | | | | | | | | End of split
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | End of split
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | End of split
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | Case 2:
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | (324) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 251.75/60.15 | | | | | | | op(e1, e0) = e2)
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | REF_CLOSE: (19), (32), (38), (106), (120), (324) are inconsistent
% 251.75/60.15 | | | | | | | by sub-proof #819.
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | End of split
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | End of split
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | End of split
% 251.75/60.15 | | | |
% 251.75/60.15 | | | Case 2:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (325) all_58_2 = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | COMBINE_EQS: (94), (325) imply:
% 251.75/60.15 | | | | (326) all_20_2 = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | SIMP: (326) implies:
% 251.75/60.15 | | | | (327) all_20_2 = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (108), (327) imply:
% 251.75/60.15 | | | | (328) ~ (all_244_15 = e3)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (122), (327) imply:
% 251.75/60.15 | | | | (329) ~ (all_22_2 = e3)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (37), (327) imply:
% 251.75/60.15 | | | | (330) ~ (all_12_2 = e3)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (127), (327) imply:
% 251.75/60.15 | | | | (331) ~ (e4 = e3)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (62), (327) imply:
% 251.75/60.15 | | | | (332) op(e3, e1) = e0
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (107), (327) imply:
% 251.75/60.15 | | | | (333) op(e0, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | BETA: splitting (46) gives:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | Case 1:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | (334) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 &
% 251.75/60.15 | | | | | op(e3, e1) = e3)
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | BETA: splitting (334) gives:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | Case 1:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (335) all_252_9 = e3 & op(e4, e1) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | ALPHA: (335) implies:
% 251.75/60.15 | | | | | | (336) op(e4, e1) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REF_CLOSE: (19), (97), (112), (336) are inconsistent by sub-proof
% 251.75/60.15 | | | | | | #834.
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | Case 2:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (337) all_252_10 = e3 & op(e3, e1) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | ALPHA: (337) implies:
% 251.75/60.15 | | | | | | (338) op(e3, e1) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REF_CLOSE: (19), (60), (68), (332), (338) are inconsistent by
% 251.75/60.15 | | | | | | sub-proof #748.
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | End of split
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | Case 2:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | (339) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 &
% 251.75/60.15 | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | BETA: splitting (339) gives:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | Case 1:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (340) all_252_11 = e3 & op(e2, e1) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REF_CLOSE: (70), (105), (340) are inconsistent by sub-proof #791.
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | Case 2:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (341) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.75/60.15 | | | | | | op(e0, e1) = e3)
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | BETA: splitting (341) gives:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | Case 1:
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | (342) all_252_15 = e3 & op(e1, e1) = e3
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | REF_CLOSE: (16), (19), (39), (42), (65), (68), (70), (121), (150),
% 251.75/60.15 | | | | | | | (332), (333), (342) are inconsistent by sub-proof #746.
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | Case 2:
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | (343) all_252_23 = e3 & op(e0, e1) = e3
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | ALPHA: (343) implies:
% 251.75/60.15 | | | | | | | (344) all_252_23 = e3
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | GROUND_INST: instantiating (19) with all_36_2, e0, e1, e3,
% 251.75/60.15 | | | | | | | simplifying with (68), (332) gives:
% 251.75/60.15 | | | | | | | (345) all_36_2 = e0
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | REDUCE: (14), (345) imply:
% 251.75/60.15 | | | | | | | (346) op(all_62_2, e0) = e3
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | BETA: splitting (30) gives:
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | | Case 1:
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | (347) ~ (all_68_2 = e4)
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | REDUCE: (86), (347) imply:
% 251.75/60.15 | | | | | | | | (348) ~ (all_22_2 = e4)
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | BETA: splitting (76) gives:
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | Case 1:
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | (349) ~ (all_70_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (64), (349) imply:
% 251.75/60.15 | | | | | | | | | (350) ~ (all_62_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REF_CLOSE: (19), (32), (35), (38), (47), (58), (69), (81),
% 251.75/60.15 | | | | | | | | | (106), (115), (120), (134), (151), (350) are
% 251.75/60.15 | | | | | | | | | inconsistent by sub-proof #793.
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | Case 2:
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | (351) all_70_2 = e2
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | COMBINE_EQS: (64), (351) imply:
% 251.75/60.15 | | | | | | | | | (352) all_62_2 = e2
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | SIMP: (352) implies:
% 251.75/60.15 | | | | | | | | | (353) all_62_2 = e2
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REF_CLOSE: (18), (19), (50), (66), (73), (99), (111), (329),
% 251.75/60.15 | | | | | | | | | (348), (353) are inconsistent by sub-proof #852.
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | End of split
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | Case 2:
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | (354) all_68_2 = e4
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | COMBINE_EQS: (86), (354) imply:
% 251.75/60.15 | | | | | | | | (355) all_22_2 = e4
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | REDUCE: (85), (355) imply:
% 251.75/60.15 | | | | | | | | (356) op(e4, e3) = e0
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | REDUCE: (88), (355) imply:
% 251.75/60.15 | | | | | | | | (357) op(e0, e3) = e4
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | BETA: splitting (76) gives:
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | | Case 1:
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | (358) ~ (all_70_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (64), (358) imply:
% 251.75/60.15 | | | | | | | | | (359) ~ (all_62_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REF_CLOSE: (19), (32), (35), (38), (47), (58), (69), (81),
% 251.75/60.15 | | | | | | | | | (106), (115), (120), (134), (151), (359) are
% 251.75/60.15 | | | | | | | | | inconsistent by sub-proof #793.
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | Case 2:
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | (360) all_70_2 = e2
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | COMBINE_EQS: (64), (360) imply:
% 251.75/60.15 | | | | | | | | | (361) all_62_2 = e2
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (49), (361) imply:
% 251.75/60.15 | | | | | | | | | (362) ~ (all_34_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (101), (361) imply:
% 251.75/60.15 | | | | | | | | | (363) ~ (all_16_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (138), (361) imply:
% 251.75/60.15 | | | | | | | | | (364) ~ (all_4_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | SIMP: (364) implies:
% 251.75/60.15 | | | | | | | | | (365) ~ (all_4_2 = e2)
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REDUCE: (346), (361) imply:
% 251.75/60.15 | | | | | | | | | (366) op(e2, e0) = e3
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | | REF_CLOSE: (11), (17), (19), (21), (23), (32), (38), (41),
% 251.75/60.15 | | | | | | | | | (53), (55), (69), (75), (105), (106), (115), (117),
% 251.75/60.15 | | | | | | | | | (120), (131), (132), (134), (135), (140), (141),
% 251.75/60.15 | | | | | | | | | (149), (151), (154), (328), (344), (356), (357),
% 251.75/60.15 | | | | | | | | | (365), (366) are inconsistent by sub-proof #818.
% 251.75/60.15 | | | | | | | | |
% 251.75/60.15 | | | | | | | | End of split
% 251.75/60.15 | | | | | | | |
% 251.75/60.15 | | | | | | | End of split
% 251.75/60.15 | | | | | | |
% 251.75/60.15 | | | | | | End of split
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | End of split
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | End of split
% 251.75/60.15 | | | |
% 251.75/60.15 | | | End of split
% 251.75/60.15 | | |
% 251.75/60.15 | | Case 2:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (367) all_50_2 = e3
% 251.75/60.15 | | |
% 251.75/60.15 | | | REF_CLOSE: (5), (19), (51), (71), (123), (367) are inconsistent by
% 251.75/60.15 | | | sub-proof #802.
% 251.75/60.15 | | |
% 251.75/60.15 | | End of split
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (368) all_48_2 = e1
% 251.75/60.15 | |
% 251.75/60.15 | | COMBINE_EQS: (104), (368) imply:
% 251.75/60.15 | | (369) all_126_2 = e1
% 251.75/60.15 | |
% 251.75/60.15 | | REDUCE: (133), (368) imply:
% 251.75/60.15 | | (370) ~ (all_244_3 = e1)
% 251.75/60.15 | |
% 251.75/60.15 | | REDUCE: (111), (368) imply:
% 251.75/60.15 | | (371) op(e1, e0) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | BETA: splitting (114) gives:
% 251.75/60.15 | |
% 251.75/60.15 | | Case 1:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (372) ~ (all_126_2 = e1)
% 251.75/60.15 | | |
% 251.75/60.15 | | | REDUCE: (369), (372) imply:
% 251.75/60.15 | | | (373) $false
% 251.75/60.15 | | |
% 251.75/60.15 | | | CLOSE: (373) is inconsistent.
% 251.75/60.15 | | |
% 251.75/60.15 | | Case 2:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (374) ( ~ (all_126_0 = e4) & op(e1, all_126_1) = all_126_0 & op(e0, e1)
% 251.75/60.15 | | | = all_126_1 & $i(all_126_0) & $i(all_126_1)) | ( ~ (all_126_1 =
% 251.75/60.15 | | | e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.75/60.15 | | |
% 251.75/60.15 | | | BETA: splitting (374) gives:
% 251.75/60.15 | | |
% 251.75/60.15 | | | Case 1:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (375) ~ (all_126_0 = e4) & op(e1, all_126_1) = all_126_0 & op(e0,
% 251.75/60.15 | | | | e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | ALPHA: (375) implies:
% 251.75/60.15 | | | | (376) op(e0, e1) = all_126_1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (6), (14), (17), (19), (21), (23), (32), (41), (46), (55),
% 251.75/60.15 | | | | (61), (68), (70), (73), (80), (87), (88), (94), (95), (97),
% 251.75/60.15 | | | | (105), (106), (107), (112), (135), (141), (370), (371), (376)
% 251.75/60.15 | | | | are inconsistent by sub-proof #741.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | Case 2:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (377) ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | ALPHA: (377) implies:
% 251.75/60.15 | | | | (378) op(e0, e1) = all_126_1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (6), (14), (17), (19), (21), (23), (32), (41), (46), (55),
% 251.75/60.15 | | | | (61), (68), (70), (73), (80), (87), (88), (94), (95), (97),
% 251.75/60.15 | | | | (105), (106), (107), (112), (135), (141), (370), (371), (378)
% 251.75/60.15 | | | | are inconsistent by sub-proof #741.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | End of split
% 251.75/60.15 | | |
% 251.75/60.15 | | End of split
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #741 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) ~ (all_244_24 = all_34_2)
% 251.75/60.15 (2) op(all_62_2, all_36_2) = e3
% 251.75/60.15 (3) ~ (all_28_2 = e3)
% 251.75/60.15 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (5) op(e0, e0) = all_244_24
% 251.75/60.15 (6) ~ (all_12_2 = e3)
% 251.75/60.15 (7) ~ (all_244_3 = e1)
% 251.75/60.15 (8) op(e1, e0) = all_34_2
% 251.75/60.15 (9) op(e0, e2) = all_28_2
% 251.75/60.15 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.75/60.15 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.75/60.15 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.15 (11) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.75/60.15 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.75/60.15 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.75/60.15 (12) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.75/60.15 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.75/60.15 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.75/60.15 (13) op(e3, e1) = all_36_2
% 251.75/60.15 (14) all_252_11 = e4
% 251.75/60.15 (15) ~ (all_22_2 = e1)
% 251.75/60.15 (16) ~ (all_244_15 = all_34_2)
% 251.75/60.15 (17) op(all_20_2, all_34_2) = e1
% 251.75/60.15 (18) op(e0, e3) = all_22_2
% 251.75/60.15 (19) all_58_2 = all_20_2
% 251.75/60.15 (20) op(all_62_2, e3) = e1
% 251.75/60.15 (21) op(e4, e1) = all_26_2
% 251.75/60.15 (22) ~ (e4 = e3)
% 251.75/60.15 (23) op(e1, e1) = all_244_15
% 251.75/60.15 (24) op(e0, e1) = all_20_2
% 251.75/60.15 (25) ~ (all_26_2 = e3)
% 251.75/60.15 (26) op(e1, e0) = e3
% 251.75/60.15 (27) op(e0, e1) = all_126_1
% 251.75/60.15 (28) op(e3, e3) = all_244_3
% 251.75/60.15 (29) op(e0, e4) = all_12_2
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | GROUND_INST: instantiating (4) with all_20_2, all_126_1, e1, e0, simplifying
% 251.75/60.15 | with (24), (27) gives:
% 251.75/60.15 | (30) all_126_1 = all_20_2
% 251.75/60.15 |
% 251.75/60.15 | GROUND_INST: instantiating (4) with all_34_2, e3, e0, e1, simplifying with
% 251.75/60.15 | (8), (26) gives:
% 251.75/60.15 | (31) all_34_2 = e3
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (16), (31) imply:
% 251.75/60.15 | (32) ~ (all_244_15 = e3)
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (1), (31) imply:
% 251.75/60.15 | (33) ~ (all_244_24 = e3)
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (17), (31) imply:
% 251.75/60.15 | (34) op(all_20_2, e3) = e1
% 251.75/60.15 |
% 251.75/60.15 | BETA: splitting (12) gives:
% 251.75/60.15 |
% 251.75/60.15 | Case 1:
% 251.75/60.15 | |
% 251.75/60.15 | | (35) ~ (all_58_2 = e3)
% 251.75/60.15 | |
% 251.75/60.15 | | REDUCE: (19), (35) imply:
% 251.75/60.15 | | (36) ~ (all_20_2 = e3)
% 251.75/60.15 | |
% 251.75/60.15 | | BETA: splitting (10) gives:
% 251.75/60.15 | |
% 251.75/60.15 | | Case 1:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (37) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1)
% 251.75/60.15 | | | = e3)
% 251.75/60.15 | | |
% 251.75/60.15 | | | BETA: splitting (37) gives:
% 251.75/60.15 | | |
% 251.75/60.15 | | | Case 1:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (38) all_252_9 = e3 & op(e4, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | ALPHA: (38) implies:
% 251.75/60.15 | | | | (39) op(e4, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (4), (21), (25), (39) are inconsistent by sub-proof #834.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | Case 2:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (40) all_252_10 = e3 & op(e3, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | ALPHA: (40) implies:
% 251.75/60.15 | | | | (41) op(e3, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | BETA: splitting (11) gives:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | Case 1:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | (42) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 251.75/60.15 | | | | | op(e0, e3) = e3)
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | BETA: splitting (42) gives:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | Case 1:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (43) all_252_20 = e3 & op(e0, e4) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | ALPHA: (43) implies:
% 251.75/60.15 | | | | | | (44) op(e0, e4) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REF_CLOSE: (4), (6), (29), (44) are inconsistent by sub-proof #981.
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | Case 2:
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | (45) all_252_21 = e3 & op(e0, e3) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | ALPHA: (45) implies:
% 251.75/60.15 | | | | | | (46) op(e0, e3) = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | GROUND_INST: instantiating (4) with all_22_2, e3, e3, e0,
% 251.75/60.15 | | | | | | simplifying with (18), (46) gives:
% 251.75/60.15 | | | | | | (47) all_22_2 = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | GROUND_INST: instantiating (4) with all_36_2, e3, e1, e3,
% 251.75/60.15 | | | | | | simplifying with (13), (41) gives:
% 251.75/60.15 | | | | | | (48) all_36_2 = e3
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REDUCE: (15), (47) imply:
% 251.75/60.15 | | | | | | (49) ~ (e3 = e1)
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | | REF_CLOSE: (2), (4), (20), (48), (49) are inconsistent by sub-proof
% 251.75/60.15 | | | | | | #745.
% 251.75/60.15 | | | | | |
% 251.75/60.15 | | | | | End of split
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | Case 2:
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | (50) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 251.75/60.15 | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | | REF_CLOSE: (3), (4), (5), (9), (24), (33), (36), (50) are inconsistent
% 251.75/60.15 | | | | | by sub-proof #743.
% 251.75/60.15 | | | | |
% 251.75/60.15 | | | | End of split
% 251.75/60.15 | | | |
% 251.75/60.15 | | | End of split
% 251.75/60.15 | | |
% 251.75/60.15 | | Case 2:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (51) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1,
% 251.75/60.15 | | | e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.15 | | |
% 251.75/60.15 | | | BETA: splitting (51) gives:
% 251.75/60.15 | | |
% 251.75/60.15 | | | Case 1:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (52) all_252_11 = e3 & op(e2, e1) = e3
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (14), (22), (52) are inconsistent by sub-proof #791.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | Case 2:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (53) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0,
% 251.75/60.15 | | | | e1) = e3)
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (4), (23), (24), (32), (36), (53) are inconsistent by
% 251.75/60.15 | | | | sub-proof #742.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | End of split
% 251.75/60.15 | | |
% 251.75/60.15 | | End of split
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (54) all_58_2 = e3
% 251.75/60.15 | |
% 251.75/60.15 | | COMBINE_EQS: (19), (54) imply:
% 251.75/60.15 | | (55) all_20_2 = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REDUCE: (34), (55) imply:
% 251.75/60.15 | | (56) op(e3, e3) = e1
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (4), (7), (28), (56) are inconsistent by sub-proof #801.
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #742 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (2) ~ (all_244_15 = e3)
% 251.75/60.15 (3) op(e1, e1) = all_244_15
% 251.75/60.15 (4) op(e0, e1) = all_20_2
% 251.75/60.15 (5) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.15 (6) ~ (all_20_2 = e3)
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | BETA: splitting (5) gives:
% 251.75/60.15 |
% 251.75/60.15 | Case 1:
% 251.75/60.15 | |
% 251.75/60.15 | | (7) all_252_15 = e3 & op(e1, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | ALPHA: (7) implies:
% 251.75/60.15 | | (8) op(e1, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #822.
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (9) all_252_23 = e3 & op(e0, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | ALPHA: (9) implies:
% 251.75/60.15 | | (10) op(e0, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #974.
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #743 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.75/60.15 | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.75/60.15 (2) ~ (all_28_2 = e3)
% 251.75/60.15 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (4) op(e0, e0) = all_244_24
% 251.75/60.15 (5) op(e0, e2) = all_28_2
% 251.75/60.15 (6) ~ (all_244_24 = e3)
% 251.75/60.15 (7) op(e0, e1) = all_20_2
% 251.75/60.15 (8) ~ (all_20_2 = e3)
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | BETA: splitting (1) gives:
% 251.75/60.15 |
% 251.75/60.15 | Case 1:
% 251.75/60.15 | |
% 251.75/60.15 | | (9) all_252_22 = e3 & op(e0, e2) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | ALPHA: (9) implies:
% 251.75/60.15 | | (10) op(e0, e2) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #975.
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (11) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0)
% 251.75/60.15 | | = e3)
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (3), (4), (6), (7), (8), (11) are inconsistent by sub-proof #744.
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #744 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (2) op(e0, e0) = all_244_24
% 251.75/60.15 (3) ~ (all_244_24 = e3)
% 251.75/60.15 (4) op(e0, e1) = all_20_2
% 251.75/60.15 (5) ~ (all_20_2 = e3)
% 251.75/60.15 (6) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | BETA: splitting (6) gives:
% 251.75/60.15 |
% 251.75/60.15 | Case 1:
% 251.75/60.15 | |
% 251.75/60.15 | | (7) all_252_23 = e3 & op(e0, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | ALPHA: (7) implies:
% 251.75/60.15 | | (8) op(e0, e1) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #974.
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (9) all_252_24 = e3 & op(e0, e0) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | ALPHA: (9) implies:
% 251.75/60.15 | | (10) op(e0, e0) = e3
% 251.75/60.15 | |
% 251.75/60.15 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #835.
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #745 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) op(all_62_2, all_36_2) = e3
% 251.75/60.15 (2) all_36_2 = e3
% 251.75/60.15 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (4) ~ (e3 = e1)
% 251.75/60.15 (5) op(all_62_2, e3) = e1
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (1), (2) imply:
% 251.75/60.15 | (6) op(all_62_2, e3) = e3
% 251.75/60.15 |
% 251.75/60.15 | GROUND_INST: instantiating (3) with e1, e3, e3, all_62_2, simplifying with
% 251.75/60.15 | (5), (6) gives:
% 251.75/60.15 | (7) e3 = e1
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (4), (7) imply:
% 251.75/60.15 | (8) $false
% 251.75/60.15 |
% 251.75/60.15 | CLOSE: (8) is inconsistent.
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #746 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) ~ (e1 = e0)
% 251.75/60.15 (2) op(e4, e1) = e2
% 251.75/60.15 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (4) all_252_15 = e3 & op(e1, e1) = e3
% 251.75/60.15 (5) ~ (e2 = e1)
% 251.75/60.15 (6) ~ (e4 = e1)
% 251.75/60.15 (7) ~ (e3 = e1)
% 251.75/60.15 (8) op(e3, e1) = all_36_2
% 251.75/60.15 (9) all_252_11 = e4
% 251.75/60.15 (10) op(e0, e1) = e3
% 251.75/60.15 (11) op(e3, e1) = e0
% 251.75/60.15 (12) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 251.75/60.15 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 251.75/60.15 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | ALPHA: (4) implies:
% 251.75/60.15 | (13) all_252_15 = e3
% 251.75/60.15 |
% 251.75/60.15 | BETA: splitting (12) gives:
% 251.75/60.15 |
% 251.75/60.15 | Case 1:
% 251.75/60.15 | |
% 251.75/60.15 | | (14) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.75/60.15 | | e1)
% 251.75/60.15 | |
% 251.75/60.15 | | BETA: splitting (14) gives:
% 251.75/60.15 | |
% 251.75/60.15 | | Case 1:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (15) all_252_9 = e1 & op(e4, e1) = e1
% 251.75/60.15 | | |
% 251.75/60.15 | | | ALPHA: (15) implies:
% 251.75/60.15 | | | (16) op(e4, e1) = e1
% 251.75/60.15 | | |
% 251.75/60.15 | | | REF_CLOSE: (2), (3), (5), (16) are inconsistent by sub-proof #785.
% 251.75/60.15 | | |
% 251.75/60.15 | | Case 2:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (17) all_252_10 = e1 & op(e3, e1) = e1
% 251.75/60.15 | | |
% 251.75/60.15 | | | ALPHA: (17) implies:
% 251.75/60.15 | | | (18) op(e3, e1) = e1
% 251.75/60.15 | | |
% 251.75/60.15 | | | REF_CLOSE: (1), (3), (8), (11), (18) are inconsistent by sub-proof #922.
% 251.75/60.15 | | |
% 251.75/60.15 | | End of split
% 251.75/60.15 | |
% 251.75/60.15 | Case 2:
% 251.75/60.15 | |
% 251.75/60.15 | | (19) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1)
% 251.75/60.15 | | = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 251.75/60.15 | |
% 251.75/60.15 | | BETA: splitting (19) gives:
% 251.75/60.15 | |
% 251.75/60.15 | | Case 1:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (20) all_252_11 = e1 & op(e2, e1) = e1
% 251.75/60.15 | | |
% 251.75/60.15 | | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #747.
% 251.75/60.15 | | |
% 251.75/60.15 | | Case 2:
% 251.75/60.15 | | |
% 251.75/60.15 | | | (21) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & op(e0,
% 251.75/60.15 | | | e1) = e1)
% 251.75/60.15 | | |
% 251.75/60.15 | | | BETA: splitting (21) gives:
% 251.75/60.15 | | |
% 251.75/60.15 | | | Case 1:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (22) all_252_15 = e1 & op(e1, e1) = e1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REF_CLOSE: (7), (13), (22) are inconsistent by sub-proof #752.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | Case 2:
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | (23) all_252_23 = e1 & op(e0, e1) = e1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | ALPHA: (23) implies:
% 251.75/60.15 | | | | (24) op(e0, e1) = e1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | GROUND_INST: instantiating (3) with e1, e3, e1, e0, simplifying with
% 251.75/60.15 | | | | (10), (24) gives:
% 251.75/60.15 | | | | (25) e3 = e1
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | REDUCE: (7), (25) imply:
% 251.75/60.15 | | | | (26) $false
% 251.75/60.15 | | | |
% 251.75/60.15 | | | | CLOSE: (26) is inconsistent.
% 251.75/60.15 | | | |
% 251.75/60.15 | | | End of split
% 251.75/60.15 | | |
% 251.75/60.15 | | End of split
% 251.75/60.15 | |
% 251.75/60.15 | End of split
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #747 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) all_252_11 = e1 & op(e2, e1) = e1
% 251.75/60.15 (2) all_252_11 = e4
% 251.75/60.15 (3) ~ (e4 = e1)
% 251.75/60.15
% 251.75/60.15 Begin of proof
% 251.75/60.15 |
% 251.75/60.15 | ALPHA: (1) implies:
% 251.75/60.15 | (4) all_252_11 = e1
% 251.75/60.15 |
% 251.75/60.15 | COMBINE_EQS: (2), (4) imply:
% 251.75/60.15 | (5) e4 = e1
% 251.75/60.15 |
% 251.75/60.15 | REDUCE: (3), (5) imply:
% 251.75/60.15 | (6) $false
% 251.75/60.15 |
% 251.75/60.15 | CLOSE: (6) is inconsistent.
% 251.75/60.15 |
% 251.75/60.15 End of proof
% 251.75/60.15
% 251.75/60.15 Sub-proof #748 shows that the following formulas are inconsistent:
% 251.75/60.15 ----------------------------------------------------------------
% 251.75/60.15 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.15 (2) op(e3, e1) = e3
% 251.75/60.15 (3) ~ (e3 = e0)
% 251.75/60.15 (4) op(e3, e1) = all_36_2
% 251.75/60.16 (5) op(e3, e1) = e0
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | GROUND_INST: instantiating (1) with all_36_2, e0, e1, e3, simplifying with
% 251.75/60.16 | (4), (5) gives:
% 251.75/60.16 | (6) all_36_2 = e0
% 251.75/60.16 |
% 251.75/60.16 | GROUND_INST: instantiating (1) with all_36_2, e3, e1, e3, simplifying with
% 251.75/60.16 | (2), (4) gives:
% 251.75/60.16 | (7) all_36_2 = e3
% 251.75/60.16 |
% 251.75/60.16 | COMBINE_EQS: (6), (7) imply:
% 251.75/60.16 | (8) e3 = e0
% 251.75/60.16 |
% 251.75/60.16 | REDUCE: (3), (8) imply:
% 251.75/60.16 | (9) $false
% 251.75/60.16 |
% 251.75/60.16 | CLOSE: (9) is inconsistent.
% 251.75/60.16 |
% 251.75/60.16 End of proof
% 251.75/60.16
% 251.75/60.16 Sub-proof #749 shows that the following formulas are inconsistent:
% 251.75/60.16 ----------------------------------------------------------------
% 251.75/60.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.16 (2) ~ (e4 = e0)
% 251.75/60.16 (3) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.75/60.16 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.75/60.16 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.75/60.16 (4) ~ (all_244_15 = e4)
% 251.75/60.16 (5) op(all_16_2, all_26_2) = e4
% 251.75/60.16 (6) ~ (all_84_2 = e4)
% 251.75/60.16 (7) ~ (all_36_2 = e4)
% 251.75/60.16 (8) op(e3, e1) = all_36_2
% 251.75/60.16 (9) op(e4, e1) = all_26_2
% 251.75/60.16 (10) op(e1, e1) = all_244_15
% 251.75/60.16 (11) op(e0, e1) = all_20_2
% 251.75/60.16 (12) all_252_11 = e0
% 251.75/60.16 (13) op(e4, e3) = all_84_2
% 251.75/60.16 (14) ~ (all_20_2 = e4)
% 251.75/60.16 (15) op(all_16_2, e4) = e1
% 251.75/60.16 (16) op(e4, e3) = e1
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | BETA: splitting (3) gives:
% 251.75/60.16 |
% 251.75/60.16 | Case 1:
% 251.75/60.16 | |
% 251.75/60.16 | | (17) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.75/60.16 | | e4)
% 251.75/60.16 | |
% 251.75/60.16 | | BETA: splitting (17) gives:
% 251.75/60.16 | |
% 251.75/60.16 | | Case 1:
% 251.75/60.16 | | |
% 251.75/60.16 | | | (18) all_252_9 = e4 & op(e4, e1) = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | ALPHA: (18) implies:
% 251.75/60.16 | | | (19) op(e4, e1) = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | GROUND_INST: instantiating (1) with all_26_2, e4, e1, e4, simplifying with
% 251.75/60.16 | | | (9), (19) gives:
% 251.75/60.16 | | | (20) all_26_2 = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | GROUND_INST: instantiating (1) with all_84_2, e1, e3, e4, simplifying with
% 251.75/60.16 | | | (13), (16) gives:
% 251.75/60.16 | | | (21) all_84_2 = e1
% 251.75/60.16 | | |
% 251.75/60.16 | | | REDUCE: (6), (21) imply:
% 251.75/60.16 | | | (22) ~ (e4 = e1)
% 251.75/60.16 | | |
% 251.75/60.16 | | | SIMP: (22) implies:
% 251.75/60.16 | | | (23) ~ (e4 = e1)
% 251.75/60.16 | | |
% 251.75/60.16 | | | REF_CLOSE: (1), (5), (15), (20), (23) are inconsistent by sub-proof #918.
% 251.75/60.16 | | |
% 251.75/60.16 | | Case 2:
% 251.75/60.16 | | |
% 251.75/60.16 | | | (24) all_252_10 = e4 & op(e3, e1) = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | REF_CLOSE: (1), (7), (8), (24) are inconsistent by sub-proof #914.
% 251.75/60.16 | | |
% 251.75/60.16 | | End of split
% 251.75/60.16 | |
% 251.75/60.16 | Case 2:
% 251.75/60.16 | |
% 251.75/60.16 | | (25) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 251.75/60.16 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.75/60.16 | |
% 251.75/60.16 | | BETA: splitting (25) gives:
% 251.75/60.16 | |
% 251.75/60.16 | | Case 1:
% 251.75/60.16 | | |
% 251.75/60.16 | | | (26) all_252_11 = e4 & op(e2, e1) = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | ALPHA: (26) implies:
% 251.75/60.16 | | | (27) all_252_11 = e4
% 251.75/60.16 | | |
% 251.75/60.16 | | | REF_CLOSE: (2), (12), (27) are inconsistent by sub-proof #766.
% 251.75/60.16 | | |
% 251.75/60.16 | | Case 2:
% 251.75/60.16 | | |
% 251.75/60.16 | | | (28) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0,
% 251.75/60.16 | | | e1) = e4)
% 251.75/60.16 | | |
% 251.75/60.16 | | | REF_CLOSE: (1), (4), (10), (11), (14), (28) are inconsistent by sub-proof
% 251.75/60.16 | | | #750.
% 251.75/60.16 | | |
% 251.75/60.16 | | End of split
% 251.75/60.16 | |
% 251.75/60.16 | End of split
% 251.75/60.16 |
% 251.75/60.16 End of proof
% 251.75/60.16
% 251.75/60.16 Sub-proof #750 shows that the following formulas are inconsistent:
% 251.75/60.16 ----------------------------------------------------------------
% 251.75/60.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.75/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.75/60.16 (2) ~ (all_244_15 = e4)
% 251.75/60.16 (3) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.75/60.16 (4) op(e1, e1) = all_244_15
% 251.75/60.16 (5) op(e0, e1) = all_20_2
% 251.75/60.16 (6) ~ (all_20_2 = e4)
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | BETA: splitting (3) gives:
% 251.75/60.16 |
% 251.75/60.16 | Case 1:
% 251.75/60.16 | |
% 251.75/60.16 | | (7) all_252_15 = e4 & op(e1, e1) = e4
% 251.75/60.16 | |
% 251.75/60.16 | | ALPHA: (7) implies:
% 251.75/60.16 | | (8) op(e1, e1) = e4
% 251.75/60.16 | |
% 251.75/60.16 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #756.
% 251.75/60.16 | |
% 251.75/60.16 | Case 2:
% 251.75/60.16 | |
% 251.75/60.16 | | (9) all_252_23 = e4 & op(e0, e1) = e4
% 251.75/60.16 | |
% 251.75/60.16 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #912.
% 251.75/60.16 | |
% 251.75/60.16 | End of split
% 251.75/60.16 |
% 251.75/60.16 End of proof
% 251.75/60.16
% 251.75/60.16 Sub-proof #751 shows that the following formulas are inconsistent:
% 251.75/60.16 ----------------------------------------------------------------
% 251.75/60.16 (1) all_252_14 = e0 & op(e1, e2) = e0
% 251.75/60.16 (2) all_252_14 = e2
% 251.75/60.16 (3) ~ (e2 = e0)
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | ALPHA: (1) implies:
% 251.75/60.16 | (4) all_252_14 = e0
% 251.75/60.16 |
% 251.75/60.16 | COMBINE_EQS: (2), (4) imply:
% 251.75/60.16 | (5) e2 = e0
% 251.75/60.16 |
% 251.75/60.16 | REDUCE: (3), (5) imply:
% 251.75/60.16 | (6) $false
% 251.75/60.16 |
% 251.75/60.16 | CLOSE: (6) is inconsistent.
% 251.75/60.16 |
% 251.75/60.16 End of proof
% 251.75/60.16
% 251.75/60.16 Sub-proof #752 shows that the following formulas are inconsistent:
% 251.75/60.16 ----------------------------------------------------------------
% 251.75/60.16 (1) all_252_15 = e1 & op(e1, e1) = e1
% 251.75/60.16 (2) all_252_15 = e3
% 251.75/60.16 (3) ~ (e3 = e1)
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | ALPHA: (1) implies:
% 251.75/60.16 | (4) all_252_15 = e1
% 251.75/60.16 |
% 251.75/60.16 | COMBINE_EQS: (2), (4) imply:
% 251.75/60.16 | (5) e3 = e1
% 251.75/60.16 |
% 251.75/60.16 | SIMP: (5) implies:
% 251.75/60.16 | (6) e3 = e1
% 251.75/60.16 |
% 251.75/60.16 | REDUCE: (3), (6) imply:
% 251.75/60.16 | (7) $false
% 251.75/60.16 |
% 251.75/60.16 | CLOSE: (7) is inconsistent.
% 251.75/60.16 |
% 251.75/60.16 End of proof
% 251.75/60.16
% 251.75/60.16 Sub-proof #753 shows that the following formulas are inconsistent:
% 251.75/60.16 ----------------------------------------------------------------
% 251.75/60.16 (1) all_252_14 = e1 & op(e1, e2) = e1
% 251.75/60.16 (2) all_252_14 = e2
% 251.75/60.16 (3) ~ (e2 = e1)
% 251.75/60.16
% 251.75/60.16 Begin of proof
% 251.75/60.16 |
% 251.75/60.16 | ALPHA: (1) implies:
% 251.75/60.16 | (4) all_252_14 = e1
% 251.75/60.16 |
% 251.75/60.16 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.16 | (5) e2 = e1
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (3), (5) imply:
% 251.89/60.16 | (6) $false
% 251.89/60.16 |
% 251.89/60.16 | CLOSE: (6) is inconsistent.
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #754 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) all_252_13 = e1 & op(e1, e3) = e1
% 251.89/60.16 (2) all_252_13 = e4
% 251.89/60.16 (3) ~ (e4 = e1)
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | ALPHA: (1) implies:
% 251.89/60.16 | (4) all_252_13 = e1
% 251.89/60.16 |
% 251.89/60.16 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.16 | (5) e4 = e1
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (3), (5) imply:
% 251.89/60.16 | (6) $false
% 251.89/60.16 |
% 251.89/60.16 | CLOSE: (6) is inconsistent.
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #755 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) ~ (all_10_2 = e4)
% 251.89/60.16 (2) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.89/60.16 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.16 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.16 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (4) op(e2, e3) = all_10_2
% 251.89/60.16 (5) ~ (all_244_3 = e4)
% 251.89/60.16 (6) ~ (all_84_2 = e4)
% 251.89/60.16 (7) ~ (all_22_2 = e4)
% 251.89/60.16 (8) all_252_13 = e3
% 251.89/60.16 (9) op(e0, e3) = all_22_2
% 251.89/60.16 (10) ~ (e4 = e3)
% 251.89/60.16 (11) op(e4, e3) = all_84_2
% 251.89/60.16 (12) op(e3, e3) = all_244_3
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | BETA: splitting (2) gives:
% 251.89/60.16 |
% 251.89/60.16 | Case 1:
% 251.89/60.16 | |
% 251.89/60.16 | | (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 251.89/60.16 | | e4)
% 251.89/60.16 | |
% 251.89/60.16 | | BETA: splitting (13) gives:
% 251.89/60.16 | |
% 251.89/60.16 | | Case 1:
% 251.89/60.16 | | |
% 251.89/60.16 | | | (14) all_252_1 = e4 & op(e4, e3) = e4
% 251.89/60.16 | | |
% 251.89/60.16 | | | REF_CLOSE: (3), (6), (11), (14) are inconsistent by sub-proof #815.
% 251.89/60.16 | | |
% 251.89/60.16 | | Case 2:
% 251.89/60.16 | | |
% 251.89/60.16 | | | (15) all_252_3 = e4 & op(e3, e3) = e4
% 251.89/60.16 | | |
% 251.89/60.16 | | | REF_CLOSE: (3), (5), (12), (15) are inconsistent by sub-proof #846.
% 251.89/60.16 | | |
% 251.89/60.16 | | End of split
% 251.89/60.16 | |
% 251.89/60.16 | Case 2:
% 251.89/60.16 | |
% 251.89/60.16 | | (16) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.89/60.16 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.16 | |
% 251.89/60.16 | | BETA: splitting (16) gives:
% 251.89/60.16 | |
% 251.89/60.16 | | Case 1:
% 251.89/60.16 | | |
% 251.89/60.16 | | | (17) all_252_7 = e4 & op(e2, e3) = e4
% 251.89/60.16 | | |
% 251.89/60.16 | | | ALPHA: (17) implies:
% 251.89/60.16 | | | (18) op(e2, e3) = e4
% 251.89/60.16 | | |
% 251.89/60.16 | | | REF_CLOSE: (1), (3), (4), (18) are inconsistent by sub-proof #953.
% 251.89/60.16 | | |
% 251.89/60.16 | | Case 2:
% 251.89/60.16 | | |
% 251.89/60.16 | | | (19) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 251.89/60.16 | | | e3) = e4)
% 251.89/60.16 | | |
% 251.89/60.16 | | | BETA: splitting (19) gives:
% 251.89/60.16 | | |
% 251.89/60.16 | | | Case 1:
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | (20) all_252_13 = e4 & op(e1, e3) = e4
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | ALPHA: (20) implies:
% 251.89/60.16 | | | | (21) all_252_13 = e4
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | COMBINE_EQS: (8), (21) imply:
% 251.89/60.16 | | | | (22) e4 = e3
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | REDUCE: (10), (22) imply:
% 251.89/60.16 | | | | (23) $false
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | CLOSE: (23) is inconsistent.
% 251.89/60.16 | | | |
% 251.89/60.16 | | | Case 2:
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | (24) all_252_21 = e4 & op(e0, e3) = e4
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | REF_CLOSE: (3), (7), (9), (24) are inconsistent by sub-proof #805.
% 251.89/60.16 | | | |
% 251.89/60.16 | | | End of split
% 251.89/60.16 | | |
% 251.89/60.16 | | End of split
% 251.89/60.16 | |
% 251.89/60.16 | End of split
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #756 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (2) op(e1, e1) = all_244_15
% 251.89/60.16 (3) op(e1, e1) = e4
% 251.89/60.16 (4) ~ (all_244_15 = e4)
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | GROUND_INST: instantiating (1) with all_244_15, e4, e1, e1, simplifying with
% 251.89/60.16 | (2), (3) gives:
% 251.89/60.16 | (5) all_244_15 = e4
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (4), (5) imply:
% 251.89/60.16 | (6) $false
% 251.89/60.16 |
% 251.89/60.16 | CLOSE: (6) is inconsistent.
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #757 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) all_252_12 = e4 & op(e1, e4) = e4
% 251.89/60.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (3) op(e1, e4) = all_16_2
% 251.89/60.16 (4) ~ (all_16_2 = e4)
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | ALPHA: (1) implies:
% 251.89/60.16 | (5) op(e1, e4) = e4
% 251.89/60.16 |
% 251.89/60.16 | GROUND_INST: instantiating (2) with all_16_2, e4, e4, e1, simplifying with
% 251.89/60.16 | (3), (5) gives:
% 251.89/60.16 | (6) all_16_2 = e4
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (4), (6) imply:
% 251.89/60.16 | (7) $false
% 251.89/60.16 |
% 251.89/60.16 | CLOSE: (7) is inconsistent.
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #758 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = e2)
% 251.89/60.16 | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.89/60.16 (2) op(all_6_2, e2) = e4
% 251.89/60.16 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (4) op(all_6_2, all_64_2) = e2
% 251.89/60.16 (5) op(e1, e4) = all_16_2
% 251.89/60.16 (6) ~ (all_12_2 = e2)
% 251.89/60.16 (7) ~ (all_16_2 = e2)
% 251.89/60.16 (8) op(e2, e4) = all_64_2
% 251.89/60.16 (9) ~ (all_64_2 = e4)
% 251.89/60.16 (10) op(e0, e4) = all_12_2
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | BETA: splitting (1) gives:
% 251.89/60.16 |
% 251.89/60.16 | Case 1:
% 251.89/60.16 | |
% 251.89/60.16 | | (11) all_252_6 = e2 & op(e2, e4) = e2
% 251.89/60.16 | |
% 251.89/60.16 | | ALPHA: (11) implies:
% 251.89/60.16 | | (12) op(e2, e4) = e2
% 251.89/60.16 | |
% 251.89/60.16 | | REF_CLOSE: (2), (3), (4), (8), (9), (12) are inconsistent by sub-proof #790.
% 251.89/60.16 | |
% 251.89/60.16 | Case 2:
% 251.89/60.16 | |
% 251.89/60.16 | | (13) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4)
% 251.89/60.16 | | = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REF_CLOSE: (3), (5), (6), (7), (10), (13) are inconsistent by sub-proof
% 251.89/60.16 | | #891.
% 251.89/60.16 | |
% 251.89/60.16 | End of split
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #759 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) ~ (all_28_2 = e3)
% 251.89/60.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (3) op(e0, e0) = all_244_24
% 251.89/60.16 (4) ~ (all_12_2 = e3)
% 251.89/60.16 (5) op(e0, e2) = all_28_2
% 251.89/60.16 (6) ~ (all_244_3 = all_84_2)
% 251.89/60.16 (7) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.16 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 251.89/60.16 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.16 (8) op(all_22_2, e3) = e0
% 251.89/60.16 (9) all_68_2 = all_22_2
% 251.89/60.16 (10) op(e0, e3) = all_22_2
% 251.89/60.16 (11) ~ (e4 = e3)
% 251.89/60.16 (12) op(e0, e1) = all_20_2
% 251.89/60.16 (13) op(e4, e3) = all_84_2
% 251.89/60.16 (14) ~ (all_20_2 = e3)
% 251.89/60.16 (15) all_68_2 = e4
% 251.89/60.16 (16) op(e3, e3) = all_244_3
% 251.89/60.16 (17) op(all_244_24, all_244_24) = e0
% 251.89/60.16 (18) op(e0, e4) = all_12_2
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | COMBINE_EQS: (9), (15) imply:
% 251.89/60.16 | (19) all_22_2 = e4
% 251.89/60.16 |
% 251.89/60.16 | SIMP: (19) implies:
% 251.89/60.16 | (20) all_22_2 = e4
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (8), (20) imply:
% 251.89/60.16 | (21) op(e4, e3) = e0
% 251.89/60.16 |
% 251.89/60.16 | REDUCE: (10), (20) imply:
% 251.89/60.16 | (22) op(e0, e3) = e4
% 251.89/60.16 |
% 251.89/60.16 | BETA: splitting (7) gives:
% 251.89/60.16 |
% 251.89/60.16 | Case 1:
% 251.89/60.16 | |
% 251.89/60.16 | | (23) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 251.89/60.16 | | = e3)
% 251.89/60.16 | |
% 251.89/60.16 | | REF_CLOSE: (2), (4), (11), (18), (22), (23) are inconsistent by sub-proof
% 251.89/60.16 | | #963.
% 251.89/60.16 | |
% 251.89/60.16 | Case 2:
% 251.89/60.16 | |
% 251.89/60.16 | | (24) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 251.89/60.16 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.16 | |
% 251.89/60.16 | | REF_CLOSE: (1), (2), (3), (5), (6), (12), (13), (14), (16), (17), (21), (24)
% 251.89/60.16 | | are inconsistent by sub-proof #961.
% 251.89/60.16 | |
% 251.89/60.16 | End of split
% 251.89/60.16 |
% 251.89/60.16 End of proof
% 251.89/60.16
% 251.89/60.16 Sub-proof #760 shows that the following formulas are inconsistent:
% 251.89/60.16 ----------------------------------------------------------------
% 251.89/60.16 (1) ~ (all_10_2 = e4)
% 251.89/60.16 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.89/60.16 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.89/60.16 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.89/60.16 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.89/60.16 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.16 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.16 (4) all_172_2 = all_10_2
% 251.89/60.16 (5) op(e3, e4) = e2
% 251.89/60.16 (6) ~ (e2 = e0)
% 251.89/60.16 (7) ~ (e1 = e0)
% 251.89/60.16 (8) op(e4, e1) = e2
% 251.89/60.16 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.16 (10) op(e2, e3) = all_10_2
% 251.89/60.16 (11) ~ (e3 = e2)
% 251.89/60.16 (12) ~ (all_10_2 = e3)
% 251.89/60.16 (13) ~ (e4 = e0)
% 251.89/60.16 (14) ~ (all_12_2 = e3)
% 251.89/60.16 (15) op(all_244_8, all_244_8) = e2
% 251.89/60.16 (16) op(e2, e2) = all_244_8
% 251.89/60.16 (17) ~ (all_36_2 = all_20_2)
% 251.89/60.16 (18) op(e1, e0) = all_34_2
% 251.89/60.16 (19) ~ (all_40_2 = e4)
% 251.89/60.16 (20) op(e4, e2) = all_6_2
% 251.89/60.16 (21) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.89/60.16 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.89/60.16 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.89/60.16 (22) ~ (all_34_2 = e2)
% 251.89/60.16 (23) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.89/60.16 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.89/60.16 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.89/60.16 (24) ~ (all_6_2 = e1)
% 251.89/60.16 (25) ~ (all_62_2 = all_34_2)
% 251.89/60.16 (26) op(all_34_2, e0) = e1
% 251.89/60.16 (27) op(e1, e4) = all_16_2
% 251.89/60.16 (28) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 251.89/60.16 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 251.89/60.16 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 251.89/60.16 (29) op(e1, e3) = all_62_2
% 251.89/60.16 (30) ~ (e3 = e0)
% 251.89/60.16 (31) ~ (all_22_2 = e4)
% 251.89/60.16 (32) all_70_2 = all_62_2
% 251.89/60.16 (33) op(e3, e1) = all_36_2
% 251.89/60.16 (34) ~ (all_16_2 = e2)
% 251.89/60.16 (35) all_252_11 = e4
% 251.89/60.16 (36) ~ (all_8_2 = e1)
% 251.89/60.16 (37) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.89/60.16 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.89/60.16 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.16 (38) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.16 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.16 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.16 (39) all_130_2 = all_62_2
% 251.89/60.16 (40) op(e4, all_4_2) = e1
% 251.89/60.16 (41) op(e0, e3) = all_22_2
% 251.89/60.16 (42) ~ (all_244_0 = all_100_2)
% 251.89/60.16 (43) op(all_34_2, all_20_2) = e0
% 251.89/60.16 (44) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.16 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.16 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.16 (45) op(all_62_2, e3) = e1
% 251.89/60.16 (46) ~ (all_130_2 = e2) | ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 &
% 251.89/60.16 op(e2, all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) | ( ~
% 251.89/60.16 (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 251.89/60.16 (47) op(e4, e1) = all_26_2
% 251.89/60.16 (48) op(all_10_2, e3) = e2
% 251.89/60.16 (49) ~ (all_244_15 = all_62_2)
% 251.89/60.16 (50) ~ (all_62_2 = all_16_2)
% 251.89/60.16 (51) op(e3, e4) = all_100_2
% 251.89/60.16 (52) op(e4, e4) = all_244_0
% 251.89/60.16 (53) ~ (e4 = e3)
% 251.89/60.16 (54) op(e1, e1) = all_244_15
% 251.89/60.16 (55) op(e0, e1) = all_20_2
% 251.89/60.16 (56) op(e3, e0) = all_48_2
% 251.89/60.16 (57) ~ (all_26_2 = e3)
% 251.89/60.16 (58) op(e1, e2) = all_4_2
% 251.89/60.16 (59) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.89/60.16 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.89/60.16 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.16 (60) all_252_2 = e2
% 251.89/60.16 (61) ~ (all_48_2 = e1)
% 251.89/60.16 (62) ~ (all_62_2 = all_10_2)
% 251.89/60.16 (63) ~ (all_244_15 = e2)
% 251.89/60.16 (64) op(e3, e2) = all_8_2
% 251.89/60.16 (65) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.16 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.16 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.16 (66) op(e2, e0) = all_40_2
% 251.89/60.16 (67) ~ (all_20_2 = e3)
% 251.89/60.16 (68) ~ (all_16_2 = e3)
% 251.89/60.16 (69) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.16 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.16 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.16 (70) ~ (all_244_0 = e3)
% 251.89/60.16 (71) ~ (all_62_2 = e4)
% 251.89/60.16 (72) ~ (all_62_2 = all_4_2)
% 251.89/60.16 (73) op(e0, e4) = all_12_2
% 251.89/60.16
% 251.89/60.16 Begin of proof
% 251.89/60.16 |
% 251.89/60.16 | BETA: splitting (38) gives:
% 251.89/60.16 |
% 251.89/60.16 | Case 1:
% 251.89/60.16 | |
% 251.89/60.16 | | (74) ~ (all_70_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (32), (74) imply:
% 251.89/60.16 | | (75) ~ (all_62_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REF_CLOSE: (9), (18), (20), (22), (24), (27), (29), (34), (40), (54), (58),
% 251.89/60.16 | | (63), (69), (75) are inconsistent by sub-proof #793.
% 251.89/60.16 | |
% 251.89/60.16 | Case 2:
% 251.89/60.16 | |
% 251.89/60.16 | | (76) all_70_2 = e2
% 251.89/60.16 | |
% 251.89/60.16 | | COMBINE_EQS: (32), (76) imply:
% 251.89/60.16 | | (77) all_62_2 = e2
% 251.89/60.16 | |
% 251.89/60.16 | | SIMP: (77) implies:
% 251.89/60.16 | | (78) all_62_2 = e2
% 251.89/60.16 | |
% 251.89/60.16 | | COMBINE_EQS: (39), (78) imply:
% 251.89/60.16 | | (79) all_130_2 = e2
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (25), (78) imply:
% 251.89/60.16 | | (80) ~ (all_34_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (50), (78) imply:
% 251.89/60.16 | | (81) ~ (all_16_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (62), (78) imply:
% 251.89/60.16 | | (82) ~ (all_10_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | SIMP: (82) implies:
% 251.89/60.16 | | (83) ~ (all_10_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (72), (78) imply:
% 251.89/60.16 | | (84) ~ (all_4_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | SIMP: (84) implies:
% 251.89/60.16 | | (85) ~ (all_4_2 = e2)
% 251.89/60.16 | |
% 251.89/60.16 | | REDUCE: (45), (78) imply:
% 251.89/60.16 | | (86) op(e2, e3) = e1
% 251.89/60.16 | |
% 251.89/60.16 | | BETA: splitting (69) gives:
% 251.89/60.16 | |
% 251.89/60.16 | | Case 1:
% 251.89/60.16 | | |
% 251.89/60.16 | | | (87) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 251.89/60.16 | | | e3) = e2)
% 251.89/60.16 | | |
% 251.89/60.16 | | | BETA: splitting (87) gives:
% 251.89/60.16 | | |
% 251.89/60.16 | | | Case 1:
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | (88) all_252_12 = e2 & op(e1, e4) = e2
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | REF_CLOSE: (9), (27), (34), (88) are inconsistent by sub-proof #926.
% 251.89/60.16 | | | |
% 251.89/60.16 | | | Case 2:
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | (89) all_252_13 = e2 & op(e1, e3) = e2
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | ALPHA: (89) implies:
% 251.89/60.16 | | | | (90) all_252_13 = e2
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | BETA: splitting (46) gives:
% 251.89/60.16 | | | |
% 251.89/60.16 | | | | Case 1:
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | (91) ~ (all_130_2 = e2)
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | REDUCE: (79), (91) imply:
% 251.89/60.16 | | | | | (92) $false
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | CLOSE: (92) is inconsistent.
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | Case 2:
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | (93) ( ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 & op(e2,
% 251.89/60.16 | | | | | all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)) |
% 251.89/60.16 | | | | | ( ~ (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1))
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | BETA: splitting (93) gives:
% 251.89/60.16 | | | | |
% 251.89/60.16 | | | | | Case 1:
% 251.89/60.16 | | | | | |
% 251.89/60.16 | | | | | | (94) ~ (all_130_0 = e4) & op(e3, e2) = all_130_1 & op(e2,
% 251.89/60.16 | | | | | | all_130_1) = all_130_0 & $i(all_130_0) & $i(all_130_1)
% 251.89/60.16 | | | | | |
% 251.89/60.16 | | | | | | ALPHA: (94) implies:
% 251.89/60.16 | | | | | | (95) op(e3, e2) = all_130_1
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.89/60.17 | | | | | | (12), (13), (14), (15), (16), (17), (19), (21), (23),
% 251.89/60.17 | | | | | | (26), (27), (28), (29), (30), (31), (33), (35), (36),
% 251.89/60.17 | | | | | | (37), (41), (42), (43), (44), (47), (48), (51), (52),
% 251.89/60.17 | | | | | | (53), (55), (56), (57), (59), (60), (61), (64), (65),
% 251.89/60.17 | | | | | | (66), (67), (68), (70), (71), (73), (83), (86), (90),
% 251.89/60.17 | | | | | | (95) are inconsistent by sub-proof #761.
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | Case 2:
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | (96) ~ (all_130_1 = e0) & op(e3, e2) = all_130_1 & $i(all_130_1)
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | ALPHA: (96) implies:
% 251.89/60.17 | | | | | | (97) op(e3, e2) = all_130_1
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 251.89/60.17 | | | | | | (12), (13), (14), (15), (16), (17), (19), (21), (23),
% 251.89/60.17 | | | | | | (26), (27), (28), (29), (30), (31), (33), (35), (36),
% 251.89/60.17 | | | | | | (37), (41), (42), (43), (44), (47), (48), (51), (52),
% 251.89/60.17 | | | | | | (53), (55), (56), (57), (59), (60), (61), (64), (65),
% 251.89/60.17 | | | | | | (66), (67), (68), (70), (71), (73), (83), (86), (90),
% 251.89/60.17 | | | | | | (97) are inconsistent by sub-proof #761.
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | End of split
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | End of split
% 251.89/60.17 | | | |
% 251.89/60.17 | | | End of split
% 251.89/60.17 | | |
% 251.89/60.17 | | Case 2:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (98) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.17 | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.17 | | |
% 251.89/60.17 | | | BETA: splitting (98) gives:
% 251.89/60.17 | | |
% 251.89/60.17 | | | Case 1:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (99) all_252_14 = e2 & op(e1, e2) = e2
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (9), (58), (85), (99) are inconsistent by sub-proof #820.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | Case 2:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (100) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.89/60.17 | | | | e0) = e2)
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (9), (18), (22), (54), (63), (100) are inconsistent by
% 251.89/60.17 | | | | sub-proof #819.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | End of split
% 251.89/60.17 | | |
% 251.89/60.17 | | End of split
% 251.89/60.17 | |
% 251.89/60.17 | End of split
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #761 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) ~ (all_10_2 = e4)
% 251.89/60.17 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.89/60.17 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.89/60.17 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.89/60.17 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.89/60.17 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.17 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.17 (4) all_172_2 = all_10_2
% 251.89/60.17 (5) op(e3, e4) = e2
% 251.89/60.17 (6) ~ (e2 = e0)
% 251.89/60.17 (7) ~ (e1 = e0)
% 251.89/60.17 (8) op(e4, e1) = e2
% 251.89/60.17 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.17 (10) op(e2, e3) = all_10_2
% 251.89/60.17 (11) ~ (e3 = e2)
% 251.89/60.17 (12) ~ (all_10_2 = e3)
% 251.89/60.17 (13) ~ (e4 = e0)
% 251.89/60.17 (14) ~ (all_12_2 = e3)
% 251.89/60.17 (15) op(all_244_8, all_244_8) = e2
% 251.89/60.17 (16) op(e2, e2) = all_244_8
% 251.89/60.17 (17) ~ (all_36_2 = all_20_2)
% 251.89/60.17 (18) ~ (all_40_2 = e4)
% 251.89/60.17 (19) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.89/60.17 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.89/60.17 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.89/60.17 (20) all_252_13 = e2
% 251.89/60.17 (21) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3)
% 251.89/60.17 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.89/60.17 e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.89/60.17 (22) op(all_34_2, e0) = e1
% 251.89/60.17 (23) op(e1, e4) = all_16_2
% 251.89/60.17 (24) ~ (all_172_2 = e1) | ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 &
% 251.89/60.17 op(e1, all_172_1) = all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~
% 251.89/60.17 (all_172_1 = e4) & op(e3, e1) = all_172_1 & $i(all_172_1))
% 251.89/60.17 (25) op(e1, e3) = all_62_2
% 251.89/60.17 (26) op(e3, e2) = all_130_1
% 251.89/60.17 (27) ~ (e3 = e0)
% 251.89/60.17 (28) op(e2, e3) = e1
% 251.89/60.17 (29) ~ (all_22_2 = e4)
% 251.89/60.17 (30) op(e3, e1) = all_36_2
% 251.89/60.17 (31) all_252_11 = e4
% 251.89/60.17 (32) ~ (all_8_2 = e1)
% 251.89/60.17 (33) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.89/60.17 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.89/60.17 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.17 (34) op(e0, e3) = all_22_2
% 251.89/60.17 (35) ~ (all_244_0 = all_100_2)
% 251.89/60.17 (36) op(all_34_2, all_20_2) = e0
% 251.89/60.17 (37) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.17 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.17 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.17 (38) op(e4, e1) = all_26_2
% 251.89/60.17 (39) op(all_10_2, e3) = e2
% 251.89/60.17 (40) op(e3, e4) = all_100_2
% 251.89/60.17 (41) op(e4, e4) = all_244_0
% 251.89/60.17 (42) ~ (e4 = e3)
% 251.89/60.17 (43) op(e0, e1) = all_20_2
% 251.89/60.17 (44) op(e3, e0) = all_48_2
% 251.89/60.17 (45) ~ (all_26_2 = e3)
% 251.89/60.17 (46) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.89/60.17 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.89/60.17 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.17 (47) all_252_2 = e2
% 251.89/60.17 (48) ~ (all_48_2 = e1)
% 251.89/60.17 (49) op(e3, e2) = all_8_2
% 251.89/60.17 (50) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.17 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.17 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.17 (51) op(e2, e0) = all_40_2
% 251.89/60.17 (52) ~ (all_20_2 = e3)
% 251.89/60.17 (53) ~ (all_16_2 = e3)
% 251.89/60.17 (54) ~ (all_244_0 = e3)
% 251.89/60.17 (55) ~ (all_62_2 = e4)
% 251.89/60.17 (56) op(e0, e4) = all_12_2
% 251.89/60.17 (57) ~ (all_10_2 = e2)
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | GROUND_INST: instantiating (9) with all_10_2, e1, e3, e2, simplifying with
% 251.89/60.17 | (10), (28) gives:
% 251.89/60.17 | (58) all_10_2 = e1
% 251.89/60.17 |
% 251.89/60.17 | GROUND_INST: instantiating (9) with all_8_2, all_130_1, e2, e3, simplifying
% 251.89/60.17 | with (26), (49) gives:
% 251.89/60.17 | (59) all_130_1 = all_8_2
% 251.89/60.17 |
% 251.89/60.17 | COMBINE_EQS: (4), (58) imply:
% 251.89/60.17 | (60) all_172_2 = e1
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (1), (58) imply:
% 251.89/60.17 | (61) ~ (e4 = e1)
% 251.89/60.17 |
% 251.89/60.17 | SIMP: (61) implies:
% 251.89/60.17 | (62) ~ (e4 = e1)
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (12), (58) imply:
% 251.89/60.17 | (63) ~ (e3 = e1)
% 251.89/60.17 |
% 251.89/60.17 | SIMP: (63) implies:
% 251.89/60.17 | (64) ~ (e3 = e1)
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (57), (58) imply:
% 251.89/60.17 | (65) ~ (e2 = e1)
% 251.89/60.17 |
% 251.89/60.17 | SIMP: (65) implies:
% 251.89/60.17 | (66) ~ (e2 = e1)
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (39), (58) imply:
% 251.89/60.17 | (67) op(e1, e3) = e2
% 251.89/60.17 |
% 251.89/60.17 | BETA: splitting (24) gives:
% 251.89/60.17 |
% 251.89/60.17 | Case 1:
% 251.89/60.17 | |
% 251.89/60.17 | | (68) ~ (all_172_2 = e1)
% 251.89/60.17 | |
% 251.89/60.17 | | REDUCE: (60), (68) imply:
% 251.89/60.17 | | (69) $false
% 251.89/60.17 | |
% 251.89/60.17 | | CLOSE: (69) is inconsistent.
% 251.89/60.17 | |
% 251.89/60.17 | Case 2:
% 251.89/60.17 | |
% 251.89/60.17 | | (70) ( ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1, all_172_1) =
% 251.89/60.17 | | all_172_0 & $i(all_172_0) & $i(all_172_1)) | ( ~ (all_172_1 = e4)
% 251.89/60.17 | | & op(e3, e1) = all_172_1 & $i(all_172_1))
% 251.89/60.17 | |
% 251.89/60.17 | | BETA: splitting (19) gives:
% 251.89/60.17 | |
% 251.89/60.17 | | Case 1:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (71) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3)
% 251.89/60.17 | | | = e1)
% 251.89/60.17 | | |
% 251.89/60.17 | | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (13), (20), (25), (27),
% 251.89/60.17 | | | (28), (29), (33), (34), (42), (46), (47), (55), (62), (64),
% 251.89/60.17 | | | (66), (67), (71) are inconsistent by sub-proof #770.
% 251.89/60.17 | | |
% 251.89/60.17 | | Case 2:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (72) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1)
% 251.89/60.17 | | | = e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.89/60.17 | | |
% 251.89/60.17 | | | BETA: splitting (72) gives:
% 251.89/60.17 | | |
% 251.89/60.17 | | | Case 1:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (73) all_252_5 = e1 & op(e3, e2) = e1
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | ALPHA: (73) implies:
% 251.89/60.17 | | | | (74) op(e3, e2) = e1
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (9), (32), (49), (74) are inconsistent by sub-proof #929.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | Case 2:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (75) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 251.89/60.17 | | | | e0) = e1)
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | BETA: splitting (75) gives:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | Case 1:
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | (76) all_252_10 = e1 & op(e3, e1) = e1
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | ALPHA: (76) implies:
% 251.89/60.17 | | | | | (77) all_252_10 = e1
% 251.89/60.17 | | | | | (78) op(e3, e1) = e1
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | BETA: splitting (21) gives:
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | Case 1:
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | (79) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 &
% 251.89/60.17 | | | | | | op(e3, e1) = e3)
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | BETA: splitting (79) gives:
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | Case 1:
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | (80) all_252_9 = e3 & op(e4, e1) = e3
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | ALPHA: (80) implies:
% 251.89/60.17 | | | | | | | (81) op(e4, e1) = e3
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | REF_CLOSE: (9), (38), (45), (81) are inconsistent by sub-proof
% 251.89/60.17 | | | | | | | #834.
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | Case 2:
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | (82) all_252_10 = e3 & op(e3, e1) = e3
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | REF_CLOSE: (64), (77), (82) are inconsistent by sub-proof #769.
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | End of split
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | Case 2:
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | (83) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 &
% 251.89/60.17 | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | BETA: splitting (83) gives:
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | | Case 1:
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | (84) all_252_11 = e3 & op(e2, e1) = e3
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | REF_CLOSE: (31), (42), (84) are inconsistent by sub-proof #768.
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | Case 2:
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | (85) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 &
% 251.89/60.17 | | | | | | | op(e0, e1) = e3)
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | BETA: splitting (85) gives:
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | | Case 1:
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | (86) all_252_15 = e3 & op(e1, e1) = e3
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | ALPHA: (86) implies:
% 251.89/60.17 | | | | | | | | (87) all_252_15 = e3
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | BETA: splitting (70) gives:
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | Case 1:
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | (88) ~ (all_172_0 = e0) & op(e3, e1) = all_172_1 & op(e1,
% 251.89/60.17 | | | | | | | | | all_172_1) = all_172_0 & $i(all_172_0) &
% 251.89/60.17 | | | | | | | | | $i(all_172_1)
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | ALPHA: (88) implies:
% 251.89/60.17 | | | | | | | | | (89) op(e3, e1) = all_172_1
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11),
% 251.89/60.17 | | | | | | | | | (13), (14), (15), (16), (17), (18), (22), (23),
% 251.89/60.17 | | | | | | | | | (27), (30), (35), (36), (37), (40), (41), (42),
% 251.89/60.17 | | | | | | | | | (43), (50), (51), (53), (54), (56), (76), (78),
% 251.89/60.17 | | | | | | | | | (87), (89) are inconsistent by sub-proof #762.
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | Case 2:
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | (90) ~ (all_172_1 = e4) & op(e3, e1) = all_172_1 &
% 251.89/60.17 | | | | | | | | | $i(all_172_1)
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | ALPHA: (90) implies:
% 251.89/60.17 | | | | | | | | | (91) op(e3, e1) = all_172_1
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11),
% 251.89/60.17 | | | | | | | | | (13), (14), (15), (16), (17), (18), (22), (23),
% 251.89/60.17 | | | | | | | | | (27), (30), (35), (36), (37), (40), (41), (42),
% 251.89/60.17 | | | | | | | | | (43), (50), (51), (53), (54), (56), (76), (78),
% 251.89/60.17 | | | | | | | | | (87), (91) are inconsistent by sub-proof #762.
% 251.89/60.17 | | | | | | | | |
% 251.89/60.17 | | | | | | | | End of split
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | Case 2:
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | (92) all_252_23 = e3 & op(e0, e1) = e3
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | ALPHA: (92) implies:
% 251.89/60.17 | | | | | | | | (93) op(e0, e1) = e3
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | | REF_CLOSE: (9), (43), (52), (93) are inconsistent by sub-proof
% 251.89/60.17 | | | | | | | | #974.
% 251.89/60.17 | | | | | | | |
% 251.89/60.17 | | | | | | | End of split
% 251.89/60.17 | | | | | | |
% 251.89/60.17 | | | | | | End of split
% 251.89/60.17 | | | | | |
% 251.89/60.17 | | | | | End of split
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | Case 2:
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | (94) all_252_17 = e1 & op(e3, e0) = e1
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | ALPHA: (94) implies:
% 251.89/60.17 | | | | | (95) op(e3, e0) = e1
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | REF_CLOSE: (9), (44), (48), (95) are inconsistent by sub-proof #889.
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | End of split
% 251.89/60.17 | | | |
% 251.89/60.17 | | | End of split
% 251.89/60.17 | | |
% 251.89/60.17 | | End of split
% 251.89/60.17 | |
% 251.89/60.17 | End of split
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #762 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) ~ (all_10_2 = e4)
% 251.89/60.17 (2) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0)
% 251.89/60.17 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) =
% 251.89/60.17 e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.89/60.17 (3) op(e3, e4) = e2
% 251.89/60.17 (4) ~ (e2 = e0)
% 251.89/60.17 (5) ~ (e1 = e0)
% 251.89/60.17 (6) op(e4, e1) = e2
% 251.89/60.17 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.17 (8) op(e2, e3) = all_10_2
% 251.89/60.17 (9) ~ (e3 = e2)
% 251.89/60.17 (10) ~ (e4 = e0)
% 251.89/60.17 (11) ~ (all_12_2 = e3)
% 251.89/60.17 (12) op(all_244_8, all_244_8) = e2
% 251.89/60.17 (13) op(e2, e2) = all_244_8
% 251.89/60.17 (14) ~ (all_36_2 = all_20_2)
% 251.89/60.17 (15) ~ (all_40_2 = e4)
% 251.89/60.17 (16) all_252_10 = e1 & op(e3, e1) = e1
% 251.89/60.17 (17) op(all_34_2, e0) = e1
% 251.89/60.17 (18) op(e1, e4) = all_16_2
% 251.89/60.17 (19) ~ (e3 = e0)
% 251.89/60.17 (20) op(e3, e1) = all_36_2
% 251.89/60.17 (21) op(e3, e1) = all_172_1
% 251.89/60.17 (22) op(e3, e1) = e1
% 251.89/60.17 (23) ~ (all_244_0 = all_100_2)
% 251.89/60.17 (24) op(all_34_2, all_20_2) = e0
% 251.89/60.17 (25) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.17 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.17 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.17 (26) op(e3, e4) = all_100_2
% 251.89/60.17 (27) op(e4, e4) = all_244_0
% 251.89/60.17 (28) ~ (e4 = e3)
% 251.89/60.17 (29) op(e0, e1) = all_20_2
% 251.89/60.17 (30) all_252_15 = e3
% 251.89/60.17 (31) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.17 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.17 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.17 (32) op(e2, e0) = all_40_2
% 251.89/60.17 (33) ~ (all_16_2 = e3)
% 251.89/60.17 (34) ~ (all_244_0 = e3)
% 251.89/60.17 (35) op(e0, e4) = all_12_2
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | BETA: splitting (2) gives:
% 251.89/60.17 |
% 251.89/60.17 | Case 1:
% 251.89/60.17 | |
% 251.89/60.17 | | (36) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) =
% 251.89/60.17 | | e0)
% 251.89/60.17 | |
% 251.89/60.17 | | BETA: splitting (36) gives:
% 251.89/60.17 | |
% 251.89/60.17 | | Case 1:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (37) all_252_9 = e0 & op(e4, e1) = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | ALPHA: (37) implies:
% 251.89/60.17 | | | (38) op(e4, e1) = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | REF_CLOSE: (4), (6), (7), (38) are inconsistent by sub-proof #767.
% 251.89/60.17 | | |
% 251.89/60.17 | | Case 2:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (39) all_252_10 = e0 & op(e3, e1) = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | ALPHA: (39) implies:
% 251.89/60.17 | | | (40) op(e3, e1) = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | REF_CLOSE: (5), (7), (20), (22), (40) are inconsistent by sub-proof #922.
% 251.89/60.17 | | |
% 251.89/60.17 | | End of split
% 251.89/60.17 | |
% 251.89/60.17 | Case 2:
% 251.89/60.17 | |
% 251.89/60.17 | | (41) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1)
% 251.89/60.17 | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0)
% 251.89/60.17 | |
% 251.89/60.17 | | BETA: splitting (41) gives:
% 251.89/60.17 | |
% 251.89/60.17 | | Case 1:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (42) all_252_11 = e0 & op(e2, e1) = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | ALPHA: (42) implies:
% 251.89/60.17 | | | (43) all_252_11 = e0
% 251.89/60.17 | | |
% 251.89/60.17 | | | REF_CLOSE: (1), (3), (7), (8), (9), (10), (11), (12), (13), (15), (18),
% 251.89/60.17 | | | (23), (25), (26), (27), (28), (31), (32), (33), (34), (35),
% 251.89/60.17 | | | (43) are inconsistent by sub-proof #764.
% 251.89/60.17 | | |
% 251.89/60.17 | | Case 2:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (44) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0,
% 251.89/60.17 | | | e1) = e0)
% 251.89/60.17 | | |
% 251.89/60.17 | | | BETA: splitting (44) gives:
% 251.89/60.17 | | |
% 251.89/60.17 | | | Case 1:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (45) all_252_15 = e0 & op(e1, e1) = e0
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (19), (30), (45) are inconsistent by sub-proof #763.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | Case 2:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (46) all_252_23 = e0 & op(e0, e1) = e0
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | ALPHA: (46) implies:
% 251.89/60.17 | | | | (47) op(e0, e1) = e0
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | GROUND_INST: instantiating (7) with all_20_2, e0, e1, e0, simplifying
% 251.89/60.17 | | | | with (29), (47) gives:
% 251.89/60.17 | | | | (48) all_20_2 = e0
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | GROUND_INST: instantiating (7) with all_36_2, all_172_1, e1, e3,
% 251.89/60.17 | | | | simplifying with (20), (21) gives:
% 251.89/60.17 | | | | (49) all_172_1 = all_36_2
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | GROUND_INST: instantiating (7) with e1, all_172_1, e1, e3, simplifying
% 251.89/60.17 | | | | with (21), (22) gives:
% 251.89/60.17 | | | | (50) all_172_1 = e1
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | COMBINE_EQS: (49), (50) imply:
% 251.89/60.17 | | | | (51) all_36_2 = e1
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (5), (7), (17), (24), (48) are inconsistent by sub-proof
% 251.89/60.17 | | | | #781.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | End of split
% 251.89/60.17 | | |
% 251.89/60.17 | | End of split
% 251.89/60.17 | |
% 251.89/60.17 | End of split
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #763 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) all_252_15 = e0 & op(e1, e1) = e0
% 251.89/60.17 (2) all_252_15 = e3
% 251.89/60.17 (3) ~ (e3 = e0)
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | ALPHA: (1) implies:
% 251.89/60.17 | (4) all_252_15 = e0
% 251.89/60.17 |
% 251.89/60.17 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.17 | (5) e3 = e0
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (3), (5) imply:
% 251.89/60.17 | (6) $false
% 251.89/60.17 |
% 251.89/60.17 | CLOSE: (6) is inconsistent.
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #764 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) ~ (all_10_2 = e4)
% 251.89/60.17 (2) op(e3, e4) = e2
% 251.89/60.17 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.17 (4) op(e2, e3) = all_10_2
% 251.89/60.17 (5) ~ (e3 = e2)
% 251.89/60.17 (6) ~ (e4 = e0)
% 251.89/60.17 (7) ~ (all_12_2 = e3)
% 251.89/60.17 (8) op(all_244_8, all_244_8) = e2
% 251.89/60.17 (9) op(e2, e2) = all_244_8
% 251.89/60.17 (10) ~ (all_40_2 = e4)
% 251.89/60.17 (11) op(e1, e4) = all_16_2
% 251.89/60.17 (12) ~ (all_244_0 = all_100_2)
% 251.89/60.17 (13) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.17 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.17 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.17 (14) op(e3, e4) = all_100_2
% 251.89/60.17 (15) op(e4, e4) = all_244_0
% 251.89/60.17 (16) ~ (e4 = e3)
% 251.89/60.17 (17) all_252_11 = e0
% 251.89/60.17 (18) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.17 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.17 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.17 (19) op(e2, e0) = all_40_2
% 251.89/60.17 (20) ~ (all_16_2 = e3)
% 251.89/60.17 (21) ~ (all_244_0 = e3)
% 251.89/60.17 (22) op(e0, e4) = all_12_2
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | BETA: splitting (18) gives:
% 251.89/60.17 |
% 251.89/60.17 | Case 1:
% 251.89/60.17 | |
% 251.89/60.17 | | (23) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 251.89/60.17 | | e3)
% 251.89/60.17 | |
% 251.89/60.17 | | REF_CLOSE: (2), (3), (5), (14), (15), (21), (23) are inconsistent by
% 251.89/60.17 | | sub-proof #812.
% 251.89/60.17 | |
% 251.89/60.17 | Case 2:
% 251.89/60.17 | |
% 251.89/60.17 | | (24) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.17 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.17 | |
% 251.89/60.17 | | BETA: splitting (24) gives:
% 251.89/60.17 | |
% 251.89/60.17 | | Case 1:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (25) all_252_6 = e3 & op(e2, e4) = e3
% 251.89/60.17 | | |
% 251.89/60.17 | | | ALPHA: (25) implies:
% 251.89/60.17 | | | (26) all_252_6 = e3
% 251.89/60.17 | | |
% 251.89/60.17 | | | BETA: splitting (13) gives:
% 251.89/60.17 | | |
% 251.89/60.17 | | | Case 1:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (27) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 251.89/60.17 | | | | e3) = e4)
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | REF_CLOSE: (1), (3), (4), (16), (26), (27) are inconsistent by sub-proof
% 251.89/60.17 | | | | #810.
% 251.89/60.17 | | | |
% 251.89/60.17 | | | Case 2:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | (28) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2,
% 251.89/60.17 | | | | e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | BETA: splitting (28) gives:
% 251.89/60.17 | | | |
% 251.89/60.17 | | | | Case 1:
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | (29) all_252_8 = e4 & op(e2, e2) = e4
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | REF_CLOSE: (2), (3), (8), (9), (12), (14), (15), (29) are inconsistent
% 251.89/60.17 | | | | | by sub-proof #808.
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | Case 2:
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | (30) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 251.89/60.17 | | | | | op(e2, e0) = e4)
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | | REF_CLOSE: (3), (6), (10), (17), (19), (30) are inconsistent by
% 251.89/60.17 | | | | | sub-proof #765.
% 251.89/60.17 | | | | |
% 251.89/60.17 | | | | End of split
% 251.89/60.17 | | | |
% 251.89/60.17 | | | End of split
% 251.89/60.17 | | |
% 251.89/60.17 | | Case 2:
% 251.89/60.17 | | |
% 251.89/60.17 | | | (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 251.89/60.17 | | | e4) = e3)
% 251.89/60.17 | | |
% 251.89/60.17 | | | REF_CLOSE: (3), (7), (11), (20), (22), (31) are inconsistent by sub-proof
% 251.89/60.17 | | | #894.
% 251.89/60.17 | | |
% 251.89/60.17 | | End of split
% 251.89/60.17 | |
% 251.89/60.17 | End of split
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #765 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.17 (2) ~ (e4 = e0)
% 251.89/60.17 (3) ~ (all_40_2 = e4)
% 251.89/60.17 (4) all_252_11 = e0
% 251.89/60.17 (5) op(e2, e0) = all_40_2
% 251.89/60.17 (6) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | BETA: splitting (6) gives:
% 251.89/60.17 |
% 251.89/60.17 | Case 1:
% 251.89/60.17 | |
% 251.89/60.17 | | (7) all_252_11 = e4 & op(e2, e1) = e4
% 251.89/60.17 | |
% 251.89/60.17 | | ALPHA: (7) implies:
% 251.89/60.17 | | (8) all_252_11 = e4
% 251.89/60.17 | |
% 251.89/60.17 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #766.
% 251.89/60.17 | |
% 251.89/60.17 | Case 2:
% 251.89/60.17 | |
% 251.89/60.17 | | (9) all_252_18 = e4 & op(e2, e0) = e4
% 251.89/60.17 | |
% 251.89/60.17 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #934.
% 251.89/60.17 | |
% 251.89/60.17 | End of split
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #766 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.17 (1) all_252_11 = e4
% 251.89/60.17 (2) all_252_11 = e0
% 251.89/60.17 (3) ~ (e4 = e0)
% 251.89/60.17
% 251.89/60.17 Begin of proof
% 251.89/60.17 |
% 251.89/60.17 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.17 | (4) e4 = e0
% 251.89/60.17 |
% 251.89/60.17 | SIMP: (4) implies:
% 251.89/60.17 | (5) e4 = e0
% 251.89/60.17 |
% 251.89/60.17 | REDUCE: (3), (5) imply:
% 251.89/60.17 | (6) $false
% 251.89/60.17 |
% 251.89/60.17 | CLOSE: (6) is inconsistent.
% 251.89/60.17 |
% 251.89/60.17 End of proof
% 251.89/60.17
% 251.89/60.17 Sub-proof #767 shows that the following formulas are inconsistent:
% 251.89/60.17 ----------------------------------------------------------------
% 251.89/60.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (2) op(e4, e1) = e2
% 251.89/60.18 (3) op(e4, e1) = e0
% 251.89/60.18 (4) ~ (e2 = e0)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | GROUND_INST: instantiating (1) with e2, e0, e1, e4, simplifying with (2), (3)
% 251.89/60.18 | gives:
% 251.89/60.18 | (5) e2 = e0
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (4), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #768 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_11 = e3 & op(e2, e1) = e3
% 251.89/60.18 (2) all_252_11 = e4
% 251.89/60.18 (3) ~ (e4 = e3)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_11 = e3
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e4 = e3
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (5) implies:
% 251.89/60.18 | (6) e4 = e3
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (6) imply:
% 251.89/60.18 | (7) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (7) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #769 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_10 = e3 & op(e3, e1) = e3
% 251.89/60.18 (2) all_252_10 = e1
% 251.89/60.18 (3) ~ (e3 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_10 = e3
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e3 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #770 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) ~ (all_10_2 = e4)
% 251.89/60.18 (2) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.89/60.18 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.18 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.18 (3) ~ (e2 = e0)
% 251.89/60.18 (4) ~ (e1 = e0)
% 251.89/60.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (6) op(e2, e3) = all_10_2
% 251.89/60.18 (7) ~ (e3 = e2)
% 251.89/60.18 (8) ~ (e4 = e0)
% 251.89/60.18 (9) ~ (e2 = e1)
% 251.89/60.18 (10) all_252_13 = e2
% 251.89/60.18 (11) ~ (e4 = e1)
% 251.89/60.18 (12) op(e1, e3) = all_62_2
% 251.89/60.18 (13) ~ (e3 = e0)
% 251.89/60.18 (14) op(e2, e3) = e1
% 251.89/60.18 (15) ~ (all_22_2 = e4)
% 251.89/60.18 (16) ~ (e3 = e1)
% 251.89/60.18 (17) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.89/60.18 (18) op(e1, e3) = e2
% 251.89/60.18 (19) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.89/60.18 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.89/60.18 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.18 (20) op(e0, e3) = all_22_2
% 251.89/60.18 (21) ~ (e4 = e3)
% 251.89/60.18 (22) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.89/60.18 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.89/60.18 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.18 (23) all_252_2 = e2
% 251.89/60.18 (24) ~ (all_62_2 = e4)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | BETA: splitting (17) gives:
% 251.89/60.18 |
% 251.89/60.18 | Case 1:
% 251.89/60.18 | |
% 251.89/60.18 | | (25) all_252_2 = e1 & op(e3, e4) = e1
% 251.89/60.18 | |
% 251.89/60.18 | | REF_CLOSE: (9), (23), (25) are inconsistent by sub-proof #778.
% 251.89/60.18 | |
% 251.89/60.18 | Case 2:
% 251.89/60.18 | |
% 251.89/60.18 | | (26) all_252_3 = e1 & op(e3, e3) = e1
% 251.89/60.18 | |
% 251.89/60.18 | | ALPHA: (26) implies:
% 251.89/60.18 | | (27) all_252_3 = e1
% 251.89/60.18 | |
% 251.89/60.18 | | BETA: splitting (2) gives:
% 251.89/60.18 | |
% 251.89/60.18 | | Case 1:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (28) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3)
% 251.89/60.18 | | | = e4)
% 251.89/60.18 | | |
% 251.89/60.18 | | | BETA: splitting (28) gives:
% 251.89/60.18 | | |
% 251.89/60.18 | | | Case 1:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | (29) all_252_1 = e4 & op(e4, e3) = e4
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | ALPHA: (29) implies:
% 251.89/60.18 | | | | (30) all_252_1 = e4
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | BETA: splitting (19) gives:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | Case 1:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | (31) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 251.89/60.18 | | | | | e3) = e0)
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | BETA: splitting (31) gives:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | Case 1:
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | (32) all_252_1 = e0 & op(e4, e3) = e0
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | REF_CLOSE: (8), (30), (32) are inconsistent by sub-proof #947.
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | Case 2:
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | (33) all_252_3 = e0 & op(e3, e3) = e0
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | REF_CLOSE: (4), (27), (33) are inconsistent by sub-proof #777.
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | End of split
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | Case 2:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | (34) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1,
% 251.89/60.18 | | | | | e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | BETA: splitting (34) gives:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | Case 1:
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | (35) all_252_7 = e0 & op(e2, e3) = e0
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | ALPHA: (35) implies:
% 251.89/60.18 | | | | | | (36) op(e2, e3) = e0
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | GROUND_INST: instantiating (5) with e1, e0, e3, e2, simplifying with
% 251.89/60.18 | | | | | | (14), (36) gives:
% 251.89/60.18 | | | | | | (37) e1 = e0
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | REDUCE: (4), (37) imply:
% 251.89/60.18 | | | | | | (38) $false
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | CLOSE: (38) is inconsistent.
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | Case 2:
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | (39) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.89/60.18 | | | | | | op(e0, e3) = e0)
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | BETA: splitting (39) gives:
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | | Case 1:
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | (40) all_252_13 = e0 & op(e1, e3) = e0
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | ALPHA: (40) implies:
% 251.89/60.18 | | | | | | | (41) op(e1, e3) = e0
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | REF_CLOSE: (3), (5), (18), (41) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | #776.
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | Case 2:
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | (42) all_252_21 = e0 & op(e0, e3) = e0
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | ALPHA: (42) implies:
% 251.89/60.18 | | | | | | | (43) all_252_21 = e0
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | BETA: splitting (22) gives:
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | | Case 1:
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | (44) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 &
% 251.89/60.18 | | | | | | | | op(e3, e3) = e3)
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | BETA: splitting (44) gives:
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | Case 1:
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | (45) all_252_1 = e3 & op(e4, e3) = e3
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | REF_CLOSE: (21), (30), (45) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | | | #946.
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | Case 2:
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | (46) all_252_3 = e3 & op(e3, e3) = e3
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | REF_CLOSE: (16), (27), (46) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | | | #775.
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | End of split
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | Case 2:
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | (47) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 &
% 251.89/60.18 | | | | | | | | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | BETA: splitting (47) gives:
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | | Case 1:
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | (48) all_252_7 = e3 & op(e2, e3) = e3
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | ALPHA: (48) implies:
% 251.89/60.18 | | | | | | | | | (49) op(e2, e3) = e3
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | REF_CLOSE: (5), (14), (16), (49) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | | | #881.
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | Case 2:
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | (50) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3
% 251.89/60.18 | | | | | | | | | & op(e0, e3) = e3)
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | BETA: splitting (50) gives:
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | | Case 1:
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | | (51) all_252_13 = e3 & op(e1, e3) = e3
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | | REF_CLOSE: (7), (10), (51) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | | | | #774.
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | Case 2:
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | | (52) all_252_21 = e3 & op(e0, e3) = e3
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | | ALPHA: (52) implies:
% 251.89/60.18 | | | | | | | | | | (53) all_252_21 = e3
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | | REF_CLOSE: (13), (43), (53) are inconsistent by sub-proof
% 251.89/60.18 | | | | | | | | | | #773.
% 251.89/60.18 | | | | | | | | | |
% 251.89/60.18 | | | | | | | | | End of split
% 251.89/60.18 | | | | | | | | |
% 251.89/60.18 | | | | | | | | End of split
% 251.89/60.18 | | | | | | | |
% 251.89/60.18 | | | | | | | End of split
% 251.89/60.18 | | | | | | |
% 251.89/60.18 | | | | | | End of split
% 251.89/60.18 | | | | | |
% 251.89/60.18 | | | | | End of split
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | End of split
% 251.89/60.18 | | | |
% 251.89/60.18 | | | Case 2:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | (54) all_252_3 = e4 & op(e3, e3) = e4
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | ALPHA: (54) implies:
% 251.89/60.18 | | | | (55) all_252_3 = e4
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | REF_CLOSE: (11), (27), (55) are inconsistent by sub-proof #772.
% 251.89/60.18 | | | |
% 251.89/60.18 | | | End of split
% 251.89/60.18 | | |
% 251.89/60.18 | | Case 2:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (56) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3)
% 251.89/60.18 | | | = e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.18 | | |
% 251.89/60.18 | | | REF_CLOSE: (1), (5), (6), (12), (15), (20), (24), (56) are inconsistent by
% 251.89/60.18 | | | sub-proof #771.
% 251.89/60.18 | | |
% 251.89/60.18 | | End of split
% 251.89/60.18 | |
% 251.89/60.18 | End of split
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #771 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) ~ (all_10_2 = e4)
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) op(e2, e3) = all_10_2
% 251.89/60.18 (4) op(e1, e3) = all_62_2
% 251.89/60.18 (5) ~ (all_22_2 = e4)
% 251.89/60.18 (6) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.18 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.18 (7) op(e0, e3) = all_22_2
% 251.89/60.18 (8) ~ (all_62_2 = e4)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | BETA: splitting (6) gives:
% 251.89/60.18 |
% 251.89/60.18 | Case 1:
% 251.89/60.18 | |
% 251.89/60.18 | | (9) all_252_7 = e4 & op(e2, e3) = e4
% 251.89/60.18 | |
% 251.89/60.18 | | ALPHA: (9) implies:
% 251.89/60.18 | | (10) op(e2, e3) = e4
% 251.89/60.18 | |
% 251.89/60.18 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #953.
% 251.89/60.18 | |
% 251.89/60.18 | Case 2:
% 251.89/60.18 | |
% 251.89/60.18 | | (11) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 251.89/60.18 | | = e4)
% 251.89/60.18 | |
% 251.89/60.18 | | BETA: splitting (11) gives:
% 251.89/60.18 | |
% 251.89/60.18 | | Case 1:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (12) all_252_13 = e4 & op(e1, e3) = e4
% 251.89/60.18 | | |
% 251.89/60.18 | | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #952.
% 251.89/60.18 | | |
% 251.89/60.18 | | Case 2:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (13) all_252_21 = e4 & op(e0, e3) = e4
% 251.89/60.18 | | |
% 251.89/60.18 | | | REF_CLOSE: (2), (5), (7), (13) are inconsistent by sub-proof #805.
% 251.89/60.18 | | |
% 251.89/60.18 | | End of split
% 251.89/60.18 | |
% 251.89/60.18 | End of split
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #772 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_3 = e4
% 251.89/60.18 (2) all_252_3 = e1
% 251.89/60.18 (3) ~ (e4 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) e4 = e1
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) e4 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #773 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_21 = e3
% 251.89/60.18 (2) all_252_21 = e0
% 251.89/60.18 (3) ~ (e3 = e0)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) e3 = e0
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) e3 = e0
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #774 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_13 = e3 & op(e1, e3) = e3
% 251.89/60.18 (2) all_252_13 = e2
% 251.89/60.18 (3) ~ (e3 = e2)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_13 = e3
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e3 = e2
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (5) implies:
% 251.89/60.18 | (6) e3 = e2
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (6) imply:
% 251.89/60.18 | (7) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (7) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #775 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_3 = e3 & op(e3, e3) = e3
% 251.89/60.18 (2) all_252_3 = e1
% 251.89/60.18 (3) ~ (e3 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_3 = e3
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e3 = e1
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (5) implies:
% 251.89/60.18 | (6) e3 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (6) imply:
% 251.89/60.18 | (7) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (7) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #776 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (2) op(e1, e3) = e2
% 251.89/60.18 (3) op(e1, e3) = e0
% 251.89/60.18 (4) ~ (e2 = e0)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | GROUND_INST: instantiating (1) with e0, e2, e3, e1, simplifying with (2), (3)
% 251.89/60.18 | gives:
% 251.89/60.18 | (5) e2 = e0
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (4), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #777 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_3 = e0 & op(e3, e3) = e0
% 251.89/60.18 (2) all_252_3 = e1
% 251.89/60.18 (3) ~ (e1 = e0)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_3 = e0
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e1 = e0
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #778 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_2 = e1 & op(e3, e4) = e1
% 251.89/60.18 (2) all_252_2 = e2
% 251.89/60.18 (3) ~ (e2 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_2 = e1
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e2 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #779 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.89/60.18 all_250_23 = e0
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) op(all_34_2, e0) = e1
% 251.89/60.18 (4) ~ (all_28_2 = all_20_2)
% 251.89/60.18 (5) op(all_34_2, all_20_2) = e0
% 251.89/60.18 (6) all_82_2 = e1
% 251.89/60.18 (7) all_82_2 = all_28_2
% 251.89/60.18 (8) ~ (all_20_2 = e4)
% 251.89/60.18 (9) ~ (all_20_2 = e3)
% 251.89/60.18 (10) ~ (all_20_2 = e2)
% 251.89/60.18 (11) all_250_23 = all_20_2
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (6), (7) imply:
% 251.89/60.18 | (12) all_28_2 = e1
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (12) implies:
% 251.89/60.18 | (13) all_28_2 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (4), (13) imply:
% 251.89/60.18 | (14) ~ (all_20_2 = e1)
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (14) implies:
% 251.89/60.18 | (15) ~ (all_20_2 = e1)
% 251.89/60.18 |
% 251.89/60.18 | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (15) are inconsistent by
% 251.89/60.18 | sub-proof #780.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #780 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 |
% 251.89/60.18 all_250_23 = e0
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) ~ (all_20_2 = e1)
% 251.89/60.18 (4) op(all_34_2, e0) = e1
% 251.89/60.18 (5) op(all_34_2, all_20_2) = e0
% 251.89/60.18 (6) ~ (all_20_2 = e4)
% 251.89/60.18 (7) ~ (all_20_2 = e3)
% 251.89/60.18 (8) ~ (all_20_2 = e2)
% 251.89/60.18 (9) all_250_23 = all_20_2
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | BETA: splitting (1) gives:
% 251.89/60.18 |
% 251.89/60.18 | Case 1:
% 251.89/60.18 | |
% 251.89/60.18 | | (10) all_250_23 = e4
% 251.89/60.18 | |
% 251.89/60.18 | | REF_CLOSE: (6), (9), (10) are inconsistent by sub-proof #784.
% 251.89/60.18 | |
% 251.89/60.18 | Case 2:
% 251.89/60.18 | |
% 251.89/60.18 | | (11) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 =
% 251.89/60.18 | | e0
% 251.89/60.18 | |
% 251.89/60.18 | | BETA: splitting (11) gives:
% 251.89/60.18 | |
% 251.89/60.18 | | Case 1:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (12) all_250_23 = e3
% 251.89/60.18 | | |
% 251.89/60.18 | | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #783.
% 251.89/60.18 | | |
% 251.89/60.18 | | Case 2:
% 251.89/60.18 | | |
% 251.89/60.18 | | | (13) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0
% 251.89/60.18 | | |
% 251.89/60.18 | | | BETA: splitting (13) gives:
% 251.89/60.18 | | |
% 251.89/60.18 | | | Case 1:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | (14) all_250_23 = e2
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #782.
% 251.89/60.18 | | | |
% 251.89/60.18 | | | Case 2:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | (15) all_250_23 = e1 | all_250_23 = e0
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | BETA: splitting (15) gives:
% 251.89/60.18 | | | |
% 251.89/60.18 | | | | Case 1:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | (16) all_250_23 = e1
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | COMBINE_EQS: (9), (16) imply:
% 251.89/60.18 | | | | | (17) all_20_2 = e1
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | SIMP: (17) implies:
% 251.89/60.18 | | | | | (18) all_20_2 = e1
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | REDUCE: (3), (18) imply:
% 251.89/60.18 | | | | | (19) $false
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | CLOSE: (19) is inconsistent.
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | Case 2:
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | (20) all_250_23 = e0
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | COMBINE_EQS: (9), (20) imply:
% 251.89/60.18 | | | | | (21) all_20_2 = e0
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | SIMP: (21) implies:
% 251.89/60.18 | | | | | (22) all_20_2 = e0
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | REDUCE: (3), (22) imply:
% 251.89/60.18 | | | | | (23) ~ (e1 = e0)
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | SIMP: (23) implies:
% 251.89/60.18 | | | | | (24) ~ (e1 = e0)
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | | REF_CLOSE: (2), (4), (5), (22), (24) are inconsistent by sub-proof
% 251.89/60.18 | | | | | #781.
% 251.89/60.18 | | | | |
% 251.89/60.18 | | | | End of split
% 251.89/60.18 | | | |
% 251.89/60.18 | | | End of split
% 251.89/60.18 | | |
% 251.89/60.18 | | End of split
% 251.89/60.18 | |
% 251.89/60.18 | End of split
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #781 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) ~ (e1 = e0)
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) op(all_34_2, e0) = e1
% 251.89/60.18 (4) op(all_34_2, all_20_2) = e0
% 251.89/60.18 (5) all_20_2 = e0
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (4), (5) imply:
% 251.89/60.18 | (6) op(all_34_2, e0) = e0
% 251.89/60.18 |
% 251.89/60.18 | GROUND_INST: instantiating (2) with e1, e0, e0, all_34_2, simplifying with
% 251.89/60.18 | (3), (6) gives:
% 251.89/60.18 | (7) e1 = e0
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (1), (7) imply:
% 251.89/60.18 | (8) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (8) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #782 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_250_23 = all_20_2
% 251.89/60.18 (2) all_250_23 = e2
% 251.89/60.18 (3) ~ (all_20_2 = e2)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) all_20_2 = e2
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) all_20_2 = e2
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #783 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_250_23 = all_20_2
% 251.89/60.18 (2) all_250_23 = e3
% 251.89/60.18 (3) ~ (all_20_2 = e3)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) all_20_2 = e3
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) all_20_2 = e3
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #784 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_250_23 = all_20_2
% 251.89/60.18 (2) all_250_23 = e4
% 251.89/60.18 (3) ~ (all_20_2 = e4)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) all_20_2 = e4
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) all_20_2 = e4
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #785 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (2) op(e4, e1) = e2
% 251.89/60.18 (3) op(e4, e1) = e1
% 251.89/60.18 (4) ~ (e2 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | GROUND_INST: instantiating (1) with e2, e1, e1, e4, simplifying with (2), (3)
% 251.89/60.18 | gives:
% 251.89/60.18 | (5) e2 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (4), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #786 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_18 = e3
% 251.89/60.18 (2) all_252_18 = e2
% 251.89/60.18 (3) ~ (e3 = e2)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (1), (2) imply:
% 251.89/60.18 | (4) e3 = e2
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (4) implies:
% 251.89/60.18 | (5) e3 = e2
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #787 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_11 = e2 & op(e2, e1) = e2
% 251.89/60.18 (2) all_252_11 = e4
% 251.89/60.18 (3) ~ (e4 = e2)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_11 = e2
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e4 = e2
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (5) imply:
% 251.89/60.18 | (6) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (6) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #788 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) all_252_8 = e2 & op(e2, e2) = e2
% 251.89/60.18 (2) all_252_8 = e1
% 251.89/60.18 (3) ~ (e2 = e1)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | ALPHA: (1) implies:
% 251.89/60.18 | (4) all_252_8 = e2
% 251.89/60.18 |
% 251.89/60.18 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.18 | (5) e2 = e1
% 251.89/60.18 |
% 251.89/60.18 | SIMP: (5) implies:
% 251.89/60.18 | (6) e2 = e1
% 251.89/60.18 |
% 251.89/60.18 | REDUCE: (3), (6) imply:
% 251.89/60.18 | (7) $false
% 251.89/60.18 |
% 251.89/60.18 | CLOSE: (7) is inconsistent.
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #789 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) op(all_6_2, e2) = e4
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) op(e2, e3) = all_10_2
% 251.89/60.18 (4) ~ (e2 = e1)
% 251.89/60.18 (5) op(all_6_2, all_64_2) = e2
% 251.89/60.18 (6) op(e2, e3) = e1
% 251.89/60.18 (7) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.89/60.18 (8) op(e2, e4) = all_64_2
% 251.89/60.18 (9) ~ (all_64_2 = e4)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | BETA: splitting (7) gives:
% 251.89/60.18 |
% 251.89/60.18 | Case 1:
% 251.89/60.18 | |
% 251.89/60.18 | | (10) all_252_6 = e2 & op(e2, e4) = e2
% 251.89/60.18 | |
% 251.89/60.18 | | ALPHA: (10) implies:
% 251.89/60.18 | | (11) op(e2, e4) = e2
% 251.89/60.18 | |
% 251.89/60.18 | | REF_CLOSE: (1), (2), (5), (8), (9), (11) are inconsistent by sub-proof #790.
% 251.89/60.18 | |
% 251.89/60.18 | Case 2:
% 251.89/60.18 | |
% 251.89/60.18 | | (12) all_252_7 = e2 & op(e2, e3) = e2
% 251.89/60.18 | |
% 251.89/60.18 | | ALPHA: (12) implies:
% 251.89/60.18 | | (13) op(e2, e3) = e2
% 251.89/60.18 | |
% 251.89/60.18 | | REF_CLOSE: (2), (3), (4), (6), (13) are inconsistent by sub-proof #902.
% 251.89/60.18 | |
% 251.89/60.18 | End of split
% 251.89/60.18 |
% 251.89/60.18 End of proof
% 251.89/60.18
% 251.89/60.18 Sub-proof #790 shows that the following formulas are inconsistent:
% 251.89/60.18 ----------------------------------------------------------------
% 251.89/60.18 (1) op(all_6_2, e2) = e4
% 251.89/60.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.18 (3) op(e2, e4) = e2
% 251.89/60.18 (4) op(all_6_2, all_64_2) = e2
% 251.89/60.18 (5) op(e2, e4) = all_64_2
% 251.89/60.18 (6) ~ (all_64_2 = e4)
% 251.89/60.18
% 251.89/60.18 Begin of proof
% 251.89/60.18 |
% 251.89/60.18 | GROUND_INST: instantiating (2) with all_64_2, e2, e4, e2, simplifying with
% 251.89/60.18 | (3), (5) gives:
% 251.89/60.18 | (7) all_64_2 = e2
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (6), (7) imply:
% 251.89/60.19 | (8) ~ (e4 = e2)
% 251.89/60.19 |
% 251.89/60.19 | SIMP: (8) implies:
% 251.89/60.19 | (9) ~ (e4 = e2)
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (4), (7) imply:
% 251.89/60.19 | (10) op(all_6_2, e2) = e2
% 251.89/60.19 |
% 251.89/60.19 | GROUND_INST: instantiating (2) with e4, e2, e2, all_6_2, simplifying with (1),
% 251.89/60.19 | (10) gives:
% 251.89/60.19 | (11) e4 = e2
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (9), (11) imply:
% 251.89/60.19 | (12) $false
% 251.89/60.19 |
% 251.89/60.19 | CLOSE: (12) is inconsistent.
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #791 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) all_252_11 = e3 & op(e2, e1) = e3
% 251.89/60.19 (2) all_252_11 = e4
% 251.89/60.19 (3) ~ (e4 = e3)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | ALPHA: (1) implies:
% 251.89/60.19 | (4) all_252_11 = e3
% 251.89/60.19 |
% 251.89/60.19 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.19 | (5) e4 = e3
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (3), (5) imply:
% 251.89/60.19 | (6) $false
% 251.89/60.19 |
% 251.89/60.19 | CLOSE: (6) is inconsistent.
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #792 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ~ (all_64_2 = e3)
% 251.89/60.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (3) op(e2, e3) = e1
% 251.89/60.19 (4) ~ (e3 = e1)
% 251.89/60.19 (5) op(e2, e4) = all_64_2
% 251.89/60.19 (6) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (6) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (7) all_252_6 = e3 & op(e2, e4) = e3
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #940.
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (8) all_252_7 = e3 & op(e2, e3) = e3
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (8) implies:
% 251.89/60.19 | | (9) op(e2, e3) = e3
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #881.
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #793 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ~ (all_62_2 = e2)
% 251.89/60.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (3) op(e1, e0) = all_34_2
% 251.89/60.19 (4) op(e4, e2) = all_6_2
% 251.89/60.19 (5) ~ (all_34_2 = e2)
% 251.89/60.19 (6) ~ (all_6_2 = e1)
% 251.89/60.19 (7) op(e1, e4) = all_16_2
% 251.89/60.19 (8) op(e1, e3) = all_62_2
% 251.89/60.19 (9) ~ (all_16_2 = e2)
% 251.89/60.19 (10) op(e4, all_4_2) = e1
% 251.89/60.19 (11) op(e1, e1) = all_244_15
% 251.89/60.19 (12) op(e1, e2) = all_4_2
% 251.89/60.19 (13) ~ (all_244_15 = e2)
% 251.89/60.19 (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.19 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.19 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (14) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 251.89/60.19 | | = e2)
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (1), (2), (7), (8), (9), (15) are inconsistent by sub-proof #925.
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (16) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 251.89/60.19 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.19 | |
% 251.89/60.19 | | BETA: splitting (16) gives:
% 251.89/60.19 | |
% 251.89/60.19 | | Case 1:
% 251.89/60.19 | | |
% 251.89/60.19 | | | (17) all_252_14 = e2 & op(e1, e2) = e2
% 251.89/60.19 | | |
% 251.89/60.19 | | | REF_CLOSE: (2), (4), (6), (10), (12), (17) are inconsistent by sub-proof
% 251.89/60.19 | | | #794.
% 251.89/60.19 | | |
% 251.89/60.19 | | Case 2:
% 251.89/60.19 | | |
% 251.89/60.19 | | | (18) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.89/60.19 | | | e0) = e2)
% 251.89/60.19 | | |
% 251.89/60.19 | | | REF_CLOSE: (2), (3), (5), (11), (13), (18) are inconsistent by sub-proof
% 251.89/60.19 | | | #819.
% 251.89/60.19 | | |
% 251.89/60.19 | | End of split
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #794 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (2) op(e4, e2) = all_6_2
% 251.89/60.19 (3) ~ (all_6_2 = e1)
% 251.89/60.19 (4) op(e4, all_4_2) = e1
% 251.89/60.19 (5) op(e1, e2) = all_4_2
% 251.89/60.19 (6) all_252_14 = e2 & op(e1, e2) = e2
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | ALPHA: (6) implies:
% 251.89/60.19 | (7) op(e1, e2) = e2
% 251.89/60.19 |
% 251.89/60.19 | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e1, simplifying with (5),
% 251.89/60.19 | (7) gives:
% 251.89/60.19 | (8) all_4_2 = e2
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (4), (8) imply:
% 251.89/60.19 | (9) op(e4, e2) = e1
% 251.89/60.19 |
% 251.89/60.19 | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #930.
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #795 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) op(e4, e1) = e2
% 251.89/60.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (3) ~ (all_36_2 = e4)
% 251.89/60.19 (4) op(e3, e1) = all_36_2
% 251.89/60.19 (5) op(e4, e1) = all_26_2
% 251.89/60.19 (6) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.89/60.19 (7) ~ (e4 = e2)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (6) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (8) all_252_9 = e4 & op(e4, e1) = e4
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (8) implies:
% 251.89/60.19 | | (9) op(e4, e1) = e4
% 251.89/60.19 | |
% 251.89/60.19 | | GROUND_INST: instantiating (2) with all_26_2, e2, e1, e4, simplifying with
% 251.89/60.19 | | (1), (5) gives:
% 251.89/60.19 | | (10) all_26_2 = e2
% 251.89/60.19 | |
% 251.89/60.19 | | GROUND_INST: instantiating (2) with all_26_2, e4, e1, e4, simplifying with
% 251.89/60.19 | | (5), (9) gives:
% 251.89/60.19 | | (11) all_26_2 = e4
% 251.89/60.19 | |
% 251.89/60.19 | | COMBINE_EQS: (10), (11) imply:
% 251.89/60.19 | | (12) e4 = e2
% 251.89/60.19 | |
% 251.89/60.19 | | SIMP: (12) implies:
% 251.89/60.19 | | (13) e4 = e2
% 251.89/60.19 | |
% 251.89/60.19 | | REDUCE: (7), (13) imply:
% 251.89/60.19 | | (14) $false
% 251.89/60.19 | |
% 251.89/60.19 | | CLOSE: (14) is inconsistent.
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (15) all_252_10 = e4 & op(e3, e1) = e4
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (2), (3), (4), (15) are inconsistent by sub-proof #914.
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #796 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) op(all_62_2, all_36_2) = e3
% 251.89/60.19 (2) op(all_38_2, all_4_2) = e1
% 251.89/60.19 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (4) op(e2, e2) = all_244_8
% 251.89/60.19 (5) op(e2, e1) = all_38_2
% 251.89/60.19 (6) op(e1, e0) = all_34_2
% 251.89/60.19 (7) all_36_2 = e2
% 251.89/60.19 (8) ~ (all_34_2 = e2)
% 251.89/60.19 (9) ~ (all_244_8 = all_38_2)
% 251.89/60.19 (10) op(e1, e4) = all_16_2
% 251.89/60.19 (11) op(e1, e3) = all_62_2
% 251.89/60.19 (12) all_70_2 = all_62_2
% 251.89/60.19 (13) ( ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.89/60.19 all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e4) & op(e1,
% 251.89/60.19 e2) = all_46_1 & $i(all_46_1))
% 251.89/60.19 (14) ~ (all_16_2 = e2)
% 251.89/60.19 (15) ~ (all_8_2 = e1)
% 251.89/60.19 (16) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.19 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.19 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.19 (17) op(e1, e1) = all_244_15
% 251.89/60.19 (18) op(e1, e2) = all_4_2
% 251.89/60.19 (19) op(e3, e2) = all_8_2
% 251.89/60.19 (20) op(all_36_2, e1) = e3
% 251.89/60.19 (21) ~ (all_244_15 = all_36_2)
% 251.89/60.19 (22) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.19 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.19 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (7), (21) imply:
% 251.89/60.19 | (23) ~ (all_244_15 = e2)
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (1), (7) imply:
% 251.89/60.19 | (24) op(all_62_2, e2) = e3
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (7), (20) imply:
% 251.89/60.19 | (25) op(e2, e1) = e3
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (13) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (26) ~ (all_46_0 = e0) & op(e2, all_46_1) = all_46_0 & op(e1, e2) =
% 251.89/60.19 | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (26) implies:
% 251.89/60.19 | | (27) op(e1, e2) = all_46_1
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 251.89/60.19 | | (16), (17), (18), (19), (22), (23), (24), (25), (27) are
% 251.89/60.19 | | inconsistent by sub-proof #797.
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (28) ~ (all_46_1 = e4) & op(e1, e2) = all_46_1 & $i(all_46_1)
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (28) implies:
% 251.89/60.19 | | (29) op(e1, e2) = all_46_1
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 251.89/60.19 | | (16), (17), (18), (19), (22), (23), (24), (25), (29) are
% 251.89/60.19 | | inconsistent by sub-proof #797.
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #797 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) op(all_38_2, all_4_2) = e1
% 251.89/60.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (3) op(e2, e2) = all_244_8
% 251.89/60.19 (4) op(e2, e1) = all_38_2
% 251.89/60.19 (5) op(e1, e0) = all_34_2
% 251.89/60.19 (6) ~ (all_34_2 = e2)
% 251.89/60.19 (7) op(all_62_2, e2) = e3
% 251.89/60.19 (8) ~ (all_244_8 = all_38_2)
% 251.89/60.19 (9) op(e1, e4) = all_16_2
% 251.89/60.19 (10) op(e1, e3) = all_62_2
% 251.89/60.19 (11) all_70_2 = all_62_2
% 251.89/60.19 (12) op(e2, e1) = e3
% 251.89/60.19 (13) ~ (all_16_2 = e2)
% 251.89/60.19 (14) ~ (all_8_2 = e1)
% 251.89/60.19 (15) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.19 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.19 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.19 (16) op(e1, e1) = all_244_15
% 251.89/60.19 (17) op(e1, e2) = all_46_1
% 251.89/60.19 (18) op(e1, e2) = all_4_2
% 251.89/60.19 (19) ~ (all_244_15 = e2)
% 251.89/60.19 (20) op(e3, e2) = all_8_2
% 251.89/60.19 (21) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.19 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.19 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | GROUND_INST: instantiating (2) with all_4_2, all_46_1, e2, e1, simplifying
% 251.89/60.19 | with (17), (18) gives:
% 251.89/60.19 | (22) all_46_1 = all_4_2
% 251.89/60.19 |
% 251.89/60.19 | GROUND_INST: instantiating (2) with all_38_2, e3, e1, e2, simplifying with
% 251.89/60.19 | (4), (12) gives:
% 251.89/60.19 | (23) all_38_2 = e3
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (8), (23) imply:
% 251.89/60.19 | (24) ~ (all_244_8 = e3)
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (1), (23) imply:
% 251.89/60.19 | (25) op(e3, all_4_2) = e1
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (15) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (26) ~ (all_70_2 = e2)
% 251.89/60.19 | |
% 251.89/60.19 | | REDUCE: (11), (26) imply:
% 251.89/60.19 | | (27) ~ (all_62_2 = e2)
% 251.89/60.19 | |
% 251.89/60.19 | | BETA: splitting (21) gives:
% 251.89/60.19 | |
% 251.89/60.19 | | Case 1:
% 251.89/60.19 | | |
% 251.89/60.19 | | | (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 251.89/60.19 | | | e3) = e2)
% 251.89/60.19 | | |
% 251.89/60.19 | | | REF_CLOSE: (2), (9), (10), (13), (27), (28) are inconsistent by sub-proof
% 251.89/60.19 | | | #925.
% 251.89/60.19 | | |
% 251.89/60.19 | | Case 2:
% 251.89/60.19 | | |
% 251.89/60.19 | | | (29) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.19 | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.19 | | |
% 251.89/60.19 | | | BETA: splitting (29) gives:
% 251.89/60.19 | | |
% 251.89/60.19 | | | Case 1:
% 251.89/60.19 | | | |
% 251.89/60.19 | | | | (30) all_252_14 = e2 & op(e1, e2) = e2
% 251.89/60.19 | | | |
% 251.89/60.19 | | | | REF_CLOSE: (2), (14), (18), (20), (25), (30) are inconsistent by
% 251.89/60.19 | | | | sub-proof #798.
% 251.89/60.19 | | | |
% 251.89/60.19 | | | Case 2:
% 251.89/60.19 | | | |
% 251.89/60.19 | | | | (31) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 251.89/60.19 | | | | e0) = e2)
% 251.89/60.19 | | | |
% 251.89/60.19 | | | | REF_CLOSE: (2), (5), (6), (16), (19), (31) are inconsistent by sub-proof
% 251.89/60.19 | | | | #819.
% 251.89/60.19 | | | |
% 251.89/60.19 | | | End of split
% 251.89/60.19 | | |
% 251.89/60.19 | | End of split
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (32) all_70_2 = e2
% 251.89/60.19 | |
% 251.89/60.19 | | COMBINE_EQS: (11), (32) imply:
% 251.89/60.19 | | (33) all_62_2 = e2
% 251.89/60.19 | |
% 251.89/60.19 | | REDUCE: (7), (33) imply:
% 251.89/60.19 | | (34) op(e2, e2) = e3
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (2), (3), (24), (34) are inconsistent by sub-proof #877.
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #798 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (2) ~ (all_8_2 = e1)
% 251.89/60.19 (3) op(e3, all_4_2) = e1
% 251.89/60.19 (4) op(e1, e2) = all_4_2
% 251.89/60.19 (5) all_252_14 = e2 & op(e1, e2) = e2
% 251.89/60.19 (6) op(e3, e2) = all_8_2
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | ALPHA: (5) implies:
% 251.89/60.19 | (7) op(e1, e2) = e2
% 251.89/60.19 |
% 251.89/60.19 | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e1, simplifying with (4),
% 251.89/60.19 | (7) gives:
% 251.89/60.19 | (8) all_4_2 = e2
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (3), (8) imply:
% 251.89/60.19 | (9) op(e3, e2) = e1
% 251.89/60.19 |
% 251.89/60.19 | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #929.
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #799 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ~ (all_26_2 = e2)
% 251.89/60.19 (2) ~ (all_10_2 = e4)
% 251.89/60.19 (3) op(all_4_2, e2) = e1
% 251.89/60.19 (4) all_94_2 = all_38_2
% 251.89/60.19 (5) op(all_38_2, e1) = e2
% 251.89/60.19 (6) all_250_13 = all_38_2
% 251.89/60.19 (7) ~ (all_28_2 = e3)
% 251.89/60.19 (8) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.89/60.19 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.89/60.19 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.89/60.19 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (10) op(e2, e3) = all_10_2
% 251.89/60.19 (11) op(e0, e0) = all_244_24
% 251.89/60.19 (12) ~ (all_12_2 = e3)
% 251.89/60.19 (13) op(e2, e2) = all_244_8
% 251.89/60.19 (14) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.89/60.19 all_250_11 = e0
% 251.89/60.19 (15) op(e2, e1) = all_38_2
% 251.89/60.19 (16) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.89/60.19 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.89/60.19 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.89/60.19 (17) op(e1, e0) = all_34_2
% 251.89/60.19 (18) ~ (all_36_2 = e2)
% 251.89/60.19 (19) all_78_2 = all_10_2
% 251.89/60.19 (20) ~ (all_34_2 = e2)
% 251.89/60.19 (21) op(e0, e2) = all_28_2
% 251.89/60.19 (22) all_106_2 = all_38_2
% 251.89/60.19 (23) ~ (all_244_8 = all_38_2)
% 251.89/60.19 (24) op(all_244_15, all_244_15) = e1
% 251.89/60.19 (25) all_250_21 = all_22_2
% 251.89/60.19 (26) ~ (all_244_3 = all_84_2)
% 251.89/60.19 (27) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.89/60.19 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.89/60.19 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.89/60.19 (28) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.89/60.19 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.89/60.19 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.19 (29) op(e1, e3) = all_62_2
% 251.89/60.19 (30) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.89/60.19 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.89/60.19 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.89/60.19 (31) ~ (all_244_3 = all_10_2)
% 251.89/60.19 (32) all_70_2 = all_62_2
% 251.89/60.19 (33) op(all_48_2, all_22_2) = e0
% 251.89/60.19 (34) op(e3, e1) = all_36_2
% 251.89/60.19 (35) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.89/60.19 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.89/60.19 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.89/60.19 (36) ~ (all_22_2 = e1)
% 251.89/60.19 (37) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.89/60.19 all_250_13 = e0
% 251.89/60.19 (38) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.19 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.19 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.19 (39) ~ (all_38_2 = e4)
% 251.89/60.19 (40) op(all_22_2, e3) = e0
% 251.89/60.19 (41) all_68_2 = all_22_2
% 251.89/60.19 (42) op(all_20_2, all_34_2) = e1
% 251.89/60.19 (43) op(e0, e3) = all_22_2
% 251.89/60.19 (44) ~ (all_28_2 = all_22_2)
% 251.89/60.19 (45) all_58_2 = all_20_2
% 251.89/60.19 (46) op(all_62_2, e3) = e1
% 251.89/60.19 (47) op(e4, e1) = all_26_2
% 251.89/60.19 (48) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.89/60.19 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.89/60.19 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.89/60.19 (49) op(all_10_2, e3) = e2
% 251.89/60.19 (50) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.89/60.19 all_250_21 = e0
% 251.89/60.19 (51) ~ (all_244_15 = all_62_2)
% 251.89/60.19 (52) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.89/60.19 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.89/60.19 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.89/60.19 (53) all_250_11 = all_10_2
% 251.89/60.19 (54) all_126_2 = all_48_2
% 251.89/60.19 (55) ~ (all_22_2 = all_12_2)
% 251.89/60.19 (56) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.89/60.19 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.89/60.19 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.89/60.19 (57) ~ (e4 = e3)
% 251.89/60.19 (58) op(e1, e1) = all_244_15
% 251.89/60.19 (59) op(e0, e1) = all_20_2
% 251.89/60.19 (60) op(all_48_2, e0) = e3
% 251.89/60.19 (61) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.89/60.19 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.89/60.19 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.89/60.19 (62) op(all_4_2, all_38_2) = e2
% 251.89/60.19 (63) all_48_2 = e1
% 251.89/60.19 (64) op(e4, e3) = all_84_2
% 251.89/60.19 (65) ~ (all_62_2 = all_10_2)
% 251.89/60.19 (66) ~ (all_22_2 = all_10_2)
% 251.89/60.19 (67) ~ (all_22_2 = all_20_2)
% 251.89/60.19 (68) ~ (all_38_2 = all_10_2)
% 251.89/60.19 (69) ~ (all_244_24 = all_22_2)
% 251.89/60.19 (70) ~ (all_244_3 = all_48_2)
% 251.89/60.19 (71) ( ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 & op(e0, e1) =
% 251.89/60.19 all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e4) & op(e0,
% 251.89/60.19 e1) = all_48_1 & $i(all_48_1))
% 251.89/60.19 (72) op(e3, e3) = all_244_3
% 251.89/60.19 (73) all_90_2 = all_22_2
% 251.89/60.19 (74) op(all_244_24, all_244_24) = e0
% 251.89/60.19 (75) op(e0, e4) = all_12_2
% 251.89/60.19 (76) ~ (all_20_2 = e2)
% 251.89/60.19 (77) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.89/60.19 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.89/60.19 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.89/60.19 (78) all_124_2 = all_10_2
% 251.89/60.19
% 251.89/60.19 Begin of proof
% 251.89/60.19 |
% 251.89/60.19 | COMBINE_EQS: (54), (63) imply:
% 251.89/60.19 | (79) all_126_2 = e1
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (63), (70) imply:
% 251.89/60.19 | (80) ~ (all_244_3 = e1)
% 251.89/60.19 |
% 251.89/60.19 | REDUCE: (60), (63) imply:
% 251.89/60.19 | (81) op(e1, e0) = e3
% 251.89/60.19 |
% 251.89/60.19 | BETA: splitting (71) gives:
% 251.89/60.19 |
% 251.89/60.19 | Case 1:
% 251.89/60.19 | |
% 251.89/60.19 | | (82) ~ (all_48_0 = e2) & op(e1, all_48_1) = all_48_0 & op(e0, e1) =
% 251.89/60.19 | | all_48_1 & $i(all_48_0) & $i(all_48_1)
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (82) implies:
% 251.89/60.19 | | (83) op(e0, e1) = all_48_1
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.89/60.19 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.89/60.19 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 251.89/60.19 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 251.89/60.19 | | (46), (47), (48), (49), (50), (51), (52), (53), (55), (56), (57),
% 251.89/60.19 | | (58), (59), (60), (61), (62), (64), (65), (66), (67), (68), (69),
% 251.89/60.19 | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (83)
% 251.89/60.19 | | are inconsistent by sub-proof #800.
% 251.89/60.19 | |
% 251.89/60.19 | Case 2:
% 251.89/60.19 | |
% 251.89/60.19 | | (84) ~ (all_48_1 = e4) & op(e0, e1) = all_48_1 & $i(all_48_1)
% 251.89/60.19 | |
% 251.89/60.19 | | ALPHA: (84) implies:
% 251.89/60.19 | | (85) op(e0, e1) = all_48_1
% 251.89/60.19 | |
% 251.89/60.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.89/60.19 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 251.89/60.19 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 251.89/60.19 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 251.89/60.19 | | (46), (47), (48), (49), (50), (51), (52), (53), (55), (56), (57),
% 251.89/60.19 | | (58), (59), (60), (61), (62), (64), (65), (66), (67), (68), (69),
% 251.89/60.19 | | (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (85)
% 251.89/60.19 | | are inconsistent by sub-proof #800.
% 251.89/60.19 | |
% 251.89/60.19 | End of split
% 251.89/60.19 |
% 251.89/60.19 End of proof
% 251.89/60.19
% 251.89/60.19 Sub-proof #800 shows that the following formulas are inconsistent:
% 251.89/60.19 ----------------------------------------------------------------
% 251.89/60.19 (1) ~ (all_26_2 = e2)
% 251.89/60.19 (2) ~ (all_10_2 = e4)
% 251.89/60.19 (3) op(all_4_2, e2) = e1
% 251.89/60.19 (4) all_94_2 = all_38_2
% 251.89/60.19 (5) op(all_38_2, e1) = e2
% 251.89/60.19 (6) all_250_13 = all_38_2
% 251.89/60.19 (7) ~ (all_28_2 = e3)
% 251.89/60.19 (8) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 251.89/60.19 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 251.89/60.19 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 251.89/60.19 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.19 (10) op(e2, e3) = all_10_2
% 251.89/60.19 (11) op(e0, e0) = all_244_24
% 251.89/60.19 (12) ~ (all_12_2 = e3)
% 251.89/60.19 (13) op(e2, e2) = all_244_8
% 251.89/60.19 (14) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.89/60.19 all_250_11 = e0
% 251.89/60.19 (15) ~ (all_244_3 = e1)
% 251.89/60.19 (16) op(e2, e1) = all_38_2
% 251.89/60.19 (17) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.89/60.19 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.89/60.19 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.89/60.19 (18) op(e1, e0) = all_34_2
% 251.89/60.19 (19) ~ (all_36_2 = e2)
% 251.89/60.19 (20) all_78_2 = all_10_2
% 251.89/60.19 (21) ~ (all_34_2 = e2)
% 251.89/60.20 (22) op(e0, e2) = all_28_2
% 251.89/60.20 (23) all_106_2 = all_38_2
% 251.89/60.20 (24) ~ (all_244_8 = all_38_2)
% 251.89/60.20 (25) op(e0, e1) = all_48_1
% 251.89/60.20 (26) op(all_244_15, all_244_15) = e1
% 251.89/60.20 (27) all_250_21 = all_22_2
% 251.89/60.20 (28) ~ (all_244_3 = all_84_2)
% 251.89/60.20 (29) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 251.89/60.20 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 251.89/60.20 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 251.89/60.20 (30) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.89/60.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.89/60.20 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.20 (31) op(e1, e3) = all_62_2
% 251.89/60.20 (32) ~ (all_58_2 = e3) | ( ~ (all_58_0 = e2) & op(e3, all_58_1) = all_58_0 &
% 251.89/60.20 op(e1, e3) = all_58_1 & $i(all_58_0) & $i(all_58_1)) | ( ~ (all_58_1 =
% 251.89/60.20 e4) & op(e1, e3) = all_58_1 & $i(all_58_1))
% 251.89/60.20 (33) ~ (all_244_3 = all_10_2)
% 251.89/60.20 (34) all_70_2 = all_62_2
% 251.89/60.20 (35) op(all_48_2, all_22_2) = e0
% 251.89/60.20 (36) op(e3, e1) = all_36_2
% 251.89/60.20 (37) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.89/60.20 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.89/60.20 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.89/60.20 (38) ~ (all_22_2 = e1)
% 251.89/60.20 (39) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.89/60.20 all_250_13 = e0
% 251.89/60.20 (40) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.20 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.20 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.20 (41) ~ (all_38_2 = e4)
% 251.89/60.20 (42) op(all_22_2, e3) = e0
% 251.89/60.20 (43) all_68_2 = all_22_2
% 251.89/60.20 (44) op(all_20_2, all_34_2) = e1
% 251.89/60.20 (45) op(e0, e3) = all_22_2
% 251.89/60.20 (46) ~ (all_28_2 = all_22_2)
% 251.89/60.20 (47) all_58_2 = all_20_2
% 251.89/60.20 (48) op(all_62_2, e3) = e1
% 251.89/60.20 (49) op(e4, e1) = all_26_2
% 251.89/60.20 (50) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.89/60.20 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.89/60.20 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.89/60.20 (51) op(all_10_2, e3) = e2
% 251.89/60.20 (52) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.89/60.20 all_250_21 = e0
% 251.89/60.20 (53) ~ (all_244_15 = all_62_2)
% 251.89/60.20 (54) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.89/60.20 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.89/60.20 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.89/60.20 (55) all_250_11 = all_10_2
% 251.89/60.20 (56) ~ (all_22_2 = all_12_2)
% 251.89/60.20 (57) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 251.89/60.20 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 251.89/60.20 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.89/60.20 (58) ~ (e4 = e3)
% 251.89/60.20 (59) op(e1, e1) = all_244_15
% 251.89/60.20 (60) op(e0, e1) = all_20_2
% 251.89/60.20 (61) op(all_48_2, e0) = e3
% 251.89/60.20 (62) ~ (all_126_2 = e1) | ( ~ (all_126_0 = e4) & op(e1, all_126_1) =
% 251.89/60.20 all_126_0 & op(e0, e1) = all_126_1 & $i(all_126_0) & $i(all_126_1)) |
% 251.89/60.20 ( ~ (all_126_1 = e2) & op(e0, e1) = all_126_1 & $i(all_126_1))
% 251.89/60.20 (63) op(all_4_2, all_38_2) = e2
% 251.89/60.20 (64) op(e4, e3) = all_84_2
% 251.89/60.20 (65) ~ (all_62_2 = all_10_2)
% 251.89/60.20 (66) ~ (all_22_2 = all_10_2)
% 251.89/60.20 (67) op(e1, e0) = e3
% 251.89/60.20 (68) ~ (all_22_2 = all_20_2)
% 251.89/60.20 (69) ~ (all_38_2 = all_10_2)
% 251.89/60.20 (70) ~ (all_244_24 = all_22_2)
% 251.89/60.20 (71) op(e3, e3) = all_244_3
% 251.89/60.20 (72) all_90_2 = all_22_2
% 251.89/60.20 (73) all_126_2 = e1
% 251.89/60.20 (74) op(all_244_24, all_244_24) = e0
% 251.89/60.20 (75) op(e0, e4) = all_12_2
% 251.89/60.20 (76) ~ (all_20_2 = e2)
% 251.89/60.20 (77) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 251.89/60.20 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 251.89/60.20 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 251.89/60.20 (78) all_124_2 = all_10_2
% 251.89/60.20
% 251.89/60.20 Begin of proof
% 251.89/60.20 |
% 251.89/60.20 | BETA: splitting (62) gives:
% 251.89/60.20 |
% 251.89/60.20 | Case 1:
% 251.89/60.20 | |
% 251.89/60.20 | | (79) ~ (all_126_2 = e1)
% 251.89/60.20 | |
% 251.89/60.20 | | REDUCE: (73), (79) imply:
% 251.89/60.20 | | (80) $false
% 251.89/60.20 | |
% 251.89/60.20 | | CLOSE: (80) is inconsistent.
% 251.89/60.20 | |
% 251.89/60.20 | Case 2:
% 251.89/60.20 | |
% 251.89/60.20 | |
% 251.89/60.20 | | GROUND_INST: instantiating (9) with all_20_2, all_48_1, e1, e0, simplifying
% 251.89/60.20 | | with (25), (60) gives:
% 251.89/60.20 | | (81) all_48_1 = all_20_2
% 251.89/60.20 | |
% 251.89/60.20 | | GROUND_INST: instantiating (9) with all_34_2, e3, e0, e1, simplifying with
% 251.89/60.20 | | (18), (67) gives:
% 251.89/60.20 | | (82) all_34_2 = e3
% 251.89/60.20 | |
% 251.89/60.20 | | REDUCE: (21), (82) imply:
% 251.89/60.20 | | (83) ~ (e3 = e2)
% 251.89/60.20 | |
% 251.89/60.20 | | REDUCE: (44), (82) imply:
% 251.89/60.20 | | (84) op(all_20_2, e3) = e1
% 251.89/60.20 | |
% 251.89/60.20 | | BETA: splitting (32) gives:
% 251.89/60.20 | |
% 251.89/60.20 | | Case 1:
% 251.89/60.20 | | |
% 251.89/60.20 | | | (85) ~ (all_58_2 = e3)
% 251.89/60.20 | | |
% 251.89/60.20 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 251.89/60.20 | | | (13), (14), (16), (17), (19), (20), (22), (23), (24), (26),
% 251.89/60.20 | | | (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 251.89/60.20 | | | (38), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 251.89/60.20 | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 251.89/60.20 | | | (59), (60), (61), (63), (64), (65), (66), (68), (69), (70),
% 251.89/60.20 | | | (71), (72), (74), (75), (76), (77), (78), (83), (85) are
% 251.89/60.20 | | | inconsistent by sub-proof #960.
% 251.89/60.20 | | |
% 251.89/60.20 | | Case 2:
% 251.89/60.20 | | |
% 251.89/60.20 | | | (86) all_58_2 = e3
% 251.89/60.20 | | |
% 251.89/60.20 | | | COMBINE_EQS: (47), (86) imply:
% 251.89/60.20 | | | (87) all_20_2 = e3
% 251.89/60.20 | | |
% 251.89/60.20 | | | SIMP: (87) implies:
% 251.89/60.20 | | | (88) all_20_2 = e3
% 251.89/60.20 | | |
% 251.89/60.20 | | | REDUCE: (84), (88) imply:
% 251.89/60.20 | | | (89) op(e3, e3) = e1
% 251.89/60.20 | | |
% 251.89/60.20 | | | REF_CLOSE: (9), (15), (71), (89) are inconsistent by sub-proof #801.
% 251.89/60.20 | | |
% 251.89/60.20 | | End of split
% 251.89/60.20 | |
% 251.89/60.20 | End of split
% 251.89/60.20 |
% 251.89/60.20 End of proof
% 251.89/60.20
% 251.89/60.20 Sub-proof #801 shows that the following formulas are inconsistent:
% 251.89/60.20 ----------------------------------------------------------------
% 251.89/60.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.20 (2) op(e3, e3) = all_244_3
% 251.89/60.20 (3) op(e3, e3) = e1
% 251.89/60.20 (4) ~ (all_244_3 = e1)
% 251.89/60.20
% 251.89/60.20 Begin of proof
% 251.89/60.20 |
% 251.89/60.20 | GROUND_INST: instantiating (1) with all_244_3, e1, e3, e3, simplifying with
% 251.89/60.20 | (2), (3) gives:
% 251.89/60.20 | (5) all_244_3 = e1
% 251.89/60.20 |
% 251.89/60.20 | REDUCE: (4), (5) imply:
% 251.89/60.20 | (6) $false
% 251.89/60.20 |
% 251.89/60.20 | CLOSE: (6) is inconsistent.
% 251.89/60.20 |
% 251.89/60.20 End of proof
% 251.89/60.20
% 251.89/60.20 Sub-proof #802 shows that the following formulas are inconsistent:
% 251.89/60.20 ----------------------------------------------------------------
% 251.89/60.20 (1) op(all_4_2, e2) = e1
% 251.89/60.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.20 (3) all_50_2 = all_4_2
% 251.89/60.20 (4) all_50_2 = e3
% 251.89/60.20 (5) ~ (all_8_2 = e1)
% 251.89/60.20 (6) op(e3, e2) = all_8_2
% 251.89/60.20
% 251.89/60.20 Begin of proof
% 251.89/60.20 |
% 251.89/60.20 | COMBINE_EQS: (3), (4) imply:
% 251.89/60.20 | (7) all_4_2 = e3
% 251.89/60.20 |
% 251.89/60.20 | SIMP: (7) implies:
% 251.89/60.20 | (8) all_4_2 = e3
% 251.89/60.20 |
% 251.89/60.20 | REDUCE: (1), (8) imply:
% 251.89/60.20 | (9) op(e3, e2) = e1
% 251.89/60.20 |
% 251.89/60.20 | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #929.
% 251.89/60.20 |
% 251.89/60.20 End of proof
% 251.89/60.20
% 251.89/60.20 Sub-proof #803 shows that the following formulas are inconsistent:
% 251.89/60.20 ----------------------------------------------------------------
% 251.89/60.20 (1) ~ (all_244_8 = all_4_2)
% 251.89/60.20 (2) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 251.89/60.20 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 251.89/60.20 | (all_252_20 = e0 & op(e0, e4) = e0)
% 251.89/60.20 (3) ~ (all_74_2 = e0) | ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0,
% 251.89/60.20 all_74_1) = all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 =
% 251.89/60.20 e4) & op(e1, e0) = all_74_1 & $i(all_74_1))
% 251.89/60.20 (4) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 251.89/60.20 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 251.89/60.20 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 251.89/60.20 (5) ~ (all_26_2 = e2)
% 251.89/60.20 (6) ~ (all_4_2 = e4)
% 251.89/60.20 (7) ~ (all_178_2 = e3) | ( ~ (all_178_0 = e4) & op(e3, all_178_1) =
% 251.89/60.20 all_178_0 & op(e0, e3) = all_178_1 & $i(all_178_0) & $i(all_178_1)) | (
% 251.89/60.20 ~ (all_178_1 = e1) & op(e0, e3) = all_178_1 & $i(all_178_1))
% 251.89/60.20 (8) ~ (all_10_2 = e4)
% 251.89/60.20 (9) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 251.89/60.20 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 251.89/60.20 (all_252_16 = e3 & op(e4, e0) = e3)
% 251.89/60.20 (10) all_74_2 = e0
% 251.89/60.20 (11) ~ (all_40_2 = all_38_2)
% 251.89/60.20 (12) op(all_6_2, e2) = e4
% 251.89/60.20 (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.89/60.20 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.89/60.20 e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.20 (14) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2)
% 251.89/60.20 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.20 e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 251.89/60.20 (15) op(e4, e0) = all_30_2
% 251.89/60.20 (16) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.89/60.20 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 251.89/60.20 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.89/60.20 (17) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 251.89/60.20 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 251.89/60.20 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 251.89/60.20 (18) op(e1, e0) = all_122_1
% 251.89/60.20 (19) ~ (all_244_8 = all_6_2)
% 251.89/60.20 (20) ~ (all_84_2 = all_10_2)
% 251.89/60.20 (21) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 251.89/60.20 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 251.89/60.20 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 251.89/60.20 (22) op(all_62_2, e0) = e3
% 251.89/60.20 (23) all_162_2 = all_28_2
% 251.89/60.20 (24) op(all_38_2, e1) = e2
% 251.89/60.20 (25) all_250_13 = all_38_2
% 251.89/60.20 (26) ~ (all_28_2 = all_6_2)
% 251.89/60.20 (27) ~ (e2 = e0)
% 251.89/60.20 (28) op(all_64_2, e4) = e2
% 251.89/60.20 (29) ~ (e1 = e0)
% 251.89/60.20 (30) ~ (all_22_2 = e3)
% 251.89/60.20 (31) ~ (all_28_2 = e3)
% 251.89/60.20 (32) ~ (all_62_2 = all_22_2)
% 251.89/60.20 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.20 (34) op(e2, e3) = all_10_2
% 251.89/60.20 (35) ~ (e3 = e2)
% 251.89/60.20 (36) op(e0, e0) = all_244_24
% 251.89/60.20 (37) ~ (e4 = e0)
% 251.89/60.20 (38) ~ (all_12_2 = e3)
% 251.89/60.20 (39) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 251.89/60.20 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 251.89/60.20 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 251.89/60.20 (40) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 251.89/60.20 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 251.89/60.20 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 251.89/60.20 (41) all_252_23 = e3
% 251.89/60.20 (42) op(all_244_8, all_244_8) = e2
% 251.89/60.20 (43) op(e2, e2) = all_244_8
% 251.89/60.20 (44) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 251.89/60.20 all_250_11 = e0
% 251.89/60.20 (45) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 251.89/60.20 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 251.89/60.20 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 251.89/60.20 (46) op(e2, e1) = all_38_2
% 251.89/60.20 (47) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 251.89/60.20 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 251.89/60.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 251.89/60.20 (48) ~ (all_84_2 = all_62_2)
% 251.89/60.20 (49) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 251.89/60.20 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 251.89/60.20 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.89/60.20 (50) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 251.89/60.20 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 251.89/60.20 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 251.89/60.20 (51) ~ (all_244_3 = all_22_2)
% 251.89/60.20 (52) op(e1, e0) = all_34_2
% 251.89/60.20 (53) ~ (all_80_2 = e0) | ( ~ (all_80_0 = e3) & op(e2, e0) = all_80_1 &
% 251.89/60.20 op(e0, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1)) | ( ~
% 251.89/60.20 (all_80_1 = e1) & op(e2, e0) = all_80_1 & $i(all_80_1))
% 251.89/60.20 (54) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 251.89/60.20 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 251.89/60.20 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 251.89/60.20 (55) ~ (all_40_2 = e4)
% 251.89/60.20 (56) ~ (all_36_2 = e2)
% 251.89/60.20 (57) op(all_28_2, e2) = e0
% 251.89/60.20 (58) op(e4, e2) = all_6_2
% 251.89/60.20 (59) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.89/60.20 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.89/60.20 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 251.89/60.20 (60) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 251.89/60.20 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 251.89/60.20 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.20 (61) all_78_2 = all_10_2
% 251.89/60.20 (62) ~ (all_8_2 = all_4_2)
% 251.89/60.20 (63) ~ (all_34_2 = e2)
% 251.89/60.20 (64) ~ (e2 = e1)
% 251.89/60.20 (65) op(e0, e2) = all_28_2
% 251.89/60.20 (66) ~ (e4 = e1)
% 251.89/60.20 (67) op(all_6_2, all_64_2) = e2
% 251.89/60.20 (68) ~ (all_244_8 = all_10_2)
% 251.89/60.20 (69) ~ (all_6_2 = e1)
% 251.89/60.20 (70) ~ (all_64_2 = e3) | ( ~ (all_64_0 = e0) & op(e4, e3) = all_64_1 &
% 251.89/60.20 op(e3, all_64_1) = all_64_0 & $i(all_64_0) & $i(all_64_1)) | ( ~
% 251.89/60.20 (all_64_1 = e1) & op(e4, e3) = all_64_1 & $i(all_64_1))
% 251.89/60.20 (71) ~ (all_62_2 = all_34_2)
% 251.89/60.20 (72) ~ (all_244_8 = all_38_2)
% 251.89/60.20 (73) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 251.89/60.20 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 251.89/60.20 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 251.89/60.20 (74) op(all_244_15, all_244_15) = e1
% 251.89/60.20 (75) all_80_2 = all_6_2
% 251.89/60.20 (76) all_250_21 = all_22_2
% 251.89/60.20 (77) op(all_34_2, e0) = e1
% 251.89/60.20 (78) ~ (all_244_3 = all_84_2)
% 251.89/60.20 (79) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 251.89/60.20 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 251.89/60.20 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 251.89/60.20 (80) op(e1, e4) = all_16_2
% 251.89/60.20 (81) ~ (all_244_0 = all_64_2)
% 251.89/60.20 (82) all_96_2 = all_34_2
% 251.89/60.20 (83) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 251.89/60.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 251.89/60.20 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 251.89/60.20 (84) all_178_2 = all_40_2
% 251.89/60.20 (85) op(e1, e3) = all_62_2
% 251.89/60.20 (86) op(all_16_2, all_26_2) = e4
% 251.89/60.20 (87) all_140_2 = all_84_2
% 251.89/60.20 (88) ~ (e3 = e0)
% 251.89/60.20 (89) ~ (all_38_2 = e0)
% 251.89/60.20 (90) ~ (all_40_2 = all_10_2)
% 251.89/60.20 (91) ~ (all_244_3 = all_10_2)
% 251.89/60.20 (92) ~ (all_30_2 = e2)
% 251.89/60.20 (93) ~ (all_36_2 = e4)
% 251.89/60.20 (94) all_70_2 = all_62_2
% 251.89/60.20 (95) ~ (all_244_24 = e3)
% 251.89/60.20 (96) ~ (e3 = e1)
% 251.89/60.20 (97) op(all_48_2, all_22_2) = e0
% 251.89/60.20 (98) ~ (all_12_2 = e2)
% 251.89/60.20 (99) op(e3, e1) = all_36_2
% 251.89/60.20 (100) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 251.89/60.20 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 251.89/60.20 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 251.89/60.20 (101) ~ (all_16_2 = e2)
% 251.89/60.20 (102) ~ (all_8_2 = e1)
% 251.89/60.20 (103) ~ (all_244_3 = all_62_2)
% 251.89/60.20 (104) op(all_40_2, e0) = e2
% 251.89/60.20 (105) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 251.89/60.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 251.89/60.20 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.89/60.20 (106) ~ (all_22_2 = e1)
% 251.89/60.20 (107) ~ (all_244_8 = all_40_2)
% 251.89/60.20 (108) ~ (all_28_2 = all_4_2)
% 251.89/60.20 (109) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 251.89/60.20 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 251.89/60.20 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.20 (110) ~ (all_40_2 = all_34_2)
% 251.89/60.20 (111) op(e0, e1) = e3
% 251.89/60.20 (112) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 251.89/60.20 all_250_13 = e0
% 251.89/60.20 (113) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 251.89/60.20 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 251.89/60.20 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 251.89/60.20 (114) ~ (all_8_2 = e0)
% 251.89/60.20 (115) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 251.89/60.20 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 251.89/60.20 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 251.89/60.20 (116) ~ (all_38_2 = e4)
% 251.89/60.20 (117) ~ (all_64_2 = all_12_2)
% 251.89/60.20 (118) op(all_22_2, e3) = e0
% 251.89/60.20 (119) all_68_2 = all_22_2
% 251.89/60.20 (120) op(e0, e3) = all_22_2
% 251.89/60.20 (121) ~ (all_244_0 = all_100_2)
% 251.89/60.20 (122) ~ (all_28_2 = all_22_2)
% 251.89/60.20 (123) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 251.89/60.20 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 251.89/60.20 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 251.89/60.20 (124) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.89/60.20 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 251.89/60.20 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 251.89/60.20 (125) op(all_84_2, e3) = e4
% 251.89/60.20 (126) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.20 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.20 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.20 (127) op(e4, e1) = all_26_2
% 251.89/60.20 (128) ~ (all_244_15 = e3)
% 251.89/60.20 (129) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 251.89/60.20 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 251.89/60.20 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 251.89/60.20 (130) op(all_10_2, e3) = e2
% 251.89/60.20 (131) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 251.89/60.20 all_250_21 = e0
% 251.89/60.20 (132) ~ (all_244_15 = all_62_2)
% 251.89/60.20 (133) ~ (all_62_2 = all_16_2)
% 251.89/60.20 (134) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.89/60.20 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 251.89/60.20 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 251.89/60.20 (135) ~ (all_8_2 = all_6_2)
% 251.89/60.20 (136) op(e3, e4) = all_100_2
% 251.89/60.20 (137) all_250_11 = all_10_2
% 251.89/60.20 (138) op(e4, e4) = all_244_0
% 251.89/60.20 (139) ~ (all_22_2 = all_12_2)
% 251.89/60.20 (140) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) =
% 251.89/60.20 e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.20 e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 251.89/60.20 (141) ~ (e4 = e3)
% 251.89/60.20 (142) op(e1, e1) = all_244_15
% 251.89/60.20 (143) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 251.89/60.20 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 251.89/60.20 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 251.89/60.20 (144) ~ (all_34_2 = all_30_2)
% 251.89/60.20 (145) op(e0, e1) = all_20_2
% 251.89/60.20 (146) op(e3, e0) = all_48_2
% 251.89/60.20 (147) ~ (all_62_2 = e4) | ( ~ (all_62_0 = e2) & op(e4, all_62_1) = all_62_0
% 251.89/60.20 & op(e3, e4) = all_62_1 & $i(all_62_0) & $i(all_62_1)) | ( ~
% 251.89/60.20 (all_62_1 = e0) & op(e3, e4) = all_62_1 & $i(all_62_1))
% 251.89/60.20 (148) op(all_48_2, e0) = e3
% 251.89/60.20 (149) ~ (all_26_2 = e3)
% 251.89/60.20 (150) all_82_2 = all_28_2
% 251.89/60.20 (151) ~ (all_84_2 = all_22_2)
% 251.89/60.20 (152) op(e1, e2) = all_4_2
% 251.89/60.20 (153) op(e3, e1) = e0
% 251.89/60.20 (154) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 251.89/60.20 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 251.89/60.20 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 251.89/60.20 (155) ~ (all_28_2 = all_8_2)
% 251.89/60.20 (156) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 251.89/60.20 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 251.89/60.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 251.89/60.20 (157) ~ (all_48_2 = e1)
% 251.89/60.20 (158) op(e4, e3) = all_84_2
% 251.89/60.20 (159) all_86_2 = all_40_2
% 251.89/60.20 (160) ~ (all_62_2 = all_10_2)
% 251.89/60.20 (161) op(e2, e4) = all_64_2
% 251.89/60.20 (162) ~ (all_22_2 = all_10_2)
% 251.89/60.20 (163) ~ (all_6_2 = all_4_2)
% 251.89/60.20 (164) ~ (e4 = e2)
% 251.89/60.20 (165) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 251.89/60.20 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 251.89/60.20 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 251.89/60.20 (166) op(e3, e2) = all_8_2
% 251.89/60.20 (167) ~ (all_64_2 = all_16_2)
% 251.89/60.20 (168) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.20 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.20 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.20 (169) ~ (all_38_2 = all_10_2)
% 251.89/60.20 (170) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 251.89/60.20 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 251.89/60.20 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 251.89/60.20 (171) ~ (all_20_2 = e4)
% 251.89/60.20 (172) ~ (all_84_2 = all_6_2)
% 251.89/60.20 (173) ~ (all_244_24 = all_22_2)
% 251.89/60.20 (174) op(all_16_2, e4) = e1
% 251.89/60.20 (175) ~ (all_244_3 = e0)
% 251.89/60.20 (176) op(e2, e0) = all_40_2
% 251.89/60.21 (177) ~ (all_16_2 = e3)
% 251.89/60.21 (178) ~ (all_244_8 = all_28_2)
% 251.89/60.21 (179) ~ (all_38_2 = e3)
% 251.89/60.21 (180) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 251.89/60.21 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 251.89/60.21 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 251.89/60.21 (181) op(e3, e3) = all_244_3
% 251.89/60.21 (182) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 251.89/60.21 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 251.89/60.21 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 251.89/60.21 (183) ~ (all_4_2 = e3)
% 251.89/60.21 (184) all_90_2 = all_22_2
% 251.89/60.21 (185) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 251.89/60.21 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 251.89/60.21 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 251.89/60.21 (186) ~ (all_140_2 = e0) | ( ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 &
% 251.89/60.21 op(e0, all_140_1) = all_140_0 & $i(all_140_0) & $i(all_140_1)) | ( ~
% 251.89/60.21 (all_140_1 = e1) & op(e3, e0) = all_140_1 & $i(all_140_1))
% 251.89/60.21 (187) ~ (all_62_2 = all_4_2)
% 251.89/60.21 (188) ~ (all_96_2 = e3) | ( ~ (all_96_0 = e2) & op(e3, all_96_1) = all_96_0
% 251.89/60.21 & op(e0, e3) = all_96_1 & $i(all_96_0) & $i(all_96_1)) | ( ~
% 251.89/60.21 (all_96_1 = e4) & op(e0, e3) = all_96_1 & $i(all_96_1))
% 251.89/60.21 (189) op(e0, all_62_2) = e1
% 251.89/60.21 (190) op(all_244_24, all_244_24) = e0
% 251.89/60.21 (191) op(e0, e4) = all_12_2
% 251.89/60.21 (192) op(all_22_2, all_48_2) = e3
% 251.89/60.21 (193) ~ (all_20_2 = e2)
% 251.89/60.21
% 251.89/60.21 Begin of proof
% 251.89/60.21 |
% 251.89/60.21 | GROUND_INST: instantiating (33) with all_34_2, all_122_1, e0, e1, simplifying
% 251.89/60.21 | with (18), (52) gives:
% 251.89/60.21 | (194) all_122_1 = all_34_2
% 251.89/60.21 |
% 251.89/60.21 | BETA: splitting (147) gives:
% 251.89/60.21 |
% 251.89/60.21 | Case 1:
% 251.89/60.21 | |
% 251.89/60.21 | | (195) ~ (all_62_2 = e4)
% 251.89/60.21 | |
% 251.89/60.21 | | BETA: splitting (70) gives:
% 251.89/60.21 | |
% 251.89/60.21 | | Case 1:
% 251.89/60.21 | | |
% 251.89/60.21 | | | (196) ~ (all_64_2 = e3)
% 251.89/60.21 | | |
% 251.89/60.21 | | | BETA: splitting (50) gives:
% 251.89/60.21 | | |
% 251.89/60.21 | | | Case 1:
% 251.89/60.21 | | | |
% 251.89/60.21 | | | | (197) ~ (all_68_2 = e4)
% 251.89/60.21 | | | |
% 251.89/60.21 | | | | REDUCE: (119), (197) imply:
% 251.89/60.21 | | | | (198) ~ (all_22_2 = e4)
% 251.89/60.21 | | | |
% 251.89/60.21 | | | | BETA: splitting (113) gives:
% 251.89/60.21 | | | |
% 251.89/60.21 | | | | Case 1:
% 251.89/60.21 | | | | |
% 251.89/60.21 | | | | | (199) ~ (all_70_2 = e2)
% 251.89/60.21 | | | | |
% 251.89/60.21 | | | | | REDUCE: (94), (199) imply:
% 251.89/60.21 | | | | | (200) ~ (all_62_2 = e2)
% 251.89/60.21 | | | | |
% 251.89/60.21 | | | | | BETA: splitting (100) gives:
% 251.89/60.21 | | | | |
% 251.89/60.21 | | | | | Case 1:
% 251.89/60.21 | | | | | |
% 251.89/60.21 | | | | | | (201) ~ (all_78_2 = e1)
% 251.89/60.21 | | | | | |
% 251.89/60.21 | | | | | | REDUCE: (61), (201) imply:
% 251.89/60.21 | | | | | | (202) ~ (all_10_2 = e1)
% 251.89/60.21 | | | | | |
% 251.89/60.21 | | | | | | BETA: splitting (53) gives:
% 251.89/60.21 | | | | | |
% 251.89/60.21 | | | | | | Case 1:
% 251.89/60.21 | | | | | | |
% 251.89/60.21 | | | | | | | (203) ~ (all_80_2 = e0)
% 251.89/60.21 | | | | | | |
% 251.89/60.21 | | | | | | | REDUCE: (75), (203) imply:
% 251.89/60.21 | | | | | | | (204) ~ (all_6_2 = e0)
% 251.89/60.21 | | | | | | |
% 251.89/60.21 | | | | | | | BETA: splitting (21) gives:
% 251.89/60.21 | | | | | | |
% 251.89/60.21 | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | |
% 251.89/60.21 | | | | | | | | (205) ~ (all_82_2 = e1)
% 251.89/60.21 | | | | | | | |
% 251.89/60.21 | | | | | | | | REDUCE: (150), (205) imply:
% 251.89/60.21 | | | | | | | | (206) ~ (all_28_2 = e1)
% 251.89/60.21 | | | | | | | |
% 251.89/60.21 | | | | | | | | BETA: splitting (40) gives:
% 251.89/60.21 | | | | | | | |
% 251.89/60.21 | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | |
% 251.89/60.21 | | | | | | | | | (207) ~ (all_86_2 = e3)
% 251.89/60.21 | | | | | | | | |
% 251.89/60.21 | | | | | | | | | REDUCE: (159), (207) imply:
% 251.89/60.21 | | | | | | | | | (208) ~ (all_40_2 = e3)
% 251.89/60.21 | | | | | | | | |
% 251.89/60.21 | | | | | | | | | BETA: splitting (134) gives:
% 251.89/60.21 | | | | | | | | |
% 251.89/60.21 | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | (209) ~ (all_90_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (184), (209) imply:
% 251.89/60.21 | | | | | | | | | | (210) ~ (all_22_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REF_CLOSE: (30), (33), (76), (97), (106), (131), (148),
% 251.89/60.21 | | | | | | | | | | (198), (210) are inconsistent by sub-proof #957.
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | (211) all_90_2 = e2
% 251.89/60.21 | | | | | | | | | | (212) ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.89/60.21 | | | | | | | | | | op(e2, all_90_1) = all_90_0 & $i(all_90_0) &
% 251.89/60.21 | | | | | | | | | | $i(all_90_1)) | ( ~ (all_90_1 = e1) & op(e3, e2)
% 251.89/60.21 | | | | | | | | | | = all_90_1 & $i(all_90_1))
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | COMBINE_EQS: (184), (211) imply:
% 251.89/60.21 | | | | | | | | | | (213) all_22_2 = e2
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (173), (213) imply:
% 251.89/60.21 | | | | | | | | | | (214) ~ (all_244_24 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (151), (213) imply:
% 251.89/60.21 | | | | | | | | | | (215) ~ (all_84_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (122), (213) imply:
% 251.89/60.21 | | | | | | | | | | (216) ~ (all_28_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (139), (213) imply:
% 251.89/60.21 | | | | | | | | | | (217) ~ (all_12_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (162), (213) imply:
% 251.89/60.21 | | | | | | | | | | (218) ~ (all_10_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | SIMP: (218) implies:
% 251.89/60.21 | | | | | | | | | | (219) ~ (all_10_2 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (198), (213) imply:
% 251.89/60.21 | | | | | | | | | | (220) ~ (e4 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (30), (213) imply:
% 251.89/60.21 | | | | | | | | | | (221) ~ (e3 = e2)
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (118), (213) imply:
% 251.89/60.21 | | | | | | | | | | (222) op(e2, e3) = e0
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | REDUCE: (120), (213) imply:
% 251.89/60.21 | | | | | | | | | | (223) op(e0, e3) = e2
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | BETA: splitting (212) gives:
% 251.89/60.21 | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | (224) ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 251.89/60.21 | | | | | | | | | | | op(e2, all_90_1) = all_90_0 & $i(all_90_0) &
% 251.89/60.21 | | | | | | | | | | | $i(all_90_1)
% 251.89/60.21 | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | ALPHA: (224) implies:
% 251.89/60.21 | | | | | | | | | | | (225) op(e3, e2) = all_90_1
% 251.89/60.21 | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | BETA: splitting (14) gives:
% 251.89/60.21 | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | (226) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | BETA: splitting (226) gives:
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | (227) all_252_1 = e2 & op(e4, e3) = e2
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | REF_CLOSE: (33), (158), (215), (227) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | sub-proof #956.
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | (228) all_252_3 = e2 & op(e3, e3) = e2
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | ALPHA: (228) implies:
% 251.89/60.21 | | | | | | | | | | | | | (229) all_252_3 = e2
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | BETA: splitting (185) gives:
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | (230) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | | | e1 & op(e3, e3) = e1)
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (231) all_252_1 = e1 & op(e4, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | (232) all_252_1 = e1
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | (233) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | (234) all_252_1 = e4 & op(e4, e3) = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (232), (234) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | #955.
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | (235) all_252_3 = e4 & op(e3, e3) = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | (236) all_252_3 = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (229), (236) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | #954.
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | (237) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.89/60.21 | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (34), (85), (120), (164), (195), (223),
% 251.89/60.21 | | | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #950.
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (238) all_252_3 = e1 & op(e3, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | REF_CLOSE: (64), (229), (238) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | #949.
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | (239) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 &
% 251.89/60.21 | | | | | | | | | | | | | | op(e0, e3) = e1)
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (240) all_252_7 = e1 & op(e2, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | (241) op(e2, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | REF_CLOSE: (33), (34), (202), (241) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | sub-proof #948.
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (242) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21
% 251.89/60.21 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | (243) all_252_13 = e1 & op(e1, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | (244) all_252_13 = e1
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | (245) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.89/60.21 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (246) all_252_20 = e2 & op(e0, e4) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (247) op(e0, e4) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (98), (191), (247) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | sub-proof #980.
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (248) all_252_21 = e2 & op(e0, e3) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (249) all_252_21 = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (250) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (251) all_252_1 = e4 & op(e4, e3) = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (252) all_252_1 = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | (253) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (254) all_252_1 = e0 & op(e4, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (252), (254) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | #947.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (255) all_252_3 = e0 & op(e3, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (256) op(e3, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (175), (181), (256) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #973.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | (257) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (258) all_252_7 = e0 & op(e2, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (259) all_252_7 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (260) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (261) all_252_1 = e3 & op(e4, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (252), (261) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | #946.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_252_3 = e3 & op(e3, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_252_3 = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (263) imply:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (264) e3 = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (264) imply:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (265) $false
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (266) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (267) all_252_7 = e3 & op(e2, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (259), (267) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | #945.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (268) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_252_13 = e3 & op(e1, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (244), (269) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | #944.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_252_21 = e3 & op(e0, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (33), (120), (270) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #959.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (271) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (272) all_252_13 = e0 & op(e1, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (273) all_252_13 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (244), (273) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | #943.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (274) all_252_21 = e0 & op(e0, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (275) all_252_21 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (249), (275) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | #942.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (276) all_252_3 = e4 & op(e3, e3) = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (277) all_252_3 = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (229), (277) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | #954.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (278) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (34), (85), (120), (164), (195), (223),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (278) are inconsistent by sub-proof #950.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | (279) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.89/60.21 | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (280) all_252_22 = e2 & op(e0, e2) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (65), (216), (280) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | sub-proof #979.
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (281) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.89/60.21 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (36), (145), (193), (214), (281) are
% 251.89/60.21 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | (282) all_252_21 = e1 & op(e0, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | (283) op(e0, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (64), (223), (283) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | sub-proof #941.
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | (284) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 251.89/60.21 | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 251.89/60.21 | | | | | | | | | | | | op(e0, e3) = e2)
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | BETA: splitting (284) gives:
% 251.89/60.21 | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | (285) all_252_7 = e2 & op(e2, e3) = e2
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | ALPHA: (285) implies:
% 251.89/60.21 | | | | | | | | | | | | | (286) all_252_7 = e2
% 251.89/60.21 | | | | | | | | | | | | | (287) op(e2, e3) = e2
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | BETA: splitting (45) gives:
% 251.89/60.21 | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | (288) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 251.89/60.21 | | | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (289) all_252_6 = e3 & op(e2, e4) = e3
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | REF_CLOSE: (33), (161), (196), (289) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | sub-proof #940.
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (290) all_252_7 = e3 & op(e2, e3) = e3
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | (291) all_252_7 = e3
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | REF_CLOSE: (35), (286), (291) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | #939.
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | (292) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 251.89/60.21 | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 251.89/60.21 | | | | | | | | | | | | | | op(e2, e0) = e3)
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 251.89/60.21 | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | (293) all_252_8 = e3 & op(e2, e2) = e3
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | (294) all_252_8 = e3
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 251.89/60.21 | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | (295) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 251.89/60.21 | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | (296) all_252_6 = e4 & op(e2, e4) = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | (297) all_252_6 = e4
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (298) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (299) all_252_6 = e0 & op(e2, e4) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (300) all_252_6 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (34), (37), (46), (55), (116), (126),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (141), (176), (294), (300) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | sub-proof #931.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (301) all_252_7 = e0 & op(e2, e3) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (302) all_252_7 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (29), (33), (35), (46), (47), (52),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (54), (58), (63), (64), (65), (66), (69), (80),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (85), (86), (93), (96), (99), (101), (102), (111),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (115), (116), (127), (145), (152), (153), (164),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (165), (166), (171), (174), (180), (200), (206),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (294), (297), (302) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | #906.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | (303) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | op(e2, e0) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (304) all_252_8 = e0 & op(e2, e2) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (305) all_252_8 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (294), (305) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | #905.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | (306) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (307) all_252_11 = e0 & op(e2, e1) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (46), (89), (307) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | sub-proof #904.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (308) all_252_18 = e0 & op(e2, e0) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | (309) op(e2, e0) = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | (310) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (311) all_252_6 = e1 & op(e2, e4) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (297), (311) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | #903.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (312) all_252_7 = e1 & op(e2, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (313) op(e2, e3) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (34), (64), (287), (313) are inconsistent by
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #902.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | (314) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (315) all_252_8 = e1 & op(e2, e2) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (316) all_252_8 = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (294), (316) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | #927.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | (317) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (318) all_252_11 = e1 & op(e2, e1) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | (319) all_252_11 = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (320) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (33), (56), (99), (127), (320) are
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #969.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | (321) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_252_11 = e2 & op(e2, e1) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (319), (322) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | #919.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | (323) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_252_15 = e2 & op(e1, e1) = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (58), (69), (102), (166), (325) are
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #928.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_8 = e1 & op(e2, e2) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_252_8 = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (294), (328) are inconsistent by sub-proof
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #927.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_252_14 = e1 & op(e1, e2) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) op(e1, e2) = e1
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_252_15 = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_10_2, e0, e3, e2,
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (34), (222) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_10_2 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_10_2, e2, e3, e2,
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (34), (287) gives:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_10_2 = e2
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (334) imply:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) e2 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (335) implies:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) e2 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (336) imply:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_252_7 = e0
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (29), (33), (35), (46), (54), (64),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (66), (86), (93), (96), (99), (111), (115), (116),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (145), (152), (153), (164), (165), (171),
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174), (294), (297), (331), (332), (337) are
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #910.
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_252_22 = e1 & op(e0, e2) = e1
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) op(e0, e2) = e1
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (65), (206), (339) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_252_23 = e2 & op(e0, e1) = e2
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies:
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) op(e0, e1) = e2
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (145), (193), (341) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #985.
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | (342) all_252_18 = e1 & op(e2, e0) = e1
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | (343) op(e2, e0) = e1
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (33), (309), (343) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #901.
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | (344) all_252_7 = e4 & op(e2, e3) = e4
% 251.89/60.22 | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 251.89/60.22 | | | | | | | | | | | | | | | | | (345) op(e2, e3) = e4
% 251.89/60.22 | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (34), (345) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | | sub-proof #953.
% 251.89/60.22 | | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | (346) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 251.89/60.22 | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 251.89/60.22 | | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (46), (55), (116), (141), (176), (294),
% 251.89/60.22 | | | | | | | | | | | | | | | | (346) are inconsistent by sub-proof #932.
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | (347) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 251.89/60.22 | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 251.89/60.22 | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 251.89/60.22 | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | (348) all_252_11 = e3 & op(e2, e1) = e3
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (46), (179), (348) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | sub-proof #900.
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | (349) all_252_18 = e3 & op(e2, e0) = e3
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (176), (208), (349) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | | | sub-proof #899.
% 251.89/60.22 | | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | (350) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 251.89/60.22 | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | BETA: splitting (350) gives:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | (351) all_252_13 = e2 & op(e1, e3) = e2
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | ALPHA: (351) implies:
% 251.89/60.22 | | | | | | | | | | | | | | (352) op(e1, e3) = e2
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | REF_CLOSE: (33), (85), (200), (352) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | sub-proof #972.
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | (353) all_252_21 = e2 & op(e0, e3) = e2
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | ALPHA: (353) implies:
% 251.89/60.22 | | | | | | | | | | | | | | (354) all_252_21 = e2
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_10_2, e0, e3, e2,
% 251.89/60.22 | | | | | | | | | | | | | | simplifying with (34), (222) gives:
% 251.89/60.22 | | | | | | | | | | | | | | (355) all_10_2 = e0
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_8_2, all_90_1, e2, e3,
% 251.89/60.22 | | | | | | | | | | | | | | simplifying with (166), (225) gives:
% 251.89/60.22 | | | | | | | | | | | | | | (356) all_90_1 = all_8_2
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | REDUCE: (68), (355) imply:
% 251.89/60.22 | | | | | | | | | | | | | | (357) ~ (all_244_8 = e0)
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13), (17), (30), (33), (34), (35),
% 251.89/60.22 | | | | | | | | | | | | | | (38), (43), (45), (46), (47), (52), (54), (55),
% 251.89/60.22 | | | | | | | | | | | | | | (58), (59), (63), (64), (65), (66), (69), (80),
% 251.89/60.22 | | | | | | | | | | | | | | (85), (86), (88), (90), (93), (96), (98), (99),
% 251.89/60.22 | | | | | | | | | | | | | | (101), (102), (109), (111), (115), (116), (120),
% 251.89/60.22 | | | | | | | | | | | | | | (126), (127), (130), (136), (141), (145), (146),
% 251.89/60.22 | | | | | | | | | | | | | | (152), (153), (154), (157), (161), (164), (165),
% 251.89/60.22 | | | | | | | | | | | | | | (168), (169), (170), (171), (174), (175), (176),
% 251.89/60.22 | | | | | | | | | | | | | | (177), (179), (180), (181), (185), (191), (195),
% 251.89/60.22 | | | | | | | | | | | | | | (196), (200), (202), (206), (208), (219), (225),
% 251.89/60.22 | | | | | | | | | | | | | | (354), (355), (356), (357) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | | sub-proof #878.
% 251.89/60.22 | | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | (358) ~ (all_90_1 = e1) & op(e3, e2) = all_90_1 &
% 251.89/60.22 | | | | | | | | | | | $i(all_90_1)
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | ALPHA: (358) implies:
% 251.89/60.22 | | | | | | | | | | | (359) ~ (all_90_1 = e1)
% 251.89/60.22 | | | | | | | | | | | (360) op(e3, e2) = all_90_1
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | BETA: splitting (129) gives:
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | (361) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 251.89/60.22 | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | BETA: splitting (361) gives:
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | (362) all_252_20 = e2 & op(e0, e4) = e2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | ALPHA: (362) implies:
% 251.89/60.22 | | | | | | | | | | | | | (363) op(e0, e4) = e2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | REF_CLOSE: (33), (98), (191), (363) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | sub-proof #980.
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | (364) all_252_21 = e2 & op(e0, e3) = e2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | ALPHA: (364) implies:
% 251.89/60.22 | | | | | | | | | | | | | (365) all_252_21 = e2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_10_2, e0, e3, e2,
% 251.89/60.22 | | | | | | | | | | | | | simplifying with (34), (222) gives:
% 251.89/60.22 | | | | | | | | | | | | | (366) all_10_2 = e0
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_8_2, all_90_1, e2, e3,
% 251.89/60.22 | | | | | | | | | | | | | simplifying with (166), (360) gives:
% 251.89/60.22 | | | | | | | | | | | | | (367) all_90_1 = all_8_2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | REDUCE: (68), (366) imply:
% 251.89/60.22 | | | | | | | | | | | | | (368) ~ (all_244_8 = e0)
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13), (17), (30), (33), (34), (35),
% 251.89/60.22 | | | | | | | | | | | | | (38), (43), (45), (46), (47), (52), (54), (55),
% 251.89/60.22 | | | | | | | | | | | | | (58), (59), (63), (64), (65), (66), (69), (80),
% 251.89/60.22 | | | | | | | | | | | | | (85), (86), (88), (90), (93), (96), (98), (99),
% 251.89/60.22 | | | | | | | | | | | | | (101), (102), (109), (111), (115), (116), (120),
% 251.89/60.22 | | | | | | | | | | | | | (126), (127), (130), (136), (141), (145), (146),
% 251.89/60.22 | | | | | | | | | | | | | (152), (153), (154), (157), (161), (164), (165),
% 251.89/60.22 | | | | | | | | | | | | | (168), (169), (170), (171), (174), (175), (176),
% 251.89/60.22 | | | | | | | | | | | | | (177), (179), (180), (181), (185), (191), (195),
% 251.89/60.22 | | | | | | | | | | | | | (196), (200), (202), (206), (208), (219), (360),
% 251.89/60.22 | | | | | | | | | | | | | (365), (366), (367), (368) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | sub-proof #878.
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | (369) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 251.89/60.22 | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 251.89/60.22 | | | | | | | | | | | | op(e0, e0) = e2)
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | BETA: splitting (369) gives:
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | (370) all_252_22 = e2 & op(e0, e2) = e2
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | REF_CLOSE: (33), (65), (216), (370) are inconsistent by
% 251.89/60.22 | | | | | | | | | | | | | sub-proof #979.
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | (371) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 251.89/60.22 | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | | REF_CLOSE: (33), (36), (145), (193), (214), (371) are
% 251.89/60.22 | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 251.89/60.22 | | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | | |
% 251.89/60.22 | | | | | | | | | End of split
% 251.89/60.22 | | | | | | | | |
% 251.89/60.22 | | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | | |
% 251.89/60.22 | | | | | | | | | (372) all_86_2 = e3
% 251.89/60.22 | | | | | | | | |
% 251.89/60.22 | | | | | | | | | REF_CLOSE: (7), (30), (33), (43), (76), (84), (97), (104),
% 251.89/60.22 | | | | | | | | | (106), (107), (131), (134), (146), (148), (159),
% 251.89/60.22 | | | | | | | | | (184), (192), (198), (372) are inconsistent by
% 251.89/60.22 | | | | | | | | | sub-proof #876.
% 251.89/60.22 | | | | | | | | |
% 251.89/60.22 | | | | | | | | End of split
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | (373) all_82_2 = e1
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | COMBINE_EQS: (150), (373) imply:
% 251.89/60.22 | | | | | | | | (374) all_28_2 = e1
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | REF_CLOSE: (1), (26), (27), (29), (33), (43), (47), (52), (57),
% 251.89/60.22 | | | | | | | | (58), (62), (63), (65), (73), (74), (80), (85),
% 251.89/60.22 | | | | | | | | (101), (108), (114), (142), (152), (155), (163),
% 251.89/60.22 | | | | | | | | (166), (178), (180), (200), (204), (374) are
% 251.89/60.22 | | | | | | | | inconsistent by sub-proof #867.
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | End of split
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | Case 2:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | (375) all_80_2 = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | COMBINE_EQS: (75), (375) imply:
% 251.89/60.22 | | | | | | | (376) all_6_2 = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | SIMP: (376) implies:
% 251.89/60.22 | | | | | | | (377) all_6_2 = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (19), (377) imply:
% 251.89/60.22 | | | | | | | (378) ~ (all_244_8 = e0)
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (163), (377) imply:
% 251.89/60.22 | | | | | | | (379) ~ (all_4_2 = e0)
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | SIMP: (379) implies:
% 251.89/60.22 | | | | | | | (380) ~ (all_4_2 = e0)
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (67), (377) imply:
% 251.89/60.22 | | | | | | | (381) op(e0, all_64_2) = e2
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (12), (377) imply:
% 251.89/60.22 | | | | | | | (382) op(e0, e2) = e4
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REF_CLOSE: (4), (8), (23), (27), (31), (33), (34), (35), (37),
% 251.89/60.22 | | | | | | | (43), (46), (47), (55), (58), (64), (65), (66), (69),
% 251.89/60.22 | | | | | | | (73), (88), (98), (102), (114), (116), (126), (152),
% 251.89/60.22 | | | | | | | (156), (161), (164), (166), (176), (182), (183), (191),
% 251.89/60.22 | | | | | | | (378), (380), (381), (382) are inconsistent by
% 251.89/60.22 | | | | | | | sub-proof #853.
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | End of split
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | Case 2:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | (383) all_78_2 = e1
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | REF_CLOSE: (33), (61), (85), (130), (200), (383) are inconsistent by
% 251.89/60.22 | | | | | | sub-proof #971.
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | End of split
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | Case 2:
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | (384) all_70_2 = e2
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | COMBINE_EQS: (94), (384) imply:
% 251.89/60.22 | | | | | (385) all_62_2 = e2
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | SIMP: (385) implies:
% 251.89/60.22 | | | | | (386) all_62_2 = e2
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | REF_CLOSE: (30), (32), (33), (76), (97), (106), (131), (148), (198),
% 251.89/60.22 | | | | | (386) are inconsistent by sub-proof #852.
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | End of split
% 251.89/60.22 | | | |
% 251.89/60.22 | | | Case 2:
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | (387) all_68_2 = e4
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | COMBINE_EQS: (119), (387) imply:
% 251.89/60.22 | | | | (388) all_22_2 = e4
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (51), (388) imply:
% 251.89/60.22 | | | | (389) ~ (all_244_3 = e4)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (151), (388) imply:
% 251.89/60.22 | | | | (390) ~ (all_84_2 = e4)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (162), (388) imply:
% 251.89/60.22 | | | | (391) ~ (all_10_2 = e4)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (118), (388) imply:
% 251.89/60.22 | | | | (392) op(e4, e3) = e0
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | GROUND_INST: instantiating (33) with all_84_2, e0, e3, e4, simplifying
% 251.89/60.22 | | | | with (158), (392) gives:
% 251.89/60.22 | | | | (393) all_84_2 = e0
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | COMBINE_EQS: (87), (393) imply:
% 251.89/60.22 | | | | (394) all_140_2 = e0
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (48), (393) imply:
% 251.89/60.22 | | | | (395) ~ (all_62_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | SIMP: (395) implies:
% 251.89/60.22 | | | | (396) ~ (all_62_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (20), (393) imply:
% 251.89/60.22 | | | | (397) ~ (all_10_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | SIMP: (397) implies:
% 251.89/60.22 | | | | (398) ~ (all_10_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (172), (393) imply:
% 251.89/60.22 | | | | (399) ~ (all_6_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | SIMP: (399) implies:
% 251.89/60.22 | | | | (400) ~ (all_6_2 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (390), (393) imply:
% 251.89/60.22 | | | | (401) ~ (e4 = e0)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REDUCE: (125), (393) imply:
% 251.89/60.22 | | | | (402) op(e0, e3) = e4
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | BETA: splitting (109) gives:
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | Case 1:
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | (403) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3,
% 251.89/60.22 | | | | | e3) = e0)
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | BETA: splitting (403) gives:
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | Case 1:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | (404) all_252_1 = e0 & op(e4, e3) = e0
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | ALPHA: (404) implies:
% 251.89/60.22 | | | | | | (405) all_252_1 = e0
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | BETA: splitting (186) gives:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | Case 1:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | (406) ~ (all_140_2 = e0)
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (394), (406) imply:
% 251.89/60.22 | | | | | | | (407) $false
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | CLOSE: (407) is inconsistent.
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | Case 2:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | (408) ( ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 & op(e0,
% 251.89/60.22 | | | | | | | all_140_1) = all_140_0 & $i(all_140_0) &
% 251.89/60.22 | | | | | | | $i(all_140_1)) | ( ~ (all_140_1 = e1) & op(e3, e0) =
% 251.89/60.22 | | | | | | | all_140_1 & $i(all_140_1))
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | BETA: splitting (408) gives:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | Case 1:
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | (409) ~ (all_140_0 = e2) & op(e3, e0) = all_140_1 & op(e0,
% 251.89/60.22 | | | | | | | | all_140_1) = all_140_0 & $i(all_140_0) &
% 251.89/60.22 | | | | | | | | $i(all_140_1)
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | ALPHA: (409) implies:
% 251.89/60.22 | | | | | | | | (410) op(e3, e0) = all_140_1
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (13), (14), (15),
% 251.89/60.22 | | | | | | | | (16), (17), (21), (22), (24), (25), (26), (27), (29),
% 251.89/60.22 | | | | | | | | (31), (33), (34), (35), (36), (37), (38), (39), (40),
% 251.89/60.22 | | | | | | | | (41), (43), (44), (45), (46), (47), (49), (52), (54),
% 251.89/60.22 | | | | | | | | (55), (57), (58), (60), (61), (62), (63), (64), (65),
% 251.89/60.22 | | | | | | | | (66), (69), (71), (72), (73), (74), (77), (78), (79),
% 251.89/60.22 | | | | | | | | (80), (82), (83), (85), (86), (88), (89), (90), (92),
% 251.89/60.22 | | | | | | | | (93), (94), (95), (96), (98), (99), (100), (101),
% 251.89/60.22 | | | | | | | | (102), (105), (108), (110), (111), (112), (113),
% 251.89/60.22 | | | | | | | | (114), (115), (116), (120), (123), (124), (126),
% 251.89/60.22 | | | | | | | | (127), (128), (129), (130), (132), (133), (136),
% 251.89/60.22 | | | | | | | | (137), (141), (142), (143), (145), (146), (149),
% 251.89/60.22 | | | | | | | | (150), (152), (153), (155), (157), (158), (159),
% 251.89/60.22 | | | | | | | | (161), (163), (164), (165), (166), (168), (169),
% 251.89/60.22 | | | | | | | | (170), (171), (174), (176), (177), (178), (179),
% 251.89/60.22 | | | | | | | | (180), (181), (182), (183), (185), (187), (188),
% 251.89/60.22 | | | | | | | | (189), (190), (191), (195), (196), (389), (392),
% 251.89/60.22 | | | | | | | | (398), (400), (402), (405), (410) are inconsistent by
% 251.89/60.22 | | | | | | | | sub-proof #817.
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | Case 2:
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | (411) ~ (all_140_1 = e1) & op(e3, e0) = all_140_1 &
% 251.89/60.22 | | | | | | | | $i(all_140_1)
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | ALPHA: (411) implies:
% 251.89/60.22 | | | | | | | | (412) op(e3, e0) = all_140_1
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (13), (14), (15),
% 251.89/60.22 | | | | | | | | (16), (17), (21), (22), (24), (25), (26), (27), (29),
% 251.89/60.22 | | | | | | | | (31), (33), (34), (35), (36), (37), (38), (39), (40),
% 251.89/60.22 | | | | | | | | (41), (43), (44), (45), (46), (47), (49), (52), (54),
% 251.89/60.22 | | | | | | | | (55), (57), (58), (60), (61), (62), (63), (64), (65),
% 251.89/60.22 | | | | | | | | (66), (69), (71), (72), (73), (74), (77), (78), (79),
% 251.89/60.22 | | | | | | | | (80), (82), (83), (85), (86), (88), (89), (90), (92),
% 251.89/60.22 | | | | | | | | (93), (94), (95), (96), (98), (99), (100), (101),
% 251.89/60.22 | | | | | | | | (102), (105), (108), (110), (111), (112), (113),
% 251.89/60.22 | | | | | | | | (114), (115), (116), (120), (123), (124), (126),
% 251.89/60.22 | | | | | | | | (127), (128), (129), (130), (132), (133), (136),
% 251.89/60.22 | | | | | | | | (137), (141), (142), (143), (145), (146), (149),
% 251.89/60.22 | | | | | | | | (150), (152), (153), (155), (157), (158), (159),
% 251.89/60.22 | | | | | | | | (161), (163), (164), (165), (166), (168), (169),
% 251.89/60.22 | | | | | | | | (170), (171), (174), (176), (177), (178), (179),
% 251.89/60.22 | | | | | | | | (180), (181), (182), (183), (185), (187), (188),
% 251.89/60.22 | | | | | | | | (189), (190), (191), (195), (196), (389), (392),
% 251.89/60.22 | | | | | | | | (398), (400), (402), (405), (412) are inconsistent by
% 251.89/60.22 | | | | | | | | sub-proof #817.
% 251.89/60.22 | | | | | | | |
% 251.89/60.22 | | | | | | | End of split
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | End of split
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | Case 2:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | (413) all_252_3 = e0 & op(e3, e3) = e0
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | ALPHA: (413) implies:
% 251.89/60.22 | | | | | | (414) op(e3, e3) = e0
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | REF_CLOSE: (33), (175), (181), (414) are inconsistent by sub-proof
% 251.89/60.22 | | | | | | #973.
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | End of split
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | Case 2:
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | (415) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 251.89/60.22 | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | BETA: splitting (415) gives:
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | | Case 1:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | (416) all_252_7 = e0 & op(e2, e3) = e0
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | REF_CLOSE: (33), (34), (398), (416) are inconsistent by sub-proof
% 251.89/60.22 | | | | | | #816.
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | Case 2:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | (417) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 251.89/60.22 | | | | | | op(e0, e3) = e0)
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | BETA: splitting (417) gives:
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | | Case 1:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | (418) all_252_13 = e0 & op(e1, e3) = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | ALPHA: (418) implies:
% 251.89/60.22 | | | | | | | (419) op(e1, e3) = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | GROUND_INST: instantiating (33) with all_62_2, e0, e3, e1,
% 251.89/60.22 | | | | | | | simplifying with (85), (419) gives:
% 251.89/60.22 | | | | | | | (420) all_62_2 = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REDUCE: (396), (420) imply:
% 251.89/60.22 | | | | | | | (421) $false
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | CLOSE: (421) is inconsistent.
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | Case 2:
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | (422) all_252_21 = e0 & op(e0, e3) = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | ALPHA: (422) implies:
% 251.89/60.22 | | | | | | | (423) all_252_21 = e0
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | | REF_CLOSE: (8), (13), (33), (34), (37), (85), (158), (181), (195),
% 251.89/60.22 | | | | | | | (389), (390), (423) are inconsistent by sub-proof #814.
% 251.89/60.22 | | | | | | |
% 251.89/60.22 | | | | | | End of split
% 251.89/60.22 | | | | | |
% 251.89/60.22 | | | | | End of split
% 251.89/60.22 | | | | |
% 251.89/60.22 | | | | End of split
% 251.89/60.22 | | | |
% 251.89/60.22 | | | End of split
% 251.89/60.22 | | |
% 251.89/60.22 | | Case 2:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (424) all_64_2 = e3
% 251.89/60.22 | | |
% 251.89/60.22 | | | REDUCE: (81), (424) imply:
% 251.89/60.22 | | | (425) ~ (all_244_0 = e3)
% 251.89/60.22 | | |
% 251.89/60.22 | | | REDUCE: (167), (424) imply:
% 251.89/60.22 | | | (426) ~ (all_16_2 = e3)
% 251.89/60.22 | | |
% 251.89/60.22 | | | REDUCE: (117), (424) imply:
% 251.89/60.22 | | | (427) ~ (all_12_2 = e3)
% 251.89/60.22 | | |
% 251.89/60.22 | | | REDUCE: (28), (424) imply:
% 251.89/60.22 | | | (428) op(e3, e4) = e2
% 251.89/60.22 | | |
% 251.89/60.22 | | | REF_CLOSE: (8), (33), (34), (35), (38), (42), (43), (46), (55), (80),
% 251.89/60.22 | | | (116), (121), (126), (136), (138), (141), (168), (176), (177),
% 251.89/60.22 | | | (191), (425), (428) are inconsistent by sub-proof #807.
% 251.89/60.22 | | |
% 251.89/60.22 | | End of split
% 251.89/60.22 | |
% 251.89/60.22 | Case 2:
% 251.89/60.22 | |
% 251.89/60.22 | | (429) all_62_2 = e4
% 251.89/60.22 | |
% 251.89/60.22 | | REDUCE: (103), (429) imply:
% 251.89/60.22 | | (430) ~ (all_244_3 = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | REDUCE: (48), (429) imply:
% 251.89/60.22 | | (431) ~ (all_84_2 = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | REDUCE: (32), (429) imply:
% 251.89/60.22 | | (432) ~ (all_22_2 = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | SIMP: (432) implies:
% 251.89/60.22 | | (433) ~ (all_22_2 = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | REDUCE: (160), (429) imply:
% 251.89/60.22 | | (434) ~ (all_10_2 = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | REDUCE: (22), (429) imply:
% 251.89/60.22 | | (435) op(e4, e0) = e3
% 251.89/60.22 | |
% 251.89/60.22 | | BETA: splitting (3) gives:
% 251.89/60.22 | |
% 251.89/60.22 | | Case 1:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (436) ~ (all_74_2 = e0)
% 251.89/60.22 | | |
% 251.89/60.22 | | | REDUCE: (10), (436) imply:
% 251.89/60.22 | | | (437) $false
% 251.89/60.22 | | |
% 251.89/60.22 | | | CLOSE: (437) is inconsistent.
% 251.89/60.22 | | |
% 251.89/60.22 | | Case 2:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (438) ( ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0, all_74_1) =
% 251.89/60.22 | | | all_74_0 & $i(all_74_0) & $i(all_74_1)) | ( ~ (all_74_1 = e4) &
% 251.89/60.22 | | | op(e1, e0) = all_74_1 & $i(all_74_1))
% 251.89/60.22 | | |
% 251.89/60.22 | | | BETA: splitting (438) gives:
% 251.89/60.22 | | |
% 251.89/60.22 | | | Case 1:
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | (439) ~ (all_74_0 = e2) & op(e1, e0) = all_74_1 & op(e0, all_74_1) =
% 251.89/60.22 | | | | all_74_0 & $i(all_74_0) & $i(all_74_1)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | ALPHA: (439) implies:
% 251.89/60.22 | | | | (440) op(e1, e0) = all_74_1
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REF_CLOSE: (8), (13), (15), (16), (33), (34), (52), (80), (120), (128),
% 251.89/60.22 | | | | (141), (142), (144), (152), (158), (177), (181), (183),
% 251.89/60.22 | | | | (430), (431), (433), (435), (440) are inconsistent by
% 251.89/60.22 | | | | sub-proof #804.
% 251.89/60.22 | | | |
% 251.89/60.22 | | | Case 2:
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | (441) ~ (all_74_1 = e4) & op(e1, e0) = all_74_1 & $i(all_74_1)
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | ALPHA: (441) implies:
% 251.89/60.22 | | | | (442) op(e1, e0) = all_74_1
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | REF_CLOSE: (8), (13), (15), (16), (33), (34), (52), (80), (120), (128),
% 251.89/60.22 | | | | (141), (142), (144), (152), (158), (177), (181), (183),
% 251.89/60.22 | | | | (430), (431), (433), (435), (442) are inconsistent by
% 251.89/60.22 | | | | sub-proof #804.
% 251.89/60.22 | | | |
% 251.89/60.22 | | | End of split
% 251.89/60.22 | | |
% 251.89/60.22 | | End of split
% 251.89/60.22 | |
% 251.89/60.22 | End of split
% 251.89/60.22 |
% 251.89/60.22 End of proof
% 251.89/60.22
% 251.89/60.22 Sub-proof #804 shows that the following formulas are inconsistent:
% 251.89/60.22 ----------------------------------------------------------------
% 251.89/60.22 (1) ~ (all_10_2 = e4)
% 251.89/60.22 (2) op(e4, e0) = e3
% 251.89/60.22 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 251.89/60.22 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 251.89/60.22 | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.22 (4) op(e4, e0) = all_30_2
% 251.89/60.22 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.89/60.22 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 251.89/60.22 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.89/60.22 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.22 (7) op(e2, e3) = all_10_2
% 251.89/60.22 (8) op(e1, e0) = all_34_2
% 251.89/60.22 (9) op(e1, e0) = all_74_1
% 251.89/60.22 (10) ~ (all_244_3 = e4)
% 251.89/60.22 (11) op(e1, e4) = all_16_2
% 251.89/60.22 (12) ~ (all_84_2 = e4)
% 251.89/60.22 (13) ~ (all_22_2 = e4)
% 251.89/60.22 (14) op(e0, e3) = all_22_2
% 251.89/60.22 (15) ~ (all_244_15 = e3)
% 251.89/60.22 (16) ~ (e4 = e3)
% 251.89/60.22 (17) op(e1, e1) = all_244_15
% 251.89/60.22 (18) ~ (all_34_2 = all_30_2)
% 251.89/60.22 (19) op(e1, e2) = all_4_2
% 251.89/60.22 (20) op(e4, e3) = all_84_2
% 251.89/60.22 (21) ~ (all_16_2 = e3)
% 251.89/60.22 (22) op(e3, e3) = all_244_3
% 251.89/60.22 (23) ~ (all_4_2 = e3)
% 251.89/60.22
% 251.89/60.22 Begin of proof
% 251.89/60.22 |
% 251.89/60.22 | BETA: splitting (3) gives:
% 251.89/60.22 |
% 251.89/60.22 | Case 1:
% 251.89/60.22 | |
% 251.89/60.22 | | (24) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 251.89/60.22 | | e4)
% 251.89/60.22 | |
% 251.89/60.22 | | BETA: splitting (24) gives:
% 251.89/60.22 | |
% 251.89/60.22 | | Case 1:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (25) all_252_1 = e4 & op(e4, e3) = e4
% 251.89/60.22 | | |
% 251.89/60.22 | | | REF_CLOSE: (6), (12), (20), (25) are inconsistent by sub-proof #815.
% 251.89/60.22 | | |
% 251.89/60.22 | | Case 2:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (26) all_252_3 = e4 & op(e3, e3) = e4
% 251.89/60.22 | | |
% 251.89/60.22 | | | REF_CLOSE: (6), (10), (22), (26) are inconsistent by sub-proof #846.
% 251.89/60.22 | | |
% 251.89/60.22 | | End of split
% 251.89/60.22 | |
% 251.89/60.22 | Case 2:
% 251.89/60.22 | |
% 251.89/60.22 | | (27) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 251.89/60.22 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 251.89/60.22 | |
% 251.89/60.22 | | BETA: splitting (27) gives:
% 251.89/60.22 | |
% 251.89/60.22 | | Case 1:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (28) all_252_7 = e4 & op(e2, e3) = e4
% 251.89/60.22 | | |
% 251.89/60.22 | | | ALPHA: (28) implies:
% 251.89/60.22 | | | (29) op(e2, e3) = e4
% 251.89/60.22 | | |
% 251.89/60.22 | | | REF_CLOSE: (1), (6), (7), (29) are inconsistent by sub-proof #953.
% 251.89/60.22 | | |
% 251.89/60.22 | | Case 2:
% 251.89/60.22 | | |
% 251.89/60.22 | | | (30) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 251.89/60.22 | | | e3) = e4)
% 251.89/60.22 | | |
% 251.89/60.22 | | | BETA: splitting (30) gives:
% 251.89/60.22 | | |
% 251.89/60.22 | | | Case 1:
% 251.89/60.22 | | | |
% 251.89/60.22 | | | | (31) all_252_13 = e4 & op(e1, e3) = e4
% 251.89/60.22 | | | |
% 251.89/60.23 | | | | ALPHA: (31) implies:
% 251.89/60.23 | | | | (32) all_252_13 = e4
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | BETA: splitting (5) gives:
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | Case 1:
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | (33) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 &
% 251.89/60.23 | | | | | op(e1, e3) = e3)
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | REF_CLOSE: (6), (11), (16), (21), (32), (33) are inconsistent by
% 251.89/60.23 | | | | | sub-proof #806.
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | Case 2:
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | (34) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 251.89/60.23 | | | | | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | BETA: splitting (34) gives:
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | Case 1:
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | | (35) all_252_14 = e3 & op(e1, e2) = e3
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | | REF_CLOSE: (6), (19), (23), (35) are inconsistent by sub-proof #858.
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | Case 2:
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | | (36) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 &
% 251.89/60.23 | | | | | | op(e1, e0) = e3)
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | | BETA: splitting (36) gives:
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | | Case 1:
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | (37) all_252_15 = e3 & op(e1, e1) = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | ALPHA: (37) implies:
% 251.89/60.23 | | | | | | | (38) op(e1, e1) = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | REF_CLOSE: (6), (15), (17), (38) are inconsistent by sub-proof
% 251.89/60.23 | | | | | | | #822.
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | Case 2:
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | (39) all_252_19 = e3 & op(e1, e0) = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | ALPHA: (39) implies:
% 251.89/60.23 | | | | | | | (40) op(e1, e0) = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | GROUND_INST: instantiating (6) with all_34_2, all_74_1, e0, e1,
% 251.89/60.23 | | | | | | | simplifying with (8), (9) gives:
% 251.89/60.23 | | | | | | | (41) all_74_1 = all_34_2
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | GROUND_INST: instantiating (6) with e3, all_74_1, e0, e1,
% 251.89/60.23 | | | | | | | simplifying with (9), (40) gives:
% 251.89/60.23 | | | | | | | (42) all_74_1 = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | GROUND_INST: instantiating (6) with all_30_2, e3, e0, e4,
% 251.89/60.23 | | | | | | | simplifying with (2), (4) gives:
% 251.89/60.23 | | | | | | | (43) all_30_2 = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | COMBINE_EQS: (41), (42) imply:
% 251.89/60.23 | | | | | | | (44) all_34_2 = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | SIMP: (44) implies:
% 251.89/60.23 | | | | | | | (45) all_34_2 = e3
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | REDUCE: (18), (43), (45) imply:
% 251.89/60.23 | | | | | | | (46) $false
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | | CLOSE: (46) is inconsistent.
% 251.89/60.23 | | | | | | |
% 251.89/60.23 | | | | | | End of split
% 251.89/60.23 | | | | | |
% 251.89/60.23 | | | | | End of split
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | End of split
% 251.89/60.23 | | | |
% 251.89/60.23 | | | Case 2:
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | (47) all_252_21 = e4 & op(e0, e3) = e4
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | REF_CLOSE: (6), (13), (14), (47) are inconsistent by sub-proof #805.
% 251.89/60.23 | | | |
% 251.89/60.23 | | | End of split
% 251.89/60.23 | | |
% 251.89/60.23 | | End of split
% 251.89/60.23 | |
% 251.89/60.23 | End of split
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #805 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) all_252_21 = e4 & op(e0, e3) = e4
% 251.89/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (3) op(e0, e3) = all_22_2
% 251.89/60.23 (4) ~ (all_22_2 = e4)
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | ALPHA: (1) implies:
% 251.89/60.23 | (5) op(e0, e3) = e4
% 251.89/60.23 |
% 251.89/60.23 | GROUND_INST: instantiating (2) with all_22_2, e4, e3, e0, simplifying with
% 251.89/60.23 | (3), (5) gives:
% 251.89/60.23 | (6) all_22_2 = e4
% 251.89/60.23 |
% 251.89/60.23 | REDUCE: (4), (6) imply:
% 251.89/60.23 | (7) $false
% 251.89/60.23 |
% 251.89/60.23 | CLOSE: (7) is inconsistent.
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #806 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 251.89/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (3) op(e1, e4) = all_16_2
% 251.89/60.23 (4) ~ (e4 = e3)
% 251.89/60.23 (5) all_252_13 = e4
% 251.89/60.23 (6) ~ (all_16_2 = e3)
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | BETA: splitting (1) gives:
% 251.89/60.23 |
% 251.89/60.23 | Case 1:
% 251.89/60.23 | |
% 251.89/60.23 | | (7) all_252_12 = e3 & op(e1, e4) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #895.
% 251.89/60.23 | |
% 251.89/60.23 | Case 2:
% 251.89/60.23 | |
% 251.89/60.23 | | (8) all_252_13 = e3 & op(e1, e3) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | ALPHA: (8) implies:
% 251.89/60.23 | | (9) all_252_13 = e3
% 251.89/60.23 | |
% 251.89/60.23 | | COMBINE_EQS: (5), (9) imply:
% 251.89/60.23 | | (10) e4 = e3
% 251.89/60.23 | |
% 251.89/60.23 | | SIMP: (10) implies:
% 251.89/60.23 | | (11) e4 = e3
% 251.89/60.23 | |
% 251.89/60.23 | | REDUCE: (4), (11) imply:
% 251.89/60.23 | | (12) $false
% 251.89/60.23 | |
% 251.89/60.23 | | CLOSE: (12) is inconsistent.
% 251.89/60.23 | |
% 251.89/60.23 | End of split
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #807 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) ~ (all_10_2 = e4)
% 251.89/60.23 (2) op(e3, e4) = e2
% 251.89/60.23 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (4) op(e2, e3) = all_10_2
% 251.89/60.23 (5) ~ (e3 = e2)
% 251.89/60.23 (6) ~ (all_12_2 = e3)
% 251.89/60.23 (7) op(all_244_8, all_244_8) = e2
% 251.89/60.23 (8) op(e2, e2) = all_244_8
% 251.89/60.23 (9) op(e2, e1) = all_38_2
% 251.89/60.23 (10) ~ (all_40_2 = e4)
% 251.89/60.23 (11) op(e1, e4) = all_16_2
% 251.89/60.23 (12) ~ (all_38_2 = e4)
% 251.89/60.23 (13) ~ (all_244_0 = all_100_2)
% 251.89/60.23 (14) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.23 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 251.89/60.23 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.23 (15) op(e3, e4) = all_100_2
% 251.89/60.23 (16) op(e4, e4) = all_244_0
% 251.89/60.23 (17) ~ (e4 = e3)
% 251.89/60.23 (18) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.23 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.23 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.23 (19) op(e2, e0) = all_40_2
% 251.89/60.23 (20) ~ (all_16_2 = e3)
% 251.89/60.23 (21) ~ (all_244_0 = e3)
% 251.89/60.23 (22) op(e0, e4) = all_12_2
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | BETA: splitting (18) gives:
% 251.89/60.23 |
% 251.89/60.23 | Case 1:
% 251.89/60.23 | |
% 251.89/60.23 | | (23) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) =
% 251.89/60.23 | | e3)
% 251.89/60.23 | |
% 251.89/60.23 | | REF_CLOSE: (2), (3), (5), (15), (16), (21), (23) are inconsistent by
% 251.89/60.23 | | sub-proof #812.
% 251.89/60.23 | |
% 251.89/60.23 | Case 2:
% 251.89/60.23 | |
% 251.89/60.23 | | (24) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 251.89/60.23 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 251.89/60.23 | |
% 251.89/60.23 | | BETA: splitting (24) gives:
% 251.89/60.23 | |
% 251.89/60.23 | | Case 1:
% 251.89/60.23 | | |
% 251.89/60.23 | | | (25) all_252_6 = e3 & op(e2, e4) = e3
% 251.89/60.23 | | |
% 251.89/60.23 | | | ALPHA: (25) implies:
% 251.89/60.23 | | | (26) all_252_6 = e3
% 251.89/60.23 | | |
% 251.89/60.23 | | | BETA: splitting (14) gives:
% 251.89/60.23 | | |
% 251.89/60.23 | | | Case 1:
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | (27) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 251.89/60.23 | | | | e3) = e4)
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | REF_CLOSE: (1), (3), (4), (17), (26), (27) are inconsistent by sub-proof
% 251.89/60.23 | | | | #810.
% 251.89/60.23 | | | |
% 251.89/60.23 | | | Case 2:
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | (28) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2,
% 251.89/60.23 | | | | e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | BETA: splitting (28) gives:
% 251.89/60.23 | | | |
% 251.89/60.23 | | | | Case 1:
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | (29) all_252_8 = e4 & op(e2, e2) = e4
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | REF_CLOSE: (2), (3), (7), (8), (13), (15), (16), (29) are inconsistent
% 251.89/60.23 | | | | | by sub-proof #808.
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | Case 2:
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | (30) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 251.89/60.23 | | | | | op(e2, e0) = e4)
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | | REF_CLOSE: (3), (9), (10), (12), (19), (30) are inconsistent by
% 251.89/60.23 | | | | | sub-proof #933.
% 251.89/60.23 | | | | |
% 251.89/60.23 | | | | End of split
% 251.89/60.23 | | | |
% 251.89/60.23 | | | End of split
% 251.89/60.23 | | |
% 251.89/60.23 | | Case 2:
% 251.89/60.23 | | |
% 251.89/60.23 | | | (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0,
% 251.89/60.23 | | | e4) = e3)
% 251.89/60.23 | | |
% 251.89/60.23 | | | REF_CLOSE: (3), (6), (11), (20), (22), (31) are inconsistent by sub-proof
% 251.89/60.23 | | | #894.
% 251.89/60.23 | | |
% 251.89/60.23 | | End of split
% 251.89/60.23 | |
% 251.89/60.23 | End of split
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #808 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) op(e3, e4) = e2
% 251.89/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (3) op(all_244_8, all_244_8) = e2
% 251.89/60.23 (4) op(e2, e2) = all_244_8
% 251.89/60.23 (5) all_252_8 = e4 & op(e2, e2) = e4
% 251.89/60.23 (6) ~ (all_244_0 = all_100_2)
% 251.89/60.23 (7) op(e3, e4) = all_100_2
% 251.89/60.23 (8) op(e4, e4) = all_244_0
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | ALPHA: (5) implies:
% 251.89/60.23 | (9) op(e2, e2) = e4
% 251.89/60.23 |
% 251.89/60.23 | GROUND_INST: instantiating (2) with all_244_8, e4, e2, e2, simplifying with
% 251.89/60.23 | (4), (9) gives:
% 251.89/60.23 | (10) all_244_8 = e4
% 251.89/60.23 |
% 251.89/60.23 | GROUND_INST: instantiating (2) with all_100_2, e2, e4, e3, simplifying with
% 251.89/60.23 | (1), (7) gives:
% 251.89/60.23 | (11) all_100_2 = e2
% 251.89/60.23 |
% 251.89/60.23 | REDUCE: (6), (11) imply:
% 251.89/60.23 | (12) ~ (all_244_0 = e2)
% 251.89/60.23 |
% 251.89/60.23 | REDUCE: (3), (10) imply:
% 251.89/60.23 | (13) op(e4, e4) = e2
% 251.89/60.23 |
% 251.89/60.23 | REF_CLOSE: (2), (8), (12), (13) are inconsistent by sub-proof #809.
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #809 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (2) op(e4, e4) = all_244_0
% 251.89/60.23 (3) op(e4, e4) = e2
% 251.89/60.23 (4) ~ (all_244_0 = e2)
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | GROUND_INST: instantiating (1) with all_244_0, e2, e4, e4, simplifying with
% 251.89/60.23 | (2), (3) gives:
% 251.89/60.23 | (5) all_244_0 = e2
% 251.89/60.23 |
% 251.89/60.23 | REDUCE: (4), (5) imply:
% 251.89/60.23 | (6) $false
% 251.89/60.23 |
% 251.89/60.23 | CLOSE: (6) is inconsistent.
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #810 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) ~ (all_10_2 = e4)
% 251.89/60.23 (2) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 251.89/60.23 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (4) op(e2, e3) = all_10_2
% 251.89/60.23 (5) ~ (e4 = e3)
% 251.89/60.23 (6) all_252_6 = e3
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | BETA: splitting (2) gives:
% 251.89/60.23 |
% 251.89/60.23 | Case 1:
% 251.89/60.23 | |
% 251.89/60.23 | | (7) all_252_6 = e4 & op(e2, e4) = e4
% 251.89/60.23 | |
% 251.89/60.23 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #811.
% 251.89/60.23 | |
% 251.89/60.23 | Case 2:
% 251.89/60.23 | |
% 251.89/60.23 | | (8) all_252_7 = e4 & op(e2, e3) = e4
% 251.89/60.23 | |
% 251.89/60.23 | | ALPHA: (8) implies:
% 251.89/60.23 | | (9) op(e2, e3) = e4
% 251.89/60.23 | |
% 251.89/60.23 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #953.
% 251.89/60.23 | |
% 251.89/60.23 | End of split
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #811 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) all_252_6 = e4 & op(e2, e4) = e4
% 251.89/60.23 (2) all_252_6 = e3
% 251.89/60.23 (3) ~ (e4 = e3)
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | ALPHA: (1) implies:
% 251.89/60.23 | (4) all_252_6 = e4
% 251.89/60.23 |
% 251.89/60.23 | COMBINE_EQS: (2), (4) imply:
% 251.89/60.23 | (5) e4 = e3
% 251.89/60.23 |
% 251.89/60.23 | SIMP: (5) implies:
% 251.89/60.23 | (6) e4 = e3
% 251.89/60.23 |
% 251.89/60.23 | REDUCE: (3), (6) imply:
% 251.89/60.23 | (7) $false
% 251.89/60.23 |
% 251.89/60.23 | CLOSE: (7) is inconsistent.
% 251.89/60.23 |
% 251.89/60.23 End of proof
% 251.89/60.23
% 251.89/60.23 Sub-proof #812 shows that the following formulas are inconsistent:
% 251.89/60.23 ----------------------------------------------------------------
% 251.89/60.23 (1) op(e3, e4) = e2
% 251.89/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 251.89/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 251.89/60.23 (3) ~ (e3 = e2)
% 251.89/60.23 (4) op(e3, e4) = all_100_2
% 251.89/60.23 (5) op(e4, e4) = all_244_0
% 251.89/60.23 (6) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 251.89/60.23 (7) ~ (all_244_0 = e3)
% 251.89/60.23
% 251.89/60.23 Begin of proof
% 251.89/60.23 |
% 251.89/60.23 | BETA: splitting (6) gives:
% 251.89/60.23 |
% 251.89/60.23 | Case 1:
% 251.89/60.23 | |
% 251.89/60.23 | | (8) all_252_0 = e3 & op(e4, e4) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | ALPHA: (8) implies:
% 251.89/60.23 | | (9) op(e4, e4) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #813.
% 251.89/60.23 | |
% 251.89/60.23 | Case 2:
% 251.89/60.23 | |
% 251.89/60.23 | | (10) all_252_2 = e3 & op(e3, e4) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | ALPHA: (10) implies:
% 251.89/60.23 | | (11) op(e3, e4) = e3
% 251.89/60.23 | |
% 251.89/60.23 | | GROUND_INST: instantiating (2) with all_100_2, e2, e4, e3, simplifying with
% 251.89/60.23 | | (1), (4) gives:
% 251.89/60.23 | | (12) all_100_2 = e2
% 251.89/60.23 | |
% 252.14/60.23 | | GROUND_INST: instantiating (2) with all_100_2, e3, e4, e3, simplifying with
% 252.14/60.23 | | (4), (11) gives:
% 252.14/60.23 | | (13) all_100_2 = e3
% 252.14/60.23 | |
% 252.14/60.23 | | COMBINE_EQS: (12), (13) imply:
% 252.14/60.23 | | (14) e3 = e2
% 252.14/60.23 | |
% 252.14/60.23 | | SIMP: (14) implies:
% 252.14/60.23 | | (15) e3 = e2
% 252.14/60.23 | |
% 252.14/60.23 | | REDUCE: (3), (15) imply:
% 252.14/60.23 | | (16) $false
% 252.14/60.23 | |
% 252.14/60.23 | | CLOSE: (16) is inconsistent.
% 252.14/60.23 | |
% 252.14/60.23 | End of split
% 252.14/60.23 |
% 252.14/60.23 End of proof
% 252.14/60.23
% 252.14/60.23 Sub-proof #813 shows that the following formulas are inconsistent:
% 252.14/60.23 ----------------------------------------------------------------
% 252.14/60.23 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.23 (2) op(e4, e4) = all_244_0
% 252.14/60.23 (3) op(e4, e4) = e3
% 252.14/60.23 (4) ~ (all_244_0 = e3)
% 252.14/60.23
% 252.14/60.23 Begin of proof
% 252.14/60.23 |
% 252.14/60.23 | GROUND_INST: instantiating (1) with all_244_0, e3, e4, e4, simplifying with
% 252.14/60.23 | (2), (3) gives:
% 252.14/60.23 | (5) all_244_0 = e3
% 252.14/60.23 |
% 252.14/60.23 | REDUCE: (4), (5) imply:
% 252.14/60.23 | (6) $false
% 252.14/60.23 |
% 252.14/60.23 | CLOSE: (6) is inconsistent.
% 252.14/60.23 |
% 252.14/60.23 End of proof
% 252.14/60.23
% 252.14/60.23 Sub-proof #814 shows that the following formulas are inconsistent:
% 252.14/60.23 ----------------------------------------------------------------
% 252.14/60.23 (1) ~ (all_10_2 = e4)
% 252.14/60.23 (2) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 252.14/60.23 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.14/60.23 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.14/60.23 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.23 (4) op(e2, e3) = all_10_2
% 252.14/60.23 (5) ~ (e4 = e0)
% 252.14/60.23 (6) ~ (all_244_3 = e4)
% 252.14/60.23 (7) op(e1, e3) = all_62_2
% 252.14/60.23 (8) ~ (all_84_2 = e4)
% 252.14/60.23 (9) all_252_21 = e0
% 252.14/60.23 (10) op(e4, e3) = all_84_2
% 252.14/60.23 (11) op(e3, e3) = all_244_3
% 252.14/60.23 (12) ~ (all_62_2 = e4)
% 252.14/60.23
% 252.14/60.23 Begin of proof
% 252.14/60.23 |
% 252.14/60.23 | BETA: splitting (2) gives:
% 252.14/60.23 |
% 252.14/60.23 | Case 1:
% 252.14/60.23 | |
% 252.14/60.23 | | (13) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 252.14/60.23 | | e4)
% 252.14/60.23 | |
% 252.14/60.23 | | BETA: splitting (13) gives:
% 252.14/60.23 | |
% 252.14/60.23 | | Case 1:
% 252.14/60.23 | | |
% 252.14/60.23 | | | (14) all_252_1 = e4 & op(e4, e3) = e4
% 252.14/60.23 | | |
% 252.14/60.23 | | | REF_CLOSE: (3), (8), (10), (14) are inconsistent by sub-proof #815.
% 252.14/60.23 | | |
% 252.14/60.23 | | Case 2:
% 252.14/60.23 | | |
% 252.14/60.23 | | | (15) all_252_3 = e4 & op(e3, e3) = e4
% 252.14/60.23 | | |
% 252.14/60.23 | | | REF_CLOSE: (3), (6), (11), (15) are inconsistent by sub-proof #846.
% 252.14/60.23 | | |
% 252.14/60.23 | | End of split
% 252.14/60.23 | |
% 252.14/60.23 | Case 2:
% 252.14/60.23 | |
% 252.14/60.23 | | (16) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 252.14/60.23 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.14/60.23 | |
% 252.14/60.23 | | BETA: splitting (16) gives:
% 252.14/60.23 | |
% 252.14/60.23 | | Case 1:
% 252.14/60.23 | | |
% 252.14/60.23 | | | (17) all_252_7 = e4 & op(e2, e3) = e4
% 252.14/60.23 | | |
% 252.14/60.23 | | | ALPHA: (17) implies:
% 252.14/60.23 | | | (18) op(e2, e3) = e4
% 252.14/60.23 | | |
% 252.14/60.23 | | | REF_CLOSE: (1), (3), (4), (18) are inconsistent by sub-proof #953.
% 252.14/60.23 | | |
% 252.14/60.23 | | Case 2:
% 252.14/60.23 | | |
% 252.14/60.23 | | | (19) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0,
% 252.14/60.23 | | | e3) = e4)
% 252.14/60.23 | | |
% 252.14/60.23 | | | BETA: splitting (19) gives:
% 252.14/60.23 | | |
% 252.14/60.23 | | | Case 1:
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | (20) all_252_13 = e4 & op(e1, e3) = e4
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | REF_CLOSE: (3), (7), (12), (20) are inconsistent by sub-proof #952.
% 252.14/60.23 | | | |
% 252.14/60.23 | | | Case 2:
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | (21) all_252_21 = e4 & op(e0, e3) = e4
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | ALPHA: (21) implies:
% 252.14/60.23 | | | | (22) all_252_21 = e4
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | COMBINE_EQS: (9), (22) imply:
% 252.14/60.23 | | | | (23) e4 = e0
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | REDUCE: (5), (23) imply:
% 252.14/60.23 | | | | (24) $false
% 252.14/60.23 | | | |
% 252.14/60.23 | | | | CLOSE: (24) is inconsistent.
% 252.14/60.23 | | | |
% 252.14/60.23 | | | End of split
% 252.14/60.23 | | |
% 252.14/60.23 | | End of split
% 252.14/60.23 | |
% 252.14/60.23 | End of split
% 252.14/60.23 |
% 252.14/60.23 End of proof
% 252.14/60.23
% 252.14/60.23 Sub-proof #815 shows that the following formulas are inconsistent:
% 252.14/60.23 ----------------------------------------------------------------
% 252.14/60.23 (1) all_252_1 = e4 & op(e4, e3) = e4
% 252.14/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.23 (3) op(e4, e3) = all_84_2
% 252.14/60.23 (4) ~ (all_84_2 = e4)
% 252.14/60.23
% 252.14/60.23 Begin of proof
% 252.14/60.23 |
% 252.14/60.23 | ALPHA: (1) implies:
% 252.14/60.23 | (5) op(e4, e3) = e4
% 252.14/60.23 |
% 252.14/60.23 | GROUND_INST: instantiating (2) with all_84_2, e4, e3, e4, simplifying with
% 252.14/60.23 | (3), (5) gives:
% 252.14/60.23 | (6) all_84_2 = e4
% 252.14/60.23 |
% 252.14/60.23 | REDUCE: (4), (6) imply:
% 252.14/60.23 | (7) $false
% 252.14/60.23 |
% 252.14/60.23 | CLOSE: (7) is inconsistent.
% 252.14/60.23 |
% 252.14/60.23 End of proof
% 252.14/60.23
% 252.14/60.23 Sub-proof #816 shows that the following formulas are inconsistent:
% 252.14/60.23 ----------------------------------------------------------------
% 252.14/60.23 (1) all_252_7 = e0 & op(e2, e3) = e0
% 252.14/60.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.23 (3) op(e2, e3) = all_10_2
% 252.14/60.23 (4) ~ (all_10_2 = e0)
% 252.14/60.23
% 252.14/60.23 Begin of proof
% 252.14/60.23 |
% 252.14/60.23 | ALPHA: (1) implies:
% 252.14/60.23 | (5) op(e2, e3) = e0
% 252.14/60.23 |
% 252.14/60.23 | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e2, simplifying with
% 252.14/60.23 | (3), (5) gives:
% 252.14/60.23 | (6) all_10_2 = e0
% 252.14/60.23 |
% 252.14/60.23 | REDUCE: (4), (6) imply:
% 252.14/60.23 | (7) $false
% 252.14/60.23 |
% 252.14/60.23 | CLOSE: (7) is inconsistent.
% 252.14/60.23 |
% 252.14/60.23 End of proof
% 252.14/60.23
% 252.14/60.23 Sub-proof #817 shows that the following formulas are inconsistent:
% 252.14/60.23 ----------------------------------------------------------------
% 252.14/60.23 (1) ~ (all_244_8 = all_4_2)
% 252.14/60.23 (2) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) |
% 252.14/60.23 (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = e0)
% 252.14/60.23 | (all_252_20 = e0 & op(e0, e4) = e0)
% 252.14/60.23 (3) ~ (all_4_2 = e4)
% 252.14/60.23 (4) ~ (all_10_2 = e4)
% 252.14/60.23 (5) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) |
% 252.14/60.23 (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = e3) |
% 252.14/60.23 (all_252_16 = e3 & op(e4, e0) = e3)
% 252.14/60.23 (6) ~ (all_40_2 = all_38_2)
% 252.14/60.23 (7) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 252.14/60.23 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.14/60.23 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.14/60.23 (8) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) |
% 252.14/60.23 (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 252.14/60.23 | (all_252_21 = e2 & op(e0, e3) = e2)
% 252.14/60.23 (9) op(e4, e0) = all_30_2
% 252.14/60.23 (10) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 252.14/60.23 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1,
% 252.14/60.23 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 252.14/60.23 (11) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0)
% 252.14/60.23 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) =
% 252.14/60.23 e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 252.14/60.23 (12) ~ (all_82_2 = e1) | ( ~ (all_82_0 = e3) & op(e2, e1) = all_82_1 &
% 252.14/60.23 op(e1, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1)) | ( ~
% 252.14/60.23 (all_82_1 = e4) & op(e2, e1) = all_82_1 & $i(all_82_1))
% 252.14/60.23 (13) op(all_62_2, e0) = e3
% 252.14/60.23 (14) op(all_38_2, e1) = e2
% 252.14/60.23 (15) ~ (all_64_2 = e3)
% 252.14/60.23 (16) all_250_13 = all_38_2
% 252.14/60.23 (17) ~ (all_28_2 = all_6_2)
% 252.14/60.23 (18) ~ (e2 = e0)
% 252.14/60.23 (19) ~ (e1 = e0)
% 252.14/60.23 (20) ~ (all_28_2 = e3)
% 252.14/60.23 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.23 (22) op(e2, e3) = all_10_2
% 252.14/60.23 (23) ~ (e3 = e2)
% 252.14/60.23 (24) op(e0, e0) = all_244_24
% 252.14/60.23 (25) ~ (e4 = e0)
% 252.14/60.23 (26) ~ (all_12_2 = e3)
% 252.14/60.23 (27) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1)
% 252.14/60.23 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) =
% 252.14/60.23 e1) | (all_252_18 = e1 & op(e2, e0) = e1)
% 252.14/60.23 (28) ~ (all_86_2 = e3) | ( ~ (all_86_0 = e1) & op(e3, all_86_1) = all_86_0 &
% 252.14/60.23 op(e0, e3) = all_86_1 & $i(all_86_0) & $i(all_86_1)) | ( ~ (all_86_1 =
% 252.14/60.23 e4) & op(e0, e3) = all_86_1 & $i(all_86_1))
% 252.14/60.23 (29) all_252_23 = e3
% 252.14/60.23 (30) op(e2, e2) = all_244_8
% 252.14/60.23 (31) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 252.14/60.23 all_250_11 = e0
% 252.14/60.23 (32) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 252.14/60.23 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 252.14/60.23 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 252.14/60.23 (33) op(e2, e1) = all_38_2
% 252.14/60.23 (34) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 252.14/60.23 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 252.14/60.23 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.14/60.23 (35) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) =
% 252.14/60.23 e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1,
% 252.14/60.23 e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.14/60.23 (36) op(e1, e0) = all_34_2
% 252.14/60.23 (37) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 252.14/60.23 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 252.14/60.23 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.14/60.23 (38) ~ (all_40_2 = e4)
% 252.14/60.23 (39) op(all_28_2, e2) = e0
% 252.14/60.23 (40) op(e4, e2) = all_6_2
% 252.14/60.23 (41) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) =
% 252.14/60.23 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1,
% 252.14/60.23 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.14/60.24 (42) all_78_2 = all_10_2
% 252.14/60.24 (43) ~ (all_8_2 = all_4_2)
% 252.14/60.24 (44) ~ (all_34_2 = e2)
% 252.14/60.24 (45) ~ (e2 = e1)
% 252.14/60.24 (46) op(e0, e2) = all_28_2
% 252.14/60.24 (47) ~ (e4 = e1)
% 252.14/60.24 (48) ~ (all_6_2 = e1)
% 252.14/60.24 (49) ~ (all_62_2 = all_34_2)
% 252.14/60.24 (50) ~ (all_244_8 = all_38_2)
% 252.14/60.24 (51) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 252.14/60.24 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.14/60.24 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.14/60.24 (52) op(all_244_15, all_244_15) = e1
% 252.14/60.24 (53) op(all_34_2, e0) = e1
% 252.14/60.24 (54) ~ (all_244_3 = all_84_2)
% 252.14/60.24 (55) ~ (all_244_3 = e4)
% 252.14/60.24 (56) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1)
% 252.14/60.24 | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) =
% 252.14/60.24 e1) | (all_252_16 = e1 & op(e4, e0) = e1)
% 252.14/60.24 (57) op(e1, e4) = all_16_2
% 252.14/60.24 (58) all_96_2 = all_34_2
% 252.14/60.24 (59) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 252.14/60.24 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 252.14/60.24 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.14/60.24 (60) op(e1, e3) = all_62_2
% 252.14/60.24 (61) op(all_16_2, all_26_2) = e4
% 252.14/60.24 (62) ~ (e3 = e0)
% 252.14/60.24 (63) ~ (all_38_2 = e0)
% 252.14/60.24 (64) ~ (all_40_2 = all_10_2)
% 252.14/60.24 (65) ~ (all_30_2 = e2)
% 252.14/60.24 (66) ~ (all_36_2 = e4)
% 252.14/60.24 (67) all_70_2 = all_62_2
% 252.14/60.24 (68) ~ (all_244_24 = e3)
% 252.14/60.24 (69) ~ (e3 = e1)
% 252.14/60.24 (70) ~ (all_12_2 = e2)
% 252.14/60.24 (71) op(e3, e1) = all_36_2
% 252.14/60.24 (72) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 252.14/60.24 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 252.14/60.24 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 252.14/60.24 (73) ~ (all_16_2 = e2)
% 252.14/60.24 (74) ~ (all_8_2 = e1)
% 252.14/60.24 (75) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) =
% 252.14/60.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0,
% 252.14/60.24 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 252.14/60.24 (76) ~ (all_28_2 = all_4_2)
% 252.14/60.24 (77) ~ (all_40_2 = all_34_2)
% 252.14/60.24 (78) op(e0, e1) = e3
% 252.14/60.24 (79) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.14/60.24 all_250_13 = e0
% 252.14/60.24 (80) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 252.14/60.24 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 252.14/60.24 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 252.14/60.24 (81) ~ (all_8_2 = e0)
% 252.14/60.24 (82) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.14/60.24 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.14/60.24 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.14/60.24 (83) ~ (all_38_2 = e4)
% 252.14/60.24 (84) op(e0, e3) = all_22_2
% 252.14/60.24 (85) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) =
% 252.14/60.24 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1,
% 252.14/60.24 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)
% 252.14/60.24 (86) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 252.14/60.24 e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & op(e1,
% 252.14/60.24 e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)
% 252.14/60.24 (87) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 252.14/60.24 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 252.14/60.24 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.14/60.24 (88) op(e4, e1) = all_26_2
% 252.14/60.24 (89) ~ (all_244_15 = e3)
% 252.14/60.24 (90) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 252.14/60.24 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 252.14/60.24 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.14/60.24 (91) op(all_10_2, e3) = e2
% 252.14/60.24 (92) ~ (all_244_15 = all_62_2)
% 252.14/60.24 (93) ~ (all_62_2 = all_16_2)
% 252.14/60.24 (94) op(e3, e4) = all_100_2
% 252.14/60.24 (95) all_250_11 = all_10_2
% 252.14/60.24 (96) ~ (e4 = e3)
% 252.14/60.24 (97) op(e1, e1) = all_244_15
% 252.14/60.24 (98) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4)
% 252.14/60.24 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 252.14/60.24 e4) | (all_252_17 = e4 & op(e3, e0) = e4)
% 252.14/60.24 (99) op(e0, e1) = all_20_2
% 252.14/60.24 (100) op(e3, e0) = all_48_2
% 252.14/60.24 (101) ~ (all_26_2 = e3)
% 252.14/60.24 (102) all_82_2 = all_28_2
% 252.14/60.24 (103) op(e1, e2) = all_4_2
% 252.14/60.24 (104) op(e3, e1) = e0
% 252.14/60.24 (105) ~ (all_28_2 = all_8_2)
% 252.14/60.24 (106) ~ (all_48_2 = e1)
% 252.14/60.24 (107) op(e4, e3) = all_84_2
% 252.14/60.24 (108) all_86_2 = all_40_2
% 252.14/60.24 (109) op(e2, e4) = all_64_2
% 252.14/60.24 (110) op(e0, e3) = e4
% 252.14/60.24 (111) all_252_1 = e0
% 252.14/60.24 (112) ~ (all_6_2 = all_4_2)
% 252.14/60.24 (113) op(e3, e0) = all_140_1
% 252.14/60.24 (114) ~ (e4 = e2)
% 252.14/60.24 (115) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 252.14/60.24 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 252.14/60.24 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.14/60.24 (116) ~ (all_6_2 = e0)
% 252.14/60.24 (117) op(e3, e2) = all_8_2
% 252.14/60.24 (118) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 252.14/60.24 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 252.14/60.24 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 252.14/60.24 (119) ~ (all_38_2 = all_10_2)
% 252.14/60.24 (120) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 252.14/60.24 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 252.14/60.24 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 252.14/60.24 (121) ~ (all_20_2 = e4)
% 252.14/60.24 (122) op(e4, e3) = e0
% 252.14/60.24 (123) op(all_16_2, e4) = e1
% 252.14/60.24 (124) op(e2, e0) = all_40_2
% 252.14/60.24 (125) ~ (all_16_2 = e3)
% 252.14/60.24 (126) ~ (all_244_8 = all_28_2)
% 252.14/60.24 (127) ~ (all_10_2 = e0)
% 252.14/60.24 (128) ~ (all_38_2 = e3)
% 252.14/60.24 (129) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.14/60.24 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.14/60.24 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.14/60.24 (130) op(e3, e3) = all_244_3
% 252.14/60.24 (131) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 252.14/60.24 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 252.14/60.24 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 252.14/60.24 (132) ~ (all_4_2 = e3)
% 252.14/60.24 (133) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 252.14/60.24 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 252.14/60.24 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 252.14/60.24 (134) ~ (all_62_2 = e4)
% 252.14/60.24 (135) ~ (all_62_2 = all_4_2)
% 252.14/60.24 (136) ~ (all_96_2 = e3) | ( ~ (all_96_0 = e2) & op(e3, all_96_1) = all_96_0
% 252.14/60.24 & op(e0, e3) = all_96_1 & $i(all_96_0) & $i(all_96_1)) | ( ~
% 252.14/60.24 (all_96_1 = e4) & op(e0, e3) = all_96_1 & $i(all_96_1))
% 252.14/60.24 (137) op(e0, all_62_2) = e1
% 252.14/60.24 (138) op(all_244_24, all_244_24) = e0
% 252.14/60.24 (139) op(e0, e4) = all_12_2
% 252.14/60.24
% 252.14/60.24 Begin of proof
% 252.14/60.24 |
% 252.14/60.24 | GROUND_INST: instantiating (21) with all_48_2, all_140_1, e0, e3, simplifying
% 252.14/60.24 | with (100), (113) gives:
% 252.14/60.24 | (140) all_140_1 = all_48_2
% 252.14/60.24 |
% 252.14/60.24 | BETA: splitting (80) gives:
% 252.14/60.24 |
% 252.14/60.24 | Case 1:
% 252.14/60.24 | |
% 252.14/60.24 | | (141) ~ (all_70_2 = e2)
% 252.14/60.24 | |
% 252.14/60.24 | | REDUCE: (67), (141) imply:
% 252.14/60.24 | | (142) ~ (all_62_2 = e2)
% 252.14/60.24 | |
% 252.14/60.24 | | BETA: splitting (72) gives:
% 252.14/60.24 | |
% 252.14/60.24 | | Case 1:
% 252.14/60.24 | | |
% 252.14/60.24 | | | (143) ~ (all_78_2 = e1)
% 252.14/60.24 | | |
% 252.14/60.24 | | | REDUCE: (42), (143) imply:
% 252.14/60.24 | | | (144) ~ (all_10_2 = e1)
% 252.14/60.24 | | |
% 252.14/60.24 | | | BETA: splitting (12) gives:
% 252.14/60.24 | | |
% 252.14/60.24 | | | Case 1:
% 252.14/60.24 | | | |
% 252.14/60.24 | | | | (145) ~ (all_82_2 = e1)
% 252.14/60.24 | | | |
% 252.14/60.24 | | | | REDUCE: (102), (145) imply:
% 252.14/60.24 | | | | (146) ~ (all_28_2 = e1)
% 252.14/60.24 | | | |
% 252.14/60.24 | | | | BETA: splitting (28) gives:
% 252.14/60.24 | | | |
% 252.14/60.24 | | | | Case 1:
% 252.14/60.24 | | | | |
% 252.14/60.24 | | | | | (147) ~ (all_86_2 = e3)
% 252.14/60.24 | | | | |
% 252.14/60.24 | | | | | REDUCE: (108), (147) imply:
% 252.14/60.24 | | | | | (148) ~ (all_40_2 = e3)
% 252.14/60.24 | | | | |
% 252.14/60.24 | | | | | BETA: splitting (136) gives:
% 252.14/60.24 | | | | |
% 252.14/60.24 | | | | | Case 1:
% 252.14/60.24 | | | | | |
% 252.14/60.24 | | | | | | (149) ~ (all_96_2 = e3)
% 252.14/60.24 | | | | | |
% 252.14/60.24 | | | | | | REDUCE: (58), (149) imply:
% 252.14/60.24 | | | | | | (150) ~ (all_34_2 = e3)
% 252.14/60.24 | | | | | |
% 252.14/60.24 | | | | | | BETA: splitting (10) gives:
% 252.14/60.24 | | | | | |
% 252.14/60.24 | | | | | | Case 1:
% 252.14/60.24 | | | | | | |
% 252.14/60.24 | | | | | | | (151) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 &
% 252.14/60.24 | | | | | | | op(e1, e3) = e3)
% 252.14/60.24 | | | | | | |
% 252.14/60.24 | | | | | | | BETA: splitting (151) gives:
% 252.14/60.24 | | | | | | |
% 252.14/60.24 | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | (152) all_252_12 = e3 & op(e1, e4) = e3
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | REF_CLOSE: (21), (57), (125), (152) are inconsistent by
% 252.14/60.24 | | | | | | | | sub-proof #895.
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | (153) all_252_13 = e3 & op(e1, e3) = e3
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | ALPHA: (153) implies:
% 252.14/60.24 | | | | | | | | (154) all_252_13 = e3
% 252.14/60.24 | | | | | | | | (155) op(e1, e3) = e3
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | BETA: splitting (133) gives:
% 252.14/60.24 | | | | | | | |
% 252.14/60.24 | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | |
% 252.14/60.24 | | | | | | | | | (156) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1
% 252.14/60.24 | | | | | | | | | & op(e3, e3) = e1)
% 252.14/60.24 | | | | | | | | |
% 252.14/60.24 | | | | | | | | | BETA: splitting (156) gives:
% 252.14/60.24 | | | | | | | | |
% 252.14/60.24 | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | (157) all_252_1 = e1 & op(e4, e3) = e1
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | REF_CLOSE: (19), (111), (157) are inconsistent by sub-proof
% 252.14/60.24 | | | | | | | | | | #851.
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | (158) all_252_3 = e1 & op(e3, e3) = e1
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | ALPHA: (158) implies:
% 252.14/60.24 | | | | | | | | | | (159) all_252_3 = e1
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | BETA: splitting (8) gives:
% 252.14/60.24 | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | (160) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 =
% 252.14/60.24 | | | | | | | | | | | e2 & op(e3, e3) = e2)
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | BETA: splitting (160) gives:
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | (161) all_252_1 = e2 & op(e4, e3) = e2
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | ALPHA: (161) implies:
% 252.14/60.24 | | | | | | | | | | | | (162) op(e4, e3) = e2
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | REF_CLOSE: (18), (21), (107), (122), (162) are inconsistent
% 252.14/60.24 | | | | | | | | | | | | by sub-proof #850.
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | (163) all_252_3 = e2 & op(e3, e3) = e2
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | REF_CLOSE: (45), (159), (163) are inconsistent by sub-proof
% 252.14/60.24 | | | | | | | | | | | | #849.
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | End of split
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | (164) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 =
% 252.14/60.24 | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 &
% 252.14/60.24 | | | | | | | | | | | op(e0, e3) = e2)
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | BETA: splitting (164) gives:
% 252.14/60.24 | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | (165) all_252_7 = e2 & op(e2, e3) = e2
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | ALPHA: (165) implies:
% 252.14/60.24 | | | | | | | | | | | | (166) all_252_7 = e2
% 252.14/60.24 | | | | | | | | | | | | (167) op(e2, e3) = e2
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | BETA: splitting (32) gives:
% 252.14/60.24 | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | (168) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 =
% 252.14/60.24 | | | | | | | | | | | | | e3 & op(e2, e3) = e3)
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | BETA: splitting (168) gives:
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | (169) all_252_6 = e3 & op(e2, e4) = e3
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | REF_CLOSE: (15), (21), (109), (169) are inconsistent by
% 252.14/60.24 | | | | | | | | | | | | | | sub-proof #940.
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | (170) all_252_7 = e3 & op(e2, e3) = e3
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | ALPHA: (170) implies:
% 252.14/60.24 | | | | | | | | | | | | | | (171) all_252_7 = e3
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | COMBINE_EQS: (166), (171) imply:
% 252.14/60.24 | | | | | | | | | | | | | | (172) e3 = e2
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | SIMP: (172) implies:
% 252.14/60.24 | | | | | | | | | | | | | | (173) e3 = e2
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | COMBINE_EQS: (29), (173) imply:
% 252.14/60.24 | | | | | | | | | | | | | | (174) all_252_23 = e2
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.24 | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.24 | | | | | | | | | | | | | | (174) are inconsistent by sub-proof #847.
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | End of split
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | (175) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 =
% 252.14/60.24 | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 252.14/60.24 | | | | | | | | | | | | | op(e2, e0) = e3)
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | BETA: splitting (175) gives:
% 252.14/60.24 | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | (176) all_252_8 = e3 & op(e2, e2) = e3
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | ALPHA: (176) implies:
% 252.14/60.24 | | | | | | | | | | | | | | (177) all_252_8 = e3
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 252.14/60.24 | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | (178) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 =
% 252.14/60.24 | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4)
% 252.14/60.24 | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 252.14/60.24 | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | (179) all_252_6 = e4 & op(e2, e4) = e4
% 252.14/60.24 | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 252.14/60.24 | | | | | | | | | | | | | | | | (180) all_252_6 = e4
% 252.14/60.24 | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 252.14/60.24 | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | (181) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 =
% 252.14/60.24 | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1)
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (48), (74), (117), (181) are
% 252.14/60.24 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #928.
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | (182) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 =
% 252.14/60.24 | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 &
% 252.14/60.24 | | | | | | | | | | | | | | | | | op(e0, e2) = e1)
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 252.14/60.24 | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | (183) all_252_8 = e1 & op(e2, e2) = e1
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | (184) all_252_8 = e1
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (177), (184) are inconsistent by sub-proof
% 252.14/60.24 | | | | | | | | | | | | | | | | | | #927.
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | (185) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22
% 252.14/60.24 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1)
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 252.14/60.24 | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | (186) all_252_14 = e1 & op(e1, e2) = e1
% 252.14/60.24 | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | (187) all_252_14 = e1
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | (188) op(e1, e2) = e1
% 252.14/60.24 | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | (189) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 =
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0)
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | (190) all_252_6 = e0 & op(e2, e4) = e0
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | (191) all_252_6 = e0
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (22), (25), (33), (38), (83), (87),
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | (96), (124), (177), (191) are inconsistent by
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | sub-proof #931.
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | (192) all_252_7 = e0 & op(e2, e3) = e0
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | | (193) all_252_7 = e0
% 252.14/60.24 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (19), (21), (23), (33), (36), (37),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (44), (45), (47), (57), (60), (61), (66), (69),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (71), (73), (78), (82), (83), (88), (99), (103),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (104), (114), (115), (121), (123), (129), (142),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (177), (180), (187), (188), (193) are inconsistent
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | by sub-proof #908.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | (194) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (195) all_252_8 = e0 & op(e2, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (196) all_252_8 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (177), (196) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | #905.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | (197) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | (198) all_252_11 = e0 & op(e2, e1) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (63), (198) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | sub-proof #904.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | (199) all_252_18 = e0 & op(e2, e0) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | (200) all_252_18 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | (201) op(e2, e0) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | (202) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_4 = e0 & op(e4, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (116), (203) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #875.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | (204) all_252_5 = e0 & op(e3, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (81), (117), (204) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #874.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | (205) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_8 = e0 & op(e2, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | (207) all_252_8 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (177), (207) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | #905.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | (208) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_252_14 = e0 & op(e1, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | (210) op(e1, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (103), (188), (210) are inconsistent
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #870.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_252_22 = e0 & op(e0, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_252_22 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | (213) op(e0, e2) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_20 = e2 & op(e0, e4) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) op(e0, e4) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (70), (139), (216) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #980.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_21 = e2 & op(e0, e3) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (21), (22), (25), (55), (60), (84),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (114), (130), (134), (217) are inconsistent
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #845.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_252_22 = e2 & op(e0, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_22 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (220) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) e2 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (221) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_252_7 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (19), (21), (23), (33), (36), (37),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (45), (47), (57), (60), (61), (66), (69),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (73), (78), (82), (83), (88), (99), (103),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (114), (115), (121), (123), (129), (142),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (177), (180), (187), (188), (222) are inconsistent
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #908.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_252_23 = e2 & op(e0, e1) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_23 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) are inconsistent by sub-proof #847.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_252_24 = e2 & op(e0, e0) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_24 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (57), (60), (73), (142), (228) are
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_14 = e2 & op(e1, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_252_14 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (187), (231) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #861.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_15 = e2 & op(e1, e1) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_15 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_252_6 = e1 & op(e2, e4) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_6 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (180), (237) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #844.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_7 = e1 & op(e2, e3) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) op(e2, e3) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (22), (45), (167), (239) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #902.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_252_8 = e1 & op(e2, e2) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_8 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (177), (242) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #927.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_252_11 = e1 & op(e2, e1) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_11 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_252_9 = e4 & op(e4, e1) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_9 = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) op(e4, e1) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_252_20 = e1 & op(e0, e4) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_252_20 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_252_0 = e0 & op(e4, e4) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_252_0 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_252_0 = e1 & op(e4, e4) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (255), (257) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #843.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_252_1 = e1 & op(e4, e3) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (111), (258) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_252_4 = e1 & op(e4, e2) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) op(e4, e2) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (40), (48), (261) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #930.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_252_9 = e1 & op(e4, e1) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_252_9 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (248), (264) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #842.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_252_16 = e1 & op(e4, e0) = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_252_16 = e1
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_252_0 = e3 & op(e4, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (255), (268) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #841.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_252_1 = e3 & op(e4, e3) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (111), (269) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #840.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_252_4 = e3 & op(e4, e2) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_252_4 = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_252_4 = e2 & op(e4, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_252_4 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (275) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) e3 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (276) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_252_23 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) are inconsistent by sub-proof #847.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_252_5 = e2 & op(e3, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_252_5 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_16 = e3 & op(e4, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (266), (281) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #839.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_252_17 = e3 & op(e3, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_252_17 = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_252_2 = e4 & op(e3, e4) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_252_2 = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_252_0 = e3 & op(e4, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (255), (288) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #841.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_252_2 = e3 & op(e3, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_252_2 = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (286), (290) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #838.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_252_6 = e3 & op(e2, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (21), (109), (292) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #940.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (26), (57), (125), (139), (293) are
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #894.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_252_3 = e4 & op(e3, e3) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (55), (130), (294) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #846.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e4)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_252_5 = e4 & op(e3, e2) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_252_5 = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (297) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) e4 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (298) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) $false
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_252_10 = e4 & op(e3, e1) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (66), (71), (301) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_252_17 = e4 & op(e3, e0) = e4
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (283), (302) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #837.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_252_18 = e3 & op(e2, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (124), (148), (304) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_252_19 = e3 & op(e1, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (36), (150), (306) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #836.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_252_24 = e3 & op(e0, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) op(e0, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (68), (308) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #835.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_252_8 = e2 & op(e2, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_252_8 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (311) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) e3 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) e3 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (313) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_252_23 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) are inconsistent by sub-proof #847.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_252_14 = e2 & op(e1, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (187), (316) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #924.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_252_22 = e2 & op(e0, e2) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_252_22 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (318) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) e2 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (319) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) e2 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (320) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_252_7 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (21), (23), (45), (61), (82), (88),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (114), (123), (177), (180), (188), (245),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (321) are inconsistent by sub-proof #917.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) all_252_9 = e3 & op(e4, e1) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) op(e4, e1) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (88), (101), (324) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #834.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_252_16 = e3 & op(e4, e0) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (266), (325) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #839.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_252_2 = e0 & op(e3, e4) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_2 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) op(e3, e4) = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_252_0 = e3 & op(e4, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_252_0 = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_252_0 = e2 & op(e4, e4) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_252_0 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (334) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) e3 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (335) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) all_252_23 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) are inconsistent by sub-proof #847.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) all_252_2 = e2 & op(e3, e4) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) all_252_2 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (338) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) e2 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (339) imply:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_252_7 = e0
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (21), (23), (45), (61), (82), (88),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (114), (123), (177), (180), (188), (245),
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (340) are inconsistent by sub-proof #917.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 =
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_252_6 = e2 & op(e2, e4) = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) all_252_6 = e2
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (180), (343) are inconsistent by sub-proof
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #833.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2)
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (57), (70), (73), (139), (344) are
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #891.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) all_252_2 = e3 & op(e3, e4) = e3
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (62), (94), (328), (345) are inconsistent by
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #832.
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 =
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_252_6 = e3 & op(e2, e4) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (21), (109), (347) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #940.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (26), (57), (125), (139), (348) are
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #894.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 =
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_252_6 = e0 & op(e2, e4) = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_252_6 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (22), (25), (33), (38), (83), (87),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (124), (177), (351) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #931.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_252_12 = e0 & op(e1, e4) = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_252_12 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_252_12 = e4 & op(e1, e4) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_252_12 = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (357) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) e4 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (358) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) e4 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (359) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) all_252_6 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (22), (25), (33), (38), (83), (87),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (124), (177), (360) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #931.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_252_13 = e4 & op(e1, e3) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (60), (134), (361) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #952.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (362) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_252_14 = e4 & op(e1, e2) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (363) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) op(e1, e2) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (21), (103), (364) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #831.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_252_15 = e4 & op(e1, e1) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (234), (366) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #913.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_252_19 = e4 & op(e1, e0) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_252_19 = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) op(e1, e0) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_252_16 = e1 & op(e4, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_252_16 = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_252_16 = e3 & op(e4, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (372), (374) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #839.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_252_17 = e3 & op(e3, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_252_17 = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_252_16 = e2 & op(e4, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) op(e4, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21), (65), (379) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #830.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_252_17 = e2 & op(e3, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_252_17 = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (376), (381) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) e3 = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (382) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) e3 = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (383) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_252_23 = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (21), (23), (24), (26), (46), (54), (59),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (96), (107), (110), (122), (130), (138), (139),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) are inconsistent by sub-proof #847.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) | (all_252_24 = e2 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_252_18 = e2 & op(e2, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) all_252_18 = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (387) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) e2 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (388) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_252_7 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (21), (23), (45), (61), (82), (88),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (114), (123), (177), (180), (188), (245),
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (389) are inconsistent by sub-proof #917.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_252_19 = e2 & op(e1, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) op(e1, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (114), (369), (392) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #829.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_4_2, e1, e2, e1,
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (103), (188) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) all_4_2 = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_62_2, e3, e3, e1,
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (60), (155) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_62_2 = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (393) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (e4 = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (394) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) op(e0, e3) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (47), (110), (396) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #828.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_252_18 = e3 & op(e2, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (124), (148), (398) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_252_19 = e3 & op(e1, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) op(e1, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (96), (369), (401) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #827.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) all_252_24 = e3 & op(e0, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (402) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) op(e0, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (68), (403) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #835.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_252_17 = e1 & op(e3, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) op(e3, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (100), (106), (405) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_252_18 = e1 & op(e2, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) op(e2, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (201), (408) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #901.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) all_252_19 = e1 & op(e1, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (368), (410) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #826.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_252_24 = e1 & op(e0, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_252_24 = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (227), (412) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #825.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_252_20 = e0 & op(e0, e4) = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_252_20 = e0
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (252), (414) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #824.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_252_21 = e1 & op(e0, e3) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) op(e0, e3) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (47), (110), (416) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #828.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (417) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_252_22 = e1 & op(e0, e2) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) op(e0, e2) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (213), (419) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #871.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_252_23 = e1 & op(e0, e1) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (421) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) op(e0, e1) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (69), (78), (422) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #915.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) all_252_24 = e1 & op(e0, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_252_24 = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (424) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) e2 = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (425) imply:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) $false
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (426) is inconsistent.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_252_10 = e4 & op(e3, e1) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (66), (71), (427) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #914.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 &
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (83), (99), (114), (121), (234), (428)
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #911.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_252_18 = e1 & op(e2, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (429) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) op(e2, e0) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (201), (430) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #901.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_252_19 = e2 & op(e1, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) op(e1, e0) = e2
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (36), (44), (432) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #909.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | (433) all_252_22 = e1 & op(e0, e2) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | (434) op(e0, e2) = e1
% 252.14/60.26 | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (46), (146), (434) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 252.14/60.26 | | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | (435) all_252_7 = e4 & op(e2, e3) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | ALPHA: (435) implies:
% 252.14/60.26 | | | | | | | | | | | | | | | | (436) op(e2, e3) = e4
% 252.14/60.26 | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (22), (436) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | | sub-proof #953.
% 252.14/60.26 | | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | (437) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 =
% 252.14/60.26 | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 252.14/60.26 | | | | | | | | | | | | | | | op(e2, e0) = e4)
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (38), (83), (96), (124), (177), (437)
% 252.14/60.26 | | | | | | | | | | | | | | | are inconsistent by sub-proof #932.
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | (438) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18
% 252.14/60.26 | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3)
% 252.14/60.26 | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 252.14/60.26 | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | (439) all_252_11 = e3 & op(e2, e1) = e3
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (128), (439) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | sub-proof #900.
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | (440) all_252_18 = e3 & op(e2, e0) = e3
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | | REF_CLOSE: (21), (124), (148), (440) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | | | sub-proof #899.
% 252.14/60.26 | | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | (441) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21
% 252.14/60.26 | | | | | | | | | | | | = e2 & op(e0, e3) = e2)
% 252.14/60.26 | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | BETA: splitting (441) gives:
% 252.14/60.26 | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | (442) all_252_13 = e2 & op(e1, e3) = e2
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | ALPHA: (442) implies:
% 252.14/60.26 | | | | | | | | | | | | | (443) op(e1, e3) = e2
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | REF_CLOSE: (21), (60), (142), (443) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | | | sub-proof #972.
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | (444) all_252_21 = e2 & op(e0, e3) = e2
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (21), (22), (25), (55), (60), (84),
% 252.14/60.26 | | | | | | | | | | | | | (111), (114), (130), (134), (444) are inconsistent
% 252.14/60.26 | | | | | | | | | | | | | by sub-proof #845.
% 252.14/60.26 | | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | |
% 252.14/60.26 | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | |
% 252.14/60.26 | | | | | | | | | (445) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1
% 252.14/60.26 | | | | | | | | | & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3)
% 252.14/60.26 | | | | | | | | | = e1)
% 252.14/60.26 | | | | | | | | |
% 252.14/60.26 | | | | | | | | | BETA: splitting (445) gives:
% 252.14/60.26 | | | | | | | | |
% 252.14/60.26 | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | (446) all_252_7 = e1 & op(e2, e3) = e1
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | ALPHA: (446) implies:
% 252.14/60.26 | | | | | | | | | | (447) op(e2, e3) = e1
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | REF_CLOSE: (21), (22), (144), (447) are inconsistent by
% 252.14/60.26 | | | | | | | | | | sub-proof #948.
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | (448) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 =
% 252.14/60.26 | | | | | | | | | | e1 & op(e0, e3) = e1)
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | BETA: splitting (448) gives:
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | (449) all_252_13 = e1 & op(e1, e3) = e1
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | REF_CLOSE: (69), (154), (449) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | | | | | | #823.
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | (450) all_252_21 = e1 & op(e0, e3) = e1
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | ALPHA: (450) implies:
% 252.14/60.26 | | | | | | | | | | | (451) op(e0, e3) = e1
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | | REF_CLOSE: (21), (47), (110), (451) are inconsistent by
% 252.14/60.26 | | | | | | | | | | | sub-proof #828.
% 252.14/60.26 | | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | | |
% 252.14/60.26 | | | | | | | | | End of split
% 252.14/60.26 | | | | | | | | |
% 252.14/60.26 | | | | | | | | End of split
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | End of split
% 252.14/60.26 | | | | | | |
% 252.14/60.26 | | | | | | Case 2:
% 252.14/60.26 | | | | | | |
% 252.14/60.26 | | | | | | | (452) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 &
% 252.14/60.26 | | | | | | | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 252.14/60.26 | | | | | | |
% 252.14/60.26 | | | | | | | BETA: splitting (452) gives:
% 252.14/60.26 | | | | | | |
% 252.14/60.26 | | | | | | | Case 1:
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | | (453) all_252_14 = e3 & op(e1, e2) = e3
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | | REF_CLOSE: (21), (103), (132), (453) are inconsistent by
% 252.14/60.26 | | | | | | | | sub-proof #858.
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | Case 2:
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | | (454) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3
% 252.14/60.26 | | | | | | | | & op(e1, e0) = e3)
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | | REF_CLOSE: (21), (36), (89), (97), (150), (454) are inconsistent
% 252.14/60.26 | | | | | | | | by sub-proof #821.
% 252.14/60.26 | | | | | | | |
% 252.14/60.26 | | | | | | | End of split
% 252.14/60.26 | | | | | | |
% 252.14/60.26 | | | | | | End of split
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | Case 2:
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | | (455) all_96_2 = e3
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | | COMBINE_EQS: (58), (455) imply:
% 252.14/60.26 | | | | | | (456) all_34_2 = e3
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | | SIMP: (456) implies:
% 252.14/60.26 | | | | | | (457) all_34_2 = e3
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | | REDUCE: (53), (457) imply:
% 252.14/60.26 | | | | | | (458) op(e3, e0) = e1
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | | REF_CLOSE: (21), (100), (106), (458) are inconsistent by sub-proof
% 252.14/60.26 | | | | | | #889.
% 252.14/60.26 | | | | | |
% 252.14/60.26 | | | | | End of split
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | Case 2:
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | | (459) all_86_2 = e3
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | | COMBINE_EQS: (108), (459) imply:
% 252.14/60.26 | | | | | (460) all_40_2 = e3
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | | REDUCE: (6), (460) imply:
% 252.14/60.26 | | | | | (461) ~ (all_38_2 = e3)
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | | REDUCE: (64), (460) imply:
% 252.14/60.26 | | | | | (462) ~ (all_10_2 = e3)
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | | REF_CLOSE: (4), (14), (16), (21), (30), (31), (50), (52), (63), (79),
% 252.14/60.26 | | | | | (83), (95), (97), (119), (127), (128), (144), (462) are
% 252.14/60.26 | | | | | inconsistent by sub-proof #989.
% 252.14/60.26 | | | | |
% 252.14/60.26 | | | | End of split
% 252.14/60.26 | | | |
% 252.14/60.26 | | | Case 2:
% 252.14/60.26 | | | |
% 252.14/60.26 | | | | (463) all_82_2 = e1
% 252.14/60.26 | | | |
% 252.14/60.26 | | | | COMBINE_EQS: (102), (463) imply:
% 252.14/60.26 | | | | (464) all_28_2 = e1
% 252.14/60.26 | | | |
% 252.14/60.26 | | | | REF_CLOSE: (1), (17), (18), (19), (21), (30), (34), (36), (39), (40),
% 252.14/60.26 | | | | (43), (44), (46), (51), (52), (57), (60), (73), (76), (81),
% 252.14/60.26 | | | | (97), (103), (105), (112), (116), (117), (126), (129), (142),
% 252.14/60.26 | | | | (464) are inconsistent by sub-proof #867.
% 252.14/60.26 | | | |
% 252.14/60.26 | | | End of split
% 252.14/60.26 | | |
% 252.14/60.26 | | Case 2:
% 252.14/60.26 | | |
% 252.14/60.26 | | | (465) all_78_2 = e1
% 252.14/60.26 | | |
% 252.14/60.26 | | | REF_CLOSE: (21), (42), (60), (91), (142), (465) are inconsistent by
% 252.14/60.26 | | | sub-proof #971.
% 252.14/60.26 | | |
% 252.14/60.26 | | End of split
% 252.14/60.26 | |
% 252.14/60.26 | Case 2:
% 252.14/60.26 | |
% 252.14/60.26 | | (466) all_70_2 = e2
% 252.14/60.26 | |
% 252.14/60.26 | | COMBINE_EQS: (67), (466) imply:
% 252.14/60.26 | | (467) all_62_2 = e2
% 252.14/60.26 | |
% 252.14/60.26 | | REDUCE: (92), (467) imply:
% 252.14/60.26 | | (468) ~ (all_244_15 = e2)
% 252.14/60.26 | |
% 252.14/60.26 | | REDUCE: (49), (467) imply:
% 252.14/60.26 | | (469) ~ (all_34_2 = e2)
% 252.14/60.26 | |
% 252.14/60.26 | | REDUCE: (93), (467) imply:
% 252.14/60.26 | | (470) ~ (all_16_2 = e2)
% 252.14/60.26 | |
% 252.14/60.26 | | REDUCE: (135), (467) imply:
% 252.14/60.26 | | (471) ~ (all_4_2 = e2)
% 252.14/60.26 | |
% 252.14/60.26 | | SIMP: (471) implies:
% 252.14/60.26 | | (472) ~ (all_4_2 = e2)
% 252.14/60.26 | |
% 252.14/60.26 | | REDUCE: (13), (467) imply:
% 252.14/60.26 | | (473) op(e2, e0) = e3
% 252.14/60.26 | |
% 252.14/60.26 | | REF_CLOSE: (10), (20), (21), (23), (24), (26), (29), (36), (44), (46), (54),
% 252.14/60.26 | | (57), (59), (73), (77), (89), (96), (97), (103), (107), (110),
% 252.14/60.26 | | (122), (124), (125), (129), (130), (132), (138), (139), (468),
% 252.14/60.26 | | (472), (473) are inconsistent by sub-proof #818.
% 252.14/60.26 | |
% 252.14/60.26 | End of split
% 252.14/60.26 |
% 252.14/60.26 End of proof
% 252.14/60.26
% 252.14/60.26 Sub-proof #818 shows that the following formulas are inconsistent:
% 252.14/60.26 ----------------------------------------------------------------
% 252.14/60.26 (1) op(e2, e0) = e3
% 252.14/60.26 (2) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 252.14/60.26 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) =
% 252.14/60.26 e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 252.14/60.26 (3) ~ (all_28_2 = e3)
% 252.14/60.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.26 (5) ~ (e3 = e2)
% 252.14/60.26 (6) op(e0, e0) = all_244_24
% 252.14/60.26 (7) ~ (all_12_2 = e3)
% 252.14/60.26 (8) all_252_23 = e3
% 252.14/60.26 (9) op(e1, e0) = all_34_2
% 252.14/60.26 (10) ~ (all_34_2 = e2)
% 252.14/60.26 (11) op(e0, e2) = all_28_2
% 252.14/60.26 (12) ~ (all_244_3 = all_84_2)
% 252.14/60.26 (13) op(e1, e4) = all_16_2
% 252.14/60.26 (14) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 252.14/60.26 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 252.14/60.26 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.14/60.26 (15) ~ (all_16_2 = e2)
% 252.14/60.26 (16) ~ (all_40_2 = all_34_2)
% 252.14/60.26 (17) ~ (all_244_15 = e3)
% 252.14/60.26 (18) ~ (e4 = e3)
% 252.14/60.26 (19) op(e1, e1) = all_244_15
% 252.14/60.26 (20) op(e1, e2) = all_4_2
% 252.14/60.26 (21) op(e4, e3) = all_84_2
% 252.14/60.26 (22) op(e0, e3) = e4
% 252.14/60.26 (23) ~ (all_244_15 = e2)
% 252.14/60.26 (24) op(e4, e3) = e0
% 252.14/60.26 (25) op(e2, e0) = all_40_2
% 252.14/60.26 (26) ~ (all_16_2 = e3)
% 252.14/60.26 (27) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.14/60.26 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.14/60.26 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.14/60.26 (28) op(e3, e3) = all_244_3
% 252.14/60.26 (29) ~ (all_4_2 = e3)
% 252.14/60.26 (30) ~ (all_4_2 = e2)
% 252.14/60.26 (31) op(all_244_24, all_244_24) = e0
% 252.14/60.26 (32) op(e0, e4) = all_12_2
% 252.14/60.26
% 252.14/60.26 Begin of proof
% 252.14/60.26 |
% 252.14/60.26 | BETA: splitting (2) gives:
% 252.14/60.26 |
% 252.14/60.26 | Case 1:
% 252.14/60.26 | |
% 252.14/60.26 | | (33) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3)
% 252.14/60.26 | | = e3)
% 252.14/60.26 | |
% 252.14/60.26 | | BETA: splitting (33) gives:
% 252.14/60.26 | |
% 252.14/60.26 | | Case 1:
% 252.14/60.26 | | |
% 252.14/60.26 | | | (34) all_252_12 = e3 & op(e1, e4) = e3
% 252.14/60.26 | | |
% 252.14/60.26 | | | REF_CLOSE: (4), (13), (26), (34) are inconsistent by sub-proof #895.
% 252.14/60.26 | | |
% 252.14/60.26 | | Case 2:
% 252.14/60.26 | | |
% 252.14/60.27 | | | (35) all_252_13 = e3 & op(e1, e3) = e3
% 252.14/60.27 | | |
% 252.14/60.27 | | | ALPHA: (35) implies:
% 252.14/60.27 | | | (36) all_252_13 = e3
% 252.14/60.27 | | |
% 252.14/60.27 | | | BETA: splitting (27) gives:
% 252.14/60.27 | | |
% 252.14/60.27 | | | Case 1:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | (37) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1,
% 252.14/60.27 | | | | e3) = e2)
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | BETA: splitting (37) gives:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | Case 1:
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | (38) all_252_12 = e2 & op(e1, e4) = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | REF_CLOSE: (4), (13), (15), (38) are inconsistent by sub-proof #926.
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | Case 2:
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | (39) all_252_13 = e2 & op(e1, e3) = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | ALPHA: (39) implies:
% 252.14/60.27 | | | | | (40) all_252_13 = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | COMBINE_EQS: (36), (40) imply:
% 252.14/60.27 | | | | | (41) e3 = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | SIMP: (41) implies:
% 252.14/60.27 | | | | | (42) e3 = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | COMBINE_EQS: (8), (42) imply:
% 252.14/60.27 | | | | | (43) all_252_23 = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (12), (14), (18), (21),
% 252.14/60.27 | | | | | (22), (24), (28), (31), (32), (43) are inconsistent by
% 252.14/60.27 | | | | | sub-proof #847.
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | End of split
% 252.14/60.27 | | | |
% 252.14/60.27 | | | Case 2:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | (44) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.14/60.27 | | | | e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | BETA: splitting (44) gives:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | Case 1:
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | (45) all_252_14 = e2 & op(e1, e2) = e2
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | REF_CLOSE: (4), (20), (30), (45) are inconsistent by sub-proof #820.
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | Case 2:
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | (46) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 &
% 252.14/60.27 | | | | | op(e1, e0) = e2)
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | | REF_CLOSE: (4), (9), (10), (19), (23), (46) are inconsistent by
% 252.14/60.27 | | | | | sub-proof #819.
% 252.14/60.27 | | | | |
% 252.14/60.27 | | | | End of split
% 252.14/60.27 | | | |
% 252.14/60.27 | | | End of split
% 252.14/60.27 | | |
% 252.14/60.27 | | End of split
% 252.14/60.27 | |
% 252.14/60.27 | Case 2:
% 252.14/60.27 | |
% 252.14/60.27 | | (47) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1)
% 252.14/60.27 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 252.14/60.27 | |
% 252.14/60.27 | | BETA: splitting (47) gives:
% 252.14/60.27 | |
% 252.14/60.27 | | Case 1:
% 252.14/60.27 | | |
% 252.14/60.27 | | | (48) all_252_14 = e3 & op(e1, e2) = e3
% 252.14/60.27 | | |
% 252.14/60.27 | | | REF_CLOSE: (4), (20), (29), (48) are inconsistent by sub-proof #858.
% 252.14/60.27 | | |
% 252.14/60.27 | | Case 2:
% 252.14/60.27 | | |
% 252.14/60.27 | | | (49) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1,
% 252.14/60.27 | | | e0) = e3)
% 252.14/60.27 | | |
% 252.14/60.27 | | | BETA: splitting (49) gives:
% 252.14/60.27 | | |
% 252.14/60.27 | | | Case 1:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | (50) all_252_15 = e3 & op(e1, e1) = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | ALPHA: (50) implies:
% 252.14/60.27 | | | | (51) op(e1, e1) = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | REF_CLOSE: (4), (17), (19), (51) are inconsistent by sub-proof #822.
% 252.14/60.27 | | | |
% 252.14/60.27 | | | Case 2:
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | (52) all_252_19 = e3 & op(e1, e0) = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | ALPHA: (52) implies:
% 252.14/60.27 | | | | (53) op(e1, e0) = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | GROUND_INST: instantiating (4) with all_34_2, e3, e0, e1, simplifying
% 252.14/60.27 | | | | with (9), (53) gives:
% 252.14/60.27 | | | | (54) all_34_2 = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | GROUND_INST: instantiating (4) with all_40_2, e3, e0, e2, simplifying
% 252.14/60.27 | | | | with (1), (25) gives:
% 252.14/60.27 | | | | (55) all_40_2 = e3
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | REDUCE: (16), (54), (55) imply:
% 252.14/60.27 | | | | (56) $false
% 252.14/60.27 | | | |
% 252.14/60.27 | | | | CLOSE: (56) is inconsistent.
% 252.14/60.27 | | | |
% 252.14/60.27 | | | End of split
% 252.14/60.27 | | |
% 252.14/60.27 | | End of split
% 252.14/60.27 | |
% 252.14/60.27 | End of split
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #819 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.14/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (3) op(e1, e0) = all_34_2
% 252.14/60.27 (4) ~ (all_34_2 = e2)
% 252.14/60.27 (5) op(e1, e1) = all_244_15
% 252.14/60.27 (6) ~ (all_244_15 = e2)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | BETA: splitting (1) gives:
% 252.14/60.27 |
% 252.14/60.27 | Case 1:
% 252.14/60.27 | |
% 252.14/60.27 | | (7) all_252_15 = e2 & op(e1, e1) = e2
% 252.14/60.27 | |
% 252.14/60.27 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #966.
% 252.14/60.27 | |
% 252.14/60.27 | Case 2:
% 252.14/60.27 | |
% 252.14/60.27 | | (8) all_252_19 = e2 & op(e1, e0) = e2
% 252.14/60.27 | |
% 252.14/60.27 | | ALPHA: (8) implies:
% 252.14/60.27 | | (9) op(e1, e0) = e2
% 252.14/60.27 | |
% 252.14/60.27 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #909.
% 252.14/60.27 | |
% 252.14/60.27 | End of split
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #820 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) all_252_14 = e2 & op(e1, e2) = e2
% 252.14/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (3) op(e1, e2) = all_4_2
% 252.14/60.27 (4) ~ (all_4_2 = e2)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | ALPHA: (1) implies:
% 252.14/60.27 | (5) op(e1, e2) = e2
% 252.14/60.27 |
% 252.14/60.27 | GROUND_INST: instantiating (2) with all_4_2, e2, e2, e1, simplifying with (3),
% 252.14/60.27 | (5) gives:
% 252.14/60.27 | (6) all_4_2 = e2
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (4), (6) imply:
% 252.14/60.27 | (7) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (7) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #821 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e1, e0) = all_34_2
% 252.14/60.27 (3) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)
% 252.14/60.27 (4) ~ (all_244_15 = e3)
% 252.14/60.27 (5) op(e1, e1) = all_244_15
% 252.14/60.27 (6) ~ (all_34_2 = e3)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | BETA: splitting (3) gives:
% 252.14/60.27 |
% 252.14/60.27 | Case 1:
% 252.14/60.27 | |
% 252.14/60.27 | | (7) all_252_15 = e3 & op(e1, e1) = e3
% 252.14/60.27 | |
% 252.14/60.27 | | ALPHA: (7) implies:
% 252.14/60.27 | | (8) op(e1, e1) = e3
% 252.14/60.27 | |
% 252.14/60.27 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #822.
% 252.14/60.27 | |
% 252.14/60.27 | Case 2:
% 252.14/60.27 | |
% 252.14/60.27 | | (9) all_252_19 = e3 & op(e1, e0) = e3
% 252.14/60.27 | |
% 252.14/60.27 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #836.
% 252.14/60.27 | |
% 252.14/60.27 | End of split
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #822 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e1, e1) = all_244_15
% 252.14/60.27 (3) op(e1, e1) = e3
% 252.14/60.27 (4) ~ (all_244_15 = e3)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | GROUND_INST: instantiating (1) with all_244_15, e3, e1, e1, simplifying with
% 252.14/60.27 | (2), (3) gives:
% 252.14/60.27 | (5) all_244_15 = e3
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (4), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #823 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) all_252_13 = e1 & op(e1, e3) = e1
% 252.14/60.27 (2) all_252_13 = e3
% 252.14/60.27 (3) ~ (e3 = e1)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | ALPHA: (1) implies:
% 252.14/60.27 | (4) all_252_13 = e1
% 252.14/60.27 |
% 252.14/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.14/60.27 | (5) e3 = e1
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (3), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #824 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) all_252_20 = e1
% 252.14/60.27 (2) all_252_20 = e0
% 252.14/60.27 (3) ~ (e1 = e0)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.14/60.27 | (4) e1 = e0
% 252.14/60.27 |
% 252.14/60.27 | SIMP: (4) implies:
% 252.14/60.27 | (5) e1 = e0
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (3), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #825 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) all_252_24 = e2
% 252.14/60.27 (2) all_252_24 = e1
% 252.14/60.27 (3) ~ (e2 = e1)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.14/60.27 | (4) e2 = e1
% 252.14/60.27 |
% 252.14/60.27 | SIMP: (4) implies:
% 252.14/60.27 | (5) e2 = e1
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (3), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #826 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) all_252_19 = e1 & op(e1, e0) = e1
% 252.14/60.27 (2) all_252_19 = e4
% 252.14/60.27 (3) ~ (e4 = e1)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | ALPHA: (1) implies:
% 252.14/60.27 | (4) all_252_19 = e1
% 252.14/60.27 |
% 252.14/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.14/60.27 | (5) e4 = e1
% 252.14/60.27 |
% 252.14/60.27 | SIMP: (5) implies:
% 252.14/60.27 | (6) e4 = e1
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (3), (6) imply:
% 252.14/60.27 | (7) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (7) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #827 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e1, e0) = e4
% 252.14/60.27 (3) op(e1, e0) = e3
% 252.14/60.27 (4) ~ (e4 = e3)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | GROUND_INST: instantiating (1) with e3, e4, e0, e1, simplifying with (2), (3)
% 252.14/60.27 | gives:
% 252.14/60.27 | (5) e4 = e3
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (4), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #828 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e0, e3) = e4
% 252.14/60.27 (3) op(e0, e3) = e1
% 252.14/60.27 (4) ~ (e4 = e1)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | GROUND_INST: instantiating (1) with e1, e4, e3, e0, simplifying with (2), (3)
% 252.14/60.27 | gives:
% 252.14/60.27 | (5) e4 = e1
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (4), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #829 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e1, e0) = e4
% 252.14/60.27 (3) op(e1, e0) = e2
% 252.14/60.27 (4) ~ (e4 = e2)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.14/60.27 | GROUND_INST: instantiating (1) with e2, e4, e0, e1, simplifying with (2), (3)
% 252.14/60.27 | gives:
% 252.14/60.27 | (5) e4 = e2
% 252.14/60.27 |
% 252.14/60.27 | REDUCE: (4), (5) imply:
% 252.14/60.27 | (6) $false
% 252.14/60.27 |
% 252.14/60.27 | CLOSE: (6) is inconsistent.
% 252.14/60.27 |
% 252.14/60.27 End of proof
% 252.14/60.27
% 252.14/60.27 Sub-proof #830 shows that the following formulas are inconsistent:
% 252.14/60.27 ----------------------------------------------------------------
% 252.14/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.14/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.14/60.27 (2) op(e4, e0) = all_30_2
% 252.14/60.27 (3) op(e4, e0) = e2
% 252.14/60.27 (4) ~ (all_30_2 = e2)
% 252.14/60.27
% 252.14/60.27 Begin of proof
% 252.14/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (1) with all_30_2, e2, e0, e4, simplifying with
% 252.31/60.27 | (2), (3) gives:
% 252.31/60.27 | (5) all_30_2 = e2
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #831 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (2) op(e1, e2) = all_4_2
% 252.31/60.27 (3) op(e1, e2) = e4
% 252.31/60.27 (4) ~ (all_4_2 = e4)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (1) with all_4_2, e4, e2, e1, simplifying with (2),
% 252.31/60.27 | (3) gives:
% 252.31/60.27 | (5) all_4_2 = e4
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #832 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) op(e3, e4) = e0
% 252.31/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (3) ~ (e3 = e0)
% 252.31/60.27 (4) op(e3, e4) = all_100_2
% 252.31/60.27 (5) all_252_2 = e3 & op(e3, e4) = e3
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (5) implies:
% 252.31/60.27 | (6) op(e3, e4) = e3
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (2) with all_100_2, e0, e4, e3, simplifying with
% 252.31/60.27 | (1), (4) gives:
% 252.31/60.27 | (7) all_100_2 = e0
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (2) with all_100_2, e3, e4, e3, simplifying with
% 252.31/60.27 | (4), (6) gives:
% 252.31/60.27 | (8) all_100_2 = e3
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (7), (8) imply:
% 252.31/60.27 | (9) e3 = e0
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (9) imply:
% 252.31/60.27 | (10) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (10) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #833 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_6 = e4
% 252.31/60.27 (2) all_252_6 = e2
% 252.31/60.27 (3) ~ (e4 = e2)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.27 | (4) e4 = e2
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (4) implies:
% 252.31/60.27 | (5) e4 = e2
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #834 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (2) op(e4, e1) = all_26_2
% 252.31/60.27 (3) op(e4, e1) = e3
% 252.31/60.27 (4) ~ (all_26_2 = e3)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (1) with all_26_2, e3, e1, e4, simplifying with
% 252.31/60.27 | (2), (3) gives:
% 252.31/60.27 | (5) all_26_2 = e3
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #835 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (2) op(e0, e0) = all_244_24
% 252.31/60.27 (3) op(e0, e0) = e3
% 252.31/60.27 (4) ~ (all_244_24 = e3)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (1) with all_244_24, e3, e0, e0, simplifying with
% 252.31/60.27 | (2), (3) gives:
% 252.31/60.27 | (5) all_244_24 = e3
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #836 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_19 = e3 & op(e1, e0) = e3
% 252.31/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (3) op(e1, e0) = all_34_2
% 252.31/60.27 (4) ~ (all_34_2 = e3)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (5) op(e1, e0) = e3
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (2) with all_34_2, e3, e0, e1, simplifying with
% 252.31/60.27 | (3), (5) gives:
% 252.31/60.27 | (6) all_34_2 = e3
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #837 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_17 = e4 & op(e3, e0) = e4
% 252.31/60.27 (2) all_252_17 = e3
% 252.31/60.27 (3) ~ (e4 = e3)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (4) all_252_17 = e4
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.27 | (5) e4 = e3
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (5) implies:
% 252.31/60.27 | (6) e4 = e3
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #838 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_2 = e4
% 252.31/60.27 (2) all_252_2 = e3
% 252.31/60.27 (3) ~ (e4 = e3)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.27 | (4) e4 = e3
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (4) implies:
% 252.31/60.27 | (5) e4 = e3
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #839 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_16 = e3 & op(e4, e0) = e3
% 252.31/60.27 (2) all_252_16 = e1
% 252.31/60.27 (3) ~ (e3 = e1)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (4) all_252_16 = e3
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.27 | (5) e3 = e1
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #840 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_1 = e3 & op(e4, e3) = e3
% 252.31/60.27 (2) all_252_1 = e0
% 252.31/60.27 (3) ~ (e3 = e0)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (4) all_252_1 = e3
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.27 | (5) e3 = e0
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (5) implies:
% 252.31/60.27 | (6) e3 = e0
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #841 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_0 = e3 & op(e4, e4) = e3
% 252.31/60.27 (2) all_252_0 = e0
% 252.31/60.27 (3) ~ (e3 = e0)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (4) all_252_0 = e3
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.27 | (5) e3 = e0
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (5) implies:
% 252.31/60.27 | (6) e3 = e0
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #842 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_9 = e4
% 252.31/60.27 (2) all_252_9 = e1
% 252.31/60.27 (3) ~ (e4 = e1)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.27 | (4) e4 = e1
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (4) implies:
% 252.31/60.27 | (5) e4 = e1
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #843 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_0 = e1 & op(e4, e4) = e1
% 252.31/60.27 (2) all_252_0 = e0
% 252.31/60.27 (3) ~ (e1 = e0)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (4) all_252_0 = e1
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.27 | (5) e1 = e0
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (5) implies:
% 252.31/60.27 | (6) e1 = e0
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #844 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_6 = e4
% 252.31/60.27 (2) all_252_6 = e1
% 252.31/60.27 (3) ~ (e4 = e1)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.27 | (4) e4 = e1
% 252.31/60.27 |
% 252.31/60.27 | SIMP: (4) implies:
% 252.31/60.27 | (5) e4 = e1
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (3), (5) imply:
% 252.31/60.27 | (6) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (6) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #845 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) ~ (all_10_2 = e4)
% 252.31/60.27 (2) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 252.31/60.27 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.31/60.27 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.31/60.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (4) op(e2, e3) = all_10_2
% 252.31/60.27 (5) ~ (e4 = e0)
% 252.31/60.27 (6) ~ (all_244_3 = e4)
% 252.31/60.27 (7) op(e1, e3) = all_62_2
% 252.31/60.27 (8) all_252_21 = e2 & op(e0, e3) = e2
% 252.31/60.27 (9) op(e0, e3) = all_22_2
% 252.31/60.27 (10) all_252_1 = e0
% 252.31/60.27 (11) ~ (e4 = e2)
% 252.31/60.27 (12) op(e3, e3) = all_244_3
% 252.31/60.27 (13) ~ (all_62_2 = e4)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (8) implies:
% 252.31/60.27 | (14) op(e0, e3) = e2
% 252.31/60.27 |
% 252.31/60.27 | BETA: splitting (2) gives:
% 252.31/60.27 |
% 252.31/60.27 | Case 1:
% 252.31/60.27 | |
% 252.31/60.27 | | (15) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) =
% 252.31/60.27 | | e4)
% 252.31/60.27 | |
% 252.31/60.27 | | BETA: splitting (15) gives:
% 252.31/60.27 | |
% 252.31/60.27 | | Case 1:
% 252.31/60.27 | | |
% 252.31/60.27 | | | (16) all_252_1 = e4 & op(e4, e3) = e4
% 252.31/60.27 | | |
% 252.31/60.27 | | | REF_CLOSE: (5), (10), (16) are inconsistent by sub-proof #898.
% 252.31/60.27 | | |
% 252.31/60.27 | | Case 2:
% 252.31/60.27 | | |
% 252.31/60.27 | | | (17) all_252_3 = e4 & op(e3, e3) = e4
% 252.31/60.27 | | |
% 252.31/60.27 | | | REF_CLOSE: (3), (6), (12), (17) are inconsistent by sub-proof #846.
% 252.31/60.27 | | |
% 252.31/60.27 | | End of split
% 252.31/60.27 | |
% 252.31/60.27 | Case 2:
% 252.31/60.27 | |
% 252.31/60.27 | | (18) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) =
% 252.31/60.27 | | e4) | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.31/60.27 | |
% 252.31/60.27 | | REF_CLOSE: (1), (3), (4), (7), (9), (11), (13), (14), (18) are inconsistent
% 252.31/60.27 | | by sub-proof #950.
% 252.31/60.27 | |
% 252.31/60.27 | End of split
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #846 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) all_252_3 = e4 & op(e3, e3) = e4
% 252.31/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (3) op(e3, e3) = all_244_3
% 252.31/60.27 (4) ~ (all_244_3 = e4)
% 252.31/60.27
% 252.31/60.27 Begin of proof
% 252.31/60.27 |
% 252.31/60.27 | ALPHA: (1) implies:
% 252.31/60.27 | (5) op(e3, e3) = e4
% 252.31/60.27 |
% 252.31/60.27 | GROUND_INST: instantiating (2) with all_244_3, e4, e3, e3, simplifying with
% 252.31/60.27 | (3), (5) gives:
% 252.31/60.27 | (6) all_244_3 = e4
% 252.31/60.27 |
% 252.31/60.27 | REDUCE: (4), (6) imply:
% 252.31/60.27 | (7) $false
% 252.31/60.27 |
% 252.31/60.27 | CLOSE: (7) is inconsistent.
% 252.31/60.27 |
% 252.31/60.27 End of proof
% 252.31/60.27
% 252.31/60.27 Sub-proof #847 shows that the following formulas are inconsistent:
% 252.31/60.27 ----------------------------------------------------------------
% 252.31/60.27 (1) ~ (all_28_2 = e3)
% 252.31/60.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.27 (3) ~ (e3 = e2)
% 252.31/60.27 (4) op(e0, e0) = all_244_24
% 252.31/60.27 (5) ~ (all_12_2 = e3)
% 252.31/60.27 (6) op(e0, e2) = all_28_2
% 252.31/60.27 (7) ~ (all_244_3 = all_84_2)
% 252.31/60.27 (8) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.31/60.27 | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) =
% 252.31/60.27 e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.31/60.27 (9) ~ (e4 = e3)
% 252.31/60.27 (10) all_252_23 = e2
% 252.31/60.28 (11) op(e4, e3) = all_84_2
% 252.31/60.28 (12) op(e0, e3) = e4
% 252.31/60.28 (13) op(e4, e3) = e0
% 252.31/60.28 (14) op(e3, e3) = all_244_3
% 252.31/60.28 (15) op(all_244_24, all_244_24) = e0
% 252.31/60.28 (16) op(e0, e4) = all_12_2
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | BETA: splitting (8) gives:
% 252.31/60.28 |
% 252.31/60.28 | Case 1:
% 252.31/60.28 | |
% 252.31/60.28 | | (17) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3)
% 252.31/60.28 | | = e3)
% 252.31/60.28 | |
% 252.31/60.28 | | REF_CLOSE: (2), (5), (9), (12), (16), (17) are inconsistent by sub-proof
% 252.31/60.28 | | #963.
% 252.31/60.28 | |
% 252.31/60.28 | Case 2:
% 252.31/60.28 | |
% 252.31/60.28 | | (18) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1)
% 252.31/60.28 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.31/60.28 | |
% 252.31/60.28 | | BETA: splitting (18) gives:
% 252.31/60.28 | |
% 252.31/60.28 | | Case 1:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (19) all_252_22 = e3 & op(e0, e2) = e3
% 252.31/60.28 | | |
% 252.31/60.28 | | | ALPHA: (19) implies:
% 252.31/60.28 | | | (20) op(e0, e2) = e3
% 252.31/60.28 | | |
% 252.31/60.28 | | | REF_CLOSE: (1), (2), (6), (20) are inconsistent by sub-proof #975.
% 252.31/60.28 | | |
% 252.31/60.28 | | Case 2:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (21) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0,
% 252.31/60.28 | | | e0) = e3)
% 252.31/60.28 | | |
% 252.31/60.28 | | | BETA: splitting (21) gives:
% 252.31/60.28 | | |
% 252.31/60.28 | | | Case 1:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (22) all_252_23 = e3 & op(e0, e1) = e3
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | REF_CLOSE: (3), (10), (22) are inconsistent by sub-proof #848.
% 252.31/60.28 | | | |
% 252.31/60.28 | | | Case 2:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (23) all_252_24 = e3 & op(e0, e0) = e3
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | REF_CLOSE: (2), (4), (7), (11), (13), (14), (15), (23) are inconsistent
% 252.31/60.28 | | | | by sub-proof #962.
% 252.31/60.28 | | | |
% 252.31/60.28 | | | End of split
% 252.31/60.28 | | |
% 252.31/60.28 | | End of split
% 252.31/60.28 | |
% 252.31/60.28 | End of split
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #848 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_23 = e3 & op(e0, e1) = e3
% 252.31/60.28 (2) all_252_23 = e2
% 252.31/60.28 (3) ~ (e3 = e2)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | ALPHA: (1) implies:
% 252.31/60.28 | (4) all_252_23 = e3
% 252.31/60.28 |
% 252.31/60.28 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.28 | (5) e3 = e2
% 252.31/60.28 |
% 252.31/60.28 | SIMP: (5) implies:
% 252.31/60.28 | (6) e3 = e2
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (3), (6) imply:
% 252.31/60.28 | (7) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (7) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #849 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_3 = e2 & op(e3, e3) = e2
% 252.31/60.28 (2) all_252_3 = e1
% 252.31/60.28 (3) ~ (e2 = e1)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | ALPHA: (1) implies:
% 252.31/60.28 | (4) all_252_3 = e2
% 252.31/60.28 |
% 252.31/60.28 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.28 | (5) e2 = e1
% 252.31/60.28 |
% 252.31/60.28 | SIMP: (5) implies:
% 252.31/60.28 | (6) e2 = e1
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (3), (6) imply:
% 252.31/60.28 | (7) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (7) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #850 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) ~ (e2 = e0)
% 252.31/60.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (3) op(e4, e3) = e2
% 252.31/60.28 (4) op(e4, e3) = all_84_2
% 252.31/60.28 (5) op(e4, e3) = e0
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_84_2, e0, e3, e4, simplifying with
% 252.31/60.28 | (4), (5) gives:
% 252.31/60.28 | (6) all_84_2 = e0
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_84_2, e2, e3, e4, simplifying with
% 252.31/60.28 | (3), (4) gives:
% 252.31/60.28 | (7) all_84_2 = e2
% 252.31/60.28 |
% 252.31/60.28 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.28 | (8) e2 = e0
% 252.31/60.28 |
% 252.31/60.28 | SIMP: (8) implies:
% 252.31/60.28 | (9) e2 = e0
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (1), (9) imply:
% 252.31/60.28 | (10) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (10) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #851 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_1 = e1 & op(e4, e3) = e1
% 252.31/60.28 (2) all_252_1 = e0
% 252.31/60.28 (3) ~ (e1 = e0)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | ALPHA: (1) implies:
% 252.31/60.28 | (4) all_252_1 = e1
% 252.31/60.28 |
% 252.31/60.28 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.28 | (5) e1 = e0
% 252.31/60.28 |
% 252.31/60.28 | SIMP: (5) implies:
% 252.31/60.28 | (6) e1 = e0
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (3), (6) imply:
% 252.31/60.28 | (7) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (7) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #852 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) ~ (all_22_2 = e3)
% 252.31/60.28 (2) ~ (all_62_2 = all_22_2)
% 252.31/60.28 (3) all_62_2 = e2
% 252.31/60.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (5) all_250_21 = all_22_2
% 252.31/60.28 (6) ~ (all_22_2 = e4)
% 252.31/60.28 (7) op(all_48_2, all_22_2) = e0
% 252.31/60.28 (8) ~ (all_22_2 = e1)
% 252.31/60.28 (9) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.31/60.28 all_250_21 = e0
% 252.31/60.28 (10) op(all_48_2, e0) = e3
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (2), (3) imply:
% 252.31/60.28 | (11) ~ (all_22_2 = e2)
% 252.31/60.28 |
% 252.31/60.28 | SIMP: (11) implies:
% 252.31/60.28 | (12) ~ (all_22_2 = e2)
% 252.31/60.28 |
% 252.31/60.28 | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (12) are inconsistent by
% 252.31/60.28 | sub-proof #957.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #853 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) ~ (all_162_2 = e4) | ( ~ (all_162_0 = e1) & op(e4, all_162_1) =
% 252.31/60.28 all_162_0 & op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) | (
% 252.31/60.28 ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 & $i(all_162_1))
% 252.31/60.28 (2) ~ (all_10_2 = e4)
% 252.31/60.28 (3) op(e0, e2) = e4
% 252.31/60.28 (4) ~ (all_244_8 = e0)
% 252.31/60.28 (5) all_162_2 = all_28_2
% 252.31/60.28 (6) ~ (e2 = e0)
% 252.31/60.28 (7) ~ (all_28_2 = e3)
% 252.31/60.28 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (9) op(e2, e3) = all_10_2
% 252.31/60.28 (10) ~ (e3 = e2)
% 252.31/60.28 (11) ~ (e4 = e0)
% 252.31/60.28 (12) op(e2, e2) = all_244_8
% 252.31/60.28 (13) op(e2, e1) = all_38_2
% 252.31/60.28 (14) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 252.31/60.28 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 252.31/60.28 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.28 (15) ~ (all_40_2 = e4)
% 252.31/60.28 (16) op(e4, e2) = all_6_2
% 252.31/60.28 (17) ~ (e2 = e1)
% 252.31/60.28 (18) op(e0, e2) = all_28_2
% 252.31/60.28 (19) ~ (e4 = e1)
% 252.31/60.28 (20) ~ (all_6_2 = e1)
% 252.31/60.28 (21) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 252.31/60.28 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.31/60.28 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.28 (22) ~ (e3 = e0)
% 252.31/60.28 (23) ~ (all_12_2 = e2)
% 252.31/60.28 (24) ~ (all_8_2 = e1)
% 252.31/60.28 (25) ~ (all_8_2 = e0)
% 252.31/60.28 (26) ~ (all_38_2 = e4)
% 252.31/60.28 (27) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 252.31/60.28 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 252.31/60.28 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.28 (28) op(e1, e2) = all_4_2
% 252.31/60.28 (29) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3)
% 252.31/60.28 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) =
% 252.31/60.28 e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 252.31/60.28 (30) op(e2, e4) = all_64_2
% 252.31/60.28 (31) ~ (e4 = e2)
% 252.31/60.28 (32) op(e0, all_64_2) = e2
% 252.31/60.28 (33) op(e3, e2) = all_8_2
% 252.31/60.28 (34) op(e2, e0) = all_40_2
% 252.31/60.28 (35) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2)
% 252.31/60.28 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) =
% 252.31/60.28 e2) | (all_252_22 = e2 & op(e0, e2) = e2)
% 252.31/60.28 (36) ~ (all_4_2 = e3)
% 252.31/60.28 (37) ~ (all_4_2 = e0)
% 252.31/60.28 (38) op(e0, e4) = all_12_2
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | BETA: splitting (21) gives:
% 252.31/60.28 |
% 252.31/60.28 | Case 1:
% 252.31/60.28 | |
% 252.31/60.28 | | (39) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 252.31/60.28 | | e0)
% 252.31/60.28 | |
% 252.31/60.28 | | BETA: splitting (39) gives:
% 252.31/60.28 | |
% 252.31/60.28 | | Case 1:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (40) all_252_4 = e0 & op(e4, e2) = e0
% 252.31/60.28 | | |
% 252.31/60.28 | | | ALPHA: (40) implies:
% 252.31/60.28 | | | (41) all_252_4 = e0
% 252.31/60.28 | | |
% 252.31/60.28 | | | GROUND_INST: instantiating (8) with all_28_2, e4, e2, e0, simplifying with
% 252.31/60.28 | | | (3), (18) gives:
% 252.31/60.28 | | | (42) all_28_2 = e4
% 252.31/60.28 | | |
% 252.31/60.28 | | | COMBINE_EQS: (5), (42) imply:
% 252.31/60.28 | | | (43) all_162_2 = e4
% 252.31/60.28 | | |
% 252.31/60.28 | | | REDUCE: (7), (42) imply:
% 252.31/60.28 | | | (44) ~ (e4 = e3)
% 252.31/60.28 | | |
% 252.31/60.28 | | | BETA: splitting (27) gives:
% 252.31/60.28 | | |
% 252.31/60.28 | | | Case 1:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (45) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2,
% 252.31/60.28 | | | | e3) = e4)
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | BETA: splitting (45) gives:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | Case 1:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | (46) all_252_6 = e4 & op(e2, e4) = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | ALPHA: (46) implies:
% 252.31/60.28 | | | | | (47) op(e2, e4) = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | BETA: splitting (1) gives:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | Case 1:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | (48) ~ (all_162_2 = e4)
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | REDUCE: (43), (48) imply:
% 252.31/60.28 | | | | | | (49) $false
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | CLOSE: (49) is inconsistent.
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | Case 2:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | (50) ( ~ (all_162_0 = e1) & op(e4, all_162_1) = all_162_0 &
% 252.31/60.28 | | | | | | op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)) |
% 252.31/60.28 | | | | | | ( ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 &
% 252.31/60.28 | | | | | | $i(all_162_1))
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | BETA: splitting (50) gives:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | Case 1:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (51) ~ (all_162_0 = e1) & op(e4, all_162_1) = all_162_0 &
% 252.31/60.28 | | | | | | | op(e2, e4) = all_162_1 & $i(all_162_0) & $i(all_162_1)
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | ALPHA: (51) implies:
% 252.31/60.28 | | | | | | | (52) op(e2, e4) = all_162_1
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | REF_CLOSE: (8), (23), (30), (32), (38), (47), (52) are
% 252.31/60.28 | | | | | | | inconsistent by sub-proof #866.
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | Case 2:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (53) ~ (all_162_1 = e3) & op(e2, e4) = all_162_1 &
% 252.31/60.28 | | | | | | | $i(all_162_1)
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | ALPHA: (53) implies:
% 252.31/60.28 | | | | | | | (54) op(e2, e4) = all_162_1
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | REF_CLOSE: (8), (23), (30), (32), (38), (47), (54) are
% 252.31/60.28 | | | | | | | inconsistent by sub-proof #866.
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | End of split
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | End of split
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | Case 2:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | (55) all_252_7 = e4 & op(e2, e3) = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | ALPHA: (55) implies:
% 252.31/60.28 | | | | | (56) op(e2, e3) = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | REF_CLOSE: (2), (8), (9), (56) are inconsistent by sub-proof #953.
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | End of split
% 252.31/60.28 | | | |
% 252.31/60.28 | | | Case 2:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (57) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2,
% 252.31/60.28 | | | | e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | BETA: splitting (57) gives:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | Case 1:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | (58) all_252_8 = e4 & op(e2, e2) = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | ALPHA: (58) implies:
% 252.31/60.28 | | | | | (59) all_252_8 = e4
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | BETA: splitting (29) gives:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | Case 1:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | (60) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 &
% 252.31/60.28 | | | | | | op(e3, e2) = e3)
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | BETA: splitting (60) gives:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | Case 1:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (61) all_252_4 = e3 & op(e4, e2) = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | REF_CLOSE: (22), (41), (61) are inconsistent by sub-proof #865.
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | Case 2:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (62) all_252_5 = e3 & op(e3, e2) = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | ALPHA: (62) implies:
% 252.31/60.28 | | | | | | | (63) all_252_5 = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | BETA: splitting (14) gives:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | | (64) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 &
% 252.31/60.28 | | | | | | | | op(e3, e2) = e1)
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | | REF_CLOSE: (8), (16), (20), (24), (33), (64) are inconsistent by
% 252.31/60.28 | | | | | | | | sub-proof #928.
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | | (65) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 &
% 252.31/60.28 | | | | | | | | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | | BETA: splitting (65) gives:
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | (66) all_252_8 = e1 & op(e2, e2) = e1
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | ALPHA: (66) implies:
% 252.31/60.28 | | | | | | | | | (67) all_252_8 = e1
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | REF_CLOSE: (19), (59), (67) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | #864.
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | (68) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1
% 252.31/60.28 | | | | | | | | | & op(e0, e2) = e1)
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | BETA: splitting (68) gives:
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | (69) all_252_14 = e1 & op(e1, e2) = e1
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | ALPHA: (69) implies:
% 252.31/60.28 | | | | | | | | | | (70) all_252_14 = e1
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | BETA: splitting (35) gives:
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | (71) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 =
% 252.31/60.28 | | | | | | | | | | | e2 & op(e3, e2) = e2)
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | BETA: splitting (71) gives:
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | (72) all_252_4 = e2 & op(e4, e2) = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | REF_CLOSE: (6), (41), (72) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | | | | #863.
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | (73) all_252_5 = e2 & op(e3, e2) = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | REF_CLOSE: (10), (63), (73) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | | | | #862.
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | End of split
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | (74) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 =
% 252.31/60.28 | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 &
% 252.31/60.28 | | | | | | | | | | | op(e0, e2) = e2)
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | BETA: splitting (74) gives:
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | (75) all_252_8 = e2 & op(e2, e2) = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | ALPHA: (75) implies:
% 252.31/60.28 | | | | | | | | | | | | (76) all_252_8 = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | COMBINE_EQS: (59), (76) imply:
% 252.31/60.28 | | | | | | | | | | | | (77) e4 = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | SIMP: (77) implies:
% 252.31/60.28 | | | | | | | | | | | | (78) e4 = e2
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | REDUCE: (31), (78) imply:
% 252.31/60.28 | | | | | | | | | | | | (79) $false
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | CLOSE: (79) is inconsistent.
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | (80) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22
% 252.31/60.28 | | | | | | | | | | | | = e2 & op(e0, e2) = e2)
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | BETA: splitting (80) gives:
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | Case 1:
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | | (81) all_252_14 = e2 & op(e1, e2) = e2
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | | ALPHA: (81) implies:
% 252.31/60.28 | | | | | | | | | | | | | (82) all_252_14 = e2
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | | REF_CLOSE: (17), (70), (82) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | | | | | #861.
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | | (83) all_252_22 = e2 & op(e0, e2) = e2
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | | REF_CLOSE: (3), (8), (31), (83) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | | | | | #860.
% 252.31/60.28 | | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | | End of split
% 252.31/60.28 | | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | | End of split
% 252.31/60.28 | | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | End of split
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | Case 2:
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | (84) all_252_22 = e1 & op(e0, e2) = e1
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | ALPHA: (84) implies:
% 252.31/60.28 | | | | | | | | | | (85) op(e0, e2) = e1
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | | REF_CLOSE: (3), (8), (19), (85) are inconsistent by sub-proof
% 252.31/60.28 | | | | | | | | | | #859.
% 252.31/60.28 | | | | | | | | | |
% 252.31/60.28 | | | | | | | | | End of split
% 252.31/60.28 | | | | | | | | |
% 252.31/60.28 | | | | | | | | End of split
% 252.31/60.28 | | | | | | | |
% 252.31/60.28 | | | | | | | End of split
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | End of split
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | Case 2:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | (86) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 &
% 252.31/60.28 | | | | | | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | BETA: splitting (86) gives:
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | | Case 1:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (87) all_252_8 = e3 & op(e2, e2) = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | ALPHA: (87) implies:
% 252.31/60.28 | | | | | | | (88) all_252_8 = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | COMBINE_EQS: (59), (88) imply:
% 252.31/60.28 | | | | | | | (89) e4 = e3
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | REDUCE: (44), (89) imply:
% 252.31/60.28 | | | | | | | (90) $false
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | CLOSE: (90) is inconsistent.
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | Case 2:
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | (91) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 &
% 252.31/60.28 | | | | | | | op(e0, e2) = e3)
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | | REF_CLOSE: (3), (8), (28), (36), (44), (91) are inconsistent by
% 252.31/60.28 | | | | | | | sub-proof #856.
% 252.31/60.28 | | | | | | |
% 252.31/60.28 | | | | | | End of split
% 252.31/60.28 | | | | | |
% 252.31/60.28 | | | | | End of split
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | Case 2:
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | (92) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 &
% 252.31/60.28 | | | | | op(e2, e0) = e4)
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | | REF_CLOSE: (8), (13), (15), (26), (34), (92) are inconsistent by
% 252.31/60.28 | | | | | sub-proof #933.
% 252.31/60.28 | | | | |
% 252.31/60.28 | | | | End of split
% 252.31/60.28 | | | |
% 252.31/60.28 | | | End of split
% 252.31/60.28 | | |
% 252.31/60.28 | | Case 2:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (93) all_252_5 = e0 & op(e3, e2) = e0
% 252.31/60.28 | | |
% 252.31/60.28 | | | REF_CLOSE: (8), (25), (33), (93) are inconsistent by sub-proof #874.
% 252.31/60.28 | | |
% 252.31/60.28 | | End of split
% 252.31/60.28 | |
% 252.31/60.28 | Case 2:
% 252.31/60.28 | |
% 252.31/60.28 | | (94) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.31/60.28 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.28 | |
% 252.31/60.28 | | BETA: splitting (94) gives:
% 252.31/60.28 | |
% 252.31/60.28 | | Case 1:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (95) all_252_8 = e0 & op(e2, e2) = e0
% 252.31/60.28 | | |
% 252.31/60.28 | | | ALPHA: (95) implies:
% 252.31/60.28 | | | (96) op(e2, e2) = e0
% 252.31/60.28 | | |
% 252.31/60.28 | | | REF_CLOSE: (4), (8), (12), (96) are inconsistent by sub-proof #880.
% 252.31/60.28 | | |
% 252.31/60.28 | | Case 2:
% 252.31/60.28 | | |
% 252.31/60.28 | | | (97) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 252.31/60.28 | | | e2) = e0)
% 252.31/60.28 | | |
% 252.31/60.28 | | | BETA: splitting (97) gives:
% 252.31/60.28 | | |
% 252.31/60.28 | | | Case 1:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (98) all_252_14 = e0 & op(e1, e2) = e0
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | REF_CLOSE: (8), (28), (37), (98) are inconsistent by sub-proof #855.
% 252.31/60.28 | | | |
% 252.31/60.28 | | | Case 2:
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | (99) all_252_22 = e0 & op(e0, e2) = e0
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | ALPHA: (99) implies:
% 252.31/60.28 | | | | (100) op(e0, e2) = e0
% 252.31/60.28 | | | |
% 252.31/60.28 | | | | REF_CLOSE: (3), (8), (11), (18), (100) are inconsistent by sub-proof
% 252.31/60.28 | | | | #854.
% 252.31/60.28 | | | |
% 252.31/60.28 | | | End of split
% 252.31/60.28 | | |
% 252.31/60.28 | | End of split
% 252.31/60.28 | |
% 252.31/60.28 | End of split
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #854 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) op(e0, e2) = e4
% 252.31/60.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (3) ~ (e4 = e0)
% 252.31/60.28 (4) op(e0, e2) = all_28_2
% 252.31/60.28 (5) op(e0, e2) = e0
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_28_2, e0, e2, e0, simplifying with
% 252.31/60.28 | (4), (5) gives:
% 252.31/60.28 | (6) all_28_2 = e0
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_28_2, e4, e2, e0, simplifying with
% 252.31/60.28 | (1), (4) gives:
% 252.31/60.28 | (7) all_28_2 = e4
% 252.31/60.28 |
% 252.31/60.28 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.28 | (8) e4 = e0
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (3), (8) imply:
% 252.31/60.28 | (9) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (9) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #855 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_14 = e0 & op(e1, e2) = e0
% 252.31/60.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (3) op(e1, e2) = all_4_2
% 252.31/60.28 (4) ~ (all_4_2 = e0)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | ALPHA: (1) implies:
% 252.31/60.28 | (5) op(e1, e2) = e0
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_4_2, e0, e2, e1, simplifying with (3),
% 252.31/60.28 | (5) gives:
% 252.31/60.28 | (6) all_4_2 = e0
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (4), (6) imply:
% 252.31/60.28 | (7) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (7) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #856 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) op(e0, e2) = e4
% 252.31/60.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (3) ~ (e4 = e3)
% 252.31/60.28 (4) op(e1, e2) = all_4_2
% 252.31/60.28 (5) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)
% 252.31/60.28 (6) ~ (all_4_2 = e3)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | BETA: splitting (5) gives:
% 252.31/60.28 |
% 252.31/60.28 | Case 1:
% 252.31/60.28 | |
% 252.31/60.28 | | (7) all_252_14 = e3 & op(e1, e2) = e3
% 252.31/60.28 | |
% 252.31/60.28 | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #858.
% 252.31/60.28 | |
% 252.31/60.28 | Case 2:
% 252.31/60.28 | |
% 252.31/60.28 | | (8) all_252_22 = e3 & op(e0, e2) = e3
% 252.31/60.28 | |
% 252.31/60.28 | | ALPHA: (8) implies:
% 252.31/60.28 | | (9) op(e0, e2) = e3
% 252.31/60.28 | |
% 252.31/60.28 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #857.
% 252.31/60.28 | |
% 252.31/60.28 | End of split
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #857 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (2) op(e0, e2) = e4
% 252.31/60.28 (3) op(e0, e2) = e3
% 252.31/60.28 (4) ~ (e4 = e3)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (1) with e3, e4, e2, e0, simplifying with (2), (3)
% 252.31/60.28 | gives:
% 252.31/60.28 | (5) e4 = e3
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (4), (5) imply:
% 252.31/60.28 | (6) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (6) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #858 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_14 = e3 & op(e1, e2) = e3
% 252.31/60.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (3) op(e1, e2) = all_4_2
% 252.31/60.28 (4) ~ (all_4_2 = e3)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | ALPHA: (1) implies:
% 252.31/60.28 | (5) op(e1, e2) = e3
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (2) with all_4_2, e3, e2, e1, simplifying with (3),
% 252.31/60.28 | (5) gives:
% 252.31/60.28 | (6) all_4_2 = e3
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (4), (6) imply:
% 252.31/60.28 | (7) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (7) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #859 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.28 (2) op(e0, e2) = e4
% 252.31/60.28 (3) op(e0, e2) = e1
% 252.31/60.28 (4) ~ (e4 = e1)
% 252.31/60.28
% 252.31/60.28 Begin of proof
% 252.31/60.28 |
% 252.31/60.28 | GROUND_INST: instantiating (1) with e4, e1, e2, e0, simplifying with (2), (3)
% 252.31/60.28 | gives:
% 252.31/60.28 | (5) e4 = e1
% 252.31/60.28 |
% 252.31/60.28 | REDUCE: (4), (5) imply:
% 252.31/60.28 | (6) $false
% 252.31/60.28 |
% 252.31/60.28 | CLOSE: (6) is inconsistent.
% 252.31/60.28 |
% 252.31/60.28 End of proof
% 252.31/60.28
% 252.31/60.28 Sub-proof #860 shows that the following formulas are inconsistent:
% 252.31/60.28 ----------------------------------------------------------------
% 252.31/60.28 (1) all_252_22 = e2 & op(e0, e2) = e2
% 252.31/60.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (3) op(e0, e2) = e4
% 252.31/60.29 (4) ~ (e4 = e2)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (5) op(e0, e2) = e2
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (2) with e4, e2, e2, e0, simplifying with (3), (5)
% 252.31/60.29 | gives:
% 252.31/60.29 | (6) e4 = e2
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (4), (6) imply:
% 252.31/60.29 | (7) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (7) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #861 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_14 = e2
% 252.31/60.29 (2) all_252_14 = e1
% 252.31/60.29 (3) ~ (e2 = e1)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.29 | (4) e2 = e1
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (4) implies:
% 252.31/60.29 | (5) e2 = e1
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #862 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_5 = e2 & op(e3, e2) = e2
% 252.31/60.29 (2) all_252_5 = e3
% 252.31/60.29 (3) ~ (e3 = e2)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (4) all_252_5 = e2
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.29 | (5) e3 = e2
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #863 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_4 = e2 & op(e4, e2) = e2
% 252.31/60.29 (2) all_252_4 = e0
% 252.31/60.29 (3) ~ (e2 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (4) all_252_4 = e2
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.29 | (5) e2 = e0
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (5) implies:
% 252.31/60.29 | (6) e2 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (6) imply:
% 252.31/60.29 | (7) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (7) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #864 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_8 = e4
% 252.31/60.29 (2) all_252_8 = e1
% 252.31/60.29 (3) ~ (e4 = e1)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.29 | (4) e4 = e1
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (4) implies:
% 252.31/60.29 | (5) e4 = e1
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #865 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_4 = e3 & op(e4, e2) = e3
% 252.31/60.29 (2) all_252_4 = e0
% 252.31/60.29 (3) ~ (e3 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (4) all_252_4 = e3
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.29 | (5) e3 = e0
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (5) implies:
% 252.31/60.29 | (6) e3 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (6) imply:
% 252.31/60.29 | (7) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (7) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #866 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (2) op(e2, e4) = e4
% 252.31/60.29 (3) ~ (all_12_2 = e2)
% 252.31/60.29 (4) op(e2, e4) = all_64_2
% 252.31/60.29 (5) op(e0, all_64_2) = e2
% 252.31/60.29 (6) op(e2, e4) = all_162_1
% 252.31/60.29 (7) op(e0, e4) = all_12_2
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (1) with all_64_2, all_162_1, e4, e2, simplifying
% 252.31/60.29 | with (4), (6) gives:
% 252.31/60.29 | (8) all_162_1 = all_64_2
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (1) with e4, all_162_1, e4, e2, simplifying with
% 252.31/60.29 | (2), (6) gives:
% 252.31/60.29 | (9) all_162_1 = e4
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (8), (9) imply:
% 252.31/60.29 | (10) all_64_2 = e4
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (10) implies:
% 252.31/60.29 | (11) all_64_2 = e4
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (5), (11) imply:
% 252.31/60.29 | (12) op(e0, e4) = e2
% 252.31/60.29 |
% 252.31/60.29 | REF_CLOSE: (1), (3), (7), (12) are inconsistent by sub-proof #980.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #867 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ~ (all_244_8 = all_4_2)
% 252.31/60.29 (2) ~ (all_28_2 = all_6_2)
% 252.31/60.29 (3) ~ (e2 = e0)
% 252.31/60.29 (4) ~ (e1 = e0)
% 252.31/60.29 (5) ~ (all_62_2 = e2)
% 252.31/60.29 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (7) op(e2, e2) = all_244_8
% 252.31/60.29 (8) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 252.31/60.29 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 252.31/60.29 | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.29 (9) op(e1, e0) = all_34_2
% 252.31/60.29 (10) op(all_28_2, e2) = e0
% 252.31/60.29 (11) op(e4, e2) = all_6_2
% 252.31/60.29 (12) ~ (all_8_2 = all_4_2)
% 252.31/60.29 (13) ~ (all_34_2 = e2)
% 252.31/60.29 (14) op(e0, e2) = all_28_2
% 252.31/60.29 (15) all_28_2 = e1
% 252.31/60.29 (16) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 252.31/60.29 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.31/60.29 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.29 (17) op(all_244_15, all_244_15) = e1
% 252.31/60.29 (18) op(e1, e4) = all_16_2
% 252.31/60.29 (19) op(e1, e3) = all_62_2
% 252.31/60.29 (20) ~ (all_16_2 = e2)
% 252.31/60.29 (21) ~ (all_28_2 = all_4_2)
% 252.31/60.29 (22) ~ (all_8_2 = e0)
% 252.31/60.29 (23) op(e1, e1) = all_244_15
% 252.31/60.29 (24) op(e1, e2) = all_4_2
% 252.31/60.29 (25) ~ (all_28_2 = all_8_2)
% 252.31/60.29 (26) ~ (all_6_2 = all_4_2)
% 252.31/60.29 (27) ~ (all_6_2 = e0)
% 252.31/60.29 (28) op(e3, e2) = all_8_2
% 252.31/60.29 (29) ~ (all_244_8 = all_28_2)
% 252.31/60.29 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.29 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.29 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (15), (29) imply:
% 252.31/60.29 | (31) ~ (all_244_8 = e1)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (15), (25) imply:
% 252.31/60.29 | (32) ~ (all_8_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (32) implies:
% 252.31/60.29 | (33) ~ (all_8_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (2), (15) imply:
% 252.31/60.29 | (34) ~ (all_6_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (34) implies:
% 252.31/60.29 | (35) ~ (all_6_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (15), (21) imply:
% 252.31/60.29 | (36) ~ (all_4_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (36) implies:
% 252.31/60.29 | (37) ~ (all_4_2 = e1)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (10), (15) imply:
% 252.31/60.29 | (38) op(e1, e2) = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (14), (15) imply:
% 252.31/60.29 | (39) op(e0, e2) = e1
% 252.31/60.29 |
% 252.31/60.29 | BETA: splitting (8) gives:
% 252.31/60.29 |
% 252.31/60.29 | Case 1:
% 252.31/60.29 | |
% 252.31/60.29 | | (40) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 252.31/60.29 | | e1)
% 252.31/60.29 | |
% 252.31/60.29 | | REF_CLOSE: (6), (11), (28), (33), (35), (40) are inconsistent by sub-proof
% 252.31/60.29 | | #928.
% 252.31/60.29 | |
% 252.31/60.29 | Case 2:
% 252.31/60.29 | |
% 252.31/60.29 | | (41) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 252.31/60.29 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.29 | |
% 252.31/60.29 | | BETA: splitting (41) gives:
% 252.31/60.29 | |
% 252.31/60.29 | | Case 1:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (42) all_252_8 = e1 & op(e2, e2) = e1
% 252.31/60.29 | | |
% 252.31/60.29 | | | ALPHA: (42) implies:
% 252.31/60.29 | | | (43) all_252_8 = e1
% 252.31/60.29 | | |
% 252.31/60.29 | | | BETA: splitting (16) gives:
% 252.31/60.29 | | |
% 252.31/60.29 | | | Case 1:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (44) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3,
% 252.31/60.29 | | | | e2) = e0)
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | BETA: splitting (44) gives:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | Case 1:
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | (45) all_252_4 = e0 & op(e4, e2) = e0
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | REF_CLOSE: (6), (11), (27), (45) are inconsistent by sub-proof #875.
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | Case 2:
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | (46) all_252_5 = e0 & op(e3, e2) = e0
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | REF_CLOSE: (6), (22), (28), (46) are inconsistent by sub-proof #874.
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | End of split
% 252.31/60.29 | | | |
% 252.31/60.29 | | | Case 2:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (47) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1,
% 252.31/60.29 | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | BETA: splitting (47) gives:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | Case 1:
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | (48) all_252_8 = e0 & op(e2, e2) = e0
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | REF_CLOSE: (4), (43), (48) are inconsistent by sub-proof #873.
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | Case 2:
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | (49) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 &
% 252.31/60.29 | | | | | op(e0, e2) = e0)
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | BETA: splitting (49) gives:
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | | Case 1:
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | | (50) all_252_14 = e0 & op(e1, e2) = e0
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | | REF_CLOSE: (3), (5), (6), (7), (9), (13), (17), (18), (19), (20),
% 252.31/60.29 | | | | | | (23), (30), (31), (50) are inconsistent by sub-proof
% 252.31/60.29 | | | | | | #872.
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | Case 2:
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | | (51) all_252_22 = e0 & op(e0, e2) = e0
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | | ALPHA: (51) implies:
% 252.31/60.29 | | | | | | (52) op(e0, e2) = e0
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | | REF_CLOSE: (4), (6), (39), (52) are inconsistent by sub-proof #871.
% 252.31/60.29 | | | | | |
% 252.31/60.29 | | | | | End of split
% 252.31/60.29 | | | | |
% 252.31/60.29 | | | | End of split
% 252.31/60.29 | | | |
% 252.31/60.29 | | | End of split
% 252.31/60.29 | | |
% 252.31/60.29 | | Case 2:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (53) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 252.31/60.29 | | | e2) = e1)
% 252.31/60.29 | | |
% 252.31/60.29 | | | BETA: splitting (53) gives:
% 252.31/60.29 | | |
% 252.31/60.29 | | | Case 1:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (54) all_252_14 = e1 & op(e1, e2) = e1
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | ALPHA: (54) implies:
% 252.31/60.29 | | | | (55) op(e1, e2) = e1
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (4), (6), (24), (38), (55) are inconsistent by sub-proof
% 252.31/60.29 | | | | #870.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | Case 2:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (56) all_252_22 = e1 & op(e0, e2) = e1
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | ALPHA: (56) implies:
% 252.31/60.29 | | | | (57) all_252_22 = e1
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (11), (12), (13), (16), (17),
% 252.31/60.29 | | | | (18), (19), (20), (23), (24), (26), (28), (30), (31), (37),
% 252.31/60.29 | | | | (38), (57) are inconsistent by sub-proof #868.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | End of split
% 252.31/60.29 | | |
% 252.31/60.29 | | End of split
% 252.31/60.29 | |
% 252.31/60.29 | End of split
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #868 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ~ (all_244_8 = all_4_2)
% 252.31/60.29 (2) ~ (e2 = e0)
% 252.31/60.29 (3) ~ (all_62_2 = e2)
% 252.31/60.29 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (5) op(e2, e2) = all_244_8
% 252.31/60.29 (6) op(e1, e0) = all_34_2
% 252.31/60.29 (7) op(e4, e2) = all_6_2
% 252.31/60.29 (8) ~ (all_8_2 = all_4_2)
% 252.31/60.29 (9) ~ (all_34_2 = e2)
% 252.31/60.29 (10) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0)
% 252.31/60.29 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.31/60.29 e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.29 (11) op(all_244_15, all_244_15) = e1
% 252.31/60.29 (12) op(e1, e4) = all_16_2
% 252.31/60.29 (13) all_252_22 = e1
% 252.31/60.29 (14) op(e1, e3) = all_62_2
% 252.31/60.29 (15) ~ (all_16_2 = e2)
% 252.31/60.29 (16) op(e1, e2) = e0
% 252.31/60.29 (17) ~ (all_244_8 = e1)
% 252.31/60.29 (18) op(e1, e1) = all_244_15
% 252.31/60.29 (19) op(e1, e2) = all_4_2
% 252.31/60.29 (20) ~ (all_6_2 = all_4_2)
% 252.31/60.29 (21) op(e3, e2) = all_8_2
% 252.31/60.29 (22) ~ (all_4_2 = e1)
% 252.31/60.29 (23) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.29 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.29 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (4) with all_4_2, e0, e2, e1, simplifying with
% 252.31/60.29 | (16), (19) gives:
% 252.31/60.29 | (24) all_4_2 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (1), (24) imply:
% 252.31/60.29 | (25) ~ (all_244_8 = e0)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (8), (24) imply:
% 252.31/60.29 | (26) ~ (all_8_2 = e0)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (20), (24) imply:
% 252.31/60.29 | (27) ~ (all_6_2 = e0)
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (22), (24) imply:
% 252.31/60.29 | (28) ~ (e1 = e0)
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (28) implies:
% 252.31/60.29 | (29) ~ (e1 = e0)
% 252.31/60.29 |
% 252.31/60.29 | BETA: splitting (10) gives:
% 252.31/60.29 |
% 252.31/60.29 | Case 1:
% 252.31/60.29 | |
% 252.31/60.29 | | (30) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) =
% 252.31/60.29 | | e0)
% 252.31/60.29 | |
% 252.31/60.29 | | BETA: splitting (30) gives:
% 252.31/60.29 | |
% 252.31/60.29 | | Case 1:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (31) all_252_4 = e0 & op(e4, e2) = e0
% 252.31/60.29 | | |
% 252.31/60.29 | | | REF_CLOSE: (4), (7), (27), (31) are inconsistent by sub-proof #875.
% 252.31/60.29 | | |
% 252.31/60.29 | | Case 2:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (32) all_252_5 = e0 & op(e3, e2) = e0
% 252.31/60.29 | | |
% 252.31/60.29 | | | REF_CLOSE: (4), (21), (26), (32) are inconsistent by sub-proof #874.
% 252.31/60.29 | | |
% 252.31/60.29 | | End of split
% 252.31/60.29 | |
% 252.31/60.29 | Case 2:
% 252.31/60.29 | |
% 252.31/60.29 | | (33) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) =
% 252.31/60.29 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0)
% 252.31/60.29 | |
% 252.31/60.29 | | BETA: splitting (33) gives:
% 252.31/60.29 | |
% 252.31/60.29 | | Case 1:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (34) all_252_8 = e0 & op(e2, e2) = e0
% 252.31/60.29 | | |
% 252.31/60.29 | | | ALPHA: (34) implies:
% 252.31/60.29 | | | (35) op(e2, e2) = e0
% 252.31/60.29 | | |
% 252.31/60.29 | | | REF_CLOSE: (4), (5), (25), (35) are inconsistent by sub-proof #880.
% 252.31/60.29 | | |
% 252.31/60.29 | | Case 2:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (36) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0,
% 252.31/60.29 | | | e2) = e0)
% 252.31/60.29 | | |
% 252.31/60.29 | | | BETA: splitting (36) gives:
% 252.31/60.29 | | |
% 252.31/60.29 | | | Case 1:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (37) all_252_14 = e0 & op(e1, e2) = e0
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (11), (12), (14), (15), (17),
% 252.31/60.29 | | | | (18), (23), (37) are inconsistent by sub-proof #872.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | Case 2:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (38) all_252_22 = e0 & op(e0, e2) = e0
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (13), (29), (38) are inconsistent by sub-proof #869.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | End of split
% 252.31/60.29 | | |
% 252.31/60.29 | | End of split
% 252.31/60.29 | |
% 252.31/60.29 | End of split
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #869 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_22 = e0 & op(e0, e2) = e0
% 252.31/60.29 (2) all_252_22 = e1
% 252.31/60.29 (3) ~ (e1 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (4) all_252_22 = e0
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.29 | (5) e1 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #870 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ~ (e1 = e0)
% 252.31/60.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (3) op(e1, e2) = e1
% 252.31/60.29 (4) op(e1, e2) = e0
% 252.31/60.29 (5) op(e1, e2) = all_4_2
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (2) with all_4_2, e0, e2, e1, simplifying with (4),
% 252.31/60.29 | (5) gives:
% 252.31/60.29 | (6) all_4_2 = e0
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (2) with all_4_2, e1, e2, e1, simplifying with (3),
% 252.31/60.29 | (5) gives:
% 252.31/60.29 | (7) all_4_2 = e1
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.29 | (8) e1 = e0
% 252.31/60.29 |
% 252.31/60.29 | SIMP: (8) implies:
% 252.31/60.29 | (9) e1 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (1), (9) imply:
% 252.31/60.29 | (10) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (10) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #871 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (2) op(e0, e2) = e1
% 252.31/60.29 (3) op(e0, e2) = e0
% 252.31/60.29 (4) ~ (e1 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (1) with e0, e1, e2, e0, simplifying with (2), (3)
% 252.31/60.29 | gives:
% 252.31/60.29 | (5) e1 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (4), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #872 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ~ (e2 = e0)
% 252.31/60.29 (2) ~ (all_62_2 = e2)
% 252.31/60.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (4) op(e2, e2) = all_244_8
% 252.31/60.29 (5) op(e1, e0) = all_34_2
% 252.31/60.29 (6) ~ (all_34_2 = e2)
% 252.31/60.29 (7) op(all_244_15, all_244_15) = e1
% 252.31/60.29 (8) op(e1, e4) = all_16_2
% 252.31/60.29 (9) op(e1, e3) = all_62_2
% 252.31/60.29 (10) ~ (all_16_2 = e2)
% 252.31/60.29 (11) ~ (all_244_8 = e1)
% 252.31/60.29 (12) op(e1, e1) = all_244_15
% 252.31/60.29 (13) all_252_14 = e0 & op(e1, e2) = e0
% 252.31/60.29 (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.29 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.29 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (13) implies:
% 252.31/60.29 | (15) all_252_14 = e0
% 252.31/60.29 |
% 252.31/60.29 | BETA: splitting (14) gives:
% 252.31/60.29 |
% 252.31/60.29 | Case 1:
% 252.31/60.29 | |
% 252.31/60.29 | | (16) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 252.31/60.29 | | = e2)
% 252.31/60.29 | |
% 252.31/60.29 | | REF_CLOSE: (2), (3), (8), (9), (10), (16) are inconsistent by sub-proof
% 252.31/60.29 | | #925.
% 252.31/60.29 | |
% 252.31/60.29 | Case 2:
% 252.31/60.29 | |
% 252.31/60.29 | | (17) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 252.31/60.29 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.29 | |
% 252.31/60.29 | | BETA: splitting (17) gives:
% 252.31/60.29 | |
% 252.31/60.29 | | Case 1:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (18) all_252_14 = e2 & op(e1, e2) = e2
% 252.31/60.29 | | |
% 252.31/60.29 | | | ALPHA: (18) implies:
% 252.31/60.29 | | | (19) all_252_14 = e2
% 252.31/60.29 | | |
% 252.31/60.29 | | | COMBINE_EQS: (15), (19) imply:
% 252.31/60.29 | | | (20) e2 = e0
% 252.31/60.29 | | |
% 252.31/60.29 | | | REDUCE: (1), (20) imply:
% 252.31/60.29 | | | (21) $false
% 252.31/60.29 | | |
% 252.31/60.29 | | | CLOSE: (21) is inconsistent.
% 252.31/60.29 | | |
% 252.31/60.29 | | Case 2:
% 252.31/60.29 | | |
% 252.31/60.29 | | | (22) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 252.31/60.29 | | | e0) = e2)
% 252.31/60.29 | | |
% 252.31/60.29 | | | BETA: splitting (22) gives:
% 252.31/60.29 | | |
% 252.31/60.29 | | | Case 1:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (23) all_252_15 = e2 & op(e1, e1) = e2
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | ALPHA: (23) implies:
% 252.31/60.29 | | | | (24) op(e1, e1) = e2
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (3), (4), (7), (11), (12), (24) are inconsistent by sub-proof
% 252.31/60.29 | | | | #991.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | Case 2:
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | (25) all_252_19 = e2 & op(e1, e0) = e2
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | ALPHA: (25) implies:
% 252.31/60.29 | | | | (26) op(e1, e0) = e2
% 252.31/60.29 | | | |
% 252.31/60.29 | | | | REF_CLOSE: (3), (5), (6), (26) are inconsistent by sub-proof #909.
% 252.31/60.29 | | | |
% 252.31/60.29 | | | End of split
% 252.31/60.29 | | |
% 252.31/60.29 | | End of split
% 252.31/60.29 | |
% 252.31/60.29 | End of split
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #873 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_8 = e0 & op(e2, e2) = e0
% 252.31/60.29 (2) all_252_8 = e1
% 252.31/60.29 (3) ~ (e1 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (4) all_252_8 = e0
% 252.31/60.29 |
% 252.31/60.29 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.29 | (5) e1 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (3), (5) imply:
% 252.31/60.29 | (6) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (6) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #874 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_5 = e0 & op(e3, e2) = e0
% 252.31/60.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (3) op(e3, e2) = all_8_2
% 252.31/60.29 (4) ~ (all_8_2 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (5) op(e3, e2) = e0
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (2) with all_8_2, e0, e2, e3, simplifying with (3),
% 252.31/60.29 | (5) gives:
% 252.31/60.29 | (6) all_8_2 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (4), (6) imply:
% 252.31/60.29 | (7) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (7) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #875 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) all_252_4 = e0 & op(e4, e2) = e0
% 252.31/60.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (3) op(e4, e2) = all_6_2
% 252.31/60.29 (4) ~ (all_6_2 = e0)
% 252.31/60.29
% 252.31/60.29 Begin of proof
% 252.31/60.29 |
% 252.31/60.29 | ALPHA: (1) implies:
% 252.31/60.29 | (5) op(e4, e2) = e0
% 252.31/60.29 |
% 252.31/60.29 | GROUND_INST: instantiating (2) with all_6_2, e0, e2, e4, simplifying with (3),
% 252.31/60.29 | (5) gives:
% 252.31/60.29 | (6) all_6_2 = e0
% 252.31/60.29 |
% 252.31/60.29 | REDUCE: (4), (6) imply:
% 252.31/60.29 | (7) $false
% 252.31/60.29 |
% 252.31/60.29 | CLOSE: (7) is inconsistent.
% 252.31/60.29 |
% 252.31/60.29 End of proof
% 252.31/60.29
% 252.31/60.29 Sub-proof #876 shows that the following formulas are inconsistent:
% 252.31/60.29 ----------------------------------------------------------------
% 252.31/60.29 (1) ~ (all_178_2 = e3) | ( ~ (all_178_0 = e4) & op(e3, all_178_1) =
% 252.31/60.29 all_178_0 & op(e0, e3) = all_178_1 & $i(all_178_0) & $i(all_178_1)) | (
% 252.31/60.29 ~ (all_178_1 = e1) & op(e0, e3) = all_178_1 & $i(all_178_1))
% 252.31/60.29 (2) all_86_2 = e3
% 252.31/60.29 (3) ~ (all_22_2 = e3)
% 252.31/60.29 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.29 (5) op(e2, e2) = all_244_8
% 252.31/60.29 (6) all_250_21 = all_22_2
% 252.31/60.29 (7) all_178_2 = all_40_2
% 252.31/60.29 (8) ~ (all_22_2 = e4)
% 252.31/60.29 (9) op(all_48_2, all_22_2) = e0
% 252.31/60.29 (10) op(all_40_2, e0) = e2
% 252.31/60.29 (11) ~ (all_22_2 = e1)
% 252.31/60.29 (12) ~ (all_244_8 = all_40_2)
% 252.31/60.29 (13) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.31/60.29 all_250_21 = e0
% 252.31/60.30 (14) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 252.31/60.30 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 252.31/60.30 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 252.31/60.30 (15) op(e3, e0) = all_48_2
% 252.31/60.30 (16) op(all_48_2, e0) = e3
% 252.31/60.30 (17) all_86_2 = all_40_2
% 252.31/60.30 (18) all_90_2 = all_22_2
% 252.31/60.30 (19) op(all_22_2, all_48_2) = e3
% 252.31/60.30
% 252.31/60.30 Begin of proof
% 252.31/60.30 |
% 252.31/60.30 | COMBINE_EQS: (2), (17) imply:
% 252.31/60.30 | (20) all_40_2 = e3
% 252.31/60.30 |
% 252.31/60.30 | COMBINE_EQS: (7), (20) imply:
% 252.31/60.30 | (21) all_178_2 = e3
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (12), (20) imply:
% 252.31/60.30 | (22) ~ (all_244_8 = e3)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (10), (20) imply:
% 252.31/60.30 | (23) op(e3, e0) = e2
% 252.31/60.30 |
% 252.31/60.30 | BETA: splitting (1) gives:
% 252.31/60.30 |
% 252.31/60.30 | Case 1:
% 252.31/60.30 | |
% 252.31/60.30 | | (24) ~ (all_178_2 = e3)
% 252.31/60.30 | |
% 252.31/60.30 | | REDUCE: (21), (24) imply:
% 252.31/60.30 | | (25) $false
% 252.31/60.30 | |
% 252.31/60.30 | | CLOSE: (25) is inconsistent.
% 252.31/60.30 | |
% 252.31/60.30 | Case 2:
% 252.31/60.30 | |
% 252.31/60.30 | |
% 252.31/60.30 | | GROUND_INST: instantiating (4) with all_48_2, e2, e0, e3, simplifying with
% 252.31/60.30 | | (15), (23) gives:
% 252.31/60.30 | | (26) all_48_2 = e2
% 252.31/60.30 | |
% 252.31/60.30 | | REDUCE: (19), (26) imply:
% 252.31/60.30 | | (27) op(all_22_2, e2) = e3
% 252.31/60.30 | |
% 252.31/60.30 | | BETA: splitting (14) gives:
% 252.31/60.30 | |
% 252.31/60.30 | | Case 1:
% 252.31/60.30 | | |
% 252.31/60.30 | | | (28) ~ (all_90_2 = e2)
% 252.31/60.30 | | |
% 252.31/60.30 | | | REDUCE: (18), (28) imply:
% 252.31/60.30 | | | (29) ~ (all_22_2 = e2)
% 252.31/60.30 | | |
% 252.31/60.30 | | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (13), (16), (29) are
% 252.31/60.30 | | | inconsistent by sub-proof #957.
% 252.31/60.30 | | |
% 252.31/60.30 | | Case 2:
% 252.31/60.30 | | |
% 252.31/60.30 | | | (30) all_90_2 = e2
% 252.31/60.30 | | |
% 252.31/60.30 | | | COMBINE_EQS: (18), (30) imply:
% 252.31/60.30 | | | (31) all_22_2 = e2
% 252.31/60.30 | | |
% 252.31/60.30 | | | SIMP: (31) implies:
% 252.31/60.30 | | | (32) all_22_2 = e2
% 252.31/60.30 | | |
% 252.31/60.30 | | | REDUCE: (27), (32) imply:
% 252.31/60.30 | | | (33) op(e2, e2) = e3
% 252.31/60.30 | | |
% 252.31/60.30 | | | REF_CLOSE: (4), (5), (22), (33) are inconsistent by sub-proof #877.
% 252.31/60.30 | | |
% 252.31/60.30 | | End of split
% 252.31/60.30 | |
% 252.31/60.30 | End of split
% 252.31/60.30 |
% 252.31/60.30 End of proof
% 252.31/60.30
% 252.31/60.30 Sub-proof #877 shows that the following formulas are inconsistent:
% 252.31/60.30 ----------------------------------------------------------------
% 252.31/60.30 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.30 (2) op(e2, e2) = all_244_8
% 252.31/60.30 (3) op(e2, e2) = e3
% 252.31/60.30 (4) ~ (all_244_8 = e3)
% 252.31/60.30
% 252.31/60.30 Begin of proof
% 252.31/60.30 |
% 252.31/60.30 | GROUND_INST: instantiating (1) with all_244_8, e3, e2, e2, simplifying with
% 252.31/60.30 | (2), (3) gives:
% 252.31/60.30 | (5) all_244_8 = e3
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (4), (5) imply:
% 252.31/60.30 | (6) $false
% 252.31/60.30 |
% 252.31/60.30 | CLOSE: (6) is inconsistent.
% 252.31/60.30 |
% 252.31/60.30 End of proof
% 252.31/60.30
% 252.31/60.30 Sub-proof #878 shows that the following formulas are inconsistent:
% 252.31/60.30 ----------------------------------------------------------------
% 252.31/60.30 (1) all_252_21 = e2
% 252.31/60.30 (2) ~ (all_10_2 = e1)
% 252.31/60.30 (3) ~ (all_4_2 = e4)
% 252.31/60.30 (4) ~ (all_10_2 = e4)
% 252.31/60.30 (5) ~ (all_244_8 = e0)
% 252.31/60.30 (6) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) |
% 252.31/60.30 (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.31/60.30 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.31/60.30 (7) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) |
% 252.31/60.30 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 252.31/60.30 | (all_252_18 = e0 & op(e2, e0) = e0)
% 252.31/60.30 (8) ~ (all_40_2 = e3)
% 252.31/60.30 (9) ~ (all_64_2 = e3)
% 252.31/60.30 (10) ~ (all_22_2 = e3)
% 252.31/60.30 (11) ~ (all_62_2 = e2)
% 252.31/60.30 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.30 (13) op(e2, e3) = all_10_2
% 252.31/60.30 (14) ~ (e3 = e2)
% 252.31/60.30 (15) ~ (all_12_2 = e3)
% 252.31/60.30 (16) op(e2, e2) = all_244_8
% 252.31/60.30 (17) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3)
% 252.31/60.30 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) =
% 252.31/60.30 e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 252.31/60.30 (18) op(e2, e1) = all_38_2
% 252.31/60.30 (19) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 252.31/60.30 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 252.31/60.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.30 (20) op(e1, e0) = all_34_2
% 252.31/60.30 (21) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 252.31/60.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 252.31/60.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.30 (22) ~ (all_40_2 = e4)
% 252.31/60.30 (23) op(e4, e2) = all_6_2
% 252.31/60.30 (24) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 252.31/60.30 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 252.31/60.30 e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 252.31/60.30 (25) ~ (all_34_2 = e2)
% 252.31/60.30 (26) ~ (e2 = e1)
% 252.31/60.30 (27) op(e0, e2) = all_28_2
% 252.31/60.30 (28) ~ (e4 = e1)
% 252.31/60.30 (29) ~ (all_28_2 = e1)
% 252.31/60.30 (30) ~ (all_6_2 = e1)
% 252.31/60.30 (31) op(e1, e4) = all_16_2
% 252.31/60.30 (32) op(e1, e3) = all_62_2
% 252.31/60.30 (33) op(all_16_2, all_26_2) = e4
% 252.31/60.30 (34) ~ (e3 = e0)
% 252.31/60.30 (35) ~ (all_40_2 = all_10_2)
% 252.31/60.30 (36) ~ (all_36_2 = e4)
% 252.31/60.30 (37) ~ (e3 = e1)
% 252.31/60.30 (38) ~ (all_12_2 = e2)
% 252.31/60.30 (39) op(e3, e1) = all_36_2
% 252.31/60.30 (40) ~ (all_16_2 = e2)
% 252.31/60.30 (41) ~ (all_8_2 = e1)
% 252.31/60.30 (42) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0)
% 252.31/60.30 | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) =
% 252.31/60.30 e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 252.31/60.30 (43) op(e0, e1) = e3
% 252.31/60.30 (44) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.31/60.30 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.30 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.30 (45) ~ (all_38_2 = e4)
% 252.31/60.30 (46) op(e0, e3) = all_22_2
% 252.31/60.30 (47) op(e3, e2) = all_90_1
% 252.31/60.30 (48) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 252.31/60.30 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 252.31/60.30 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.30 (49) op(e4, e1) = all_26_2
% 252.31/60.30 (50) op(all_10_2, e3) = e2
% 252.31/60.30 (51) op(e3, e4) = all_100_2
% 252.31/60.30 (52) ~ (e4 = e3)
% 252.31/60.30 (53) op(e0, e1) = all_20_2
% 252.31/60.30 (54) op(e3, e0) = all_48_2
% 252.31/60.30 (55) op(e1, e2) = all_4_2
% 252.31/60.30 (56) op(e3, e1) = e0
% 252.31/60.30 (57) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 252.31/60.30 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) =
% 252.31/60.30 e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.31/60.30 (58) ~ (all_48_2 = e1)
% 252.31/60.30 (59) op(e2, e4) = all_64_2
% 252.31/60.30 (60) ~ (e4 = e2)
% 252.31/60.30 (61) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 252.31/60.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 252.31/60.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.31/60.30 (62) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 252.31/60.30 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 252.31/60.30 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 252.31/60.30 (63) ~ (all_38_2 = all_10_2)
% 252.31/60.30 (64) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 252.31/60.30 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 252.31/60.30 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 252.31/60.30 (65) ~ (all_20_2 = e4)
% 252.31/60.30 (66) op(all_16_2, e4) = e1
% 252.31/60.30 (67) ~ (all_244_3 = e0)
% 252.31/60.30 (68) op(e2, e0) = all_40_2
% 252.31/60.30 (69) ~ (all_16_2 = e3)
% 252.31/60.30 (70) all_10_2 = e0
% 252.31/60.30 (71) ~ (all_38_2 = e3)
% 252.31/60.30 (72) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.30 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.30 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.30 (73) op(e3, e3) = all_244_3
% 252.31/60.30 (74) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1)
% 252.31/60.30 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) =
% 252.31/60.30 e1) | (all_252_21 = e1 & op(e0, e3) = e1)
% 252.31/60.30 (75) ~ (all_62_2 = e4)
% 252.31/60.30 (76) all_90_1 = all_8_2
% 252.31/60.30 (77) op(e0, e4) = all_12_2
% 252.31/60.30 (78) ~ (all_10_2 = e2)
% 252.31/60.30
% 252.31/60.30 Begin of proof
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (35), (70) imply:
% 252.31/60.30 | (79) ~ (all_40_2 = e0)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (63), (70) imply:
% 252.31/60.30 | (80) ~ (all_38_2 = e0)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (4), (70) imply:
% 252.31/60.30 | (81) ~ (e4 = e0)
% 252.31/60.30 |
% 252.31/60.30 | SIMP: (81) implies:
% 252.31/60.30 | (82) ~ (e4 = e0)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (70), (78) imply:
% 252.31/60.30 | (83) ~ (e2 = e0)
% 252.31/60.30 |
% 252.31/60.30 | SIMP: (83) implies:
% 252.31/60.30 | (84) ~ (e2 = e0)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (2), (70) imply:
% 252.31/60.30 | (85) ~ (e1 = e0)
% 252.31/60.30 |
% 252.31/60.30 | SIMP: (85) implies:
% 252.31/60.30 | (86) ~ (e1 = e0)
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (50), (70) imply:
% 252.31/60.30 | (87) op(e0, e3) = e2
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (47), (76) imply:
% 252.31/60.30 | (88) op(e3, e2) = all_8_2
% 252.31/60.30 |
% 252.31/60.30 | REDUCE: (13), (70) imply:
% 252.31/60.30 | (89) op(e2, e3) = e0
% 252.31/60.30 |
% 252.31/60.30 | BETA: splitting (7) gives:
% 252.31/60.30 |
% 252.31/60.30 | Case 1:
% 252.31/60.30 | |
% 252.31/60.30 | | (90) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) =
% 252.31/60.30 | | e0)
% 252.31/60.30 | |
% 252.31/60.30 | | BETA: splitting (90) gives:
% 252.31/60.30 | |
% 252.31/60.30 | | Case 1:
% 252.31/60.30 | | |
% 252.31/60.30 | | | (91) all_252_6 = e0 & op(e2, e4) = e0
% 252.31/60.30 | | |
% 252.31/60.30 | | | ALPHA: (91) implies:
% 252.31/60.30 | | | (92) all_252_6 = e0
% 252.31/60.30 | | |
% 252.31/60.30 | | | BETA: splitting (17) gives:
% 252.31/60.30 | | |
% 252.31/60.30 | | | Case 1:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | (93) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 252.31/60.30 | | | | e3) = e3)
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | BETA: splitting (93) gives:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | Case 1:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (94) all_252_6 = e3 & op(e2, e4) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | REF_CLOSE: (9), (12), (59), (94) are inconsistent by sub-proof #940.
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | Case 2:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (95) all_252_7 = e3 & op(e2, e3) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | ALPHA: (95) implies:
% 252.31/60.30 | | | | | (96) all_252_7 = e3
% 252.31/60.30 | | | | | (97) op(e2, e3) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | BETA: splitting (42) gives:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | Case 1:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (98) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 &
% 252.31/60.30 | | | | | | op(e3, e3) = e0)
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | BETA: splitting (98) gives:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | Case 1:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | (99) all_252_1 = e0 & op(e4, e3) = e0
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | ALPHA: (99) implies:
% 252.31/60.30 | | | | | | | (100) all_252_1 = e0
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | BETA: splitting (6) gives:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | (101) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 &
% 252.31/60.30 | | | | | | | | op(e3, e3) = e4)
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | BETA: splitting (101) gives:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | (102) all_252_1 = e4 & op(e4, e3) = e4
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | REF_CLOSE: (82), (100), (102) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | #898.
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | (103) all_252_3 = e4 & op(e3, e3) = e4
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | ALPHA: (103) implies:
% 252.31/60.30 | | | | | | | | | (104) all_252_3 = e4
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (24), (26), (28), (31),
% 252.31/60.30 | | | | | | | | | (37), (38), (39), (40), (41), (51), (54), (56),
% 252.31/60.30 | | | | | | | | | (58), (59), (62), (64), (69), (77), (84), (86),
% 252.31/60.30 | | | | | | | | | (88), (92), (104) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | #888.
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | End of split
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | (105) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 &
% 252.31/60.30 | | | | | | | | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) =
% 252.31/60.30 | | | | | | | | e4)
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | REF_CLOSE: (4), (12), (13), (32), (46), (60), (75), (87), (105)
% 252.31/60.30 | | | | | | | | are inconsistent by sub-proof #950.
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | End of split
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | Case 2:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | (106) all_252_3 = e0 & op(e3, e3) = e0
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | ALPHA: (106) implies:
% 252.31/60.30 | | | | | | | (107) op(e3, e3) = e0
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | REF_CLOSE: (12), (67), (73), (107) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | #973.
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | End of split
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | Case 2:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (108) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 &
% 252.31/60.30 | | | | | | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | BETA: splitting (108) gives:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | Case 1:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | (109) all_252_7 = e0 & op(e2, e3) = e0
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | REF_CLOSE: (34), (96), (109) are inconsistent by sub-proof #887.
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | Case 2:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | (110) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = e0 &
% 252.31/60.30 | | | | | | | op(e0, e3) = e0)
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | BETA: splitting (110) gives:
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | (111) all_252_13 = e0 & op(e1, e3) = e0
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | ALPHA: (111) implies:
% 252.31/60.30 | | | | | | | | (112) all_252_13 = e0
% 252.31/60.30 | | | | | | | | (113) op(e1, e3) = e0
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | BETA: splitting (74) gives:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | (114) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1
% 252.31/60.30 | | | | | | | | | & op(e3, e3) = e1)
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | BETA: splitting (114) gives:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | (115) all_252_1 = e1 & op(e4, e3) = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | ALPHA: (115) implies:
% 252.31/60.30 | | | | | | | | | | (116) all_252_1 = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | BETA: splitting (6) gives:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (117) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 252.31/60.30 | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | BETA: splitting (117) gives:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | (118) all_252_1 = e4 & op(e4, e3) = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | REF_CLOSE: (28), (116), (118) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | | | | #955.
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | (119) all_252_3 = e4 & op(e3, e3) = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | ALPHA: (119) implies:
% 252.31/60.30 | | | | | | | | | | | | (120) all_252_3 = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (24), (26), (28), (31),
% 252.31/60.30 | | | | | | | | | | | | (37), (38), (39), (40), (41), (51), (54), (56),
% 252.31/60.30 | | | | | | | | | | | | (58), (59), (62), (64), (69), (77), (84), (86),
% 252.31/60.30 | | | | | | | | | | | | (88), (92), (120) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | | | | #888.
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (121) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 252.31/60.30 | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 252.31/60.30 | | | | | | | | | | | op(e0, e3) = e4)
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (46), (60), (82), (87), (113),
% 252.31/60.30 | | | | | | | | | | | (121) are inconsistent by sub-proof #885.
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | (122) all_252_3 = e1 & op(e3, e3) = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | ALPHA: (122) implies:
% 252.31/60.30 | | | | | | | | | | (123) all_252_3 = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | BETA: splitting (6) gives:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (124) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 =
% 252.31/60.30 | | | | | | | | | | | e4 & op(e3, e3) = e4)
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | BETA: splitting (124) gives:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | (125) all_252_1 = e4 & op(e4, e3) = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | ALPHA: (125) implies:
% 252.31/60.30 | | | | | | | | | | | | (126) all_252_1 = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | GROUND_INST: instantiating (12) with e0, e3, e3, e2,
% 252.31/60.30 | | | | | | | | | | | | simplifying with (89), (97) gives:
% 252.31/60.30 | | | | | | | | | | | | (127) e3 = e0
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | COMBINE_EQS: (96), (127) imply:
% 252.31/60.30 | | | | | | | | | | | | (128) all_252_7 = e0
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | BETA: splitting (57) gives:
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | | (129) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 =
% 252.31/60.30 | | | | | | | | | | | | | e3 & op(e3, e3) = e3)
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | | REF_CLOSE: (37), (52), (123), (126), (129) are inconsistent
% 252.31/60.30 | | | | | | | | | | | | | by sub-proof #884.
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | | (130) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 =
% 252.31/60.30 | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 &
% 252.31/60.30 | | | | | | | | | | | | | op(e0, e3) = e3)
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | | REF_CLOSE: (10), (12), (34), (46), (112), (128), (130) are
% 252.31/60.30 | | | | | | | | | | | | | inconsistent by sub-proof #882.
% 252.31/60.30 | | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | (131) all_252_3 = e4 & op(e3, e3) = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | ALPHA: (131) implies:
% 252.31/60.30 | | | | | | | | | | | | (132) all_252_3 = e4
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (24), (26), (28), (31),
% 252.31/60.30 | | | | | | | | | | | | (37), (38), (39), (40), (41), (51), (54), (56),
% 252.31/60.30 | | | | | | | | | | | | (58), (59), (62), (64), (69), (77), (84), (86),
% 252.31/60.30 | | | | | | | | | | | | (88), (92), (132) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | | | | #888.
% 252.31/60.30 | | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (133) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 =
% 252.31/60.30 | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 &
% 252.31/60.30 | | | | | | | | | | | op(e0, e3) = e4)
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (46), (60), (82), (87), (113),
% 252.31/60.30 | | | | | | | | | | | (133) are inconsistent by sub-proof #885.
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | (134) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1
% 252.31/60.30 | | | | | | | | | & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3)
% 252.31/60.30 | | | | | | | | | = e1)
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | BETA: splitting (134) gives:
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | (135) all_252_7 = e1 & op(e2, e3) = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | ALPHA: (135) implies:
% 252.31/60.30 | | | | | | | | | | (136) op(e2, e3) = e1
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | REF_CLOSE: (12), (37), (97), (136) are inconsistent by
% 252.31/60.30 | | | | | | | | | | sub-proof #881.
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | (137) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 =
% 252.31/60.30 | | | | | | | | | | e1 & op(e0, e3) = e1)
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | BETA: splitting (137) gives:
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 1:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (138) all_252_13 = e1 & op(e1, e3) = e1
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | ALPHA: (138) implies:
% 252.31/60.30 | | | | | | | | | | | (139) all_252_13 = e1
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | REF_CLOSE: (86), (112), (139) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | | | | | | #943.
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | (140) all_252_21 = e1 & op(e0, e3) = e1
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | ALPHA: (140) implies:
% 252.31/60.30 | | | | | | | | | | | (141) op(e0, e3) = e1
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | | REF_CLOSE: (12), (26), (87), (141) are inconsistent by
% 252.31/60.30 | | | | | | | | | | | sub-proof #941.
% 252.31/60.30 | | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | | |
% 252.31/60.30 | | | | | | | | | End of split
% 252.31/60.30 | | | | | | | | |
% 252.31/60.30 | | | | | | | | End of split
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | Case 2:
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | (142) all_252_21 = e0 & op(e0, e3) = e0
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | ALPHA: (142) implies:
% 252.31/60.30 | | | | | | | | (143) all_252_21 = e0
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | | REF_CLOSE: (1), (84), (143) are inconsistent by sub-proof #942.
% 252.31/60.30 | | | | | | | |
% 252.31/60.30 | | | | | | | End of split
% 252.31/60.30 | | | | | | |
% 252.31/60.30 | | | | | | End of split
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | End of split
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | End of split
% 252.31/60.30 | | | |
% 252.31/60.30 | | | Case 2:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | (144) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2,
% 252.31/60.30 | | | | e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | BETA: splitting (144) gives:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | Case 1:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (145) all_252_8 = e3 & op(e2, e2) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | ALPHA: (145) implies:
% 252.31/60.30 | | | | | (146) all_252_8 = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | BETA: splitting (48) gives:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | Case 1:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (147) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 252.31/60.30 | | | | | | op(e2, e3) = e4)
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | REF_CLOSE: (4), (12), (13), (82), (92), (147) are inconsistent by
% 252.31/60.30 | | | | | | sub-proof #937.
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | Case 2:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (148) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 252.31/60.30 | | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | REF_CLOSE: (12), (18), (22), (45), (52), (68), (146), (148) are
% 252.31/60.30 | | | | | | inconsistent by sub-proof #932.
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | End of split
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | Case 2:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (149) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 252.31/60.30 | | | | | op(e2, e0) = e3)
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | BETA: splitting (149) gives:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | Case 1:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (150) all_252_11 = e3 & op(e2, e1) = e3
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | REF_CLOSE: (12), (18), (71), (150) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | #900.
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | Case 2:
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | (151) all_252_18 = e3 & op(e2, e0) = e3
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | | REF_CLOSE: (8), (12), (68), (151) are inconsistent by sub-proof
% 252.31/60.30 | | | | | | #899.
% 252.31/60.30 | | | | | |
% 252.31/60.30 | | | | | End of split
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | End of split
% 252.31/60.30 | | | |
% 252.31/60.30 | | | End of split
% 252.31/60.30 | | |
% 252.31/60.30 | | Case 2:
% 252.31/60.30 | | |
% 252.31/60.30 | | | (152) all_252_7 = e0 & op(e2, e3) = e0
% 252.31/60.30 | | |
% 252.31/60.30 | | | ALPHA: (152) implies:
% 252.31/60.30 | | | (153) all_252_7 = e0
% 252.31/60.30 | | |
% 252.31/60.30 | | | BETA: splitting (17) gives:
% 252.31/60.30 | | |
% 252.31/60.30 | | | Case 1:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | (154) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2,
% 252.31/60.30 | | | | e3) = e3)
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | BETA: splitting (154) gives:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | Case 1:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (155) all_252_6 = e3 & op(e2, e4) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | REF_CLOSE: (9), (12), (59), (155) are inconsistent by sub-proof #940.
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | Case 2:
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | (156) all_252_7 = e3 & op(e2, e3) = e3
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | | REF_CLOSE: (34), (153), (156) are inconsistent by sub-proof #945.
% 252.31/60.30 | | | | |
% 252.31/60.30 | | | | End of split
% 252.31/60.30 | | | |
% 252.31/60.30 | | | Case 2:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | (157) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2,
% 252.31/60.30 | | | | e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | BETA: splitting (157) gives:
% 252.31/60.30 | | | |
% 252.31/60.30 | | | | Case 1:
% 252.31/60.30 | | | | |
% 252.31/60.31 | | | | | (158) all_252_8 = e3 & op(e2, e2) = e3
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | ALPHA: (158) implies:
% 252.31/60.31 | | | | | (159) all_252_8 = e3
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | BETA: splitting (48) gives:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | Case 1:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (160) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 &
% 252.31/60.31 | | | | | | op(e2, e3) = e4)
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | BETA: splitting (160) gives:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | Case 1:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (161) all_252_6 = e4 & op(e2, e4) = e4
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | ALPHA: (161) implies:
% 252.31/60.31 | | | | | | | (162) all_252_6 = e4
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (3), (11), (12), (14), (18), (19), (20), (21), (23),
% 252.31/60.31 | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 252.31/60.31 | | | | | | | (36), (37), (39), (40), (41), (43), (44), (45), (49),
% 252.31/60.31 | | | | | | | (53), (55), (56), (60), (61), (65), (66), (72), (84),
% 252.31/60.31 | | | | | | | (86), (88), (153), (159), (162) are inconsistent by
% 252.31/60.31 | | | | | | | sub-proof #906.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | Case 2:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (163) all_252_7 = e4 & op(e2, e3) = e4
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | ALPHA: (163) implies:
% 252.31/60.31 | | | | | | | (164) op(e2, e3) = e4
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (4), (12), (13), (164) are inconsistent by sub-proof
% 252.31/60.31 | | | | | | | #953.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | End of split
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | Case 2:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (165) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 &
% 252.31/60.31 | | | | | | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | REF_CLOSE: (12), (18), (22), (45), (52), (68), (159), (165) are
% 252.31/60.31 | | | | | | inconsistent by sub-proof #932.
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | End of split
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | Case 2:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | (166) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 &
% 252.31/60.31 | | | | | op(e2, e0) = e3)
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | BETA: splitting (166) gives:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | Case 1:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (167) all_252_11 = e3 & op(e2, e1) = e3
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | REF_CLOSE: (12), (18), (71), (167) are inconsistent by sub-proof
% 252.31/60.31 | | | | | | #900.
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | Case 2:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (168) all_252_18 = e3 & op(e2, e0) = e3
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | REF_CLOSE: (8), (12), (68), (168) are inconsistent by sub-proof
% 252.31/60.31 | | | | | | #899.
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | End of split
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | End of split
% 252.31/60.31 | | | |
% 252.31/60.31 | | | End of split
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (169) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1)
% 252.31/60.31 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0)
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (5), (12), (16), (18), (68), (79), (80), (169) are inconsistent
% 252.31/60.31 | | by sub-proof #879.
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #879 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ~ (all_244_8 = e0)
% 252.31/60.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (3) op(e2, e2) = all_244_8
% 252.31/60.31 (4) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = e0)
% 252.31/60.31 | (all_252_18 = e0 & op(e2, e0) = e0)
% 252.31/60.31 (5) op(e2, e1) = all_38_2
% 252.31/60.31 (6) ~ (all_38_2 = e0)
% 252.31/60.31 (7) ~ (all_40_2 = e0)
% 252.31/60.31 (8) op(e2, e0) = all_40_2
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (4) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (9) all_252_8 = e0 & op(e2, e2) = e0
% 252.31/60.31 | |
% 252.31/60.31 | | ALPHA: (9) implies:
% 252.31/60.31 | | (10) op(e2, e2) = e0
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #880.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (11) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0)
% 252.31/60.31 | | = e0)
% 252.31/60.31 | |
% 252.31/60.31 | | BETA: splitting (11) gives:
% 252.31/60.31 | |
% 252.31/60.31 | | Case 1:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (12) all_252_11 = e0 & op(e2, e1) = e0
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (2), (5), (6), (12) are inconsistent by sub-proof #904.
% 252.31/60.31 | | |
% 252.31/60.31 | | Case 2:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (13) all_252_18 = e0 & op(e2, e0) = e0
% 252.31/60.31 | | |
% 252.31/60.31 | | | ALPHA: (13) implies:
% 252.31/60.31 | | | (14) op(e2, e0) = e0
% 252.31/60.31 | | |
% 252.31/60.31 | | | GROUND_INST: instantiating (2) with all_40_2, e0, e0, e2, simplifying with
% 252.31/60.31 | | | (8), (14) gives:
% 252.31/60.31 | | | (15) all_40_2 = e0
% 252.31/60.31 | | |
% 252.31/60.31 | | | REDUCE: (7), (15) imply:
% 252.31/60.31 | | | (16) $false
% 252.31/60.31 | | |
% 252.31/60.31 | | | CLOSE: (16) is inconsistent.
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #880 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) op(e2, e2) = all_244_8
% 252.31/60.31 (3) op(e2, e2) = e0
% 252.31/60.31 (4) ~ (all_244_8 = e0)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | GROUND_INST: instantiating (1) with all_244_8, e0, e2, e2, simplifying with
% 252.31/60.31 | (2), (3) gives:
% 252.31/60.31 | (5) all_244_8 = e0
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (4), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #881 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) op(e2, e3) = e3
% 252.31/60.31 (3) op(e2, e3) = e1
% 252.31/60.31 (4) ~ (e3 = e1)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | GROUND_INST: instantiating (1) with e1, e3, e3, e2, simplifying with (2), (3)
% 252.31/60.31 | gives:
% 252.31/60.31 | (5) e3 = e1
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (4), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #882 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ~ (all_22_2 = e3)
% 252.31/60.31 (2) all_252_13 = e0
% 252.31/60.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (4) all_252_7 = e0
% 252.31/60.31 (5) ~ (e3 = e0)
% 252.31/60.31 (6) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = e3)
% 252.31/60.31 | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.31/60.31 (7) op(e0, e3) = all_22_2
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (6) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (8) all_252_7 = e3 & op(e2, e3) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #945.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (9) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 252.31/60.31 | | e3)
% 252.31/60.31 | |
% 252.31/60.31 | | BETA: splitting (9) gives:
% 252.31/60.31 | |
% 252.31/60.31 | | Case 1:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (10) all_252_13 = e3 & op(e1, e3) = e3
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #883.
% 252.31/60.31 | | |
% 252.31/60.31 | | Case 2:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (11) all_252_21 = e3 & op(e0, e3) = e3
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (1), (3), (7), (11) are inconsistent by sub-proof #959.
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #883 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_13 = e3 & op(e1, e3) = e3
% 252.31/60.31 (2) all_252_13 = e0
% 252.31/60.31 (3) ~ (e3 = e0)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (4) all_252_13 = e3
% 252.31/60.31 |
% 252.31/60.31 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.31 | (5) e3 = e0
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (3), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #884 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_3 = e1
% 252.31/60.31 (2) ~ (e3 = e1)
% 252.31/60.31 (3) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3)
% 252.31/60.31 (4) ~ (e4 = e3)
% 252.31/60.31 (5) all_252_1 = e4
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (3) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (6) all_252_1 = e3 & op(e4, e3) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #946.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (7) all_252_3 = e3 & op(e3, e3) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | ALPHA: (7) implies:
% 252.31/60.31 | | (8) all_252_3 = e3
% 252.31/60.31 | |
% 252.31/60.31 | | COMBINE_EQS: (1), (8) imply:
% 252.31/60.31 | | (9) e3 = e1
% 252.31/60.31 | |
% 252.31/60.31 | | REDUCE: (2), (9) imply:
% 252.31/60.31 | | (10) $false
% 252.31/60.31 | |
% 252.31/60.31 | | CLOSE: (10) is inconsistent.
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #885 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) op(e0, e3) = e2
% 252.31/60.31 (2) op(e1, e3) = e0
% 252.31/60.31 (3) ~ (all_10_2 = e4)
% 252.31/60.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (5) op(e2, e3) = all_10_2
% 252.31/60.31 (6) ~ (e4 = e0)
% 252.31/60.31 (7) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.31/60.31 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.31/60.31 (8) op(e0, e3) = all_22_2
% 252.31/60.31 (9) ~ (e4 = e2)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (7) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (10) all_252_7 = e4 & op(e2, e3) = e4
% 252.31/60.31 | |
% 252.31/60.31 | | ALPHA: (10) implies:
% 252.31/60.31 | | (11) op(e2, e3) = e4
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #953.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (12) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 252.31/60.31 | | = e4)
% 252.31/60.31 | |
% 252.31/60.31 | | BETA: splitting (12) gives:
% 252.31/60.31 | |
% 252.31/60.31 | | Case 1:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (13) all_252_13 = e4 & op(e1, e3) = e4
% 252.31/60.31 | | |
% 252.31/60.31 | | | ALPHA: (13) implies:
% 252.31/60.31 | | | (14) op(e1, e3) = e4
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (2), (4), (6), (14) are inconsistent by sub-proof #886.
% 252.31/60.31 | | |
% 252.31/60.31 | | Case 2:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (15) all_252_21 = e4 & op(e0, e3) = e4
% 252.31/60.31 | | |
% 252.31/60.31 | | | ALPHA: (15) implies:
% 252.31/60.31 | | | (16) op(e0, e3) = e4
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (1), (4), (8), (9), (16) are inconsistent by sub-proof #951.
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #886 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) op(e1, e3) = e4
% 252.31/60.31 (3) op(e1, e3) = e0
% 252.31/60.31 (4) ~ (e4 = e0)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | GROUND_INST: instantiating (1) with e0, e4, e3, e1, simplifying with (2), (3)
% 252.31/60.31 | gives:
% 252.31/60.31 | (5) e4 = e0
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (4), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #887 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_7 = e0 & op(e2, e3) = e0
% 252.31/60.31 (2) all_252_7 = e3
% 252.31/60.31 (3) ~ (e3 = e0)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (4) all_252_7 = e0
% 252.31/60.31 |
% 252.31/60.31 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.31 | (5) e3 = e0
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (3), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #888 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_3 = e4
% 252.31/60.31 (2) all_252_6 = e0
% 252.31/60.31 (3) ~ (all_64_2 = e3)
% 252.31/60.31 (4) ~ (e2 = e0)
% 252.31/60.31 (5) ~ (e1 = e0)
% 252.31/60.31 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (7) ~ (e3 = e2)
% 252.31/60.31 (8) ~ (all_12_2 = e3)
% 252.31/60.31 (9) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) |
% 252.31/60.31 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 252.31/60.31 | (all_252_17 = e1 & op(e3, e0) = e1)
% 252.31/60.31 (10) ~ (e2 = e1)
% 252.31/60.31 (11) ~ (e4 = e1)
% 252.31/60.31 (12) op(e1, e4) = all_16_2
% 252.31/60.31 (13) ~ (e3 = e1)
% 252.31/60.31 (14) ~ (all_12_2 = e2)
% 252.31/60.31 (15) op(e3, e1) = all_36_2
% 252.31/60.31 (16) ~ (all_16_2 = e2)
% 252.31/60.31 (17) ~ (all_8_2 = e1)
% 252.31/60.31 (18) op(e3, e4) = all_100_2
% 252.31/60.31 (19) op(e3, e0) = all_48_2
% 252.31/60.31 (20) op(e3, e1) = e0
% 252.31/60.31 (21) ~ (all_48_2 = e1)
% 252.31/60.31 (22) op(e2, e4) = all_64_2
% 252.31/60.31 (23) op(e3, e2) = all_8_2
% 252.31/60.31 (24) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3)
% 252.31/60.31 | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) =
% 252.31/60.31 e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 252.31/60.31 (25) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2)
% 252.31/60.31 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) =
% 252.31/60.31 e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 252.31/60.31 (26) ~ (all_16_2 = e3)
% 252.31/60.31 (27) op(e0, e4) = all_12_2
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (9) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (28) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) =
% 252.31/60.31 | | e1)
% 252.31/60.31 | |
% 252.31/60.31 | | BETA: splitting (28) gives:
% 252.31/60.31 | |
% 252.31/60.31 | | Case 1:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (29) all_252_2 = e1 & op(e3, e4) = e1
% 252.31/60.31 | | |
% 252.31/60.31 | | | ALPHA: (29) implies:
% 252.31/60.31 | | | (30) all_252_2 = e1
% 252.31/60.31 | | | (31) op(e3, e4) = e1
% 252.31/60.31 | | |
% 252.31/60.31 | | | BETA: splitting (25) gives:
% 252.31/60.31 | | |
% 252.31/60.31 | | | Case 1:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | (32) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3,
% 252.31/60.31 | | | | e4) = e2)
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | BETA: splitting (32) gives:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | Case 1:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | (33) all_252_0 = e2 & op(e4, e4) = e2
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | ALPHA: (33) implies:
% 252.31/60.31 | | | | | (34) all_252_0 = e2
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | BETA: splitting (24) gives:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | Case 1:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (35) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 &
% 252.31/60.31 | | | | | | op(e3, e4) = e3)
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | BETA: splitting (35) gives:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | Case 1:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (36) all_252_0 = e3 & op(e4, e4) = e3
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (7), (34), (36) are inconsistent by sub-proof #897.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | Case 2:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (37) all_252_2 = e3 & op(e3, e4) = e3
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | ALPHA: (37) implies:
% 252.31/60.31 | | | | | | | (38) op(e3, e4) = e3
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (6), (13), (18), (31), (38) are inconsistent by
% 252.31/60.31 | | | | | | | sub-proof #896.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | End of split
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | Case 2:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | (39) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 &
% 252.31/60.31 | | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | BETA: splitting (39) gives:
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | | Case 1:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (40) all_252_6 = e3 & op(e2, e4) = e3
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (3), (6), (22), (40) are inconsistent by sub-proof
% 252.31/60.31 | | | | | | | #940.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | Case 2:
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | (41) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 &
% 252.31/60.31 | | | | | | | op(e0, e4) = e3)
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | | REF_CLOSE: (6), (8), (12), (26), (27), (41) are inconsistent by
% 252.31/60.31 | | | | | | | sub-proof #894.
% 252.31/60.31 | | | | | | |
% 252.31/60.31 | | | | | | End of split
% 252.31/60.31 | | | | | |
% 252.31/60.31 | | | | | End of split
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | Case 2:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | (42) all_252_2 = e2 & op(e3, e4) = e2
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | REF_CLOSE: (10), (30), (42) are inconsistent by sub-proof #893.
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | End of split
% 252.31/60.31 | | | |
% 252.31/60.31 | | | Case 2:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | (43) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1,
% 252.31/60.31 | | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | BETA: splitting (43) gives:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | Case 1:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | (44) all_252_6 = e2 & op(e2, e4) = e2
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | REF_CLOSE: (2), (4), (44) are inconsistent by sub-proof #892.
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | Case 2:
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | (45) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 &
% 252.31/60.31 | | | | | op(e0, e4) = e2)
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | | REF_CLOSE: (6), (12), (14), (16), (27), (45) are inconsistent by
% 252.31/60.31 | | | | | sub-proof #891.
% 252.31/60.31 | | | | |
% 252.31/60.31 | | | | End of split
% 252.31/60.31 | | | |
% 252.31/60.31 | | | End of split
% 252.31/60.31 | | |
% 252.31/60.31 | | Case 2:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (46) all_252_3 = e1 & op(e3, e3) = e1
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (1), (11), (46) are inconsistent by sub-proof #890.
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (47) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) =
% 252.31/60.31 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1)
% 252.31/60.31 | |
% 252.31/60.31 | | BETA: splitting (47) gives:
% 252.31/60.31 | |
% 252.31/60.31 | | Case 1:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (48) all_252_5 = e1 & op(e3, e2) = e1
% 252.31/60.31 | | |
% 252.31/60.31 | | | ALPHA: (48) implies:
% 252.31/60.31 | | | (49) op(e3, e2) = e1
% 252.31/60.31 | | |
% 252.31/60.31 | | | REF_CLOSE: (6), (17), (23), (49) are inconsistent by sub-proof #929.
% 252.31/60.31 | | |
% 252.31/60.31 | | Case 2:
% 252.31/60.31 | | |
% 252.31/60.31 | | | (50) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3,
% 252.31/60.31 | | | e0) = e1)
% 252.31/60.31 | | |
% 252.31/60.31 | | | BETA: splitting (50) gives:
% 252.31/60.31 | | |
% 252.31/60.31 | | | Case 1:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | (51) all_252_10 = e1 & op(e3, e1) = e1
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | ALPHA: (51) implies:
% 252.31/60.31 | | | | (52) op(e3, e1) = e1
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | REF_CLOSE: (5), (6), (15), (20), (52) are inconsistent by sub-proof
% 252.31/60.31 | | | | #922.
% 252.31/60.31 | | | |
% 252.31/60.31 | | | Case 2:
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | (53) all_252_17 = e1 & op(e3, e0) = e1
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | ALPHA: (53) implies:
% 252.31/60.31 | | | | (54) op(e3, e0) = e1
% 252.31/60.31 | | | |
% 252.31/60.31 | | | | REF_CLOSE: (6), (19), (21), (54) are inconsistent by sub-proof #889.
% 252.31/60.31 | | | |
% 252.31/60.31 | | | End of split
% 252.31/60.31 | | |
% 252.31/60.31 | | End of split
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #889 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) op(e3, e0) = all_48_2
% 252.31/60.31 (3) op(e3, e0) = e1
% 252.31/60.31 (4) ~ (all_48_2 = e1)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | GROUND_INST: instantiating (1) with all_48_2, e1, e0, e3, simplifying with
% 252.31/60.31 | (2), (3) gives:
% 252.31/60.31 | (5) all_48_2 = e1
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (4), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #890 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_3 = e1 & op(e3, e3) = e1
% 252.31/60.31 (2) all_252_3 = e4
% 252.31/60.31 (3) ~ (e4 = e1)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (4) all_252_3 = e1
% 252.31/60.31 |
% 252.31/60.31 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.31 | (5) e4 = e1
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (3), (5) imply:
% 252.31/60.31 | (6) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (6) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #891 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) op(e1, e4) = all_16_2
% 252.31/60.31 (3) ~ (all_12_2 = e2)
% 252.31/60.31 (4) ~ (all_16_2 = e2)
% 252.31/60.31 (5) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)
% 252.31/60.31 (6) op(e0, e4) = all_12_2
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (5) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (7) all_252_12 = e2 & op(e1, e4) = e2
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #926.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (8) all_252_20 = e2 & op(e0, e4) = e2
% 252.31/60.31 | |
% 252.31/60.31 | | ALPHA: (8) implies:
% 252.31/60.31 | | (9) op(e0, e4) = e2
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #980.
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #892 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_6 = e2 & op(e2, e4) = e2
% 252.31/60.31 (2) all_252_6 = e0
% 252.31/60.31 (3) ~ (e2 = e0)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (4) all_252_6 = e2
% 252.31/60.31 |
% 252.31/60.31 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.31 | (5) e2 = e0
% 252.31/60.31 |
% 252.31/60.31 | SIMP: (5) implies:
% 252.31/60.31 | (6) e2 = e0
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (3), (6) imply:
% 252.31/60.31 | (7) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (7) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #893 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_2 = e2 & op(e3, e4) = e2
% 252.31/60.31 (2) all_252_2 = e1
% 252.31/60.31 (3) ~ (e2 = e1)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (4) all_252_2 = e2
% 252.31/60.31 |
% 252.31/60.31 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.31 | (5) e2 = e1
% 252.31/60.31 |
% 252.31/60.31 | SIMP: (5) implies:
% 252.31/60.31 | (6) e2 = e1
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (3), (6) imply:
% 252.31/60.31 | (7) $false
% 252.31/60.31 |
% 252.31/60.31 | CLOSE: (7) is inconsistent.
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #894 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (2) ~ (all_12_2 = e3)
% 252.31/60.31 (3) op(e1, e4) = all_16_2
% 252.31/60.31 (4) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)
% 252.31/60.31 (5) ~ (all_16_2 = e3)
% 252.31/60.31 (6) op(e0, e4) = all_12_2
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | BETA: splitting (4) gives:
% 252.31/60.31 |
% 252.31/60.31 | Case 1:
% 252.31/60.31 | |
% 252.31/60.31 | | (7) all_252_12 = e3 & op(e1, e4) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #895.
% 252.31/60.31 | |
% 252.31/60.31 | Case 2:
% 252.31/60.31 | |
% 252.31/60.31 | | (8) all_252_20 = e3 & op(e0, e4) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | ALPHA: (8) implies:
% 252.31/60.31 | | (9) op(e0, e4) = e3
% 252.31/60.31 | |
% 252.31/60.31 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #981.
% 252.31/60.31 | |
% 252.31/60.31 | End of split
% 252.31/60.31 |
% 252.31/60.31 End of proof
% 252.31/60.31
% 252.31/60.31 Sub-proof #895 shows that the following formulas are inconsistent:
% 252.31/60.31 ----------------------------------------------------------------
% 252.31/60.31 (1) all_252_12 = e3 & op(e1, e4) = e3
% 252.31/60.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.31 (3) op(e1, e4) = all_16_2
% 252.31/60.31 (4) ~ (all_16_2 = e3)
% 252.31/60.31
% 252.31/60.31 Begin of proof
% 252.31/60.31 |
% 252.31/60.31 | ALPHA: (1) implies:
% 252.31/60.31 | (5) op(e1, e4) = e3
% 252.31/60.31 |
% 252.31/60.31 | GROUND_INST: instantiating (2) with all_16_2, e3, e4, e1, simplifying with
% 252.31/60.31 | (3), (5) gives:
% 252.31/60.31 | (6) all_16_2 = e3
% 252.31/60.31 |
% 252.31/60.31 | REDUCE: (4), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #896 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e3, e4) = e1
% 252.31/60.32 (3) op(e3, e4) = e3
% 252.31/60.32 (4) ~ (e3 = e1)
% 252.31/60.32 (5) op(e3, e4) = all_100_2
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_100_2, e1, e4, e3, simplifying with
% 252.31/60.32 | (2), (5) gives:
% 252.31/60.32 | (6) all_100_2 = e1
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_100_2, e3, e4, e3, simplifying with
% 252.31/60.32 | (3), (5) gives:
% 252.31/60.32 | (7) all_100_2 = e3
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.32 | (8) e3 = e1
% 252.31/60.32 |
% 252.31/60.32 | SIMP: (8) implies:
% 252.31/60.32 | (9) e3 = e1
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (9) imply:
% 252.31/60.32 | (10) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (10) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #897 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_0 = e3 & op(e4, e4) = e3
% 252.31/60.32 (2) all_252_0 = e2
% 252.31/60.32 (3) ~ (e3 = e2)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (4) all_252_0 = e3
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.32 | (5) e3 = e2
% 252.31/60.32 |
% 252.31/60.32 | SIMP: (5) implies:
% 252.31/60.32 | (6) e3 = e2
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (3), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #898 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_1 = e4 & op(e4, e3) = e4
% 252.31/60.32 (2) all_252_1 = e0
% 252.31/60.32 (3) ~ (e4 = e0)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (4) all_252_1 = e4
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.32 | (5) e4 = e0
% 252.31/60.32 |
% 252.31/60.32 | SIMP: (5) implies:
% 252.31/60.32 | (6) e4 = e0
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (3), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #899 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_18 = e3 & op(e2, e0) = e3
% 252.31/60.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (3) op(e2, e0) = all_40_2
% 252.31/60.32 (4) ~ (all_40_2 = e3)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (5) op(e2, e0) = e3
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (2) with all_40_2, e3, e0, e2, simplifying with
% 252.31/60.32 | (3), (5) gives:
% 252.31/60.32 | (6) all_40_2 = e3
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #900 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_11 = e3 & op(e2, e1) = e3
% 252.31/60.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (3) op(e2, e1) = all_38_2
% 252.31/60.32 (4) ~ (all_38_2 = e3)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (5) op(e2, e1) = e3
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (2) with all_38_2, e3, e1, e2, simplifying with
% 252.31/60.32 | (3), (5) gives:
% 252.31/60.32 | (6) all_38_2 = e3
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #901 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e2, e0) = e1
% 252.31/60.32 (3) op(e2, e0) = e0
% 252.31/60.32 (4) ~ (e1 = e0)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with e1, e0, e0, e2, simplifying with (2), (3)
% 252.31/60.32 | gives:
% 252.31/60.32 | (5) e1 = e0
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (5) imply:
% 252.31/60.32 | (6) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (6) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #902 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e2, e3) = all_10_2
% 252.31/60.32 (3) ~ (e2 = e1)
% 252.31/60.32 (4) op(e2, e3) = e1
% 252.31/60.32 (5) op(e2, e3) = e2
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_10_2, e1, e3, e2, simplifying with
% 252.31/60.32 | (2), (4) gives:
% 252.31/60.32 | (6) all_10_2 = e1
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_10_2, e2, e3, e2, simplifying with
% 252.31/60.32 | (2), (5) gives:
% 252.31/60.32 | (7) all_10_2 = e2
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.32 | (8) e2 = e1
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (3), (8) imply:
% 252.31/60.32 | (9) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (9) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #903 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_6 = e1 & op(e2, e4) = e1
% 252.31/60.32 (2) all_252_6 = e4
% 252.31/60.32 (3) ~ (e4 = e1)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (4) all_252_6 = e1
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.32 | (5) e4 = e1
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (3), (5) imply:
% 252.31/60.32 | (6) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (6) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #904 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_11 = e0 & op(e2, e1) = e0
% 252.31/60.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (3) op(e2, e1) = all_38_2
% 252.31/60.32 (4) ~ (all_38_2 = e0)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | ALPHA: (1) implies:
% 252.31/60.32 | (5) op(e2, e1) = e0
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (2) with all_38_2, e0, e1, e2, simplifying with
% 252.31/60.32 | (3), (5) gives:
% 252.31/60.32 | (6) all_38_2 = e0
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (6) imply:
% 252.31/60.32 | (7) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (7) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #905 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) all_252_8 = e3
% 252.31/60.32 (2) all_252_8 = e0
% 252.31/60.32 (3) ~ (e3 = e0)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.32 | (4) e3 = e0
% 252.31/60.32 |
% 252.31/60.32 | SIMP: (4) implies:
% 252.31/60.32 | (5) e3 = e0
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (3), (5) imply:
% 252.31/60.32 | (6) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (6) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #906 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ~ (all_4_2 = e4)
% 252.31/60.32 (2) all_252_6 = e4
% 252.31/60.32 (3) ~ (e2 = e0)
% 252.31/60.32 (4) ~ (e1 = e0)
% 252.31/60.32 (5) ~ (all_62_2 = e2)
% 252.31/60.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (7) ~ (e3 = e2)
% 252.31/60.32 (8) op(e2, e1) = all_38_2
% 252.31/60.32 (9) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) |
% 252.31/60.32 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = e1)
% 252.31/60.32 | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.32 (10) op(e1, e0) = all_34_2
% 252.31/60.32 (11) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 252.31/60.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 252.31/60.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.32 (12) op(e4, e2) = all_6_2
% 252.31/60.32 (13) all_252_8 = e3
% 252.31/60.32 (14) ~ (all_34_2 = e2)
% 252.31/60.32 (15) ~ (e2 = e1)
% 252.31/60.32 (16) op(e0, e2) = all_28_2
% 252.31/60.32 (17) ~ (e4 = e1)
% 252.31/60.32 (18) ~ (all_28_2 = e1)
% 252.31/60.32 (19) all_252_7 = e0
% 252.31/60.32 (20) ~ (all_6_2 = e1)
% 252.31/60.32 (21) op(e1, e4) = all_16_2
% 252.31/60.32 (22) op(e1, e3) = all_62_2
% 252.31/60.32 (23) op(all_16_2, all_26_2) = e4
% 252.31/60.32 (24) ~ (all_36_2 = e4)
% 252.31/60.32 (25) ~ (e3 = e1)
% 252.31/60.32 (26) op(e3, e1) = all_36_2
% 252.31/60.32 (27) ~ (all_16_2 = e2)
% 252.31/60.32 (28) ~ (all_8_2 = e1)
% 252.31/60.32 (29) op(e0, e1) = e3
% 252.31/60.32 (30) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.31/60.32 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.32 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.32 (31) ~ (all_38_2 = e4)
% 252.31/60.32 (32) op(e4, e1) = all_26_2
% 252.31/60.32 (33) op(e0, e1) = all_20_2
% 252.31/60.32 (34) op(e1, e2) = all_4_2
% 252.31/60.32 (35) op(e3, e1) = e0
% 252.31/60.32 (36) ~ (e4 = e2)
% 252.31/60.32 (37) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 252.31/60.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 252.31/60.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.31/60.32 (38) op(e3, e2) = all_8_2
% 252.31/60.32 (39) ~ (all_20_2 = e4)
% 252.31/60.32 (40) op(all_16_2, e4) = e1
% 252.31/60.32 (41) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.32 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.32 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | BETA: splitting (9) gives:
% 252.31/60.32 |
% 252.31/60.32 | Case 1:
% 252.31/60.32 | |
% 252.31/60.32 | | (42) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) =
% 252.31/60.32 | | e1)
% 252.31/60.32 | |
% 252.31/60.32 | | REF_CLOSE: (6), (12), (20), (28), (38), (42) are inconsistent by sub-proof
% 252.31/60.32 | | #928.
% 252.31/60.32 | |
% 252.31/60.32 | Case 2:
% 252.31/60.32 | |
% 252.31/60.32 | | (43) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) =
% 252.31/60.32 | | e1) | (all_252_22 = e1 & op(e0, e2) = e1)
% 252.31/60.32 | |
% 252.31/60.32 | | BETA: splitting (43) gives:
% 252.31/60.32 | |
% 252.31/60.32 | | Case 1:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (44) all_252_8 = e1 & op(e2, e2) = e1
% 252.31/60.32 | | |
% 252.31/60.32 | | | ALPHA: (44) implies:
% 252.31/60.32 | | | (45) all_252_8 = e1
% 252.31/60.32 | | |
% 252.31/60.32 | | | REF_CLOSE: (13), (25), (45) are inconsistent by sub-proof #927.
% 252.31/60.32 | | |
% 252.31/60.32 | | Case 2:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (46) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0,
% 252.31/60.32 | | | e2) = e1)
% 252.31/60.32 | | |
% 252.31/60.32 | | | BETA: splitting (46) gives:
% 252.31/60.32 | | |
% 252.31/60.32 | | | Case 1:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (47) all_252_14 = e1 & op(e1, e2) = e1
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | ALPHA: (47) implies:
% 252.31/60.32 | | | | (48) all_252_14 = e1
% 252.31/60.32 | | | | (49) op(e1, e2) = e1
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13),
% 252.31/60.32 | | | | (14), (15), (17), (19), (21), (22), (23), (24), (25), (26),
% 252.31/60.32 | | | | (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 252.31/60.32 | | | | (39), (40), (41), (48), (49) are inconsistent by sub-proof
% 252.31/60.32 | | | | #908.
% 252.31/60.32 | | | |
% 252.31/60.32 | | | Case 2:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (50) all_252_22 = e1 & op(e0, e2) = e1
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | ALPHA: (50) implies:
% 252.31/60.32 | | | | (51) op(e0, e2) = e1
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | REF_CLOSE: (6), (16), (18), (51) are inconsistent by sub-proof #907.
% 252.31/60.32 | | | |
% 252.31/60.32 | | | End of split
% 252.31/60.32 | | |
% 252.31/60.32 | | End of split
% 252.31/60.32 | |
% 252.31/60.32 | End of split
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #907 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e0, e2) = all_28_2
% 252.31/60.32 (3) op(e0, e2) = e1
% 252.31/60.32 (4) ~ (all_28_2 = e1)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_28_2, e1, e2, e0, simplifying with
% 252.31/60.32 | (2), (3) gives:
% 252.31/60.32 | (5) all_28_2 = e1
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (5) imply:
% 252.31/60.32 | (6) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (6) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #908 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ~ (all_4_2 = e4)
% 252.31/60.32 (2) all_252_6 = e4
% 252.31/60.32 (3) ~ (e2 = e0)
% 252.31/60.32 (4) ~ (e1 = e0)
% 252.31/60.32 (5) ~ (all_62_2 = e2)
% 252.31/60.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (7) ~ (e3 = e2)
% 252.31/60.32 (8) op(e2, e1) = all_38_2
% 252.31/60.32 (9) op(e1, e0) = all_34_2
% 252.31/60.32 (10) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 252.31/60.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 252.31/60.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.32 (11) all_252_8 = e3
% 252.31/60.32 (12) ~ (all_34_2 = e2)
% 252.31/60.32 (13) ~ (e2 = e1)
% 252.31/60.32 (14) ~ (e4 = e1)
% 252.31/60.32 (15) all_252_7 = e0
% 252.31/60.32 (16) op(e1, e4) = all_16_2
% 252.31/60.32 (17) op(e1, e3) = all_62_2
% 252.31/60.32 (18) op(all_16_2, all_26_2) = e4
% 252.31/60.32 (19) op(e1, e2) = e1
% 252.31/60.32 (20) ~ (all_36_2 = e4)
% 252.31/60.32 (21) ~ (e3 = e1)
% 252.31/60.32 (22) op(e3, e1) = all_36_2
% 252.31/60.32 (23) ~ (all_16_2 = e2)
% 252.31/60.32 (24) op(e0, e1) = e3
% 252.31/60.32 (25) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.31/60.32 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.32 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.32 (26) ~ (all_38_2 = e4)
% 252.31/60.32 (27) op(e4, e1) = all_26_2
% 252.31/60.32 (28) all_252_14 = e1
% 252.31/60.32 (29) op(e0, e1) = all_20_2
% 252.31/60.32 (30) op(e1, e2) = all_4_2
% 252.31/60.32 (31) op(e3, e1) = e0
% 252.31/60.32 (32) ~ (e4 = e2)
% 252.31/60.32 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 252.31/60.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 252.31/60.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.31/60.32 (34) ~ (all_20_2 = e4)
% 252.31/60.32 (35) op(all_16_2, e4) = e1
% 252.31/60.32 (36) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) =
% 252.31/60.32 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1,
% 252.31/60.32 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | BETA: splitting (36) gives:
% 252.31/60.32 |
% 252.31/60.32 | Case 1:
% 252.31/60.32 | |
% 252.31/60.32 | | (37) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3)
% 252.31/60.32 | | = e2)
% 252.31/60.32 | |
% 252.31/60.32 | | REF_CLOSE: (5), (6), (16), (17), (23), (37) are inconsistent by sub-proof
% 252.31/60.32 | | #925.
% 252.31/60.32 | |
% 252.31/60.32 | Case 2:
% 252.31/60.32 | |
% 252.31/60.32 | | (38) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1)
% 252.31/60.32 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2)
% 252.31/60.32 | |
% 252.31/60.32 | | BETA: splitting (38) gives:
% 252.31/60.32 | |
% 252.31/60.32 | | Case 1:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (39) all_252_14 = e2 & op(e1, e2) = e2
% 252.31/60.32 | | |
% 252.31/60.32 | | | REF_CLOSE: (13), (28), (39) are inconsistent by sub-proof #924.
% 252.31/60.32 | | |
% 252.31/60.32 | | Case 2:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (40) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1,
% 252.31/60.32 | | | e0) = e2)
% 252.31/60.32 | | |
% 252.31/60.32 | | | BETA: splitting (40) gives:
% 252.31/60.32 | | |
% 252.31/60.32 | | | Case 1:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (41) all_252_15 = e2 & op(e1, e1) = e2
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | ALPHA: (41) implies:
% 252.31/60.32 | | | | (42) all_252_15 = e2
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13), (14),
% 252.31/60.32 | | | | (15), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 252.31/60.32 | | | | (29), (30), (31), (32), (33), (34), (35), (42) are
% 252.31/60.32 | | | | inconsistent by sub-proof #910.
% 252.31/60.32 | | | |
% 252.31/60.32 | | | Case 2:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (43) all_252_19 = e2 & op(e1, e0) = e2
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | ALPHA: (43) implies:
% 252.31/60.32 | | | | (44) op(e1, e0) = e2
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | REF_CLOSE: (6), (9), (12), (44) are inconsistent by sub-proof #909.
% 252.31/60.32 | | | |
% 252.31/60.32 | | | End of split
% 252.31/60.32 | | |
% 252.31/60.32 | | End of split
% 252.31/60.32 | |
% 252.31/60.32 | End of split
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #909 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e1, e0) = all_34_2
% 252.31/60.32 (3) op(e1, e0) = e2
% 252.31/60.32 (4) ~ (all_34_2 = e2)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | GROUND_INST: instantiating (1) with all_34_2, e2, e0, e1, simplifying with
% 252.31/60.32 | (2), (3) gives:
% 252.31/60.32 | (5) all_34_2 = e2
% 252.31/60.32 |
% 252.31/60.32 | REDUCE: (4), (5) imply:
% 252.31/60.32 | (6) $false
% 252.31/60.32 |
% 252.31/60.32 | CLOSE: (6) is inconsistent.
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #910 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ~ (all_4_2 = e4)
% 252.31/60.32 (2) all_252_6 = e4
% 252.31/60.32 (3) ~ (e2 = e0)
% 252.31/60.32 (4) ~ (e1 = e0)
% 252.31/60.32 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (6) ~ (e3 = e2)
% 252.31/60.32 (7) op(e2, e1) = all_38_2
% 252.31/60.32 (8) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4)
% 252.31/60.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) =
% 252.31/60.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.32 (9) all_252_8 = e3
% 252.31/60.32 (10) ~ (e2 = e1)
% 252.31/60.32 (11) ~ (e4 = e1)
% 252.31/60.32 (12) all_252_7 = e0
% 252.31/60.32 (13) op(all_16_2, all_26_2) = e4
% 252.31/60.32 (14) op(e1, e2) = e1
% 252.31/60.32 (15) ~ (all_36_2 = e4)
% 252.31/60.32 (16) ~ (e3 = e1)
% 252.31/60.32 (17) op(e3, e1) = all_36_2
% 252.31/60.32 (18) op(e0, e1) = e3
% 252.31/60.32 (19) all_252_15 = e2
% 252.31/60.32 (20) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.31/60.32 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.32 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.32 (21) ~ (all_38_2 = e4)
% 252.31/60.32 (22) op(e4, e1) = all_26_2
% 252.31/60.32 (23) op(e0, e1) = all_20_2
% 252.31/60.32 (24) op(e1, e2) = all_4_2
% 252.31/60.32 (25) op(e3, e1) = e0
% 252.31/60.32 (26) ~ (e4 = e2)
% 252.31/60.32 (27) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1)
% 252.31/60.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) =
% 252.31/60.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.31/60.32 (28) ~ (all_20_2 = e4)
% 252.31/60.32 (29) op(all_16_2, e4) = e1
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | BETA: splitting (8) gives:
% 252.31/60.32 |
% 252.31/60.32 | Case 1:
% 252.31/60.32 | |
% 252.31/60.32 | | (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) =
% 252.31/60.32 | | e4)
% 252.31/60.32 | |
% 252.31/60.32 | | BETA: splitting (30) gives:
% 252.31/60.32 | |
% 252.31/60.32 | | Case 1:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (31) all_252_9 = e4 & op(e4, e1) = e4
% 252.31/60.32 | | |
% 252.31/60.32 | | | ALPHA: (31) implies:
% 252.31/60.32 | | | (32) all_252_9 = e4
% 252.31/60.32 | | | (33) op(e4, e1) = e4
% 252.31/60.32 | | |
% 252.31/60.32 | | | BETA: splitting (27) gives:
% 252.31/60.32 | | |
% 252.31/60.32 | | | Case 1:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (34) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3,
% 252.31/60.32 | | | | e1) = e1)
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | BETA: splitting (34) gives:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | Case 1:
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | (35) all_252_9 = e1 & op(e4, e1) = e1
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | REF_CLOSE: (11), (32), (35) are inconsistent by sub-proof #923.
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | Case 2:
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | (36) all_252_10 = e1 & op(e3, e1) = e1
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | ALPHA: (36) implies:
% 252.31/60.32 | | | | | (37) op(e3, e1) = e1
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | REF_CLOSE: (4), (5), (17), (25), (37) are inconsistent by sub-proof
% 252.31/60.32 | | | | | #922.
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | End of split
% 252.31/60.32 | | | |
% 252.31/60.32 | | | Case 2:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | (38) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1,
% 252.31/60.32 | | | | e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | BETA: splitting (38) gives:
% 252.31/60.32 | | | |
% 252.31/60.32 | | | | Case 1:
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | (39) all_252_11 = e1 & op(e2, e1) = e1
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | ALPHA: (39) implies:
% 252.31/60.32 | | | | | (40) all_252_11 = e1
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (12), (13), (14), (20),
% 252.31/60.32 | | | | | (22), (24), (26), (29), (33), (40) are inconsistent by
% 252.31/60.32 | | | | | sub-proof #917.
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | Case 2:
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | (41) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 = e1 &
% 252.31/60.32 | | | | | op(e0, e1) = e1)
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | BETA: splitting (41) gives:
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | | Case 1:
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | | (42) all_252_15 = e1 & op(e1, e1) = e1
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | | REF_CLOSE: (10), (19), (42) are inconsistent by sub-proof #916.
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | Case 2:
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | | (43) all_252_23 = e1 & op(e0, e1) = e1
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | | ALPHA: (43) implies:
% 252.31/60.32 | | | | | | (44) op(e0, e1) = e1
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | | REF_CLOSE: (5), (16), (18), (44) are inconsistent by sub-proof #915.
% 252.31/60.32 | | | | | |
% 252.31/60.32 | | | | | End of split
% 252.31/60.32 | | | | |
% 252.31/60.32 | | | | End of split
% 252.31/60.32 | | | |
% 252.31/60.32 | | | End of split
% 252.31/60.32 | | |
% 252.31/60.32 | | Case 2:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (45) all_252_10 = e4 & op(e3, e1) = e4
% 252.31/60.32 | | |
% 252.31/60.32 | | | REF_CLOSE: (5), (15), (17), (45) are inconsistent by sub-proof #914.
% 252.31/60.32 | | |
% 252.31/60.32 | | End of split
% 252.31/60.32 | |
% 252.31/60.32 | Case 2:
% 252.31/60.32 | |
% 252.31/60.32 | | (46) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1)
% 252.31/60.32 | | = e4) | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.32 | |
% 252.31/60.32 | | REF_CLOSE: (5), (7), (19), (21), (23), (26), (28), (46) are inconsistent by
% 252.31/60.32 | | sub-proof #911.
% 252.31/60.32 | |
% 252.31/60.32 | End of split
% 252.31/60.32 |
% 252.31/60.32 End of proof
% 252.31/60.32
% 252.31/60.32 Sub-proof #911 shows that the following formulas are inconsistent:
% 252.31/60.32 ----------------------------------------------------------------
% 252.31/60.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.32 (2) op(e2, e1) = all_38_2
% 252.31/60.32 (3) all_252_15 = e2
% 252.31/60.32 (4) ~ (all_38_2 = e4)
% 252.31/60.32 (5) op(e0, e1) = all_20_2
% 252.31/60.32 (6) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = e4)
% 252.31/60.32 | (all_252_23 = e4 & op(e0, e1) = e4)
% 252.31/60.32 (7) ~ (e4 = e2)
% 252.31/60.32 (8) ~ (all_20_2 = e4)
% 252.31/60.32
% 252.31/60.32 Begin of proof
% 252.31/60.32 |
% 252.31/60.32 | BETA: splitting (6) gives:
% 252.31/60.32 |
% 252.31/60.32 | Case 1:
% 252.31/60.32 | |
% 252.31/60.32 | | (9) all_252_11 = e4 & op(e2, e1) = e4
% 252.31/60.32 | |
% 252.31/60.32 | | ALPHA: (9) implies:
% 252.31/60.32 | | (10) op(e2, e1) = e4
% 252.31/60.32 | |
% 252.31/60.32 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #935.
% 252.31/60.32 | |
% 252.31/60.32 | Case 2:
% 252.31/60.32 | |
% 252.31/60.32 | | (11) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1)
% 252.31/60.32 | | = e4)
% 252.31/60.32 | |
% 252.31/60.32 | | BETA: splitting (11) gives:
% 252.31/60.32 | |
% 252.31/60.32 | | Case 1:
% 252.31/60.32 | | |
% 252.31/60.32 | | | (12) all_252_15 = e4 & op(e1, e1) = e4
% 252.31/60.32 | | |
% 252.31/60.32 | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #913.
% 252.31/60.32 | | |
% 252.31/60.32 | | Case 2:
% 252.31/60.32 | | |
% 252.31/60.33 | | | (13) all_252_23 = e4 & op(e0, e1) = e4
% 252.31/60.33 | | |
% 252.31/60.33 | | | REF_CLOSE: (1), (5), (8), (13) are inconsistent by sub-proof #912.
% 252.31/60.33 | | |
% 252.31/60.33 | | End of split
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #912 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_23 = e4 & op(e0, e1) = e4
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e0, e1) = all_20_2
% 252.31/60.33 (4) ~ (all_20_2 = e4)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (5) op(e0, e1) = e4
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_20_2, e4, e1, e0, simplifying with
% 252.31/60.33 | (3), (5) gives:
% 252.31/60.33 | (6) all_20_2 = e4
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #913 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_15 = e4 & op(e1, e1) = e4
% 252.31/60.33 (2) all_252_15 = e2
% 252.31/60.33 (3) ~ (e4 = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_15 = e4
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e4 = e2
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #914 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_10 = e4 & op(e3, e1) = e4
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e3, e1) = all_36_2
% 252.31/60.33 (4) ~ (all_36_2 = e4)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (5) op(e3, e1) = e4
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_36_2, e4, e1, e3, simplifying with
% 252.31/60.33 | (3), (5) gives:
% 252.31/60.33 | (6) all_36_2 = e4
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #915 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e0, e1) = e3
% 252.31/60.33 (3) op(e0, e1) = e1
% 252.31/60.33 (4) ~ (e3 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (1) with e1, e3, e1, e0, simplifying with (2), (3)
% 252.31/60.33 | gives:
% 252.31/60.33 | (5) e3 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #916 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_15 = e1 & op(e1, e1) = e1
% 252.31/60.33 (2) all_252_15 = e2
% 252.31/60.33 (3) ~ (e2 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_15 = e1
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e2 = e1
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (5) implies:
% 252.31/60.33 | (6) e2 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #917 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ~ (all_4_2 = e4)
% 252.31/60.33 (2) all_252_6 = e4
% 252.31/60.33 (3) ~ (e2 = e0)
% 252.31/60.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (5) ~ (e3 = e2)
% 252.31/60.33 (6) all_252_11 = e1
% 252.31/60.33 (7) all_252_8 = e3
% 252.31/60.33 (8) ~ (e2 = e1)
% 252.31/60.33 (9) all_252_7 = e0
% 252.31/60.33 (10) op(all_16_2, all_26_2) = e4
% 252.31/60.33 (11) op(e1, e2) = e1
% 252.31/60.33 (12) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2)
% 252.31/60.33 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.33 e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.33 (13) op(e4, e1) = all_26_2
% 252.31/60.33 (14) op(e1, e2) = all_4_2
% 252.31/60.33 (15) ~ (e4 = e2)
% 252.31/60.33 (16) op(all_16_2, e4) = e1
% 252.31/60.33 (17) op(e4, e1) = e4
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (12) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (18) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) =
% 252.31/60.33 | | e2)
% 252.31/60.33 | |
% 252.31/60.33 | | BETA: splitting (18) gives:
% 252.31/60.33 | |
% 252.31/60.33 | | Case 1:
% 252.31/60.33 | | |
% 252.31/60.33 | | | (19) all_252_6 = e2 & op(e2, e4) = e2
% 252.31/60.33 | | |
% 252.31/60.33 | | | REF_CLOSE: (2), (15), (19) are inconsistent by sub-proof #921.
% 252.31/60.33 | | |
% 252.31/60.33 | | Case 2:
% 252.31/60.33 | | |
% 252.31/60.33 | | | (20) all_252_7 = e2 & op(e2, e3) = e2
% 252.31/60.33 | | |
% 252.31/60.33 | | | ALPHA: (20) implies:
% 252.31/60.33 | | | (21) all_252_7 = e2
% 252.31/60.33 | | |
% 252.31/60.33 | | | COMBINE_EQS: (9), (21) imply:
% 252.31/60.33 | | | (22) e2 = e0
% 252.31/60.33 | | |
% 252.31/60.33 | | | SIMP: (22) implies:
% 252.31/60.33 | | | (23) e2 = e0
% 252.31/60.33 | | |
% 252.31/60.33 | | | REDUCE: (3), (23) imply:
% 252.31/60.33 | | | (24) $false
% 252.31/60.33 | | |
% 252.31/60.33 | | | CLOSE: (24) is inconsistent.
% 252.31/60.33 | | |
% 252.31/60.33 | | End of split
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (25) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) =
% 252.31/60.33 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2)
% 252.31/60.33 | |
% 252.31/60.33 | | BETA: splitting (25) gives:
% 252.31/60.33 | |
% 252.31/60.33 | | Case 1:
% 252.31/60.33 | | |
% 252.31/60.33 | | | (26) all_252_8 = e2 & op(e2, e2) = e2
% 252.31/60.33 | | |
% 252.31/60.33 | | | ALPHA: (26) implies:
% 252.31/60.33 | | | (27) all_252_8 = e2
% 252.31/60.33 | | |
% 252.31/60.33 | | | REF_CLOSE: (5), (7), (27) are inconsistent by sub-proof #920.
% 252.31/60.33 | | |
% 252.31/60.33 | | Case 2:
% 252.31/60.33 | | |
% 252.31/60.33 | | | (28) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2,
% 252.31/60.33 | | | e0) = e2)
% 252.31/60.33 | | |
% 252.31/60.33 | | | BETA: splitting (28) gives:
% 252.31/60.33 | | |
% 252.31/60.33 | | | Case 1:
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | (29) all_252_11 = e2 & op(e2, e1) = e2
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | REF_CLOSE: (6), (8), (29) are inconsistent by sub-proof #919.
% 252.31/60.33 | | | |
% 252.31/60.33 | | | Case 2:
% 252.31/60.33 | | | |
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | GROUND_INST: instantiating (4) with all_4_2, e1, e2, e1, simplifying
% 252.31/60.33 | | | | with (11), (14) gives:
% 252.31/60.33 | | | | (30) all_4_2 = e1
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | GROUND_INST: instantiating (4) with all_26_2, e4, e1, e4, simplifying
% 252.31/60.33 | | | | with (13), (17) gives:
% 252.31/60.33 | | | | (31) all_26_2 = e4
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | REDUCE: (1), (30) imply:
% 252.31/60.33 | | | | (32) ~ (e4 = e1)
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | SIMP: (32) implies:
% 252.31/60.33 | | | | (33) ~ (e4 = e1)
% 252.31/60.33 | | | |
% 252.31/60.33 | | | | REF_CLOSE: (4), (10), (16), (31), (33) are inconsistent by sub-proof
% 252.31/60.33 | | | | #918.
% 252.31/60.33 | | | |
% 252.31/60.33 | | | End of split
% 252.31/60.33 | | |
% 252.31/60.33 | | End of split
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #918 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) ~ (e4 = e1)
% 252.31/60.33 (3) op(all_16_2, all_26_2) = e4
% 252.31/60.33 (4) all_26_2 = e4
% 252.31/60.33 (5) op(all_16_2, e4) = e1
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (4) imply:
% 252.31/60.33 | (6) op(all_16_2, e4) = e4
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (1) with e1, e4, e4, all_16_2, simplifying with
% 252.31/60.33 | (5), (6) gives:
% 252.31/60.33 | (7) e4 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (2), (7) imply:
% 252.31/60.33 | (8) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (8) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #919 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_11 = e2 & op(e2, e1) = e2
% 252.31/60.33 (2) all_252_11 = e1
% 252.31/60.33 (3) ~ (e2 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_11 = e2
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e2 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #920 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_8 = e3
% 252.31/60.33 (2) all_252_8 = e2
% 252.31/60.33 (3) ~ (e3 = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.33 | (4) e3 = e2
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (4) implies:
% 252.31/60.33 | (5) e3 = e2
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #921 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_6 = e2 & op(e2, e4) = e2
% 252.31/60.33 (2) all_252_6 = e4
% 252.31/60.33 (3) ~ (e4 = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_6 = e2
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e4 = e2
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #922 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ~ (e1 = e0)
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e3, e1) = all_36_2
% 252.31/60.33 (4) op(e3, e1) = e1
% 252.31/60.33 (5) op(e3, e1) = e0
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_36_2, e0, e1, e3, simplifying with
% 252.31/60.33 | (3), (5) gives:
% 252.31/60.33 | (6) all_36_2 = e0
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_36_2, e1, e1, e3, simplifying with
% 252.31/60.33 | (3), (4) gives:
% 252.31/60.33 | (7) all_36_2 = e1
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (6), (7) imply:
% 252.31/60.33 | (8) e1 = e0
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (8) implies:
% 252.31/60.33 | (9) e1 = e0
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (1), (9) imply:
% 252.31/60.33 | (10) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (10) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #923 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_9 = e1 & op(e4, e1) = e1
% 252.31/60.33 (2) all_252_9 = e4
% 252.31/60.33 (3) ~ (e4 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_9 = e1
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e4 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #924 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_14 = e2 & op(e1, e2) = e2
% 252.31/60.33 (2) all_252_14 = e1
% 252.31/60.33 (3) ~ (e2 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_14 = e2
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e2 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #925 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ~ (all_62_2 = e2)
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e1, e4) = all_16_2
% 252.31/60.33 (4) op(e1, e3) = all_62_2
% 252.31/60.33 (5) ~ (all_16_2 = e2)
% 252.31/60.33 (6) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (6) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (7) all_252_12 = e2 & op(e1, e4) = e2
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #926.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (8) all_252_13 = e2 & op(e1, e3) = e2
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (8) implies:
% 252.31/60.33 | | (9) op(e1, e3) = e2
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #972.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #926 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_12 = e2 & op(e1, e4) = e2
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e1, e4) = all_16_2
% 252.31/60.33 (4) ~ (all_16_2 = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (5) op(e1, e4) = e2
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_16_2, e2, e4, e1, simplifying with
% 252.31/60.33 | (3), (5) gives:
% 252.31/60.33 | (6) all_16_2 = e2
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #927 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_8 = e3
% 252.31/60.33 (2) all_252_8 = e1
% 252.31/60.33 (3) ~ (e3 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.33 | (4) e3 = e1
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (4) implies:
% 252.31/60.33 | (5) e3 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #928 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e4, e2) = all_6_2
% 252.31/60.33 (3) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1)
% 252.31/60.33 (4) ~ (all_6_2 = e1)
% 252.31/60.33 (5) ~ (all_8_2 = e1)
% 252.31/60.33 (6) op(e3, e2) = all_8_2
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (3) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (7) all_252_4 = e1 & op(e4, e2) = e1
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (7) implies:
% 252.31/60.33 | | (8) op(e4, e2) = e1
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #930.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (9) all_252_5 = e1 & op(e3, e2) = e1
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (9) implies:
% 252.31/60.33 | | (10) op(e3, e2) = e1
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #929.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #929 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e3, e2) = all_8_2
% 252.31/60.33 (3) op(e3, e2) = e1
% 252.31/60.33 (4) ~ (all_8_2 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (1) with all_8_2, e1, e2, e3, simplifying with (2),
% 252.31/60.33 | (3) gives:
% 252.31/60.33 | (5) all_8_2 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #930 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e4, e2) = all_6_2
% 252.31/60.33 (3) op(e4, e2) = e1
% 252.31/60.33 (4) ~ (all_6_2 = e1)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (1) with all_6_2, e1, e2, e4, simplifying with (2),
% 252.31/60.33 | (3) gives:
% 252.31/60.33 | (5) all_6_2 = e1
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #931 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ~ (all_10_2 = e4)
% 252.31/60.33 (2) all_252_6 = e0
% 252.31/60.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (4) op(e2, e3) = all_10_2
% 252.31/60.33 (5) ~ (e4 = e0)
% 252.31/60.33 (6) op(e2, e1) = all_38_2
% 252.31/60.33 (7) ~ (all_40_2 = e4)
% 252.31/60.33 (8) all_252_8 = e3
% 252.31/60.33 (9) ~ (all_38_2 = e4)
% 252.31/60.33 (10) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 252.31/60.33 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 252.31/60.33 e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.33 (11) ~ (e4 = e3)
% 252.31/60.33 (12) op(e2, e0) = all_40_2
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (10) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (13) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) =
% 252.31/60.33 | | e4)
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (2), (3), (4), (5), (13) are inconsistent by sub-proof #937.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (14) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) =
% 252.31/60.33 | | e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (12), (14) are inconsistent by
% 252.31/60.33 | | sub-proof #932.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #932 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e2, e1) = all_38_2
% 252.31/60.33 (3) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = e4)
% 252.31/60.33 | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.33 (4) ~ (all_40_2 = e4)
% 252.31/60.33 (5) all_252_8 = e3
% 252.31/60.33 (6) ~ (all_38_2 = e4)
% 252.31/60.33 (7) ~ (e4 = e3)
% 252.31/60.33 (8) op(e2, e0) = all_40_2
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (3) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (9) all_252_8 = e4 & op(e2, e2) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (9) implies:
% 252.31/60.33 | | (10) all_252_8 = e4
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (5), (7), (10) are inconsistent by sub-proof #936.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (11) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0)
% 252.31/60.33 | | = e4)
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (2), (4), (6), (8), (11) are inconsistent by sub-proof #933.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #933 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e2, e1) = all_38_2
% 252.31/60.33 (3) ~ (all_40_2 = e4)
% 252.31/60.33 (4) ~ (all_38_2 = e4)
% 252.31/60.33 (5) op(e2, e0) = all_40_2
% 252.31/60.33 (6) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (6) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (7) all_252_11 = e4 & op(e2, e1) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (7) implies:
% 252.31/60.33 | | (8) op(e2, e1) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #935.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (9) all_252_18 = e4 & op(e2, e0) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #934.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #934 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_18 = e4 & op(e2, e0) = e4
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e2, e0) = all_40_2
% 252.31/60.33 (4) ~ (all_40_2 = e4)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (5) op(e2, e0) = e4
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (2) with all_40_2, e4, e0, e2, simplifying with
% 252.31/60.33 | (3), (5) gives:
% 252.31/60.33 | (6) all_40_2 = e4
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #935 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (2) op(e2, e1) = all_38_2
% 252.31/60.33 (3) op(e2, e1) = e4
% 252.31/60.33 (4) ~ (all_38_2 = e4)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | GROUND_INST: instantiating (1) with all_38_2, e4, e1, e2, simplifying with
% 252.31/60.33 | (2), (3) gives:
% 252.31/60.33 | (5) all_38_2 = e4
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (4), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #936 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_8 = e4
% 252.31/60.33 (2) all_252_8 = e3
% 252.31/60.33 (3) ~ (e4 = e3)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.33 | (4) e4 = e3
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (4) implies:
% 252.31/60.33 | (5) e4 = e3
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #937 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) ~ (all_10_2 = e4)
% 252.31/60.33 (2) all_252_6 = e0
% 252.31/60.33 (3) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4)
% 252.31/60.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (5) op(e2, e3) = all_10_2
% 252.31/60.33 (6) ~ (e4 = e0)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | BETA: splitting (3) gives:
% 252.31/60.33 |
% 252.31/60.33 | Case 1:
% 252.31/60.33 | |
% 252.31/60.33 | | (7) all_252_6 = e4 & op(e2, e4) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #938.
% 252.31/60.33 | |
% 252.31/60.33 | Case 2:
% 252.31/60.33 | |
% 252.31/60.33 | | (8) all_252_7 = e4 & op(e2, e3) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | ALPHA: (8) implies:
% 252.31/60.33 | | (9) op(e2, e3) = e4
% 252.31/60.33 | |
% 252.31/60.33 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #953.
% 252.31/60.33 | |
% 252.31/60.33 | End of split
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #938 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_6 = e4 & op(e2, e4) = e4
% 252.31/60.33 (2) all_252_6 = e0
% 252.31/60.33 (3) ~ (e4 = e0)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (4) all_252_6 = e4
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.33 | (5) e4 = e0
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (5) implies:
% 252.31/60.33 | (6) e4 = e0
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (6) imply:
% 252.31/60.33 | (7) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (7) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #939 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_7 = e3
% 252.31/60.33 (2) all_252_7 = e2
% 252.31/60.33 (3) ~ (e3 = e2)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.33 | (4) e3 = e2
% 252.31/60.33 |
% 252.31/60.33 | SIMP: (4) implies:
% 252.31/60.33 | (5) e3 = e2
% 252.31/60.33 |
% 252.31/60.33 | REDUCE: (3), (5) imply:
% 252.31/60.33 | (6) $false
% 252.31/60.33 |
% 252.31/60.33 | CLOSE: (6) is inconsistent.
% 252.31/60.33 |
% 252.31/60.33 End of proof
% 252.31/60.33
% 252.31/60.33 Sub-proof #940 shows that the following formulas are inconsistent:
% 252.31/60.33 ----------------------------------------------------------------
% 252.31/60.33 (1) all_252_6 = e3 & op(e2, e4) = e3
% 252.31/60.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.33 (3) op(e2, e4) = all_64_2
% 252.31/60.33 (4) ~ (all_64_2 = e3)
% 252.31/60.33
% 252.31/60.33 Begin of proof
% 252.31/60.33 |
% 252.31/60.33 | ALPHA: (1) implies:
% 252.31/60.33 | (5) op(e2, e4) = e3
% 252.31/60.33 |
% 252.31/60.34 | GROUND_INST: instantiating (2) with all_64_2, e3, e4, e2, simplifying with
% 252.31/60.34 | (3), (5) gives:
% 252.31/60.34 | (6) all_64_2 = e3
% 252.31/60.34 |
% 252.31/60.34 | REDUCE: (4), (6) imply:
% 252.31/60.34 | (7) $false
% 252.31/60.34 |
% 252.31/60.34 | CLOSE: (7) is inconsistent.
% 252.31/60.34 |
% 252.31/60.34 End of proof
% 252.31/60.34
% 252.31/60.34 Sub-proof #941 shows that the following formulas are inconsistent:
% 252.31/60.34 ----------------------------------------------------------------
% 252.31/60.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.31/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.31/60.34 (2) op(e0, e3) = e2
% 252.31/60.34 (3) op(e0, e3) = e1
% 252.31/60.34 (4) ~ (e2 = e1)
% 252.31/60.34
% 252.31/60.34 Begin of proof
% 252.31/60.34 |
% 252.31/60.34 | GROUND_INST: instantiating (1) with e1, e2, e3, e0, simplifying with (2), (3)
% 252.31/60.34 | gives:
% 252.31/60.34 | (5) e2 = e1
% 252.31/60.34 |
% 252.31/60.34 | REDUCE: (4), (5) imply:
% 252.31/60.34 | (6) $false
% 252.31/60.34 |
% 252.31/60.34 | CLOSE: (6) is inconsistent.
% 252.31/60.34 |
% 252.31/60.34 End of proof
% 252.31/60.34
% 252.31/60.34 Sub-proof #942 shows that the following formulas are inconsistent:
% 252.31/60.34 ----------------------------------------------------------------
% 252.31/60.34 (1) all_252_21 = e2
% 252.31/60.34 (2) all_252_21 = e0
% 252.31/60.34 (3) ~ (e2 = e0)
% 252.31/60.34
% 252.31/60.34 Begin of proof
% 252.31/60.34 |
% 252.31/60.34 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.34 | (4) e2 = e0
% 252.31/60.34 |
% 252.31/60.34 | SIMP: (4) implies:
% 252.31/60.34 | (5) e2 = e0
% 252.31/60.34 |
% 252.31/60.34 | REDUCE: (3), (5) imply:
% 252.31/60.34 | (6) $false
% 252.31/60.34 |
% 252.31/60.34 | CLOSE: (6) is inconsistent.
% 252.31/60.34 |
% 252.31/60.34 End of proof
% 252.31/60.34
% 252.31/60.34 Sub-proof #943 shows that the following formulas are inconsistent:
% 252.31/60.34 ----------------------------------------------------------------
% 252.31/60.34 (1) all_252_13 = e1
% 252.31/60.34 (2) all_252_13 = e0
% 252.31/60.34 (3) ~ (e1 = e0)
% 252.31/60.34
% 252.31/60.34 Begin of proof
% 252.31/60.34 |
% 252.31/60.34 | COMBINE_EQS: (1), (2) imply:
% 252.31/60.34 | (4) e1 = e0
% 252.31/60.34 |
% 252.31/60.34 | SIMP: (4) implies:
% 252.31/60.34 | (5) e1 = e0
% 252.31/60.34 |
% 252.31/60.34 | REDUCE: (3), (5) imply:
% 252.31/60.34 | (6) $false
% 252.31/60.34 |
% 252.31/60.34 | CLOSE: (6) is inconsistent.
% 252.31/60.34 |
% 252.31/60.34 End of proof
% 252.31/60.34
% 252.31/60.34 Sub-proof #944 shows that the following formulas are inconsistent:
% 252.31/60.34 ----------------------------------------------------------------
% 252.31/60.34 (1) all_252_13 = e3 & op(e1, e3) = e3
% 252.31/60.34 (2) all_252_13 = e1
% 252.31/60.34 (3) ~ (e3 = e1)
% 252.31/60.34
% 252.31/60.34 Begin of proof
% 252.31/60.34 |
% 252.31/60.34 | ALPHA: (1) implies:
% 252.31/60.34 | (4) all_252_13 = e3
% 252.31/60.34 |
% 252.31/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.34 | (5) e3 = e1
% 252.31/60.34 |
% 252.31/60.34 | REDUCE: (3), (5) imply:
% 252.31/60.34 | (6) $false
% 252.31/60.34 |
% 252.31/60.34 | CLOSE: (6) is inconsistent.
% 252.31/60.34 |
% 252.31/60.34 End of proof
% 252.31/60.34
% 252.31/60.34 Sub-proof #945 shows that the following formulas are inconsistent:
% 252.31/60.34 ----------------------------------------------------------------
% 252.31/60.34 (1) all_252_7 = e3 & op(e2, e3) = e3
% 252.31/60.34 (2) all_252_7 = e0
% 252.31/60.34 (3) ~ (e3 = e0)
% 252.31/60.34
% 252.31/60.34 Begin of proof
% 252.31/60.34 |
% 252.31/60.34 | ALPHA: (1) implies:
% 252.31/60.34 | (4) all_252_7 = e3
% 252.31/60.34 |
% 252.31/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.31/60.34 | (5) e3 = e0
% 252.31/60.34 |
% 252.58/60.34 | SIMP: (5) implies:
% 252.58/60.34 | (6) e3 = e0
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (6) imply:
% 252.58/60.34 | (7) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (7) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #946 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_1 = e3 & op(e4, e3) = e3
% 252.58/60.34 (2) all_252_1 = e4
% 252.58/60.34 (3) ~ (e4 = e3)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (4) all_252_1 = e3
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.58/60.34 | (5) e4 = e3
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #947 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_1 = e0 & op(e4, e3) = e0
% 252.58/60.34 (2) all_252_1 = e4
% 252.58/60.34 (3) ~ (e4 = e0)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (4) all_252_1 = e0
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.58/60.34 | (5) e4 = e0
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #948 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (2) op(e2, e3) = all_10_2
% 252.58/60.34 (3) op(e2, e3) = e1
% 252.58/60.34 (4) ~ (all_10_2 = e1)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (1) with all_10_2, e1, e3, e2, simplifying with
% 252.58/60.34 | (2), (3) gives:
% 252.58/60.34 | (5) all_10_2 = e1
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (4), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #949 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_3 = e1 & op(e3, e3) = e1
% 252.58/60.34 (2) all_252_3 = e2
% 252.58/60.34 (3) ~ (e2 = e1)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (4) all_252_3 = e1
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.58/60.34 | (5) e2 = e1
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #950 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) op(e0, e3) = e2
% 252.58/60.34 (2) ~ (all_10_2 = e4)
% 252.58/60.34 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (4) op(e2, e3) = all_10_2
% 252.58/60.34 (5) op(e1, e3) = all_62_2
% 252.58/60.34 (6) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = e4)
% 252.58/60.34 | (all_252_21 = e4 & op(e0, e3) = e4)
% 252.58/60.34 (7) op(e0, e3) = all_22_2
% 252.58/60.34 (8) ~ (e4 = e2)
% 252.58/60.34 (9) ~ (all_62_2 = e4)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | BETA: splitting (6) gives:
% 252.58/60.34 |
% 252.58/60.34 | Case 1:
% 252.58/60.34 | |
% 252.58/60.34 | | (10) all_252_7 = e4 & op(e2, e3) = e4
% 252.58/60.34 | |
% 252.58/60.34 | | ALPHA: (10) implies:
% 252.58/60.34 | | (11) op(e2, e3) = e4
% 252.58/60.34 | |
% 252.58/60.34 | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #953.
% 252.58/60.34 | |
% 252.58/60.34 | Case 2:
% 252.58/60.34 | |
% 252.58/60.34 | | (12) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3)
% 252.58/60.34 | | = e4)
% 252.58/60.34 | |
% 252.58/60.34 | | BETA: splitting (12) gives:
% 252.58/60.34 | |
% 252.58/60.34 | | Case 1:
% 252.58/60.34 | | |
% 252.58/60.34 | | | (13) all_252_13 = e4 & op(e1, e3) = e4
% 252.58/60.34 | | |
% 252.58/60.34 | | | REF_CLOSE: (3), (5), (9), (13) are inconsistent by sub-proof #952.
% 252.58/60.34 | | |
% 252.58/60.34 | | Case 2:
% 252.58/60.34 | | |
% 252.58/60.34 | | | (14) all_252_21 = e4 & op(e0, e3) = e4
% 252.58/60.34 | | |
% 252.58/60.34 | | | ALPHA: (14) implies:
% 252.58/60.34 | | | (15) op(e0, e3) = e4
% 252.58/60.34 | | |
% 252.58/60.34 | | | REF_CLOSE: (1), (3), (7), (8), (15) are inconsistent by sub-proof #951.
% 252.58/60.34 | | |
% 252.58/60.34 | | End of split
% 252.58/60.34 | |
% 252.58/60.34 | End of split
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #951 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) op(e0, e3) = e2
% 252.58/60.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (3) op(e0, e3) = all_22_2
% 252.58/60.34 (4) op(e0, e3) = e4
% 252.58/60.34 (5) ~ (e4 = e2)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (2) with all_22_2, e2, e3, e0, simplifying with
% 252.58/60.34 | (1), (3) gives:
% 252.58/60.34 | (6) all_22_2 = e2
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (2) with all_22_2, e4, e3, e0, simplifying with
% 252.58/60.34 | (3), (4) gives:
% 252.58/60.34 | (7) all_22_2 = e4
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (6), (7) imply:
% 252.58/60.34 | (8) e4 = e2
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (5), (8) imply:
% 252.58/60.34 | (9) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (9) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #952 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_13 = e4 & op(e1, e3) = e4
% 252.58/60.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (3) op(e1, e3) = all_62_2
% 252.58/60.34 (4) ~ (all_62_2 = e4)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (5) op(e1, e3) = e4
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (2) with all_62_2, e4, e3, e1, simplifying with
% 252.58/60.34 | (3), (5) gives:
% 252.58/60.34 | (6) all_62_2 = e4
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (4), (6) imply:
% 252.58/60.34 | (7) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (7) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #953 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (2) op(e2, e3) = all_10_2
% 252.58/60.34 (3) op(e2, e3) = e4
% 252.58/60.34 (4) ~ (all_10_2 = e4)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (1) with all_10_2, e4, e3, e2, simplifying with
% 252.58/60.34 | (2), (3) gives:
% 252.58/60.34 | (5) all_10_2 = e4
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (4), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #954 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_3 = e4
% 252.58/60.34 (2) all_252_3 = e2
% 252.58/60.34 (3) ~ (e4 = e2)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (1), (2) imply:
% 252.58/60.34 | (4) e4 = e2
% 252.58/60.34 |
% 252.58/60.34 | SIMP: (4) implies:
% 252.58/60.34 | (5) e4 = e2
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (5) imply:
% 252.58/60.34 | (6) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (6) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #955 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_1 = e4 & op(e4, e3) = e4
% 252.58/60.34 (2) all_252_1 = e1
% 252.58/60.34 (3) ~ (e4 = e1)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (4) all_252_1 = e4
% 252.58/60.34 |
% 252.58/60.34 | COMBINE_EQS: (2), (4) imply:
% 252.58/60.34 | (5) e4 = e1
% 252.58/60.34 |
% 252.58/60.34 | SIMP: (5) implies:
% 252.58/60.34 | (6) e4 = e1
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (3), (6) imply:
% 252.58/60.34 | (7) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (7) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #956 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_1 = e2 & op(e4, e3) = e2
% 252.58/60.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (3) op(e4, e3) = all_84_2
% 252.58/60.34 (4) ~ (all_84_2 = e2)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (5) op(e4, e3) = e2
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (2) with all_84_2, e2, e3, e4, simplifying with
% 252.58/60.34 | (3), (5) gives:
% 252.58/60.34 | (6) all_84_2 = e2
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (4), (6) imply:
% 252.58/60.34 | (7) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (7) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #957 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) ~ (all_22_2 = e2)
% 252.58/60.34 (2) ~ (all_22_2 = e3)
% 252.58/60.34 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (4) all_250_21 = all_22_2
% 252.58/60.34 (5) ~ (all_22_2 = e4)
% 252.58/60.34 (6) op(all_48_2, all_22_2) = e0
% 252.58/60.34 (7) ~ (all_22_2 = e1)
% 252.58/60.34 (8) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.58/60.34 all_250_21 = e0
% 252.58/60.34 (9) op(all_48_2, e0) = e3
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | BETA: splitting (8) gives:
% 252.58/60.34 |
% 252.58/60.34 | Case 1:
% 252.58/60.34 | |
% 252.58/60.34 | | (10) all_250_21 = e4
% 252.58/60.34 | |
% 252.58/60.34 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #993.
% 252.58/60.34 | |
% 252.58/60.34 | Case 2:
% 252.58/60.34 | |
% 252.58/60.34 | | (11) all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | all_250_21 =
% 252.58/60.34 | | e0
% 252.58/60.34 | |
% 252.58/60.34 | | BETA: splitting (11) gives:
% 252.58/60.34 | |
% 252.58/60.34 | | Case 1:
% 252.58/60.34 | | |
% 252.58/60.34 | | | (12) all_250_21 = e3
% 252.58/60.34 | | |
% 252.58/60.34 | | | COMBINE_EQS: (4), (12) imply:
% 252.58/60.34 | | | (13) all_22_2 = e3
% 252.58/60.34 | | |
% 252.58/60.34 | | | SIMP: (13) implies:
% 252.58/60.34 | | | (14) all_22_2 = e3
% 252.58/60.34 | | |
% 252.58/60.34 | | | REDUCE: (2), (14) imply:
% 252.58/60.34 | | | (15) $false
% 252.58/60.34 | | |
% 252.58/60.34 | | | CLOSE: (15) is inconsistent.
% 252.58/60.34 | | |
% 252.58/60.34 | | Case 2:
% 252.58/60.34 | | |
% 252.58/60.34 | | | (16) ~ (all_250_21 = e3)
% 252.58/60.34 | | | (17) all_250_21 = e2 | all_250_21 = e1 | all_250_21 = e0
% 252.58/60.34 | | |
% 252.58/60.34 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (17) are inconsistent by
% 252.58/60.34 | | | sub-proof #988.
% 252.58/60.34 | | |
% 252.58/60.34 | | End of split
% 252.58/60.34 | |
% 252.58/60.34 | End of split
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #958 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) ~ (all_22_2 = e3)
% 252.58/60.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (3) ~ (all_12_2 = e3)
% 252.58/60.34 (4) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.58/60.34 (5) op(e0, e3) = all_22_2
% 252.58/60.34 (6) op(e0, e4) = all_12_2
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | BETA: splitting (4) gives:
% 252.58/60.34 |
% 252.58/60.34 | Case 1:
% 252.58/60.34 | |
% 252.58/60.34 | | (7) all_252_20 = e3 & op(e0, e4) = e3
% 252.58/60.34 | |
% 252.58/60.34 | | ALPHA: (7) implies:
% 252.58/60.34 | | (8) op(e0, e4) = e3
% 252.58/60.34 | |
% 252.58/60.34 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #981.
% 252.58/60.34 | |
% 252.58/60.34 | Case 2:
% 252.58/60.34 | |
% 252.58/60.34 | | (9) all_252_21 = e3 & op(e0, e3) = e3
% 252.58/60.34 | |
% 252.58/60.34 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #959.
% 252.58/60.34 | |
% 252.58/60.34 | End of split
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #959 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) all_252_21 = e3 & op(e0, e3) = e3
% 252.58/60.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (3) op(e0, e3) = all_22_2
% 252.58/60.34 (4) ~ (all_22_2 = e3)
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | ALPHA: (1) implies:
% 252.58/60.34 | (5) op(e0, e3) = e3
% 252.58/60.34 |
% 252.58/60.34 | GROUND_INST: instantiating (2) with all_22_2, e3, e3, e0, simplifying with
% 252.58/60.34 | (3), (5) gives:
% 252.58/60.34 | (6) all_22_2 = e3
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (4), (6) imply:
% 252.58/60.34 | (7) $false
% 252.58/60.34 |
% 252.58/60.34 | CLOSE: (7) is inconsistent.
% 252.58/60.34 |
% 252.58/60.34 End of proof
% 252.58/60.34
% 252.58/60.34 Sub-proof #960 shows that the following formulas are inconsistent:
% 252.58/60.34 ----------------------------------------------------------------
% 252.58/60.34 (1) ~ (all_26_2 = e2)
% 252.58/60.34 (2) ~ (all_10_2 = e4)
% 252.58/60.34 (3) op(all_4_2, e2) = e1
% 252.58/60.34 (4) all_94_2 = all_38_2
% 252.58/60.34 (5) op(all_38_2, e1) = e2
% 252.58/60.34 (6) all_250_13 = all_38_2
% 252.58/60.34 (7) ~ (all_28_2 = e3)
% 252.58/60.34 (8) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 252.58/60.34 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 252.58/60.34 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 252.58/60.34 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.34 (10) op(e2, e3) = all_10_2
% 252.58/60.34 (11) ~ (e3 = e2)
% 252.58/60.34 (12) op(e0, e0) = all_244_24
% 252.58/60.34 (13) ~ (all_12_2 = e3)
% 252.58/60.34 (14) op(e2, e2) = all_244_8
% 252.58/60.34 (15) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 252.58/60.34 all_250_11 = e0
% 252.58/60.34 (16) op(e2, e1) = all_38_2
% 252.58/60.34 (17) ~ (all_68_2 = e4) | ( ~ (all_68_0 = e2) & op(e4, all_68_1) = all_68_0 &
% 252.58/60.34 op(e3, e4) = all_68_1 & $i(all_68_0) & $i(all_68_1)) | ( ~ (all_68_1 =
% 252.58/60.34 e1) & op(e3, e4) = all_68_1 & $i(all_68_1))
% 252.58/60.34 (18) ~ (all_58_2 = e3)
% 252.58/60.34 (19) ~ (all_36_2 = e2)
% 252.58/60.34 (20) all_78_2 = all_10_2
% 252.58/60.34 (21) op(e0, e2) = all_28_2
% 252.58/60.34 (22) all_106_2 = all_38_2
% 252.58/60.34 (23) ~ (all_244_8 = all_38_2)
% 252.58/60.34 (24) op(all_244_15, all_244_15) = e1
% 252.58/60.34 (25) all_250_21 = all_22_2
% 252.58/60.34 (26) ~ (all_244_3 = all_84_2)
% 252.58/60.34 (27) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 252.58/60.34 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 252.58/60.34 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 252.58/60.34 (28) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) =
% 252.58/60.34 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 252.58/60.34 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.58/60.34 (29) op(e1, e3) = all_62_2
% 252.58/60.34 (30) ~ (all_244_3 = all_10_2)
% 252.58/60.34 (31) all_70_2 = all_62_2
% 252.58/60.34 (32) op(all_48_2, all_22_2) = e0
% 252.58/60.34 (33) op(e3, e1) = all_36_2
% 252.58/60.34 (34) ~ (all_78_2 = e1) | ( ~ (all_78_0 = e4) & op(e3, e1) = all_78_1 &
% 252.58/60.34 op(e1, all_78_1) = all_78_0 & $i(all_78_0) & $i(all_78_1)) | ( ~
% 252.58/60.34 (all_78_1 = e0) & op(e3, e1) = all_78_1 & $i(all_78_1))
% 252.58/60.34 (35) ~ (all_22_2 = e1)
% 252.58/60.34 (36) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.58/60.34 all_250_13 = e0
% 252.58/60.34 (37) ~ (all_70_2 = e2) | ( ~ (all_70_0 = e0) & op(e3, e2) = all_70_1 &
% 252.58/60.34 op(e2, all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1)) | ( ~
% 252.58/60.34 (all_70_1 = e4) & op(e3, e2) = all_70_1 & $i(all_70_1))
% 252.58/60.34 (38) ~ (all_38_2 = e4)
% 252.58/60.34 (39) op(all_22_2, e3) = e0
% 252.58/60.34 (40) all_68_2 = all_22_2
% 252.58/60.34 (41) op(e0, e3) = all_22_2
% 252.58/60.34 (42) ~ (all_28_2 = all_22_2)
% 252.58/60.34 (43) all_58_2 = all_20_2
% 252.58/60.34 (44) op(all_62_2, e3) = e1
% 252.58/60.34 (45) op(e4, e1) = all_26_2
% 252.58/60.34 (46) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) =
% 252.58/60.34 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 252.58/60.34 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.58/60.34 (47) op(all_10_2, e3) = e2
% 252.58/60.34 (48) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.58/60.34 all_250_21 = e0
% 252.58/60.34 (49) ~ (all_244_15 = all_62_2)
% 252.58/60.34 (50) ~ (all_90_2 = e2) | ( ~ (all_90_0 = e4) & op(e3, e2) = all_90_1 &
% 252.58/60.34 op(e2, all_90_1) = all_90_0 & $i(all_90_0) & $i(all_90_1)) | ( ~
% 252.58/60.34 (all_90_1 = e1) & op(e3, e2) = all_90_1 & $i(all_90_1))
% 252.58/60.34 (51) all_250_11 = all_10_2
% 252.58/60.34 (52) ~ (all_22_2 = all_12_2)
% 252.58/60.34 (53) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 252.58/60.34 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) =
% 252.58/60.34 e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 252.58/60.34 (54) ~ (e4 = e3)
% 252.58/60.34 (55) op(e1, e1) = all_244_15
% 252.58/60.34 (56) op(e0, e1) = all_20_2
% 252.58/60.34 (57) op(all_48_2, e0) = e3
% 252.58/60.34 (58) op(all_4_2, all_38_2) = e2
% 252.58/60.34 (59) op(e4, e3) = all_84_2
% 252.58/60.34 (60) ~ (all_62_2 = all_10_2)
% 252.58/60.34 (61) ~ (all_22_2 = all_10_2)
% 252.58/60.34 (62) ~ (all_22_2 = all_20_2)
% 252.58/60.34 (63) ~ (all_38_2 = all_10_2)
% 252.58/60.34 (64) ~ (all_244_24 = all_22_2)
% 252.58/60.34 (65) op(e3, e3) = all_244_3
% 252.58/60.34 (66) all_90_2 = all_22_2
% 252.58/60.34 (67) op(all_244_24, all_244_24) = e0
% 252.58/60.34 (68) op(e0, e4) = all_12_2
% 252.58/60.34 (69) ~ (all_20_2 = e2)
% 252.58/60.34 (70) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 252.58/60.34 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 252.58/60.34 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 252.58/60.34 (71) all_124_2 = all_10_2
% 252.58/60.34
% 252.58/60.34 Begin of proof
% 252.58/60.34 |
% 252.58/60.34 | REDUCE: (18), (43) imply:
% 252.58/60.34 | (72) ~ (all_20_2 = e3)
% 252.58/60.34 |
% 252.58/60.34 | BETA: splitting (17) gives:
% 252.58/60.34 |
% 252.58/60.34 | Case 1:
% 252.58/60.34 | |
% 252.58/60.34 | | (73) ~ (all_68_2 = e4)
% 252.58/60.34 | |
% 252.58/60.34 | | REDUCE: (40), (73) imply:
% 252.58/60.34 | | (74) ~ (all_22_2 = e4)
% 252.58/60.34 | |
% 252.58/60.34 | | BETA: splitting (37) gives:
% 252.58/60.34 | |
% 252.58/60.34 | | Case 1:
% 252.58/60.34 | | |
% 252.58/60.34 | | | (75) ~ (all_70_2 = e2)
% 252.58/60.34 | | |
% 252.58/60.34 | | | REDUCE: (31), (75) imply:
% 252.58/60.34 | | | (76) ~ (all_62_2 = e2)
% 252.58/60.34 | | |
% 252.58/60.34 | | | BETA: splitting (34) gives:
% 252.58/60.34 | | |
% 252.58/60.34 | | | Case 1:
% 252.58/60.34 | | | |
% 252.58/60.34 | | | | (77) ~ (all_78_2 = e1)
% 252.58/60.34 | | | |
% 252.58/60.34 | | | | REDUCE: (20), (77) imply:
% 252.58/60.34 | | | | (78) ~ (all_10_2 = e1)
% 252.58/60.34 | | | |
% 252.58/60.34 | | | | BETA: splitting (50) gives:
% 252.58/60.34 | | | |
% 252.58/60.34 | | | | Case 1:
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | (79) ~ (all_90_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (66), (79) imply:
% 252.58/60.34 | | | | | (80) ~ (all_22_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (14), (15), (19), (22), (23),
% 252.58/60.34 | | | | | (24), (25), (27), (32), (33), (35), (36), (38), (41), (47),
% 252.58/60.34 | | | | | (48), (51), (55), (56), (57), (61), (63), (69), (70), (71),
% 252.58/60.34 | | | | | (74), (78), (80) are inconsistent by sub-proof #982.
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | Case 2:
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | (81) all_90_2 = e2
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | COMBINE_EQS: (66), (81) imply:
% 252.58/60.34 | | | | | (82) all_22_2 = e2
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (64), (82) imply:
% 252.58/60.34 | | | | | (83) ~ (all_244_24 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (42), (82) imply:
% 252.58/60.34 | | | | | (84) ~ (all_28_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (62), (82) imply:
% 252.58/60.34 | | | | | (85) ~ (all_20_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (52), (82) imply:
% 252.58/60.34 | | | | | (86) ~ (all_12_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | SIMP: (86) implies:
% 252.58/60.34 | | | | | (87) ~ (all_12_2 = e2)
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | REDUCE: (39), (82) imply:
% 252.58/60.34 | | | | | (88) op(e2, e3) = e0
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | BETA: splitting (28) gives:
% 252.58/60.34 | | | | |
% 252.58/60.34 | | | | | Case 1:
% 252.58/60.34 | | | | | |
% 252.58/60.34 | | | | | | (89) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 &
% 252.58/60.34 | | | | | | op(e0, e3) = e3)
% 252.58/60.34 | | | | | |
% 252.58/60.35 | | | | | | REF_CLOSE: (9), (11), (12), (13), (21), (46), (56), (68), (69),
% 252.58/60.35 | | | | | | (83), (84), (87), (89) are inconsistent by sub-proof
% 252.58/60.35 | | | | | | #976.
% 252.58/60.35 | | | | | |
% 252.58/60.35 | | | | | Case 2:
% 252.58/60.35 | | | | | |
% 252.58/60.35 | | | | | | (90) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 &
% 252.58/60.35 | | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.58/60.35 | | | | | |
% 252.58/60.35 | | | | | | BETA: splitting (90) gives:
% 252.58/60.35 | | | | | |
% 252.58/60.35 | | | | | | Case 1:
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | (91) all_252_22 = e3 & op(e0, e2) = e3
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | ALPHA: (91) implies:
% 252.58/60.35 | | | | | | | (92) op(e0, e2) = e3
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | REF_CLOSE: (7), (9), (21), (92) are inconsistent by sub-proof
% 252.58/60.35 | | | | | | | #975.
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | Case 2:
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | (93) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 &
% 252.58/60.35 | | | | | | | op(e0, e0) = e3)
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | BETA: splitting (93) gives:
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | | Case 1:
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | (94) all_252_23 = e3 & op(e0, e1) = e3
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | ALPHA: (94) implies:
% 252.58/60.35 | | | | | | | | (95) op(e0, e1) = e3
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | REF_CLOSE: (9), (56), (72), (95) are inconsistent by sub-proof
% 252.58/60.35 | | | | | | | | #974.
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | Case 2:
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | (96) all_252_24 = e3 & op(e0, e0) = e3
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | ALPHA: (96) implies:
% 252.58/60.35 | | | | | | | | (97) op(e0, e0) = e3
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | GROUND_INST: instantiating (9) with all_244_24, e3, e0, e0,
% 252.58/60.35 | | | | | | | | simplifying with (12), (97) gives:
% 252.58/60.35 | | | | | | | | (98) all_244_24 = e3
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | GROUND_INST: instantiating (9) with all_10_2, e0, e3, e2,
% 252.58/60.35 | | | | | | | | simplifying with (10), (88) gives:
% 252.58/60.35 | | | | | | | | (99) all_10_2 = e0
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | REDUCE: (30), (99) imply:
% 252.58/60.35 | | | | | | | | (100) ~ (all_244_3 = e0)
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | REDUCE: (67), (98) imply:
% 252.58/60.35 | | | | | | | | (101) op(e3, e3) = e0
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | | REF_CLOSE: (9), (65), (100), (101) are inconsistent by sub-proof
% 252.58/60.35 | | | | | | | | #973.
% 252.58/60.35 | | | | | | | |
% 252.58/60.35 | | | | | | | End of split
% 252.58/60.35 | | | | | | |
% 252.58/60.35 | | | | | | End of split
% 252.58/60.35 | | | | | |
% 252.58/60.35 | | | | | End of split
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | End of split
% 252.58/60.35 | | | |
% 252.58/60.35 | | | Case 2:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (102) all_78_2 = e1
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REF_CLOSE: (9), (20), (29), (47), (76), (102) are inconsistent by
% 252.58/60.35 | | | | sub-proof #971.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | End of split
% 252.58/60.35 | | |
% 252.58/60.35 | | Case 2:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (103) all_70_2 = e2
% 252.58/60.35 | | |
% 252.58/60.35 | | | COMBINE_EQS: (31), (103) imply:
% 252.58/60.35 | | | (104) all_62_2 = e2
% 252.58/60.35 | | |
% 252.58/60.35 | | | SIMP: (104) implies:
% 252.58/60.35 | | | (105) all_62_2 = e2
% 252.58/60.35 | | |
% 252.58/60.35 | | | REDUCE: (49), (105) imply:
% 252.58/60.35 | | | (106) ~ (all_244_15 = e2)
% 252.58/60.35 | | |
% 252.58/60.35 | | | REDUCE: (60), (105) imply:
% 252.58/60.35 | | | (107) ~ (all_10_2 = e2)
% 252.58/60.35 | | |
% 252.58/60.35 | | | SIMP: (107) implies:
% 252.58/60.35 | | | (108) ~ (all_10_2 = e2)
% 252.58/60.35 | | |
% 252.58/60.35 | | | REDUCE: (44), (105) imply:
% 252.58/60.35 | | | (109) op(e2, e3) = e1
% 252.58/60.35 | | |
% 252.58/60.35 | | | BETA: splitting (53) gives:
% 252.58/60.35 | | |
% 252.58/60.35 | | | Case 1:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (110) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3,
% 252.58/60.35 | | | | e1) = e2)
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REF_CLOSE: (1), (9), (19), (33), (45), (110) are inconsistent by
% 252.58/60.35 | | | | sub-proof #969.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | Case 2:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (111) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1,
% 252.58/60.35 | | | | e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | BETA: splitting (111) gives:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | Case 1:
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | | (112) all_252_11 = e2 & op(e2, e1) = e2
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | | REF_CLOSE: (3), (9), (10), (16), (58), (108), (109), (112) are
% 252.58/60.35 | | | | | inconsistent by sub-proof #967.
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | Case 2:
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | | (113) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 &
% 252.58/60.35 | | | | | op(e0, e1) = e2)
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | | REF_CLOSE: (9), (55), (56), (69), (106), (113) are inconsistent by
% 252.58/60.35 | | | | | sub-proof #965.
% 252.58/60.35 | | | | |
% 252.58/60.35 | | | | End of split
% 252.58/60.35 | | | |
% 252.58/60.35 | | | End of split
% 252.58/60.35 | | |
% 252.58/60.35 | | End of split
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (114) all_68_2 = e4
% 252.58/60.35 | |
% 252.58/60.35 | | COMBINE_EQS: (40), (114) imply:
% 252.58/60.35 | | (115) all_22_2 = e4
% 252.58/60.35 | |
% 252.58/60.35 | | SIMP: (115) implies:
% 252.58/60.35 | | (116) all_22_2 = e4
% 252.58/60.35 | |
% 252.58/60.35 | | REDUCE: (39), (116) imply:
% 252.58/60.35 | | (117) op(e4, e3) = e0
% 252.58/60.35 | |
% 252.58/60.35 | | REDUCE: (41), (116) imply:
% 252.58/60.35 | | (118) op(e0, e3) = e4
% 252.58/60.35 | |
% 252.58/60.35 | | BETA: splitting (28) gives:
% 252.58/60.35 | |
% 252.58/60.35 | | Case 1:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (119) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0,
% 252.58/60.35 | | | e3) = e3)
% 252.58/60.35 | | |
% 252.58/60.35 | | | REF_CLOSE: (9), (13), (54), (68), (118), (119) are inconsistent by
% 252.58/60.35 | | | sub-proof #963.
% 252.58/60.35 | | |
% 252.58/60.35 | | Case 2:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (120) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0,
% 252.58/60.35 | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.58/60.35 | | |
% 252.58/60.35 | | | REF_CLOSE: (7), (9), (12), (21), (26), (56), (59), (65), (67), (72),
% 252.58/60.35 | | | (117), (120) are inconsistent by sub-proof #961.
% 252.58/60.35 | | |
% 252.58/60.35 | | End of split
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #961 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)
% 252.58/60.35 | (all_252_24 = e3 & op(e0, e0) = e3)
% 252.58/60.35 (2) ~ (all_28_2 = e3)
% 252.58/60.35 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (4) op(e0, e0) = all_244_24
% 252.58/60.35 (5) op(e0, e2) = all_28_2
% 252.58/60.35 (6) ~ (all_244_3 = all_84_2)
% 252.58/60.35 (7) op(e0, e1) = all_20_2
% 252.58/60.35 (8) op(e4, e3) = all_84_2
% 252.58/60.35 (9) op(e4, e3) = e0
% 252.58/60.35 (10) ~ (all_20_2 = e3)
% 252.58/60.35 (11) op(e3, e3) = all_244_3
% 252.58/60.35 (12) op(all_244_24, all_244_24) = e0
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (1) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (13) all_252_22 = e3 & op(e0, e2) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (13) implies:
% 252.58/60.35 | | (14) op(e0, e2) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (2), (3), (5), (14) are inconsistent by sub-proof #975.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (15) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0)
% 252.58/60.35 | | = e3)
% 252.58/60.35 | |
% 252.58/60.35 | | BETA: splitting (15) gives:
% 252.58/60.35 | |
% 252.58/60.35 | | Case 1:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (16) all_252_23 = e3 & op(e0, e1) = e3
% 252.58/60.35 | | |
% 252.58/60.35 | | | ALPHA: (16) implies:
% 252.58/60.35 | | | (17) op(e0, e1) = e3
% 252.58/60.35 | | |
% 252.58/60.35 | | | REF_CLOSE: (3), (7), (10), (17) are inconsistent by sub-proof #974.
% 252.58/60.35 | | |
% 252.58/60.35 | | Case 2:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (18) all_252_24 = e3 & op(e0, e0) = e3
% 252.58/60.35 | | |
% 252.58/60.35 | | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (12), (18) are inconsistent by
% 252.58/60.35 | | | sub-proof #962.
% 252.58/60.35 | | |
% 252.58/60.35 | | End of split
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #962 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e0) = all_244_24
% 252.58/60.35 (3) ~ (all_244_3 = all_84_2)
% 252.58/60.35 (4) all_252_24 = e3 & op(e0, e0) = e3
% 252.58/60.35 (5) op(e4, e3) = all_84_2
% 252.58/60.35 (6) op(e4, e3) = e0
% 252.58/60.35 (7) op(e3, e3) = all_244_3
% 252.58/60.35 (8) op(all_244_24, all_244_24) = e0
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | ALPHA: (4) implies:
% 252.58/60.35 | (9) op(e0, e0) = e3
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_244_24, e3, e0, e0, simplifying with
% 252.58/60.35 | (2), (9) gives:
% 252.58/60.35 | (10) all_244_24 = e3
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_84_2, e0, e3, e4, simplifying with
% 252.58/60.35 | (5), (6) gives:
% 252.58/60.35 | (11) all_84_2 = e0
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (3), (11) imply:
% 252.58/60.35 | (12) ~ (all_244_3 = e0)
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (8), (10) imply:
% 252.58/60.35 | (13) op(e3, e3) = e0
% 252.58/60.35 |
% 252.58/60.35 | REF_CLOSE: (1), (7), (12), (13) are inconsistent by sub-proof #973.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #963 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) ~ (all_12_2 = e3)
% 252.58/60.35 (3) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.58/60.35 (4) ~ (e4 = e3)
% 252.58/60.35 (5) op(e0, e3) = e4
% 252.58/60.35 (6) op(e0, e4) = all_12_2
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (3) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (7) all_252_20 = e3 & op(e0, e4) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (7) implies:
% 252.58/60.35 | | (8) op(e0, e4) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #981.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (9) all_252_21 = e3 & op(e0, e3) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (9) implies:
% 252.58/60.35 | | (10) op(e0, e3) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #964.
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #964 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e3) = e4
% 252.58/60.35 (3) op(e0, e3) = e3
% 252.58/60.35 (4) ~ (e4 = e3)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with e3, e4, e3, e0, simplifying with (2), (3)
% 252.58/60.35 | gives:
% 252.58/60.35 | (5) e4 = e3
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (5) imply:
% 252.58/60.35 | (6) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (6) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #965 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)
% 252.58/60.35 (3) op(e1, e1) = all_244_15
% 252.58/60.35 (4) op(e0, e1) = all_20_2
% 252.58/60.35 (5) ~ (all_244_15 = e2)
% 252.58/60.35 (6) ~ (all_20_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (2) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (7) all_252_15 = e2 & op(e1, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #966.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (8) all_252_23 = e2 & op(e0, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (8) implies:
% 252.58/60.35 | | (9) op(e0, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #985.
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #966 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) all_252_15 = e2 & op(e1, e1) = e2
% 252.58/60.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (3) op(e1, e1) = all_244_15
% 252.58/60.35 (4) ~ (all_244_15 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | ALPHA: (1) implies:
% 252.58/60.35 | (5) op(e1, e1) = e2
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (2) with all_244_15, e2, e1, e1, simplifying with
% 252.58/60.35 | (3), (5) gives:
% 252.58/60.35 | (6) all_244_15 = e2
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (6) imply:
% 252.58/60.35 | (7) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (7) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #967 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) all_252_11 = e2 & op(e2, e1) = e2
% 252.58/60.35 (2) op(all_4_2, e2) = e1
% 252.58/60.35 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (4) op(e2, e3) = all_10_2
% 252.58/60.35 (5) op(e2, e1) = all_38_2
% 252.58/60.35 (6) op(e2, e3) = e1
% 252.58/60.35 (7) op(all_4_2, all_38_2) = e2
% 252.58/60.35 (8) ~ (all_10_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | ALPHA: (1) implies:
% 252.58/60.35 | (9) op(e2, e1) = e2
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (3) with all_38_2, e2, e1, e2, simplifying with
% 252.58/60.35 | (5), (9) gives:
% 252.58/60.35 | (10) all_38_2 = e2
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (3) with all_10_2, e1, e3, e2, simplifying with
% 252.58/60.35 | (4), (6) gives:
% 252.58/60.35 | (11) all_10_2 = e1
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (8), (11) imply:
% 252.58/60.35 | (12) ~ (e2 = e1)
% 252.58/60.35 |
% 252.58/60.35 | REF_CLOSE: (2), (3), (7), (10), (12) are inconsistent by sub-proof #968.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #968 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) op(all_4_2, e2) = e1
% 252.58/60.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (3) all_38_2 = e2
% 252.58/60.35 (4) op(all_4_2, all_38_2) = e2
% 252.58/60.35 (5) ~ (e2 = e1)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | SIMP: (5) implies:
% 252.58/60.35 | (6) ~ (e2 = e1)
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (3), (4) imply:
% 252.58/60.35 | (7) op(all_4_2, e2) = e2
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (2) with e1, e2, e2, all_4_2, simplifying with (1),
% 252.58/60.35 | (7) gives:
% 252.58/60.35 | (8) e2 = e1
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (6), (8) imply:
% 252.58/60.35 | (9) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (9) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #969 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ~ (all_26_2 = e2)
% 252.58/60.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (3) ~ (all_36_2 = e2)
% 252.58/60.35 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2)
% 252.58/60.35 (5) op(e3, e1) = all_36_2
% 252.58/60.35 (6) op(e4, e1) = all_26_2
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (4) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (7) all_252_9 = e2 & op(e4, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #970.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (8) all_252_10 = e2 & op(e3, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (8) implies:
% 252.58/60.35 | | (9) op(e3, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #984.
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #970 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) all_252_9 = e2 & op(e4, e1) = e2
% 252.58/60.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (3) op(e4, e1) = all_26_2
% 252.58/60.35 (4) ~ (all_26_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | ALPHA: (1) implies:
% 252.58/60.35 | (5) op(e4, e1) = e2
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (2) with all_26_2, e2, e1, e4, simplifying with
% 252.58/60.35 | (3), (5) gives:
% 252.58/60.35 | (6) all_26_2 = e2
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (6) imply:
% 252.58/60.35 | (7) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (7) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #971 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ~ (all_62_2 = e2)
% 252.58/60.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (3) all_78_2 = all_10_2
% 252.58/60.35 (4) op(e1, e3) = all_62_2
% 252.58/60.35 (5) op(all_10_2, e3) = e2
% 252.58/60.35 (6) all_78_2 = e1
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | COMBINE_EQS: (3), (6) imply:
% 252.58/60.35 | (7) all_10_2 = e1
% 252.58/60.35 |
% 252.58/60.35 | SIMP: (7) implies:
% 252.58/60.35 | (8) all_10_2 = e1
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (5), (8) imply:
% 252.58/60.35 | (9) op(e1, e3) = e2
% 252.58/60.35 |
% 252.58/60.35 | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #972.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #972 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e1, e3) = all_62_2
% 252.58/60.35 (3) op(e1, e3) = e2
% 252.58/60.35 (4) ~ (all_62_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_62_2, e2, e3, e1, simplifying with
% 252.58/60.35 | (2), (3) gives:
% 252.58/60.35 | (5) all_62_2 = e2
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (5) imply:
% 252.58/60.35 | (6) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (6) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #973 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e3, e3) = all_244_3
% 252.58/60.35 (3) op(e3, e3) = e0
% 252.58/60.35 (4) ~ (all_244_3 = e0)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_244_3, e0, e3, e3, simplifying with
% 252.58/60.35 | (2), (3) gives:
% 252.58/60.35 | (5) all_244_3 = e0
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (5) imply:
% 252.58/60.35 | (6) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (6) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #974 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e1) = all_20_2
% 252.58/60.35 (3) op(e0, e1) = e3
% 252.58/60.35 (4) ~ (all_20_2 = e3)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_20_2, e3, e1, e0, simplifying with
% 252.58/60.35 | (2), (3) gives:
% 252.58/60.35 | (5) all_20_2 = e3
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (5) imply:
% 252.58/60.35 | (6) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (6) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #975 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e2) = all_28_2
% 252.58/60.35 (3) op(e0, e2) = e3
% 252.58/60.35 (4) ~ (all_28_2 = e3)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | GROUND_INST: instantiating (1) with all_28_2, e3, e2, e0, simplifying with
% 252.58/60.35 | (2), (3) gives:
% 252.58/60.35 | (5) all_28_2 = e3
% 252.58/60.35 |
% 252.58/60.35 | REDUCE: (4), (5) imply:
% 252.58/60.35 | (6) $false
% 252.58/60.35 |
% 252.58/60.35 | CLOSE: (6) is inconsistent.
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #976 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) ~ (e3 = e2)
% 252.58/60.35 (3) op(e0, e0) = all_244_24
% 252.58/60.35 (4) ~ (all_12_2 = e3)
% 252.58/60.35 (5) op(e0, e2) = all_28_2
% 252.58/60.35 (6) ~ (all_12_2 = e2)
% 252.58/60.35 (7) ~ (all_28_2 = e2)
% 252.58/60.35 (8) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)
% 252.58/60.35 (9) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)
% 252.58/60.35 | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) =
% 252.58/60.35 e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.58/60.35 (10) op(e0, e1) = all_20_2
% 252.58/60.35 (11) ~ (all_244_24 = e2)
% 252.58/60.35 (12) op(e0, e4) = all_12_2
% 252.58/60.35 (13) ~ (all_20_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (8) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (14) all_252_20 = e3 & op(e0, e4) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (14) implies:
% 252.58/60.35 | | (15) op(e0, e4) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (4), (12), (15) are inconsistent by sub-proof #981.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (16) all_252_21 = e3 & op(e0, e3) = e3
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (16) implies:
% 252.58/60.35 | | (17) all_252_21 = e3
% 252.58/60.35 | |
% 252.58/60.35 | | BETA: splitting (9) gives:
% 252.58/60.35 | |
% 252.58/60.35 | | Case 1:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (18) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0,
% 252.58/60.35 | | | e3) = e2)
% 252.58/60.35 | | |
% 252.58/60.35 | | | BETA: splitting (18) gives:
% 252.58/60.35 | | |
% 252.58/60.35 | | | Case 1:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (19) all_252_20 = e2 & op(e0, e4) = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | ALPHA: (19) implies:
% 252.58/60.35 | | | | (20) op(e0, e4) = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REF_CLOSE: (1), (6), (12), (20) are inconsistent by sub-proof #980.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | Case 2:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (21) all_252_21 = e2 & op(e0, e3) = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | ALPHA: (21) implies:
% 252.58/60.35 | | | | (22) all_252_21 = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | COMBINE_EQS: (17), (22) imply:
% 252.58/60.35 | | | | (23) e3 = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REDUCE: (2), (23) imply:
% 252.58/60.35 | | | | (24) $false
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | CLOSE: (24) is inconsistent.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | End of split
% 252.58/60.35 | | |
% 252.58/60.35 | | Case 2:
% 252.58/60.35 | | |
% 252.58/60.35 | | | (25) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0,
% 252.58/60.35 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.58/60.35 | | |
% 252.58/60.35 | | | BETA: splitting (25) gives:
% 252.58/60.35 | | |
% 252.58/60.35 | | | Case 1:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (26) all_252_22 = e2 & op(e0, e2) = e2
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REF_CLOSE: (1), (5), (7), (26) are inconsistent by sub-proof #979.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | Case 2:
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | (27) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0,
% 252.58/60.35 | | | | e0) = e2)
% 252.58/60.35 | | | |
% 252.58/60.35 | | | | REF_CLOSE: (1), (3), (10), (11), (13), (27) are inconsistent by
% 252.58/60.35 | | | | sub-proof #977.
% 252.58/60.35 | | | |
% 252.58/60.35 | | | End of split
% 252.58/60.35 | | |
% 252.58/60.35 | | End of split
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #977 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e0) = all_244_24
% 252.58/60.35 (3) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)
% 252.58/60.35 (4) op(e0, e1) = all_20_2
% 252.58/60.35 (5) ~ (all_244_24 = e2)
% 252.58/60.35 (6) ~ (all_20_2 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.35 | BETA: splitting (3) gives:
% 252.58/60.35 |
% 252.58/60.35 | Case 1:
% 252.58/60.35 | |
% 252.58/60.35 | | (7) all_252_23 = e2 & op(e0, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (7) implies:
% 252.58/60.35 | | (8) op(e0, e1) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #985.
% 252.58/60.35 | |
% 252.58/60.35 | Case 2:
% 252.58/60.35 | |
% 252.58/60.35 | | (9) all_252_24 = e2 & op(e0, e0) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | ALPHA: (9) implies:
% 252.58/60.35 | | (10) op(e0, e0) = e2
% 252.58/60.35 | |
% 252.58/60.35 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #978.
% 252.58/60.35 | |
% 252.58/60.35 | End of split
% 252.58/60.35 |
% 252.58/60.35 End of proof
% 252.58/60.35
% 252.58/60.35 Sub-proof #978 shows that the following formulas are inconsistent:
% 252.58/60.35 ----------------------------------------------------------------
% 252.58/60.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.35 (2) op(e0, e0) = all_244_24
% 252.58/60.35 (3) op(e0, e0) = e2
% 252.58/60.35 (4) ~ (all_244_24 = e2)
% 252.58/60.35
% 252.58/60.35 Begin of proof
% 252.58/60.35 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_244_24, e2, e0, e0, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_244_24 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #979 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) all_252_22 = e2 & op(e0, e2) = e2
% 252.58/60.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (3) op(e0, e2) = all_28_2
% 252.58/60.36 (4) ~ (all_28_2 = e2)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | ALPHA: (1) implies:
% 252.58/60.36 | (5) op(e0, e2) = e2
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (2) with all_28_2, e2, e2, e0, simplifying with
% 252.58/60.36 | (3), (5) gives:
% 252.58/60.36 | (6) all_28_2 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (6) imply:
% 252.58/60.36 | (7) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (7) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #980 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (2) op(e0, e4) = all_12_2
% 252.58/60.36 (3) op(e0, e4) = e2
% 252.58/60.36 (4) ~ (all_12_2 = e2)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_12_2, e2, e4, e0, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_12_2 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #981 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (2) op(e0, e4) = all_12_2
% 252.58/60.36 (3) op(e0, e4) = e3
% 252.58/60.36 (4) ~ (all_12_2 = e3)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_12_2, e3, e4, e0, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_12_2 = e3
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #982 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ~ (all_10_2 = e1)
% 252.58/60.36 (2) ~ (all_10_2 = e4)
% 252.58/60.36 (3) ~ (all_22_2 = e2)
% 252.58/60.36 (4) all_94_2 = all_38_2
% 252.58/60.36 (5) op(all_38_2, e1) = e2
% 252.58/60.36 (6) all_250_13 = all_38_2
% 252.58/60.36 (7) ~ (all_94_2 = e3) | ( ~ (all_94_0 = e4) & op(e3, all_94_1) = all_94_0 &
% 252.58/60.36 op(e1, e3) = all_94_1 & $i(all_94_0) & $i(all_94_1)) | ( ~ (all_94_1 =
% 252.58/60.36 e0) & op(e1, e3) = all_94_1 & $i(all_94_1))
% 252.58/60.36 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (9) op(e2, e2) = all_244_8
% 252.58/60.36 (10) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 252.58/60.36 all_250_11 = e0
% 252.58/60.36 (11) ~ (all_36_2 = e2)
% 252.58/60.36 (12) all_106_2 = all_38_2
% 252.58/60.36 (13) ~ (all_244_8 = all_38_2)
% 252.58/60.36 (14) op(all_244_15, all_244_15) = e1
% 252.58/60.36 (15) all_250_21 = all_22_2
% 252.58/60.36 (16) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 252.58/60.36 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 252.58/60.36 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 252.58/60.36 (17) ~ (all_22_2 = e4)
% 252.58/60.36 (18) op(all_48_2, all_22_2) = e0
% 252.58/60.36 (19) op(e3, e1) = all_36_2
% 252.58/60.36 (20) ~ (all_22_2 = e1)
% 252.58/60.36 (21) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.58/60.36 all_250_13 = e0
% 252.58/60.36 (22) ~ (all_38_2 = e4)
% 252.58/60.36 (23) op(e0, e3) = all_22_2
% 252.58/60.36 (24) op(all_10_2, e3) = e2
% 252.58/60.36 (25) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.58/60.36 all_250_21 = e0
% 252.58/60.36 (26) all_250_11 = all_10_2
% 252.58/60.36 (27) op(e1, e1) = all_244_15
% 252.58/60.36 (28) op(e0, e1) = all_20_2
% 252.58/60.36 (29) op(all_48_2, e0) = e3
% 252.58/60.36 (30) ~ (all_22_2 = all_10_2)
% 252.58/60.36 (31) ~ (all_38_2 = all_10_2)
% 252.58/60.36 (32) ~ (all_20_2 = e2)
% 252.58/60.36 (33) ~ (all_106_2 = e0) | ( ~ (all_106_0 = e4) & op(e1, e0) = all_106_1 &
% 252.58/60.36 op(e0, all_106_1) = all_106_0 & $i(all_106_0) & $i(all_106_1)) | ( ~
% 252.58/60.36 (all_106_1 = e3) & op(e1, e0) = all_106_1 & $i(all_106_1))
% 252.58/60.36 (34) all_124_2 = all_10_2
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | BETA: splitting (7) gives:
% 252.58/60.36 |
% 252.58/60.36 | Case 1:
% 252.58/60.36 | |
% 252.58/60.36 | | (35) ~ (all_94_2 = e3)
% 252.58/60.36 | |
% 252.58/60.36 | | REDUCE: (4), (35) imply:
% 252.58/60.36 | | (36) ~ (all_38_2 = e3)
% 252.58/60.36 | |
% 252.58/60.36 | | BETA: splitting (33) gives:
% 252.58/60.36 | |
% 252.58/60.36 | | Case 1:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (37) ~ (all_106_2 = e0)
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (12), (37) imply:
% 252.58/60.36 | | | (38) ~ (all_38_2 = e0)
% 252.58/60.36 | | |
% 252.58/60.36 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (13), (14), (15),
% 252.58/60.36 | | | (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 252.58/60.36 | | | (27), (29), (30), (31), (34), (36), (38) are inconsistent by
% 252.58/60.36 | | | sub-proof #986.
% 252.58/60.36 | | |
% 252.58/60.36 | | Case 2:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (39) all_106_2 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | COMBINE_EQS: (12), (39) imply:
% 252.58/60.36 | | | (40) all_38_2 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | SIMP: (40) implies:
% 252.58/60.36 | | | (41) all_38_2 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (5), (41) imply:
% 252.58/60.36 | | | (42) op(e0, e1) = e2
% 252.58/60.36 | | |
% 252.58/60.36 | | | REF_CLOSE: (8), (28), (32), (42) are inconsistent by sub-proof #985.
% 252.58/60.36 | | |
% 252.58/60.36 | | End of split
% 252.58/60.36 | |
% 252.58/60.36 | Case 2:
% 252.58/60.36 | |
% 252.58/60.36 | | (43) all_94_2 = e3
% 252.58/60.36 | |
% 252.58/60.36 | | REF_CLOSE: (4), (5), (8), (11), (19), (43) are inconsistent by sub-proof
% 252.58/60.36 | | #983.
% 252.58/60.36 | |
% 252.58/60.36 | End of split
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #983 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) all_94_2 = all_38_2
% 252.58/60.36 (2) op(all_38_2, e1) = e2
% 252.58/60.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (4) ~ (all_36_2 = e2)
% 252.58/60.36 (5) op(e3, e1) = all_36_2
% 252.58/60.36 (6) all_94_2 = e3
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | COMBINE_EQS: (1), (6) imply:
% 252.58/60.36 | (7) all_38_2 = e3
% 252.58/60.36 |
% 252.58/60.36 | SIMP: (7) implies:
% 252.58/60.36 | (8) all_38_2 = e3
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (2), (8) imply:
% 252.58/60.36 | (9) op(e3, e1) = e2
% 252.58/60.36 |
% 252.58/60.36 | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #984.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #984 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (2) op(e3, e1) = all_36_2
% 252.58/60.36 (3) op(e3, e1) = e2
% 252.58/60.36 (4) ~ (all_36_2 = e2)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_36_2, e2, e1, e3, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_36_2 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #985 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (2) op(e0, e1) = all_20_2
% 252.58/60.36 (3) op(e0, e1) = e2
% 252.58/60.36 (4) ~ (all_20_2 = e2)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_20_2, e2, e1, e0, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_20_2 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #986 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ~ (all_10_2 = e1)
% 252.58/60.36 (2) ~ (all_10_2 = e4)
% 252.58/60.36 (3) ~ (all_22_2 = e2)
% 252.58/60.36 (4) op(all_38_2, e1) = e2
% 252.58/60.36 (5) all_250_13 = all_38_2
% 252.58/60.36 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (7) op(e2, e2) = all_244_8
% 252.58/60.36 (8) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 252.58/60.36 all_250_11 = e0
% 252.58/60.36 (9) ~ (all_244_8 = all_38_2)
% 252.58/60.36 (10) op(all_244_15, all_244_15) = e1
% 252.58/60.36 (11) all_250_21 = all_22_2
% 252.58/60.36 (12) ~ (all_124_2 = e0) | ( ~ (all_124_0 = e1) & op(e3, e0) = all_124_1 &
% 252.58/60.36 op(e0, all_124_1) = all_124_0 & $i(all_124_0) & $i(all_124_1)) | ( ~
% 252.58/60.36 (all_124_1 = e4) & op(e3, e0) = all_124_1 & $i(all_124_1))
% 252.58/60.36 (13) ~ (all_38_2 = e0)
% 252.58/60.36 (14) ~ (all_22_2 = e4)
% 252.58/60.36 (15) op(all_48_2, all_22_2) = e0
% 252.58/60.36 (16) ~ (all_22_2 = e1)
% 252.58/60.36 (17) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.58/60.36 all_250_13 = e0
% 252.58/60.36 (18) ~ (all_38_2 = e4)
% 252.58/60.36 (19) op(e0, e3) = all_22_2
% 252.58/60.36 (20) op(all_10_2, e3) = e2
% 252.58/60.36 (21) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 |
% 252.58/60.36 all_250_21 = e0
% 252.58/60.36 (22) all_250_11 = all_10_2
% 252.58/60.36 (23) op(e1, e1) = all_244_15
% 252.58/60.36 (24) op(all_48_2, e0) = e3
% 252.58/60.36 (25) ~ (all_22_2 = all_10_2)
% 252.58/60.36 (26) ~ (all_38_2 = all_10_2)
% 252.58/60.36 (27) ~ (all_38_2 = e3)
% 252.58/60.36 (28) all_124_2 = all_10_2
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | BETA: splitting (12) gives:
% 252.58/60.36 |
% 252.58/60.36 | Case 1:
% 252.58/60.36 | |
% 252.58/60.36 | | (29) ~ (all_124_2 = e0)
% 252.58/60.36 | |
% 252.58/60.36 | | REDUCE: (28), (29) imply:
% 252.58/60.36 | | (30) ~ (all_10_2 = e0)
% 252.58/60.36 | |
% 252.58/60.36 | | BETA: splitting (21) gives:
% 252.58/60.36 | |
% 252.58/60.36 | | Case 1:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (31) all_250_21 = e4
% 252.58/60.36 | | |
% 252.58/60.36 | | | REF_CLOSE: (11), (14), (31) are inconsistent by sub-proof #993.
% 252.58/60.36 | | |
% 252.58/60.36 | | Case 2:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (32) all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | all_250_21 =
% 252.58/60.36 | | | e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | BETA: splitting (32) gives:
% 252.58/60.36 | | |
% 252.58/60.36 | | | Case 1:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | (33) all_250_21 = e3
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | COMBINE_EQS: (11), (33) imply:
% 252.58/60.36 | | | | (34) all_22_2 = e3
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | SIMP: (34) implies:
% 252.58/60.36 | | | | (35) all_22_2 = e3
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | REDUCE: (25), (35) imply:
% 252.58/60.36 | | | | (36) ~ (all_10_2 = e3)
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13), (17),
% 252.58/60.36 | | | | (18), (22), (23), (26), (27), (30), (36) are inconsistent by
% 252.58/60.36 | | | | sub-proof #989.
% 252.58/60.36 | | | |
% 252.58/60.36 | | | Case 2:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | (37) ~ (all_250_21 = e3)
% 252.58/60.36 | | | | (38) all_250_21 = e2 | all_250_21 = e1 | all_250_21 = e0
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | REDUCE: (11), (37) imply:
% 252.58/60.36 | | | | (39) ~ (all_22_2 = e3)
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | REF_CLOSE: (3), (6), (11), (15), (16), (24), (38), (39) are inconsistent
% 252.58/60.36 | | | | by sub-proof #988.
% 252.58/60.36 | | | |
% 252.58/60.36 | | | End of split
% 252.58/60.36 | | |
% 252.58/60.36 | | End of split
% 252.58/60.36 | |
% 252.58/60.36 | Case 2:
% 252.58/60.36 | |
% 252.58/60.36 | | (40) all_124_2 = e0
% 252.58/60.36 | |
% 252.58/60.36 | | COMBINE_EQS: (28), (40) imply:
% 252.58/60.36 | | (41) all_10_2 = e0
% 252.58/60.36 | |
% 252.58/60.36 | | SIMP: (41) implies:
% 252.58/60.36 | | (42) all_10_2 = e0
% 252.58/60.36 | |
% 252.58/60.36 | | REDUCE: (20), (42) imply:
% 252.58/60.36 | | (43) op(e0, e3) = e2
% 252.58/60.36 | |
% 252.58/60.36 | | REF_CLOSE: (3), (6), (19), (43) are inconsistent by sub-proof #987.
% 252.58/60.36 | |
% 252.58/60.36 | End of split
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #987 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (2) op(e0, e3) = all_22_2
% 252.58/60.36 (3) op(e0, e3) = e2
% 252.58/60.36 (4) ~ (all_22_2 = e2)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | GROUND_INST: instantiating (1) with all_22_2, e2, e3, e0, simplifying with
% 252.58/60.36 | (2), (3) gives:
% 252.58/60.36 | (5) all_22_2 = e2
% 252.58/60.36 |
% 252.58/60.36 | REDUCE: (4), (5) imply:
% 252.58/60.36 | (6) $false
% 252.58/60.36 |
% 252.58/60.36 | CLOSE: (6) is inconsistent.
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #988 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ~ (all_22_2 = e2)
% 252.58/60.36 (2) ~ (all_22_2 = e3)
% 252.58/60.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (4) all_250_21 = all_22_2
% 252.58/60.36 (5) op(all_48_2, all_22_2) = e0
% 252.58/60.36 (6) ~ (all_22_2 = e1)
% 252.58/60.36 (7) op(all_48_2, e0) = e3
% 252.58/60.36 (8) all_250_21 = e2 | all_250_21 = e1 | all_250_21 = e0
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | BETA: splitting (8) gives:
% 252.58/60.36 |
% 252.58/60.36 | Case 1:
% 252.58/60.36 | |
% 252.58/60.36 | | (9) all_250_21 = e2
% 252.58/60.36 | |
% 252.58/60.36 | | COMBINE_EQS: (4), (9) imply:
% 252.58/60.36 | | (10) all_22_2 = e2
% 252.58/60.36 | |
% 252.58/60.36 | | SIMP: (10) implies:
% 252.58/60.36 | | (11) all_22_2 = e2
% 252.58/60.36 | |
% 252.58/60.36 | | REDUCE: (1), (11) imply:
% 252.58/60.36 | | (12) $false
% 252.58/60.36 | |
% 252.58/60.36 | | CLOSE: (12) is inconsistent.
% 252.58/60.36 | |
% 252.58/60.36 | Case 2:
% 252.58/60.36 | |
% 252.58/60.36 | | (13) all_250_21 = e1 | all_250_21 = e0
% 252.58/60.36 | |
% 252.58/60.36 | | BETA: splitting (13) gives:
% 252.58/60.36 | |
% 252.58/60.36 | | Case 1:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (14) all_250_21 = e1
% 252.58/60.36 | | |
% 252.58/60.36 | | | COMBINE_EQS: (4), (14) imply:
% 252.58/60.36 | | | (15) all_22_2 = e1
% 252.58/60.36 | | |
% 252.58/60.36 | | | SIMP: (15) implies:
% 252.58/60.36 | | | (16) all_22_2 = e1
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (6), (16) imply:
% 252.58/60.36 | | | (17) $false
% 252.58/60.36 | | |
% 252.58/60.36 | | | CLOSE: (17) is inconsistent.
% 252.58/60.36 | | |
% 252.58/60.36 | | Case 2:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (18) all_250_21 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | COMBINE_EQS: (4), (18) imply:
% 252.58/60.36 | | | (19) all_22_2 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | SIMP: (19) implies:
% 252.58/60.36 | | | (20) all_22_2 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (2), (20) imply:
% 252.58/60.36 | | | (21) ~ (e3 = e0)
% 252.58/60.36 | | |
% 252.58/60.36 | | | SIMP: (21) implies:
% 252.58/60.36 | | | (22) ~ (e3 = e0)
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (5), (20) imply:
% 252.58/60.36 | | | (23) op(all_48_2, e0) = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | GROUND_INST: instantiating (3) with e3, e0, e0, all_48_2, simplifying with
% 252.58/60.36 | | | (7), (23) gives:
% 252.58/60.36 | | | (24) e3 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (22), (24) imply:
% 252.58/60.36 | | | (25) $false
% 252.58/60.36 | | |
% 252.58/60.36 | | | CLOSE: (25) is inconsistent.
% 252.58/60.36 | | |
% 252.58/60.36 | | End of split
% 252.58/60.36 | |
% 252.58/60.36 | End of split
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #989 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) ~ (all_10_2 = e1)
% 252.58/60.36 (2) ~ (all_10_2 = e4)
% 252.58/60.36 (3) op(all_38_2, e1) = e2
% 252.58/60.36 (4) all_250_13 = all_38_2
% 252.58/60.36 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.58/60.36 (6) op(e2, e2) = all_244_8
% 252.58/60.36 (7) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 |
% 252.58/60.36 all_250_11 = e0
% 252.58/60.36 (8) ~ (all_10_2 = e3)
% 252.58/60.36 (9) ~ (all_244_8 = all_38_2)
% 252.58/60.36 (10) op(all_244_15, all_244_15) = e1
% 252.58/60.36 (11) ~ (all_38_2 = e0)
% 252.58/60.36 (12) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.58/60.36 all_250_13 = e0
% 252.58/60.36 (13) ~ (all_38_2 = e4)
% 252.58/60.36 (14) all_250_11 = all_10_2
% 252.58/60.36 (15) op(e1, e1) = all_244_15
% 252.58/60.36 (16) ~ (all_38_2 = all_10_2)
% 252.58/60.36 (17) ~ (all_10_2 = e0)
% 252.58/60.36 (18) ~ (all_38_2 = e3)
% 252.58/60.36
% 252.58/60.36 Begin of proof
% 252.58/60.36 |
% 252.58/60.36 | SIMP: (8) implies:
% 252.58/60.36 | (19) ~ (all_10_2 = e3)
% 252.58/60.36 |
% 252.58/60.36 | BETA: splitting (7) gives:
% 252.58/60.36 |
% 252.58/60.36 | Case 1:
% 252.58/60.36 | |
% 252.58/60.36 | | (20) all_250_11 = e4
% 252.58/60.36 | |
% 252.58/60.36 | | COMBINE_EQS: (14), (20) imply:
% 252.58/60.36 | | (21) all_10_2 = e4
% 252.58/60.36 | |
% 252.58/60.36 | | SIMP: (21) implies:
% 252.58/60.36 | | (22) all_10_2 = e4
% 252.58/60.36 | |
% 252.58/60.36 | | REDUCE: (2), (22) imply:
% 252.58/60.36 | | (23) $false
% 252.58/60.36 | |
% 252.58/60.36 | | CLOSE: (23) is inconsistent.
% 252.58/60.36 | |
% 252.58/60.36 | Case 2:
% 252.58/60.36 | |
% 252.58/60.36 | | (24) all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | all_250_11 =
% 252.58/60.36 | | e0
% 252.58/60.36 | |
% 252.58/60.36 | | BETA: splitting (24) gives:
% 252.58/60.36 | |
% 252.58/60.36 | | Case 1:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (25) all_250_11 = e3
% 252.58/60.36 | | |
% 252.58/60.36 | | | COMBINE_EQS: (14), (25) imply:
% 252.58/60.36 | | | (26) all_10_2 = e3
% 252.58/60.36 | | |
% 252.58/60.36 | | | SIMP: (26) implies:
% 252.58/60.36 | | | (27) all_10_2 = e3
% 252.58/60.36 | | |
% 252.58/60.36 | | | REDUCE: (19), (27) imply:
% 252.58/60.36 | | | (28) $false
% 252.58/60.36 | | |
% 252.58/60.36 | | | CLOSE: (28) is inconsistent.
% 252.58/60.36 | | |
% 252.58/60.36 | | Case 2:
% 252.58/60.36 | | |
% 252.58/60.36 | | | (29) all_250_11 = e2 | all_250_11 = e1 | all_250_11 = e0
% 252.58/60.36 | | |
% 252.58/60.36 | | | BETA: splitting (29) gives:
% 252.58/60.36 | | |
% 252.58/60.36 | | | Case 1:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | (30) all_250_11 = e2
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | COMBINE_EQS: (14), (30) imply:
% 252.58/60.36 | | | | (31) all_10_2 = e2
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | SIMP: (31) implies:
% 252.58/60.36 | | | | (32) all_10_2 = e2
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | REDUCE: (16), (32) imply:
% 252.58/60.36 | | | | (33) ~ (all_38_2 = e2)
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | BETA: splitting (12) gives:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | Case 1:
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | (34) all_250_13 = e4
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | REF_CLOSE: (4), (13), (34) are inconsistent by sub-proof #992.
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | Case 2:
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | (35) all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 |
% 252.58/60.36 | | | | | all_250_13 = e0
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | BETA: splitting (35) gives:
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | Case 1:
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | (36) all_250_13 = e3
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | COMBINE_EQS: (4), (36) imply:
% 252.58/60.36 | | | | | | (37) all_38_2 = e3
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | SIMP: (37) implies:
% 252.58/60.36 | | | | | | (38) all_38_2 = e3
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | REDUCE: (18), (38) imply:
% 252.58/60.36 | | | | | | (39) $false
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | CLOSE: (39) is inconsistent.
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | Case 2:
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | (40) all_250_13 = e2 | all_250_13 = e1 | all_250_13 = e0
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (11), (15), (33), (40) are
% 252.58/60.36 | | | | | | inconsistent by sub-proof #990.
% 252.58/60.36 | | | | | |
% 252.58/60.36 | | | | | End of split
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | End of split
% 252.58/60.36 | | | |
% 252.58/60.36 | | | Case 2:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | (41) all_250_11 = e1 | all_250_11 = e0
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | BETA: splitting (41) gives:
% 252.58/60.36 | | | |
% 252.58/60.36 | | | | Case 1:
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | (42) all_250_11 = e1
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | COMBINE_EQS: (14), (42) imply:
% 252.58/60.36 | | | | | (43) all_10_2 = e1
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | REDUCE: (1), (43) imply:
% 252.58/60.36 | | | | | (44) $false
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | CLOSE: (44) is inconsistent.
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | Case 2:
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | (45) all_250_11 = e0
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | COMBINE_EQS: (14), (45) imply:
% 252.58/60.36 | | | | | (46) all_10_2 = e0
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | REDUCE: (17), (46) imply:
% 252.58/60.36 | | | | | (47) $false
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | | CLOSE: (47) is inconsistent.
% 252.58/60.36 | | | | |
% 252.58/60.36 | | | | End of split
% 252.58/60.36 | | | |
% 252.58/60.36 | | | End of split
% 252.58/60.36 | | |
% 252.58/60.36 | | End of split
% 252.58/60.36 | |
% 252.58/60.36 | End of split
% 252.58/60.36 |
% 252.58/60.36 End of proof
% 252.58/60.36
% 252.58/60.36 Sub-proof #990 shows that the following formulas are inconsistent:
% 252.58/60.36 ----------------------------------------------------------------
% 252.58/60.36 (1) all_250_13 = e2 | all_250_13 = e1 | all_250_13 = e0
% 252.58/60.36 (2) op(all_38_2, e1) = e2
% 252.58/60.36 (3) all_250_13 = all_38_2
% 252.58/60.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.58/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.68/60.36 (5) op(e2, e2) = all_244_8
% 252.68/60.36 (6) ~ (all_244_8 = all_38_2)
% 252.68/60.36 (7) op(all_244_15, all_244_15) = e1
% 252.68/60.36 (8) ~ (all_38_2 = e0)
% 252.68/60.36 (9) ~ (all_38_2 = e2)
% 252.68/60.36 (10) op(e1, e1) = all_244_15
% 252.68/60.36
% 252.68/60.36 Begin of proof
% 252.68/60.36 |
% 252.68/60.36 | BETA: splitting (1) gives:
% 252.68/60.36 |
% 252.68/60.36 | Case 1:
% 252.68/60.36 | |
% 252.68/60.36 | | (11) all_250_13 = e2
% 252.68/60.36 | |
% 252.68/60.36 | | COMBINE_EQS: (3), (11) imply:
% 252.68/60.36 | | (12) all_38_2 = e2
% 252.68/60.36 | |
% 252.68/60.36 | | SIMP: (12) implies:
% 252.68/60.36 | | (13) all_38_2 = e2
% 252.68/60.36 | |
% 252.68/60.36 | | REDUCE: (9), (13) imply:
% 252.68/60.36 | | (14) $false
% 252.68/60.36 | |
% 252.68/60.36 | | CLOSE: (14) is inconsistent.
% 252.68/60.36 | |
% 252.68/60.36 | Case 2:
% 252.68/60.36 | |
% 252.68/60.36 | | (15) all_250_13 = e1 | all_250_13 = e0
% 252.68/60.36 | |
% 252.68/60.36 | | BETA: splitting (15) gives:
% 252.68/60.36 | |
% 252.68/60.36 | | Case 1:
% 252.68/60.36 | | |
% 252.68/60.36 | | | (16) all_250_13 = e1
% 252.68/60.36 | | |
% 252.68/60.36 | | | COMBINE_EQS: (3), (16) imply:
% 252.68/60.36 | | | (17) all_38_2 = e1
% 252.68/60.36 | | |
% 252.68/60.36 | | | SIMP: (17) implies:
% 252.68/60.36 | | | (18) all_38_2 = e1
% 252.68/60.36 | | |
% 252.68/60.36 | | | REDUCE: (6), (18) imply:
% 252.68/60.36 | | | (19) ~ (all_244_8 = e1)
% 252.68/60.36 | | |
% 252.68/60.36 | | | REDUCE: (2), (18) imply:
% 252.68/60.36 | | | (20) op(e1, e1) = e2
% 252.68/60.36 | | |
% 252.68/60.36 | | | REF_CLOSE: (4), (5), (7), (10), (19), (20) are inconsistent by sub-proof
% 252.68/60.36 | | | #991.
% 252.68/60.36 | | |
% 252.68/60.36 | | Case 2:
% 252.68/60.36 | | |
% 252.68/60.36 | | | (21) all_250_13 = e0
% 252.68/60.36 | | |
% 252.68/60.36 | | | COMBINE_EQS: (3), (21) imply:
% 252.68/60.36 | | | (22) all_38_2 = e0
% 252.68/60.36 | | |
% 252.68/60.36 | | | SIMP: (22) implies:
% 252.68/60.36 | | | (23) all_38_2 = e0
% 252.68/60.36 | | |
% 252.68/60.36 | | | REDUCE: (8), (23) imply:
% 252.68/60.36 | | | (24) $false
% 252.68/60.36 | | |
% 252.68/60.36 | | | CLOSE: (24) is inconsistent.
% 252.68/60.36 | | |
% 252.68/60.36 | | End of split
% 252.68/60.36 | |
% 252.68/60.36 | End of split
% 252.68/60.36 |
% 252.68/60.36 End of proof
% 252.68/60.36
% 252.68/60.36 Sub-proof #991 shows that the following formulas are inconsistent:
% 252.68/60.36 ----------------------------------------------------------------
% 252.68/60.36 (1) op(e1, e1) = e2
% 252.68/60.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 252.68/60.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 252.68/60.36 (3) op(e2, e2) = all_244_8
% 252.68/60.36 (4) op(all_244_15, all_244_15) = e1
% 252.68/60.36 (5) ~ (all_244_8 = e1)
% 252.68/60.36 (6) op(e1, e1) = all_244_15
% 252.68/60.36
% 252.68/60.36 Begin of proof
% 252.68/60.36 |
% 252.68/60.36 | GROUND_INST: instantiating (2) with all_244_15, e2, e1, e1, simplifying with
% 252.68/60.36 | (1), (6) gives:
% 252.68/60.36 | (7) all_244_15 = e2
% 252.68/60.36 |
% 252.68/60.36 | REDUCE: (4), (7) imply:
% 252.68/60.36 | (8) op(e2, e2) = e1
% 252.68/60.36 |
% 252.68/60.36 | GROUND_INST: instantiating (2) with all_244_8, e1, e2, e2, simplifying with
% 252.68/60.36 | (3), (8) gives:
% 252.68/60.36 | (9) all_244_8 = e1
% 252.68/60.36 |
% 252.68/60.36 | REDUCE: (5), (9) imply:
% 252.68/60.36 | (10) $false
% 252.68/60.36 |
% 252.68/60.36 | CLOSE: (10) is inconsistent.
% 252.68/60.36 |
% 252.68/60.36 End of proof
% 252.68/60.36
% 252.68/60.36 Sub-proof #992 shows that the following formulas are inconsistent:
% 252.68/60.36 ----------------------------------------------------------------
% 252.68/60.36 (1) all_250_13 = all_38_2
% 252.68/60.36 (2) all_250_13 = e4
% 252.68/60.36 (3) ~ (all_38_2 = e4)
% 252.68/60.36
% 252.68/60.36 Begin of proof
% 252.68/60.36 |
% 252.68/60.36 | COMBINE_EQS: (1), (2) imply:
% 252.68/60.36 | (4) all_38_2 = e4
% 252.68/60.36 |
% 252.68/60.36 | SIMP: (4) implies:
% 252.68/60.36 | (5) all_38_2 = e4
% 252.68/60.36 |
% 252.68/60.36 | REDUCE: (3), (5) imply:
% 252.68/60.36 | (6) $false
% 252.68/60.36 |
% 252.68/60.36 | CLOSE: (6) is inconsistent.
% 252.68/60.36 |
% 252.68/60.36 End of proof
% 252.68/60.36
% 252.68/60.36 Sub-proof #993 shows that the following formulas are inconsistent:
% 252.68/60.36 ----------------------------------------------------------------
% 252.68/60.36 (1) all_250_21 = all_22_2
% 252.68/60.36 (2) all_250_21 = e4
% 252.68/60.36 (3) ~ (all_22_2 = e4)
% 252.68/60.36
% 252.68/60.36 Begin of proof
% 252.68/60.36 |
% 252.68/60.36 | COMBINE_EQS: (1), (2) imply:
% 252.68/60.36 | (4) all_22_2 = e4
% 252.68/60.36 |
% 252.68/60.36 | SIMP: (4) implies:
% 252.68/60.36 | (5) all_22_2 = e4
% 252.68/60.36 |
% 252.68/60.36 | REDUCE: (3), (5) imply:
% 252.68/60.36 | (6) $false
% 252.68/60.36 |
% 252.68/60.36 | CLOSE: (6) is inconsistent.
% 252.68/60.36 |
% 252.68/60.36 End of proof
% 252.68/60.36 % SZS output end Proof for theBenchmark
% 252.68/60.37
% 252.68/60.37 59756ms
%------------------------------------------------------------------------------