TSTP Solution File: KRS102+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS102+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:51:15 EDT 2023
% Result : Unsatisfiable 12.46s 2.42s
% Output : Proof 16.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS102+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 02:12:07 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.16 Prover 1: Preprocessing ...
% 3.32/1.16 Prover 4: Preprocessing ...
% 3.32/1.19 Prover 5: Preprocessing ...
% 3.32/1.19 Prover 6: Preprocessing ...
% 3.32/1.19 Prover 0: Preprocessing ...
% 3.65/1.20 Prover 2: Preprocessing ...
% 3.65/1.21 Prover 3: Preprocessing ...
% 6.25/1.58 Prover 6: Constructing countermodel ...
% 6.25/1.59 Prover 2: Proving ...
% 6.25/1.59 Prover 3: Constructing countermodel ...
% 6.25/1.60 Prover 5: Proving ...
% 6.43/1.60 Prover 0: Proving ...
% 6.43/1.62 Prover 4: Constructing countermodel ...
% 6.60/1.63 Prover 1: Constructing countermodel ...
% 7.88/1.86 Prover 3: gave up
% 7.88/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.78/1.94 Prover 7: Preprocessing ...
% 8.78/2.03 Prover 6: gave up
% 8.78/2.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.78/2.08 Prover 7: Warning: ignoring some quantifiers
% 8.78/2.09 Prover 7: Constructing countermodel ...
% 8.78/2.09 Prover 1: gave up
% 8.78/2.10 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.78/2.11 Prover 8: Preprocessing ...
% 9.93/2.13 Prover 4: gave up
% 9.93/2.13 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.93/2.18 Prover 10: Preprocessing ...
% 10.72/2.20 Prover 9: Preprocessing ...
% 10.72/2.23 Prover 8: Warning: ignoring some quantifiers
% 10.72/2.24 Prover 8: Constructing countermodel ...
% 11.52/2.31 Prover 9: Constructing countermodel ...
% 11.70/2.32 Prover 10: Warning: ignoring some quantifiers
% 11.70/2.33 Prover 10: Constructing countermodel ...
% 12.46/2.42 Prover 9: gave up
% 12.46/2.42 Prover 2: proved (1796ms)
% 12.46/2.42
% 12.46/2.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.46/2.42
% 12.46/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.46/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.46/2.42 Prover 5: stopped
% 12.46/2.43 Prover 0: stopped
% 12.46/2.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.46/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.46/2.44 Prover 8: gave up
% 12.46/2.46 Prover 11: Preprocessing ...
% 12.46/2.49 Prover 13: Preprocessing ...
% 13.02/2.50 Prover 19: Preprocessing ...
% 13.02/2.50 Prover 16: Preprocessing ...
% 13.02/2.54 Prover 13: Warning: ignoring some quantifiers
% 13.02/2.55 Prover 13: Constructing countermodel ...
% 13.02/2.57 Prover 16: Warning: ignoring some quantifiers
% 13.61/2.58 Prover 16: Constructing countermodel ...
% 13.79/2.61 Prover 11: Constructing countermodel ...
% 13.79/2.65 Prover 19: Warning: ignoring some quantifiers
% 13.79/2.66 Prover 19: Constructing countermodel ...
% 14.34/2.76 Prover 11: gave up
% 15.87/2.89 Prover 7: Found proof (size 3478)
% 15.87/2.89 Prover 7: proved (1035ms)
% 15.87/2.89 Prover 19: stopped
% 15.87/2.89 Prover 16: stopped
% 15.87/2.90 Prover 10: Found proof (size 3006)
% 15.87/2.90 Prover 10: proved (766ms)
% 15.87/2.90 Prover 13: stopped
% 15.87/2.90
% 15.87/2.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.87/2.90
% 15.87/2.93 % SZS output start Proof for theBenchmark
% 15.87/2.93 Assumptions after simplification:
% 15.87/2.93 ---------------------------------
% 15.87/2.93
% 15.87/2.93 (axiom_10)
% 15.87/2.94 $i(iplus6) & $i(iminus6) & cTorF(iplus6) & cTorF(iminus6) & ! [v0: $i] : (v0
% 15.87/2.94 = iplus6 | v0 = iminus6 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.94
% 15.87/2.94 (axiom_11)
% 15.87/2.94 $i(iplus9) & $i(iminus9) & cTorF(iplus9) & cTorF(iminus9) & ! [v0: $i] : (v0
% 15.87/2.94 = iplus9 | v0 = iminus9 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.94
% 15.87/2.94 (axiom_15)
% 15.87/2.94 $i(iplus8) & $i(iT) & $i(iminus3) & $i(iplus7) & (iplus8 = iT | iT = iminus3 |
% 15.87/2.94 iT = iplus7)
% 15.87/2.94
% 15.87/2.94 (axiom_17)
% 15.87/2.94 $i(iplus9) & $i(iminus6) & $i(iT) & $i(iplus1) & (iplus9 = iT | iminus6 = iT |
% 15.87/2.94 iT = iplus1)
% 15.87/2.94
% 15.87/2.94 (axiom_18)
% 15.87/2.94 $i(iminus9) & $i(iT) & $i(iplus3) & $i(iplus4) & (iminus9 = iT | iT = iplus3 |
% 15.87/2.94 iT = iplus4)
% 15.87/2.94
% 15.87/2.94 (axiom_19)
% 15.87/2.94 $i(iminus9) & $i(iminus6) & $i(iT) & $i(iplus1) & (iminus9 = iT | iminus6 = iT
% 15.87/2.94 | iT = iplus1)
% 15.87/2.94
% 15.87/2.94 (axiom_2)
% 15.87/2.94 $i(iminus1) & $i(iplus1) & cTorF(iminus1) & cTorF(iplus1) & ! [v0: $i] : (v0
% 15.87/2.94 = iminus1 | v0 = iplus1 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.94
% 15.87/2.94 (axiom_22)
% 15.87/2.94 $i(iplus6) & $i(iT) & $i(iplus3) & $i(iplus4) & (iplus6 = iT | iT = iplus3 |
% 15.87/2.94 iT = iplus4)
% 15.87/2.94
% 15.87/2.94 (axiom_24)
% 15.87/2.94 $i(iminus8) & $i(iT) & $i(iplus3) & $i(iminus2) & (iminus8 = iT | iT = iplus3
% 15.87/2.94 | iT = iminus2)
% 15.87/2.94
% 15.87/2.94 (axiom_26)
% 15.87/2.94 $i(iminus9) & $i(iT) & $i(iplus3) & $i(iminus2) & (iminus9 = iT | iT = iplus3
% 15.87/2.94 | iT = iminus2)
% 15.87/2.94
% 15.87/2.94 (axiom_27)
% 15.87/2.95 $i(iplus6) & $i(iT) & $i(iminus7) & $i(iminus2) & (iplus6 = iT | iT = iminus7
% 15.87/2.95 | iT = iminus2)
% 15.87/2.95
% 15.87/2.95 (axiom_3)
% 15.87/2.95 $i(iplus4) & $i(iminus4) & cTorF(iplus4) & cTorF(iminus4) & ! [v0: $i] : (v0
% 15.87/2.95 = iplus4 | v0 = iminus4 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.95
% 15.87/2.95 (axiom_31)
% 15.87/2.95 $i(iplus8) & $i(iT) & $i(iplus2) & $i(iminus4) & (iplus8 = iT | iT = iplus2 |
% 15.87/2.95 iT = iminus4)
% 15.87/2.95
% 15.87/2.95 (axiom_34)
% 15.87/2.95 $i(iplus8) & $i(iT) & $i(iminus5) & $i(iplus7) & (iplus8 = iT | iT = iminus5 |
% 15.87/2.95 iT = iplus7)
% 15.87/2.95
% 15.87/2.95 (axiom_36)
% 15.87/2.95 $i(iT) & $i(iminus3) & $i(iminus7) & $i(iminus4) & (iT = iminus3 | iT =
% 15.87/2.95 iminus7 | iT = iminus4)
% 15.87/2.95
% 15.87/2.95 (axiom_38)
% 15.87/2.95 $i(iT) & $i(iminus3) & $i(iminus2) & $i(iplus1) & (iT = iminus3 | iT = iminus2
% 15.87/2.95 | iT = iplus1)
% 15.87/2.95
% 15.87/2.95 (axiom_39)
% 15.87/2.95 $i(iplus6) & $i(iT) & $i(iplus3) & $i(iminus4) & (iplus6 = iT | iT = iplus3 |
% 15.87/2.95 iT = iminus4)
% 15.87/2.95
% 15.87/2.95 (axiom_4)
% 15.87/2.95 $i(iminus2) & $i(iplus2) & cTorF(iminus2) & cTorF(iplus2) & ! [v0: $i] : (v0
% 15.87/2.95 = iminus2 | v0 = iplus2 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.95
% 15.87/2.95 (axiom_40)
% 15.87/2.95 $i(iminus9) & $i(iminus8) & $i(iT) & $i(iminus4) & (iminus9 = iT | iminus8 =
% 15.87/2.95 iT | iT = iminus4)
% 15.87/2.95
% 15.87/2.95 (axiom_41)
% 15.87/2.95 $i(iT) & $i(iplus3) & $i(iplus4) & $i(iplus1) & (iT = iplus3 | iT = iplus4 |
% 15.87/2.95 iT = iplus1)
% 15.87/2.95
% 15.87/2.95 (axiom_42)
% 15.87/2.95 $i(iplus8) & $i(iT) & $i(iminus3) & $i(iplus2) & (iplus8 = iT | iT = iminus3 |
% 15.87/2.95 iT = iplus2)
% 15.87/2.95
% 15.87/2.95 (axiom_43)
% 15.87/2.95 $i(iplus9) & $i(iminus8) & $i(iT) & $i(iplus3) & (iplus9 = iT | iminus8 = iT |
% 15.87/2.95 iT = iplus3)
% 15.87/2.95
% 15.87/2.95 (axiom_44)
% 15.87/2.96 $i(iplus8) & $i(iT) & $i(iplus3) & $i(iminus7) & (iplus8 = iT | iT = iplus3 |
% 15.87/2.96 iT = iminus7)
% 15.87/2.96
% 15.87/2.96 (axiom_45)
% 15.87/2.96 $i(iminus8) & $i(iT) & $i(iminus3) & $i(iminus5) & (iminus8 = iT | iT =
% 15.87/2.96 iminus3 | iT = iminus5)
% 15.87/2.96
% 15.87/2.96 (axiom_46)
% 15.87/2.96 $i(iplus9) & $i(iT) & $i(iplus3) & $i(iplus4) & (iplus9 = iT | iT = iplus3 |
% 15.87/2.96 iT = iplus4)
% 15.87/2.96
% 15.87/2.96 (axiom_49)
% 15.87/2.96 $i(iminus8) & $i(iT) & $i(iminus3) & $i(iplus5) & (iminus8 = iT | iT = iminus3
% 15.87/2.96 | iT = iplus5)
% 15.87/2.96
% 15.87/2.96 (axiom_5)
% 15.87/2.96 $i(iminus7) & $i(iplus7) & cTorF(iminus7) & cTorF(iplus7) & ! [v0: $i] : (v0
% 15.87/2.96 = iminus7 | v0 = iplus7 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.96
% 15.87/2.96 (axiom_56)
% 15.87/2.96 $i(iminus6) & $i(iT) & $i(iminus2) & $i(iplus4) & (iminus6 = iT | iT = iminus2
% 15.87/2.96 | iT = iplus4)
% 15.87/2.96
% 15.87/2.96 (axiom_58)
% 15.87/2.96 $i(iplus9) & $i(iT) & $i(iplus7) & $i(iminus4) & (iplus9 = iT | iT = iplus7 |
% 15.87/2.96 iT = iminus4)
% 15.87/2.96
% 15.87/2.96 (axiom_6)
% 15.87/2.96 $i(iminus5) & $i(iplus5) & cTorF(iminus5) & cTorF(iplus5) & ! [v0: $i] : (v0
% 15.87/2.96 = iminus5 | v0 = iplus5 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.96
% 15.87/2.96 (axiom_7)
% 15.87/2.96 $i(iminus3) & $i(iplus3) & cTorF(iminus3) & cTorF(iplus3) & ! [v0: $i] : (v0
% 15.87/2.96 = iminus3 | v0 = iplus3 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.96
% 15.87/2.96 (axiom_77)
% 15.87/2.96 ~ (iF = iT) & $i(iF) & $i(iT)
% 15.87/2.96
% 15.87/2.96 (axiom_8)
% 15.87/2.96 $i(iF) & $i(iT) & cTorF(iF) & cTorF(iT) & ! [v0: $i] : (v0 = iF | v0 = iT |
% 15.87/2.96 ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.96
% 15.87/2.96 (axiom_9)
% 15.87/2.96 $i(iminus8) & $i(iplus8) & cTorF(iminus8) & cTorF(iplus8) & ! [v0: $i] : (v0
% 15.87/2.96 = iminus8 | v0 = iplus8 | ~ $i(v0) | ~ cTorF(v0))
% 15.87/2.96
% 15.87/2.96 Further assumptions not needed in the proof:
% 15.87/2.96 --------------------------------------------
% 15.87/2.96 axiom_0, axiom_1, axiom_12, axiom_13, axiom_14, axiom_16, axiom_20, axiom_21,
% 15.87/2.96 axiom_23, axiom_25, axiom_28, axiom_29, axiom_30, axiom_32, axiom_33, axiom_35,
% 15.87/2.96 axiom_37, axiom_47, axiom_48, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54,
% 15.87/2.96 axiom_55, axiom_57, axiom_59, axiom_60, axiom_61, axiom_62, axiom_63, axiom_64,
% 15.87/2.96 axiom_65, axiom_66, axiom_67, axiom_68, axiom_69, axiom_70, axiom_71, axiom_72,
% 15.87/2.96 axiom_73, axiom_74, axiom_75, axiom_76, cTorF_substitution_1,
% 15.87/2.96 cowlNothing_substitution_1, cowlThing_substitution_1,
% 15.87/2.96 xsd_integer_substitution_1, xsd_string_substitution_1
% 15.87/2.96
% 15.87/2.96 Those formulas are unsatisfiable:
% 15.87/2.96 ---------------------------------
% 15.87/2.96
% 15.87/2.96 Begin of proof
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_77) implies:
% 15.87/2.97 | (1) ~ (iF = iT)
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_58) implies:
% 15.87/2.97 | (2) iplus9 = iT | iT = iplus7 | iT = iminus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_56) implies:
% 15.87/2.97 | (3) iminus6 = iT | iT = iminus2 | iT = iplus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_49) implies:
% 15.87/2.97 | (4) iminus8 = iT | iT = iminus3 | iT = iplus5
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_46) implies:
% 15.87/2.97 | (5) iplus9 = iT | iT = iplus3 | iT = iplus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_45) implies:
% 15.87/2.97 | (6) iminus8 = iT | iT = iminus3 | iT = iminus5
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_44) implies:
% 15.87/2.97 | (7) iplus8 = iT | iT = iplus3 | iT = iminus7
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_43) implies:
% 15.87/2.97 | (8) iplus9 = iT | iminus8 = iT | iT = iplus3
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_42) implies:
% 15.87/2.97 | (9) iplus8 = iT | iT = iminus3 | iT = iplus2
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_41) implies:
% 15.87/2.97 | (10) iT = iplus3 | iT = iplus4 | iT = iplus1
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_40) implies:
% 15.87/2.97 | (11) iminus9 = iT | iminus8 = iT | iT = iminus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_39) implies:
% 15.87/2.97 | (12) iplus6 = iT | iT = iplus3 | iT = iminus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_38) implies:
% 15.87/2.97 | (13) iT = iminus3 | iT = iminus2 | iT = iplus1
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_36) implies:
% 15.87/2.97 | (14) iT = iminus3 | iT = iminus7 | iT = iminus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_34) implies:
% 15.87/2.97 | (15) iplus8 = iT | iT = iminus5 | iT = iplus7
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_31) implies:
% 15.87/2.97 | (16) iplus8 = iT | iT = iplus2 | iT = iminus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_27) implies:
% 15.87/2.97 | (17) iplus6 = iT | iT = iminus7 | iT = iminus2
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_26) implies:
% 15.87/2.97 | (18) iminus9 = iT | iT = iplus3 | iT = iminus2
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_24) implies:
% 15.87/2.97 | (19) iminus8 = iT | iT = iplus3 | iT = iminus2
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_22) implies:
% 15.87/2.97 | (20) iplus6 = iT | iT = iplus3 | iT = iplus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_19) implies:
% 15.87/2.97 | (21) iminus9 = iT | iminus6 = iT | iT = iplus1
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_18) implies:
% 15.87/2.97 | (22) iminus9 = iT | iT = iplus3 | iT = iplus4
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_17) implies:
% 15.87/2.97 | (23) iplus9 = iT | iminus6 = iT | iT = iplus1
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_15) implies:
% 15.87/2.97 | (24) iplus8 = iT | iT = iminus3 | iT = iplus7
% 15.87/2.97 |
% 15.87/2.97 | ALPHA: (axiom_11) implies:
% 16.34/2.97 | (25) cTorF(iplus9)
% 16.34/2.97 | (26) $i(iplus9)
% 16.34/2.97 | (27) ! [v0: $i] : (v0 = iplus9 | v0 = iminus9 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.97 |
% 16.34/2.97 | ALPHA: (axiom_10) implies:
% 16.34/2.97 | (28) cTorF(iminus6)
% 16.34/2.97 | (29) $i(iminus6)
% 16.34/2.97 | (30) ! [v0: $i] : (v0 = iplus6 | v0 = iminus6 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.97 |
% 16.34/2.97 | ALPHA: (axiom_9) implies:
% 16.34/2.98 | (31) cTorF(iplus8)
% 16.34/2.98 | (32) cTorF(iminus8)
% 16.34/2.98 | (33) $i(iplus8)
% 16.34/2.98 | (34) $i(iminus8)
% 16.34/2.98 | (35) ! [v0: $i] : (v0 = iminus8 | v0 = iplus8 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_8) implies:
% 16.34/2.98 | (36) cTorF(iT)
% 16.34/2.98 | (37) cTorF(iF)
% 16.34/2.98 | (38) $i(iT)
% 16.34/2.98 | (39) $i(iF)
% 16.34/2.98 | (40) ! [v0: $i] : (v0 = iF | v0 = iT | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_7) implies:
% 16.34/2.98 | (41) cTorF(iplus3)
% 16.34/2.98 | (42) cTorF(iminus3)
% 16.34/2.98 | (43) $i(iplus3)
% 16.34/2.98 | (44) $i(iminus3)
% 16.34/2.98 | (45) ! [v0: $i] : (v0 = iminus3 | v0 = iplus3 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_6) implies:
% 16.34/2.98 | (46) cTorF(iplus5)
% 16.34/2.98 | (47) $i(iplus5)
% 16.34/2.98 | (48) ! [v0: $i] : (v0 = iminus5 | v0 = iplus5 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_5) implies:
% 16.34/2.98 | (49) ! [v0: $i] : (v0 = iminus7 | v0 = iplus7 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_4) implies:
% 16.34/2.98 | (50) cTorF(iminus2)
% 16.34/2.98 | (51) $i(iminus2)
% 16.34/2.98 | (52) ! [v0: $i] : (v0 = iminus2 | v0 = iplus2 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_3) implies:
% 16.34/2.98 | (53) ! [v0: $i] : (v0 = iplus4 | v0 = iminus4 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | ALPHA: (axiom_2) implies:
% 16.34/2.98 | (54) cTorF(iminus1)
% 16.34/2.98 | (55) $i(iminus1)
% 16.34/2.98 | (56) ! [v0: $i] : (v0 = iminus1 | v0 = iplus1 | ~ $i(v0) | ~ cTorF(v0))
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (30) with iminus1, simplifying with (54), (55)
% 16.34/2.98 | gives:
% 16.34/2.98 | (57) iplus6 = iminus1 | iminus6 = iminus1
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (49) with iminus1, simplifying with (54), (55)
% 16.34/2.98 | gives:
% 16.34/2.98 | (58) iminus7 = iminus1 | iplus7 = iminus1
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (56) with iminus2, simplifying with (50), (51)
% 16.34/2.98 | gives:
% 16.34/2.98 | (59) iminus2 = iminus1 | iminus2 = iplus1
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (52) with iplus5, simplifying with (46), (47)
% 16.34/2.98 | gives:
% 16.34/2.98 | (60) iplus5 = iminus2 | iplus5 = iplus2
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (40) with iplus3, simplifying with (41), (43)
% 16.34/2.98 | gives:
% 16.34/2.98 | (61) iF = iplus3 | iT = iplus3
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (49) with iplus3, simplifying with (41), (43)
% 16.34/2.98 | gives:
% 16.34/2.98 | (62) iplus3 = iminus7 | iplus3 = iplus7
% 16.34/2.98 |
% 16.34/2.98 | GROUND_INST: instantiating (35) with iminus3, simplifying with (42), (44)
% 16.34/2.98 | gives:
% 16.34/2.99 | (63) iminus8 = iminus3 | iplus8 = iminus3
% 16.34/2.99 |
% 16.34/2.99 | GROUND_INST: instantiating (53) with iminus3, simplifying with (42), (44)
% 16.34/2.99 | gives:
% 16.34/2.99 | (64) iminus3 = iplus4 | iminus3 = iminus4
% 16.34/2.99 |
% 16.34/2.99 | GROUND_INST: instantiating (45) with iT, simplifying with (36), (38) gives:
% 16.34/2.99 | (65) iT = iminus3 | iT = iplus3
% 16.34/2.99 |
% 16.34/2.99 | GROUND_INST: instantiating (27) with iF, simplifying with (37), (39) gives:
% 16.34/2.99 | (66) iplus9 = iF | iminus9 = iF
% 16.34/2.99 |
% 16.34/2.99 | GROUND_INST: instantiating (30) with iF, simplifying with (37), (39) gives:
% 16.34/2.99 | (67) iplus6 = iF | iminus6 = iF
% 16.34/2.99 |
% 16.34/2.99 | GROUND_INST: instantiating (35) with iF, simplifying with (37), (39) gives:
% 16.34/2.99 | (68) iminus8 = iF | iplus8 = iF
% 16.34/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (45) with iF, simplifying with (37), (39) gives:
% 16.41/2.99 | (69) iF = iminus3 | iF = iplus3
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (53) with iF, simplifying with (37), (39) gives:
% 16.41/2.99 | (70) iF = iplus4 | iF = iminus4
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (56) with iF, simplifying with (37), (39) gives:
% 16.41/2.99 | (71) iF = iminus1 | iF = iplus1
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (40) with iplus8, simplifying with (31), (33)
% 16.41/2.99 | gives:
% 16.41/2.99 | (72) iplus8 = iF | iplus8 = iT
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (48) with iplus8, simplifying with (31), (33)
% 16.41/2.99 | gives:
% 16.41/2.99 | (73) iplus8 = iminus5 | iplus8 = iplus5
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (52) with iplus8, simplifying with (31), (33)
% 16.41/2.99 | gives:
% 16.41/2.99 | (74) iplus8 = iminus2 | iplus8 = iplus2
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (53) with iplus8, simplifying with (31), (33)
% 16.41/2.99 | gives:
% 16.41/2.99 | (75) iplus8 = iplus4 | iplus8 = iminus4
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (48) with iminus8, simplifying with (32), (34)
% 16.41/2.99 | gives:
% 16.41/2.99 | (76) iminus8 = iminus5 | iminus8 = iplus5
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (53) with iminus6, simplifying with (28), (29)
% 16.41/2.99 | gives:
% 16.41/2.99 | (77) iminus6 = iplus4 | iminus6 = iminus4
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (40) with iplus9, simplifying with (25), (26)
% 16.41/2.99 | gives:
% 16.41/2.99 | (78) iplus9 = iF | iplus9 = iT
% 16.41/2.99 |
% 16.41/2.99 | GROUND_INST: instantiating (56) with iplus9, simplifying with (25), (26)
% 16.41/2.99 | gives:
% 16.41/2.99 | (79) iplus9 = iminus1 | iplus9 = iplus1
% 16.41/2.99 |
% 16.41/2.99 | BETA: splitting (10) gives:
% 16.41/2.99 |
% 16.41/2.99 | Case 1:
% 16.41/2.99 | |
% 16.41/2.99 | | (80) iT = iplus3
% 16.41/2.99 | |
% 16.41/2.99 | | REDUCE: (1), (80) imply:
% 16.41/2.99 | | (81) ~ (iF = iplus3)
% 16.41/2.99 | |
% 16.41/2.99 | | BETA: splitting (69) gives:
% 16.41/2.99 | |
% 16.41/2.99 | | Case 1:
% 16.41/2.99 | | |
% 16.41/2.99 | | | (82) iF = iplus3
% 16.41/2.99 | | |
% 16.41/2.99 | | | REDUCE: (81), (82) imply:
% 16.41/2.99 | | | (83) $false
% 16.41/2.99 | | |
% 16.41/2.99 | | | CLOSE: (83) is inconsistent.
% 16.41/2.99 | | |
% 16.41/2.99 | | Case 2:
% 16.41/2.99 | | |
% 16.41/2.99 | | | (84) iF = iminus3
% 16.41/2.99 | | |
% 16.41/2.99 | | | REDUCE: (81), (84) imply:
% 16.41/2.99 | | | (85) ~ (iminus3 = iplus3)
% 16.41/2.99 | | |
% 16.41/3.00 | | | REF_CLOSE: (3), (4), (6), (9), (13), (14), (17), (24), (57), (58), (59),
% 16.41/3.00 | | | (64), (68), (72), (74), (76), (80), (84), (85) are inconsistent
% 16.41/3.00 | | | by sub-proof #11.
% 16.41/3.00 | | |
% 16.41/3.00 | | End of split
% 16.41/3.00 | |
% 16.41/3.00 | Case 2:
% 16.41/3.00 | |
% 16.41/3.00 | | (86) ~ (iT = iplus3)
% 16.41/3.00 | |
% 16.41/3.00 | | BETA: splitting (61) gives:
% 16.41/3.00 | |
% 16.41/3.00 | | Case 1:
% 16.41/3.00 | | |
% 16.41/3.00 | | | (87) iT = iplus3
% 16.41/3.00 | | |
% 16.41/3.00 | | | REDUCE: (86), (87) imply:
% 16.41/3.00 | | | (88) $false
% 16.41/3.00 | | |
% 16.41/3.00 | | | CLOSE: (88) is inconsistent.
% 16.41/3.00 | | |
% 16.41/3.00 | | Case 2:
% 16.41/3.00 | | |
% 16.41/3.00 | | | (89) iF = iplus3
% 16.41/3.00 | | |
% 16.41/3.00 | | | REDUCE: (1), (89) imply:
% 16.41/3.00 | | | (90) ~ (iT = iplus3)
% 16.41/3.00 | | |
% 16.41/3.00 | | | BETA: splitting (65) gives:
% 16.41/3.00 | | |
% 16.41/3.00 | | | Case 1:
% 16.41/3.00 | | | |
% 16.41/3.00 | | | | (91) iT = iminus3
% 16.41/3.00 | | | |
% 16.41/3.00 | | | | REDUCE: (86), (91) imply:
% 16.41/3.00 | | | | (92) ~ (iminus3 = iplus3)
% 16.41/3.00 | | | |
% 16.41/3.00 | | | | BETA: splitting (12) gives:
% 16.41/3.00 | | | |
% 16.41/3.00 | | | | Case 1:
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | (93) iplus6 = iT
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | COMBINE_EQS: (91), (93) imply:
% 16.41/3.00 | | | | | (94) iplus6 = iminus3
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 16.41/3.00 | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24), (57),
% 16.41/3.00 | | | | | (58), (59), (60), (62), (63), (64), (66), (67), (68), (70),
% 16.41/3.00 | | | | | (71), (72), (73), (74), (75), (76), (77), (78), (79), (89),
% 16.41/3.00 | | | | | (91), (92), (94) are inconsistent by sub-proof #1.
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | Case 2:
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | (95) iT = iplus3 | iT = iminus4
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | BETA: splitting (20) gives:
% 16.41/3.00 | | | | |
% 16.41/3.00 | | | | | Case 1:
% 16.41/3.00 | | | | | |
% 16.41/3.00 | | | | | | (96) iplus6 = iT
% 16.41/3.00 | | | | | |
% 16.41/3.00 | | | | | | COMBINE_EQS: (91), (96) imply:
% 16.41/3.00 | | | | | | (97) iplus6 = iminus3
% 16.41/3.00 | | | | | |
% 16.53/3.01 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 16.53/3.01 | | | | | | (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 16.53/3.01 | | | | | | (57), (58), (59), (60), (62), (63), (64), (66), (67),
% 16.53/3.01 | | | | | | (68), (70), (71), (72), (73), (74), (75), (76), (77),
% 16.53/3.01 | | | | | | (78), (79), (89), (91), (92), (97) are inconsistent by
% 16.53/3.01 | | | | | | sub-proof #1.
% 16.53/3.01 | | | | | |
% 16.53/3.01 | | | | | Case 2:
% 16.53/3.01 | | | | | |
% 16.53/3.01 | | | | | | (98) iT = iplus3 | iT = iplus4
% 16.53/3.01 | | | | | |
% 16.53/3.01 | | | | | | BETA: splitting (95) gives:
% 16.53/3.01 | | | | | |
% 16.53/3.01 | | | | | | Case 1:
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | (99) iT = iplus3
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | REF_CLOSE: (91), (92), (99) are inconsistent by sub-proof #15.
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | Case 2:
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | (100) iT = iminus4
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | COMBINE_EQS: (91), (100) imply:
% 16.53/3.01 | | | | | | | (101) iminus3 = iminus4
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | SIMP: (101) implies:
% 16.53/3.01 | | | | | | | (102) iminus3 = iminus4
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | REDUCE: (92), (102) imply:
% 16.53/3.01 | | | | | | | (103) ~ (iplus3 = iminus4)
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | SIMP: (103) implies:
% 16.53/3.01 | | | | | | | (104) ~ (iplus3 = iminus4)
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | BETA: splitting (70) gives:
% 16.53/3.01 | | | | | | |
% 16.53/3.01 | | | | | | | Case 1:
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | (105) iF = iminus4
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | COMBINE_EQS: (89), (105) imply:
% 16.53/3.01 | | | | | | | | (106) iplus3 = iminus4
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | REDUCE: (104), (106) imply:
% 16.53/3.01 | | | | | | | | (107) $false
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | CLOSE: (107) is inconsistent.
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | Case 2:
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | (108) iF = iplus4
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | COMBINE_EQS: (89), (108) imply:
% 16.53/3.01 | | | | | | | | (109) iplus3 = iplus4
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | BETA: splitting (98) gives:
% 16.53/3.01 | | | | | | | |
% 16.53/3.01 | | | | | | | | Case 1:
% 16.53/3.01 | | | | | | | | |
% 16.53/3.01 | | | | | | | | | (110) iT = iplus3
% 16.53/3.01 | | | | | | | | |
% 16.53/3.01 | | | | | | | | | COMBINE_EQS: (100), (110) imply:
% 16.53/3.01 | | | | | | | | | (111) iplus3 = iminus4
% 16.53/3.01 | | | | | | | | |
% 16.53/3.01 | | | | | | | | | COMBINE_EQS: (109), (111) imply:
% 16.53/3.01 | | | | | | | | | (112) iplus4 = iminus4
% 16.53/3.01 | | | | | | | | |
% 16.53/3.02 | | | | | | | | | SIMP: (112) implies:
% 16.53/3.02 | | | | | | | | | (113) iplus4 = iminus4
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | | REF_CLOSE: (70), (89), (104), (113) are inconsistent by
% 16.53/3.02 | | | | | | | | | sub-proof #3.
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | Case 2:
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | | (114) iT = iplus4
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | | COMBINE_EQS: (100), (114) imply:
% 16.53/3.02 | | | | | | | | | (115) iplus4 = iminus4
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | | REF_CLOSE: (70), (89), (104), (115) are inconsistent by
% 16.53/3.02 | | | | | | | | | sub-proof #3.
% 16.53/3.02 | | | | | | | | |
% 16.53/3.02 | | | | | | | | End of split
% 16.53/3.02 | | | | | | | |
% 16.53/3.02 | | | | | | | End of split
% 16.53/3.02 | | | | | | |
% 16.53/3.02 | | | | | | End of split
% 16.53/3.02 | | | | | |
% 16.53/3.02 | | | | | End of split
% 16.53/3.02 | | | | |
% 16.53/3.02 | | | | End of split
% 16.53/3.02 | | | |
% 16.53/3.02 | | | Case 2:
% 16.53/3.02 | | | |
% 16.53/3.02 | | | | (116) iT = iplus3
% 16.53/3.02 | | | |
% 16.53/3.02 | | | | REDUCE: (86), (116) imply:
% 16.53/3.02 | | | | (117) $false
% 16.53/3.02 | | | |
% 16.53/3.02 | | | | CLOSE: (117) is inconsistent.
% 16.53/3.02 | | | |
% 16.53/3.02 | | | End of split
% 16.53/3.02 | | |
% 16.53/3.02 | | End of split
% 16.53/3.02 | |
% 16.53/3.02 | End of split
% 16.53/3.02 |
% 16.53/3.02 End of proof
% 16.53/3.02
% 16.53/3.02 Sub-proof #1 shows that the following formulas are inconsistent:
% 16.53/3.02 ----------------------------------------------------------------
% 16.53/3.02 (1) iminus6 = iT | iT = iminus2 | iT = iplus4
% 16.53/3.02 (2) iminus8 = iT | iT = iminus3 | iT = iplus5
% 16.53/3.02 (3) iminus8 = iT | iT = iminus3 | iT = iminus5
% 16.53/3.02 (4) iminus2 = iminus1 | iminus2 = iplus1
% 16.53/3.02 (5) iF = iplus3
% 16.53/3.02 (6) iplus8 = iplus4 | iplus8 = iminus4
% 16.53/3.02 (7) iplus6 = iminus3
% 16.53/3.02 (8) iT = iminus3
% 16.53/3.02 (9) iplus9 = iT | iminus8 = iT | iT = iplus3
% 16.53/3.02 (10) iF = iplus4 | iF = iminus4
% 16.53/3.02 (11) iplus9 = iT | iT = iplus7 | iT = iminus4
% 16.58/3.02 (12) iplus8 = iminus5 | iplus8 = iplus5
% 16.58/3.02 (13) iT = iminus3 | iT = iminus7 | iT = iminus4
% 16.58/3.02 (14) iplus9 = iF | iplus9 = iT
% 16.58/3.02 (15) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.02 (16) iplus5 = iminus2 | iplus5 = iplus2
% 16.58/3.02 (17) iminus9 = iT | iminus8 = iT | iT = iminus4
% 16.58/3.02 (18) iplus6 = iF | iminus6 = iF
% 16.58/3.02 (19) iminus7 = iminus1 | iplus7 = iminus1
% 16.58/3.02 (20) iminus6 = iplus4 | iminus6 = iminus4
% 16.58/3.02 (21) iminus9 = iT | iminus6 = iT | iT = iplus1
% 16.58/3.02 (22) iF = iminus1 | iF = iplus1
% 16.58/3.02 (23) iplus8 = iT | iT = iplus2 | iT = iminus4
% 16.58/3.02 (24) iplus9 = iminus1 | iplus9 = iplus1
% 16.58/3.02 (25) iminus9 = iT | iT = iplus3 | iT = iplus4
% 16.58/3.02 (26) iminus8 = iT | iT = iplus3 | iT = iminus2
% 16.58/3.02 (27) iplus9 = iT | iminus6 = iT | iT = iplus1
% 16.58/3.02 (28) iplus8 = iT | iT = iminus3 | iT = iplus2
% 16.58/3.02 (29) iminus9 = iT | iT = iplus3 | iT = iminus2
% 16.58/3.02 (30) iplus8 = iminus2 | iplus8 = iplus2
% 16.58/3.02 (31) iminus8 = iF | iplus8 = iF
% 16.58/3.02 (32) iplus8 = iF | iplus8 = iT
% 16.58/3.02 (33) iplus6 = iT | iT = iminus7 | iT = iminus2
% 16.58/3.02 (34) iplus8 = iT | iT = iplus3 | iT = iminus7
% 16.58/3.02 (35) iplus8 = iT | iT = iminus5 | iT = iplus7
% 16.58/3.02 (36) iplus3 = iminus7 | iplus3 = iplus7
% 16.58/3.02 (37) iplus9 = iF | iminus9 = iF
% 16.58/3.02 (38) iminus8 = iminus3 | iplus8 = iminus3
% 16.58/3.02 (39) iT = iminus3 | iT = iminus2 | iT = iplus1
% 16.58/3.02 (40) iplus9 = iT | iT = iplus3 | iT = iplus4
% 16.58/3.02 (41) ~ (iminus3 = iplus3)
% 16.58/3.02 (42) iminus8 = iminus5 | iminus8 = iplus5
% 16.58/3.02 (43) iminus3 = iplus4 | iminus3 = iminus4
% 16.58/3.02 (44) iplus8 = iT | iT = iminus3 | iT = iplus7
% 16.58/3.02
% 16.58/3.02 Begin of proof
% 16.58/3.02 |
% 16.58/3.02 | BETA: splitting (18) gives:
% 16.58/3.02 |
% 16.58/3.02 | Case 1:
% 16.58/3.02 | |
% 16.58/3.02 | | (45) iplus6 = iF
% 16.58/3.02 | |
% 16.58/3.02 | | COMBINE_EQS: (7), (45) imply:
% 16.58/3.02 | | (46) iF = iminus3
% 16.58/3.02 | |
% 16.58/3.02 | | SIMP: (46) implies:
% 16.58/3.02 | | (47) iF = iminus3
% 16.58/3.02 | |
% 16.58/3.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (13), (15), (19), (28), (30), (31),
% 16.58/3.02 | | (32), (33), (39), (41), (42), (43), (44), (47) are inconsistent
% 16.58/3.02 | | by sub-proof #10.
% 16.58/3.02 | |
% 16.58/3.02 | Case 2:
% 16.58/3.02 | |
% 16.58/3.02 | | (48) iminus6 = iF
% 16.58/3.02 | | (49) ~ (iplus6 = iF)
% 16.58/3.02 | |
% 16.58/3.02 | | COMBINE_EQS: (5), (48) imply:
% 16.58/3.02 | | (50) iminus6 = iplus3
% 16.58/3.02 | |
% 16.58/3.02 | | BETA: splitting (26) gives:
% 16.58/3.02 | |
% 16.58/3.02 | | Case 1:
% 16.58/3.02 | | |
% 16.58/3.02 | | | (51) iminus8 = iT
% 16.58/3.02 | | |
% 16.58/3.02 | | | COMBINE_EQS: (8), (51) imply:
% 16.58/3.02 | | | (52) iminus8 = iminus3
% 16.58/3.02 | | |
% 16.58/3.02 | | | BETA: splitting (31) gives:
% 16.58/3.02 | | |
% 16.58/3.02 | | | Case 1:
% 16.58/3.02 | | | |
% 16.58/3.02 | | | | (53) iminus8 = iF
% 16.58/3.02 | | | |
% 16.58/3.02 | | | | COMBINE_EQS: (52), (53) imply:
% 16.58/3.02 | | | | (54) iF = iminus3
% 16.58/3.02 | | | |
% 16.58/3.02 | | | | COMBINE_EQS: (5), (54) imply:
% 16.58/3.02 | | | | (55) iminus3 = iplus3
% 16.58/3.02 | | | |
% 16.58/3.02 | | | | SIMP: (55) implies:
% 16.58/3.02 | | | | (56) iminus3 = iplus3
% 16.58/3.02 | | | |
% 16.58/3.02 | | | | COMBINE_EQS: (8), (56) imply:
% 16.58/3.02 | | | | (57) iT = iplus3
% 16.58/3.03 | | | |
% 16.58/3.03 | | | | REF_CLOSE: (2), (3), (41), (42), (52), (57) are inconsistent by
% 16.58/3.03 | | | | sub-proof #14.
% 16.58/3.03 | | | |
% 16.58/3.03 | | | Case 2:
% 16.58/3.03 | | | |
% 16.58/3.03 | | | | (58) iplus8 = iF
% 16.58/3.03 | | | | (59) ~ (iminus8 = iF)
% 16.58/3.03 | | | |
% 16.58/3.03 | | | | COMBINE_EQS: (5), (58) imply:
% 16.58/3.03 | | | | (60) iplus8 = iplus3
% 16.58/3.03 | | | |
% 16.58/3.03 | | | | BETA: splitting (34) gives:
% 16.58/3.03 | | | |
% 16.58/3.03 | | | | Case 1:
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | (61) iplus8 = iT
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | COMBINE_EQS: (60), (61) imply:
% 16.58/3.03 | | | | | (62) iT = iplus3
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | REF_CLOSE: (2), (3), (41), (42), (52), (62) are inconsistent by
% 16.58/3.03 | | | | | sub-proof #14.
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | Case 2:
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | (63) ~ (iplus8 = iT)
% 16.58/3.03 | | | | | (64) iT = iplus3 | iT = iminus7
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | REDUCE: (8), (60), (63) imply:
% 16.58/3.03 | | | | | (65) ~ (iminus3 = iplus3)
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | BETA: splitting (64) gives:
% 16.58/3.03 | | | | |
% 16.58/3.03 | | | | | Case 1:
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | (66) iT = iplus3
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | REF_CLOSE: (2), (3), (41), (42), (52), (66) are inconsistent by
% 16.58/3.03 | | | | | | sub-proof #14.
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | Case 2:
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | (67) iT = iminus7
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | COMBINE_EQS: (8), (67) imply:
% 16.58/3.03 | | | | | | (68) iminus3 = iminus7
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | COMBINE_EQS: (7), (68) imply:
% 16.58/3.03 | | | | | | (69) iplus6 = iminus7
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | REDUCE: (41), (68) imply:
% 16.58/3.03 | | | | | | (70) ~ (iplus3 = iminus7)
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | SIMP: (70) implies:
% 16.58/3.03 | | | | | | (71) ~ (iplus3 = iminus7)
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | BETA: splitting (36) gives:
% 16.58/3.03 | | | | | |
% 16.58/3.03 | | | | | | Case 1:
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | (72) iplus3 = iminus7
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | REDUCE: (71), (72) imply:
% 16.58/3.03 | | | | | | | (73) $false
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | CLOSE: (73) is inconsistent.
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | Case 2:
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | (74) iplus3 = iplus7
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | COMBINE_EQS: (5), (74) imply:
% 16.58/3.03 | | | | | | | (75) iF = iplus7
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | COMBINE_EQS: (60), (74) imply:
% 16.58/3.03 | | | | | | | (76) iplus8 = iplus7
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | COMBINE_EQS: (50), (74) imply:
% 16.58/3.03 | | | | | | | (77) iminus6 = iplus7
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | REDUCE: (71), (74) imply:
% 16.58/3.03 | | | | | | | (78) ~ (iminus7 = iplus7)
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | SIMP: (78) implies:
% 16.58/3.03 | | | | | | | (79) ~ (iminus7 = iplus7)
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | BETA: splitting (35) gives:
% 16.58/3.03 | | | | | | |
% 16.58/3.03 | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | (80) iplus8 = iT
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | COMBINE_EQS: (76), (80) imply:
% 16.58/3.03 | | | | | | | | (81) iT = iplus7
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | REF_CLOSE: (67), (79), (81) are inconsistent by sub-proof #9.
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | (82) iT = iminus5 | iT = iplus7
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | BETA: splitting (82) gives:
% 16.58/3.03 | | | | | | | |
% 16.58/3.03 | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | |
% 16.58/3.03 | | | | | | | | | (83) iT = iminus5
% 16.58/3.03 | | | | | | | | |
% 16.58/3.03 | | | | | | | | | COMBINE_EQS: (67), (83) imply:
% 16.58/3.03 | | | | | | | | | (84) iminus5 = iminus7
% 16.58/3.03 | | | | | | | | |
% 16.58/3.03 | | | | | | | | | BETA: splitting (12) gives:
% 16.58/3.03 | | | | | | | | |
% 16.58/3.03 | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | (85) iplus8 = iminus5
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | COMBINE_EQS: (76), (85) imply:
% 16.58/3.03 | | | | | | | | | | (86) iminus5 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | SIMP: (86) implies:
% 16.58/3.03 | | | | | | | | | | (87) iminus5 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | COMBINE_EQS: (84), (87) imply:
% 16.58/3.03 | | | | | | | | | | (88) iminus7 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | SIMP: (88) implies:
% 16.58/3.03 | | | | | | | | | | (89) iminus7 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | REDUCE: (79), (89) imply:
% 16.58/3.03 | | | | | | | | | | (90) $false
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | CLOSE: (90) is inconsistent.
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | (91) iplus8 = iplus5
% 16.58/3.03 | | | | | | | | | | (92) ~ (iplus8 = iminus5)
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | COMBINE_EQS: (76), (91) imply:
% 16.58/3.03 | | | | | | | | | | (93) iplus5 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | SIMP: (93) implies:
% 16.58/3.03 | | | | | | | | | | (94) iplus5 = iplus7
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | BETA: splitting (25) gives:
% 16.58/3.03 | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | (95) iminus9 = iT
% 16.58/3.03 | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | COMBINE_EQS: (67), (95) imply:
% 16.58/3.03 | | | | | | | | | | | (96) iminus9 = iminus7
% 16.58/3.03 | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | BETA: splitting (37) gives:
% 16.58/3.03 | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | (97) iplus9 = iF
% 16.58/3.03 | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | COMBINE_EQS: (75), (97) imply:
% 16.58/3.03 | | | | | | | | | | | | (98) iplus9 = iplus7
% 16.58/3.03 | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | BETA: splitting (27) gives:
% 16.58/3.03 | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | (99) iplus9 = iT
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | COMBINE_EQS: (98), (99) imply:
% 16.58/3.03 | | | | | | | | | | | | | (100) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | SIMP: (100) implies:
% 16.58/3.03 | | | | | | | | | | | | | (101) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | COMBINE_EQS: (67), (101) imply:
% 16.58/3.03 | | | | | | | | | | | | | (102) iminus7 = iplus7
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | REDUCE: (79), (102) imply:
% 16.58/3.03 | | | | | | | | | | | | | (103) $false
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | (104) ~ (iplus9 = iT)
% 16.58/3.03 | | | | | | | | | | | | | (105) iminus6 = iT | iT = iplus1
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | BETA: splitting (105) gives:
% 16.58/3.03 | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | (106) iminus6 = iT
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | COMBINE_EQS: (77), (106) imply:
% 16.58/3.03 | | | | | | | | | | | | | | (107) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | SIMP: (107) implies:
% 16.58/3.03 | | | | | | | | | | | | | | (108) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | REF_CLOSE: (67), (79), (108) are inconsistent by sub-proof
% 16.58/3.03 | | | | | | | | | | | | | | #9.
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | (109) iT = iplus1
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | COMBINE_EQS: (67), (109) imply:
% 16.58/3.03 | | | | | | | | | | | | | | (110) iminus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | SIMP: (110) implies:
% 16.58/3.03 | | | | | | | | | | | | | | (111) iminus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | COMBINE_EQS: (69), (111) imply:
% 16.58/3.03 | | | | | | | | | | | | | | (112) iplus6 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | REDUCE: (79), (111) imply:
% 16.58/3.03 | | | | | | | | | | | | | | (113) ~ (iplus7 = iplus1)
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | SIMP: (113) implies:
% 16.58/3.03 | | | | | | | | | | | | | | (114) ~ (iplus7 = iplus1)
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 16.58/3.03 | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | (115) iplus9 = iT
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | COMBINE_EQS: (98), (115) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | (116) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | SIMP: (116) implies:
% 16.58/3.03 | | | | | | | | | | | | | | | (117) iT = iplus7
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | COMBINE_EQS: (109), (117) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | (118) iplus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | SIMP: (118) implies:
% 16.58/3.03 | | | | | | | | | | | | | | | (119) iplus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | REDUCE: (114), (119) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | (120) $false
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | CLOSE: (120) is inconsistent.
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | (121) iT = iplus3 | iT = iplus4
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 16.58/3.03 | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | Case 1:
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | (122) iF = iplus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (122) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | | (123) iplus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | SIMP: (123) implies:
% 16.58/3.03 | | | | | | | | | | | | | | | | (124) iplus7 = iplus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | REDUCE: (114), (124) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | | (125) $false
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | Case 2:
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | (126) iF = iminus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (126) imply:
% 16.58/3.03 | | | | | | | | | | | | | | | | (127) iplus7 = iminus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.03 | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 16.58/3.03 | | | | | | | | | | | | | | | | (128) iplus7 = iminus1
% 16.58/3.03 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (128) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (129) iplus3 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (128) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (130) iminus6 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (128) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (131) iplus9 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | REDUCE: (114), (128) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (132) ~ (iminus1 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | (133) iplus9 = iT
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (133) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (134) iT = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | SIMP: (134) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (135) iT = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (135) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (136) iminus1 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (112), (130), (132), (136) are inconsistent
% 16.58/3.04 | | | | | | | | | | | | | | | | | by sub-proof #8.
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | (137) iT = iplus7 | iT = iminus4
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (138) iT = iplus3
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (41), (42), (52), (138) are inconsistent
% 16.58/3.04 | | | | | | | | | | | | | | | | | | by sub-proof #14.
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (139) iT = iplus4
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (140) ~ (iT = iplus3)
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (139) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (141) iplus4 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | REDUCE: (109), (129), (140) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (142) ~ (iminus1 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (143) iminus6 = iminus4
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (143) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (144) iminus4 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | SIMP: (144) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (145) iminus4 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | (146) iT = iplus7
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (146) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | (147) iplus7 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | SIMP: (147) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | (148) iplus7 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (148) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | (149) iminus1 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (112), (130), (132), (149) are inconsistent
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | by sub-proof #8.
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | (150) iT = iminus4
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (109), (112), (130), (132), (145), (150) are
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7.
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (151) iminus6 = iplus4
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (151) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (152) iplus4 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | SIMP: (152) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (153) iplus4 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (112), (130), (132), (141), (153) are
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | (154) iminus9 = iF
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | COMBINE_EQS: (96), (154) imply:
% 16.58/3.04 | | | | | | | | | | | | (155) iF = iminus7
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | SIMP: (155) implies:
% 16.58/3.04 | | | | | | | | | | | | (156) iF = iminus7
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | COMBINE_EQS: (75), (156) imply:
% 16.58/3.04 | | | | | | | | | | | | (157) iminus7 = iplus7
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | REDUCE: (79), (157) imply:
% 16.58/3.04 | | | | | | | | | | | | (158) $false
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | End of split
% 16.58/3.04 | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | (159) ~ (iminus9 = iT)
% 16.58/3.04 | | | | | | | | | | | (160) iT = iplus3 | iT = iplus4
% 16.58/3.04 | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | REDUCE: (67), (159) imply:
% 16.58/3.04 | | | | | | | | | | | (161) ~ (iminus9 = iminus7)
% 16.58/3.04 | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | BETA: splitting (21) gives:
% 16.58/3.04 | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | (162) iminus9 = iT
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | COMBINE_EQS: (67), (162) imply:
% 16.58/3.04 | | | | | | | | | | | | (163) iminus9 = iminus7
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | REDUCE: (161), (163) imply:
% 16.58/3.04 | | | | | | | | | | | | (164) $false
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | (165) iminus6 = iT | iT = iplus1
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | BETA: splitting (160) gives:
% 16.58/3.04 | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | (166) iT = iplus3
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (41), (42), (52), (166) are inconsistent
% 16.58/3.04 | | | | | | | | | | | | | by sub-proof #14.
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | (167) iT = iplus4
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | COMBINE_EQS: (67), (167) imply:
% 16.58/3.04 | | | | | | | | | | | | | (168) iminus7 = iplus4
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | SIMP: (168) implies:
% 16.58/3.04 | | | | | | | | | | | | | (169) iminus7 = iplus4
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | COMBINE_EQS: (69), (169) imply:
% 16.58/3.04 | | | | | | | | | | | | | (170) iplus6 = iplus4
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | REDUCE: (161), (169) imply:
% 16.58/3.04 | | | | | | | | | | | | | (171) ~ (iminus9 = iplus4)
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | REDUCE: (79), (169) imply:
% 16.58/3.04 | | | | | | | | | | | | | (172) ~ (iplus7 = iplus4)
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | SIMP: (172) implies:
% 16.58/3.04 | | | | | | | | | | | | | (173) ~ (iplus7 = iplus4)
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | BETA: splitting (165) gives:
% 16.58/3.04 | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | (174) iminus6 = iT
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | COMBINE_EQS: (77), (174) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (175) iT = iplus7
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | SIMP: (175) implies:
% 16.58/3.04 | | | | | | | | | | | | | | (176) iT = iplus7
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | COMBINE_EQS: (167), (176) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (177) iplus7 = iplus4
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | SIMP: (177) implies:
% 16.58/3.04 | | | | | | | | | | | | | | (178) iplus7 = iplus4
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | REDUCE: (173), (178) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (179) $false
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | (180) iT = iplus1
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | COMBINE_EQS: (167), (180) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (181) iplus4 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | SIMP: (181) implies:
% 16.58/3.04 | | | | | | | | | | | | | | (182) iplus4 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | COMBINE_EQS: (170), (182) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (183) iplus6 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | REDUCE: (171), (182) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (184) ~ (iminus9 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | REDUCE: (173), (182) imply:
% 16.58/3.04 | | | | | | | | | | | | | | (185) ~ (iplus7 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 16.58/3.04 | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | (186) iminus9 = iT
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | COMBINE_EQS: (180), (186) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | (187) iminus9 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | REDUCE: (184), (187) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | (188) $false
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | (189) iT = iplus3 | iT = iminus2
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 16.58/3.04 | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | (190) iF = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (190) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (191) iplus7 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | REDUCE: (185), (191) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (192) $false
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | (193) iF = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (193) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (194) iplus7 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (194) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (195) iplus5 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (194) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (196) iplus3 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (194) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (197) iplus8 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (194) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | (198) iminus6 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | (199) iT = iplus3
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (41), (42), (52), (199) are inconsistent
% 16.58/3.04 | | | | | | | | | | | | | | | | | by sub-proof #14.
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | (200) iT = iminus2
% 16.58/3.04 | | | | | | | | | | | | | | | | | (201) ~ (iT = iplus3)
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (200) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (202) iminus2 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | SIMP: (202) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (203) iminus2 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | REDUCE: (180), (196), (201) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (204) ~ (iminus1 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | SIMP: (204) implies:
% 16.58/3.04 | | | | | | | | | | | | | | | | | (205) ~ (iminus1 = iplus1)
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (206) iplus8 = iminus4
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (206) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | (207) iminus4 = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 16.58/3.04 | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (208) iplus8 = iT
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (208) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (209) iT = iminus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (209) imply:
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | (210) iminus1 = iplus1
% 16.58/3.04 | | | | | | | | | | | | | | | | | | |
% 16.58/3.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (183), (198), (205), (210) are inconsistent
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | by sub-proof #8.
% 16.58/3.05 | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | (211) iT = iplus2 | iT = iminus4
% 16.58/3.05 | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (212) iplus5 = iminus2
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (212) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (213) iminus2 = iminus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (213) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (214) iminus1 = iplus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (183), (198), (205), (214) are inconsistent
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | by sub-proof #8.
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (215) iplus5 = iplus2
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (216) ~ (iplus5 = iminus2)
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (215) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | (217) iplus2 = iminus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | (218) iT = iplus2
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (218) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | (219) iplus2 = iplus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | (220) iplus2 = iplus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (220) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | (221) iminus1 = iplus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (183), (198), (205), (221) are inconsistent
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | by sub-proof #8.
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | (222) iT = iminus4
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (180), (183), (198), (205), (207), (222) are
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7.
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | (223) iplus8 = iplus4
% 16.58/3.05 | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (223) imply:
% 16.58/3.05 | | | | | | | | | | | | | | | | | | (224) iplus4 = iminus1
% 16.58/3.05 | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (182), (183), (198), (205), (224) are
% 16.58/3.05 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 16.58/3.05 | | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | (225) iT = iplus7
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | COMBINE_EQS: (67), (225) imply:
% 16.58/3.05 | | | | | | | | | (226) iminus7 = iplus7
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | SIMP: (226) implies:
% 16.58/3.05 | | | | | | | | | (227) iminus7 = iplus7
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | REDUCE: (79), (227) imply:
% 16.58/3.05 | | | | | | | | | (228) $false
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | CLOSE: (228) is inconsistent.
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | End of split
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | End of split
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | End of split
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | End of split
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | End of split
% 16.58/3.05 | | | |
% 16.58/3.05 | | | End of split
% 16.58/3.05 | | |
% 16.58/3.05 | | Case 2:
% 16.58/3.05 | | |
% 16.58/3.05 | | | (229) ~ (iminus8 = iT)
% 16.58/3.05 | | |
% 16.58/3.05 | | | REDUCE: (8), (229) imply:
% 16.58/3.05 | | | (230) ~ (iminus8 = iminus3)
% 16.58/3.05 | | |
% 16.58/3.05 | | | BETA: splitting (38) gives:
% 16.58/3.05 | | |
% 16.58/3.05 | | | Case 1:
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | (231) iminus8 = iminus3
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | REDUCE: (230), (231) imply:
% 16.58/3.05 | | | | (232) $false
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | CLOSE: (232) is inconsistent.
% 16.58/3.05 | | | |
% 16.58/3.05 | | | Case 2:
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | (233) iplus8 = iminus3
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | BETA: splitting (9) gives:
% 16.58/3.05 | | | |
% 16.58/3.05 | | | | Case 1:
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | (234) iplus9 = iT
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | COMBINE_EQS: (8), (234) imply:
% 16.58/3.05 | | | | | (235) iplus9 = iminus3
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (13), (15), (17), (19),
% 16.58/3.05 | | | | | (25), (28), (30), (31), (32), (33), (37), (39), (41), (42),
% 16.58/3.05 | | | | | (43), (44), (230), (233), (235) are inconsistent by
% 16.58/3.05 | | | | | sub-proof #2.
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | Case 2:
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | (236) ~ (iplus9 = iT)
% 16.58/3.05 | | | | | (237) iminus8 = iT | iT = iplus3
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | REDUCE: (8), (236) imply:
% 16.58/3.05 | | | | | (238) ~ (iplus9 = iminus3)
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | BETA: splitting (14) gives:
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | | Case 1:
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | (239) iplus9 = iT
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | COMBINE_EQS: (8), (239) imply:
% 16.58/3.05 | | | | | | (240) iplus9 = iminus3
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (13), (15), (17),
% 16.58/3.05 | | | | | | (19), (25), (28), (30), (31), (32), (33), (37), (39),
% 16.58/3.05 | | | | | | (41), (42), (43), (44), (230), (233), (240) are
% 16.58/3.05 | | | | | | inconsistent by sub-proof #2.
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | Case 2:
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | (241) iplus9 = iF
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | COMBINE_EQS: (5), (241) imply:
% 16.58/3.05 | | | | | | (242) iplus9 = iplus3
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | REDUCE: (238), (242) imply:
% 16.58/3.05 | | | | | | (243) ~ (iminus3 = iplus3)
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | BETA: splitting (27) gives:
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | | Case 1:
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | (244) iplus9 = iT
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | COMBINE_EQS: (242), (244) imply:
% 16.58/3.05 | | | | | | | (245) iT = iplus3
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | SIMP: (245) implies:
% 16.58/3.05 | | | | | | | (246) iT = iplus3
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | COMBINE_EQS: (8), (246) imply:
% 16.58/3.05 | | | | | | | (247) iminus3 = iplus3
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | REDUCE: (41), (247) imply:
% 16.58/3.05 | | | | | | | (248) $false
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | CLOSE: (248) is inconsistent.
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | Case 2:
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | (249) iminus6 = iT | iT = iplus1
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | BETA: splitting (249) gives:
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | | Case 1:
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | (250) iminus6 = iT
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | COMBINE_EQS: (50), (250) imply:
% 16.58/3.05 | | | | | | | | (251) iT = iplus3
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | REF_CLOSE: (8), (41), (251) are inconsistent by sub-proof #5.
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | (252) iT = iplus1
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | COMBINE_EQS: (8), (252) imply:
% 16.58/3.05 | | | | | | | | (253) iminus3 = iplus1
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | SIMP: (253) implies:
% 16.58/3.05 | | | | | | | | (254) iminus3 = iplus1
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | COMBINE_EQS: (7), (254) imply:
% 16.58/3.05 | | | | | | | | (255) iplus6 = iplus1
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | REDUCE: (230), (254) imply:
% 16.58/3.05 | | | | | | | | (256) ~ (iminus8 = iplus1)
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | REDUCE: (41), (254) imply:
% 16.58/3.05 | | | | | | | | (257) ~ (iplus3 = iplus1)
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | SIMP: (257) implies:
% 16.58/3.05 | | | | | | | | (258) ~ (iplus3 = iplus1)
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | BETA: splitting (24) gives:
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | | Case 1:
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | (259) iplus9 = iminus1
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | COMBINE_EQS: (242), (259) imply:
% 16.58/3.05 | | | | | | | | | (260) iplus3 = iminus1
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | COMBINE_EQS: (50), (260) imply:
% 16.58/3.05 | | | | | | | | | (261) iminus6 = iminus1
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | REDUCE: (258), (260) imply:
% 16.58/3.05 | | | | | | | | | (262) ~ (iminus1 = iplus1)
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | BETA: splitting (237) gives:
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | Case 1:
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | (263) iminus8 = iT
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | COMBINE_EQS: (252), (263) imply:
% 16.58/3.05 | | | | | | | | | | (264) iminus8 = iplus1
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | REDUCE: (256), (264) imply:
% 16.58/3.05 | | | | | | | | | | (265) $false
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | CLOSE: (265) is inconsistent.
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | (266) iT = iplus3
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | COMBINE_EQS: (252), (266) imply:
% 16.58/3.05 | | | | | | | | | | (267) iplus3 = iplus1
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | COMBINE_EQS: (260), (267) imply:
% 16.58/3.05 | | | | | | | | | | (268) iminus1 = iplus1
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | COMBINE_EQS: (261), (268) imply:
% 16.58/3.05 | | | | | | | | | | (269) iminus6 = iplus1
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | | REF_CLOSE: (15), (255), (262), (269) are inconsistent by
% 16.58/3.05 | | | | | | | | | | sub-proof #13.
% 16.58/3.05 | | | | | | | | | |
% 16.58/3.05 | | | | | | | | | End of split
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | Case 2:
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | (270) iplus9 = iplus1
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | COMBINE_EQS: (242), (270) imply:
% 16.58/3.05 | | | | | | | | | (271) iplus3 = iplus1
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | REDUCE: (258), (271) imply:
% 16.58/3.05 | | | | | | | | | (272) $false
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | | CLOSE: (272) is inconsistent.
% 16.58/3.05 | | | | | | | | |
% 16.58/3.05 | | | | | | | | End of split
% 16.58/3.05 | | | | | | | |
% 16.58/3.05 | | | | | | | End of split
% 16.58/3.05 | | | | | | |
% 16.58/3.05 | | | | | | End of split
% 16.58/3.05 | | | | | |
% 16.58/3.05 | | | | | End of split
% 16.58/3.05 | | | | |
% 16.58/3.05 | | | | End of split
% 16.58/3.05 | | | |
% 16.58/3.05 | | | End of split
% 16.58/3.05 | | |
% 16.58/3.05 | | End of split
% 16.58/3.05 | |
% 16.58/3.05 | End of split
% 16.58/3.05 |
% 16.58/3.05 End of proof
% 16.58/3.05
% 16.58/3.05 Sub-proof #2 shows that the following formulas are inconsistent:
% 16.58/3.05 ----------------------------------------------------------------
% 16.58/3.05 (1) iminus6 = iT | iT = iminus2 | iT = iplus4
% 16.58/3.05 (2) iminus8 = iT | iT = iminus3 | iT = iplus5
% 16.58/3.05 (3) iminus8 = iT | iT = iminus3 | iT = iminus5
% 16.58/3.05 (4) iminus2 = iminus1 | iminus2 = iplus1
% 16.58/3.05 (5) iF = iplus3
% 16.58/3.05 (6) iT = iminus3
% 16.58/3.05 (7) iplus8 = iminus3
% 16.58/3.05 (8) iF = iplus4 | iF = iminus4
% 16.58/3.05 (9) iT = iminus3 | iT = iminus7 | iT = iminus4
% 16.58/3.05 (10) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.05 (11) iminus9 = iT | iminus8 = iT | iT = iminus4
% 16.58/3.05 (12) iminus7 = iminus1 | iplus7 = iminus1
% 16.58/3.05 (13) iplus9 = iminus3
% 16.58/3.05 (14) iminus9 = iT | iT = iplus3 | iT = iplus4
% 16.58/3.05 (15) iplus8 = iT | iT = iminus3 | iT = iplus2
% 16.58/3.05 (16) iplus8 = iminus2 | iplus8 = iplus2
% 16.58/3.05 (17) iminus8 = iF | iplus8 = iF
% 16.58/3.05 (18) iplus8 = iF | iplus8 = iT
% 16.58/3.05 (19) iplus6 = iT | iT = iminus7 | iT = iminus2
% 16.58/3.05 (20) iplus9 = iF | iminus9 = iF
% 16.58/3.05 (21) ~ (iminus8 = iminus3)
% 16.58/3.05 (22) iT = iminus3 | iT = iminus2 | iT = iplus1
% 16.58/3.05 (23) ~ (iminus3 = iplus3)
% 16.58/3.05 (24) iminus8 = iminus5 | iminus8 = iplus5
% 16.58/3.05 (25) iminus3 = iplus4 | iminus3 = iminus4
% 16.58/3.05 (26) iplus8 = iT | iT = iminus3 | iT = iplus7
% 16.58/3.05
% 16.58/3.05 Begin of proof
% 16.58/3.05 |
% 16.58/3.05 | BETA: splitting (17) gives:
% 16.58/3.05 |
% 16.58/3.05 | Case 1:
% 16.58/3.05 | |
% 16.58/3.05 | | (27) iminus8 = iF
% 16.58/3.05 | |
% 16.58/3.05 | | COMBINE_EQS: (5), (27) imply:
% 16.58/3.05 | | (28) iminus8 = iplus3
% 16.58/3.05 | |
% 16.58/3.05 | | REDUCE: (21), (28) imply:
% 16.58/3.05 | | (29) ~ (iminus3 = iplus3)
% 16.58/3.05 | |
% 16.58/3.05 | | BETA: splitting (20) gives:
% 16.58/3.05 | |
% 16.58/3.05 | | Case 1:
% 16.58/3.05 | | |
% 16.58/3.05 | | | (30) iplus9 = iF
% 16.58/3.05 | | |
% 16.58/3.05 | | | COMBINE_EQS: (13), (30) imply:
% 16.58/3.06 | | | (31) iF = iminus3
% 16.58/3.06 | | |
% 16.58/3.06 | | | SIMP: (31) implies:
% 16.58/3.06 | | | (32) iF = iminus3
% 16.58/3.06 | | |
% 16.58/3.06 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (15), (16),
% 16.58/3.06 | | | (17), (18), (19), (22), (23), (24), (25), (26), (32) are
% 16.58/3.06 | | | inconsistent by sub-proof #10.
% 16.58/3.06 | | |
% 16.58/3.06 | | Case 2:
% 16.58/3.06 | | |
% 16.58/3.06 | | | (33) iminus9 = iF
% 16.58/3.06 | | | (34) ~ (iplus9 = iF)
% 16.58/3.06 | | |
% 16.58/3.06 | | | COMBINE_EQS: (5), (33) imply:
% 16.58/3.06 | | | (35) iminus9 = iplus3
% 16.58/3.06 | | |
% 16.58/3.06 | | | BETA: splitting (14) gives:
% 16.58/3.06 | | |
% 16.58/3.06 | | | Case 1:
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | (36) iminus9 = iT
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | COMBINE_EQS: (35), (36) imply:
% 16.58/3.06 | | | | (37) iT = iplus3
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | SIMP: (37) implies:
% 16.58/3.06 | | | | (38) iT = iplus3
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | REF_CLOSE: (6), (23), (38) are inconsistent by sub-proof #5.
% 16.58/3.06 | | | |
% 16.58/3.06 | | | Case 2:
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | (39) ~ (iminus9 = iT)
% 16.58/3.06 | | | | (40) iT = iplus3 | iT = iplus4
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | BETA: splitting (40) gives:
% 16.58/3.06 | | | |
% 16.58/3.06 | | | | Case 1:
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | (41) iT = iplus3
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | COMBINE_EQS: (6), (41) imply:
% 16.58/3.06 | | | | | (42) iminus3 = iplus3
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | REDUCE: (23), (42) imply:
% 16.58/3.06 | | | | | (43) $false
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | CLOSE: (43) is inconsistent.
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | Case 2:
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | (44) iT = iplus4
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | COMBINE_EQS: (6), (44) imply:
% 16.58/3.06 | | | | | (45) iminus3 = iplus4
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | REDUCE: (23), (45) imply:
% 16.58/3.06 | | | | | (46) ~ (iplus3 = iplus4)
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | SIMP: (46) implies:
% 16.58/3.06 | | | | | (47) ~ (iplus3 = iplus4)
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | BETA: splitting (11) gives:
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | | Case 1:
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | (48) iminus9 = iT
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | COMBINE_EQS: (35), (48) imply:
% 16.58/3.06 | | | | | | (49) iT = iplus3
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | SIMP: (49) implies:
% 16.58/3.06 | | | | | | (50) iT = iplus3
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | REF_CLOSE: (44), (47), (50) are inconsistent by sub-proof #4.
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | Case 2:
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | (51) iminus8 = iT | iT = iminus4
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | BETA: splitting (51) gives:
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | | Case 1:
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | (52) iminus8 = iT
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | COMBINE_EQS: (28), (52) imply:
% 16.58/3.06 | | | | | | | (53) iT = iplus3
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | REF_CLOSE: (44), (47), (53) are inconsistent by sub-proof #4.
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | Case 2:
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | (54) iT = iminus4
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | COMBINE_EQS: (44), (54) imply:
% 16.58/3.06 | | | | | | | (55) iplus4 = iminus4
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | SIMP: (55) implies:
% 16.58/3.06 | | | | | | | (56) iplus4 = iminus4
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | REDUCE: (47), (56) imply:
% 16.58/3.06 | | | | | | | (57) ~ (iplus3 = iminus4)
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | | REF_CLOSE: (5), (8), (56), (57) are inconsistent by sub-proof #3.
% 16.58/3.06 | | | | | | |
% 16.58/3.06 | | | | | | End of split
% 16.58/3.06 | | | | | |
% 16.58/3.06 | | | | | End of split
% 16.58/3.06 | | | | |
% 16.58/3.06 | | | | End of split
% 16.58/3.06 | | | |
% 16.58/3.06 | | | End of split
% 16.58/3.06 | | |
% 16.58/3.06 | | End of split
% 16.58/3.06 | |
% 16.58/3.06 | Case 2:
% 16.58/3.06 | |
% 16.58/3.06 | | (58) iplus8 = iF
% 16.58/3.06 | |
% 16.58/3.06 | | COMBINE_EQS: (7), (58) imply:
% 16.58/3.06 | | (59) iF = iminus3
% 16.58/3.06 | |
% 16.58/3.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (15), (16), (17),
% 16.58/3.06 | | (18), (19), (22), (23), (24), (25), (26), (59) are inconsistent
% 16.58/3.06 | | by sub-proof #10.
% 16.58/3.06 | |
% 16.58/3.06 | End of split
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #3 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iF = iplus4 | iF = iminus4
% 16.58/3.06 (2) iF = iplus3
% 16.58/3.06 (3) ~ (iplus3 = iminus4)
% 16.58/3.06 (4) iplus4 = iminus4
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | BETA: splitting (1) gives:
% 16.58/3.06 |
% 16.58/3.06 | Case 1:
% 16.58/3.06 | |
% 16.58/3.06 | | (5) iF = iminus4
% 16.58/3.06 | |
% 16.58/3.06 | | COMBINE_EQS: (2), (5) imply:
% 16.58/3.06 | | (6) iplus3 = iminus4
% 16.58/3.06 | |
% 16.58/3.06 | | SIMP: (6) implies:
% 16.58/3.06 | | (7) iplus3 = iminus4
% 16.58/3.06 | |
% 16.58/3.06 | | REDUCE: (3), (7) imply:
% 16.58/3.06 | | (8) $false
% 16.58/3.06 | |
% 16.58/3.06 | | CLOSE: (8) is inconsistent.
% 16.58/3.06 | |
% 16.58/3.06 | Case 2:
% 16.58/3.06 | |
% 16.58/3.06 | | (9) iF = iplus4
% 16.58/3.06 | |
% 16.58/3.06 | | COMBINE_EQS: (2), (9) imply:
% 16.58/3.06 | | (10) iplus3 = iplus4
% 16.58/3.06 | |
% 16.58/3.06 | | SIMP: (10) implies:
% 16.58/3.06 | | (11) iplus3 = iplus4
% 16.58/3.06 | |
% 16.58/3.06 | | COMBINE_EQS: (4), (11) imply:
% 16.58/3.06 | | (12) iplus3 = iminus4
% 16.58/3.06 | |
% 16.58/3.06 | | REDUCE: (3), (12) imply:
% 16.58/3.06 | | (13) $false
% 16.58/3.06 | |
% 16.58/3.06 | | CLOSE: (13) is inconsistent.
% 16.58/3.06 | |
% 16.58/3.06 | End of split
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #4 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iT = iplus3
% 16.58/3.06 (2) iT = iplus4
% 16.58/3.06 (3) ~ (iplus3 = iplus4)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (1), (2) imply:
% 16.58/3.06 | (4) iplus3 = iplus4
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (4) implies:
% 16.58/3.06 | (5) iplus3 = iplus4
% 16.58/3.06 |
% 16.58/3.06 | REDUCE: (3), (5) imply:
% 16.58/3.06 | (6) $false
% 16.58/3.06 |
% 16.58/3.06 | CLOSE: (6) is inconsistent.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #5 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iT = iminus3
% 16.58/3.06 (2) iT = iplus3
% 16.58/3.06 (3) ~ (iminus3 = iplus3)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (1), (2) imply:
% 16.58/3.06 | (4) iminus3 = iplus3
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (4) implies:
% 16.58/3.06 | (5) iminus3 = iplus3
% 16.58/3.06 |
% 16.58/3.06 | REDUCE: (3), (5) imply:
% 16.58/3.06 | (6) $false
% 16.58/3.06 |
% 16.58/3.06 | CLOSE: (6) is inconsistent.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #6 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iplus4 = iplus1
% 16.58/3.06 (2) iplus6 = iplus1
% 16.58/3.06 (3) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.06 (4) iplus4 = iminus1
% 16.58/3.06 (5) iminus6 = iminus1
% 16.58/3.06 (6) ~ (iminus1 = iplus1)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (1), (4) imply:
% 16.58/3.06 | (7) iminus1 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (5), (7) imply:
% 16.58/3.06 | (8) iminus6 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #13.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #7 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iplus6 = iplus1
% 16.58/3.06 (2) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.06 (3) iT = iplus1
% 16.58/3.06 (4) iT = iminus4
% 16.58/3.06 (5) iminus6 = iminus1
% 16.58/3.06 (6) iminus4 = iminus1
% 16.58/3.06 (7) ~ (iminus1 = iplus1)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (3), (4) imply:
% 16.58/3.06 | (8) iminus4 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (8) implies:
% 16.58/3.06 | (9) iminus4 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (6), (9) imply:
% 16.58/3.06 | (10) iminus1 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (5), (10) imply:
% 16.58/3.06 | (11) iminus6 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | REF_CLOSE: (1), (2), (7), (11) are inconsistent by sub-proof #13.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #8 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iplus6 = iplus1
% 16.58/3.06 (2) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.06 (3) iminus1 = iplus1
% 16.58/3.06 (4) iminus6 = iminus1
% 16.58/3.06 (5) ~ (iminus1 = iplus1)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (3) implies:
% 16.58/3.06 | (6) iminus1 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (4), (6) imply:
% 16.58/3.06 | (7) iminus6 = iplus1
% 16.58/3.06 |
% 16.58/3.06 | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #13.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #9 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iT = iminus7
% 16.58/3.06 (2) iT = iplus7
% 16.58/3.06 (3) ~ (iminus7 = iplus7)
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (1), (2) imply:
% 16.58/3.06 | (4) iminus7 = iplus7
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (4) implies:
% 16.58/3.06 | (5) iminus7 = iplus7
% 16.58/3.06 |
% 16.58/3.06 | REDUCE: (3), (5) imply:
% 16.58/3.06 | (6) $false
% 16.58/3.06 |
% 16.58/3.06 | CLOSE: (6) is inconsistent.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #10 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iminus6 = iT | iT = iminus2 | iT = iplus4
% 16.58/3.06 (2) iminus8 = iT | iT = iminus3 | iT = iplus5
% 16.58/3.06 (3) iminus8 = iT | iT = iminus3 | iT = iminus5
% 16.58/3.06 (4) iminus2 = iminus1 | iminus2 = iplus1
% 16.58/3.06 (5) iF = iplus3
% 16.58/3.06 (6) iT = iminus3
% 16.58/3.06 (7) iT = iminus3 | iT = iminus7 | iT = iminus4
% 16.58/3.06 (8) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.06 (9) iF = iminus3
% 16.58/3.06 (10) iminus7 = iminus1 | iplus7 = iminus1
% 16.58/3.06 (11) iplus8 = iT | iT = iminus3 | iT = iplus2
% 16.58/3.06 (12) iplus8 = iminus2 | iplus8 = iplus2
% 16.58/3.06 (13) iminus8 = iF | iplus8 = iF
% 16.58/3.06 (14) iplus8 = iF | iplus8 = iT
% 16.58/3.06 (15) iplus6 = iT | iT = iminus7 | iT = iminus2
% 16.58/3.06 (16) iT = iminus3 | iT = iminus2 | iT = iplus1
% 16.58/3.06 (17) ~ (iminus3 = iplus3)
% 16.58/3.06 (18) iminus8 = iminus5 | iminus8 = iplus5
% 16.58/3.06 (19) iminus3 = iplus4 | iminus3 = iminus4
% 16.58/3.06 (20) iplus8 = iT | iT = iminus3 | iT = iplus7
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (5), (9) imply:
% 16.58/3.06 | (21) iminus3 = iplus3
% 16.58/3.06 |
% 16.58/3.06 | SIMP: (21) implies:
% 16.58/3.06 | (22) iminus3 = iplus3
% 16.58/3.06 |
% 16.58/3.06 | COMBINE_EQS: (6), (22) imply:
% 16.58/3.06 | (23) iT = iplus3
% 16.58/3.06 |
% 16.58/3.06 | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 16.58/3.06 | (15), (16), (17), (18), (19), (20), (23) are inconsistent by
% 16.58/3.06 | sub-proof #11.
% 16.58/3.06 |
% 16.58/3.06 End of proof
% 16.58/3.06
% 16.58/3.06 Sub-proof #11 shows that the following formulas are inconsistent:
% 16.58/3.06 ----------------------------------------------------------------
% 16.58/3.06 (1) iminus6 = iT | iT = iminus2 | iT = iplus4
% 16.58/3.06 (2) iminus8 = iT | iT = iminus3 | iT = iplus5
% 16.58/3.06 (3) iminus8 = iT | iT = iminus3 | iT = iminus5
% 16.58/3.06 (4) iminus2 = iminus1 | iminus2 = iplus1
% 16.58/3.06 (5) iT = iminus3 | iT = iminus7 | iT = iminus4
% 16.58/3.06 (6) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.06 (7) iF = iminus3
% 16.58/3.06 (8) iminus7 = iminus1 | iplus7 = iminus1
% 16.58/3.06 (9) iplus8 = iT | iT = iminus3 | iT = iplus2
% 16.58/3.06 (10) iplus8 = iminus2 | iplus8 = iplus2
% 16.58/3.06 (11) iminus8 = iF | iplus8 = iF
% 16.58/3.06 (12) iplus8 = iF | iplus8 = iT
% 16.58/3.06 (13) iplus6 = iT | iT = iminus7 | iT = iminus2
% 16.58/3.06 (14) iT = iplus3
% 16.58/3.06 (15) iT = iminus3 | iT = iminus2 | iT = iplus1
% 16.58/3.06 (16) ~ (iminus3 = iplus3)
% 16.58/3.06 (17) iminus8 = iminus5 | iminus8 = iplus5
% 16.58/3.06 (18) iminus3 = iplus4 | iminus3 = iminus4
% 16.58/3.06 (19) iplus8 = iT | iT = iminus3 | iT = iplus7
% 16.58/3.06
% 16.58/3.06 Begin of proof
% 16.58/3.06 |
% 16.58/3.06 | BETA: splitting (15) gives:
% 16.58/3.06 |
% 16.58/3.06 | Case 1:
% 16.58/3.06 | |
% 16.58/3.06 | | (20) iT = iminus3
% 16.58/3.06 | |
% 16.58/3.06 | | COMBINE_EQS: (14), (20) imply:
% 16.58/3.06 | | (21) iminus3 = iplus3
% 16.58/3.06 | |
% 16.58/3.06 | | REDUCE: (16), (21) imply:
% 16.58/3.06 | | (22) $false
% 16.58/3.06 | |
% 16.58/3.06 | | CLOSE: (22) is inconsistent.
% 16.58/3.06 | |
% 16.58/3.06 | Case 2:
% 16.58/3.06 | |
% 16.58/3.06 | | (23) ~ (iT = iminus3)
% 16.58/3.07 | | (24) iT = iminus2 | iT = iplus1
% 16.58/3.07 | |
% 16.58/3.07 | | REDUCE: (14), (23) imply:
% 16.58/3.07 | | (25) ~ (iminus3 = iplus3)
% 16.58/3.07 | |
% 16.58/3.07 | | BETA: splitting (9) gives:
% 16.58/3.07 | |
% 16.58/3.07 | | Case 1:
% 16.58/3.07 | | |
% 16.58/3.07 | | | (26) iplus8 = iT
% 16.58/3.07 | | |
% 16.58/3.07 | | | COMBINE_EQS: (14), (26) imply:
% 16.58/3.07 | | | (27) iplus8 = iplus3
% 16.58/3.07 | | |
% 16.58/3.07 | | | BETA: splitting (11) gives:
% 16.58/3.07 | | |
% 16.58/3.07 | | | Case 1:
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | (28) iminus8 = iF
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | COMBINE_EQS: (7), (28) imply:
% 16.58/3.07 | | | | (29) iminus8 = iminus3
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | REF_CLOSE: (2), (3), (14), (16), (17), (29) are inconsistent by
% 16.58/3.07 | | | | sub-proof #14.
% 16.58/3.07 | | | |
% 16.58/3.07 | | | Case 2:
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | (30) iplus8 = iF
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | COMBINE_EQS: (27), (30) imply:
% 16.58/3.07 | | | | (31) iF = iplus3
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | SIMP: (31) implies:
% 16.58/3.07 | | | | (32) iF = iplus3
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | COMBINE_EQS: (7), (32) imply:
% 16.58/3.07 | | | | (33) iminus3 = iplus3
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | REDUCE: (16), (33) imply:
% 16.58/3.07 | | | | (34) $false
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | CLOSE: (34) is inconsistent.
% 16.58/3.07 | | | |
% 16.58/3.07 | | | End of split
% 16.58/3.07 | | |
% 16.58/3.07 | | Case 2:
% 16.58/3.07 | | |
% 16.58/3.07 | | | (35) ~ (iplus8 = iT)
% 16.58/3.07 | | | (36) iT = iminus3 | iT = iplus2
% 16.58/3.07 | | |
% 16.58/3.07 | | | REDUCE: (14), (35) imply:
% 16.58/3.07 | | | (37) ~ (iplus8 = iplus3)
% 16.58/3.07 | | |
% 16.58/3.07 | | | BETA: splitting (19) gives:
% 16.58/3.07 | | |
% 16.58/3.07 | | | Case 1:
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | (38) iplus8 = iT
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | COMBINE_EQS: (14), (38) imply:
% 16.58/3.07 | | | | (39) iplus8 = iplus3
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | REDUCE: (37), (39) imply:
% 16.58/3.07 | | | | (40) $false
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | CLOSE: (40) is inconsistent.
% 16.58/3.07 | | | |
% 16.58/3.07 | | | Case 2:
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | (41) iT = iminus3 | iT = iplus7
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | BETA: splitting (12) gives:
% 16.58/3.07 | | | |
% 16.58/3.07 | | | | Case 1:
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | (42) iplus8 = iT
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | COMBINE_EQS: (14), (42) imply:
% 16.58/3.07 | | | | | (43) iplus8 = iplus3
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | REDUCE: (37), (43) imply:
% 16.58/3.07 | | | | | (44) $false
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | CLOSE: (44) is inconsistent.
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | Case 2:
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | (45) iplus8 = iF
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | COMBINE_EQS: (7), (45) imply:
% 16.58/3.07 | | | | | (46) iplus8 = iminus3
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | BETA: splitting (36) gives:
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | | Case 1:
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | (47) iT = iminus3
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | REF_CLOSE: (14), (16), (47) are inconsistent by sub-proof #15.
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | Case 2:
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | (48) iT = iplus2
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | COMBINE_EQS: (14), (48) imply:
% 16.58/3.07 | | | | | | (49) iplus3 = iplus2
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | REDUCE: (16), (49) imply:
% 16.58/3.07 | | | | | | (50) ~ (iminus3 = iplus2)
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | BETA: splitting (10) gives:
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | | Case 1:
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | (51) iplus8 = iminus2
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | COMBINE_EQS: (46), (51) imply:
% 16.58/3.07 | | | | | | | (52) iminus3 = iminus2
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | REDUCE: (50), (52) imply:
% 16.58/3.07 | | | | | | | (53) ~ (iminus2 = iplus2)
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | BETA: splitting (24) gives:
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | (54) iT = iminus2
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | COMBINE_EQS: (48), (54) imply:
% 16.58/3.07 | | | | | | | | (55) iminus2 = iplus2
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | REDUCE: (53), (55) imply:
% 16.58/3.07 | | | | | | | | (56) $false
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | CLOSE: (56) is inconsistent.
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | (57) iT = iplus1
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | COMBINE_EQS: (48), (57) imply:
% 16.58/3.07 | | | | | | | | (58) iplus2 = iplus1
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | SIMP: (58) implies:
% 16.58/3.07 | | | | | | | | (59) iplus2 = iplus1
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | REDUCE: (53), (59) imply:
% 16.58/3.07 | | | | | | | | (60) ~ (iminus2 = iplus1)
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | BETA: splitting (4) gives:
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | (61) iminus2 = iplus1
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | REDUCE: (60), (61) imply:
% 16.58/3.07 | | | | | | | | | (62) $false
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | CLOSE: (62) is inconsistent.
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | (63) iminus2 = iminus1
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | COMBINE_EQS: (52), (63) imply:
% 16.58/3.07 | | | | | | | | | (64) iminus3 = iminus1
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | REDUCE: (60), (63) imply:
% 16.58/3.07 | | | | | | | | | (65) ~ (iminus1 = iplus1)
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | BETA: splitting (41) gives:
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | (66) iT = iminus3
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | COMBINE_EQS: (57), (66) imply:
% 16.58/3.07 | | | | | | | | | | (67) iminus3 = iplus1
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | COMBINE_EQS: (64), (67) imply:
% 16.58/3.07 | | | | | | | | | | (68) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | REDUCE: (65), (68) imply:
% 16.58/3.07 | | | | | | | | | | (69) $false
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | CLOSE: (69) is inconsistent.
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | (70) iT = iplus7
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | COMBINE_EQS: (57), (70) imply:
% 16.58/3.07 | | | | | | | | | | (71) iplus7 = iplus1
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | REDUCE: (23), (57), (64) imply:
% 16.58/3.07 | | | | | | | | | | (72) ~ (iminus1 = iplus1)
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | BETA: splitting (8) gives:
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | (73) iminus7 = iminus1
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | BETA: splitting (5) gives:
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | (74) iT = iminus3
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | COMBINE_EQS: (57), (74) imply:
% 16.58/3.07 | | | | | | | | | | | | (75) iminus3 = iplus1
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | SIMP: (75) implies:
% 16.58/3.07 | | | | | | | | | | | | (76) iminus3 = iplus1
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | COMBINE_EQS: (64), (76) imply:
% 16.58/3.07 | | | | | | | | | | | | (77) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | REDUCE: (65), (77) imply:
% 16.58/3.07 | | | | | | | | | | | | (78) $false
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | CLOSE: (78) is inconsistent.
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | (79) iT = iminus7 | iT = iminus4
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | BETA: splitting (79) gives:
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | (80) iT = iminus7
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | COMBINE_EQS: (57), (80) imply:
% 16.58/3.07 | | | | | | | | | | | | | (81) iminus7 = iplus1
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | SIMP: (81) implies:
% 16.58/3.07 | | | | | | | | | | | | | (82) iminus7 = iplus1
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | COMBINE_EQS: (73), (82) imply:
% 16.58/3.07 | | | | | | | | | | | | | (83) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | REDUCE: (65), (83) imply:
% 16.58/3.07 | | | | | | | | | | | | | (84) $false
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | CLOSE: (84) is inconsistent.
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | (85) iT = iminus4
% 16.58/3.07 | | | | | | | | | | | | | (86) ~ (iT = iminus7)
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | COMBINE_EQS: (57), (85) imply:
% 16.58/3.07 | | | | | | | | | | | | | (87) iminus4 = iplus1
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | SIMP: (87) implies:
% 16.58/3.07 | | | | | | | | | | | | | (88) iminus4 = iplus1
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | BETA: splitting (18) gives:
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | (89) iminus3 = iminus4
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | COMBINE_EQS: (64), (89) imply:
% 16.58/3.07 | | | | | | | | | | | | | | (90) iminus4 = iminus1
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | SIMP: (90) implies:
% 16.58/3.07 | | | | | | | | | | | | | | (91) iminus4 = iminus1
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | COMBINE_EQS: (88), (91) imply:
% 16.58/3.07 | | | | | | | | | | | | | | (92) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | REDUCE: (65), (92) imply:
% 16.58/3.07 | | | | | | | | | | | | | | (93) $false
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | CLOSE: (93) is inconsistent.
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | (94) iminus3 = iplus4
% 16.58/3.07 | | | | | | | | | | | | | | (95) ~ (iminus3 = iminus4)
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | COMBINE_EQS: (64), (94) imply:
% 16.58/3.07 | | | | | | | | | | | | | | (96) iplus4 = iminus1
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | SIMP: (96) implies:
% 16.58/3.07 | | | | | | | | | | | | | | (97) iplus4 = iminus1
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | (98) iplus6 = iT
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | COMBINE_EQS: (57), (98) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | (99) iplus6 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | (100) iminus6 = iT
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (100) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | (101) iminus6 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (65), (99), (101) are inconsistent by
% 16.58/3.07 | | | | | | | | | | | | | | | | sub-proof #13.
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | (102) iT = iminus2 | iT = iplus4
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | (103) iT = iminus2
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (63), (65), (103) are inconsistent by
% 16.58/3.07 | | | | | | | | | | | | | | | | | sub-proof #12.
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | (104) iT = iplus4
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (104) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | | (105) iplus4 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | SIMP: (105) implies:
% 16.58/3.07 | | | | | | | | | | | | | | | | | (106) iplus4 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (106) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | | (107) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | SIMP: (107) implies:
% 16.58/3.07 | | | | | | | | | | | | | | | | | (108) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | REDUCE: (65), (108) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | | (109) $false
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 16.58/3.07 | | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | (110) iT = iminus7 | iT = iminus2
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | Case 1:
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | (111) iT = iminus7
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (111) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | (112) iminus7 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | SIMP: (112) implies:
% 16.58/3.07 | | | | | | | | | | | | | | | | (113) iminus7 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (113) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | (114) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | SIMP: (114) implies:
% 16.58/3.07 | | | | | | | | | | | | | | | | (115) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | REDUCE: (65), (115) imply:
% 16.58/3.07 | | | | | | | | | | | | | | | | (116) $false
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | (117) iT = iminus2
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | | REF_CLOSE: (57), (63), (65), (117) are inconsistent by
% 16.58/3.07 | | | | | | | | | | | | | | | | sub-proof #12.
% 16.58/3.07 | | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | Case 2:
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | (118) iplus7 = iminus1
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | COMBINE_EQS: (71), (118) imply:
% 16.58/3.07 | | | | | | | | | | | (119) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | SIMP: (119) implies:
% 16.58/3.07 | | | | | | | | | | | (120) iminus1 = iplus1
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | REDUCE: (65), (120) imply:
% 16.58/3.07 | | | | | | | | | | | (121) $false
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | | CLOSE: (121) is inconsistent.
% 16.58/3.07 | | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | | |
% 16.58/3.07 | | | | | | | | | End of split
% 16.58/3.07 | | | | | | | | |
% 16.58/3.07 | | | | | | | | End of split
% 16.58/3.07 | | | | | | | |
% 16.58/3.07 | | | | | | | End of split
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | Case 2:
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | (122) iplus8 = iplus2
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | COMBINE_EQS: (46), (122) imply:
% 16.58/3.07 | | | | | | | (123) iminus3 = iplus2
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | REDUCE: (50), (123) imply:
% 16.58/3.07 | | | | | | | (124) $false
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | | CLOSE: (124) is inconsistent.
% 16.58/3.07 | | | | | | |
% 16.58/3.07 | | | | | | End of split
% 16.58/3.07 | | | | | |
% 16.58/3.07 | | | | | End of split
% 16.58/3.07 | | | | |
% 16.58/3.07 | | | | End of split
% 16.58/3.07 | | | |
% 16.58/3.07 | | | End of split
% 16.58/3.07 | | |
% 16.58/3.07 | | End of split
% 16.58/3.07 | |
% 16.58/3.07 | End of split
% 16.58/3.07 |
% 16.58/3.07 End of proof
% 16.58/3.07
% 16.58/3.07 Sub-proof #12 shows that the following formulas are inconsistent:
% 16.58/3.07 ----------------------------------------------------------------
% 16.58/3.07 (1) iT = iminus2
% 16.58/3.07 (2) iT = iplus1
% 16.58/3.07 (3) iminus2 = iminus1
% 16.58/3.07 (4) ~ (iminus1 = iplus1)
% 16.58/3.07
% 16.58/3.07 Begin of proof
% 16.58/3.07 |
% 16.58/3.07 | COMBINE_EQS: (1), (2) imply:
% 16.58/3.07 | (5) iminus2 = iplus1
% 16.58/3.07 |
% 16.58/3.07 | SIMP: (5) implies:
% 16.58/3.07 | (6) iminus2 = iplus1
% 16.58/3.07 |
% 16.58/3.07 | COMBINE_EQS: (3), (6) imply:
% 16.58/3.07 | (7) iminus1 = iplus1
% 16.58/3.07 |
% 16.58/3.07 | SIMP: (7) implies:
% 16.58/3.07 | (8) iminus1 = iplus1
% 16.58/3.07 |
% 16.58/3.07 | REDUCE: (4), (8) imply:
% 16.58/3.07 | (9) $false
% 16.58/3.07 |
% 16.58/3.07 | CLOSE: (9) is inconsistent.
% 16.58/3.07 |
% 16.58/3.07 End of proof
% 16.58/3.07
% 16.58/3.07 Sub-proof #13 shows that the following formulas are inconsistent:
% 16.58/3.07 ----------------------------------------------------------------
% 16.58/3.07 (1) iplus6 = iminus1 | iminus6 = iminus1
% 16.58/3.07 (2) iplus6 = iplus1
% 16.58/3.07 (3) ~ (iminus1 = iplus1)
% 16.58/3.07 (4) iminus6 = iplus1
% 16.58/3.07
% 16.58/3.07 Begin of proof
% 16.58/3.07 |
% 16.58/3.07 | BETA: splitting (1) gives:
% 16.58/3.07 |
% 16.58/3.07 | Case 1:
% 16.58/3.07 | |
% 16.58/3.07 | | (5) iplus6 = iminus1
% 16.58/3.07 | |
% 16.58/3.07 | | COMBINE_EQS: (2), (5) imply:
% 16.58/3.07 | | (6) iminus1 = iplus1
% 16.58/3.07 | |
% 16.58/3.07 | | SIMP: (6) implies:
% 16.58/3.07 | | (7) iminus1 = iplus1
% 16.58/3.07 | |
% 16.58/3.07 | | REDUCE: (3), (7) imply:
% 16.58/3.07 | | (8) $false
% 16.58/3.07 | |
% 16.58/3.07 | | CLOSE: (8) is inconsistent.
% 16.58/3.07 | |
% 16.58/3.07 | Case 2:
% 16.58/3.07 | |
% 16.58/3.07 | | (9) iminus6 = iminus1
% 16.58/3.07 | |
% 16.58/3.07 | | COMBINE_EQS: (4), (9) imply:
% 16.58/3.07 | | (10) iminus1 = iplus1
% 16.58/3.07 | |
% 16.58/3.07 | | SIMP: (10) implies:
% 16.58/3.07 | | (11) iminus1 = iplus1
% 16.58/3.07 | |
% 16.58/3.07 | | REDUCE: (3), (11) imply:
% 16.58/3.07 | | (12) $false
% 16.58/3.07 | |
% 16.58/3.07 | | CLOSE: (12) is inconsistent.
% 16.58/3.07 | |
% 16.58/3.07 | End of split
% 16.58/3.07 |
% 16.58/3.07 End of proof
% 16.58/3.07
% 16.58/3.07 Sub-proof #14 shows that the following formulas are inconsistent:
% 16.58/3.07 ----------------------------------------------------------------
% 16.58/3.07 (1) iminus8 = iT | iT = iminus3 | iT = iplus5
% 16.58/3.07 (2) iminus8 = iT | iT = iminus3 | iT = iminus5
% 16.58/3.07 (3) iT = iplus3
% 16.58/3.07 (4) iminus8 = iminus3
% 16.58/3.07 (5) ~ (iminus3 = iplus3)
% 16.58/3.07 (6) iminus8 = iminus5 | iminus8 = iplus5
% 16.58/3.07
% 16.58/3.07 Begin of proof
% 16.58/3.07 |
% 16.58/3.07 | BETA: splitting (1) gives:
% 16.58/3.07 |
% 16.58/3.07 | Case 1:
% 16.58/3.07 | |
% 16.58/3.07 | | (7) iminus8 = iT
% 16.58/3.07 | |
% 16.58/3.07 | | COMBINE_EQS: (4), (7) imply:
% 16.58/3.07 | | (8) iT = iminus3
% 16.58/3.07 | |
% 16.58/3.07 | | SIMP: (8) implies:
% 16.58/3.07 | | (9) iT = iminus3
% 16.58/3.07 | |
% 16.58/3.07 | | COMBINE_EQS: (3), (9) imply:
% 16.58/3.07 | | (10) iminus3 = iplus3
% 16.58/3.07 | |
% 16.58/3.07 | | REDUCE: (5), (10) imply:
% 16.58/3.07 | | (11) $false
% 16.58/3.07 | |
% 16.58/3.07 | | CLOSE: (11) is inconsistent.
% 16.58/3.07 | |
% 16.58/3.07 | Case 2:
% 16.58/3.07 | |
% 16.58/3.07 | | (12) ~ (iminus8 = iT)
% 16.58/3.07 | | (13) iT = iminus3 | iT = iplus5
% 16.58/3.07 | |
% 16.58/3.07 | | BETA: splitting (13) gives:
% 16.58/3.07 | |
% 16.58/3.07 | | Case 1:
% 16.58/3.07 | | |
% 16.58/3.07 | | | (14) iT = iminus3
% 16.58/3.07 | | |
% 16.58/3.07 | | | REF_CLOSE: (3), (5), (14) are inconsistent by sub-proof #15.
% 16.58/3.07 | | |
% 16.58/3.08 | | Case 2:
% 16.58/3.08 | | |
% 16.58/3.08 | | | (15) iT = iplus5
% 16.58/3.08 | | |
% 16.58/3.08 | | | COMBINE_EQS: (3), (15) imply:
% 16.58/3.08 | | | (16) iplus3 = iplus5
% 16.58/3.08 | | |
% 16.58/3.08 | | | REDUCE: (5), (16) imply:
% 16.58/3.08 | | | (17) ~ (iminus3 = iplus5)
% 16.58/3.08 | | |
% 16.58/3.08 | | | BETA: splitting (6) gives:
% 16.58/3.08 | | |
% 16.58/3.08 | | | Case 1:
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | (18) iminus8 = iminus5
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | COMBINE_EQS: (4), (18) imply:
% 16.58/3.08 | | | | (19) iminus3 = iminus5
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | REDUCE: (17), (19) imply:
% 16.58/3.08 | | | | (20) ~ (iminus5 = iplus5)
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | BETA: splitting (2) gives:
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | Case 1:
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | (21) iminus8 = iT
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | COMBINE_EQS: (18), (21) imply:
% 16.58/3.08 | | | | | (22) iT = iminus5
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | SIMP: (22) implies:
% 16.58/3.08 | | | | | (23) iT = iminus5
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | COMBINE_EQS: (15), (23) imply:
% 16.58/3.08 | | | | | (24) iminus5 = iplus5
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | SIMP: (24) implies:
% 16.58/3.08 | | | | | (25) iminus5 = iplus5
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | REDUCE: (20), (25) imply:
% 16.58/3.08 | | | | | (26) $false
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | CLOSE: (26) is inconsistent.
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | Case 2:
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | (27) iT = iminus3 | iT = iminus5
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | BETA: splitting (27) gives:
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | | Case 1:
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | (28) iT = iminus3
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | COMBINE_EQS: (15), (28) imply:
% 16.58/3.08 | | | | | | (29) iminus3 = iplus5
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | COMBINE_EQS: (19), (29) imply:
% 16.58/3.08 | | | | | | (30) iminus5 = iplus5
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | REDUCE: (20), (30) imply:
% 16.58/3.08 | | | | | | (31) $false
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | CLOSE: (31) is inconsistent.
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | Case 2:
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | (32) iT = iminus5
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | COMBINE_EQS: (15), (32) imply:
% 16.58/3.08 | | | | | | (33) iminus5 = iplus5
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | REDUCE: (20), (33) imply:
% 16.58/3.08 | | | | | | (34) $false
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | | CLOSE: (34) is inconsistent.
% 16.58/3.08 | | | | | |
% 16.58/3.08 | | | | | End of split
% 16.58/3.08 | | | | |
% 16.58/3.08 | | | | End of split
% 16.58/3.08 | | | |
% 16.58/3.08 | | | Case 2:
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | (35) iminus8 = iplus5
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | COMBINE_EQS: (4), (35) imply:
% 16.58/3.08 | | | | (36) iminus3 = iplus5
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | REDUCE: (17), (36) imply:
% 16.58/3.08 | | | | (37) $false
% 16.58/3.08 | | | |
% 16.58/3.08 | | | | CLOSE: (37) is inconsistent.
% 16.58/3.08 | | | |
% 16.58/3.08 | | | End of split
% 16.58/3.08 | | |
% 16.58/3.08 | | End of split
% 16.58/3.08 | |
% 16.58/3.08 | End of split
% 16.58/3.08 |
% 16.58/3.08 End of proof
% 16.58/3.08
% 16.58/3.08 Sub-proof #15 shows that the following formulas are inconsistent:
% 16.58/3.08 ----------------------------------------------------------------
% 16.58/3.08 (1) iT = iminus3
% 16.58/3.08 (2) iT = iplus3
% 16.58/3.08 (3) ~ (iminus3 = iplus3)
% 16.58/3.08
% 16.58/3.08 Begin of proof
% 16.58/3.08 |
% 16.58/3.08 | COMBINE_EQS: (1), (2) imply:
% 16.58/3.08 | (4) iminus3 = iplus3
% 16.58/3.08 |
% 16.58/3.08 | SIMP: (4) implies:
% 16.58/3.08 | (5) iminus3 = iplus3
% 16.58/3.08 |
% 16.58/3.08 | REDUCE: (3), (5) imply:
% 16.58/3.08 | (6) $false
% 16.58/3.08 |
% 16.58/3.08 | CLOSE: (6) is inconsistent.
% 16.58/3.08 |
% 16.58/3.08 End of proof
% 16.58/3.08 % SZS output end Proof for theBenchmark
% 16.58/3.08
% 16.58/3.08 2473ms
%------------------------------------------------------------------------------