TSTP Solution File: GEO232+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO232+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 : 600s
% DateTime : Sat Jul 16 03:49:01 EDT 2022
% Result : Theorem 6.65s 2.17s
% Output : Proof 9.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO232+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 22:35:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.52/0.58 ____ _
% 0.52/0.58 ___ / __ \_____(_)___ ________ __________
% 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.58
% 0.52/0.58 A Theorem Prover for First-Order Logic
% 0.52/0.59 (ePrincess v.1.0)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2015
% 0.52/0.59 (c) Peter Backeman, 2014-2015
% 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.59 Bug reports to peter@backeman.se
% 0.52/0.59
% 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.59
% 0.52/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.80/0.99 Prover 0: Preprocessing ...
% 2.62/1.27 Prover 0: Warning: ignoring some quantifiers
% 2.62/1.30 Prover 0: Constructing countermodel ...
% 3.36/1.45 Prover 0: gave up
% 3.36/1.45 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.48/1.51 Prover 1: Preprocessing ...
% 4.46/1.68 Prover 1: Constructing countermodel ...
% 4.46/1.71 Prover 1: gave up
% 4.46/1.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.46/1.74 Prover 2: Preprocessing ...
% 5.84/2.02 Prover 2: Warning: ignoring some quantifiers
% 5.84/2.04 Prover 2: Constructing countermodel ...
% 6.65/2.17 Prover 2: proved (463ms)
% 6.65/2.17
% 6.65/2.17 No countermodel exists, formula is valid
% 6.65/2.17 % SZS status Theorem for theBenchmark
% 6.65/2.17
% 6.65/2.17 Generating proof ... Warning: ignoring some quantifiers
% 8.83/2.68 found it (size 21)
% 8.83/2.68
% 8.83/2.68 % SZS output start Proof for theBenchmark
% 8.83/2.68 Assumed formulas after preprocessing and simplification:
% 8.83/2.68 | (0) ? [v0] : ? [v1] : ( ~ (v1 = 0) & unequally_directed_opposite_lines(v0, v0) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v3, v8) = v9) | ~ (left_apart_point(v3, v6) = v7) | ~ (reverse_line(v5) = v8) | ~ (reverse_line(v4) = v6) | ? [v10] : ((v10 = 0 & left_apart_point(v3, v5) = 0) | (v10 = 0 & left_apart_point(v3, v4) = 0) | (v10 = 0 & left_apart_point(v2, v8) = 0) | (v10 = 0 & left_apart_point(v2, v6) = 0) | (v10 = 0 & left_apart_point(v2, v5) = 0) | (v10 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v10 = 0) & distinct_lines(v4, v5) = v10))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v2, v8) = v9) | ~ (left_apart_point(v2, v6) = v7) | ~ (reverse_line(v5) = v8) | ~ (reverse_line(v4) = v6) | ? [v10] : ((v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | (v10 = 0 & left_apart_point(v3, v4) = 0) | (v10 = 0 & left_apart_point(v2, v5) = 0) | (v10 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v10 = 0) & distinct_lines(v4, v5) = v10))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v3, v8) = v9) | ~ (left_apart_point(v2, v6) = v7) | ~ (reverse_line(v5) = v8) | ~ (reverse_line(v4) = v6) | ? [v10] : ((v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | (v10 = 0 & left_apart_point(v3, v4) = 0) | (v10 = 0 & left_apart_point(v2, v8) = 0) | (v10 = 0 & left_apart_point(v2, v5) = 0) | (v10 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v10 = 0) & distinct_lines(v4, v5) = v10) | ( ~ (v10 = 0) & distinct_points(v2, v3) = v10))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v3, v6) = v7) | ~ (left_apart_point(v2, v8) = v9) | ~ (reverse_line(v5) = v8) | ~ (reverse_line(v4) = v6) | ? [v10] : ((v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | (v10 = 0 & left_apart_point(v3, v4) = 0) | (v10 = 0 & left_apart_point(v2, v6) = 0) | (v10 = 0 & left_apart_point(v2, v5) = 0) | (v10 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v10 = 0) & distinct_lines(v4, v5) = v10) | ( ~ (v10 = 0) & distinct_points(v2, v3) = v10))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v6) = v8) | ~ (left_apart_point(v2, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v6) = v8) | ~ (left_apart_point(v2, v6) = v7) | ~ (reverse_line(v4) = v6) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v2, v5) = v6) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v2, v4) = v6) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v5) = v6) | ~ (left_apart_point(v2, v7) = v8) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v4) = v6) | ~ (left_apart_point(v2, v7) = v8) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v3, v5) = v6) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v3, v4) = v6) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v2, v7) = v8) | ~ (left_apart_point(v2, v5) = v6) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v2, v7) = v8) | ~ (left_apart_point(v2, v4) = v6) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v2, v5) = v6) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (left_apart_point(v3, v7) = v8) | ~ (left_apart_point(v2, v4) = v6) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v7) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (left_apart_point(v3, v5) = v6) | ~ (left_apart_point(v2, v7) = v8) | ~ (reverse_line(v4) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v4) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (left_apart_point(v3, v4) = v6) | ~ (left_apart_point(v2, v7) = v8) | ~ (reverse_line(v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v4) = v9) | (v10 = 0 & left_apart_point(v2, v9) = 0 & reverse_line(v4) = v9) | (v9 = 0 & left_apart_point(v3, v7) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | (v9 = 0 & left_apart_point(v2, v5) = 0) | (v9 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9) | ( ~ (v9 = 0) & distinct_points(v2, v3) = v9))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v5) = v7) | ~ (left_apart_point(v2, v5) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v3, v4) = 0) | (v8 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = 0) | ~ (left_apart_point(v3, v4) = v7) | ~ (left_apart_point(v2, v4) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v3, v5) = 0) | (v8 = 0 & left_apart_point(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v3, v5) = v7) | ~ (left_apart_point(v3, v4) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v2, v5) = 0) | (v8 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_points(v2, v3) = 0) | ~ (left_apart_point(v2, v5) = v7) | ~ (left_apart_point(v2, v4) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v3, v5) = 0) | (v8 = 0 & left_apart_point(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (left_apart_point(v3, v5) = v7) | ~ (left_apart_point(v2, v4) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v3, v4) = 0) | (v8 = 0 & left_apart_point(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (left_apart_point(v3, v4) = v6) | ~ (left_apart_point(v2, v5) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v3, v8) = 0 & reverse_line(v4) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v5) = v8) | (v9 = 0 & left_apart_point(v2, v8) = 0 & reverse_line(v4) = v8) | (v8 = 0 & left_apart_point(v3, v5) = 0) | (v8 = 0 & left_apart_point(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (left_apart_point(v2, v6) = v7) | ~ (reverse_line(v4) = v6) | ? [v8] : (( ~ (v8 = 0) & left_apart_point(v2, v3) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v3, v4) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v3 = v2 | ~ (between_on_line(v7, v6, v5, v4) = v3) | ~ (between_on_line(v7, v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v6) | ~ (reverse_line(v3) = v5) | ~ (unequally_directed_lines(v3, v6) = v7) | ~ (unequally_directed_lines(v2, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v2, v6) = 0 & unequally_directed_lines(v2, v4) = 0) | (v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v6) | ~ (reverse_line(v3) = v5) | ~ (unequally_directed_lines(v2, v6) = v7) | ~ (unequally_directed_lines(v2, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v3, v6) = 0 & unequally_directed_lines(v3, v4) = 0) | (v8 = 0 & v7 = 0 & unequally_directed_lines(v2, v4) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v6) | ~ (unequally_directed_lines(v3, v6) = v7) | ~ (unequally_directed_lines(v2, v4) = v5) | ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v4) = 0) | (v8 = 0 & v5 = 0 & unequally_directed_lines(v2, v6) = 0) | ( ~ (v9 = 0) & reverse_line(v3) = v8 & unequally_directed_lines(v2, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = v7) | ~ (unequally_directed_lines(v2, v5) = v6) | ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v4) = 0) | (v8 = 0 & v6 = 0 & unequally_directed_lines(v2, v4) = 0) | ( ~ (v9 = 0) & reverse_line(v3) = v8 & unequally_directed_lines(v2, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v4) = v7) | ~ (unequally_directed_lines(v2, v5) = v6) | ? [v8] : ? [v9] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & unequally_directed_lines(v2, v4) = 0) | ( ~ (v9 = 0) & reverse_line(v3) = v8 & unequally_directed_lines(v2, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v2, v3) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v3, v4) = v6) | ~ (distinct_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (distinct_points(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & distinct_points(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_points(v2, v3) = v5) | ~ (left_apart_point(v3, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & left_apart_point(v2, v4) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (left_convergent_lines(v2, v4) = v6) | ~ (unequally_directed_lines(v3, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & left_convergent_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (unequally_directed_lines(v3, v4) = v6) | ~ (unequally_directed_lines(v2, v4) = v5) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_lines(v2, v3) = v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (between_on_line(v2, v3, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & before_on_line(v2, v5, v4) = v7) | ( ~ (v7 = 0) & before_on_line(v2, v4, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (between_on_line(v2, v3, v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & before_on_line(v2, v4, v5) = v7) | ( ~ (v7 = 0) & before_on_line(v2, v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (line_connecting(v2, v3) = v5) | ~ (left_convergent_lines(v5, v4) = v6) | ? [v7] : ((v7 = 0 & left_apart_point(v3, v4) = 0) | ( ~ (v7 = 0) & distinct_points(v2, v3) = v7) | ( ~ (v7 = 0) & left_apart_point(v2, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_apart_point(v2, v5) = v6) | ~ (left_apart_point(v2, v3) = 0) | ~ (reverse_line(v4) = v5) | ? [v7] : ((v7 = 0 & distinct_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_apart_point(v2, v5) = v6) | ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v7] : ((v7 = 0 & distinct_lines(v3, v4) = 0) | ( ~ (v7 = 0) & left_apart_point(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v2 | ~ (before_on_line(v6, v5, v4) = v3) | ~ (before_on_line(v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v3 = v2 | ~ (divides_points(v6, v5, v4) = v3) | ~ (divides_points(v6, v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v3, v4) = v5) | ~ (equally_directed_lines(v2, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & distinct_points(v3, v4) = 0 & incident_point_and_line(v4, v2) = 0 & incident_point_and_line(v3, v2) = 0) | ( ~ (v7 = 0) & before_on_line(v2, v3, v4) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = v6) | ~ (unequally_directed_lines(v2, v3) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v2, v5) = 0 & unequally_directed_lines(v2, v4) = 0) | (v7 = 0 & v6 = 0 & unequally_directed_lines(v3, v4) = 0) | ( ~ (v8 = 0) & reverse_line(v3) = v7 & unequally_directed_lines(v2, v7) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v2, v5) = v6) | ~ (unequally_directed_lines(v2, v3) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v5) = 0 & unequally_directed_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & unequally_directed_lines(v2, v4) = 0) | ( ~ (v8 = 0) & reverse_line(v3) = v7 & unequally_directed_lines(v2, v7) = v8))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v3) = v5) | ~ (unequally_directed_lines(v3, v4) = v6) | ~ (unequally_directed_lines(v2, v5) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v7 = 0 & reverse_line(v4) = v8 & unequally_directed_lines(v2, v8) = 0 & unequally_directed_lines(v2, v4) = 0) | (v8 = 0 & v6 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v3, v7) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v3) = v5) | ~ (unequally_directed_lines(v2, v5) = 0) | ~ (unequally_directed_lines(v2, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v3, v7) = 0 & unequally_directed_lines(v3, v4) = 0) | (v8 = 0 & v6 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v2, v7) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v3, v4) = v6) | ~ (unequally_directed_lines(v2, v4) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v3, v7) = 0) | (v8 = 0 & v5 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v2, v7) = 0) | ( ~ (v8 = 0) & reverse_line(v3) = v7 & unequally_directed_lines(v2, v7) = v8) | ( ~ (v7 = 0) & unequally_directed_lines(v2, v3) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v3, v4) = v5) | ~ (left_apart_point(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v2, v6) = 0 & reverse_line(v4) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_lines(v2, v4) = v5) | ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (before_on_line(v2, v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & line_connecting(v3, v4) = v6 & equally_directed_lines(v2, v6) = v7) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6) | ( ~ (v6 = 0) & incident_point_and_line(v4, v2) = v6) | ( ~ (v6 = 0) & incident_point_and_line(v3, v2) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v3, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v4) = v5) | ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (distinct_points(v2, v3) = v5) | ~ (left_apart_point(v2, v4) = 0) | left_apart_point(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (divides_points(v4, v2, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v3, v4) = v6) | ( ~ (v6 = 0) & right_apart_point(v2, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (divides_points(v4, v2, v3) = v5) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v2, v4) = v6) | ( ~ (v6 = 0) & right_apart_point(v3, v4) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_convergent_lines(v2, v4) = v5) | ~ (left_convergent_lines(v2, v3) = 0) | unequally_directed_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_convergent_lines(v2, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v6] : ( ~ (v6 = 0) & right_convergent_lines(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_convergent_lines(v2, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v6] : ((v6 = 0 & left_convergent_lines(v2, v3) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v2, v4) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v2, v3) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_convergent_lines(v2, v3) = 0) | ~ (unequally_directed_lines(v3, v4) = v5) | left_convergent_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_apart_point(v3, v4) = v5) | ~ (left_apart_point(v2, v4) = 0) | distinct_points(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_apart_point(v2, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v6] : ( ~ (v6 = 0) & right_apart_point(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = v5) | unequally_directed_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & unequally_directed_opposite_lines(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_lines(v3, v4) = v5) | ~ (unequally_directed_lines(v2, v3) = 0) | unequally_directed_lines(v2, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_lines(v2, v4) = v5) | ~ (unequally_directed_lines(v2, v3) = 0) | unequally_directed_lines(v3, v4) = 0) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (parallel_through_point(v5, v4) = v3) | ~ (parallel_through_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (intersection_point(v5, v4) = v3) | ~ (intersection_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_lines(v5, v4) = v3) | ~ (distinct_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (line_connecting(v5, v4) = v3) | ~ (line_connecting(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (distinct_points(v5, v4) = v3) | ~ (distinct_points(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (incident_point_and_line(v5, v4) = v3) | ~ (incident_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (convergent_lines(v5, v4) = v3) | ~ (convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (apart_point_and_line(v5, v4) = v3) | ~ (apart_point_and_line(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equally_directed_opposite_lines(v5, v4) = v3) | ~ (equally_directed_opposite_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (equally_directed_lines(v5, v4) = v3) | ~ (equally_directed_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (left_convergent_lines(v5, v4) = v3) | ~ (left_convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (right_convergent_lines(v5, v4) = v3) | ~ (right_convergent_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (left_apart_point(v5, v4) = v3) | ~ (left_apart_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (right_apart_point(v5, v4) = v3) | ~ (right_apart_point(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unequally_directed_lines(v5, v4) = v3) | ~ (unequally_directed_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (unequally_directed_opposite_lines(v5, v4) = v3) | ~ (unequally_directed_opposite_lines(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) | ~ (distinct_points(v2, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v3, v6) = 0 & reverse_line(v5) = v6) | (v7 = 0 & left_apart_point(v3, v6) = 0 & reverse_line(v4) = v6) | (v7 = 0 & left_apart_point(v2, v6) = 0 & reverse_line(v5) = v6) | (v7 = 0 & left_apart_point(v2, v6) = 0 & reverse_line(v4) = v6) | (v6 = 0 & left_apart_point(v3, v5) = 0) | (v6 = 0 & left_apart_point(v3, v4) = 0) | (v6 = 0 & left_apart_point(v2, v5) = 0) | (v6 = 0 & left_apart_point(v2, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (between_on_line(v2, v3, v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & before_on_line(v2, v5, v4) = 0 & before_on_line(v2, v4, v3) = 0) | (v7 = 0 & v6 = 0 & before_on_line(v2, v4, v5) = 0 & before_on_line(v2, v3, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ~ (equally_directed_lines(v2, v5) = 0) | ? [v6] : ((v6 = 0 & before_on_line(v2, v3, v4) = 0) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6) | ( ~ (v6 = 0) & incident_point_and_line(v4, v2) = v6) | ( ~ (v6 = 0) & incident_point_and_line(v3, v2) = v6))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v3, v4) = v5) | ~ (unequally_directed_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & reverse_line(v4) = v7 & unequally_directed_lines(v2, v7) = 0 & unequally_directed_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = 0) | ( ~ (v7 = 0) & reverse_line(v3) = v6 & unequally_directed_lines(v2, v6) = v7))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v2, v4) = v5) | ~ (unequally_directed_lines(v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = 0 & unequally_directed_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & reverse_line(v4) = v6 & unequally_directed_lines(v2, v6) = 0) | ( ~ (v7 = 0) & reverse_line(v3) = v6 & unequally_directed_lines(v2, v6) = v7))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (convergent_lines(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5) | ( ~ (v5 = 0) & unequally_directed_opposite_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (apart_point_and_line(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & left_apart_point(v2, v3) = v5 & right_apart_point(v2, v3) = v6)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equally_directed_opposite_lines(v2, v3) = v4) | unequally_directed_opposite_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (equally_directed_lines(v2, v3) = v4) | unequally_directed_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_convergent_lines(v2, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & left_convergent_lines(v2, v5) = 0 & reverse_line(v3) = v5) | ( ~ (v6 = 0) & reverse_line(v3) = v5 & unequally_directed_lines(v2, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (right_convergent_lines(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & left_convergent_lines(v2, v5) = v6 & reverse_line(v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & right_apart_point(v2, v3) = 0) | ( ~ (v5 = 0) & apart_point_and_line(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (right_apart_point(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & left_apart_point(v2, v5) = v6 & reverse_line(v3) = v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (right_apart_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v2, v3) = 0) | ( ~ (v5 = 0) & apart_point_and_line(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_lines(v2, v3) = v4) | equally_directed_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_lines(v2, v3) = v4) | ? [v5] : (reverse_line(v3) = v5 & unequally_directed_lines(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_opposite_lines(v2, v3) = v4) | equally_directed_opposite_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_opposite_lines(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & reverse_line(v3) = v5 & unequally_directed_lines(v2, v5) = v6)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (point(v4) = v3) | ~ (point(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (line(v4) = v3) | ~ (line(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (reverse_line(v4) = v3) | ~ (reverse_line(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | equally_directed_lines(v4, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : ? [v6] : ((v5 = 0 & point(v4) = 0) | ( ~ (v6 = 0) & reverse_line(v3) = v5 & unequally_directed_lines(v2, v5) = v6) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection_point(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v4, v3) = v6 & apart_point_and_line(v4, v2) = v5) | ( ~ (v6 = 0) & reverse_line(v3) = v5 & unequally_directed_lines(v2, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & line_connecting(v2, v3) = v5 & equally_directed_lines(v5, v6) = 0 & reverse_line(v4) = v6) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & line_connecting(v3, v2) = v5 & equally_directed_lines(v4, v6) = 0 & reverse_line(v5) = v6) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v3, v4) = v6 & apart_point_and_line(v2, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v2, v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & point(v2) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (before_on_line(v2, v3, v4) = 0) | ? [v5] : (line_connecting(v3, v4) = v5 & distinct_points(v3, v4) = 0 & incident_point_and_line(v4, v2) = 0 & incident_point_and_line(v3, v2) = 0 & equally_directed_lines(v2, v5) = 0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (divides_points(v4, v2, v3) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & left_apart_point(v3, v4) = 0 & right_apart_point(v2, v4) = 0) | (v6 = 0 & v5 = 0 & left_apart_point(v2, v4) = 0 & right_apart_point(v3, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_convergent_lines(v2, v4) = 0) | ~ (reverse_line(v3) = v4) | right_convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_convergent_lines(v2, v4) = 0) | ~ (reverse_line(v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v2, v4) = 0) | ~ (reverse_line(v3) = v4) | right_apart_point(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v2, v4) = 0) | ~ (reverse_line(v3) = v4)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & right_apart_point(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (left_apart_point(v2, v3) = 0) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & left_apart_point(v2, v5) = 0 & reverse_line(v4) = v5) | (v5 = 0 & distinct_lines(v3, v4) = 0))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (right_apart_point(v2, v3) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & left_apart_point(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = 0) | unequally_directed_opposite_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = 0) & ~ (v6 = 0) & intersection_point(v2, v3) = v5 & apart_point_and_line(v5, v3) = v7 & apart_point_and_line(v5, v2) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & intersection_point(v2, v3) = v5 & point(v5) = 0) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ~ (unequally_directed_lines(v2, v4) = 0) | ? [v5] : ((v5 = 0 & left_convergent_lines(v2, v4) = 0) | (v5 = 0 & left_convergent_lines(v2, v3) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v2, v3) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unequally_directed_opposite_lines(v2, v3) = 0) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_opposite_lines(v2, v3) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unequally_directed_lines(v2, v3) = 0) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) & ! [v2] : ! [v3] : (v3 = 0 | ~ (equally_directed_lines(v2, v2) = v3)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v3, v4) = v6 & apart_point_and_line(v2, v4) = v5)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (line_connecting(v3, v2) = v5 & line_connecting(v2, v3) = v4 & equally_directed_lines(v4, v6) = 0 & reverse_line(v5) = v6)) & ! [v2] : ! [v3] : ( ~ (distinct_points(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & line(v4) = 0 & line_connecting(v2, v3) = v4) | ( ~ (v4 = 0) & point(v3) = v4) | ( ~ (v4 = 0) & point(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) | (unequally_directed_lines(v2, v3) = 0 & unequally_directed_opposite_lines(v2, v3) = 0)) & ! [v2] : ! [v3] : ( ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ((v4 = 0 & left_apart_point(v2, v3) = 0) | (v4 = 0 & right_apart_point(v2, v3) = 0))) & ! [v2] : ! [v3] : ( ~ (equally_directed_opposite_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (equally_directed_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ~ (left_convergent_lines(v2, v3) = 0) & ! [v2] : ! [v3] : ( ~ (right_convergent_lines(v2, v3) = 0) | ? [v4] : (left_convergent_lines(v2, v4) = 0 & reverse_line(v3) = v4)) & ! [v2] : ! [v3] : ~ (left_apart_point(v2, v3) = 0) & ! [v2] : ! [v3] : ( ~ (right_apart_point(v2, v3) = 0) | ? [v4] : (left_apart_point(v2, v4) = 0 & reverse_line(v3) = v4)) & ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ? [v4] : ( ~ (v4 = 0) & distinct_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (reverse_line(v2) = v3) | ? [v4] : ((v4 = 0 & line(v3) = 0) | ( ~ (v4 = 0) & line(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v3) = v6 & apart_point_and_line(v4, v2) = v5) | ( ~ (v5 = 0) & reverse_line(v3) = v4 & unequally_directed_lines(v2, v4) = v5))) & ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & intersection_point(v2, v3) = v4 & point(v4) = 0) | ( ~ (v5 = 0) & reverse_line(v3) = v4 & unequally_directed_lines(v2, v4) = v5) | ( ~ (v4 = 0) & line(v3) = v4) | ( ~ (v4 = 0) & line(v2) = v4))) & ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_convergent_lines(v2, v4) = 0 & reverse_line(v3) = v4) | (v4 = 0 & left_convergent_lines(v2, v3) = 0) | ( ~ (v5 = 0) & reverse_line(v3) = v4 & unequally_directed_lines(v2, v4) = v5))) & ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & equally_directed_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v2, v3) = 0) | ? [v4] : ((v4 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v4 = 0) & unequally_directed_opposite_lines(v2, v3) = v4))) & ! [v2] : ! [v3] : ( ~ (unequally_directed_opposite_lines(v2, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & equally_directed_opposite_lines(v2, v3) = v4)) & ! [v2] : ! [v3] : ( ~ (unequally_directed_opposite_lines(v2, v3) = 0) | ? [v4] : (reverse_line(v3) = v4 & unequally_directed_lines(v2, v4) = 0)) & ! [v2] : ! [v3] : ( ~ (unequally_directed_opposite_lines(v2, v3) = 0) | ? [v4] : ((v4 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v2, v3) = v4))) & ! [v2] : ( ~ (line(v2) = 0) | ? [v3] : (line(v3) = 0 & reverse_line(v2) = v3)) & ! [v2] : ~ (distinct_lines(v2, v2) = 0) & ! [v2] : ~ (distinct_points(v2, v2) = 0) & ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : between_on_line(v5, v4, v3, v2) = v6 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : before_on_line(v4, v3, v2) = v5 & ? [v2] : ? [v3] : ? [v4] : ? [v5] : divides_points(v4, v3, v2) = v5 & ? [v2] : ? [v3] : ? [v4] : parallel_through_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : intersection_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : line_connecting(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : distinct_points(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : incident_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : apart_point_and_line(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : equally_directed_opposite_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : equally_directed_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : left_convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : right_convergent_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : left_apart_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : right_apart_point(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : unequally_directed_lines(v3, v2) = v4 & ? [v2] : ? [v3] : ? [v4] : unequally_directed_opposite_lines(v3, v2) = v4 & ? [v2] : ? [v3] : point(v2) = v3 & ? [v2] : ? [v3] : line(v2) = v3 & ? [v2] : ? [v3] : reverse_line(v2) = v3)
% 9.32/2.77 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 9.32/2.77 | (1) ~ (all_0_0_0 = 0) & unequally_directed_opposite_lines(all_0_1_1, all_0_1_1) = all_0_0_0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))) & ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & ? [v0] : ? [v1] : reverse_line(v0) = v1
% 9.32/2.81 |
% 9.32/2.81 | Applying alpha-rule on (1) yields:
% 9.32/2.81 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 9.32/2.81 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.81 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.32/2.81 | (5) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2
% 9.32/2.81 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))
% 9.32/2.81 | (7) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2
% 9.32/2.81 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.32/2.81 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0))
% 9.32/2.81 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4)))
% 9.32/2.81 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5)))
% 9.32/2.81 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.32/2.81 | (13) ? [v0] : ? [v1] : reverse_line(v0) = v1
% 9.32/2.81 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 9.32/2.81 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 9.32/2.81 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.82 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3))
% 9.32/2.82 | (18) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2
% 9.32/2.82 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.32/2.82 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 9.32/2.82 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 9.32/2.82 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.32/2.82 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4)))
% 9.32/2.82 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.32/2.82 | (25) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3
% 9.32/2.82 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.32/2.82 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0)))
% 9.32/2.82 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.32/2.82 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0)))
% 9.32/2.82 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.32/2.82 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 9.32/2.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 9.32/2.82 | (33) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 9.32/2.82 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 9.32/2.82 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 9.32/2.82 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 9.32/2.82 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.32/2.82 | (38) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2
% 9.32/2.82 | (39) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 9.32/2.82 | (40) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 9.32/2.82 | (41) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3
% 9.32/2.82 | (42) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2
% 9.32/2.82 | (43) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 9.32/2.82 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 9.32/2.82 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0)))
% 9.32/2.82 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6)))
% 9.32/2.82 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.32/2.82 | (48) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 9.32/2.82 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 9.32/2.82 | (50) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 9.32/2.83 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.32/2.83 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 9.32/2.83 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 9.32/2.83 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 9.32/2.83 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 9.32/2.83 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4))
% 9.32/2.83 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.83 | (58) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2
% 9.32/2.83 | (59) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 9.32/2.83 | (60) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2
% 9.32/2.83 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.32/2.83 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.32/2.83 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 9.32/2.83 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 9.32/2.83 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 9.32/2.83 | (66) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 9.32/2.83 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 9.32/2.83 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.83 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.32/2.83 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 9.32/2.83 | (71) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 9.32/2.83 | (72) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)))
% 9.32/2.83 | (73) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)))
% 9.32/2.83 | (74) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 9.32/2.83 | (75) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3))
% 9.32/2.83 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.32/2.83 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.83 | (78) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0)))
% 9.32/2.83 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.32/2.83 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.32/2.84 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 9.32/2.84 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 9.32/2.84 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 9.32/2.84 | (84) ? [v0] : ? [v1] : point(v0) = v1
% 9.32/2.84 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.32/2.84 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)))
% 9.32/2.84 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 9.32/2.84 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 9.32/2.84 | (89) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 9.32/2.84 | (90) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 9.32/2.84 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.32/2.84 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4)))
% 9.32/2.84 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.32/2.84 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 9.32/2.84 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 9.32/2.84 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.32/2.84 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4
% 9.32/2.84 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.84 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3))
% 9.32/2.84 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.32/2.84 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.84 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.32/2.84 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 9.32/2.84 | (104) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 9.32/2.84 | (105) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.32/2.84 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 9.32/2.84 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 9.32/2.84 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4))
% 9.32/2.84 | (109) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 9.32/2.84 | (110) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2
% 9.32/2.84 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3)))
% 9.32/2.84 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3)))
% 9.32/2.84 | (113) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 9.32/2.84 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 9.32/2.85 | (115) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 9.32/2.85 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5)))
% 9.32/2.85 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3)))
% 9.32/2.85 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 9.32/2.85 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.85 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 9.32/2.85 | (121) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 9.32/2.85 | (122) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 9.32/2.85 | (123) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 9.32/2.85 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.32/2.85 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.85 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4))
% 9.32/2.85 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 9.32/2.85 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.32/2.85 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 9.32/2.85 | (130) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 9.32/2.85 | (131) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.32/2.85 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.32/2.85 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 9.32/2.85 | (134) ? [v0] : ? [v1] : line(v0) = v1
% 9.32/2.85 | (135) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2)))
% 9.32/2.85 | (136) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.32/2.85 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.32/2.85 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.32/2.85 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4)))
% 9.32/2.85 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 9.32/2.85 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.32/2.85 | (142) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.32/2.85 | (143) ~ (all_0_0_0 = 0)
% 9.32/2.85 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 9.32/2.85 | (145) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 9.32/2.86 | (146) unequally_directed_opposite_lines(all_0_1_1, all_0_1_1) = all_0_0_0
% 9.32/2.86 | (147) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.32/2.86 | (148) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 9.32/2.86 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 9.32/2.86 | (150) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4))
% 9.32/2.86 | (151) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 9.32/2.86 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 9.73/2.86 | (153) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 9.73/2.86 | (154) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.73/2.86 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))
% 9.73/2.86 | (156) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 9.73/2.86 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.73/2.86 | (158) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 9.73/2.86 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 9.73/2.86 | (160) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.73/2.86 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 9.73/2.86 | (162) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 9.73/2.86 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 9.73/2.86 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.73/2.86 | (165) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4))
% 9.73/2.86 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 9.73/2.86 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0)))
% 9.73/2.86 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4))
% 9.73/2.86 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 9.73/2.86 | (170) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.73/2.86 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5))
% 9.73/2.86 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 9.73/2.86 | (173) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.73/2.86 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 9.73/2.86 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.73/2.86 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5)))
% 9.73/2.87 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 9.73/2.87 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.73/2.87 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.73/2.87 |
% 9.73/2.87 | Instantiating formula (165) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_opposite_lines(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 9.73/2.87 | (180) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_1_1, v0) = v1)
% 9.73/2.87 |
% 9.73/2.87 +-Applying beta-rule and splitting (180), into two cases.
% 9.73/2.87 |-Branch one:
% 9.73/2.87 | (181) all_0_0_0 = 0
% 9.73/2.87 |
% 9.73/2.87 | Equations (181) can reduce 143 to:
% 9.73/2.87 | (182) $false
% 9.73/2.87 |
% 9.73/2.87 |-The branch is then unsatisfiable
% 9.73/2.87 |-Branch two:
% 9.73/2.87 | (143) ~ (all_0_0_0 = 0)
% 9.73/2.87 | (184) ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_1_1, v0) = v1)
% 9.73/2.87 |
% 9.73/2.87 | Instantiating (184) with all_62_0_70, all_62_1_71 yields:
% 9.73/2.87 | (185) ~ (all_62_0_70 = 0) & reverse_line(all_0_1_1) = all_62_1_71 & unequally_directed_lines(all_0_1_1, all_62_1_71) = all_62_0_70
% 9.73/2.87 |
% 9.73/2.87 | Applying alpha-rule on (185) yields:
% 9.73/2.87 | (186) ~ (all_62_0_70 = 0)
% 9.73/2.87 | (187) reverse_line(all_0_1_1) = all_62_1_71
% 9.73/2.87 | (188) unequally_directed_lines(all_0_1_1, all_62_1_71) = all_62_0_70
% 9.73/2.87 |
% 9.73/2.87 | Instantiating formula (14) with all_62_0_70, all_62_1_71, all_0_1_1, all_0_1_1 and discharging atoms reverse_line(all_0_1_1) = all_62_1_71, unequally_directed_lines(all_0_1_1, all_62_1_71) = all_62_0_70, yields:
% 9.73/2.87 | (189) all_62_0_70 = 0 | unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 9.73/2.87 |
% 9.73/2.87 | Instantiating formula (6) with all_62_0_70, all_62_0_70, all_62_1_71, all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_62_1_71) = all_62_0_70, yields:
% 9.73/2.87 | (190) all_62_0_70 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 9.73/2.87 |
% 9.73/2.87 +-Applying beta-rule and splitting (189), into two cases.
% 9.73/2.87 |-Branch one:
% 9.73/2.87 | (191) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 9.73/2.87 |
% 9.73/2.87 +-Applying beta-rule and splitting (190), into two cases.
% 9.73/2.87 |-Branch one:
% 9.73/2.87 | (192) all_62_0_70 = 0
% 9.73/2.87 |
% 9.73/2.87 | Equations (192) can reduce 186 to:
% 9.73/2.87 | (182) $false
% 9.73/2.87 |
% 9.73/2.87 |-The branch is then unsatisfiable
% 9.73/2.87 |-Branch two:
% 9.73/2.87 | (186) ~ (all_62_0_70 = 0)
% 9.73/2.87 | (195) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 9.73/2.87 |
% 9.73/2.87 | Instantiating (195) with all_99_0_81 yields:
% 9.73/2.87 | (196) ~ (all_99_0_81 = 0) & unequally_directed_lines(all_0_1_1, all_0_1_1) = all_99_0_81
% 9.73/2.87 |
% 9.73/2.87 | Applying alpha-rule on (196) yields:
% 9.73/2.87 | (197) ~ (all_99_0_81 = 0)
% 9.73/2.87 | (198) unequally_directed_lines(all_0_1_1, all_0_1_1) = all_99_0_81
% 9.73/2.87 |
% 9.73/2.87 | Instantiating formula (163) with all_0_1_1, all_0_1_1, 0, all_99_0_81 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = all_99_0_81, unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 9.73/2.87 | (199) all_99_0_81 = 0
% 9.73/2.87 |
% 9.73/2.87 | Equations (199) can reduce 197 to:
% 9.73/2.87 | (182) $false
% 9.73/2.87 |
% 9.73/2.87 |-The branch is then unsatisfiable
% 9.73/2.87 |-Branch two:
% 9.73/2.87 | (201) ~ (unequally_directed_lines(all_0_1_1, all_0_1_1) = 0)
% 9.73/2.87 | (192) all_62_0_70 = 0
% 9.73/2.87 |
% 9.73/2.87 | Equations (192) can reduce 186 to:
% 9.73/2.87 | (182) $false
% 9.73/2.87 |
% 9.73/2.87 |-The branch is then unsatisfiable
% 9.73/2.87 % SZS output end Proof for theBenchmark
% 9.73/2.87
% 9.73/2.87 2275ms
%------------------------------------------------------------------------------