TSTP Solution File: GEO269+3 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO269+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:49:22 EDT 2022
% Result : Theorem 16.55s 4.62s
% Output : Proof 21.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO269+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.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 : Fri Jun 17 20:33:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.52/0.58 ____ _
% 0.52/0.58 ___ / __ \_____(_)___ ________ __________
% 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.58
% 0.52/0.58 A Theorem Prover for First-Order Logic
% 0.52/0.58 (ePrincess v.1.0)
% 0.52/0.58
% 0.52/0.58 (c) Philipp Rümmer, 2009-2015
% 0.52/0.58 (c) Peter Backeman, 2014-2015
% 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.58 Bug reports to peter@backeman.se
% 0.52/0.58
% 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.58
% 0.52/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.97 Prover 0: Preprocessing ...
% 2.59/1.30 Prover 0: Warning: ignoring some quantifiers
% 2.78/1.33 Prover 0: Constructing countermodel ...
% 7.55/2.51 Prover 0: gave up
% 7.55/2.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.98/2.55 Prover 1: Preprocessing ...
% 8.51/2.68 Prover 1: Constructing countermodel ...
% 8.51/2.71 Prover 1: gave up
% 8.51/2.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.79/2.75 Prover 2: Preprocessing ...
% 10.03/3.00 Prover 2: Warning: ignoring some quantifiers
% 10.03/3.01 Prover 2: Constructing countermodel ...
% 16.55/4.62 Prover 2: proved (1914ms)
% 16.55/4.62
% 16.55/4.62 No countermodel exists, formula is valid
% 16.55/4.62 % SZS status Theorem for theBenchmark
% 16.55/4.62
% 16.55/4.62 Generating proof ... Warning: ignoring some quantifiers
% 20.73/5.59 found it (size 65)
% 20.73/5.59
% 20.73/5.59 % SZS output start Proof for theBenchmark
% 20.73/5.59 Assumed formulas after preprocessing and simplification:
% 20.73/5.59 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2 & reverse_line(v0) = v1 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v4, v9) = v10) | ~ (left_apart_point(v4, v7) = v8) | ~ (reverse_line(v6) = v9) | ~ (reverse_line(v5) = v7) | ? [v11] : ((v11 = 0 & left_apart_point(v4, v6) = 0) | (v11 = 0 & left_apart_point(v4, v5) = 0) | (v11 = 0 & left_apart_point(v3, v9) = 0) | (v11 = 0 & left_apart_point(v3, v7) = 0) | (v11 = 0 & left_apart_point(v3, v6) = 0) | (v11 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v11 = 0) & distinct_lines(v5, v6) = v11))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v3, v9) = v10) | ~ (left_apart_point(v3, v7) = v8) | ~ (reverse_line(v6) = v9) | ~ (reverse_line(v5) = v7) | ? [v11] : ((v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | (v11 = 0 & left_apart_point(v4, v5) = 0) | (v11 = 0 & left_apart_point(v3, v6) = 0) | (v11 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v11 = 0) & distinct_lines(v5, v6) = v11))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v4, v9) = v10) | ~ (left_apart_point(v3, v7) = v8) | ~ (reverse_line(v6) = v9) | ~ (reverse_line(v5) = v7) | ? [v11] : ((v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | (v11 = 0 & left_apart_point(v4, v5) = 0) | (v11 = 0 & left_apart_point(v3, v9) = 0) | (v11 = 0 & left_apart_point(v3, v6) = 0) | (v11 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v11 = 0) & distinct_lines(v5, v6) = v11) | ( ~ (v11 = 0) & distinct_points(v3, v4) = v11))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v4, v7) = v8) | ~ (left_apart_point(v3, v9) = v10) | ~ (reverse_line(v6) = v9) | ~ (reverse_line(v5) = v7) | ? [v11] : ((v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | (v11 = 0 & left_apart_point(v4, v5) = 0) | (v11 = 0 & left_apart_point(v3, v7) = 0) | (v11 = 0 & left_apart_point(v3, v6) = 0) | (v11 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v11 = 0) & distinct_lines(v5, v6) = v11) | ( ~ (v11 = 0) & distinct_points(v3, v4) = v11))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v7) = v9) | ~ (left_apart_point(v3, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v7) = v9) | ~ (left_apart_point(v3, v7) = v8) | ~ (reverse_line(v5) = v7) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v3, v6) = v7) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v3, v5) = v7) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v6) = v7) | ~ (left_apart_point(v3, v8) = v9) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v5) = v7) | ~ (left_apart_point(v3, v8) = v9) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v4, v6) = v7) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (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) & distinct_lines(v5, v6) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v4, v5) = v7) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (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) & distinct_lines(v5, v6) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v3, v8) = v9) | ~ (left_apart_point(v3, v6) = v7) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v3, v8) = v9) | ~ (left_apart_point(v3, v5) = v7) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v3, v6) = v7) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v4, v8) = v9) | ~ (left_apart_point(v3, v5) = v7) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v8) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v4, v6) = v7) | ~ (left_apart_point(v3, v8) = v9) | ~ (reverse_line(v5) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v5) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (left_apart_point(v4, v5) = v7) | ~ (left_apart_point(v3, v8) = v9) | ~ (reverse_line(v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v5) = v10) | (v11 = 0 & left_apart_point(v3, v10) = 0 & reverse_line(v5) = v10) | (v10 = 0 & left_apart_point(v4, v8) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | (v10 = 0 & left_apart_point(v3, v6) = 0) | (v10 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10) | ( ~ (v10 = 0) & distinct_points(v3, v4) = v10))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v6) = v8) | ~ (left_apart_point(v3, v6) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v4, v5) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = 0) | ~ (left_apart_point(v4, v5) = v8) | ~ (left_apart_point(v3, v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v4, v6) = 0) | (v9 = 0 & left_apart_point(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v4, v6) = v8) | ~ (left_apart_point(v4, v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v3, v6) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v3, v4) = 0) | ~ (left_apart_point(v3, v6) = v8) | ~ (left_apart_point(v3, v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v4, v6) = 0) | (v9 = 0 & left_apart_point(v4, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (left_apart_point(v4, v6) = v8) | ~ (left_apart_point(v3, v5) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v4, v5) = 0) | (v9 = 0 & left_apart_point(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (left_apart_point(v4, v5) = v7) | ~ (left_apart_point(v3, v6) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v4, v9) = 0 & reverse_line(v5) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v6) = v9) | (v10 = 0 & left_apart_point(v3, v9) = 0 & reverse_line(v5) = v9) | (v9 = 0 & left_apart_point(v4, v6) = 0) | (v9 = 0 & left_apart_point(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = v6) | ~ (left_apart_point(v3, v7) = v8) | ~ (reverse_line(v5) = v7) | ? [v9] : (( ~ (v9 = 0) & left_apart_point(v3, v4) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v4, v5) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v4 = v3 | ~ (between_on_line(v8, v7, v6, v5) = v4) | ~ (between_on_line(v8, v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ (unequally_directed_lines(v4, v7) = v8) | ~ (unequally_directed_lines(v3, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v3, v7) = 0 & unequally_directed_lines(v3, v5) = 0) | (v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v5) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v7) | ~ (reverse_line(v4) = v6) | ~ (unequally_directed_lines(v3, v7) = v8) | ~ (unequally_directed_lines(v3, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v4, v7) = 0 & unequally_directed_lines(v4, v5) = 0) | (v9 = 0 & v8 = 0 & unequally_directed_lines(v3, v5) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v4, v7) = v8) | ~ (unequally_directed_lines(v3, v5) = v6) | ? [v9] : ? [v10] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v5) = 0) | (v9 = 0 & v6 = 0 & unequally_directed_lines(v3, v7) = 0) | ( ~ (v10 = 0) & reverse_line(v4) = v9 & unequally_directed_lines(v3, v9) = v10) | ( ~ (v9 = 0) & unequally_directed_lines(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v8) | ~ (unequally_directed_lines(v3, v6) = v7) | ? [v9] : ? [v10] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v5) = 0) | (v9 = 0 & v7 = 0 & unequally_directed_lines(v3, v5) = 0) | ( ~ (v10 = 0) & reverse_line(v4) = v9 & unequally_directed_lines(v3, v9) = v10) | ( ~ (v9 = 0) & unequally_directed_lines(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v5) = v8) | ~ (unequally_directed_lines(v3, v6) = v7) | ? [v9] : ? [v10] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & unequally_directed_lines(v3, v5) = 0) | ( ~ (v10 = 0) & reverse_line(v4) = v9 & unequally_directed_lines(v3, v9) = v10) | ( ~ (v9 = 0) & unequally_directed_lines(v3, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_lines(v4, v5) = v7) | ~ (distinct_lines(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_points(v4, v5) = v7) | ~ (distinct_points(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (left_apart_point(v4, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & left_apart_point(v3, v5) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (left_convergent_lines(v3, v5) = v7) | ~ (unequally_directed_lines(v4, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & left_convergent_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = 0 | ~ (unequally_directed_lines(v4, v5) = v7) | ~ (unequally_directed_lines(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & unequally_directed_lines(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (between_on_line(v3, v4, v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & before_on_line(v3, v6, v5) = v8) | ( ~ (v8 = 0) & before_on_line(v3, v5, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (between_on_line(v3, v4, v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & before_on_line(v3, v5, v6) = v8) | ( ~ (v8 = 0) & before_on_line(v3, v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (line_connecting(v3, v4) = v6) | ~ (left_convergent_lines(v6, v5) = v7) | ? [v8] : ((v8 = 0 & left_apart_point(v4, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v3, v4) = v8) | ( ~ (v8 = 0) & left_apart_point(v3, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v3, v6) = v7) | ~ (left_apart_point(v3, v4) = 0) | ~ (reverse_line(v5) = v6) | ? [v8] : ((v8 = 0 & distinct_lines(v4, v5) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v3, v6) = v7) | ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v8] : ((v8 = 0 & distinct_lines(v4, v5) = 0) | ( ~ (v8 = 0) & left_apart_point(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (before_on_line(v7, v6, v5) = v4) | ~ (before_on_line(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (divides_points(v7, v6, v5) = v4) | ~ (divides_points(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v4, v5) = v6) | ~ (equally_directed_lines(v3, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & distinct_points(v4, v5) = 0 & incident_point_and_line(v5, v3) = 0 & incident_point_and_line(v4, v3) = 0) | ( ~ (v8 = 0) & before_on_line(v3, v4, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v7) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v3, v6) = 0 & unequally_directed_lines(v3, v5) = 0) | (v8 = 0 & v7 = 0 & unequally_directed_lines(v4, v5) = 0) | ( ~ (v9 = 0) & reverse_line(v4) = v8 & unequally_directed_lines(v3, v8) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v3, v6) = v7) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v6) = 0 & unequally_directed_lines(v4, v5) = 0) | (v8 = 0 & v7 = 0 & unequally_directed_lines(v3, v5) = 0) | ( ~ (v9 = 0) & reverse_line(v4) = v8 & unequally_directed_lines(v3, v8) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v6) | ~ (unequally_directed_lines(v4, v5) = v7) | ~ (unequally_directed_lines(v3, v6) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & reverse_line(v5) = v9 & unequally_directed_lines(v3, v9) = 0 & unequally_directed_lines(v3, v5) = 0) | (v9 = 0 & v7 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v4, v8) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v4) = v6) | ~ (unequally_directed_lines(v3, v6) = 0) | ~ (unequally_directed_lines(v3, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v4, v8) = 0 & unequally_directed_lines(v4, v5) = 0) | (v9 = 0 & v7 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v3, v8) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v4, v5) = v7) | ~ (unequally_directed_lines(v3, v5) = v6) | ? [v8] : ? [v9] : ((v9 = 0 & v7 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v4, v8) = 0) | (v9 = 0 & v6 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v3, v8) = 0) | ( ~ (v9 = 0) & reverse_line(v4) = v8 & unequally_directed_lines(v3, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v4, v5) = v6) | ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v4, v5) = v6) | ~ (left_apart_point(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v3, v7) = 0 & reverse_line(v5) = v7) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_lines(v3, v5) = v6) | ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (before_on_line(v3, v4, v5) = v6) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & line_connecting(v4, v5) = v7 & equally_directed_lines(v3, v7) = v8) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7) | ( ~ (v7 = 0) & incident_point_and_line(v5, v3) = v7) | ( ~ (v7 = 0) & incident_point_and_line(v4, v3) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v4, v5) = v6) | ~ (distinct_points(v3, v4) = 0) | distinct_points(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v3, v5) = v6) | ~ (distinct_points(v3, v4) = 0) | distinct_points(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (distinct_points(v3, v4) = v6) | ~ (left_apart_point(v3, v5) = 0) | left_apart_point(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (divides_points(v5, v3, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & left_apart_point(v4, v5) = v7) | ( ~ (v7 = 0) & right_apart_point(v3, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (divides_points(v5, v3, v4) = v6) | ? [v7] : (( ~ (v7 = 0) & left_apart_point(v3, v5) = v7) | ( ~ (v7 = 0) & right_apart_point(v4, v5) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_convergent_lines(v3, v5) = v6) | ~ (left_convergent_lines(v3, v4) = 0) | unequally_directed_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_convergent_lines(v3, v5) = v6) | ~ (reverse_line(v4) = v5) | ? [v7] : ( ~ (v7 = 0) & right_convergent_lines(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_convergent_lines(v3, v5) = v6) | ~ (reverse_line(v4) = v5) | ? [v7] : ((v7 = 0 & left_convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v3, v5) = v7) | ( ~ (v7 = 0) & unequally_directed_lines(v3, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_convergent_lines(v3, v4) = 0) | ~ (unequally_directed_lines(v4, v5) = v6) | left_convergent_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_apart_point(v4, v5) = v6) | ~ (left_apart_point(v3, v5) = 0) | distinct_points(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_apart_point(v3, v5) = v6) | ~ (reverse_line(v4) = v5) | ? [v7] : ( ~ (v7 = 0) & right_apart_point(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = v6) | unequally_directed_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_opposite_lines(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_lines(v4, v5) = v6) | ~ (unequally_directed_lines(v3, v4) = 0) | unequally_directed_lines(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_lines(v3, v5) = v6) | ~ (unequally_directed_lines(v3, v4) = 0) | unequally_directed_lines(v4, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (parallel_through_point(v6, v5) = v4) | ~ (parallel_through_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection_point(v6, v5) = v4) | ~ (intersection_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (distinct_lines(v6, v5) = v4) | ~ (distinct_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (line_connecting(v6, v5) = v4) | ~ (line_connecting(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (distinct_points(v6, v5) = v4) | ~ (distinct_points(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (incident_point_and_line(v6, v5) = v4) | ~ (incident_point_and_line(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (convergent_lines(v6, v5) = v4) | ~ (convergent_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (apart_point_and_line(v6, v5) = v4) | ~ (apart_point_and_line(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equally_directed_opposite_lines(v6, v5) = v4) | ~ (equally_directed_opposite_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equally_directed_lines(v6, v5) = v4) | ~ (equally_directed_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (left_convergent_lines(v6, v5) = v4) | ~ (left_convergent_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (right_convergent_lines(v6, v5) = v4) | ~ (right_convergent_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (left_apart_point(v6, v5) = v4) | ~ (left_apart_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (right_apart_point(v6, v5) = v4) | ~ (right_apart_point(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unequally_directed_lines(v6, v5) = v4) | ~ (unequally_directed_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unequally_directed_opposite_lines(v6, v5) = v4) | ~ (unequally_directed_opposite_lines(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) | ~ (distinct_points(v3, v4) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v4, v7) = 0 & reverse_line(v6) = v7) | (v8 = 0 & left_apart_point(v4, v7) = 0 & reverse_line(v5) = v7) | (v8 = 0 & left_apart_point(v3, v7) = 0 & reverse_line(v6) = v7) | (v8 = 0 & left_apart_point(v3, v7) = 0 & reverse_line(v5) = v7) | (v7 = 0 & left_apart_point(v4, v6) = 0) | (v7 = 0 & left_apart_point(v4, v5) = 0) | (v7 = 0 & left_apart_point(v3, v6) = 0) | (v7 = 0 & left_apart_point(v3, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (between_on_line(v3, v4, v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & before_on_line(v3, v6, v5) = 0 & before_on_line(v3, v5, v4) = 0) | (v8 = 0 & v7 = 0 & before_on_line(v3, v5, v6) = 0 & before_on_line(v3, v4, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ~ (equally_directed_lines(v3, v6) = 0) | ? [v7] : ((v7 = 0 & before_on_line(v3, v4, v5) = 0) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7) | ( ~ (v7 = 0) & incident_point_and_line(v5, v3) = v7) | ( ~ (v7 = 0) & incident_point_and_line(v4, v3) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v4, v5) = v6) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v7 = 0 & reverse_line(v5) = v8 & unequally_directed_lines(v3, v8) = 0 & unequally_directed_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = 0) | ( ~ (v8 = 0) & reverse_line(v4) = v7 & unequally_directed_lines(v3, v7) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v3, v5) = v6) | ~ (unequally_directed_lines(v3, v4) = 0) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = 0 & unequally_directed_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & reverse_line(v5) = v7 & unequally_directed_lines(v3, v7) = 0) | ( ~ (v8 = 0) & reverse_line(v4) = v7 & unequally_directed_lines(v3, v7) = v8))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (convergent_lines(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6) | ( ~ (v6 = 0) & unequally_directed_opposite_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apart_point_and_line(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & left_apart_point(v3, v4) = v6 & right_apart_point(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equally_directed_opposite_lines(v3, v4) = v5) | unequally_directed_opposite_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equally_directed_lines(v3, v4) = v5) | unequally_directed_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_convergent_lines(v3, v4) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & left_convergent_lines(v3, v6) = 0 & reverse_line(v4) = v6) | ( ~ (v7 = 0) & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (right_convergent_lines(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & left_convergent_lines(v3, v6) = v7 & reverse_line(v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (left_apart_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & right_apart_point(v3, v4) = 0) | ( ~ (v6 = 0) & apart_point_and_line(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (right_apart_point(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & left_apart_point(v3, v6) = v7 & reverse_line(v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (right_apart_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & left_apart_point(v3, v4) = 0) | ( ~ (v6 = 0) & apart_point_and_line(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_lines(v3, v4) = v5) | equally_directed_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_lines(v3, v4) = v5) | ? [v6] : (reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_opposite_lines(v3, v4) = v5) | equally_directed_opposite_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (unequally_directed_opposite_lines(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (point(v5) = v4) | ~ (point(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (line(v5) = v4) | ~ (line(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (reverse_line(v5) = v4) | ~ (reverse_line(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | equally_directed_lines(v5, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) | ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (parallel_through_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ? [v6] : ? [v7] : ((v6 = 0 & point(v5) = 0) | ( ~ (v7 = 0) & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = v7) | ( ~ (v6 = 0) & line(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (intersection_point(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ~ (v6 = 0) & apart_point_and_line(v5, v4) = v7 & apart_point_and_line(v5, v3) = v6) | ( ~ (v7 = 0) & reverse_line(v4) = v6 & unequally_directed_lines(v3, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & line_connecting(v3, v4) = v6 & equally_directed_lines(v6, v7) = 0 & reverse_line(v5) = v7) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & line_connecting(v4, v3) = v6 & equally_directed_lines(v5, v7) = 0 & reverse_line(v6) = v7) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ~ (v6 = 0) & apart_point_and_line(v4, v5) = v7 & apart_point_and_line(v3, v5) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (line_connecting(v3, v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & point(v3) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (before_on_line(v3, v4, v5) = 0) | ? [v6] : (line_connecting(v4, v5) = v6 & distinct_points(v4, v5) = 0 & incident_point_and_line(v5, v3) = 0 & incident_point_and_line(v4, v3) = 0 & equally_directed_lines(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (divides_points(v5, v3, v4) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & left_apart_point(v4, v5) = 0 & right_apart_point(v3, v5) = 0) | (v7 = 0 & v6 = 0 & left_apart_point(v3, v5) = 0 & right_apart_point(v4, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_convergent_lines(v3, v5) = 0) | ~ (reverse_line(v4) = v5) | right_convergent_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_convergent_lines(v3, v5) = 0) | ~ (reverse_line(v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_apart_point(v3, v5) = 0) | ~ (reverse_line(v4) = v5) | right_apart_point(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_apart_point(v3, v5) = 0) | ~ (reverse_line(v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_apart_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v6 = 0) & ~ (v5 = 0) & right_apart_point(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (left_apart_point(v3, v4) = 0) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v3, v6) = 0 & reverse_line(v5) = v6) | (v6 = 0 & distinct_lines(v4, v5) = 0))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (right_apart_point(v3, v4) = v5) | ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v6 = 0) & ~ (v5 = 0) & left_apart_point(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = 0) | unequally_directed_opposite_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v8 = 0) & ~ (v7 = 0) & intersection_point(v3, v4) = v6 & apart_point_and_line(v6, v4) = v8 & apart_point_and_line(v6, v3) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & intersection_point(v3, v4) = v6 & point(v6) = 0) | ( ~ (v6 = 0) & line(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ~ (unequally_directed_lines(v3, v5) = 0) | ? [v6] : ((v6 = 0 & left_convergent_lines(v3, v5) = 0) | (v6 = 0 & left_convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v3, v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_opposite_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_opposite_lines(v3, v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) & ! [v3] : ! [v4] : (v4 = 0 | ~ (equally_directed_lines(v3, v3) = v4)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & line_connecting(v3, v4) = v5 & apart_point_and_line(v4, v5) = v7 & apart_point_and_line(v3, v5) = v6)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (line_connecting(v4, v3) = v6 & line_connecting(v3, v4) = v5 & equally_directed_lines(v5, v7) = 0 & reverse_line(v6) = v7)) & ! [v3] : ! [v4] : ( ~ (distinct_points(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & line(v5) = 0 & line_connecting(v3, v4) = v5) | ( ~ (v5 = 0) & point(v4) = v5) | ( ~ (v5 = 0) & point(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) | (unequally_directed_lines(v3, v4) = 0 & unequally_directed_opposite_lines(v3, v4) = 0)) & ! [v3] : ! [v4] : ( ~ (apart_point_and_line(v3, v4) = 0) | ? [v5] : ((v5 = 0 & left_apart_point(v3, v4) = 0) | (v5 = 0 & right_apart_point(v3, v4) = 0))) & ! [v3] : ! [v4] : ( ~ (equally_directed_opposite_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_opposite_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (equally_directed_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ~ (left_convergent_lines(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (right_convergent_lines(v3, v4) = 0) | ? [v5] : (left_convergent_lines(v3, v5) = 0 & reverse_line(v4) = v5)) & ! [v3] : ! [v4] : ~ (left_apart_point(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (right_apart_point(v3, v4) = 0) | ? [v5] : (left_apart_point(v3, v5) = 0 & reverse_line(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (reverse_line(v3) = v4) | ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & line(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = 0) & ~ (v6 = 0) & intersection_point(v3, v4) = v5 & apart_point_and_line(v5, v4) = v7 & apart_point_and_line(v5, v3) = v6) | ( ~ (v6 = 0) & reverse_line(v4) = v5 & unequally_directed_lines(v3, v5) = v6))) & ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & intersection_point(v3, v4) = v5 & point(v5) = 0) | ( ~ (v6 = 0) & reverse_line(v4) = v5 & unequally_directed_lines(v3, v5) = v6) | ( ~ (v5 = 0) & line(v4) = v5) | ( ~ (v5 = 0) & line(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & left_convergent_lines(v3, v5) = 0 & reverse_line(v4) = v5) | (v5 = 0 & left_convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & reverse_line(v4) = v5 & unequally_directed_lines(v3, v5) = v6))) & ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & equally_directed_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v3, v4) = 0) | ? [v5] : ((v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v5 = 0) & unequally_directed_opposite_lines(v3, v4) = v5))) & ! [v3] : ! [v4] : ( ~ (unequally_directed_opposite_lines(v3, v4) = 0) | ? [v5] : ( ~ (v5 = 0) & equally_directed_opposite_lines(v3, v4) = v5)) & ! [v3] : ! [v4] : ( ~ (unequally_directed_opposite_lines(v3, v4) = 0) | ? [v5] : (reverse_line(v4) = v5 & unequally_directed_lines(v3, v5) = 0)) & ! [v3] : ! [v4] : ( ~ (unequally_directed_opposite_lines(v3, v4) = 0) | ? [v5] : ((v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v3, v4) = v5))) & ! [v3] : ( ~ (line(v3) = 0) | ? [v4] : (line(v4) = 0 & reverse_line(v3) = v4)) & ! [v3] : ~ (distinct_lines(v3, v3) = 0) & ! [v3] : ~ (distinct_points(v3, v3) = 0) & ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : between_on_line(v6, v5, v4, v3) = v7 & ? [v3] : ? [v4] : ? [v5] : ? [v6] : before_on_line(v5, v4, v3) = v6 & ? [v3] : ? [v4] : ? [v5] : ? [v6] : divides_points(v5, v4, v3) = v6 & ? [v3] : ? [v4] : ? [v5] : parallel_through_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : intersection_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : distinct_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : line_connecting(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : distinct_points(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : incident_point_and_line(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : convergent_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : apart_point_and_line(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : equally_directed_opposite_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : equally_directed_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : left_convergent_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : right_convergent_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : left_apart_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : right_apart_point(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : unequally_directed_lines(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : unequally_directed_opposite_lines(v4, v3) = v5 & ? [v3] : ? [v4] : point(v3) = v4 & ? [v3] : ? [v4] : line(v3) = v4 & ? [v3] : ? [v4] : reverse_line(v3) = v4)
% 21.21/5.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 21.21/5.70 | (1) ~ (all_0_0_0 = 0) & equally_directed_opposite_lines(all_0_2_2, all_0_1_1) = all_0_0_0 & reverse_line(all_0_2_2) = all_0_1_1 & ! [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
% 21.70/5.75 |
% 21.70/5.75 | Applying alpha-rule on (1) yields:
% 21.70/5.75 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 21.70/5.75 | (3) ! [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)))
% 21.70/5.75 | (4) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2
% 21.70/5.75 | (5) ! [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))
% 21.70/5.75 | (6) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 21.70/5.75 | (7) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2
% 21.70/5.75 | (8) ! [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)))
% 21.70/5.75 | (9) ! [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))
% 21.70/5.75 | (10) ! [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)))
% 21.70/5.75 | (11) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 21.70/5.75 | (12) ! [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)))
% 21.70/5.75 | (13) ! [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)))
% 21.70/5.75 | (14) equally_directed_opposite_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 21.70/5.75 | (15) ! [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)))
% 21.70/5.75 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 21.70/5.75 | (17) ! [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))
% 21.70/5.76 | (18) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2
% 21.70/5.76 | (19) ! [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)))
% 21.70/5.76 | (20) ! [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)))
% 21.70/5.76 | (21) ! [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)))
% 21.70/5.76 | (22) ! [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)))
% 21.70/5.76 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 21.70/5.76 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 21.70/5.76 | (25) ! [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)))
% 21.70/5.76 | (26) ! [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))
% 21.70/5.76 | (27) ! [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)))
% 21.70/5.76 | (28) ! [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)))
% 21.70/5.76 | (29) ! [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)))
% 21.70/5.76 | (30) ! [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)))
% 21.70/5.76 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0))
% 21.70/5.76 | (32) reverse_line(all_0_2_2) = all_0_1_1
% 21.70/5.76 | (33) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 21.70/5.76 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0))
% 21.70/5.76 | (35) ! [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)))
% 21.70/5.76 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 21.70/5.76 | (37) ? [v0] : ? [v1] : line(v0) = v1
% 21.70/5.76 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0))
% 21.70/5.76 | (39) ! [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))
% 21.70/5.76 | (40) ! [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)))
% 21.70/5.76 | (41) ! [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)))
% 21.70/5.76 | (42) ! [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)))
% 21.70/5.76 | (43) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2
% 21.70/5.76 | (44) ! [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)))
% 21.70/5.76 | (45) ! [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))
% 21.70/5.76 | (46) ? [v0] : ? [v1] : reverse_line(v0) = v1
% 21.70/5.76 | (47) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2)))
% 21.70/5.76 | (48) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 21.70/5.76 | (49) ! [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)))
% 21.70/5.76 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 21.70/5.76 | (51) ! [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)))
% 21.70/5.77 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 21.70/5.77 | (53) ! [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))
% 21.70/5.77 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 21.70/5.77 | (55) ! [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)))
% 21.70/5.77 | (56) ! [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)))
% 21.70/5.77 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 21.70/5.77 | (58) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2
% 21.70/5.77 | (59) ! [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)))
% 21.70/5.77 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0))
% 21.70/5.77 | (61) ! [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))
% 21.70/5.77 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0))
% 21.70/5.77 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 21.70/5.77 | (64) ! [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)))
% 21.70/5.77 | (65) ! [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)))
% 21.70/5.77 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 21.70/5.77 | (67) ! [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)))
% 21.70/5.77 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 21.70/5.77 | (69) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 21.70/5.77 | (70) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 21.70/5.77 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0))
% 21.70/5.77 | (72) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0)
% 21.70/5.77 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 21.70/5.77 | (74) ! [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)))
% 21.70/5.77 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0))
% 21.70/5.77 | (76) ! [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)))
% 21.70/5.77 | (77) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3
% 21.70/5.77 | (78) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 21.70/5.77 | (79) ! [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)))
% 21.70/5.77 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 21.70/5.77 | (81) ? [v0] : ? [v1] : point(v0) = v1
% 21.70/5.77 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 21.70/5.77 | (83) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 21.70/5.77 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 21.70/5.77 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4
% 21.70/5.77 | (86) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 21.70/5.77 | (87) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 21.70/5.77 | (88) ! [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)))
% 21.70/5.77 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 21.70/5.77 | (90) ! [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)))
% 21.70/5.78 | (91) ! [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))
% 21.70/5.78 | (92) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 21.70/5.78 | (93) ! [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)))
% 21.70/5.78 | (94) ! [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)))
% 21.70/5.78 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 21.70/5.78 | (96) ! [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)))
% 21.70/5.78 | (97) ! [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)))
% 21.70/5.78 | (98) ! [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))
% 21.70/5.78 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 21.70/5.78 | (100) ! [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)))
% 21.70/5.78 | (101) ! [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)))
% 21.70/5.78 | (102) ! [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)))
% 21.70/5.78 | (103) ! [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)))
% 21.70/5.78 | (104) ! [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)))
% 21.70/5.78 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 21.70/5.78 | (106) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 21.70/5.78 | (107) ! [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)))
% 21.70/5.78 | (108) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2
% 21.70/5.78 | (109) ! [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)))
% 21.70/5.78 | (110) ! [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)))
% 21.70/5.78 | (111) ! [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)))
% 21.70/5.78 | (112) ! [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)))
% 21.70/5.78 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0))
% 21.70/5.78 | (114) ! [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)))
% 21.70/5.78 | (115) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 21.70/5.78 | (116) ! [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)))
% 21.70/5.78 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 21.70/5.78 | (118) ! [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)))
% 21.70/5.78 | (119) ! [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)))
% 21.70/5.78 | (120) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 21.70/5.78 | (121) ! [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)))
% 21.70/5.78 | (122) ! [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)))
% 21.70/5.78 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 21.70/5.79 | (124) ! [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)))
% 21.70/5.79 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 21.70/5.79 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 21.70/5.79 | (127) ! [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)))
% 21.70/5.79 | (128) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 21.70/5.79 | (129) ! [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)))
% 21.70/5.79 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 21.70/5.79 | (131) ! [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)))
% 21.70/5.79 | (132) ! [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))
% 21.70/5.79 | (133) ! [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)))
% 21.70/5.79 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 21.70/5.79 | (135) ! [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)))
% 21.70/5.79 | (136) ~ (all_0_0_0 = 0)
% 21.70/5.79 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 21.70/5.79 | (138) ! [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)))
% 21.70/5.79 | (139) ! [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))
% 21.70/5.79 | (140) ! [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)))
% 21.70/5.79 | (141) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 21.70/5.79 | (142) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1))
% 21.70/5.79 | (143) ! [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)))
% 21.70/5.79 | (144) ! [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)))
% 21.70/5.79 | (145) ! [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))
% 21.70/5.79 | (146) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0)
% 21.70/5.79 | (147) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2
% 21.70/5.79 | (148) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 21.70/5.79 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 21.70/5.79 | (150) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2
% 21.70/5.79 | (151) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 21.70/5.79 | (152) ! [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)))
% 21.70/5.79 | (153) ! [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)))
% 21.70/5.79 | (154) ! [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)))
% 21.70/5.79 | (155) ! [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)))
% 21.70/5.79 | (156) ! [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))
% 21.70/5.79 | (157) ! [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)))
% 21.70/5.79 | (158) ! [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)))
% 21.70/5.79 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0))
% 21.70/5.79 | (160) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 21.70/5.79 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 21.70/5.80 | (162) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 21.70/5.80 | (163) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3
% 21.70/5.80 | (164) ! [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)))
% 21.70/5.80 | (165) ! [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)))
% 21.70/5.80 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 21.70/5.80 | (167) ! [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)))
% 21.70/5.80 | (168) ! [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)))
% 21.70/5.80 | (169) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 21.70/5.80 | (170) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 21.70/5.80 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2))
% 21.90/5.80 | (172) ! [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)))
% 21.90/5.80 | (173) ! [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))
% 21.90/5.80 | (174) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 21.90/5.80 | (175) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 21.90/5.80 | (176) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 21.90/5.80 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0))
% 21.90/5.80 | (178) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 21.90/5.80 | (179) ! [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)))
% 21.90/5.80 | (180) ! [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)))
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (170) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equally_directed_opposite_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 21.90/5.80 | (181) all_0_0_0 = 0 | unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 +-Applying beta-rule and splitting (181), into two cases.
% 21.90/5.80 |-Branch one:
% 21.90/5.80 | (182) unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (83) with all_0_1_1, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.80 | (183) ? [v0] : (reverse_line(all_0_1_1) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0)
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (167) with all_0_1_1, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.80 | (184) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = v0))
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (44) with 0, all_0_1_1, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.80 | (185) ? [v0] : ((v0 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (185) with all_64_0_72 yields:
% 21.90/5.80 | (186) (all_64_0_72 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_64_0_72 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_64_0_72)
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (184) with all_65_0_73 yields:
% 21.90/5.80 | (187) (all_65_0_73 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_65_0_73 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_65_0_73)
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (183) with all_66_0_74 yields:
% 21.90/5.80 | (188) reverse_line(all_0_1_1) = all_66_0_74 & unequally_directed_lines(all_0_2_2, all_66_0_74) = 0
% 21.90/5.80 |
% 21.90/5.80 | Applying alpha-rule on (188) yields:
% 21.90/5.80 | (189) reverse_line(all_0_1_1) = all_66_0_74
% 21.90/5.80 | (190) unequally_directed_lines(all_0_2_2, all_66_0_74) = 0
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (90) with 0, all_66_0_74, all_66_0_74, all_0_1_1, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_66_0_74, unequally_directed_lines(all_0_2_2, all_66_0_74) = 0, yields:
% 21.90/5.80 | (191) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_1_1, all_66_0_74) = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = v0))
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (122) with all_66_0_74, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_66_0_74, unequally_directed_lines(all_0_2_2, all_66_0_74) = 0, yields:
% 21.90/5.80 | (192) ? [v0] : ((v0 = 0 & left_convergent_lines(all_0_2_2, all_66_0_74) = 0) | (v0 = 0 & left_convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = v0))
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (192) with all_81_0_80 yields:
% 21.90/5.80 | (193) (all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_66_0_74) = 0) | (all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_81_0_80 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_81_0_80)
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (191) with all_90_0_95, all_90_1_96 yields:
% 21.90/5.80 | (194) (all_90_0_95 = 0 & all_90_1_96 = 0 & unequally_directed_lines(all_0_1_1, all_66_0_74) = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0) | (all_90_1_96 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_90_1_96 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_90_1_96)
% 21.90/5.80 |
% 21.90/5.80 +-Applying beta-rule and splitting (186), into two cases.
% 21.90/5.80 |-Branch one:
% 21.90/5.80 | (195) all_64_0_72 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 | Applying alpha-rule on (195) yields:
% 21.90/5.80 | (196) all_64_0_72 = 0
% 21.90/5.80 | (197) unequally_directed_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 +-Applying beta-rule and splitting (194), into two cases.
% 21.90/5.80 |-Branch one:
% 21.90/5.80 | (198) (all_90_0_95 = 0 & all_90_1_96 = 0 & unequally_directed_lines(all_0_1_1, all_66_0_74) = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0) | (all_90_1_96 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0)
% 21.90/5.80 |
% 21.90/5.80 +-Applying beta-rule and splitting (198), into two cases.
% 21.90/5.80 |-Branch one:
% 21.90/5.80 | (199) all_90_0_95 = 0 & all_90_1_96 = 0 & unequally_directed_lines(all_0_1_1, all_66_0_74) = 0 & unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 | Applying alpha-rule on (199) yields:
% 21.90/5.80 | (200) all_90_0_95 = 0
% 21.90/5.80 | (201) all_90_1_96 = 0
% 21.90/5.80 | (202) unequally_directed_lines(all_0_1_1, all_66_0_74) = 0
% 21.90/5.80 | (203) unequally_directed_lines(all_0_1_1, all_0_1_1) = 0
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (86) with all_0_1_1, all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 21.90/5.80 | (204) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = v0)
% 21.90/5.80 |
% 21.90/5.80 | Instantiating (204) with all_318_0_249 yields:
% 21.90/5.80 | (205) ~ (all_318_0_249 = 0) & equally_directed_lines(all_0_1_1, all_0_1_1) = all_318_0_249
% 21.90/5.80 |
% 21.90/5.80 | Applying alpha-rule on (205) yields:
% 21.90/5.80 | (206) ~ (all_318_0_249 = 0)
% 21.90/5.80 | (207) equally_directed_lines(all_0_1_1, all_0_1_1) = all_318_0_249
% 21.90/5.80 |
% 21.90/5.80 | Instantiating formula (142) with all_318_0_249, all_0_1_1 and discharging atoms equally_directed_lines(all_0_1_1, all_0_1_1) = all_318_0_249, yields:
% 21.90/5.80 | (208) all_318_0_249 = 0
% 21.90/5.80 |
% 21.90/5.81 | Equations (208) can reduce 206 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (210) all_90_1_96 = 0 & unequally_directed_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (210) yields:
% 21.90/5.81 | (201) all_90_1_96 = 0
% 21.90/5.81 | (197) unequally_directed_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 +-Applying beta-rule and splitting (193), into two cases.
% 21.90/5.81 |-Branch one:
% 21.90/5.81 | (213) (all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_66_0_74) = 0) | (all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_0_1_1) = 0)
% 21.90/5.81 |
% 21.90/5.81 +-Applying beta-rule and splitting (213), into two cases.
% 21.90/5.81 |-Branch one:
% 21.90/5.81 | (214) all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_66_0_74) = 0
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (214) yields:
% 21.90/5.81 | (215) all_81_0_80 = 0
% 21.90/5.81 | (216) left_convergent_lines(all_0_2_2, all_66_0_74) = 0
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (146) with all_66_0_74, all_0_2_2 and discharging atoms left_convergent_lines(all_0_2_2, all_66_0_74) = 0, yields:
% 21.90/5.81 | (217) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (218) all_81_0_80 = 0 & left_convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (218) yields:
% 21.90/5.81 | (215) all_81_0_80 = 0
% 21.90/5.81 | (220) left_convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (146) with all_0_1_1, all_0_2_2 and discharging atoms left_convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.81 | (217) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (222) ~ (all_81_0_80 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_81_0_80
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (222) yields:
% 21.90/5.81 | (223) ~ (all_81_0_80 = 0)
% 21.90/5.81 | (224) unequally_directed_lines(all_0_2_2, all_0_1_1) = all_81_0_80
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (113) with all_0_2_2, all_0_1_1, all_81_0_80, 0 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_1_1) = all_81_0_80, unequally_directed_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.81 | (215) all_81_0_80 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (215) can reduce 223 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (227) ~ (all_90_1_96 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_90_1_96
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (227) yields:
% 21.90/5.81 | (228) ~ (all_90_1_96 = 0)
% 21.90/5.81 | (229) unequally_directed_lines(all_0_2_2, all_0_1_1) = all_90_1_96
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (113) with all_0_2_2, all_0_1_1, 0, all_90_1_96 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_1_1) = all_90_1_96, unequally_directed_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.81 | (201) all_90_1_96 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (201) can reduce 228 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (232) ~ (all_64_0_72 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_64_0_72
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (232) yields:
% 21.90/5.81 | (233) ~ (all_64_0_72 = 0)
% 21.90/5.81 | (234) convergent_lines(all_0_2_2, all_0_1_1) = all_64_0_72
% 21.90/5.81 |
% 21.90/5.81 +-Applying beta-rule and splitting (187), into two cases.
% 21.90/5.81 |-Branch one:
% 21.90/5.81 | (235) all_65_0_73 = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (235) yields:
% 21.90/5.81 | (236) all_65_0_73 = 0
% 21.90/5.81 | (237) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (137) with all_0_2_2, all_0_1_1, 0, all_64_0_72 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_64_0_72, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 21.90/5.81 | (196) all_64_0_72 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (196) can reduce 233 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (240) ~ (all_65_0_73 = 0) & unequally_directed_lines(all_0_2_2, all_0_1_1) = all_65_0_73
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (240) yields:
% 21.90/5.81 | (241) ~ (all_65_0_73 = 0)
% 21.90/5.81 | (242) unequally_directed_lines(all_0_2_2, all_0_1_1) = all_65_0_73
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (63) with all_65_0_73, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms reverse_line(all_0_2_2) = all_0_1_1, unequally_directed_lines(all_0_2_2, all_0_1_1) = all_65_0_73, yields:
% 21.90/5.81 | (243) all_65_0_73 = 0 | unequally_directed_lines(all_0_2_2, all_0_2_2) = 0
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (132) with all_65_0_73, all_65_0_73, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_1_1) = all_65_0_73, yields:
% 21.90/5.81 | (244) all_65_0_73 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = v0)
% 21.90/5.81 |
% 21.90/5.81 +-Applying beta-rule and splitting (243), into two cases.
% 21.90/5.81 |-Branch one:
% 21.90/5.81 | (245) unequally_directed_lines(all_0_2_2, all_0_2_2) = 0
% 21.90/5.81 |
% 21.90/5.81 +-Applying beta-rule and splitting (244), into two cases.
% 21.90/5.81 |-Branch one:
% 21.90/5.81 | (236) all_65_0_73 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (236) can reduce 241 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (241) ~ (all_65_0_73 = 0)
% 21.90/5.81 | (249) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = v0)
% 21.90/5.81 |
% 21.90/5.81 | Instantiating (249) with all_350_0_421 yields:
% 21.90/5.81 | (250) ~ (all_350_0_421 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = all_350_0_421
% 21.90/5.81 |
% 21.90/5.81 | Applying alpha-rule on (250) yields:
% 21.90/5.81 | (251) ~ (all_350_0_421 = 0)
% 21.90/5.81 | (252) unequally_directed_lines(all_0_2_2, all_0_2_2) = all_350_0_421
% 21.90/5.81 |
% 21.90/5.81 | Instantiating formula (113) with all_0_2_2, all_0_2_2, 0, all_350_0_421 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_2_2) = all_350_0_421, unequally_directed_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 21.90/5.81 | (253) all_350_0_421 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (253) can reduce 251 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (255) ~ (unequally_directed_lines(all_0_2_2, all_0_2_2) = 0)
% 21.90/5.81 | (236) all_65_0_73 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (236) can reduce 241 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 |-Branch two:
% 21.90/5.81 | (258) ~ (unequally_directed_opposite_lines(all_0_2_2, all_0_1_1) = 0)
% 21.90/5.81 | (259) all_0_0_0 = 0
% 21.90/5.81 |
% 21.90/5.81 | Equations (259) can reduce 136 to:
% 21.90/5.81 | (209) $false
% 21.90/5.81 |
% 21.90/5.81 |-The branch is then unsatisfiable
% 21.90/5.81 % SZS output end Proof for theBenchmark
% 21.90/5.81
% 21.90/5.81 5218ms
%------------------------------------------------------------------------------