TSTP Solution File: GEO182+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEO182+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 23:21:57 EDT 2023
% Result : Theorem 18.39s 3.22s
% Output : Proof 29.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO182+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 21:18:12 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.39/1.13 Prover 4: Preprocessing ...
% 3.39/1.13 Prover 1: Preprocessing ...
% 3.39/1.17 Prover 2: Preprocessing ...
% 3.39/1.17 Prover 0: Preprocessing ...
% 3.39/1.17 Prover 3: Preprocessing ...
% 3.39/1.17 Prover 6: Preprocessing ...
% 3.39/1.18 Prover 5: Preprocessing ...
% 5.52/1.51 Prover 5: Proving ...
% 6.18/1.54 Prover 2: Proving ...
% 6.73/1.61 Prover 3: Constructing countermodel ...
% 6.73/1.63 Prover 1: Constructing countermodel ...
% 6.73/1.63 Prover 6: Constructing countermodel ...
% 7.74/1.75 Prover 3: gave up
% 7.74/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.38/1.81 Prover 6: gave up
% 8.38/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.38/1.84 Prover 7: Preprocessing ...
% 8.38/1.87 Prover 8: Preprocessing ...
% 8.38/1.91 Prover 1: gave up
% 8.38/1.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.38/1.98 Prover 7: Warning: ignoring some quantifiers
% 9.44/1.98 Prover 4: Constructing countermodel ...
% 9.44/1.99 Prover 9: Preprocessing ...
% 9.44/2.01 Prover 7: Constructing countermodel ...
% 9.44/2.03 Prover 0: Proving ...
% 10.53/2.12 Prover 8: Warning: ignoring some quantifiers
% 10.67/2.13 Prover 8: Constructing countermodel ...
% 11.35/2.26 Prover 8: gave up
% 11.35/2.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.90/2.32 Prover 9: Constructing countermodel ...
% 11.90/2.33 Prover 10: Preprocessing ...
% 12.61/2.38 Prover 10: Warning: ignoring some quantifiers
% 12.61/2.40 Prover 10: Constructing countermodel ...
% 13.02/2.50 Prover 7: gave up
% 13.02/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.02/2.55 Prover 10: gave up
% 13.02/2.55 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 13.02/2.58 Prover 11: Preprocessing ...
% 14.03/2.59 Prover 12: Preprocessing ...
% 14.67/2.73 Prover 12: Proving ...
% 15.62/2.82 Prover 11: Constructing countermodel ...
% 18.39/3.22 Prover 0: proved (2595ms)
% 18.39/3.22
% 18.39/3.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.39/3.22
% 18.39/3.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.39/3.22 Prover 2: stopped
% 18.39/3.22 Prover 5: stopped
% 18.39/3.23 Prover 12: stopped
% 18.39/3.23 Prover 9: stopped
% 18.39/3.23 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.39/3.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 18.94/3.26 Prover 19: Preprocessing ...
% 18.94/3.26 Prover 13: Preprocessing ...
% 18.94/3.27 Prover 16: Preprocessing ...
% 18.94/3.30 Prover 13: Warning: ignoring some quantifiers
% 18.94/3.30 Prover 16: Warning: ignoring some quantifiers
% 18.94/3.30 Prover 16: Constructing countermodel ...
% 18.94/3.30 Prover 13: Constructing countermodel ...
% 19.60/3.34 Prover 19: Warning: ignoring some quantifiers
% 19.94/3.37 Prover 19: Constructing countermodel ...
% 20.63/3.46 Prover 13: gave up
% 20.63/3.47 Prover 19: gave up
% 22.53/3.78 Prover 16: gave up
% 28.37/4.86 Prover 4: Found proof (size 280)
% 28.37/4.86 Prover 4: proved (4227ms)
% 28.37/4.86 Prover 11: stopped
% 28.37/4.86
% 28.37/4.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.37/4.86
% 28.37/4.90 % SZS output start Proof for theBenchmark
% 28.37/4.91 Assumptions after simplification:
% 28.37/4.91 ---------------------------------
% 28.37/4.91
% 28.37/4.91 (apart1)
% 28.81/4.95 ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 28.81/4.95
% 28.81/4.95 (apart4)
% 28.81/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 28.81/4.96 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2)
% 28.81/4.96 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 28.81/4.96 distinct_points(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 28.81/4.96 ! [v3: int] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~
% 28.81/4.96 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.81/4.96 distinct_points(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 28.81/4.96 [v3: int] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~
% 28.81/4.96 (distinct_points(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.81/4.96 distinct_points(v1, v2) = 0)
% 28.81/4.96
% 28.81/4.96 (ceq2)
% 28.81/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 =
% 28.81/4.97 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1,
% 28.81/4.97 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 =
% 28.81/4.97 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] :
% 28.81/4.97 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) |
% 28.81/4.97 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.81/4.97 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 28.81/4.97 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~
% 28.81/4.97 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 28.81/4.97 apart_point_and_line(v0, v2) = 0)
% 28.81/4.97
% 28.81/4.97 (ci1)
% 28.81/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 28.81/4.97 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 28.81/4.97 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 28.81/4.97 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.81/4.97 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 28.81/4.97 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 28.81/4.97 apart_point_and_line(v0, v2) = v3 & $i(v2)))
% 28.81/4.97
% 28.81/4.97 (ci2)
% 28.81/4.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 28.81/4.98 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 28.81/4.98 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4
% 28.81/4.98 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 28.81/4.98 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ?
% 28.81/4.98 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 &
% 28.81/4.98 apart_point_and_line(v1, v2) = v3 & $i(v2)))
% 28.81/4.98
% 28.81/4.98 (con)
% 28.81/4.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 28.81/4.98 int] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v4 & line_connecting(v0, v1)
% 28.81/4.98 = v3 & apart_point_and_line(v2, v4) = v5 & apart_point_and_line(v2, v3) = 0
% 28.81/4.98 & distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 28.81/4.98
% 28.81/4.99 (con1)
% 28.81/4.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) |
% 28.81/4.99 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 28.81/4.99 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 &
% 28.81/4.99 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) |
% 28.81/4.99 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) =
% 28.81/4.99 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 28.81/4.99 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 28.81/4.99 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 =
% 28.81/4.99 0)))
% 28.81/4.99
% 28.81/4.99 (cu1)
% 29.06/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5:
% 29.06/5.01 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~
% 29.06/5.01 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 29.06/5.01 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 29.06/5.01 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0,
% 29.06/5.01 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 29.06/5.01 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 29.06/5.01 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 29.06/5.01 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3)
% 29.06/5.01 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 29.06/5.01 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 &
% 29.06/5.01 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6
% 29.06/5.01 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 29.06/5.01 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 29.06/5.01 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 29.06/5.01 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 29.06/5.01 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 29.06/5.01 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 29.06/5.01 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 =
% 29.06/5.01 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 29.06/5.01 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) =
% 29.06/5.01 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 29.06/5.01 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9:
% 29.06/5.01 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) =
% 29.06/5.01 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7
% 29.06/5.01 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 29.06/5.01 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~
% 29.06/5.01 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4)
% 29.06/5.01 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 29.06/5.01 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 29.06/5.01 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 &
% 29.06/5.01 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0:
% 29.06/5.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int]
% 29.06/5.01 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~
% 29.06/5.01 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~
% 29.06/5.01 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 29.06/5.01 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1,
% 29.06/5.01 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 29.06/5.01 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 29.06/5.01 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3)
% 29.06/5.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 29.06/5.01 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 &
% 29.06/5.01 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 &
% 29.06/5.01 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 29.06/5.01
% 29.06/5.01 (function-axioms)
% 29.06/5.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 29.06/5.02 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~
% 29.06/5.02 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.06/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.06/5.02 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2)
% 29.06/5.02 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.06/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~
% 29.06/5.02 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.06/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.06/5.02 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0:
% 29.06/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.06/5.02 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 29.06/5.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.06/5.02 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3,
% 29.06/5.02 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 29.06/5.02 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) |
% 29.06/5.02 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.06/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~
% 29.06/5.02 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.06/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~
% 29.06/5.02 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 29.06/5.02 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~
% 29.06/5.02 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.06/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.06/5.02 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) =
% 29.06/5.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.06/5.02 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~
% 29.06/5.02 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 29.06/5.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.06/5.02 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0:
% 29.06/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 29.06/5.02 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) =
% 29.06/5.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 29.06/5.02 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0:
% 29.06/5.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 29.06/5.02 ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 29.06/5.02
% 29.06/5.02 Further assumptions not needed in the proof:
% 29.06/5.02 --------------------------------------------
% 29.06/5.02 a3, a4, a5, apart2, apart3, apart5, ax1, ax2, ax6, ceq1, ceq3, ci3, ci4, coipo1,
% 29.06/5.02 cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, ooc2, orth1, ouo1, p1,
% 29.06/5.02 par1
% 29.06/5.02
% 29.06/5.02 Those formulas are unsatisfiable:
% 29.06/5.02 ---------------------------------
% 29.06/5.02
% 29.06/5.02 Begin of proof
% 29.06/5.02 |
% 29.06/5.02 | ALPHA: (apart4) implies:
% 29.06/5.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 29.06/5.03 | (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) |
% 29.06/5.03 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v2) = 0)
% 29.06/5.03 |
% 29.06/5.03 | ALPHA: (ci1) implies:
% 29.06/5.03 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 29.06/5.03 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 29.06/5.03 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 &
% 29.06/5.03 | $i(v2)))
% 29.06/5.03 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 29.06/5.03 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 29.06/5.03 | (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 29.06/5.03 | ~ (v4 = 0) | ~ (v3 = 0))))
% 29.06/5.03 |
% 29.06/5.03 | ALPHA: (ci2) implies:
% 29.06/5.03 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 29.06/5.03 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 29.06/5.03 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 &
% 29.06/5.03 | $i(v2)))
% 29.06/5.03 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 29.06/5.03 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 29.06/5.03 | (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & (
% 29.06/5.03 | ~ (v4 = 0) | ~ (v3 = 0))))
% 29.06/5.03 |
% 29.06/5.03 | ALPHA: (cu1) implies:
% 29.06/5.03 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 29.06/5.03 | (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~
% 29.06/5.03 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 29.06/5.03 | any] : ? [v6: any] : ? [v7: any] : (apart_point_and_line(v1, v3)
% 29.06/5.03 | = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0,
% 29.06/5.03 | v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 |
% 29.06/5.03 | v5 = 0 | v4 = 0)))
% 29.06/5.04 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.06/5.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5)
% 29.06/5.04 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0,
% 29.06/5.04 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 29.06/5.04 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1,
% 29.06/5.04 | v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2,
% 29.06/5.04 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 29.06/5.04 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.06/5.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 29.06/5.04 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3)
% 29.06/5.04 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 29.06/5.04 | : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v3) = v8 &
% 29.06/5.04 | apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 &
% 29.06/5.04 | ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 29.06/5.04 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.06/5.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5)
% 29.06/5.04 | | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 29.06/5.04 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 29.06/5.04 | [v9: any] : (apart_point_and_line(v1, v3) = v9 &
% 29.06/5.04 | apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 &
% 29.06/5.04 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 29.06/5.04 | | v8 = 0)))
% 29.06/5.04 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.06/5.04 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 29.06/5.04 | v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~
% 29.06/5.04 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ?
% 29.06/5.04 | [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 &
% 29.06/5.04 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 &
% 29.06/5.04 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0
% 29.06/5.04 | | v8 = 0)))
% 29.06/5.05 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 29.06/5.05 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) =
% 29.06/5.05 | v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~
% 29.06/5.05 | (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 29.06/5.05 | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 29.06/5.05 | (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) =
% 29.06/5.05 | v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 =
% 29.06/5.05 | 0)))
% 29.06/5.05 |
% 29.06/5.05 | ALPHA: (ceq2) implies:
% 29.31/5.05 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 29.31/5.05 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0,
% 29.31/5.05 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 29.31/5.05 | distinct_lines(v1, v2) = 0)
% 29.31/5.05 |
% 29.31/5.05 | ALPHA: (con1) implies:
% 29.31/5.05 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~
% 29.31/5.05 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ?
% 29.31/5.05 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 &
% 29.31/5.05 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 29.31/5.05 | | v5 = 0)))
% 29.31/5.05 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1)
% 29.31/5.05 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 29.31/5.05 | [v5: any] : ? [v6: any] : (point(v1) = v4 & point(v0) = v3 &
% 29.31/5.05 | line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~
% 29.31/5.05 | (v4 = 0) | ~ (v3 = 0) | v6 = 0)))
% 29.31/5.05 |
% 29.31/5.05 | ALPHA: (function-axioms) implies:
% 29.31/5.05 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 29.31/5.05 | : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~
% 29.31/5.05 | (distinct_points(v3, v2) = v0))
% 29.31/5.05 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 29.31/5.05 | : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~
% 29.31/5.05 | (apart_point_and_line(v3, v2) = v0))
% 29.31/5.05 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.31/5.05 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 29.31/5.05 |
% 29.31/5.05 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2,
% 29.31/5.05 | all_38_3, all_38_4, all_38_5 gives:
% 29.31/5.06 | (18) ~ (all_38_0 = 0) & line_connecting(all_38_4, all_38_5) = all_38_1 &
% 29.31/5.06 | line_connecting(all_38_5, all_38_4) = all_38_2 &
% 29.31/5.06 | apart_point_and_line(all_38_3, all_38_1) = all_38_0 &
% 29.31/5.06 | apart_point_and_line(all_38_3, all_38_2) = 0 &
% 29.31/5.06 | distinct_points(all_38_5, all_38_4) = 0 & $i(all_38_1) & $i(all_38_2)
% 29.31/5.06 | & $i(all_38_3) & $i(all_38_4) & $i(all_38_5)
% 29.31/5.06 |
% 29.31/5.06 | ALPHA: (18) implies:
% 29.31/5.06 | (19) ~ (all_38_0 = 0)
% 29.31/5.06 | (20) $i(all_38_5)
% 29.31/5.06 | (21) $i(all_38_4)
% 29.31/5.06 | (22) $i(all_38_3)
% 29.31/5.06 | (23) $i(all_38_2)
% 29.31/5.06 | (24) $i(all_38_1)
% 29.31/5.06 | (25) distinct_points(all_38_5, all_38_4) = 0
% 29.31/5.06 | (26) apart_point_and_line(all_38_3, all_38_2) = 0
% 29.31/5.06 | (27) apart_point_and_line(all_38_3, all_38_1) = all_38_0
% 29.31/5.06 | (28) line_connecting(all_38_5, all_38_4) = all_38_2
% 29.31/5.06 | (29) line_connecting(all_38_4, all_38_5) = all_38_1
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (13) with all_38_5, all_38_4, simplifying with
% 29.31/5.06 | (20), (21), (25) gives:
% 29.31/5.06 | (30) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 29.31/5.06 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(v2) = v3 &
% 29.31/5.06 | line_connecting(all_38_5, all_38_4) = v2 & $i(v2) & ( ~ (v1 = 0) |
% 29.31/5.06 | ~ (v0 = 0) | v3 = 0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, simplifying with (20),
% 29.31/5.06 | (21), (25) gives:
% 29.31/5.06 | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5,
% 29.31/5.06 | all_38_4) = v0 & apart_point_and_line(all_38_4, v0) = v1 & $i(v0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, simplifying with (20),
% 29.31/5.06 | (21), (25) gives:
% 29.31/5.06 | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_38_5,
% 29.31/5.06 | all_38_4) = v0 & apart_point_and_line(all_38_5, v0) = v1 & $i(v0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (10) with all_38_3, all_38_3, all_38_1, all_38_1,
% 29.31/5.06 | all_38_0, all_38_0, simplifying with (22), (24), (27) gives:
% 29.31/5.06 | (33) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 29.31/5.06 | any] : (apart_point_and_line(all_38_3, all_38_1) = v3 &
% 29.31/5.06 | apart_point_and_line(all_38_3, all_38_1) = v2 &
% 29.31/5.06 | distinct_lines(all_38_1, all_38_1) = v1 & distinct_points(all_38_3,
% 29.31/5.06 | all_38_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (12) with all_38_3, all_38_2, all_38_1, all_38_0,
% 29.31/5.06 | simplifying with (22), (23), (24), (26), (27) gives:
% 29.31/5.06 | (34) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (14) with all_38_5, all_38_4, all_38_2, simplifying
% 29.31/5.06 | with (20), (21), (28) gives:
% 29.31/5.06 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 29.31/5.06 | (point(all_38_4) = v1 & point(all_38_5) = v0 & line(all_38_2) = v3 &
% 29.31/5.06 | distinct_points(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 29.31/5.06 | 0) | ~ (v0 = 0) | v3 = 0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_2, simplifying
% 29.31/5.06 | with (20), (21), (28) gives:
% 29.31/5.06 | (36) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4,
% 29.31/5.06 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~
% 29.31/5.06 | (v1 = 0) | ~ (v0 = 0)))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, all_38_2, simplifying
% 29.31/5.06 | with (20), (21), (28) gives:
% 29.31/5.06 | (37) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5,
% 29.31/5.06 | all_38_2) = v1 & distinct_points(all_38_5, all_38_4) = v0 & ( ~
% 29.31/5.06 | (v1 = 0) | ~ (v0 = 0)))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (14) with all_38_4, all_38_5, all_38_1, simplifying
% 29.31/5.06 | with (20), (21), (29) gives:
% 29.31/5.06 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 29.31/5.06 | (point(all_38_4) = v0 & point(all_38_5) = v1 & line(all_38_1) = v3 &
% 29.31/5.06 | distinct_points(all_38_4, all_38_5) = v2 & ( ~ (v2 = 0) | ~ (v1 =
% 29.31/5.06 | 0) | ~ (v0 = 0) | v3 = 0))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (5) with all_38_4, all_38_5, all_38_1, simplifying
% 29.31/5.06 | with (20), (21), (29) gives:
% 29.31/5.06 | (39) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_5,
% 29.31/5.06 | all_38_1) = v1 & distinct_points(all_38_4, all_38_5) = v0 & ( ~
% 29.31/5.06 | (v1 = 0) | ~ (v0 = 0)))
% 29.31/5.06 |
% 29.31/5.06 | GROUND_INST: instantiating (3) with all_38_4, all_38_5, all_38_1, simplifying
% 29.31/5.06 | with (20), (21), (29) gives:
% 29.31/5.06 | (40) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4,
% 29.31/5.06 | all_38_1) = v1 & distinct_points(all_38_4, all_38_5) = v0 & ( ~
% 29.31/5.06 | (v1 = 0) | ~ (v0 = 0)))
% 29.31/5.06 |
% 29.31/5.06 | DELTA: instantiating (40) with fresh symbols all_49_0, all_49_1 gives:
% 29.31/5.06 | (41) apart_point_and_line(all_38_4, all_38_1) = all_49_0 &
% 29.31/5.06 | distinct_points(all_38_4, all_38_5) = all_49_1 & ( ~ (all_49_0 = 0) |
% 29.31/5.06 | ~ (all_49_1 = 0))
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (41) implies:
% 29.31/5.07 | (42) distinct_points(all_38_4, all_38_5) = all_49_1
% 29.31/5.07 | (43) apart_point_and_line(all_38_4, all_38_1) = all_49_0
% 29.31/5.07 | (44) ~ (all_49_0 = 0) | ~ (all_49_1 = 0)
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (39) with fresh symbols all_51_0, all_51_1 gives:
% 29.31/5.07 | (45) apart_point_and_line(all_38_5, all_38_1) = all_51_0 &
% 29.31/5.07 | distinct_points(all_38_4, all_38_5) = all_51_1 & ( ~ (all_51_0 = 0) |
% 29.31/5.07 | ~ (all_51_1 = 0))
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (45) implies:
% 29.31/5.07 | (46) distinct_points(all_38_4, all_38_5) = all_51_1
% 29.31/5.07 | (47) apart_point_and_line(all_38_5, all_38_1) = all_51_0
% 29.31/5.07 | (48) ~ (all_51_0 = 0) | ~ (all_51_1 = 0)
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (32) with fresh symbols all_53_0, all_53_1 gives:
% 29.31/5.07 | (49) ~ (all_53_0 = 0) & line_connecting(all_38_5, all_38_4) = all_53_1 &
% 29.31/5.07 | apart_point_and_line(all_38_5, all_53_1) = all_53_0 & $i(all_53_1)
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (49) implies:
% 29.31/5.07 | (50) $i(all_53_1)
% 29.31/5.07 | (51) apart_point_and_line(all_38_5, all_53_1) = all_53_0
% 29.31/5.07 | (52) line_connecting(all_38_5, all_38_4) = all_53_1
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (37) with fresh symbols all_55_0, all_55_1 gives:
% 29.31/5.07 | (53) apart_point_and_line(all_38_5, all_38_2) = all_55_0 &
% 29.31/5.07 | distinct_points(all_38_5, all_38_4) = all_55_1 & ( ~ (all_55_0 = 0) |
% 29.31/5.07 | ~ (all_55_1 = 0))
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (53) implies:
% 29.31/5.07 | (54) distinct_points(all_38_5, all_38_4) = all_55_1
% 29.31/5.07 | (55) apart_point_and_line(all_38_5, all_38_2) = all_55_0
% 29.31/5.07 | (56) ~ (all_55_0 = 0) | ~ (all_55_1 = 0)
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (36) with fresh symbols all_57_0, all_57_1 gives:
% 29.31/5.07 | (57) apart_point_and_line(all_38_4, all_38_2) = all_57_0 &
% 29.31/5.07 | distinct_points(all_38_5, all_38_4) = all_57_1 & ( ~ (all_57_0 = 0) |
% 29.31/5.07 | ~ (all_57_1 = 0))
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (57) implies:
% 29.31/5.07 | (58) distinct_points(all_38_5, all_38_4) = all_57_1
% 29.31/5.07 | (59) apart_point_and_line(all_38_4, all_38_2) = all_57_0
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (31) with fresh symbols all_59_0, all_59_1 gives:
% 29.31/5.07 | (60) ~ (all_59_0 = 0) & line_connecting(all_38_5, all_38_4) = all_59_1 &
% 29.31/5.07 | apart_point_and_line(all_38_4, all_59_1) = all_59_0 & $i(all_59_1)
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (60) implies:
% 29.31/5.07 | (61) ~ (all_59_0 = 0)
% 29.31/5.07 | (62) apart_point_and_line(all_38_4, all_59_1) = all_59_0
% 29.31/5.07 | (63) line_connecting(all_38_5, all_38_4) = all_59_1
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (35) with fresh symbols all_61_0, all_61_1, all_61_2,
% 29.31/5.07 | all_61_3 gives:
% 29.31/5.07 | (64) point(all_38_4) = all_61_2 & point(all_38_5) = all_61_3 &
% 29.31/5.07 | line(all_38_2) = all_61_0 & distinct_points(all_38_5, all_38_4) =
% 29.31/5.07 | all_61_1 & ( ~ (all_61_1 = 0) | ~ (all_61_2 = 0) | ~ (all_61_3 = 0)
% 29.31/5.07 | | all_61_0 = 0)
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (64) implies:
% 29.31/5.07 | (65) distinct_points(all_38_5, all_38_4) = all_61_1
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (38) with fresh symbols all_63_0, all_63_1, all_63_2,
% 29.31/5.07 | all_63_3 gives:
% 29.31/5.07 | (66) point(all_38_4) = all_63_3 & point(all_38_5) = all_63_2 &
% 29.31/5.07 | line(all_38_1) = all_63_0 & distinct_points(all_38_4, all_38_5) =
% 29.31/5.07 | all_63_1 & ( ~ (all_63_1 = 0) | ~ (all_63_2 = 0) | ~ (all_63_3 = 0)
% 29.31/5.07 | | all_63_0 = 0)
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (66) implies:
% 29.31/5.07 | (67) distinct_points(all_38_4, all_38_5) = all_63_1
% 29.31/5.07 |
% 29.31/5.07 | DELTA: instantiating (30) with fresh symbols all_65_0, all_65_1, all_65_2,
% 29.31/5.07 | all_65_3 gives:
% 29.31/5.07 | (68) point(all_38_4) = all_65_2 & point(all_38_5) = all_65_3 &
% 29.31/5.07 | line(all_65_1) = all_65_0 & line_connecting(all_38_5, all_38_4) =
% 29.31/5.07 | all_65_1 & $i(all_65_1) & ( ~ (all_65_2 = 0) | ~ (all_65_3 = 0) |
% 29.31/5.07 | all_65_0 = 0)
% 29.31/5.07 |
% 29.31/5.07 | ALPHA: (68) implies:
% 29.31/5.07 | (69) line_connecting(all_38_5, all_38_4) = all_65_1
% 29.31/5.07 |
% 29.31/5.07 | BETA: splitting (34) gives:
% 29.31/5.07 |
% 29.31/5.07 | Case 1:
% 29.31/5.07 | |
% 29.31/5.07 | | (70) distinct_lines(all_38_2, all_38_1) = 0
% 29.31/5.07 | |
% 29.31/5.07 | | BETA: splitting (33) gives:
% 29.31/5.07 | |
% 29.31/5.07 | | Case 1:
% 29.31/5.07 | | |
% 29.31/5.07 | | | (71) all_38_0 = 0
% 29.31/5.07 | | |
% 29.31/5.07 | | | REDUCE: (19), (71) imply:
% 29.31/5.07 | | | (72) $false
% 29.31/5.07 | | |
% 29.31/5.07 | | | CLOSE: (72) is inconsistent.
% 29.31/5.07 | | |
% 29.31/5.07 | | Case 2:
% 29.31/5.07 | | |
% 29.31/5.07 | | | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 29.31/5.07 | | | (apart_point_and_line(all_38_3, all_38_1) = v3 &
% 29.31/5.07 | | | apart_point_and_line(all_38_3, all_38_1) = v2 &
% 29.31/5.07 | | | distinct_lines(all_38_1, all_38_1) = v1 &
% 29.31/5.07 | | | distinct_points(all_38_3, all_38_3) = v0 & ( ~ (v1 = 0) | ~ (v0
% 29.31/5.07 | | | = 0) | v3 = 0 | v2 = 0))
% 29.31/5.07 | | |
% 29.31/5.07 | | | DELTA: instantiating (73) with fresh symbols all_84_0, all_84_1, all_84_2,
% 29.31/5.07 | | | all_84_3 gives:
% 29.31/5.07 | | | (74) apart_point_and_line(all_38_3, all_38_1) = all_84_0 &
% 29.31/5.07 | | | apart_point_and_line(all_38_3, all_38_1) = all_84_1 &
% 29.31/5.07 | | | distinct_lines(all_38_1, all_38_1) = all_84_2 &
% 29.31/5.07 | | | distinct_points(all_38_3, all_38_3) = all_84_3 & ( ~ (all_84_2 =
% 29.31/5.07 | | | 0) | ~ (all_84_3 = 0) | all_84_0 = 0 | all_84_1 = 0)
% 29.31/5.07 | | |
% 29.31/5.07 | | | ALPHA: (74) implies:
% 29.31/5.07 | | | (75) apart_point_and_line(all_38_3, all_38_1) = all_84_1
% 29.31/5.07 | | | (76) apart_point_and_line(all_38_3, all_38_1) = all_84_0
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (15) with 0, all_57_1, all_38_4, all_38_5,
% 29.31/5.07 | | | simplifying with (25), (58) gives:
% 29.31/5.07 | | | (77) all_57_1 = 0
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (15) with all_57_1, all_61_1, all_38_4,
% 29.31/5.07 | | | all_38_5, simplifying with (58), (65) gives:
% 29.31/5.07 | | | (78) all_61_1 = all_57_1
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (15) with all_55_1, all_61_1, all_38_4,
% 29.31/5.07 | | | all_38_5, simplifying with (54), (65) gives:
% 29.31/5.07 | | | (79) all_61_1 = all_55_1
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (15) with all_51_1, all_63_1, all_38_5,
% 29.31/5.07 | | | all_38_4, simplifying with (46), (67) gives:
% 29.31/5.07 | | | (80) all_63_1 = all_51_1
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (15) with all_49_1, all_63_1, all_38_5,
% 29.31/5.07 | | | all_38_4, simplifying with (42), (67) gives:
% 29.31/5.07 | | | (81) all_63_1 = all_49_1
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (16) with all_38_0, all_84_0, all_38_1,
% 29.31/5.07 | | | all_38_3, simplifying with (27), (76) gives:
% 29.31/5.07 | | | (82) all_84_0 = all_38_0
% 29.31/5.07 | | |
% 29.31/5.07 | | | GROUND_INST: instantiating (16) with all_84_1, all_84_0, all_38_1,
% 29.31/5.07 | | | all_38_3, simplifying with (75), (76) gives:
% 29.31/5.08 | | | (83) all_84_0 = all_84_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | GROUND_INST: instantiating (17) with all_38_2, all_65_1, all_38_4,
% 29.31/5.08 | | | all_38_5, simplifying with (28), (69) gives:
% 29.31/5.08 | | | (84) all_65_1 = all_38_2
% 29.31/5.08 | | |
% 29.31/5.08 | | | GROUND_INST: instantiating (17) with all_59_1, all_65_1, all_38_4,
% 29.31/5.08 | | | all_38_5, simplifying with (63), (69) gives:
% 29.31/5.08 | | | (85) all_65_1 = all_59_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | GROUND_INST: instantiating (17) with all_53_1, all_65_1, all_38_4,
% 29.31/5.08 | | | all_38_5, simplifying with (52), (69) gives:
% 29.31/5.08 | | | (86) all_65_1 = all_53_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (82), (83) imply:
% 29.31/5.08 | | | (87) all_84_1 = all_38_0
% 29.31/5.08 | | |
% 29.31/5.08 | | | SIMP: (87) implies:
% 29.31/5.08 | | | (88) all_84_1 = all_38_0
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (84), (85) imply:
% 29.31/5.08 | | | (89) all_59_1 = all_38_2
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (85), (86) imply:
% 29.31/5.08 | | | (90) all_59_1 = all_53_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (80), (81) imply:
% 29.31/5.08 | | | (91) all_51_1 = all_49_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (78), (79) imply:
% 29.31/5.08 | | | (92) all_57_1 = all_55_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | SIMP: (92) implies:
% 29.31/5.08 | | | (93) all_57_1 = all_55_1
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (89), (90) imply:
% 29.31/5.08 | | | (94) all_53_1 = all_38_2
% 29.31/5.08 | | |
% 29.31/5.08 | | | COMBINE_EQS: (77), (93) imply:
% 29.31/5.08 | | | (95) all_55_1 = 0
% 29.31/5.08 | | |
% 29.31/5.08 | | | SIMP: (95) implies:
% 29.31/5.08 | | | (96) all_55_1 = 0
% 29.31/5.08 | | |
% 29.31/5.08 | | | REDUCE: (62), (89) imply:
% 29.31/5.08 | | | (97) apart_point_and_line(all_38_4, all_38_2) = all_59_0
% 29.31/5.08 | | |
% 29.31/5.08 | | | REDUCE: (51), (94) imply:
% 29.31/5.08 | | | (98) apart_point_and_line(all_38_5, all_38_2) = all_53_0
% 29.31/5.08 | | |
% 29.31/5.08 | | | BETA: splitting (56) gives:
% 29.31/5.08 | | |
% 29.31/5.08 | | | Case 1:
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | (99) ~ (all_55_0 = 0)
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (16) with all_55_0, all_53_0, all_38_2,
% 29.31/5.08 | | | | all_38_5, simplifying with (55), (98) gives:
% 29.31/5.08 | | | | (100) all_55_0 = all_53_0
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (16) with all_57_0, all_59_0, all_38_2,
% 29.31/5.08 | | | | all_38_4, simplifying with (59), (97) gives:
% 29.31/5.08 | | | | (101) all_59_0 = all_57_0
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | REDUCE: (61), (101) imply:
% 29.31/5.08 | | | | (102) ~ (all_57_0 = 0)
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | REDUCE: (99), (100) imply:
% 29.31/5.08 | | | | (103) ~ (all_53_0 = 0)
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (1) with all_38_5, all_38_4, all_38_5,
% 29.31/5.08 | | | | all_49_1, simplifying with (20), (21), (25), (42) gives:
% 29.31/5.08 | | | | (104) all_49_1 = 0 | distinct_points(all_38_5, all_38_5) = 0
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (6) with all_38_5, all_38_4, all_38_2,
% 29.31/5.08 | | | | all_38_1, simplifying with (20), (21), (23), (24), (25),
% 29.31/5.08 | | | | (70) gives:
% 29.31/5.08 | | | | (105) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 29.31/5.08 | | | | (apart_point_and_line(all_38_4, all_38_1) = v3 &
% 29.31/5.08 | | | | apart_point_and_line(all_38_4, all_38_2) = v2 &
% 29.31/5.08 | | | | apart_point_and_line(all_38_5, all_38_1) = v1 &
% 29.31/5.08 | | | | apart_point_and_line(all_38_5, all_38_2) = v0 & (v3 = 0 | v2
% 29.31/5.08 | | | | = 0 | v1 = 0 | v0 = 0))
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (10) with all_38_3, all_38_5, all_38_1,
% 29.31/5.08 | | | | all_38_2, all_38_0, all_53_0, simplifying with (20), (22),
% 29.31/5.08 | | | | (23), (24), (27), (98) gives:
% 29.31/5.08 | | | | (106) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.08 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.08 | | | | all_38_2) = v2 & apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.08 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.08 | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.08 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (10) with all_38_5, all_38_3, all_38_2,
% 29.31/5.08 | | | | all_38_1, all_53_0, all_38_0, simplifying with (20), (22),
% 29.31/5.08 | | | | (23), (24), (27), (98) gives:
% 29.31/5.08 | | | | (107) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.08 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.08 | | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.08 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.08 | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.08 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (9) with all_38_5, all_38_3, all_38_1,
% 29.31/5.08 | | | | all_38_2, all_53_0, all_38_0, simplifying with (20), (22),
% 29.31/5.08 | | | | (23), (24), (27), (98) gives:
% 29.31/5.08 | | | | (108) all_53_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.08 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.08 | | | | all_38_2) = v3 & apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.08 | | | | v2 & distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.08 | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.08 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (7) with all_38_5, all_38_4, all_38_2,
% 29.31/5.08 | | | | all_38_2, all_53_0, all_53_0, simplifying with (20), (21),
% 29.31/5.08 | | | | (23), (25), (98) gives:
% 29.31/5.08 | | | | (109) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.08 | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 &
% 29.31/5.08 | | | | apart_point_and_line(all_38_4, all_38_2) = v1 &
% 29.31/5.08 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 =
% 29.31/5.08 | | | | 0 | v1 = 0))
% 29.31/5.08 | | | |
% 29.31/5.08 | | | | GROUND_INST: instantiating (8) with all_38_5, all_38_5, all_38_2,
% 29.31/5.08 | | | | all_38_1, all_53_0, all_53_0, simplifying with (20), (23),
% 29.31/5.08 | | | | (24), (70), (98) gives:
% 29.31/5.09 | | | | (110) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.09 | | | | (apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_5, all_38_1) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v0 = 0) | v2
% 29.31/5.09 | | | | = 0 | v1 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (10) with all_38_5, all_38_5, all_38_2,
% 29.31/5.09 | | | | all_38_2, all_53_0, all_53_0, simplifying with (20), (23),
% 29.31/5.09 | | | | (98) gives:
% 29.31/5.09 | | | | (111) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.09 | | | | [v3: any] : (apart_point_and_line(all_38_5, all_38_2) = v3 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_5, all_38_2) = v2 &
% 29.31/5.09 | | | | distinct_lines(all_38_2, all_38_2) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.09 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (10) with all_38_3, all_38_4, all_38_1,
% 29.31/5.09 | | | | all_38_2, all_38_0, all_57_0, simplifying with (21), (22),
% 29.31/5.09 | | | | (23), (24), (27), (59) gives:
% 29.31/5.09 | | | | (112) all_57_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.09 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.09 | | | | all_38_2) = v2 & apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.09 | | | | v3 & distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.09 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (10) with all_38_4, all_38_3, all_38_2,
% 29.31/5.09 | | | | all_38_1, all_57_0, all_38_0, simplifying with (21), (22),
% 29.31/5.09 | | | | (23), (24), (27), (59) gives:
% 29.31/5.09 | | | | (113) all_57_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.09 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.09 | | | | all_38_2) = v3 & apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.09 | | | | v2 & distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.09 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (9) with all_38_4, all_38_3, all_38_1,
% 29.31/5.09 | | | | all_38_2, all_57_0, all_38_0, simplifying with (21), (22),
% 29.31/5.09 | | | | (23), (24), (27), (59) gives:
% 29.31/5.09 | | | | (114) all_57_0 = 0 | all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.09 | | | | [v2: any] : ? [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.09 | | | | all_38_2) = v3 & apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.09 | | | | v2 & distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.09 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (11) with all_38_5, all_38_4, all_38_2,
% 29.31/5.09 | | | | all_38_2, all_57_0, all_57_0, simplifying with (20), (21),
% 29.31/5.09 | | | | (23), (25), (59) gives:
% 29.31/5.09 | | | | (115) all_57_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.09 | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_5, all_38_2) = v1 &
% 29.31/5.09 | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) | v2 =
% 29.31/5.09 | | | | 0 | v1 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (8) with all_38_4, all_38_4, all_38_2,
% 29.31/5.09 | | | | all_38_1, all_57_0, all_57_0, simplifying with (21), (23),
% 29.31/5.09 | | | | (24), (59), (70) gives:
% 29.31/5.09 | | | | (116) all_57_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.09 | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_4, all_38_1) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v0 = 0) | v2
% 29.31/5.09 | | | | = 0 | v1 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | GROUND_INST: instantiating (10) with all_38_4, all_38_4, all_38_2,
% 29.31/5.09 | | | | all_38_2, all_57_0, all_57_0, simplifying with (21), (23),
% 29.31/5.09 | | | | (59) gives:
% 29.31/5.09 | | | | (117) all_57_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.09 | | | | [v3: any] : (apart_point_and_line(all_38_4, all_38_2) = v3 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_4, all_38_2) = v2 &
% 29.31/5.09 | | | | distinct_lines(all_38_2, all_38_2) = v1 &
% 29.31/5.09 | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v1 = 0) | ~
% 29.31/5.09 | | | | (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | DELTA: instantiating (105) with fresh symbols all_110_0, all_110_1,
% 29.31/5.09 | | | | all_110_2, all_110_3 gives:
% 29.31/5.09 | | | | (118) apart_point_and_line(all_38_4, all_38_1) = all_110_0 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_4, all_38_2) = all_110_1 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_5, all_38_1) = all_110_2 &
% 29.31/5.09 | | | | apart_point_and_line(all_38_5, all_38_2) = all_110_3 &
% 29.31/5.09 | | | | (all_110_0 = 0 | all_110_1 = 0 | all_110_2 = 0 | all_110_3 = 0)
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | ALPHA: (118) implies:
% 29.31/5.09 | | | | (119) apart_point_and_line(all_38_5, all_38_2) = all_110_3
% 29.31/5.09 | | | | (120) apart_point_and_line(all_38_5, all_38_1) = all_110_2
% 29.31/5.09 | | | | (121) apart_point_and_line(all_38_4, all_38_2) = all_110_1
% 29.31/5.09 | | | | (122) apart_point_and_line(all_38_4, all_38_1) = all_110_0
% 29.31/5.09 | | | | (123) all_110_0 = 0 | all_110_1 = 0 | all_110_2 = 0 | all_110_3 = 0
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | BETA: splitting (116) gives:
% 29.31/5.09 | | | |
% 29.31/5.09 | | | | Case 1:
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | (124) all_57_0 = 0
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | REDUCE: (102), (124) imply:
% 29.31/5.09 | | | | | (125) $false
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | CLOSE: (125) is inconsistent.
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | Case 2:
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | (126) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.09 | | | | | (apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.09 | | | | | apart_point_and_line(all_38_4, all_38_1) = v1 &
% 29.31/5.09 | | | | | distinct_points(all_38_4, all_38_4) = v0 & ( ~ (v0 = 0) |
% 29.31/5.09 | | | | | v2 = 0 | v1 = 0))
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | DELTA: instantiating (126) with fresh symbols all_136_0, all_136_1,
% 29.31/5.09 | | | | | all_136_2 gives:
% 29.31/5.09 | | | | | (127) apart_point_and_line(all_38_4, all_38_1) = all_136_0 &
% 29.31/5.09 | | | | | apart_point_and_line(all_38_4, all_38_1) = all_136_1 &
% 29.31/5.09 | | | | | distinct_points(all_38_4, all_38_4) = all_136_2 & ( ~
% 29.31/5.09 | | | | | (all_136_2 = 0) | all_136_0 = 0 | all_136_1 = 0)
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | ALPHA: (127) implies:
% 29.31/5.09 | | | | | (128) apart_point_and_line(all_38_4, all_38_1) = all_136_1
% 29.31/5.09 | | | | | (129) apart_point_and_line(all_38_4, all_38_1) = all_136_0
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | BETA: splitting (109) gives:
% 29.31/5.09 | | | | |
% 29.31/5.09 | | | | | Case 1:
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | (130) all_53_0 = 0
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | REDUCE: (103), (130) imply:
% 29.31/5.09 | | | | | | (131) $false
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | CLOSE: (131) is inconsistent.
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | Case 2:
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | (132) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.09 | | | | | | (apart_point_and_line(all_38_4, all_38_2) = v2 &
% 29.31/5.09 | | | | | | apart_point_and_line(all_38_4, all_38_2) = v1 &
% 29.31/5.09 | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 = 0) |
% 29.31/5.09 | | | | | | v2 = 0 | v1 = 0))
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | DELTA: instantiating (132) with fresh symbols all_151_0, all_151_1,
% 29.31/5.09 | | | | | | all_151_2 gives:
% 29.31/5.09 | | | | | | (133) apart_point_and_line(all_38_4, all_38_2) = all_151_0 &
% 29.31/5.09 | | | | | | apart_point_and_line(all_38_4, all_38_2) = all_151_1 &
% 29.31/5.09 | | | | | | distinct_lines(all_38_2, all_38_2) = all_151_2 & ( ~
% 29.31/5.09 | | | | | | (all_151_2 = 0) | all_151_0 = 0 | all_151_1 = 0)
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | ALPHA: (133) implies:
% 29.31/5.09 | | | | | | (134) apart_point_and_line(all_38_4, all_38_2) = all_151_1
% 29.31/5.09 | | | | | | (135) apart_point_and_line(all_38_4, all_38_2) = all_151_0
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | BETA: splitting (110) gives:
% 29.31/5.09 | | | | | |
% 29.31/5.09 | | | | | | Case 1:
% 29.31/5.09 | | | | | | |
% 29.31/5.10 | | | | | | | (136) all_53_0 = 0
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | REDUCE: (103), (136) imply:
% 29.31/5.10 | | | | | | | (137) $false
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | CLOSE: (137) is inconsistent.
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | Case 2:
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | (138) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.10 | | | | | | | (apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.10 | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v1 &
% 29.31/5.10 | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~ (v0 = 0)
% 29.31/5.10 | | | | | | | | v2 = 0 | v1 = 0))
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | DELTA: instantiating (138) with fresh symbols all_156_0,
% 29.31/5.10 | | | | | | | all_156_1, all_156_2 gives:
% 29.31/5.10 | | | | | | | (139) apart_point_and_line(all_38_5, all_38_1) = all_156_0 &
% 29.31/5.10 | | | | | | | apart_point_and_line(all_38_5, all_38_1) = all_156_1 &
% 29.31/5.10 | | | | | | | distinct_points(all_38_5, all_38_5) = all_156_2 & ( ~
% 29.31/5.10 | | | | | | | (all_156_2 = 0) | all_156_0 = 0 | all_156_1 = 0)
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | ALPHA: (139) implies:
% 29.31/5.10 | | | | | | | (140) apart_point_and_line(all_38_5, all_38_1) = all_156_1
% 29.31/5.10 | | | | | | | (141) apart_point_and_line(all_38_5, all_38_1) = all_156_0
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | BETA: splitting (115) gives:
% 29.31/5.10 | | | | | | |
% 29.31/5.10 | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | (142) all_57_0 = 0
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | REDUCE: (102), (142) imply:
% 29.31/5.10 | | | | | | | | (143) $false
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | CLOSE: (143) is inconsistent.
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 29.31/5.10 | | | | | | | | (apart_point_and_line(all_38_5, all_38_2) = v2 &
% 29.31/5.10 | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v1 &
% 29.31/5.10 | | | | | | | | distinct_lines(all_38_2, all_38_2) = v0 & ( ~ (v0 =
% 29.31/5.10 | | | | | | | | 0) | v2 = 0 | v1 = 0))
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | DELTA: instantiating (144) with fresh symbols all_161_0,
% 29.31/5.10 | | | | | | | | all_161_1, all_161_2 gives:
% 29.31/5.10 | | | | | | | | (145) apart_point_and_line(all_38_5, all_38_2) = all_161_0 &
% 29.31/5.10 | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = all_161_1 &
% 29.31/5.10 | | | | | | | | distinct_lines(all_38_2, all_38_2) = all_161_2 & ( ~
% 29.31/5.10 | | | | | | | | (all_161_2 = 0) | all_161_0 = 0 | all_161_1 = 0)
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | ALPHA: (145) implies:
% 29.31/5.10 | | | | | | | | (146) apart_point_and_line(all_38_5, all_38_2) = all_161_1
% 29.31/5.10 | | | | | | | | (147) apart_point_and_line(all_38_5, all_38_2) = all_161_0
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | BETA: splitting (113) gives:
% 29.31/5.10 | | | | | | | |
% 29.31/5.10 | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | (148) all_57_0 = 0
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | REDUCE: (102), (148) imply:
% 29.31/5.10 | | | | | | | | | (149) $false
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | CLOSE: (149) is inconsistent.
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | (150) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 29.31/5.10 | | | | | | | | | any] : ? [v3: any] :
% 29.31/5.10 | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v3 &
% 29.31/5.10 | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.10 | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.10 | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~ (v1
% 29.31/5.10 | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | BETA: splitting (117) gives:
% 29.31/5.10 | | | | | | | | |
% 29.31/5.10 | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | (151) all_57_0 = 0
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | REDUCE: (102), (151) imply:
% 29.31/5.10 | | | | | | | | | | (152) $false
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | CLOSE: (152) is inconsistent.
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | (153) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.10 | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_4,
% 29.31/5.10 | | | | | | | | | | all_38_2) = v3 & apart_point_and_line(all_38_4,
% 29.31/5.10 | | | | | | | | | | all_38_2) = v2 & distinct_lines(all_38_2,
% 29.31/5.10 | | | | | | | | | | all_38_2) = v1 & distinct_points(all_38_4,
% 29.31/5.10 | | | | | | | | | | all_38_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 29.31/5.10 | | | | | | | | | | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_169_0,
% 29.31/5.10 | | | | | | | | | | all_169_1, all_169_2, all_169_3 gives:
% 29.31/5.10 | | | | | | | | | | (154) apart_point_and_line(all_38_4, all_38_2) =
% 29.31/5.10 | | | | | | | | | | all_169_0 & apart_point_and_line(all_38_4,
% 29.31/5.10 | | | | | | | | | | all_38_2) = all_169_1 & distinct_lines(all_38_2,
% 29.31/5.10 | | | | | | | | | | all_38_2) = all_169_2 & distinct_points(all_38_4,
% 29.31/5.10 | | | | | | | | | | all_38_4) = all_169_3 & ( ~ (all_169_2 = 0) | ~
% 29.31/5.10 | | | | | | | | | | (all_169_3 = 0) | all_169_0 = 0 | all_169_1 = 0)
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | ALPHA: (154) implies:
% 29.31/5.10 | | | | | | | | | | (155) apart_point_and_line(all_38_4, all_38_2) =
% 29.31/5.10 | | | | | | | | | | all_169_1
% 29.31/5.10 | | | | | | | | | | (156) apart_point_and_line(all_38_4, all_38_2) =
% 29.31/5.10 | | | | | | | | | | all_169_0
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | BETA: splitting (107) gives:
% 29.31/5.10 | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | (157) all_53_0 = 0
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | REDUCE: (103), (157) imply:
% 29.31/5.10 | | | | | | | | | | | (158) $false
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | (159) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.10 | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 29.31/5.10 | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v3 &
% 29.31/5.10 | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.10 | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.10 | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~
% 29.31/5.10 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | BETA: splitting (106) gives:
% 29.31/5.10 | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | (160) all_53_0 = 0
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | REDUCE: (103), (160) imply:
% 29.31/5.10 | | | | | | | | | | | | (161) $false
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | (162) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.10 | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 29.31/5.10 | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 &
% 29.31/5.10 | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 &
% 29.31/5.10 | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.10 | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~
% 29.31/5.10 | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | BETA: splitting (112) gives:
% 29.31/5.10 | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | (163) all_57_0 = 0
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | REDUCE: (102), (163) imply:
% 29.31/5.10 | | | | | | | | | | | | | (164) $false
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | (165) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.10 | | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 29.31/5.10 | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v2 &
% 29.31/5.10 | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v3 &
% 29.31/5.10 | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.10 | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~
% 29.31/5.10 | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 29.31/5.10 | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | (166) all_53_0 = 0
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | REDUCE: (103), (166) imply:
% 29.31/5.10 | | | | | | | | | | | | | | (167) $false
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | (168) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.10 | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_5,
% 29.31/5.10 | | | | | | | | | | | | | | all_38_2) = v3 &
% 29.31/5.10 | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_2) = v2 &
% 29.31/5.10 | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_2) = v1 &
% 29.31/5.10 | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = v0 & ( ~
% 29.31/5.10 | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | DELTA: instantiating (168) with fresh symbols all_183_0,
% 29.31/5.10 | | | | | | | | | | | | | | all_183_1, all_183_2, all_183_3 gives:
% 29.31/5.10 | | | | | | | | | | | | | | (169) apart_point_and_line(all_38_5, all_38_2) =
% 29.31/5.10 | | | | | | | | | | | | | | all_183_0 & apart_point_and_line(all_38_5,
% 29.31/5.10 | | | | | | | | | | | | | | all_38_2) = all_183_1 & distinct_lines(all_38_2,
% 29.31/5.10 | | | | | | | | | | | | | | all_38_2) = all_183_2 &
% 29.31/5.10 | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_5) = all_183_3 &
% 29.31/5.10 | | | | | | | | | | | | | | ( ~ (all_183_2 = 0) | ~ (all_183_3 = 0) |
% 29.31/5.10 | | | | | | | | | | | | | | all_183_0 = 0 | all_183_1 = 0)
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | ALPHA: (169) implies:
% 29.31/5.10 | | | | | | | | | | | | | | (170) apart_point_and_line(all_38_5, all_38_2) =
% 29.31/5.10 | | | | | | | | | | | | | | all_183_1
% 29.31/5.10 | | | | | | | | | | | | | | (171) apart_point_and_line(all_38_5, all_38_2) =
% 29.31/5.10 | | | | | | | | | | | | | | all_183_0
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 29.31/5.10 | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | (172) all_57_0 = 0
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | REDUCE: (102), (172) imply:
% 29.31/5.10 | | | | | | | | | | | | | | | (173) $false
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | (174) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.10 | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 29.31/5.10 | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v3 &
% 29.31/5.10 | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.10 | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.10 | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~
% 29.31/5.10 | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 29.31/5.10 | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | Case 1:
% 29.31/5.10 | | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | | (175) all_53_0 = 0
% 29.31/5.10 | | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | | REDUCE: (103), (175) imply:
% 29.31/5.10 | | | | | | | | | | | | | | | | (176) $false
% 29.31/5.10 | | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 29.31/5.10 | | | | | | | | | | | | | | | |
% 29.31/5.10 | | | | | | | | | | | | | | | Case 2:
% 29.31/5.10 | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | (177) all_38_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] :
% 29.31/5.11 | | | | | | | | | | | | | | | | (apart_point_and_line(all_38_3, all_38_2) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | (178) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | REDUCE: (19), (178) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | (179) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | (180) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_38_2) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbols all_201_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_201_1, all_201_2, all_201_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | (181) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_201_0 & apart_point_and_line(all_38_4,
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_38_1) = all_201_1 & distinct_lines(all_38_2,
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_38_1) = all_201_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = all_201_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | ( ~ (all_201_2 = 0) | ~ (all_201_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_201_0 = 0 | all_201_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | (182) apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | all_201_1
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (183) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | REDUCE: (19), (183) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (184) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (185) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_38_2) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | distinct_lines(all_38_2, all_38_1) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | DELTA: instantiating (185) with fresh symbols all_206_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_206_1, all_206_2, all_206_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (186) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_206_0 & apart_point_and_line(all_38_5,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_38_1) = all_206_1 & distinct_lines(all_38_2,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_38_1) = all_206_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = all_206_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | ( ~ (all_206_2 = 0) | ~ (all_206_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_206_0 = 0 | all_206_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | (187) apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | all_206_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (188) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | REDUCE: (19), (188) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (189) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_38_2) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_211_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_211_1, all_211_2, all_211_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (191) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_211_1 & apart_point_and_line(all_38_5,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_38_1) = all_211_0 & distinct_lines(all_38_1,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_38_2) = all_211_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_5) = all_211_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | ( ~ (all_211_2 = 0) | ~ (all_211_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_211_0 = 0 | all_211_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | (192) apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | all_211_0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (193) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (193) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (194) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (195) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_38_2) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (195) with fresh symbols all_216_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_216_1, all_216_2, all_216_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (196) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_216_1 & apart_point_and_line(all_38_4,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_38_1) = all_216_0 & distinct_lines(all_38_1,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_38_2) = all_216_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_3, all_38_4) = all_216_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | ( ~ (all_216_2 = 0) | ~ (all_216_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_216_0 = 0 | all_216_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | (197) apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | all_216_0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (198) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (198) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (199) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (200) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_4, all_38_1) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (200) with fresh symbols all_221_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_221_1, all_221_2, all_221_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (201) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_221_0 & apart_point_and_line(all_38_4,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_221_1 & distinct_lines(all_38_1,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_221_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_4, all_38_3) = all_221_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | ( ~ (all_221_2 = 0) | ~ (all_221_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_221_0 = 0 | all_221_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | (202) apart_point_and_line(all_38_4, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | all_221_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (203) all_38_0 = 0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (203) imply:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (204) $false
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (205) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (apart_point_and_line(all_38_3,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = v3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | apart_point_and_line(all_38_5, all_38_1) = v2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | distinct_lines(all_38_1, all_38_2) = v1 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = v0 & ( ~
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_226_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_226_1, all_226_2, all_226_3 gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (206) apart_point_and_line(all_38_3, all_38_2) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_226_0 & apart_point_and_line(all_38_5,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_1) = all_226_1 & distinct_lines(all_38_1,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2) = all_226_2 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | distinct_points(all_38_5, all_38_3) = all_226_3 &
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_226_2 = 0) | ~ (all_226_3 = 0) |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_226_0 = 0 | all_226_1 = 0)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (207) apart_point_and_line(all_38_5, all_38_1) =
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_226_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_161_1, all_161_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (146), (147)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (208) all_161_0 = all_161_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_110_3, all_161_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (119), (147)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (209) all_161_0 = all_110_3
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_53_0, all_183_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (98), (171)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (210) all_183_0 = all_53_0
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_183_1, all_183_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (170), (171)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (211) all_183_0 = all_183_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_161_1, all_183_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_5, simplifying with (146), (171)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (212) all_183_0 = all_161_1
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_110_2, all_156_1,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (120), (140)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | (213) all_156_1 = all_110_2
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_51_0, all_211_0,
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (47), (192)
% 29.31/5.11 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (214) all_211_0 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_206_1, all_211_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (187), (192)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (215) all_211_0 = all_206_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_156_1, all_211_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (140), (192)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (216) all_211_0 = all_156_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_211_0, all_226_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (192), (207)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (217) all_226_1 = all_211_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_156_0, all_226_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_5, simplifying with (141), (207)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (218) all_226_1 = all_156_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_110_1, all_151_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (121), (135)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (219) all_151_0 = all_110_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_151_0, all_169_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (135), (155)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (220) all_169_1 = all_151_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_151_1, all_169_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (134), (155)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (221) all_169_1 = all_151_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_57_0, all_169_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (59), (156)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (222) all_169_0 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_151_0, all_169_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_2, all_38_4, simplifying with (135), (156)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (223) all_169_0 = all_151_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_136_0, all_201_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (129), (182)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (224) all_201_1 = all_136_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_110_0, all_201_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (122), (182)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (225) all_201_1 = all_110_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_49_0, all_216_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (43), (197)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (226) all_216_0 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_136_0, all_216_0,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (129), (197)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (227) all_216_0 = all_136_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_201_1, all_221_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (182), (202)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (228) all_221_1 = all_201_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_136_1, all_221_1,
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | all_38_1, all_38_4, simplifying with (128), (202)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (229) all_221_1 = all_136_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (218) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (230) all_211_0 = all_156_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (231) all_211_0 = all_156_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (229) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (232) all_201_1 = all_136_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (233) all_201_1 = all_136_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (227) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (234) all_136_0 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (235) all_136_0 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (216) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (236) all_206_1 = all_156_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (214), (215) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (237) all_206_1 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (231) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (238) all_206_1 = all_156_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (238) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (239) all_156_0 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (238) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (240) all_156_0 = all_156_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (233) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (241) all_136_0 = all_136_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (242) all_136_0 = all_136_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (233) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (243) all_136_1 = all_110_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (212) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (244) all_183_1 = all_161_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (211) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (245) all_183_1 = all_53_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (245) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (246) all_161_1 = all_53_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (246) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (247) all_161_1 = all_53_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (222), (223) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (248) all_151_0 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (249) all_151_0 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (221) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (250) all_151_0 = all_151_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (250) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (251) all_151_0 = all_151_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (209) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (252) all_161_1 = all_110_3
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (253) all_161_1 = all_110_3
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (253) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (254) all_110_3 = all_53_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (255) all_110_3 = all_53_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (240) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (256) all_156_1 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (257) all_156_1 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (257) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (258) all_110_2 = all_51_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (251) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (259) all_151_1 = all_110_1
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (251) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (260) all_151_1 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (260) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (261) all_110_1 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (262) all_110_1 = all_57_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (235), (242) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (263) all_136_1 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (264) all_136_1 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (264) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | (265) all_110_0 = all_49_0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_49_0 = 0)
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | (267) all_110_0 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (267) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | (268) all_49_0 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | (269) all_49_0 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (269) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | (270) $false
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | (271) all_110_1 = 0 | all_110_2 = 0 | all_110_3 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_110_1 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (272) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_57_0 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_57_0 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (274) imply:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | (275) $false
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent.
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_110_2 = 0 | all_110_3 = 0
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (277) ~ (all_51_0 = 0)
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_110_2 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (278) imply:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_51_0 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_51_0 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (277), (280) imply:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) $false
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent.
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_110_3 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (282) imply:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_53_0 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_53_0 = 0
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (284) imply:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_51_1 = 0)
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (286) imply:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_49_1 = 0)
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (104), (287), (apart1) are inconsistent by
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_49_1 = 0)
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (104), (288), (apart1) are inconsistent by
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | | |
% 29.31/5.13 | | | | | | | | | End of split
% 29.31/5.13 | | | | | | | | |
% 29.31/5.13 | | | | | | | | End of split
% 29.31/5.13 | | | | | | | |
% 29.31/5.13 | | | | | | | End of split
% 29.31/5.13 | | | | | | |
% 29.31/5.13 | | | | | | End of split
% 29.31/5.13 | | | | | |
% 29.31/5.13 | | | | | End of split
% 29.31/5.13 | | | | |
% 29.31/5.13 | | | | End of split
% 29.31/5.13 | | | |
% 29.31/5.13 | | | Case 2:
% 29.31/5.13 | | | |
% 29.31/5.13 | | | | (289) ~ (all_55_1 = 0)
% 29.31/5.13 | | | |
% 29.31/5.13 | | | | REDUCE: (96), (289) imply:
% 29.31/5.13 | | | | (290) $false
% 29.31/5.13 | | | |
% 29.31/5.13 | | | | CLOSE: (290) is inconsistent.
% 29.31/5.13 | | | |
% 29.31/5.13 | | | End of split
% 29.31/5.13 | | |
% 29.31/5.13 | | End of split
% 29.31/5.13 | |
% 29.31/5.13 | Case 2:
% 29.31/5.13 | |
% 29.31/5.13 | | (291) all_38_0 = 0
% 29.31/5.13 | |
% 29.31/5.13 | | REDUCE: (19), (291) imply:
% 29.31/5.13 | | (292) $false
% 29.31/5.13 | |
% 29.31/5.13 | | CLOSE: (292) is inconsistent.
% 29.31/5.13 | |
% 29.31/5.13 | End of split
% 29.31/5.13 |
% 29.31/5.13 End of proof
% 29.31/5.13
% 29.31/5.13 Sub-proof #1 shows that the following formulas are inconsistent:
% 29.31/5.13 ----------------------------------------------------------------
% 29.31/5.13 (1) all_49_1 = 0 | distinct_points(all_38_5, all_38_5) = 0
% 29.31/5.13 (2) ! [v0: $i] : ( ~ (distinct_points(v0, v0) = 0) | ~ $i(v0))
% 29.31/5.13 (3) $i(all_38_5)
% 29.31/5.13 (4) ~ (all_49_1 = 0)
% 29.31/5.13
% 29.31/5.13 Begin of proof
% 29.31/5.13 |
% 29.31/5.13 | BETA: splitting (1) gives:
% 29.31/5.13 |
% 29.31/5.13 | Case 1:
% 29.31/5.13 | |
% 29.31/5.13 | | (5) distinct_points(all_38_5, all_38_5) = 0
% 29.31/5.13 | |
% 29.31/5.13 | | GROUND_INST: instantiating (2) with all_38_5, simplifying with (3), (5)
% 29.31/5.13 | | gives:
% 29.31/5.13 | | (6) $false
% 29.31/5.13 | |
% 29.31/5.13 | | CLOSE: (6) is inconsistent.
% 29.31/5.13 | |
% 29.31/5.13 | Case 2:
% 29.31/5.13 | |
% 29.31/5.13 | | (7) all_49_1 = 0
% 29.31/5.13 | |
% 29.31/5.13 | | REDUCE: (4), (7) imply:
% 29.31/5.13 | | (8) $false
% 29.31/5.13 | |
% 29.31/5.13 | | CLOSE: (8) is inconsistent.
% 29.31/5.13 | |
% 29.31/5.13 | End of split
% 29.31/5.13 |
% 29.31/5.13 End of proof
% 29.31/5.13 % SZS output end Proof for theBenchmark
% 29.31/5.13
% 29.31/5.13 4527ms
%------------------------------------------------------------------------------