%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO249+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 03:49:11 EDT 2022

% Result   : Theorem 6.55s 2.16s
% Output   : Proof 9.68s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO249+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jun 17 19:19:24 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.56/0.58          ____       _                          
% 0.56/0.58    ___  / __ \_____(_)___  ________  __________
% 0.56/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.58  
% 0.56/0.58  A Theorem Prover for First-Order Logic
% 0.56/0.58  (ePrincess v.1.0)
% 0.56/0.58  
% 0.56/0.58  (c) Philipp Rümmer, 2009-2015
% 0.56/0.58  (c) Peter Backeman, 2014-2015
% 0.56/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.58  Bug reports to peter@backeman.se
% 0.56/0.58  
% 0.56/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.58  
% 0.56/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.66/0.98  Prover 0: Preprocessing ...
% 2.58/1.25  Prover 0: Warning: ignoring some quantifiers
% 2.58/1.28  Prover 0: Constructing countermodel ...
% 3.27/1.46  Prover 0: gave up
% 3.27/1.46  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.75/1.51  Prover 1: Preprocessing ...
% 4.30/1.69  Prover 1: Constructing countermodel ...
% 4.70/1.75  Prover 1: gave up
% 4.70/1.75  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.07/1.79  Prover 2: Preprocessing ...
% 5.98/2.07  Prover 2: Warning: ignoring some quantifiers
% 6.42/2.09  Prover 2: Constructing countermodel ...
% 6.55/2.16  Prover 2: proved (410ms)
% 6.55/2.16  
% 6.55/2.16  No countermodel exists, formula is valid
% 6.55/2.16  % SZS status Theorem for theBenchmark
% 6.55/2.16  
% 6.55/2.16  Generating proof ... Warning: ignoring some quantifiers
% 8.69/2.63  found it (size 7)
% 8.69/2.63  
% 8.69/2.63  % SZS output start Proof for theBenchmark
% 8.69/2.63  Assumed formulas after preprocessing and simplification: 
% 8.69/2.63  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & parallel_through_point(v2, v0) = v3 & right_apart_point(v1, v3) = 0 & right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = 0 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v10 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v6, v11) = v12) |  ~ (left_apart_point(v6, v9) = v10) |  ~ (reverse_line(v8) = v11) |  ~ (reverse_line(v7) = v9) |  ? [v13] : ((v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v10 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v5, v11) = v12) |  ~ (left_apart_point(v5, v9) = v10) |  ~ (reverse_line(v8) = v11) |  ~ (reverse_line(v7) = v9) |  ? [v13] : ((v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v10 = 0 |  ~ (left_apart_point(v6, v11) = v12) |  ~ (left_apart_point(v5, v9) = v10) |  ~ (reverse_line(v8) = v11) |  ~ (reverse_line(v7) = v9) |  ? [v13] : ((v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v10 = 0 |  ~ (left_apart_point(v6, v9) = v10) |  ~ (left_apart_point(v5, v11) = v12) |  ~ (reverse_line(v8) = v11) |  ~ (reverse_line(v7) = v9) |  ? [v13] : ((v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v9) = v11) |  ~ (left_apart_point(v5, v9) = v10) |  ~ (reverse_line(v8) = v9) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v9) = v11) |  ~ (left_apart_point(v5, v9) = v10) |  ~ (reverse_line(v7) = v9) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v5, v8) = v9) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v5, v7) = v9) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v8) = v9) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v7) = v9) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v6, v8) = v9) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v6, v7) = v9) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (left_apart_point(v5, v8) = v9) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (left_apart_point(v5, v7) = v9) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v5, v8) = v9) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v10) = v11) |  ~ (left_apart_point(v5, v7) = v9) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v8) = v9) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (reverse_line(v7) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v7) = v9) |  ~ (left_apart_point(v5, v10) = v11) |  ~ (reverse_line(v8) = v10) |  ? [v12] :  ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v8) = v10) |  ~ (left_apart_point(v5, v8) = v9) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = 0) |  ~ (left_apart_point(v6, v7) = v10) |  ~ (left_apart_point(v5, v7) = v9) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v6, v8) = v10) |  ~ (left_apart_point(v6, v7) = v9) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_points(v5, v6) = 0) |  ~ (left_apart_point(v5, v8) = v10) |  ~ (left_apart_point(v5, v7) = v9) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v8) = v10) |  ~ (left_apart_point(v5, v7) = v9) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (left_apart_point(v6, v7) = v9) |  ~ (left_apart_point(v5, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v8 = 0 |  ~ (distinct_lines(v6, v7) = v8) |  ~ (left_apart_point(v5, v9) = v10) |  ~ (reverse_line(v7) = v9) |  ? [v11] : (( ~ (v11 = 0) & left_apart_point(v5, v6) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v6 = v5 |  ~ (between_on_line(v10, v9, v8, v7) = v6) |  ~ (between_on_line(v10, v9, v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ (unequally_directed_lines(v6, v9) = v10) |  ~ (unequally_directed_lines(v5, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v5, v9) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ (unequally_directed_lines(v5, v9) = v10) |  ~ (unequally_directed_lines(v5, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v7) = v9) |  ~ (unequally_directed_lines(v6, v9) = v10) |  ~ (unequally_directed_lines(v5, v7) = v8) |  ? [v11] :  ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v8 = 0 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v7) = v8) |  ~ (unequally_directed_lines(v6, v8) = v10) |  ~ (unequally_directed_lines(v5, v8) = v9) |  ? [v11] :  ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v7) = v8) |  ~ (unequally_directed_lines(v6, v7) = v10) |  ~ (unequally_directed_lines(v5, v8) = v9) |  ? [v11] :  ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (distinct_lines(v6, v7) = v9) |  ~ (distinct_lines(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (distinct_points(v6, v7) = v9) |  ~ (distinct_points(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (distinct_points(v5, v6) = v8) |  ~ (left_apart_point(v6, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (left_convergent_lines(v5, v7) = v9) |  ~ (unequally_directed_lines(v6, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & left_convergent_lines(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (unequally_directed_lines(v6, v7) = v9) |  ~ (unequally_directed_lines(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (between_on_line(v5, v6, v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v8, v7) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v7, v6) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (between_on_line(v5, v6, v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v7, v8) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (line_connecting(v5, v6) = v8) |  ~ (left_convergent_lines(v8, v7) = v9) |  ? [v10] : ((v10 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v5, v6) = v10) | ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (left_apart_point(v5, v8) = v9) |  ~ (left_apart_point(v5, v6) = 0) |  ~ (reverse_line(v7) = v8) |  ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v7) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (left_apart_point(v5, v8) = v9) |  ~ (reverse_line(v7) = v8) |  ~ (unequally_directed_lines(v6, v7) = 0) |  ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & left_apart_point(v5, v6) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v6 = v5 |  ~ (before_on_line(v9, v8, v7) = v6) |  ~ (before_on_line(v9, v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v6 = v5 |  ~ (divides_points(v9, v8, v7) = v6) |  ~ (divides_points(v9, v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v6, v7) = v8) |  ~ (equally_directed_lines(v5, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v8) |  ~ (unequally_directed_lines(v6, v8) = v9) |  ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v8) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v8) |  ~ (unequally_directed_lines(v5, v8) = v9) |  ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v6) = v8) |  ~ (unequally_directed_lines(v6, v7) = v9) |  ~ (unequally_directed_lines(v5, v8) = 0) |  ? [v10] :  ? [v11] :  ? [v12] : ((v12 = 0 & v10 = 0 & reverse_line(v7) = v11 & unequally_directed_lines(v5, v11) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v6) = v8) |  ~ (unequally_directed_lines(v5, v8) = 0) |  ~ (unequally_directed_lines(v5, v7) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unequally_directed_lines(v6, v7) = v9) |  ~ (unequally_directed_lines(v5, v7) = v8) |  ? [v10] :  ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | (v11 = 0 & v8 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_lines(v6, v7) = v8) |  ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_lines(v6, v7) = v8) |  ~ (left_apart_point(v5, v6) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_lines(v5, v7) = v8) |  ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (before_on_line(v5, v6, v7) = v8) |  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & line_connecting(v6, v7) = v9 & equally_directed_lines(v5, v9) = v10) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_points(v6, v7) = v8) |  ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_points(v5, v7) = v8) |  ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (distinct_points(v5, v6) = v8) |  ~ (left_apart_point(v5, v7) = 0) | left_apart_point(v6, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (divides_points(v7, v5, v6) = v8) |  ? [v9] : (( ~ (v9 = 0) & left_apart_point(v6, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v5, v7) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (divides_points(v7, v5, v6) = v8) |  ? [v9] : (( ~ (v9 = 0) & left_apart_point(v5, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v6, v7) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_convergent_lines(v5, v7) = v8) |  ~ (left_convergent_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_convergent_lines(v5, v7) = v8) |  ~ (reverse_line(v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & right_convergent_lines(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_convergent_lines(v5, v7) = v8) |  ~ (reverse_line(v6) = v7) |  ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v6) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_convergent_lines(v5, v6) = 0) |  ~ (unequally_directed_lines(v6, v7) = v8) | left_convergent_lines(v5, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_apart_point(v6, v7) = v8) |  ~ (left_apart_point(v5, v7) = 0) | distinct_points(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (left_apart_point(v5, v7) = v8) |  ~ (reverse_line(v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & right_apart_point(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = v8) | unequally_directed_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & unequally_directed_opposite_lines(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unequally_directed_lines(v6, v7) = v8) |  ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v5, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unequally_directed_lines(v5, v7) = v8) |  ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (parallel_through_point(v8, v7) = v6) |  ~ (parallel_through_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection_point(v8, v7) = v6) |  ~ (intersection_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (distinct_lines(v8, v7) = v6) |  ~ (distinct_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (line_connecting(v8, v7) = v6) |  ~ (line_connecting(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (distinct_points(v8, v7) = v6) |  ~ (distinct_points(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (incident_point_and_line(v8, v7) = v6) |  ~ (incident_point_and_line(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (convergent_lines(v8, v7) = v6) |  ~ (convergent_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (apart_point_and_line(v8, v7) = v6) |  ~ (apart_point_and_line(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (equally_directed_opposite_lines(v8, v7) = v6) |  ~ (equally_directed_opposite_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (equally_directed_lines(v8, v7) = v6) |  ~ (equally_directed_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (left_convergent_lines(v8, v7) = v6) |  ~ (left_convergent_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (right_convergent_lines(v8, v7) = v6) |  ~ (right_convergent_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (left_apart_point(v8, v7) = v6) |  ~ (left_apart_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (right_apart_point(v8, v7) = v6) |  ~ (right_apart_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (unequally_directed_lines(v8, v7) = v6) |  ~ (unequally_directed_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (unequally_directed_opposite_lines(v8, v7) = v6) |  ~ (unequally_directed_opposite_lines(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) |  ~ (distinct_points(v5, v6) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v7) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | (v9 = 0 & left_apart_point(v6, v8) = 0) | (v9 = 0 & left_apart_point(v6, v7) = 0) | (v9 = 0 & left_apart_point(v5, v8) = 0) | (v9 = 0 & left_apart_point(v5, v7) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (between_on_line(v5, v6, v7, v8) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & v9 = 0 & before_on_line(v5, v8, v7) = 0 & before_on_line(v5, v7, v6) = 0) | (v10 = 0 & v9 = 0 & before_on_line(v5, v7, v8) = 0 & before_on_line(v5, v6, v7) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ (equally_directed_lines(v5, v8) = 0) |  ? [v9] : ((v9 = 0 & before_on_line(v5, v6, v7) = 0) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unequally_directed_lines(v6, v7) = v8) |  ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unequally_directed_lines(v5, v7) = v8) |  ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v9] :  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (convergent_lines(v5, v6) = v7) |  ? [v8] : (( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8) | ( ~ (v8 = 0) & unequally_directed_opposite_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) &  ~ (v8 = 0) & left_apart_point(v5, v6) = v8 & right_apart_point(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (equally_directed_opposite_lines(v5, v6) = v7) | unequally_directed_opposite_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (equally_directed_lines(v5, v6) = v7) | unequally_directed_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (left_convergent_lines(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v8) = 0 & reverse_line(v6) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (right_convergent_lines(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & left_convergent_lines(v5, v8) = v9 & reverse_line(v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (left_apart_point(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & right_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (right_apart_point(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & left_apart_point(v5, v8) = v9 & reverse_line(v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (right_apart_point(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & left_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unequally_directed_lines(v5, v6) = v7) | equally_directed_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unequally_directed_lines(v5, v6) = v7) |  ? [v8] : (reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unequally_directed_opposite_lines(v5, v6) = v7) | equally_directed_opposite_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (unequally_directed_opposite_lines(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (point(v7) = v6) |  ~ (point(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (line(v7) = v6) |  ~ (line(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (reverse_line(v7) = v6) |  ~ (reverse_line(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | equally_directed_lines(v7, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) |  ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection_point(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v8 = 0 & point(v7) = 0) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection_point(v5, v6) = v7) |  ? [v8] :  ? [v9] : (( ~ (v9 = 0) &  ~ (v8 = 0) & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v6, v5) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : ((v10 = 0 & line_connecting(v5, v6) = v8 & equally_directed_lines(v8, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : ((v10 = 0 & line_connecting(v6, v5) = v8 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ? [v8] :  ? [v9] : (( ~ (v9 = 0) &  ~ (v8 = 0) & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & point(v5) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (before_on_line(v5, v6, v7) = 0) |  ? [v8] : (line_connecting(v6, v7) = v8 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0 & equally_directed_lines(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (divides_points(v7, v5, v6) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & left_apart_point(v6, v7) = 0 & right_apart_point(v5, v7) = 0) | (v9 = 0 & v8 = 0 & left_apart_point(v5, v7) = 0 & right_apart_point(v6, v7) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) |  ~ (reverse_line(v6) = v7) | right_convergent_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) |  ~ (reverse_line(v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) |  ~ (reverse_line(v6) = v7) | right_apart_point(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) |  ~ (reverse_line(v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_apart_point(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) &  ~ (v7 = 0) & right_apart_point(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (left_apart_point(v5, v6) = 0) |  ~ (unequally_directed_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & left_apart_point(v5, v8) = 0 & reverse_line(v7) = v8) | (v8 = 0 & distinct_lines(v6, v7) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (right_apart_point(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) &  ~ (v7 = 0) & left_apart_point(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = 0) | unequally_directed_opposite_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = 0) |  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) &  ~ (v9 = 0) & intersection_point(v5, v6) = v8 & apart_point_and_line(v8, v6) = v10 & apart_point_and_line(v8, v5) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & intersection_point(v5, v6) = v8 & point(v8) = 0) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ (unequally_directed_lines(v5, v7) = 0) |  ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0) | (v8 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unequally_directed_lines(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_opposite_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unequally_directed_opposite_lines(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (equally_directed_lines(v5, v5) = v6)) &  ! [v5] :  ! [v6] : ( ~ (distinct_points(v5, v6) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v9 = 0) &  ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8)) &  ! [v5] :  ! [v6] : ( ~ (distinct_points(v5, v6) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : (line_connecting(v6, v5) = v8 & line_connecting(v5, v6) = v7 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9)) &  ! [v5] :  ! [v6] : ( ~ (distinct_points(v5, v6) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & line(v7) = 0 & line_connecting(v5, v6) = v7) | ( ~ (v7 = 0) & point(v6) = v7) | ( ~ (v7 = 0) & point(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | (unequally_directed_lines(v5, v6) = 0 & unequally_directed_opposite_lines(v5, v6) = 0)) &  ! [v5] :  ! [v6] : ( ~ (apart_point_and_line(v5, v6) = 0) |  ? [v7] : ((v7 = 0 & left_apart_point(v5, v6) = 0) | (v7 = 0 & right_apart_point(v5, v6) = 0))) &  ! [v5] :  ! [v6] : ( ~ (equally_directed_opposite_lines(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (equally_directed_lines(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ~ (left_convergent_lines(v5, v6) = 0) &  ! [v5] :  ! [v6] : ( ~ (right_convergent_lines(v5, v6) = 0) |  ? [v7] : (left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7)) &  ! [v5] :  ! [v6] :  ~ (left_apart_point(v5, v6) = 0) &  ! [v5] :  ! [v6] : ( ~ (right_apart_point(v5, v6) = 0) |  ? [v7] : (left_apart_point(v5, v7) = 0 & reverse_line(v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & distinct_lines(v5, v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & line(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : (( ~ (v9 = 0) &  ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & intersection_point(v5, v6) = v7 & point(v7) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8) | ( ~ (v7 = 0) & line(v6) = v7) | ( ~ (v7 = 0) & line(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7) | (v7 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & equally_directed_lines(v5, v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) |  ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7))) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & equally_directed_opposite_lines(v5, v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) |  ? [v7] : (reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = 0)) &  ! [v5] :  ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) |  ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7))) &  ! [v5] : ( ~ (line(v5) = 0) |  ? [v6] : (line(v6) = 0 & reverse_line(v5) = v6)) &  ! [v5] :  ~ (distinct_lines(v5, v5) = 0) &  ! [v5] :  ~ (distinct_points(v5, v5) = 0) &  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : between_on_line(v8, v7, v6, v5) = v9 &  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : before_on_line(v7, v6, v5) = v8 &  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : divides_points(v7, v6, v5) = v8 &  ? [v5] :  ? [v6] :  ? [v7] : parallel_through_point(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : intersection_point(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : distinct_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : line_connecting(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : distinct_points(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : incident_point_and_line(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : convergent_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : apart_point_and_line(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : equally_directed_opposite_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : equally_directed_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : left_convergent_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : right_convergent_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : left_apart_point(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : right_apart_point(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : unequally_directed_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : unequally_directed_opposite_lines(v6, v5) = v7 &  ? [v5] :  ? [v6] : point(v5) = v6 &  ? [v5] :  ? [v6] : line(v5) = v6 &  ? [v5] :  ? [v6] : reverse_line(v5) = v6)
% 9.12/2.74  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 9.12/2.74  | (1)  ~ (all_0_0_0 = 0) & parallel_through_point(all_0_2_2, all_0_4_4) = all_0_1_1 & right_apart_point(all_0_3_3, all_0_1_1) = 0 & right_apart_point(all_0_3_3, all_0_2_2) = all_0_0_0 & right_apart_point(all_0_4_4, all_0_2_2) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v6) = v7) |  ~ (left_apart_point(v1, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v6) = v7) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (left_apart_point(v1, v6) = v7) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (left_apart_point(v1, v4) = v5) |  ~ (left_apart_point(v0, v6) = v7) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v4) = v6) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v4) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v4) = v6) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v2) = v4) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v3) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v1, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v1, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v3) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v2) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v1, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v3) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v3) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v2) = v4) |  ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (between_on_line(v5, v4, v3, v2) = v1) |  ~ (between_on_line(v5, v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v1, v4) = v5) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v0, v4) = v5) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (unequally_directed_lines(v1, v4) = v5) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v3) = v5) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v2) = v5) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v0, v1) = v3) |  ~ (left_apart_point(v1, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v4) |  ~ (unequally_directed_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (between_on_line(v0, v1, v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (between_on_line(v0, v1, v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (line_connecting(v0, v1) = v3) |  ~ (left_convergent_lines(v3, v2) = v4) |  ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (left_apart_point(v0, v3) = v4) |  ~ (left_apart_point(v0, v1) = 0) |  ~ (reverse_line(v2) = v3) |  ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v2) = 0) |  ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (before_on_line(v4, v3, v2) = v1) |  ~ (before_on_line(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (divides_points(v4, v3, v2) = v1) |  ~ (divides_points(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v3) |  ~ (equally_directed_lines(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v3) = v4) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ~ (unequally_directed_lines(v0, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (left_apart_point(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (before_on_line(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v1) = v3) |  ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (divides_points(v2, v0, v1) = v3) |  ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (divides_points(v2, v0, v1) = v3) |  ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v1) = 0) |  ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_apart_point(v1, v2) = v3) |  ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_apart_point(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unequally_directed_lines(v0, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equally_directed_opposite_lines(v3, v2) = v1) |  ~ (equally_directed_opposite_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equally_directed_lines(v3, v2) = v1) |  ~ (equally_directed_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (left_convergent_lines(v3, v2) = v1) |  ~ (left_convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (right_convergent_lines(v3, v2) = v1) |  ~ (right_convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (left_apart_point(v3, v2) = v1) |  ~ (left_apart_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (right_apart_point(v3, v2) = v1) |  ~ (right_apart_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unequally_directed_lines(v3, v2) = v1) |  ~ (unequally_directed_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unequally_directed_opposite_lines(v3, v2) = v1) |  ~ (unequally_directed_opposite_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ (equally_directed_lines(v0, v3) = 0) |  ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) &  ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (left_convergent_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_convergent_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (left_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_apart_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) = v2) |  ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_opposite_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) |  ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) |  ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) |  ~ (reverse_line(v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) |  ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) |  ~ (reverse_line(v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) &  ~ (v2 = 0) & right_apart_point(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) |  ~ (unequally_directed_lines(v1, v2) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) &  ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ (v5 = 0) &  ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (equally_directed_lines(v0, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) &  ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) &  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0))) &  ! [v0] :  ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ~ (left_convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) |  ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) &  ! [v0] :  ! [v1] :  ~ (left_apart_point(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) |  ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))) &  ! [v0] : ( ~ (line(v0) = 0) |  ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : between_on_line(v3, v2, v1, v0) = v4 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : before_on_line(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : divides_points(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equally_directed_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : left_convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : right_convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : left_apart_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : right_apart_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unequally_directed_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] : point(v0) = v1 &  ? [v0] :  ? [v1] : line(v0) = v1 &  ? [v0] :  ? [v1] : reverse_line(v0) = v1
% 9.12/2.77  |
% 9.12/2.77  | Applying alpha-rule on (1) yields:
% 9.12/2.77  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 9.12/2.77  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v1, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.12/2.78  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.12/2.78  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) &  ~ (v2 = 0) & left_apart_point(v0, v1) = v3)))
% 9.12/2.78  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) &  ~ (v2 = 0) & right_apart_point(v0, v1) = v3)))
% 9.12/2.78  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.12/2.78  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v3) = v4) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 9.12/2.78  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 9.12/2.78  | (10)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2)))
% 9.12/2.78  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.12/2.78  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0)))
% 9.12/2.78  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0)
% 9.12/2.78  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3)))
% 9.12/2.78  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v3) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.12/2.78  | (16)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0))
% 9.12/2.78  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v2) = v5) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.12/2.78  | (18)  ? [v0] :  ? [v1] :  ? [v2] : left_convergent_lines(v1, v0) = v2
% 9.12/2.78  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (right_apart_point(v3, v2) = v1) |  ~ (right_apart_point(v3, v2) = v0))
% 9.12/2.78  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 9.12/2.78  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.12/2.78  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v3) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.12/2.78  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unequally_directed_lines(v0, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.12/2.78  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (divides_points(v2, v0, v1) = v3) |  ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4)))
% 9.12/2.78  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v1, v4) = v5) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.12/2.78  | (26)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 9.12/2.78  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) |  ~ (reverse_line(v1) = v2))
% 9.12/2.78  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0)
% 9.12/2.78  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0)
% 9.12/2.78  | (30)  ? [v0] :  ? [v1] :  ? [v2] : right_convergent_lines(v1, v0) = v2
% 9.12/2.78  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v4) = v6) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v4) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.12/2.78  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v1) = 0) |  ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0)
% 9.12/2.78  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (left_apart_point(v0, v3) = v4) |  ~ (left_apart_point(v0, v1) = 0) |  ~ (reverse_line(v2) = v3) |  ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5)))
% 9.12/2.78  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 9.12/2.79  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 9.12/2.79  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (left_apart_point(v1, v4) = v5) |  ~ (left_apart_point(v0, v6) = v7) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 9.12/2.79  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 9.12/2.79  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v1, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 9.54/2.79  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v3) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.54/2.79  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (divides_points(v2, v0, v1) = v3) |  ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4)))
% 9.54/2.79  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.54/2.79  | (42)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (left_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 9.54/2.79  | (43)  ? [v0] :  ? [v1] :  ? [v2] : unequally_directed_lines(v1, v0) = v2
% 9.54/2.79  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.54/2.79  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v4) |  ~ (unequally_directed_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5))
% 9.54/2.79  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0)
% 9.54/2.79  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 9.54/2.79  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4))
% 9.54/2.79  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 9.54/2.79  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.54/2.79  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v1 = v0 |  ~ (between_on_line(v5, v4, v3, v2) = v1) |  ~ (between_on_line(v5, v4, v3, v2) = v0))
% 9.54/2.79  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.54/2.79  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.54/2.79  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v3) |  ~ (equally_directed_lines(v0, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 9.54/2.79  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v1, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.54/2.79  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6)))
% 9.54/2.79  | (57)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.54/2.79  | (58)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.54/2.79  | (59)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 9.54/2.79  | (60)  ? [v0] :  ? [v1] : reverse_line(v0) = v1
% 9.54/2.79  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (divides_points(v4, v3, v2) = v1) |  ~ (divides_points(v4, v3, v2) = v0))
% 9.54/2.79  | (62)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2))
% 9.54/2.79  | (63)  ! [v0] :  ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))
% 9.54/2.79  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4)))
% 9.54/2.79  | (65)  ? [v0] :  ? [v1] :  ? [v2] : left_apart_point(v1, v0) = v2
% 9.54/2.79  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (left_apart_point(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4)))
% 9.54/2.79  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0)
% 9.54/2.79  | (68)  ? [v0] :  ? [v1] :  ? [v2] : equally_directed_opposite_lines(v1, v0) = v2
% 9.54/2.80  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.54/2.80  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_apart_point(v1, v2) = v3) |  ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0)
% 9.54/2.80  | (71)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) |  ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0)
% 9.54/2.80  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 9.54/2.80  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equally_directed_lines(v3, v2) = v1) |  ~ (equally_directed_lines(v3, v2) = v0))
% 9.54/2.80  | (74)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_apart_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3))
% 9.54/2.80  | (75)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 9.54/2.80  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equally_directed_opposite_lines(v3, v2) = v1) |  ~ (equally_directed_opposite_lines(v3, v2) = v0))
% 9.54/2.80  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (unequally_directed_lines(v1, v4) = v5) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.54/2.80  | (78)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : between_on_line(v3, v2, v1, v0) = v4
% 9.54/2.80  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.54/2.80  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (before_on_line(v0, v1, v2) = v3) |  ? [v4] :  ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 9.54/2.80  | (81)  ? [v0] :  ? [v1] : point(v0) = v1
% 9.54/2.80  | (82)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_opposite_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4))
% 9.54/2.80  | (83)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) &  ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4))
% 9.54/2.80  | (84)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.54/2.80  | (85)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : divides_points(v2, v1, v0) = v3
% 9.54/2.80  | (86)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_lines(v0, v1) = v2) |  ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0))
% 9.54/2.80  | (87)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 9.54/2.80  | (88)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0))
% 9.54/2.80  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.54/2.80  | (90)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v1) = v3) |  ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0)
% 9.54/2.80  | (91)  ? [v0] :  ? [v1] :  ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2
% 9.54/2.80  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.54/2.80  | (93)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (left_convergent_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.54/2.80  | (94)  ! [v0] :  ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) |  ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.54/2.80  | (95)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 9.54/2.80  | (96)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 9.54/2.80  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 9.54/2.80  | (98)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ (equally_directed_lines(v0, v3) = 0) |  ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4)))
% 9.54/2.80  | (99)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (line_connecting(v0, v1) = v3) |  ~ (left_convergent_lines(v3, v2) = v4) |  ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)))
% 9.54/2.80  | (100)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.54/2.80  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v0, v4) = v5) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.54/2.80  | (102)  ? [v0] :  ? [v1] : line(v0) = v1
% 9.54/2.80  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0)))
% 9.54/2.80  | (104)  ~ (all_0_0_0 = 0)
% 9.54/2.80  | (105)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3)))
% 9.54/2.80  | (106)  ? [v0] :  ? [v1] :  ? [v2] : right_apart_point(v1, v0) = v2
% 9.54/2.80  | (107)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4))
% 9.54/2.81  | (108) right_apart_point(all_0_4_4, all_0_2_2) = 0
% 9.54/2.81  | (109)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 9.54/2.81  | (110)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 9.54/2.81  | (111)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (equally_directed_lines(v0, v0) = v1))
% 9.54/2.81  | (112)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 9.54/2.81  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 9.54/2.81  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.54/2.81  | (115)  ? [v0] :  ? [v1] :  ? [v2] : equally_directed_lines(v1, v0) = v2
% 9.54/2.81  | (116)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_apart_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3)))
% 9.54/2.81  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.54/2.81  | (118)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : before_on_line(v2, v1, v0) = v3
% 9.54/2.81  | (119)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)))
% 9.54/2.81  | (120)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)))
% 9.54/2.81  | (121)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0)))
% 9.54/2.81  | (122)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (left_convergent_lines(v3, v2) = v1) |  ~ (left_convergent_lines(v3, v2) = v0))
% 9.54/2.81  | (123)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (right_convergent_lines(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3))
% 9.54/2.81  | (124)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 9.54/2.81  | (125)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_convergent_lines(v0, v2) = v3) |  ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0)
% 9.54/2.81  | (126)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = 0) |  ? [v3] :  ? [v4] :  ? [v5] : (( ~ (v5 = 0) &  ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.54/2.81  | (127)  ! [v0] :  ! [v1] :  ~ (left_convergent_lines(v0, v1) = 0)
% 9.54/2.81  | (128)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v2) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.54/2.81  | (129)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 9.54/2.81  | (130)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0)
% 9.54/2.81  | (131)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0)
% 9.54/2.81  | (132)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (left_apart_point(v3, v2) = v1) |  ~ (left_apart_point(v3, v2) = v0))
% 9.54/2.81  | (133)  ! [v0] :  ! [v1] :  ~ (left_apart_point(v0, v1) = 0)
% 9.54/2.81  | (134)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 9.54/2.81  | (135)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unequally_directed_opposite_lines(v3, v2) = v1) |  ~ (unequally_directed_opposite_lines(v3, v2) = v0))
% 9.54/2.81  | (136)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 9.54/2.81  | (137)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v5) = v6) |  ~ (left_apart_point(v0, v2) = v4) |  ~ (reverse_line(v3) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.54/2.81  | (138)  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2
% 9.54/2.81  | (139)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 9.54/2.81  | (140)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.54/2.81  | (141)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)))
% 9.54/2.81  | (142)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v0, v1) = v3) |  ~ (left_apart_point(v1, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))
% 9.54/2.81  | (143)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))
% 9.54/2.81  | (144)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 9.54/2.81  | (145)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0)))
% 9.54/2.81  | (146)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (left_apart_point(v0, v2) = v3) |  ~ (reverse_line(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4))
% 9.54/2.81  | (147)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) |  ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0))
% 9.64/2.82  | (148)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v3) = v5) |  ~ (unequally_directed_lines(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6)))
% 9.64/2.82  | (149)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ~ (unequally_directed_lines(v0, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.64/2.82  | (150)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 9.64/2.82  | (151)  ! [v0] :  ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2))
% 9.64/2.82  | (152)  ! [v0] :  ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))
% 9.64/2.82  | (153)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (between_on_line(v0, v1, v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))
% 9.64/2.82  | (154)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (between_on_line(v0, v1, v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5)))
% 9.64/2.82  | (155)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v0, v6) = v7) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 9.64/2.82  | (156)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (before_on_line(v4, v3, v2) = v1) |  ~ (before_on_line(v4, v3, v2) = v0))
% 9.64/2.82  | (157) right_apart_point(all_0_3_3, all_0_2_2) = all_0_0_0
% 9.64/2.82  | (158)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (left_apart_point(v1, v6) = v7) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8)))
% 9.64/2.82  | (159)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) |  ~ (unequally_directed_lines(v1, v2) = 0) |  ? [v3] :  ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0)))
% 9.64/2.82  | (160)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unequally_directed_lines(v3, v2) = v1) |  ~ (unequally_directed_lines(v3, v2) = v0))
% 9.64/2.82  | (161)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) |  ~ (unequally_directed_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5)))
% 9.64/2.82  | (162)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 9.64/2.82  | (163)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v4) = v6) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v2) = v4) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.64/2.82  | (164)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v2) = v5) |  ~ (left_apart_point(v0, v2) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.64/2.82  | (165)  ! [v0] : ( ~ (line(v0) = 0) |  ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1))
% 9.64/2.82  | (166) right_apart_point(all_0_3_3, all_0_1_1) = 0
% 9.64/2.82  | (167)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (left_apart_point(v0, v4) = v5) |  ~ (reverse_line(v2) = v4) |  ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6)))
% 9.64/2.82  | (168)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (right_convergent_lines(v3, v2) = v1) |  ~ (right_convergent_lines(v3, v2) = v0))
% 9.64/2.82  | (169)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v1) = v3) |  ~ (unequally_directed_lines(v1, v2) = v4) |  ~ (unequally_directed_lines(v0, v3) = 0) |  ? [v5] :  ? [v6] :  ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)))
% 9.64/2.82  | (170)  ! [v0] :  ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) |  ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2))
% 9.68/2.82  | (171)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v4 = 0 |  ~ (left_apart_point(v1, v3) = v4) |  ~ (left_apart_point(v0, v5) = v6) |  ~ (reverse_line(v2) = v5) |  ? [v7] :  ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7)))
% 9.68/2.82  | (172)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 9.68/2.82  | (173)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) |  ~ (reverse_line(v1) = v2))
% 9.68/2.82  | (174)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) |  ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0)
% 9.68/2.82  | (175)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v5 = 0 |  ~ (distinct_points(v0, v1) = 0) |  ~ (left_apart_point(v1, v6) = v7) |  ~ (left_apart_point(v1, v4) = v5) |  ~ (reverse_line(v3) = v6) |  ~ (reverse_line(v2) = v4) |  ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8)))
% 9.68/2.83  | (176)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.68/2.83  | (177)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (reverse_line(v1) = v2) |  ~ (unequally_directed_lines(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4))
% 9.68/2.83  | (178) parallel_through_point(all_0_2_2, all_0_4_4) = all_0_1_1
% 9.68/2.83  | (179)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (distinct_lines(v2, v3) = 0) |  ~ (left_apart_point(v1, v3) = v5) |  ~ (left_apart_point(v0, v3) = v4) |  ? [v6] :  ? [v7] : ((v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.68/2.83  | (180)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (left_apart_point(v0, v3) = v4) |  ~ (reverse_line(v2) = v3) |  ~ (unequally_directed_lines(v1, v2) = 0) |  ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5)))
% 9.68/2.83  | (181)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (( ~ (v4 = 0) &  ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3)))
% 9.68/2.83  | (182)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) &  ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3))
% 9.68/2.83  |
% 9.68/2.83  | Instantiating formula (170) with all_0_2_2, all_0_4_4 and discharging atoms right_apart_point(all_0_4_4, all_0_2_2) = 0, yields:
% 9.68/2.83  | (183)  ? [v0] : (left_apart_point(all_0_4_4, v0) = 0 & reverse_line(all_0_2_2) = v0)
% 9.68/2.83  |
% 9.68/2.83  | Instantiating (183) with all_54_0_73 yields:
% 9.68/2.83  | (184) left_apart_point(all_0_4_4, all_54_0_73) = 0 & reverse_line(all_0_2_2) = all_54_0_73
% 9.68/2.83  |
% 9.68/2.83  | Applying alpha-rule on (184) yields:
% 9.68/2.83  | (185) left_apart_point(all_0_4_4, all_54_0_73) = 0
% 9.68/2.83  | (186) reverse_line(all_0_2_2) = all_54_0_73
% 9.68/2.83  |
% 9.68/2.83  | Instantiating formula (27) with all_54_0_73, all_0_2_2, all_0_4_4 and discharging atoms left_apart_point(all_0_4_4, all_54_0_73) = 0, reverse_line(all_0_2_2) = all_54_0_73, yields:
% 9.68/2.83  | (187) $false
% 9.68/2.83  |
% 9.68/2.83  |-The branch is then unsatisfiable
% 9.68/2.83  % SZS output end Proof for theBenchmark
% 9.68/2.83  
% 9.68/2.83  2237ms
%------------------------------------------------------------------------------