TSTP Solution File: GEO188+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO188+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:22:02 EDT 2023
% Result : Theorem 16.64s 2.85s
% Output : Proof 17.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GEO188+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 29 23:17:02 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.16/0.52 ________ _____
% 0.16/0.52 ___ __ \_________(_)________________________________
% 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52
% 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52 (2023-06-19)
% 0.16/0.52
% 0.16/0.52 (c) Philipp Rümmer, 2009-2023
% 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52 Amanda Stjerna.
% 0.16/0.52 Free software under BSD-3-Clause.
% 0.16/0.52
% 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52
% 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.17/0.90 Prover 4: Preprocessing ...
% 2.17/0.90 Prover 1: Preprocessing ...
% 2.17/0.93 Prover 2: Preprocessing ...
% 2.17/0.93 Prover 3: Preprocessing ...
% 2.17/0.93 Prover 6: Preprocessing ...
% 2.17/0.93 Prover 5: Preprocessing ...
% 2.17/0.93 Prover 0: Preprocessing ...
% 3.90/1.13 Prover 5: Proving ...
% 3.90/1.14 Prover 2: Proving ...
% 3.90/1.15 Prover 6: Constructing countermodel ...
% 3.90/1.16 Prover 3: Constructing countermodel ...
% 3.90/1.16 Prover 1: Constructing countermodel ...
% 4.38/1.27 Prover 3: gave up
% 4.38/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.38/1.28 Prover 4: Constructing countermodel ...
% 4.38/1.29 Prover 0: Proving ...
% 4.38/1.30 Prover 6: gave up
% 4.38/1.31 Prover 7: Preprocessing ...
% 4.38/1.31 Prover 1: gave up
% 4.38/1.32 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.38/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.05/1.34 Prover 7: Warning: ignoring some quantifiers
% 5.05/1.34 Prover 8: Preprocessing ...
% 5.05/1.35 Prover 7: Constructing countermodel ...
% 5.59/1.35 Prover 9: Preprocessing ...
% 6.35/1.45 Prover 8: Warning: ignoring some quantifiers
% 6.35/1.45 Prover 8: Constructing countermodel ...
% 6.84/1.54 Prover 9: Constructing countermodel ...
% 6.84/1.55 Prover 8: gave up
% 7.25/1.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.25/1.59 Prover 10: Preprocessing ...
% 7.89/1.65 Prover 10: Warning: ignoring some quantifiers
% 7.89/1.66 Prover 10: Constructing countermodel ...
% 8.17/1.70 Prover 10: gave up
% 8.17/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.63/1.76 Prover 11: Preprocessing ...
% 8.63/1.84 Prover 7: gave up
% 8.63/1.84 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.63/1.87 Prover 12: Preprocessing ...
% 9.19/1.89 Prover 11: Constructing countermodel ...
% 9.91/1.99 Prover 12: Proving ...
% 11.20/2.09 Prover 11: gave up
% 11.20/2.10 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.20/2.13 Prover 13: Preprocessing ...
% 11.20/2.15 Prover 13: Warning: ignoring some quantifiers
% 11.20/2.15 Prover 13: Constructing countermodel ...
% 12.93/2.32 Prover 13: gave up
% 12.93/2.33 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 12.93/2.36 Prover 14: Preprocessing ...
% 13.54/2.46 Prover 14: Proving ...
% 16.64/2.85 Prover 4: Found proof (size 346)
% 16.64/2.85 Prover 4: proved (2311ms)
% 16.64/2.85 Prover 9: stopped
% 16.64/2.85 Prover 5: stopped
% 16.64/2.85 Prover 12: stopped
% 16.64/2.85 Prover 2: stopped
% 16.64/2.85 Prover 14: stopped
% 16.64/2.85 Prover 0: stopped
% 16.64/2.85
% 16.64/2.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.64/2.85
% 16.64/2.87 % SZS output start Proof for theBenchmark
% 16.64/2.87 Assumptions after simplification:
% 16.64/2.87 ---------------------------------
% 16.64/2.87
% 16.64/2.87 (apart1)
% 17.33/2.90 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 17.33/2.90
% 17.33/2.90 (apart4)
% 17.33/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 17.33/2.90 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2)
% 17.33/2.90 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 17.33/2.90 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.33/2.90 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~
% 17.33/2.90 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.33/2.90 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.33/2.90 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~
% 17.33/2.90 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.33/2.90 distinct_points(v1, v2) = 0)
% 17.33/2.90
% 17.33/2.90 (ceq2)
% 17.40/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 17.40/2.91 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1,
% 17.40/2.91 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 17.40/2.91 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 17.40/2.91 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) |
% 17.40/2.91 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.40/2.91 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.40/2.91 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~
% 17.40/2.91 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.40/2.91 apart_point_and_line(v0, v2) = 0)
% 17.40/2.91
% 17.40/2.91 (con)
% 17.40/2.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5:
% 17.40/2.91 $i] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1)
% 17.40/2.91 = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, v5) = 0
% 17.40/2.91 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 &
% 17.40/2.91 distinct_points(v0, v1) = 0 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.40/2.91
% 17.40/2.91 (con1)
% 17.42/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.42/2.91 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ~
% 17.42/2.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 17.42/2.91 : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 &
% 17.42/2.91 distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 17.42/2.91
% 17.42/2.91 (cu1)
% 17.42/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 17.42/2.93 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 17.42/2.93 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 17.42/2.93 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 17.42/2.93 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 17.42/2.93 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 17.42/2.93 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.42/2.93 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 17.42/2.93 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 17.42/2.93 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 17.42/2.93 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 17.42/2.93 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 17.42/2.93 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.42/2.93 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 17.42/2.93 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 17.42/2.93 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 17.42/2.93 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 17.42/2.93 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 17.42/2.93 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 17.42/2.93 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 17.42/2.93 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 17.42/2.93 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.42/2.93 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 17.42/2.93 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 17.42/2.93 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 17.42/2.93 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 17.42/2.93 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 17.42/2.93 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 17.42/2.93 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 17.42/2.93 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 17.42/2.93 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 17.42/2.93 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 17.42/2.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 17.42/2.93 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 17.42/2.93 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 17.42/2.93 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 17.42/2.93 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 17.42/2.93 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 17.42/2.93 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.42/2.93 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 17.42/2.93 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 17.42/2.93 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 17.42/2.93 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 17.42/2.93 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 17.42/2.93
% 17.42/2.93 (function-axioms)
% 17.42/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.42/2.93 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) &
% 17.42/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.42/2.93 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & !
% 17.42/2.93 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.42/2.93 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 17.42/2.93 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.42/2.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.42/2.93 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & !
% 17.42/2.93 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.42/2.93 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3,
% 17.42/2.93 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 17.42/2.93 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 17.42/2.93 (distinct_points(v3, v2) = v0))
% 17.42/2.93
% 17.42/2.93 Further assumptions not needed in the proof:
% 17.42/2.93 --------------------------------------------
% 17.42/2.93 apart2, apart3, apart5, apart6, ceq1, ceq3, con2
% 17.42/2.93
% 17.42/2.93 Those formulas are unsatisfiable:
% 17.42/2.93 ---------------------------------
% 17.42/2.93
% 17.42/2.93 Begin of proof
% 17.42/2.93 |
% 17.42/2.93 | ALPHA: (apart4) implies:
% 17.42/2.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.42/2.93 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) |
% 17.42/2.93 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0)
% 17.42/2.93 |
% 17.42/2.93 | ALPHA: (cu1) implies:
% 17.42/2.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.42/2.93 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~
% 17.42/2.93 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 17.42/2.93 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3)
% 17.42/2.93 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0,
% 17.42/2.93 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 |
% 17.42/2.93 | v5 = 0 | v4 = 0)))
% 17.42/2.94 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.42/2.94 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 17.42/2.94 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 17.42/2.94 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.42/2.94 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1,
% 17.42/2.94 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2,
% 17.42/2.94 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 17.42/2.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.42/2.94 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 17.42/2.94 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.42/2.94 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 17.42/2.94 | [v9: any] : (apart_point_and_line(v1, v3) = v9 &
% 17.42/2.94 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 &
% 17.42/2.94 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 17.42/2.94 | | v8 = 0)))
% 17.42/2.94 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.42/2.94 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 17.42/2.94 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 17.42/2.94 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 17.42/2.94 | [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 17.42/2.94 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 17.42/2.94 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 17.42/2.94 | | v8 = 0)))
% 17.42/2.94 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.42/2.94 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 17.42/2.94 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 17.42/2.94 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 17.42/2.94 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 17.42/2.94 | apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 &
% 17.42/2.94 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 17.42/2.94 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 17.42/2.94 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5)
% 17.42/2.94 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0,
% 17.42/2.94 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.42/2.94 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0,
% 17.42/2.94 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2,
% 17.42/2.94 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 17.42/2.94 |
% 17.42/2.94 | ALPHA: (ceq2) implies:
% 17.42/2.94 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.42/2.94 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0,
% 17.42/2.94 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1,
% 17.42/2.94 | v2) = 0)
% 17.42/2.94 |
% 17.42/2.94 | ALPHA: (function-axioms) implies:
% 17.42/2.94 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.42/2.94 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 17.42/2.94 | (distinct_points(v3, v2) = v0))
% 17.42/2.94 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 17.42/2.94 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 17.42/2.94 | (apart_point_and_line(v3, v2) = v0))
% 17.42/2.94 |
% 17.42/2.94 | DELTA: instantiating (con) with fresh symbols all_15_0, all_15_1, all_15_2,
% 17.42/2.94 | all_15_3, all_15_4, all_15_5 gives:
% 17.42/2.94 | (11) ~ (all_15_1 = 0) & line_connecting(all_15_3, all_15_4) = all_15_0 &
% 17.42/2.94 | line_connecting(all_15_5, all_15_4) = all_15_2 &
% 17.42/2.94 | apart_point_and_line(all_15_3, all_15_2) = all_15_1 &
% 17.42/2.94 | apart_point_and_line(all_15_5, all_15_0) = 0 &
% 17.42/2.94 | distinct_points(all_15_4, all_15_3) = 0 & distinct_points(all_15_5,
% 17.42/2.94 | all_15_3) = 0 & distinct_points(all_15_5, all_15_4) = 0 &
% 17.42/2.94 | $i(all_15_0) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) &
% 17.42/2.94 | $i(all_15_5)
% 17.42/2.94 |
% 17.42/2.94 | ALPHA: (11) implies:
% 17.42/2.94 | (12) ~ (all_15_1 = 0)
% 17.42/2.94 | (13) $i(all_15_5)
% 17.42/2.94 | (14) $i(all_15_4)
% 17.42/2.94 | (15) $i(all_15_3)
% 17.42/2.94 | (16) $i(all_15_2)
% 17.42/2.94 | (17) $i(all_15_0)
% 17.42/2.94 | (18) distinct_points(all_15_5, all_15_4) = 0
% 17.42/2.94 | (19) distinct_points(all_15_5, all_15_3) = 0
% 17.42/2.94 | (20) distinct_points(all_15_4, all_15_3) = 0
% 17.42/2.95 | (21) apart_point_and_line(all_15_5, all_15_0) = 0
% 17.42/2.95 | (22) apart_point_and_line(all_15_3, all_15_2) = all_15_1
% 17.42/2.95 | (23) line_connecting(all_15_5, all_15_4) = all_15_2
% 17.42/2.95 | (24) line_connecting(all_15_3, all_15_4) = all_15_0
% 17.42/2.95 |
% 17.42/2.95 | GROUND_INST: instantiating (7) with all_15_4, all_15_3, all_15_2, all_15_2,
% 17.42/2.95 | all_15_1, all_15_1, simplifying with (14), (15), (16), (20), (22)
% 17.42/2.95 | gives:
% 17.42/2.95 | (25) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.95 | (apart_point_and_line(all_15_4, all_15_2) = v2 &
% 17.42/2.95 | apart_point_and_line(all_15_4, all_15_2) = v1 &
% 17.42/2.95 | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 17.42/2.95 | = 0))
% 17.42/2.95 |
% 17.42/2.95 | GROUND_INST: instantiating (7) with all_15_5, all_15_3, all_15_2, all_15_2,
% 17.42/2.95 | all_15_1, all_15_1, simplifying with (13), (15), (16), (19), (22)
% 17.42/2.95 | gives:
% 17.42/2.95 | (26) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.95 | (apart_point_and_line(all_15_5, all_15_2) = v2 &
% 17.42/2.95 | apart_point_and_line(all_15_5, all_15_2) = v1 &
% 17.42/2.95 | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1
% 17.42/2.95 | = 0))
% 17.42/2.95 |
% 17.42/2.95 | GROUND_INST: instantiating (5) with all_15_3, all_15_3, all_15_2, all_15_2,
% 17.42/2.95 | all_15_1, all_15_1, simplifying with (15), (16), (22) gives:
% 17.42/2.95 | (27) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 17.42/2.95 | any] : (apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/2.95 | apart_point_and_line(all_15_3, all_15_2) = v2 &
% 17.42/2.95 | distinct_lines(all_15_2, all_15_2) = v1 & distinct_points(all_15_3,
% 17.42/2.95 | all_15_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.95 |
% 17.42/2.95 | GROUND_INST: instantiating (con1) with all_15_3, all_15_4, all_15_5, all_15_0,
% 17.42/2.95 | simplifying with (13), (14), (15), (21), (24) gives:
% 17.42/2.95 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.95 | (distinct_points(all_15_3, all_15_4) = v0 & distinct_points(all_15_5,
% 17.42/2.95 | all_15_3) = v1 & distinct_points(all_15_5, all_15_4) = v2 & ( ~
% 17.42/2.95 | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 17.42/2.95 |
% 17.42/2.95 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2
% 17.42/2.95 | gives:
% 17.42/2.95 | (29) distinct_points(all_15_3, all_15_4) = all_22_2 &
% 17.42/2.95 | distinct_points(all_15_5, all_15_3) = all_22_1 &
% 17.42/2.95 | distinct_points(all_15_5, all_15_4) = all_22_0 & ( ~ (all_22_2 = 0) |
% 17.42/2.95 | (all_22_0 = 0 & all_22_1 = 0))
% 17.42/2.95 |
% 17.42/2.95 | ALPHA: (29) implies:
% 17.42/2.95 | (30) distinct_points(all_15_5, all_15_4) = all_22_0
% 17.42/2.95 | (31) distinct_points(all_15_5, all_15_3) = all_22_1
% 17.42/2.95 |
% 17.42/2.95 | BETA: splitting (26) gives:
% 17.42/2.95 |
% 17.42/2.95 | Case 1:
% 17.42/2.95 | |
% 17.42/2.95 | | (32) all_15_1 = 0
% 17.42/2.95 | |
% 17.42/2.95 | | REDUCE: (12), (32) imply:
% 17.42/2.95 | | (33) $false
% 17.42/2.95 | |
% 17.42/2.95 | | CLOSE: (33) is inconsistent.
% 17.42/2.95 | |
% 17.42/2.95 | Case 2:
% 17.42/2.95 | |
% 17.42/2.95 | | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.95 | | (apart_point_and_line(all_15_5, all_15_2) = v2 &
% 17.42/2.95 | | apart_point_and_line(all_15_5, all_15_2) = v1 &
% 17.42/2.95 | | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0 |
% 17.42/2.95 | | v1 = 0))
% 17.42/2.95 | |
% 17.42/2.95 | | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1, all_28_2
% 17.42/2.95 | | gives:
% 17.42/2.95 | | (35) apart_point_and_line(all_15_5, all_15_2) = all_28_0 &
% 17.42/2.95 | | apart_point_and_line(all_15_5, all_15_2) = all_28_1 &
% 17.42/2.95 | | distinct_lines(all_15_2, all_15_2) = all_28_2 & ( ~ (all_28_2 = 0) |
% 17.42/2.95 | | all_28_0 = 0 | all_28_1 = 0)
% 17.42/2.95 | |
% 17.42/2.95 | | ALPHA: (35) implies:
% 17.42/2.95 | | (36) apart_point_and_line(all_15_5, all_15_2) = all_28_1
% 17.42/2.95 | | (37) apart_point_and_line(all_15_5, all_15_2) = all_28_0
% 17.42/2.95 | |
% 17.42/2.96 | | BETA: splitting (25) gives:
% 17.42/2.96 | |
% 17.42/2.96 | | Case 1:
% 17.42/2.96 | | |
% 17.42/2.96 | | | (38) all_15_1 = 0
% 17.42/2.96 | | |
% 17.42/2.96 | | | REDUCE: (12), (38) imply:
% 17.42/2.96 | | | (39) $false
% 17.42/2.96 | | |
% 17.42/2.96 | | | CLOSE: (39) is inconsistent.
% 17.42/2.96 | | |
% 17.42/2.96 | | Case 2:
% 17.42/2.96 | | |
% 17.42/2.96 | | | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.96 | | | (apart_point_and_line(all_15_4, all_15_2) = v2 &
% 17.42/2.96 | | | apart_point_and_line(all_15_4, all_15_2) = v1 &
% 17.42/2.96 | | | distinct_lines(all_15_2, all_15_2) = v0 & ( ~ (v0 = 0) | v2 = 0
% 17.42/2.96 | | | | v1 = 0))
% 17.42/2.96 | | |
% 17.42/2.96 | | | DELTA: instantiating (40) with fresh symbols all_33_0, all_33_1, all_33_2
% 17.42/2.96 | | | gives:
% 17.42/2.96 | | | (41) apart_point_and_line(all_15_4, all_15_2) = all_33_0 &
% 17.42/2.96 | | | apart_point_and_line(all_15_4, all_15_2) = all_33_1 &
% 17.42/2.96 | | | distinct_lines(all_15_2, all_15_2) = all_33_2 & ( ~ (all_33_2 = 0)
% 17.42/2.96 | | | | all_33_0 = 0 | all_33_1 = 0)
% 17.42/2.96 | | |
% 17.42/2.96 | | | ALPHA: (41) implies:
% 17.42/2.96 | | | (42) apart_point_and_line(all_15_4, all_15_2) = all_33_1
% 17.42/2.96 | | | (43) apart_point_and_line(all_15_4, all_15_2) = all_33_0
% 17.42/2.96 | | |
% 17.42/2.96 | | | BETA: splitting (27) gives:
% 17.42/2.96 | | |
% 17.42/2.96 | | | Case 1:
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | (44) all_15_1 = 0
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | REDUCE: (12), (44) imply:
% 17.42/2.96 | | | | (45) $false
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | CLOSE: (45) is inconsistent.
% 17.42/2.96 | | | |
% 17.42/2.96 | | | Case 2:
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 17.42/2.96 | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/2.96 | | | | apart_point_and_line(all_15_3, all_15_2) = v2 &
% 17.42/2.96 | | | | distinct_lines(all_15_2, all_15_2) = v1 &
% 17.42/2.96 | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v1 = 0) | ~
% 17.42/2.96 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | DELTA: instantiating (46) with fresh symbols all_38_0, all_38_1,
% 17.42/2.96 | | | | all_38_2, all_38_3 gives:
% 17.42/2.96 | | | | (47) apart_point_and_line(all_15_3, all_15_2) = all_38_0 &
% 17.42/2.96 | | | | apart_point_and_line(all_15_3, all_15_2) = all_38_1 &
% 17.42/2.96 | | | | distinct_lines(all_15_2, all_15_2) = all_38_2 &
% 17.42/2.96 | | | | distinct_points(all_15_3, all_15_3) = all_38_3 & ( ~ (all_38_2 =
% 17.42/2.96 | | | | 0) | ~ (all_38_3 = 0) | all_38_0 = 0 | all_38_1 = 0)
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | ALPHA: (47) implies:
% 17.42/2.96 | | | | (48) apart_point_and_line(all_15_3, all_15_2) = all_38_1
% 17.42/2.96 | | | | (49) apart_point_and_line(all_15_3, all_15_2) = all_38_0
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (9) with 0, all_22_0, all_15_4, all_15_5,
% 17.42/2.96 | | | | simplifying with (18), (30) gives:
% 17.42/2.96 | | | | (50) all_22_0 = 0
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (9) with 0, all_22_1, all_15_3, all_15_5,
% 17.42/2.96 | | | | simplifying with (19), (31) gives:
% 17.42/2.96 | | | | (51) all_22_1 = 0
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (10) with all_28_1, all_28_0, all_15_2,
% 17.42/2.96 | | | | all_15_5, simplifying with (36), (37) gives:
% 17.42/2.96 | | | | (52) all_28_0 = all_28_1
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (10) with all_33_1, all_33_0, all_15_2,
% 17.42/2.96 | | | | all_15_4, simplifying with (42), (43) gives:
% 17.42/2.96 | | | | (53) all_33_0 = all_33_1
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (10) with all_15_1, all_38_0, all_15_2,
% 17.42/2.96 | | | | all_15_3, simplifying with (22), (49) gives:
% 17.42/2.96 | | | | (54) all_38_0 = all_15_1
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (10) with all_38_1, all_38_0, all_15_2,
% 17.42/2.96 | | | | all_15_3, simplifying with (48), (49) gives:
% 17.42/2.96 | | | | (55) all_38_0 = all_38_1
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | COMBINE_EQS: (54), (55) imply:
% 17.42/2.96 | | | | (56) all_38_1 = all_15_1
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (8) with all_15_5, all_15_0, all_15_2,
% 17.42/2.96 | | | | all_28_1, simplifying with (13), (16), (17), (21), (36)
% 17.42/2.96 | | | | gives:
% 17.42/2.96 | | | | (57) all_28_1 = 0 | distinct_lines(all_15_0, all_15_2) = 0
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (5) with all_15_5, all_15_5, all_15_2,
% 17.42/2.96 | | | | all_15_2, all_28_1, all_28_1, simplifying with (13), (16),
% 17.42/2.96 | | | | (36) gives:
% 17.42/2.96 | | | | (58) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.42/2.96 | | | | [v3: any] : (apart_point_and_line(all_15_5, all_15_2) = v3 &
% 17.42/2.96 | | | | apart_point_and_line(all_15_5, all_15_2) = v2 &
% 17.42/2.96 | | | | distinct_lines(all_15_2, all_15_2) = v1 &
% 17.42/2.96 | | | | distinct_points(all_15_5, all_15_5) = v0 & ( ~ (v1 = 0) | ~
% 17.42/2.96 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.96 | | | |
% 17.42/2.96 | | | | GROUND_INST: instantiating (5) with all_15_3, all_15_4, all_15_2,
% 17.42/2.96 | | | | all_15_2, all_15_1, all_33_1, simplifying with (14), (15),
% 17.42/2.96 | | | | (16), (22), (42) gives:
% 17.42/2.97 | | | | (59) all_33_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/2.97 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_15_3,
% 17.42/2.97 | | | | all_15_2) = v2 & apart_point_and_line(all_15_4, all_15_2) =
% 17.42/2.97 | | | | v3 & distinct_lines(all_15_2, all_15_2) = v1 &
% 17.42/2.97 | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~ (v1 = 0) | ~
% 17.42/2.97 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.97 | | | |
% 17.42/2.97 | | | | GROUND_INST: instantiating (5) with all_15_4, all_15_4, all_15_2,
% 17.42/2.97 | | | | all_15_2, all_33_1, all_33_1, simplifying with (14), (16),
% 17.42/2.97 | | | | (42) gives:
% 17.42/2.97 | | | | (60) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.42/2.97 | | | | [v3: any] : (apart_point_and_line(all_15_4, all_15_2) = v3 &
% 17.42/2.97 | | | | apart_point_and_line(all_15_4, all_15_2) = v2 &
% 17.42/2.97 | | | | distinct_lines(all_15_2, all_15_2) = v1 &
% 17.42/2.97 | | | | distinct_points(all_15_4, all_15_4) = v0 & ( ~ (v1 = 0) | ~
% 17.42/2.97 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.97 | | | |
% 17.42/2.97 | | | | BETA: splitting (57) gives:
% 17.42/2.97 | | | |
% 17.42/2.97 | | | | Case 1:
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | (61) distinct_lines(all_15_0, all_15_2) = 0
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (6) with all_15_3, all_15_3, all_15_0,
% 17.42/2.97 | | | | | all_15_2, all_15_1, all_15_1, simplifying with (15),
% 17.42/2.97 | | | | | (16), (17), (22), (61) gives:
% 17.42/2.97 | | | | | (62) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.97 | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 &
% 17.42/2.97 | | | | | apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/2.97 | | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v0 = 0) | v2
% 17.42/2.97 | | | | | = 0 | v1 = 0))
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (6) with all_15_3, all_15_4, all_15_0,
% 17.42/2.97 | | | | | all_15_2, all_15_1, all_33_1, simplifying with (14),
% 17.42/2.97 | | | | | (15), (16), (17), (22), (42), (61) gives:
% 17.42/2.97 | | | | | (63) all_33_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/2.97 | | | | | [v2: any] : (apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/2.97 | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/2.97 | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~ (v0 = 0) | v2
% 17.42/2.97 | | | | | = 0 | v1 = 0))
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (6) with all_15_4, all_15_4, all_15_0,
% 17.42/2.97 | | | | | all_15_2, all_33_1, all_33_1, simplifying with (14),
% 17.42/2.97 | | | | | (16), (17), (42), (61) gives:
% 17.42/2.97 | | | | | (64) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.97 | | | | | (apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/2.97 | | | | | apart_point_and_line(all_15_4, all_15_0) = v1 &
% 17.42/2.97 | | | | | distinct_points(all_15_4, all_15_4) = v0 & ( ~ (v0 = 0) | v2
% 17.42/2.97 | | | | | = 0 | v1 = 0))
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (6) with all_15_3, all_15_5, all_15_0,
% 17.42/2.97 | | | | | all_15_2, all_15_1, all_28_1, simplifying with (13),
% 17.42/2.97 | | | | | (15), (16), (17), (22), (36), (61) gives:
% 17.42/2.97 | | | | | (65) all_28_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/2.97 | | | | | [v2: any] : (apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/2.97 | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/2.97 | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~ (v0 = 0) | v2
% 17.42/2.97 | | | | | = 0 | v1 = 0))
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (6) with all_15_4, all_15_5, all_15_0,
% 17.42/2.97 | | | | | all_15_2, all_33_1, all_28_1, simplifying with (13),
% 17.42/2.97 | | | | | (14), (16), (17), (36), (42), (61) gives:
% 17.42/2.97 | | | | | (66) all_33_1 = 0 | all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/2.97 | | | | | [v2: any] : (apart_point_and_line(all_15_4, all_15_0) = v1 &
% 17.42/2.97 | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/2.97 | | | | | distinct_points(all_15_4, all_15_5) = v0 & ( ~ (v0 = 0) | v2
% 17.42/2.97 | | | | | = 0 | v1 = 0))
% 17.42/2.97 | | | | |
% 17.42/2.97 | | | | | GROUND_INST: instantiating (2) with all_15_4, all_15_3, all_15_0,
% 17.42/2.97 | | | | | all_15_2, simplifying with (14), (15), (16), (17), (20),
% 17.42/2.97 | | | | | (61) gives:
% 17.42/2.98 | | | | | (67) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 17.42/2.98 | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_0) = v0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_2) = v1 & (v3 = 0 | v2
% 17.42/2.98 | | | | | = 0 | v1 = 0 | v0 = 0))
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | GROUND_INST: instantiating (2) with all_15_5, all_15_3, all_15_0,
% 17.42/2.98 | | | | | all_15_2, simplifying with (13), (15), (16), (17), (19),
% 17.42/2.98 | | | | | (61) gives:
% 17.42/2.98 | | | | | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 17.42/2.98 | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_0) = v0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & (v3 = 0 | v2
% 17.42/2.98 | | | | | = 0 | v1 = 0 | v0 = 0))
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | GROUND_INST: instantiating (2) with all_15_5, all_15_4, all_15_0,
% 17.42/2.98 | | | | | all_15_2, simplifying with (13), (14), (16), (17), (18),
% 17.42/2.98 | | | | | (61) gives:
% 17.42/2.98 | | | | | (69) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 17.42/2.98 | | | | | (apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_2) = v3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_0) = v0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 & (v3 = 0 | v2
% 17.42/2.98 | | | | | = 0 | v1 = 0 | v0 = 0))
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | DELTA: instantiating (69) with fresh symbols all_69_0, all_69_1,
% 17.42/2.98 | | | | | all_69_2, all_69_3 gives:
% 17.42/2.98 | | | | | (70) apart_point_and_line(all_15_4, all_15_0) = all_69_1 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_2) = all_69_0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_0) = all_69_3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_2) = all_69_2 &
% 17.42/2.98 | | | | | (all_69_0 = 0 | all_69_1 = 0 | all_69_2 = 0 | all_69_3 = 0)
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | ALPHA: (70) implies:
% 17.42/2.98 | | | | | (71) apart_point_and_line(all_15_5, all_15_2) = all_69_2
% 17.42/2.98 | | | | | (72) apart_point_and_line(all_15_4, all_15_2) = all_69_0
% 17.42/2.98 | | | | | (73) apart_point_and_line(all_15_4, all_15_0) = all_69_1
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | DELTA: instantiating (68) with fresh symbols all_71_0, all_71_1,
% 17.42/2.98 | | | | | all_71_2, all_71_3 gives:
% 17.42/2.98 | | | | | (74) apart_point_and_line(all_15_3, all_15_0) = all_71_1 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_3, all_15_2) = all_71_0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_0) = all_71_3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_5, all_15_2) = all_71_2 &
% 17.42/2.98 | | | | | (all_71_0 = 0 | all_71_1 = 0 | all_71_2 = 0 | all_71_3 = 0)
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | ALPHA: (74) implies:
% 17.42/2.98 | | | | | (75) apart_point_and_line(all_15_5, all_15_2) = all_71_2
% 17.42/2.98 | | | | | (76) apart_point_and_line(all_15_3, all_15_2) = all_71_0
% 17.42/2.98 | | | | | (77) apart_point_and_line(all_15_3, all_15_0) = all_71_1
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | DELTA: instantiating (67) with fresh symbols all_73_0, all_73_1,
% 17.42/2.98 | | | | | all_73_2, all_73_3 gives:
% 17.42/2.98 | | | | | (78) apart_point_and_line(all_15_3, all_15_0) = all_73_1 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_3, all_15_2) = all_73_0 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_0) = all_73_3 &
% 17.42/2.98 | | | | | apart_point_and_line(all_15_4, all_15_2) = all_73_2 &
% 17.42/2.98 | | | | | (all_73_0 = 0 | all_73_1 = 0 | all_73_2 = 0 | all_73_3 = 0)
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | ALPHA: (78) implies:
% 17.42/2.98 | | | | | (79) apart_point_and_line(all_15_4, all_15_2) = all_73_2
% 17.42/2.98 | | | | | (80) apart_point_and_line(all_15_4, all_15_0) = all_73_3
% 17.42/2.98 | | | | | (81) apart_point_and_line(all_15_3, all_15_2) = all_73_0
% 17.42/2.98 | | | | | (82) apart_point_and_line(all_15_3, all_15_0) = all_73_1
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | BETA: splitting (62) gives:
% 17.42/2.98 | | | | |
% 17.42/2.98 | | | | | Case 1:
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | (83) all_15_1 = 0
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | REDUCE: (12), (83) imply:
% 17.42/2.98 | | | | | | (84) $false
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | CLOSE: (84) is inconsistent.
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | Case 2:
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | (85) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.98 | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v2 &
% 17.42/2.98 | | | | | | apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/2.98 | | | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v0 = 0) |
% 17.42/2.98 | | | | | | v2 = 0 | v1 = 0))
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | DELTA: instantiating (85) with fresh symbols all_79_0, all_79_1,
% 17.42/2.98 | | | | | | all_79_2 gives:
% 17.42/2.98 | | | | | | (86) apart_point_and_line(all_15_3, all_15_0) = all_79_0 &
% 17.42/2.98 | | | | | | apart_point_and_line(all_15_3, all_15_0) = all_79_1 &
% 17.42/2.98 | | | | | | distinct_points(all_15_3, all_15_3) = all_79_2 & ( ~
% 17.42/2.98 | | | | | | (all_79_2 = 0) | all_79_0 = 0 | all_79_1 = 0)
% 17.42/2.98 | | | | | |
% 17.42/2.98 | | | | | | ALPHA: (86) implies:
% 17.42/2.98 | | | | | | (87) distinct_points(all_15_3, all_15_3) = all_79_2
% 17.42/2.98 | | | | | | (88) apart_point_and_line(all_15_3, all_15_0) = all_79_1
% 17.42/2.98 | | | | | | (89) apart_point_and_line(all_15_3, all_15_0) = all_79_0
% 17.42/2.98 | | | | | | (90) ~ (all_79_2 = 0) | all_79_0 = 0 | all_79_1 = 0
% 17.42/2.98 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_28_1, all_71_2, all_15_2,
% 17.42/2.99 | | | | | | all_15_5, simplifying with (36), (75) gives:
% 17.42/2.99 | | | | | | (91) all_71_2 = all_28_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_69_2, all_71_2, all_15_2,
% 17.42/2.99 | | | | | | all_15_5, simplifying with (71), (75) gives:
% 17.42/2.99 | | | | | | (92) all_71_2 = all_69_2
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_33_1, all_73_2, all_15_2,
% 17.42/2.99 | | | | | | all_15_4, simplifying with (42), (79) gives:
% 17.42/2.99 | | | | | | (93) all_73_2 = all_33_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_69_0, all_73_2, all_15_2,
% 17.42/2.99 | | | | | | all_15_4, simplifying with (72), (79) gives:
% 17.42/2.99 | | | | | | (94) all_73_2 = all_69_0
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_69_1, all_73_3, all_15_0,
% 17.42/2.99 | | | | | | all_15_4, simplifying with (73), (80) gives:
% 17.42/2.99 | | | | | | (95) all_73_3 = all_69_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_15_1, all_73_0, all_15_2,
% 17.42/2.99 | | | | | | all_15_3, simplifying with (22), (81) gives:
% 17.42/2.99 | | | | | | (96) all_73_0 = all_15_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_71_0, all_73_0, all_15_2,
% 17.42/2.99 | | | | | | all_15_3, simplifying with (76), (81) gives:
% 17.42/2.99 | | | | | | (97) all_73_0 = all_71_0
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_73_1, all_79_1, all_15_0,
% 17.42/2.99 | | | | | | all_15_3, simplifying with (82), (88) gives:
% 17.42/2.99 | | | | | | (98) all_79_1 = all_73_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_79_1, all_79_0, all_15_0,
% 17.42/2.99 | | | | | | all_15_3, simplifying with (88), (89) gives:
% 17.42/2.99 | | | | | | (99) all_79_0 = all_79_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (10) with all_71_1, all_79_0, all_15_0,
% 17.42/2.99 | | | | | | all_15_3, simplifying with (77), (89) gives:
% 17.42/2.99 | | | | | | (100) all_79_0 = all_71_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | COMBINE_EQS: (99), (100) imply:
% 17.42/2.99 | | | | | | (101) all_79_1 = all_71_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | SIMP: (101) implies:
% 17.42/2.99 | | | | | | (102) all_79_1 = all_71_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | COMBINE_EQS: (98), (102) imply:
% 17.42/2.99 | | | | | | (103) all_73_1 = all_71_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | SIMP: (103) implies:
% 17.42/2.99 | | | | | | (104) all_73_1 = all_71_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | COMBINE_EQS: (96), (97) imply:
% 17.42/2.99 | | | | | | (105) all_71_0 = all_15_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | SIMP: (105) implies:
% 17.42/2.99 | | | | | | (106) all_71_0 = all_15_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | COMBINE_EQS: (93), (94) imply:
% 17.42/2.99 | | | | | | (107) all_69_0 = all_33_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | COMBINE_EQS: (91), (92) imply:
% 17.42/2.99 | | | | | | (108) all_69_2 = all_28_1
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (3) with all_15_4, all_15_3, all_15_0,
% 17.42/2.99 | | | | | | all_15_2, all_69_1, all_33_1, simplifying with (14),
% 17.42/2.99 | | | | | | (15), (16), (17), (20), (42), (73) gives:
% 17.42/2.99 | | | | | | (109) all_69_1 = 0 | all_33_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/2.99 | | | | | | ? [v2: any] : (apart_point_and_line(all_15_3, all_15_0) =
% 17.42/2.99 | | | | | | v1 & apart_point_and_line(all_15_3, all_15_2) = v2 &
% 17.42/2.99 | | | | | | distinct_lines(all_15_0, all_15_2) = v0 & ( ~ (v0 = 0) |
% 17.42/2.99 | | | | | | v2 = 0 | v1 = 0))
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (7) with all_15_5, all_15_4, all_15_2,
% 17.42/2.99 | | | | | | all_15_0, all_33_1, all_69_1, simplifying with (13),
% 17.42/2.99 | | | | | | (14), (16), (17), (18), (42), (73) gives:
% 17.42/2.99 | | | | | | (110) all_69_1 = 0 | all_33_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/2.99 | | | | | | ? [v2: any] : (apart_point_and_line(all_15_5, all_15_0) =
% 17.42/2.99 | | | | | | v2 & apart_point_and_line(all_15_5, all_15_2) = v1 &
% 17.42/2.99 | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~ (v0 = 0) |
% 17.42/2.99 | | | | | | v2 = 0 | v1 = 0))
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (5) with all_15_4, all_15_4, all_15_0,
% 17.42/2.99 | | | | | | all_15_0, all_69_1, all_69_1, simplifying with (14),
% 17.42/2.99 | | | | | | (17), (73) gives:
% 17.42/2.99 | | | | | | (111) all_69_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/2.99 | | | | | | ? [v3: any] : (apart_point_and_line(all_15_4, all_15_0) =
% 17.42/2.99 | | | | | | v3 & apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/2.99 | | | | | | distinct_lines(all_15_0, all_15_0) = v1 &
% 17.42/2.99 | | | | | | distinct_points(all_15_4, all_15_4) = v0 & ( ~ (v1 = 0) |
% 17.42/2.99 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (7) with all_15_4, all_15_3, all_15_2,
% 17.42/2.99 | | | | | | all_15_0, all_15_1, all_71_1, simplifying with (14),
% 17.42/2.99 | | | | | | (15), (16), (17), (20), (22), (77) gives:
% 17.42/2.99 | | | | | | (112) all_71_1 = 0 | all_15_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/2.99 | | | | | | ? [v2: any] : (apart_point_and_line(all_15_4, all_15_0) =
% 17.42/2.99 | | | | | | v2 & apart_point_and_line(all_15_4, all_15_2) = v1 &
% 17.42/2.99 | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~ (v0 = 0) |
% 17.42/2.99 | | | | | | v2 = 0 | v1 = 0))
% 17.42/2.99 | | | | | |
% 17.42/2.99 | | | | | | GROUND_INST: instantiating (5) with all_15_4, all_15_3, all_15_2,
% 17.42/2.99 | | | | | | all_15_0, all_33_1, all_71_1, simplifying with (14),
% 17.42/2.99 | | | | | | (15), (16), (17), (42), (77) gives:
% 17.42/2.99 | | | | | | (113) all_71_1 = 0 | all_33_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/2.99 | | | | | | ? [v2: any] : ? [v3: any] :
% 17.42/2.99 | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/2.99 | | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.00 | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.00 | | | | | | distinct_points(all_15_4, all_15_3) = v0 & ( ~ (v1 = 0) |
% 17.42/3.00 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.00 | | | | | |
% 17.42/3.00 | | | | | | GROUND_INST: instantiating (4) with all_15_3, all_15_4, all_15_2,
% 17.42/3.00 | | | | | | all_15_0, all_71_1, all_33_1, simplifying with (14),
% 17.42/3.00 | | | | | | (15), (16), (17), (42), (77) gives:
% 17.42/3.00 | | | | | | (114) all_71_1 = 0 | all_33_1 = 0 | ? [v0: any] : ? [v1: any] :
% 17.42/3.00 | | | | | | ? [v2: any] : ? [v3: any] :
% 17.42/3.00 | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v2 &
% 17.42/3.00 | | | | | | apart_point_and_line(all_15_4, all_15_0) = v3 &
% 17.42/3.00 | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.00 | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~ (v1 = 0) |
% 17.42/3.00 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.00 | | | | | |
% 17.42/3.00 | | | | | | GROUND_INST: instantiating (5) with all_15_3, all_15_3, all_15_0,
% 17.42/3.00 | | | | | | all_15_0, all_71_1, all_71_1, simplifying with (15),
% 17.42/3.00 | | | | | | (17), (77) gives:
% 17.42/3.00 | | | | | | (115) all_71_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.00 | | | | | | ? [v3: any] : (apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.00 | | | | | | v3 & apart_point_and_line(all_15_3, all_15_0) = v2 &
% 17.42/3.00 | | | | | | distinct_lines(all_15_0, all_15_0) = v1 &
% 17.42/3.00 | | | | | | distinct_points(all_15_3, all_15_3) = v0 & ( ~ (v1 = 0) |
% 17.42/3.00 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.00 | | | | | |
% 17.42/3.00 | | | | | | BETA: splitting (60) gives:
% 17.42/3.00 | | | | | |
% 17.42/3.00 | | | | | | Case 1:
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | (116) all_33_1 = 0
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | REDUCE: (42), (116) imply:
% 17.42/3.00 | | | | | | | (117) apart_point_and_line(all_15_4, all_15_2) = 0
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | GROUND_INST: instantiating (con1) with all_15_5, all_15_4,
% 17.42/3.00 | | | | | | | all_15_4, all_15_2, simplifying with (13), (14),
% 17.42/3.00 | | | | | | | (23), (117) gives:
% 17.42/3.00 | | | | | | | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.00 | | | | | | | (distinct_points(all_15_4, all_15_4) = v2 &
% 17.42/3.00 | | | | | | | distinct_points(all_15_4, all_15_5) = v1 &
% 17.42/3.00 | | | | | | | distinct_points(all_15_5, all_15_4) = v0 & ( ~ (v0 = 0)
% 17.42/3.00 | | | | | | | | (v2 = 0 & v1 = 0)))
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | DELTA: instantiating (118) with fresh symbols all_97_0, all_97_1,
% 17.42/3.00 | | | | | | | all_97_2 gives:
% 17.42/3.00 | | | | | | | (119) distinct_points(all_15_4, all_15_4) = all_97_0 &
% 17.42/3.00 | | | | | | | distinct_points(all_15_4, all_15_5) = all_97_1 &
% 17.42/3.00 | | | | | | | distinct_points(all_15_5, all_15_4) = all_97_2 & ( ~
% 17.42/3.00 | | | | | | | (all_97_2 = 0) | (all_97_0 = 0 & all_97_1 = 0))
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | ALPHA: (119) implies:
% 17.42/3.00 | | | | | | | (120) distinct_points(all_15_5, all_15_4) = all_97_2
% 17.42/3.00 | | | | | | | (121) distinct_points(all_15_4, all_15_4) = all_97_0
% 17.42/3.00 | | | | | | | (122) ~ (all_97_2 = 0) | (all_97_0 = 0 & all_97_1 = 0)
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | GROUND_INST: instantiating (9) with 0, all_97_2, all_15_4,
% 17.42/3.00 | | | | | | | all_15_5, simplifying with (18), (120) gives:
% 17.42/3.00 | | | | | | | (123) all_97_2 = 0
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | BETA: splitting (122) gives:
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | Case 1:
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | (124) ~ (all_97_2 = 0)
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | REDUCE: (123), (124) imply:
% 17.42/3.00 | | | | | | | | (125) $false
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | CLOSE: (125) is inconsistent.
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | Case 2:
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | (126) all_97_0 = 0 & all_97_1 = 0
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | ALPHA: (126) implies:
% 17.42/3.00 | | | | | | | | (127) all_97_0 = 0
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | REDUCE: (121), (127) imply:
% 17.42/3.00 | | | | | | | | (128) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying
% 17.42/3.00 | | | | | | | | with (14), (128) gives:
% 17.42/3.00 | | | | | | | | (129) $false
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | CLOSE: (129) is inconsistent.
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | End of split
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | Case 2:
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | (130) ~ (all_33_1 = 0)
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | BETA: splitting (59) gives:
% 17.42/3.00 | | | | | | |
% 17.42/3.00 | | | | | | | Case 1:
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | (131) all_33_1 = 0
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | REDUCE: (130), (131) imply:
% 17.42/3.00 | | | | | | | | (132) $false
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | CLOSE: (132) is inconsistent.
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | Case 2:
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | (133) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 17.42/3.00 | | | | | | | | any] : ? [v3: any] : (apart_point_and_line(all_15_3,
% 17.42/3.00 | | | | | | | | all_15_2) = v2 & apart_point_and_line(all_15_4,
% 17.42/3.00 | | | | | | | | all_15_2) = v3 & distinct_lines(all_15_2, all_15_2)
% 17.42/3.00 | | | | | | | | = v1 & distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.00 | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | BETA: splitting (63) gives:
% 17.42/3.00 | | | | | | | |
% 17.42/3.00 | | | | | | | | Case 1:
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | (134) all_33_1 = 0
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | REDUCE: (130), (134) imply:
% 17.42/3.00 | | | | | | | | | (135) $false
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | CLOSE: (135) is inconsistent.
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | Case 2:
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | (136) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 17.42/3.00 | | | | | | | | | any] : (apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.00 | | | | | | | | | v1 & apart_point_and_line(all_15_4, all_15_0) = v2
% 17.42/3.00 | | | | | | | | | & distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.00 | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | BETA: splitting (133) gives:
% 17.42/3.00 | | | | | | | | |
% 17.42/3.00 | | | | | | | | | Case 1:
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | (137) all_15_1 = 0
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | REDUCE: (12), (137) imply:
% 17.42/3.00 | | | | | | | | | | (138) $false
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | CLOSE: (138) is inconsistent.
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | Case 2:
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.42/3.00 | | | | | | | | | | [v3: any] : (apart_point_and_line(all_15_3,
% 17.42/3.00 | | | | | | | | | | all_15_2) = v2 & apart_point_and_line(all_15_4,
% 17.42/3.00 | | | | | | | | | | all_15_2) = v3 & distinct_lines(all_15_2,
% 17.42/3.00 | | | | | | | | | | all_15_2) = v1 & distinct_points(all_15_3,
% 17.42/3.00 | | | | | | | | | | all_15_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 17.42/3.00 | | | | | | | | | | v3 = 0 | v2 = 0))
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | DELTA: instantiating (139) with fresh symbols all_105_0,
% 17.42/3.00 | | | | | | | | | | all_105_1, all_105_2, all_105_3 gives:
% 17.42/3.00 | | | | | | | | | | (140) apart_point_and_line(all_15_3, all_15_2) =
% 17.42/3.00 | | | | | | | | | | all_105_1 & apart_point_and_line(all_15_4,
% 17.42/3.00 | | | | | | | | | | all_15_2) = all_105_0 & distinct_lines(all_15_2,
% 17.42/3.00 | | | | | | | | | | all_15_2) = all_105_2 & distinct_points(all_15_3,
% 17.42/3.00 | | | | | | | | | | all_15_4) = all_105_3 & ( ~ (all_105_2 = 0) | ~
% 17.42/3.00 | | | | | | | | | | (all_105_3 = 0) | all_105_0 = 0 | all_105_1 = 0)
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | ALPHA: (140) implies:
% 17.42/3.00 | | | | | | | | | | (141) distinct_points(all_15_3, all_15_4) = all_105_3
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | BETA: splitting (136) gives:
% 17.42/3.00 | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | Case 1:
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | (142) all_15_1 = 0
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | REDUCE: (12), (142) imply:
% 17.42/3.00 | | | | | | | | | | | (143) $false
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | CLOSE: (143) is inconsistent.
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | Case 2:
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.00 | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/3.00 | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.00 | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.00 | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | DELTA: instantiating (144) with fresh symbols all_110_0,
% 17.42/3.00 | | | | | | | | | | | all_110_1, all_110_2 gives:
% 17.42/3.00 | | | | | | | | | | | (145) apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.00 | | | | | | | | | | | all_110_1 & apart_point_and_line(all_15_4,
% 17.42/3.00 | | | | | | | | | | | all_15_0) = all_110_0 &
% 17.42/3.00 | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_110_2 &
% 17.42/3.00 | | | | | | | | | | | ( ~ (all_110_2 = 0) | all_110_0 = 0 | all_110_1 =
% 17.42/3.00 | | | | | | | | | | | 0)
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | ALPHA: (145) implies:
% 17.42/3.00 | | | | | | | | | | | (146) distinct_points(all_15_3, all_15_4) = all_110_2
% 17.42/3.00 | | | | | | | | | | | (147) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.00 | | | | | | | | | | | all_110_0
% 17.42/3.00 | | | | | | | | | | | (148) apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.00 | | | | | | | | | | | all_110_1
% 17.42/3.00 | | | | | | | | | | | (149) ~ (all_110_2 = 0) | all_110_0 = 0 | all_110_1 = 0
% 17.42/3.00 | | | | | | | | | | |
% 17.42/3.00 | | | | | | | | | | | GROUND_INST: instantiating (9) with all_105_3, all_110_2,
% 17.42/3.00 | | | | | | | | | | | all_15_4, all_15_3, simplifying with (141), (146)
% 17.42/3.00 | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | (150) all_110_2 = all_105_3
% 17.42/3.01 | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | GROUND_INST: instantiating (10) with all_69_1, all_110_0,
% 17.42/3.01 | | | | | | | | | | | all_15_0, all_15_4, simplifying with (73), (147)
% 17.42/3.01 | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | (151) all_110_0 = all_69_1
% 17.42/3.01 | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | GROUND_INST: instantiating (10) with all_71_1, all_110_1,
% 17.42/3.01 | | | | | | | | | | | all_15_0, all_15_3, simplifying with (77), (148)
% 17.42/3.01 | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | (152) all_110_1 = all_71_1
% 17.42/3.01 | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_15_4, all_15_3,
% 17.42/3.01 | | | | | | | | | | | all_15_4, all_105_3, simplifying with (14), (15),
% 17.42/3.01 | | | | | | | | | | | (20), (141) gives:
% 17.42/3.01 | | | | | | | | | | | (153) all_105_3 = 0 | distinct_points(all_15_4,
% 17.42/3.01 | | | | | | | | | | | all_15_4) = 0
% 17.42/3.01 | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | BETA: splitting (58) gives:
% 17.42/3.01 | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | (154) all_28_1 = 0
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | REDUCE: (36), (154) imply:
% 17.42/3.01 | | | | | | | | | | | | (155) apart_point_and_line(all_15_5, all_15_2) = 0
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | REF_CLOSE: (9), (13), (14), (18), (23), (155), (apart1),
% 17.42/3.01 | | | | | | | | | | | | (con1) are inconsistent by sub-proof #3.
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | (156) ~ (all_28_1 = 0)
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | BETA: splitting (65) gives:
% 17.42/3.01 | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | (157) all_28_1 = 0
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | REDUCE: (156), (157) imply:
% 17.42/3.01 | | | | | | | | | | | | | (158) $false
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | (159) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.01 | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_3,
% 17.42/3.01 | | | | | | | | | | | | | all_15_0) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/3.01 | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | BETA: splitting (66) gives:
% 17.42/3.01 | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | (160) all_33_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | REDUCE: (130), (160) imply:
% 17.42/3.01 | | | | | | | | | | | | | | (161) $false
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | (162) all_28_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.01 | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_4,
% 17.42/3.01 | | | | | | | | | | | | | | all_15_0) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/3.01 | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_5) = v0 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 17.42/3.01 | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | (163) all_15_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | REDUCE: (12), (163) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | (164) $false
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | (165) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.01 | | | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_0) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/3.01 | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = v0 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | DELTA: instantiating (165) with fresh symbols all_147_0,
% 17.42/3.01 | | | | | | | | | | | | | | | all_147_1, all_147_2 gives:
% 17.42/3.01 | | | | | | | | | | | | | | | (166) apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | all_147_1 & apart_point_and_line(all_15_5,
% 17.42/3.01 | | | | | | | | | | | | | | | all_15_0) = all_147_0 &
% 17.42/3.01 | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_5) = all_147_2 &
% 17.42/3.01 | | | | | | | | | | | | | | | ( ~ (all_147_2 = 0) | all_147_0 = 0 | all_147_1 =
% 17.42/3.01 | | | | | | | | | | | | | | | 0)
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 17.42/3.01 | | | | | | | | | | | | | | | (167) apart_point_and_line(all_15_3, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | all_147_1
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 17.42/3.01 | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | (168) all_28_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | REDUCE: (156), (168) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | | (169) $false
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | (170) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.01 | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_4, all_15_0) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_0) = v2 &
% 17.42/3.01 | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_5) = v0 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | DELTA: instantiating (170) with fresh symbols all_157_0,
% 17.42/3.01 | | | | | | | | | | | | | | | | all_157_1, all_157_2 gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | (171) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | | all_157_1 & apart_point_and_line(all_15_5,
% 17.42/3.01 | | | | | | | | | | | | | | | | all_15_0) = all_157_0 &
% 17.42/3.01 | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_5) = all_157_2 &
% 17.42/3.01 | | | | | | | | | | | | | | | | ( ~ (all_157_2 = 0) | all_157_0 = 0 | all_157_1 =
% 17.42/3.01 | | | | | | | | | | | | | | | | 0)
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 17.42/3.01 | | | | | | | | | | | | | | | | (172) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | | all_157_1
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_69_1, all_157_1,
% 17.42/3.01 | | | | | | | | | | | | | | | | all_15_0, all_15_4, simplifying with (73), (172)
% 17.42/3.01 | | | | | | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | (173) all_157_1 = all_69_1
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_71_1, all_147_1,
% 17.42/3.01 | | | | | | | | | | | | | | | | all_15_0, all_15_3, simplifying with (77), (167)
% 17.42/3.01 | | | | | | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | (174) all_147_1 = all_71_1
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 17.42/3.01 | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | (175) all_33_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | REDUCE: (130), (175) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (176) $false
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | (177) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.01 | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = v0 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | DELTA: instantiating (177) with fresh symbols all_170_0,
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_170_1, all_170_2 gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (178) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_170_0 & apart_point_and_line(all_15_4,
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_15_0) = all_170_1 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = all_170_2 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | ( ~ (all_170_2 = 0) | all_170_0 = 0 | all_170_1 =
% 17.42/3.01 | | | | | | | | | | | | | | | | | 0)
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (179) distinct_points(all_15_4, all_15_4) = all_170_2
% 17.42/3.01 | | | | | | | | | | | | | | | | | (180) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_170_1
% 17.42/3.01 | | | | | | | | | | | | | | | | | (181) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_170_0
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_69_1, all_170_0,
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_15_0, all_15_4, simplifying with (73), (181)
% 17.42/3.01 | | | | | | | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (182) all_170_0 = all_69_1
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_170_1, all_170_0,
% 17.42/3.01 | | | | | | | | | | | | | | | | | all_15_0, all_15_4, simplifying with (180), (181)
% 17.42/3.01 | | | | | | | | | | | | | | | | | gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (183) all_170_0 = all_170_1
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (183) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | | | (184) all_170_1 = all_69_1
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | (185) ~ (all_79_2 = 0)
% 17.42/3.01 | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | (186) all_71_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | REDUCE: (77), (186) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | (187) apart_point_and_line(all_15_3, all_15_0) = 0
% 17.42/3.01 | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (188) all_69_1 = 0
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (188) imply:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (189) apart_point_and_line(all_15_4, all_15_0) = 0
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_4,
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_0, simplifying with (14), (15),
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (24), (189) gives:
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (distinct_points(all_15_3, all_15_4) = v0 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = v1 &
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = v2 & ( ~
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_4,
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | all_15_3, all_15_0, simplifying with (14), (15),
% 17.42/3.01 | | | | | | | | | | | | | | | | | | | | (24), (187) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (191) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (distinct_points(all_15_3, all_15_3) = v1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (191) with fresh symbols all_214_0,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_214_1, all_214_2 gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (192) distinct_points(all_15_3, all_15_3) = all_214_1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_214_0 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_214_2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | ( ~ (all_214_2 = 0) | (all_214_0 = 0 & all_214_1 =
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | 0))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (193) distinct_points(all_15_3, all_15_4) = all_214_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (194) distinct_points(all_15_3, all_15_4) = all_214_0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (195) distinct_points(all_15_3, all_15_3) = all_214_1
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (196) ~ (all_214_2 = 0) | (all_214_0 = 0 & all_214_1 =
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_216_0,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_216_1, all_216_2 gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (197) distinct_points(all_15_3, all_15_4) = all_216_2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = all_216_1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = all_216_0 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | ( ~ (all_216_2 = 0) | (all_216_0 = 0 & all_216_1 =
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | 0))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (198) distinct_points(all_15_4, all_15_4) = all_216_0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (199) distinct_points(all_15_3, all_15_4) = all_216_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_170_2, all_216_0,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_4, simplifying with (179), (198)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (200) all_216_0 = all_170_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_105_3, all_216_2,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (141), (199)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (201) all_216_2 = all_105_3
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_214_0, all_216_2,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (194), (199)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (202) all_216_2 = all_214_0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_214_2, all_216_2,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (193), (199)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (203) all_216_2 = all_214_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_79_2, all_214_1,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | all_15_3, all_15_3, simplifying with (87), (195)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (204) all_214_1 = all_79_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (203) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (205) all_214_0 = all_214_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (202) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (206) all_214_0 = all_105_3
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (206) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (207) all_214_2 = all_105_3
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (208) ~ (all_214_2 = 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (208) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (209) ~ (all_105_3 = 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (153), (179), (209), (apart1) are
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (210) all_214_0 = 0 & all_214_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (211) all_214_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (211) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (212) all_79_2 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (212) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (213) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (214) ~ (all_69_1 = 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (215) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (179), (215), (apart1) are inconsistent
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | by sub-proof #2.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (216) all_105_3 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (216) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (217) distinct_points(all_15_3, all_15_4) = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | (218) all_69_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (218) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | (219) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | (220) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_5,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | all_15_0) = v2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_5, all_15_2) = v1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (221) all_33_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (221) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (222) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_4,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | all_15_3, all_15_0, simplifying with (14), (15),
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (24), (187) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (223) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (distinct_points(all_15_3, all_15_3) = v1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (223) with fresh symbols all_293_0,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | all_293_1, all_293_2 gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (224) distinct_points(all_15_3, all_15_3) = all_293_1 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_293_0 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_293_2 &
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_293_2 = 0) | (all_293_0 = 0 & all_293_1 =
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | 0))
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (225) distinct_points(all_15_3, all_15_4) = all_293_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (226) distinct_points(all_15_3, all_15_4) = all_293_0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (227) distinct_points(all_15_3, all_15_3) = all_293_1
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_293_2 = 0) | (all_293_0 = 0 & all_293_1 =
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_293_0, all_15_4,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | all_15_3, simplifying with (217), (226) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (229) all_293_0 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_293_2, all_293_0,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (225), (226)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (230) all_293_0 = all_293_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_79_2, all_293_1,
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | all_15_3, all_15_3, simplifying with (87), (227)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (231) all_293_1 = all_79_2
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (230) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (232) all_293_2 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | (233) all_293_2 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_293_2 = 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (234) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (235) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (236) all_293_0 = 0 & all_293_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (237) all_293_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (237) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (238) all_79_2 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (238) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | (239) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.02 | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | (240) ~ (all_71_1 = 0)
% 17.42/3.02 | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (241) all_69_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (241) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | (242) apart_point_and_line(all_15_4, all_15_0) = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (243) all_71_1 = 0
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (240), (243) imply:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | (244) $false
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.02 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | (245) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | (246) all_71_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (240), (246) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | (247) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | (248) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | [v2: any] : (apart_point_and_line(all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | all_15_0) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_2) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | (249) all_71_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (240), (249) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | (250) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | (251) all_33_1 = 0 | ? [v0: any] : ? [v1: any] : ?
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_3, all_15_2) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (252) all_33_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (252) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (253) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (254) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_15_3,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = v3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (254) with fresh symbols all_238_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_238_1, all_238_2, all_238_3 gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (255) apart_point_and_line(all_15_3, all_15_2) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_238_0 & apart_point_and_line(all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_238_1 & distinct_lines(all_15_2,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_238_2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = all_238_3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_238_2 = 0) | ~ (all_238_3 = 0) |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_238_0 = 0 | all_238_1 = 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | (256) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | all_238_1
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_15_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (257) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (258) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (259) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (apart_point_and_line(all_15_4, all_15_0) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_2) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0 | v1 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (259) with fresh symbols all_248_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_248_1, all_248_2 gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (260) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_248_0 & apart_point_and_line(all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = all_248_1 & distinct_lines(all_15_2,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_248_2 & ( ~ (all_248_2 = 0) |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_248_0 = 0 | all_248_1 = 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | (261) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | all_248_0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_33_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (262) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (263) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (264) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_15_3,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_2) = v2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_15_4, all_15_0) = v3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_15_2, all_15_0) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = v0 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (264) with fresh symbols all_263_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_263_1, all_263_2, all_263_3 gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (265) apart_point_and_line(all_15_3, all_15_2) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_263_1 & apart_point_and_line(all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_263_0 & distinct_lines(all_15_2,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0) = all_263_2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_3, all_15_4) = all_263_3 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_263_2 = 0) | ~ (all_263_3 = 0) |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_263_0 = 0 | all_263_1 = 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (266) distinct_points(all_15_3, all_15_4) = all_263_3
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (267) apart_point_and_line(all_15_4, all_15_0) =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_263_0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_105_3, all_263_3,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (141), (266)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_263_3 = all_105_3
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_248_0, all_15_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, simplifying with (242), (261) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_248_0 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_248_0, all_263_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0, all_15_4, simplifying with (261), (267)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_263_0 = all_248_0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_238_1, all_263_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_0, all_15_4, simplifying with (256), (267)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_263_0 = all_238_1
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (271) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_248_0 = all_238_1
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_248_0 = all_238_1
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (273) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_238_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (con1) with all_15_3, all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_0, simplifying with (14), (15),
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (242) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (275) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (distinct_points(all_15_3, all_15_4) = v0 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = v1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = v2 & ( ~
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | (v2 = 0 & v1 = 0)))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (275) with fresh symbols all_284_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_284_1, all_284_2 gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (276) distinct_points(all_15_3, all_15_4) = all_284_2 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_3) = all_284_1 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_15_4, all_15_4) = all_284_0 &
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_284_2 = 0) | (all_284_0 = 0 & all_284_1 =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | 0))
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (277) distinct_points(all_15_4, all_15_4) = all_284_0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (278) distinct_points(all_15_3, all_15_4) = all_284_2
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_284_2 = 0) | (all_284_0 = 0 & all_284_1 =
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_170_2, all_284_0,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_4, simplifying with (179), (277)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_284_0 = all_170_2
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_105_3, all_284_2,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, all_15_3, simplifying with (141), (278)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_284_2 = all_105_3
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_170_2, 0, all_15_4,
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_15_4, simplifying with (179), (282) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_170_2 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_4, simplifying
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | with (14), (282) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_105_3 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (distinct_points(all_15_4, all_15_4) = 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (285) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_284_2 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_284_2 = 0)
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (287), (288) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_284_0 = 0 & all_284_1 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_284_0 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (291) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_170_2 = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (292) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (286), (293) imply:
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) $false
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.03 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | (295) ~ (all_69_1 = 0)
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_110_2 = 0)
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (296) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | (297) ~ (all_105_3 = 0)
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (153), (179), (297), (apart1) are
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | (298) all_110_0 = 0 | all_110_1 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (299) all_110_0 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (299) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (300) all_69_1 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (301) all_69_1 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (301) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (302) $false
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent.
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (303) all_110_1 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (303) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (304) all_71_1 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (240), (304) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | (305) $false
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | Case 2:
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | (306) all_79_2 = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | REDUCE: (87), (306) imply:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | (307) distinct_points(all_15_3, all_15_3) = 0
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (apart1) with all_15_3, simplifying
% 17.42/3.04 | | | | | | | | | | | | | | | | | | with (15), (307) gives:
% 17.42/3.04 | | | | | | | | | | | | | | | | | | (308) $false
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent.
% 17.42/3.04 | | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | | |
% 17.42/3.04 | | | | | | | | | End of split
% 17.42/3.04 | | | | | | | | |
% 17.42/3.04 | | | | | | | | End of split
% 17.42/3.04 | | | | | | | |
% 17.42/3.04 | | | | | | | End of split
% 17.42/3.04 | | | | | | |
% 17.42/3.04 | | | | | | End of split
% 17.42/3.04 | | | | | |
% 17.42/3.04 | | | | | End of split
% 17.42/3.04 | | | | |
% 17.42/3.04 | | | | Case 2:
% 17.42/3.04 | | | | |
% 17.42/3.04 | | | | | (309) all_28_1 = 0
% 17.42/3.04 | | | | |
% 17.42/3.04 | | | | | REDUCE: (36), (309) imply:
% 17.42/3.04 | | | | | (310) apart_point_and_line(all_15_5, all_15_2) = 0
% 17.42/3.04 | | | | |
% 17.42/3.04 | | | | | REF_CLOSE: (9), (13), (14), (18), (23), (310), (apart1), (con1) are
% 17.42/3.04 | | | | | inconsistent by sub-proof #3.
% 17.42/3.04 | | | | |
% 17.42/3.04 | | | | End of split
% 17.42/3.04 | | | |
% 17.42/3.04 | | | End of split
% 17.42/3.04 | | |
% 17.42/3.04 | | End of split
% 17.42/3.04 | |
% 17.42/3.04 | End of split
% 17.42/3.04 |
% 17.42/3.04 End of proof
% 17.42/3.04
% 17.42/3.04 Sub-proof #1 shows that the following formulas are inconsistent:
% 17.42/3.04 ----------------------------------------------------------------
% 17.42/3.04 (1) all_105_3 = 0 | distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.04 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.42/3.04 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 17.42/3.04 (distinct_points(v3, v2) = v0))
% 17.42/3.04 (3) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 17.42/3.04 (4) distinct_points(all_15_4, all_15_4) = all_170_2
% 17.42/3.04 (5) $i(all_15_4)
% 17.42/3.04 (6) ~ (all_105_3 = 0)
% 17.42/3.04
% 17.42/3.04 Begin of proof
% 17.42/3.04 |
% 17.42/3.04 | BETA: splitting (1) gives:
% 17.42/3.04 |
% 17.42/3.04 | Case 1:
% 17.42/3.04 | |
% 17.42/3.04 | | (7) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.04 | |
% 17.42/3.04 | | REF_CLOSE: (2), (3), (4), (5), (7) are inconsistent by sub-proof #2.
% 17.42/3.04 | |
% 17.42/3.04 | Case 2:
% 17.42/3.04 | |
% 17.42/3.04 | | (8) all_105_3 = 0
% 17.42/3.04 | |
% 17.42/3.04 | | REDUCE: (6), (8) imply:
% 17.42/3.04 | | (9) $false
% 17.42/3.04 | |
% 17.42/3.04 | | CLOSE: (9) is inconsistent.
% 17.42/3.04 | |
% 17.42/3.04 | End of split
% 17.42/3.04 |
% 17.42/3.04 End of proof
% 17.42/3.04
% 17.42/3.04 Sub-proof #2 shows that the following formulas are inconsistent:
% 17.42/3.04 ----------------------------------------------------------------
% 17.42/3.04 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.42/3.04 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 17.42/3.04 (distinct_points(v3, v2) = v0))
% 17.42/3.04 (2) distinct_points(all_15_4, all_15_4) = 0
% 17.42/3.04 (3) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 17.42/3.04 (4) distinct_points(all_15_4, all_15_4) = all_170_2
% 17.42/3.04 (5) $i(all_15_4)
% 17.42/3.04
% 17.42/3.04 Begin of proof
% 17.42/3.04 |
% 17.42/3.04 | GROUND_INST: instantiating (1) with all_170_2, 0, all_15_4, all_15_4,
% 17.42/3.04 | simplifying with (2), (4) gives:
% 17.42/3.04 | (6) all_170_2 = 0
% 17.42/3.04 |
% 17.42/3.04 | GROUND_INST: instantiating (3) with all_15_4, simplifying with (2), (5) gives:
% 17.42/3.04 | (7) $false
% 17.42/3.04 |
% 17.42/3.04 | CLOSE: (7) is inconsistent.
% 17.42/3.04 |
% 17.42/3.04 End of proof
% 17.42/3.04
% 17.42/3.04 Sub-proof #3 shows that the following formulas are inconsistent:
% 17.42/3.04 ----------------------------------------------------------------
% 17.42/3.04 (1) line_connecting(all_15_5, all_15_4) = all_15_2
% 17.42/3.04 (2) $i(all_15_5)
% 17.42/3.04 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.42/3.04 ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 17.42/3.04 (distinct_points(v3, v2) = v0))
% 17.42/3.04 (4) apart_point_and_line(all_15_5, all_15_2) = 0
% 17.42/3.04 (5) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 17.42/3.04 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 17.42/3.04 (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0)
% 17.42/3.04 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 17.42/3.04 [v6: any] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) =
% 17.42/3.04 v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 =
% 17.42/3.04 0))))
% 17.42/3.04 (7) $i(all_15_4)
% 17.42/3.04 (8) distinct_points(all_15_5, all_15_4) = 0
% 17.42/3.04
% 17.42/3.04 Begin of proof
% 17.42/3.04 |
% 17.42/3.04 | GROUND_INST: instantiating (6) with all_15_5, all_15_4, all_15_5, all_15_2,
% 17.42/3.04 | simplifying with (1), (2), (4), (7) gives:
% 17.42/3.04 | (9) ? [v0: any] : ? [v1: any] : ? [v2: any] : (distinct_points(all_15_5,
% 17.42/3.04 | all_15_4) = v2 & distinct_points(all_15_5, all_15_4) = v0 &
% 17.42/3.04 | distinct_points(all_15_5, all_15_5) = v1 & ( ~ (v0 = 0) | (v2 = 0 &
% 17.42/3.04 | v1 = 0)))
% 17.42/3.04 |
% 17.42/3.04 | DELTA: instantiating (9) with fresh symbols all_69_0, all_69_1, all_69_2
% 17.42/3.04 | gives:
% 17.42/3.04 | (10) distinct_points(all_15_5, all_15_4) = all_69_0 &
% 17.42/3.04 | distinct_points(all_15_5, all_15_4) = all_69_2 &
% 17.42/3.04 | distinct_points(all_15_5, all_15_5) = all_69_1 & ( ~ (all_69_2 = 0) |
% 17.42/3.04 | (all_69_0 = 0 & all_69_1 = 0))
% 17.42/3.04 |
% 17.42/3.04 | ALPHA: (10) implies:
% 17.42/3.04 | (11) distinct_points(all_15_5, all_15_5) = all_69_1
% 17.42/3.04 | (12) distinct_points(all_15_5, all_15_4) = all_69_2
% 17.42/3.04 | (13) distinct_points(all_15_5, all_15_4) = all_69_0
% 17.42/3.04 | (14) ~ (all_69_2 = 0) | (all_69_0 = 0 & all_69_1 = 0)
% 17.42/3.04 |
% 17.42/3.04 | GROUND_INST: instantiating (3) with 0, all_69_0, all_15_4, all_15_5,
% 17.42/3.04 | simplifying with (8), (13) gives:
% 17.42/3.04 | (15) all_69_0 = 0
% 17.42/3.04 |
% 17.42/3.04 | GROUND_INST: instantiating (3) with all_69_2, all_69_0, all_15_4, all_15_5,
% 17.42/3.04 | simplifying with (12), (13) gives:
% 17.42/3.04 | (16) all_69_0 = all_69_2
% 17.42/3.04 |
% 17.42/3.04 | COMBINE_EQS: (15), (16) imply:
% 17.42/3.04 | (17) all_69_2 = 0
% 17.42/3.04 |
% 17.42/3.04 | BETA: splitting (14) gives:
% 17.42/3.04 |
% 17.42/3.04 | Case 1:
% 17.42/3.04 | |
% 17.42/3.04 | | (18) ~ (all_69_2 = 0)
% 17.42/3.04 | |
% 17.42/3.04 | | REDUCE: (17), (18) imply:
% 17.42/3.04 | | (19) $false
% 17.42/3.04 | |
% 17.42/3.04 | | CLOSE: (19) is inconsistent.
% 17.42/3.04 | |
% 17.42/3.04 | Case 2:
% 17.42/3.04 | |
% 17.42/3.04 | | (20) all_69_0 = 0 & all_69_1 = 0
% 17.42/3.04 | |
% 17.42/3.04 | | ALPHA: (20) implies:
% 17.42/3.04 | | (21) all_69_1 = 0
% 17.42/3.04 | |
% 17.42/3.04 | | REDUCE: (11), (21) imply:
% 17.42/3.04 | | (22) distinct_points(all_15_5, all_15_5) = 0
% 17.42/3.04 | |
% 17.42/3.04 | | GROUND_INST: instantiating (5) with all_15_5, simplifying with (2), (22)
% 17.42/3.04 | | gives:
% 17.42/3.04 | | (23) $false
% 17.42/3.04 | |
% 17.42/3.04 | | CLOSE: (23) is inconsistent.
% 17.42/3.04 | |
% 17.42/3.04 | End of split
% 17.42/3.04 |
% 17.42/3.04 End of proof
% 17.42/3.04 % SZS output end Proof for theBenchmark
% 17.42/3.04
% 17.42/3.04 2527ms
%------------------------------------------------------------------------------