TSTP Solution File: GEO227+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO227+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 03:48:59 EDT 2022
% Result : Theorem 6.83s 2.18s
% Output : Proof 9.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO227+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 14:39:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.48/0.58 ____ _
% 0.48/0.58 ___ / __ \_____(_)___ ________ __________
% 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.58
% 0.48/0.58 A Theorem Prover for First-Order Logic
% 0.48/0.59 (ePrincess v.1.0)
% 0.48/0.59
% 0.48/0.59 (c) Philipp Rümmer, 2009-2015
% 0.48/0.59 (c) Peter Backeman, 2014-2015
% 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.59 Bug reports to peter@backeman.se
% 0.48/0.59
% 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.59
% 0.48/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.96 Prover 0: Preprocessing ...
% 2.40/1.23 Prover 0: Warning: ignoring some quantifiers
% 2.40/1.27 Prover 0: Constructing countermodel ...
% 3.36/1.44 Prover 0: gave up
% 3.36/1.44 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.57/1.48 Prover 1: Preprocessing ...
% 4.33/1.69 Prover 1: Constructing countermodel ...
% 4.74/1.74 Prover 1: gave up
% 4.74/1.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.74/1.78 Prover 2: Preprocessing ...
% 6.28/2.07 Prover 2: Warning: ignoring some quantifiers
% 6.28/2.09 Prover 2: Constructing countermodel ...
% 6.83/2.18 Prover 2: proved (445ms)
% 6.83/2.18
% 6.83/2.18 No countermodel exists, formula is valid
% 6.83/2.18 % SZS status Theorem for theBenchmark
% 6.83/2.18
% 6.83/2.18 Generating proof ... Warning: ignoring some quantifiers
% 8.38/2.54 found it (size 25)
% 8.38/2.54
% 8.38/2.54 % SZS output start Proof for theBenchmark
% 8.38/2.54 Assumed formulas after preprocessing and simplification:
% 8.38/2.54 | (0) ? [v0] : ? [v1] : (equally_directed_opposite_lines(v0, v1) = 0 & equally_directed_lines(v0, v1) = 0 & ! [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)
% 8.72/2.65 | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 8.72/2.65 | (1) equally_directed_opposite_lines(all_0_1_1, all_0_0_0) = 0 & equally_directed_lines(all_0_1_1, all_0_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
% 9.03/2.70 |
% 9.03/2.70 | Applying alpha-rule on (1) yields:
% 9.03/2.70 | (2) ! [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)))
% 9.03/2.70 | (3) ! [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)))
% 9.03/2.70 | (4) ! [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)))
% 9.03/2.70 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 9.03/2.70 | (6) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2
% 9.03/2.70 | (7) ! [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)))
% 9.03/2.70 | (8) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 9.03/2.70 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 9.03/2.70 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 9.03/2.70 | (11) ! [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)))
% 9.03/2.70 | (12) ! [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))
% 9.03/2.70 | (13) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 9.03/2.70 | (14) ! [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)))
% 9.03/2.70 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 9.03/2.70 | (16) ! [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)))
% 9.03/2.70 | (17) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.03/2.70 | (18) ! [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)))
% 9.03/2.70 | (19) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 9.03/2.70 | (20) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 9.03/2.70 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 9.03/2.70 | (22) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 9.03/2.70 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 9.03/2.70 | (24) ! [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)))
% 9.03/2.71 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 9.03/2.71 | (26) ? [v0] : ? [v1] : point(v0) = v1
% 9.03/2.71 | (27) ! [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)))
% 9.03/2.71 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 9.03/2.71 | (29) ! [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)))
% 9.03/2.71 | (30) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2
% 9.03/2.71 | (31) ! [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)))
% 9.03/2.71 | (32) ! [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)))
% 9.03/2.71 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 9.03/2.71 | (34) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2
% 9.03/2.71 | (35) ! [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)))
% 9.03/2.71 | (36) ! [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)))
% 9.03/2.71 | (37) ! [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)))
% 9.03/2.71 | (38) ! [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)))
% 9.03/2.71 | (39) ! [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)))
% 9.03/2.71 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 9.03/2.71 | (41) ! [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))
% 9.03/2.71 | (42) ! [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)))
% 9.03/2.71 | (43) ! [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)))
% 9.03/2.71 | (44) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 9.03/2.71 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 9.03/2.71 | (46) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 9.03/2.71 | (47) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 9.03/2.72 | (48) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 9.03/2.72 | (49) ! [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)))
% 9.03/2.72 | (50) ! [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))
% 9.03/2.72 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 9.03/2.72 | (52) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 9.03/2.72 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.03/2.72 | (54) ! [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)))
% 9.03/2.72 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 9.03/2.72 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 9.03/2.72 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 9.03/2.72 | (58) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 9.03/2.72 | (59) ! [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)))
% 9.03/2.72 | (60) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 9.03/2.72 | (61) ! [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)))
% 9.03/2.72 | (62) ! [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))
% 9.03/2.72 | (63) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4
% 9.03/2.72 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.03/2.72 | (65) ! [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)))
% 9.03/2.72 | (66) ! [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)))
% 9.03/2.72 | (67) ! [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)))
% 9.03/2.72 | (68) ! [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))
% 9.03/2.72 | (69) ! [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)))
% 9.03/2.72 | (70) ! [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)))
% 9.03/2.73 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 9.03/2.73 | (72) ! [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)))
% 9.03/2.73 | (73) ! [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))
% 9.03/2.73 | (74) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2
% 9.03/2.73 | (75) ! [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)))
% 9.03/2.73 | (76) ! [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)))
% 9.03/2.73 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.03/2.73 | (78) ! [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)))
% 9.03/2.73 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 9.03/2.73 | (80) ! [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)))
% 9.03/2.73 | (81) ! [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)))
% 9.03/2.73 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 9.03/2.73 | (83) ! [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)))
% 9.03/2.73 | (84) ! [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)))
% 9.03/2.73 | (85) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2
% 9.03/2.73 | (86) ! [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)))
% 9.03/2.74 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 9.03/2.74 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.03/2.74 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 9.03/2.74 | (90) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 9.03/2.74 | (91) ! [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)))
% 9.03/2.74 | (92) ! [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)))
% 9.03/2.74 | (93) ! [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)))
% 9.03/2.74 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 9.03/2.74 | (95) ! [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)))
% 9.03/2.74 | (96) ! [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)))
% 9.03/2.74 | (97) ! [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)))
% 9.03/2.74 | (98) ! [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)))
% 9.03/2.74 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 9.03/2.74 | (100) ! [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)))
% 9.03/2.74 | (101) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.03/2.74 | (102) ! [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)))
% 9.03/2.74 | (103) ! [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))
% 9.03/2.74 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 9.03/2.74 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 9.03/2.74 | (106) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2
% 9.03/2.74 | (107) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 9.03/2.75 | (108) ! [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)))
% 9.03/2.75 | (109) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 9.03/2.75 | (110) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.03/2.75 | (111) ! [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)))
% 9.03/2.75 | (112) ! [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)))
% 9.03/2.75 | (113) equally_directed_opposite_lines(all_0_1_1, all_0_0_0) = 0
% 9.03/2.75 | (114) ! [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))
% 9.03/2.75 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 9.03/2.75 | (116) ! [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)))
% 9.03/2.75 | (117) ! [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)))
% 9.03/2.75 | (118) ! [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)))
% 9.03/2.75 | (119) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 9.03/2.75 | (120) ? [v0] : ? [v1] : line(v0) = v1
% 9.03/2.75 | (121) ! [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))
% 9.03/2.75 | (122) ! [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)))
% 9.03/2.75 | (123) ! [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)))
% 9.03/2.75 | (124) ! [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)))
% 9.03/2.76 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.03/2.76 | (126) ! [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)))
% 9.03/2.76 | (127) equally_directed_lines(all_0_1_1, all_0_0_0) = 0
% 9.03/2.76 | (128) ! [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)))
% 9.03/2.76 | (129) ! [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)))
% 9.03/2.76 | (130) ! [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)))
% 9.03/2.76 | (131) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.03/2.76 | (132) ! [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))
% 9.44/2.76 | (133) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3
% 9.44/2.76 | (134) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 9.44/2.76 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 9.44/2.76 | (136) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 9.44/2.77 | (137) ! [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)))
% 9.44/2.77 | (138) ! [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)))
% 9.44/2.77 | (139) ! [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))
% 9.44/2.77 | (140) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2)))
% 9.44/2.77 | (141) ! [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)))
% 9.44/2.77 | (142) ! [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))
% 9.44/2.77 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 9.44/2.77 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 9.44/2.77 | (145) ! [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)))
% 9.44/2.78 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 9.44/2.78 | (147) ! [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)))
% 9.44/2.78 | (148) ! [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)))
% 9.44/2.78 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 9.44/2.78 | (150) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 9.44/2.78 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 9.44/2.78 | (152) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 9.44/2.78 | (153) ? [v0] : ? [v1] : reverse_line(v0) = v1
% 9.44/2.78 | (154) ! [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))
% 9.44/2.78 | (155) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2
% 9.44/2.78 | (156) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 9.44/2.78 | (157) ! [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)))
% 9.44/2.78 | (158) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.44/2.78 | (159) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2
% 9.44/2.78 | (160) ! [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)))
% 9.44/2.79 | (161) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 9.44/2.79 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 9.44/2.79 | (163) ! [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)))
% 9.44/2.79 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.44/2.79 | (165) ! [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)))
% 9.44/2.79 | (166) ! [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)))
% 9.44/2.79 | (167) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3
% 9.44/2.79 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.44/2.79 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 9.44/2.79 | (170) ! [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)))
% 9.44/2.80 | (171) ! [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)))
% 9.55/2.80 | (172) ! [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)))
% 9.55/2.80 | (173) ! [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)))
% 9.55/2.80 | (174) ! [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))
% 9.55/2.80 | (175) ! [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)))
% 9.55/2.80 | (176) ! [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)))
% 9.55/2.80 | (177) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 9.55/2.80 | (178) ! [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)))
% 9.55/2.80 | (179) ! [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))
% 9.55/2.81 |
% 9.55/2.81 | Instantiating formula (48) with all_0_0_0, all_0_1_1 and discharging atoms equally_directed_opposite_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 9.55/2.81 | (180) ? [v0] : ( ~ (v0 = 0) & unequally_directed_opposite_lines(all_0_1_1, all_0_0_0) = v0)
% 9.55/2.81 |
% 9.55/2.81 | Instantiating formula (20) with all_0_0_0, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 9.55/2.81 | (181) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_1_1, all_0_0_0) = v0)
% 9.55/2.81 |
% 9.55/2.81 | Instantiating (181) with all_52_0_69 yields:
% 9.55/2.81 | (182) ~ (all_52_0_69 = 0) & unequally_directed_lines(all_0_1_1, all_0_0_0) = all_52_0_69
% 9.55/2.81 |
% 9.55/2.81 | Applying alpha-rule on (182) yields:
% 9.55/2.81 | (183) ~ (all_52_0_69 = 0)
% 9.55/2.81 | (184) unequally_directed_lines(all_0_1_1, all_0_0_0) = all_52_0_69
% 9.55/2.81 |
% 9.55/2.81 | Instantiating (180) with all_54_0_70 yields:
% 9.55/2.81 | (185) ~ (all_54_0_70 = 0) & unequally_directed_opposite_lines(all_0_1_1, all_0_0_0) = all_54_0_70
% 9.55/2.81 |
% 9.55/2.81 | Applying alpha-rule on (185) yields:
% 9.55/2.81 | (186) ~ (all_54_0_70 = 0)
% 9.55/2.81 | (187) unequally_directed_opposite_lines(all_0_1_1, all_0_0_0) = all_54_0_70
% 9.55/2.81 |
% 9.55/2.81 | Instantiating formula (82) with all_52_0_69, all_0_0_0, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_0_0) = all_52_0_69, yields:
% 9.55/2.81 | (188) all_52_0_69 = 0 | ? [v0] : (reverse_line(all_0_0_0) = v0 & unequally_directed_lines(all_0_1_1, v0) = 0)
% 9.55/2.81 |
% 9.55/2.81 | Instantiating formula (62) with all_54_0_70, all_0_0_0, all_0_1_1 and discharging atoms unequally_directed_opposite_lines(all_0_1_1, all_0_0_0) = all_54_0_70, yields:
% 9.55/2.81 | (189) all_54_0_70 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_0_0) = v0 & unequally_directed_lines(all_0_1_1, v0) = v1)
% 9.55/2.81 |
% 9.55/2.81 +-Applying beta-rule and splitting (188), into two cases.
% 9.55/2.81 |-Branch one:
% 9.55/2.81 | (190) all_52_0_69 = 0
% 9.55/2.81 |
% 9.55/2.81 | Equations (190) can reduce 183 to:
% 9.55/2.81 | (191) $false
% 9.55/2.81 |
% 9.55/2.81 |-The branch is then unsatisfiable
% 9.55/2.81 |-Branch two:
% 9.55/2.81 | (183) ~ (all_52_0_69 = 0)
% 9.55/2.81 | (193) ? [v0] : (reverse_line(all_0_0_0) = v0 & unequally_directed_lines(all_0_1_1, v0) = 0)
% 9.55/2.81 |
% 9.55/2.81 | Instantiating (193) with all_66_0_75 yields:
% 9.55/2.81 | (194) reverse_line(all_0_0_0) = all_66_0_75 & unequally_directed_lines(all_0_1_1, all_66_0_75) = 0
% 9.55/2.81 |
% 9.55/2.81 | Applying alpha-rule on (194) yields:
% 9.55/2.81 | (195) reverse_line(all_0_0_0) = all_66_0_75
% 9.55/2.81 | (196) unequally_directed_lines(all_0_1_1, all_66_0_75) = 0
% 9.55/2.81 |
% 9.55/2.81 +-Applying beta-rule and splitting (189), into two cases.
% 9.55/2.81 |-Branch one:
% 9.55/2.81 | (197) all_54_0_70 = 0
% 9.55/2.81 |
% 9.55/2.81 | Equations (197) can reduce 186 to:
% 9.55/2.81 | (191) $false
% 9.55/2.81 |
% 9.55/2.81 |-The branch is then unsatisfiable
% 9.55/2.81 |-Branch two:
% 9.55/2.81 | (186) ~ (all_54_0_70 = 0)
% 9.55/2.81 | (200) ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_0_0) = v0 & unequally_directed_lines(all_0_1_1, v0) = v1)
% 9.55/2.82 |
% 9.55/2.82 | Instantiating (200) with all_72_0_76, all_72_1_77 yields:
% 9.55/2.82 | (201) ~ (all_72_0_76 = 0) & reverse_line(all_0_0_0) = all_72_1_77 & unequally_directed_lines(all_0_1_1, all_72_1_77) = all_72_0_76
% 9.55/2.82 |
% 9.55/2.82 | Applying alpha-rule on (201) yields:
% 9.55/2.82 | (202) ~ (all_72_0_76 = 0)
% 9.55/2.82 | (203) reverse_line(all_0_0_0) = all_72_1_77
% 9.55/2.82 | (204) unequally_directed_lines(all_0_1_1, all_72_1_77) = all_72_0_76
% 9.55/2.82 |
% 9.55/2.82 | Instantiating formula (150) with all_0_0_0, all_66_0_75, all_72_1_77 and discharging atoms reverse_line(all_0_0_0) = all_72_1_77, reverse_line(all_0_0_0) = all_66_0_75, yields:
% 9.55/2.82 | (205) all_72_1_77 = all_66_0_75
% 9.55/2.82 |
% 9.55/2.82 | From (205) and (204) follows:
% 9.55/2.82 | (206) unequally_directed_lines(all_0_1_1, all_66_0_75) = all_72_0_76
% 9.55/2.82 |
% 9.55/2.82 | Instantiating formula (28) with all_0_1_1, all_66_0_75, all_72_0_76, 0 and discharging atoms unequally_directed_lines(all_0_1_1, all_66_0_75) = all_72_0_76, unequally_directed_lines(all_0_1_1, all_66_0_75) = 0, yields:
% 9.55/2.82 | (207) all_72_0_76 = 0
% 9.55/2.82 |
% 9.55/2.82 | Equations (207) can reduce 202 to:
% 9.55/2.82 | (191) $false
% 9.55/2.82 |
% 9.55/2.82 |-The branch is then unsatisfiable
% 9.55/2.82 % SZS output end Proof for theBenchmark
% 9.55/2.82
% 9.55/2.82 2224ms
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