%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO175+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 03:48:11 EDT 2022

% Result   : Theorem 21.34s 6.10s
% Output   : Proof 25.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO175+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n005.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 : Sat Jun 18 12:23:53 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.98  Prover 0: Preprocessing ...
% 2.45/1.20  Prover 0: Warning: ignoring some quantifiers
% 2.51/1.23  Prover 0: Constructing countermodel ...
% 18.41/5.47  Prover 0: gave up
% 18.41/5.47  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.50/5.51  Prover 1: Preprocessing ...
% 19.16/5.66  Prover 1: Constructing countermodel ...
% 19.53/5.70  Prover 1: gave up
% 19.53/5.70  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.53/5.73  Prover 2: Preprocessing ...
% 20.11/5.89  Prover 2: Warning: ignoring some quantifiers
% 20.49/5.90  Prover 2: Constructing countermodel ...
% 21.34/6.10  Prover 2: proved (400ms)
% 21.34/6.10  
% 21.34/6.10  No countermodel exists, formula is valid
% 21.34/6.10  % SZS status Theorem for theBenchmark
% 21.34/6.10  
% 21.34/6.10  Generating proof ... Warning: ignoring some quantifiers
% 25.32/7.05  found it (size 117)
% 25.32/7.05  
% 25.32/7.05  % SZS output start Proof for theBenchmark
% 25.32/7.06  Assumed formulas after preprocessing and simplification: 
% 25.32/7.06  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v0, v3) = v6 & apart_point_and_line(v0, v2) = v5 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v4) = 0 & distinct_points(v0, v1) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v9, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v9, v10) = v12) |  ~ (apart_point_and_line(v7, v8) = v11) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v8, v9) = v11) |  ~ (distinct_points(v7, v8) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v7, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v10) = v11) |  ~ (distinct_lines(v9, v10) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v9) = v12) |  ~ (apart_point_and_line(v7, v10) = v11) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v9) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v9, v10) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v7, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_points(v7, v8) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v9, v8) = v11) |  ~ (distinct_points(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (convergent_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (convergent_lines(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_lines(v8, v9) = v11) |  ~ (distinct_lines(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_points(v8, v9) = v11) |  ~ (distinct_points(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & distinct_points(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (unorthogonal_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v7, v9) = v11) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v7, v9) = v11) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v9, v8) = v10) |  ~ (apart_point_and_line(v7, v8) = 0) | distinct_points(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (apart_point_and_line(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v8) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v9) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = 0) |  ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = 0) |  ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v8) = 0) |  ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_lines(v8, v9) = v10) |  ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_lines(v7, v9) = v10) |  ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_points(v8, v9) = v10) |  ~ (distinct_points(v7, v8) = 0) | distinct_points(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_points(v7, v9) = v10) |  ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (orthogonal_lines(v10, v9) = v8) |  ~ (orthogonal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (incident_point_and_line(v10, v9) = v8) |  ~ (incident_point_and_line(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (parallel_lines(v10, v9) = v8) |  ~ (parallel_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (equal_lines(v10, v9) = v8) |  ~ (equal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (equal_points(v10, v9) = v8) |  ~ (equal_points(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (orthogonal_through_point(v10, v9) = v8) |  ~ (orthogonal_through_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unorthogonal_lines(v10, v9) = v8) |  ~ (unorthogonal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (parallel_through_point(v10, v9) = v8) |  ~ (parallel_through_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (intersection_point(v10, v9) = v8) |  ~ (intersection_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (line_connecting(v10, v9) = v8) |  ~ (line_connecting(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (apart_point_and_line(v10, v9) = v8) |  ~ (apart_point_and_line(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (convergent_lines(v10, v9) = v8) |  ~ (convergent_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (distinct_lines(v10, v9) = v8) |  ~ (distinct_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (distinct_points(v10, v9) = v8) |  ~ (distinct_points(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) |  ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (unorthogonal_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ~ (convergent_lines(v8, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) |  ~ (distinct_points(v7, v8) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v8, v10) = 0) | (v11 = 0 & apart_point_and_line(v8, v9) = 0) | (v11 = 0 & apart_point_and_line(v7, v10) = 0) | (v11 = 0 & apart_point_and_line(v7, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (orthogonal_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (incident_point_and_line(v7, v8) = v9) | apart_point_and_line(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (parallel_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equal_lines(v7, v8) = v9) | distinct_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equal_points(v7, v8) = v9) | distinct_points(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (unorthogonal_lines(v7, v8) = v9) | orthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (unorthogonal_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v7, v8) = v9) | incident_point_and_line(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) | parallel_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & distinct_lines(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v7, v8) = v9) | equal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v7, v8) = v9) | equal_points(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (point(v9) = v8) |  ~ (point(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (line(v9) = v8) |  ~ (line(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & unorthogonal_lines(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & convergent_lines(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & point(v9) = 0) | ( ~ (v10 = 0) & line(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v8) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & point(v7) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] : ( ~ (orthogonal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (incident_point_and_line(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (parallel_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (equal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (equal_points(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_points(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & orthogonal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (apart_point_and_line(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & incident_point_and_line(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v8) = v10)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v7) = v10)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & point(v9) = 0 & intersection_point(v7, v8) = v9) | ( ~ (v9 = 0) & line(v8) = v9) | ( ~ (v9 = 0) & line(v7) = v9))) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & parallel_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & equal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v8, v9) = v10)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & line(v9) = 0 & line_connecting(v7, v8) = v9) | ( ~ (v9 = 0) & point(v8) = v9) | ( ~ (v9 = 0) & point(v7) = v9))) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & equal_points(v7, v8) = v9)) &  ! [v7] :  ~ (convergent_lines(v7, v7) = 0) &  ! [v7] :  ~ (distinct_lines(v7, v7) = 0) &  ! [v7] :  ~ (distinct_points(v7, v7) = 0) &  ? [v7] :  ? [v8] :  ? [v9] : orthogonal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : incident_point_and_line(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : parallel_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : equal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : equal_points(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : orthogonal_through_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : unorthogonal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : parallel_through_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : intersection_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : line_connecting(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : apart_point_and_line(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : convergent_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : distinct_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : distinct_points(v8, v7) = v9 &  ? [v7] :  ? [v8] : point(v7) = v8 &  ? [v7] :  ? [v8] : line(v7) = v8)
% 25.79/7.12  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 25.79/7.12  | (1)  ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_0_2_2 & apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0 & apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1 & convergent_lines(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_6_6, all_0_2_2) = 0 & distinct_points(all_0_6_6, all_0_5_5) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(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 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(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 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [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] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) &  ! [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(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [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] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(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 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [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 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(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 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(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 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) &  ! [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] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) &  ! [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(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = 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] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(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] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [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] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2 &  ? [v0] :  ? [v1] : point(v0) = v1 &  ? [v0] :  ? [v1] : line(v0) = v1
% 25.79/7.14  |
% 25.79/7.14  | Applying alpha-rule on (1) yields:
% 25.79/7.14  | (2)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 25.79/7.14  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 25.79/7.14  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 25.79/7.14  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 25.79/7.14  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 25.79/7.15  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 25.79/7.15  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 25.79/7.15  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.79/7.15  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 25.79/7.15  | (11)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 25.79/7.15  | (12)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 25.79/7.15  | (13) distinct_points(all_0_6_6, all_0_5_5) = 0
% 25.79/7.15  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 25.79/7.15  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 25.79/7.15  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 25.79/7.15  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 25.79/7.15  | (18)  ~ (all_0_1_1 = 0)
% 25.79/7.15  | (19)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 25.79/7.15  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 25.79/7.15  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 25.79/7.15  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 25.79/7.15  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 25.79/7.15  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 25.79/7.15  | (25)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 25.79/7.15  | (26)  ! [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)))
% 25.79/7.15  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 25.79/7.15  | (28)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 25.79/7.15  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 25.79/7.15  | (30)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 25.79/7.15  | (31)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 25.79/7.15  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 25.79/7.15  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 25.79/7.15  | (34)  ! [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)))
% 25.79/7.15  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 25.79/7.15  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 25.79/7.15  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 25.79/7.15  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 25.79/7.15  | (39)  ! [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))
% 25.79/7.15  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 25.79/7.15  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 25.79/7.15  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.79/7.15  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 25.79/7.15  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 25.79/7.15  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 25.79/7.15  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 25.79/7.15  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 25.79/7.15  | (48)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 25.79/7.15  | (49)  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2
% 25.79/7.15  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 25.79/7.15  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 25.79/7.15  | (52)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 25.79/7.15  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 25.79/7.15  | (54)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 25.79/7.15  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 25.79/7.15  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 25.79/7.15  | (57)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 25.79/7.15  | (58)  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2
% 25.79/7.16  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 25.79/7.16  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 25.79/7.16  | (61)  ? [v0] :  ? [v1] : point(v0) = v1
% 25.79/7.16  | (62)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 25.79/7.16  | (63)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 25.79/7.16  | (64)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 25.79/7.16  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 25.79/7.16  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 25.79/7.16  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 25.79/7.16  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 25.79/7.16  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 25.79/7.16  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 25.79/7.16  | (71)  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2
% 25.79/7.16  | (72)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 25.79/7.16  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 25.79/7.16  | (74)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2
% 25.79/7.16  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 25.79/7.16  | (76)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 25.79/7.16  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 25.79/7.16  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 25.79/7.16  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 25.79/7.16  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 25.79/7.16  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 25.79/7.16  | (82)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 25.79/7.16  | (83)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 25.79/7.16  | (84)  ? [v0] :  ? [v1] : line(v0) = v1
% 25.79/7.16  | (85)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 25.79/7.16  | (86)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 25.79/7.16  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 25.79/7.16  | (88)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 25.79/7.16  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 25.79/7.16  | (90)  ! [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)))
% 25.79/7.16  | (91)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 25.79/7.16  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 25.79/7.16  | (93)  ! [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))
% 25.79/7.16  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 25.79/7.16  | (95) convergent_lines(all_0_4_4, all_0_3_3) = 0
% 25.79/7.16  | (96)  ~ (all_0_0_0 = 0)
% 25.79/7.16  | (97)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 25.79/7.16  | (98)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 25.79/7.16  | (99)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 25.79/7.16  | (100)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 25.79/7.16  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 25.79/7.16  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 25.79/7.16  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 25.79/7.16  | (104)  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2
% 25.79/7.16  | (105)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 25.79/7.16  | (106)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 25.79/7.16  | (107)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 25.79/7.16  | (108)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 25.79/7.16  | (109)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 25.79/7.16  | (110)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 25.79/7.16  | (111)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 25.79/7.16  | (112)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 25.79/7.17  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 25.79/7.17  | (114)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 25.79/7.17  | (115)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 25.79/7.17  | (116) distinct_points(all_0_6_6, all_0_2_2) = 0
% 25.79/7.17  | (117)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 25.79/7.17  | (118)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 25.79/7.17  | (119)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.79/7.17  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 25.79/7.17  | (121)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 25.79/7.17  | (122)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 25.79/7.17  | (123)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 25.79/7.17  | (124)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 25.79/7.17  | (125)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 25.79/7.17  | (126) intersection_point(all_0_4_4, all_0_3_3) = all_0_2_2
% 25.79/7.17  | (127)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 25.79/7.17  | (128)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 25.79/7.17  | (129)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 25.79/7.17  | (130)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 25.79/7.17  | (131)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 25.79/7.17  | (132)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 25.79/7.17  | (133)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 25.79/7.17  | (134)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 25.79/7.17  | (135)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 25.79/7.17  | (136)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 25.79/7.17  | (137)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 25.79/7.17  | (138)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 25.79/7.17  | (139)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 25.79/7.17  | (140)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 25.79/7.17  | (141)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 25.79/7.17  | (142)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 25.79/7.17  | (143)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 25.79/7.17  | (144) apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1
% 25.79/7.17  | (145) apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0
% 25.79/7.17  | (146)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 25.79/7.17  | (147)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (114) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 25.79/7.17  | (148)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (20) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 25.79/7.17  | (149)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (133) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, yields:
% 25.79/7.17  | (150) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (70) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, yields:
% 25.79/7.17  | (151) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (133) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (152) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (133) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (153) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (70) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (154) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (70) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (155) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (133) with all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (156) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (70) with all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 25.79/7.17  | (157) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, distinct_points(all_0_6_6, all_0_2_2) = 0, yields:
% 25.79/7.17  | (158) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, distinct_points(all_0_6_6, all_0_2_2) = 0, yields:
% 25.79/7.17  | (159) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_1_1, all_0_0_0, all_0_4_4, all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, distinct_points(all_0_6_6, all_0_2_2) = 0, yields:
% 25.79/7.17  | (160) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, distinct_points(all_0_6_6, all_0_2_2) = 0, yields:
% 25.79/7.17  | (161) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 25.79/7.17  | (162) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.17  |
% 25.79/7.17  | Instantiating formula (86) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 25.79/7.18  | (163) all_0_0_0 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  |
% 25.79/7.18  | Instantiating formula (86) with all_0_1_1, all_0_1_1, all_0_4_4, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_4_4) = all_0_1_1, distinct_points(all_0_6_6, all_0_5_5) = 0, yields:
% 25.79/7.18  | (164) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.18  |
% 25.79/7.18  | Instantiating (149) with all_65_0_80 yields:
% 25.79/7.18  | (165) ( ~ (all_65_0_80 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_65_0_80) | ( ~ (all_65_0_80 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_65_0_80)
% 25.79/7.18  |
% 25.79/7.18  | Instantiating (148) with all_66_0_81 yields:
% 25.79/7.18  | (166) ( ~ (all_66_0_81 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = all_66_0_81) | ( ~ (all_66_0_81 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_66_0_81)
% 25.79/7.18  |
% 25.79/7.18  +-Applying beta-rule and splitting (166), into two cases.
% 25.79/7.18  |-Branch one:
% 25.79/7.18  | (167)  ~ (all_66_0_81 = 0) & apart_point_and_line(all_0_2_2, all_0_3_3) = all_66_0_81
% 25.79/7.18  |
% 25.79/7.18  	| Applying alpha-rule on (167) yields:
% 25.79/7.18  	| (168)  ~ (all_66_0_81 = 0)
% 25.79/7.18  	| (169) apart_point_and_line(all_0_2_2, all_0_3_3) = all_66_0_81
% 25.79/7.18  	|
% 25.79/7.18  	+-Applying beta-rule and splitting (165), into two cases.
% 25.79/7.18  	|-Branch one:
% 25.79/7.18  	| (170)  ~ (all_65_0_80 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_65_0_80
% 25.79/7.18  	|
% 25.79/7.18  		| Applying alpha-rule on (170) yields:
% 25.79/7.18  		| (171)  ~ (all_65_0_80 = 0)
% 25.79/7.18  		| (172) apart_point_and_line(all_0_2_2, all_0_4_4) = all_65_0_80
% 25.79/7.18  		|
% 25.79/7.18  		+-Applying beta-rule and splitting (150), into two cases.
% 25.79/7.18  		|-Branch one:
% 25.79/7.18  		| (173) all_0_0_0 = 0
% 25.79/7.18  		|
% 25.79/7.18  			| Equations (173) can reduce 96 to:
% 25.79/7.18  			| (174) $false
% 25.79/7.18  			|
% 25.79/7.18  			|-The branch is then unsatisfiable
% 25.79/7.18  		|-Branch two:
% 25.79/7.18  		| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  		| (176)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.18  		|
% 25.79/7.18  			+-Applying beta-rule and splitting (156), into two cases.
% 25.79/7.18  			|-Branch one:
% 25.79/7.18  			| (177) all_0_1_1 = 0
% 25.79/7.18  			|
% 25.79/7.18  				| Equations (177) can reduce 18 to:
% 25.79/7.18  				| (174) $false
% 25.79/7.18  				|
% 25.79/7.18  				|-The branch is then unsatisfiable
% 25.79/7.18  			|-Branch two:
% 25.79/7.18  			| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  			| (180)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.18  			|
% 25.79/7.18  				+-Applying beta-rule and splitting (158), into two cases.
% 25.79/7.18  				|-Branch one:
% 25.79/7.18  				| (173) all_0_0_0 = 0
% 25.79/7.18  				|
% 25.79/7.18  					| Equations (173) can reduce 96 to:
% 25.79/7.18  					| (174) $false
% 25.79/7.18  					|
% 25.79/7.18  					|-The branch is then unsatisfiable
% 25.79/7.18  				|-Branch two:
% 25.79/7.18  				| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  				| (184)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.18  				|
% 25.79/7.18  					+-Applying beta-rule and splitting (155), into two cases.
% 25.79/7.18  					|-Branch one:
% 25.79/7.18  					| (173) all_0_0_0 = 0
% 25.79/7.18  					|
% 25.79/7.18  						| Equations (173) can reduce 96 to:
% 25.79/7.18  						| (174) $false
% 25.79/7.18  						|
% 25.79/7.18  						|-The branch is then unsatisfiable
% 25.79/7.18  					|-Branch two:
% 25.79/7.18  					| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  					| (188) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  					|
% 25.79/7.18  						+-Applying beta-rule and splitting (154), into two cases.
% 25.79/7.18  						|-Branch one:
% 25.79/7.18  						| (173) all_0_0_0 = 0
% 25.79/7.18  						|
% 25.79/7.18  							| Equations (173) can reduce 96 to:
% 25.79/7.18  							| (174) $false
% 25.79/7.18  							|
% 25.79/7.18  							|-The branch is then unsatisfiable
% 25.79/7.18  						|-Branch two:
% 25.79/7.18  						| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  						| (192) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  						|
% 25.79/7.18  							+-Applying beta-rule and splitting (188), into two cases.
% 25.79/7.18  							|-Branch one:
% 25.79/7.18  							| (177) all_0_1_1 = 0
% 25.79/7.18  							|
% 25.79/7.18  								| Equations (177) can reduce 18 to:
% 25.79/7.18  								| (174) $false
% 25.79/7.18  								|
% 25.79/7.18  								|-The branch is then unsatisfiable
% 25.79/7.18  							|-Branch two:
% 25.79/7.18  							| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  							| (196)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  							|
% 25.79/7.18  								+-Applying beta-rule and splitting (192), into two cases.
% 25.79/7.18  								|-Branch one:
% 25.79/7.18  								| (177) all_0_1_1 = 0
% 25.79/7.18  								|
% 25.79/7.18  									| Equations (177) can reduce 18 to:
% 25.79/7.18  									| (174) $false
% 25.79/7.18  									|
% 25.79/7.18  									|-The branch is then unsatisfiable
% 25.79/7.18  								|-Branch two:
% 25.79/7.18  								| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  								| (200)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  								|
% 25.79/7.18  									+-Applying beta-rule and splitting (162), into two cases.
% 25.79/7.18  									|-Branch one:
% 25.79/7.18  									| (173) all_0_0_0 = 0
% 25.79/7.18  									|
% 25.79/7.18  										| Equations (173) can reduce 96 to:
% 25.79/7.18  										| (174) $false
% 25.79/7.18  										|
% 25.79/7.18  										|-The branch is then unsatisfiable
% 25.79/7.18  									|-Branch two:
% 25.79/7.18  									| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  									| (204)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 25.79/7.18  									|
% 25.79/7.18  										+-Applying beta-rule and splitting (164), into two cases.
% 25.79/7.18  										|-Branch one:
% 25.79/7.18  										| (177) all_0_1_1 = 0
% 25.79/7.18  										|
% 25.79/7.18  											| Equations (177) can reduce 18 to:
% 25.79/7.18  											| (174) $false
% 25.79/7.18  											|
% 25.79/7.18  											|-The branch is then unsatisfiable
% 25.79/7.18  										|-Branch two:
% 25.79/7.18  										| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  										| (208)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.18  										|
% 25.79/7.18  											+-Applying beta-rule and splitting (161), into two cases.
% 25.79/7.18  											|-Branch one:
% 25.79/7.18  											| (177) all_0_1_1 = 0
% 25.79/7.18  											|
% 25.79/7.18  												| Equations (177) can reduce 18 to:
% 25.79/7.18  												| (174) $false
% 25.79/7.18  												|
% 25.79/7.18  												|-The branch is then unsatisfiable
% 25.79/7.18  											|-Branch two:
% 25.79/7.18  											| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  											| (212)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 25.79/7.18  											|
% 25.79/7.18  												+-Applying beta-rule and splitting (157), into two cases.
% 25.79/7.18  												|-Branch one:
% 25.79/7.18  												| (177) all_0_1_1 = 0
% 25.79/7.18  												|
% 25.79/7.18  													| Equations (177) can reduce 18 to:
% 25.79/7.18  													| (174) $false
% 25.79/7.18  													|
% 25.79/7.18  													|-The branch is then unsatisfiable
% 25.79/7.18  												|-Branch two:
% 25.79/7.18  												| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  												| (216)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  												|
% 25.79/7.18  													+-Applying beta-rule and splitting (151), into two cases.
% 25.79/7.18  													|-Branch one:
% 25.79/7.18  													| (173) all_0_0_0 = 0
% 25.79/7.18  													|
% 25.79/7.18  														| Equations (173) can reduce 96 to:
% 25.79/7.18  														| (174) $false
% 25.79/7.18  														|
% 25.79/7.18  														|-The branch is then unsatisfiable
% 25.79/7.18  													|-Branch two:
% 25.79/7.18  													| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  													| (220)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 25.79/7.18  													|
% 25.79/7.18  														+-Applying beta-rule and splitting (153), into two cases.
% 25.79/7.18  														|-Branch one:
% 25.79/7.18  														| (173) all_0_0_0 = 0
% 25.79/7.18  														|
% 25.79/7.18  															| Equations (173) can reduce 96 to:
% 25.79/7.18  															| (174) $false
% 25.79/7.18  															|
% 25.79/7.18  															|-The branch is then unsatisfiable
% 25.79/7.18  														|-Branch two:
% 25.79/7.18  														| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  														| (224) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  														|
% 25.79/7.18  															+-Applying beta-rule and splitting (152), into two cases.
% 25.79/7.18  															|-Branch one:
% 25.79/7.18  															| (173) all_0_0_0 = 0
% 25.79/7.18  															|
% 25.79/7.18  																| Equations (173) can reduce 96 to:
% 25.79/7.18  																| (174) $false
% 25.79/7.18  																|
% 25.79/7.18  																|-The branch is then unsatisfiable
% 25.79/7.18  															|-Branch two:
% 25.79/7.18  															| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  															| (228) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.18  															|
% 25.79/7.18  																+-Applying beta-rule and splitting (163), into two cases.
% 25.79/7.18  																|-Branch one:
% 25.79/7.18  																| (173) all_0_0_0 = 0
% 25.79/7.18  																|
% 25.79/7.18  																	| Equations (173) can reduce 96 to:
% 25.79/7.18  																	| (174) $false
% 25.79/7.18  																	|
% 25.79/7.18  																	|-The branch is then unsatisfiable
% 25.79/7.18  																|-Branch two:
% 25.79/7.18  																| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  																| (232) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  																|
% 25.79/7.18  																	+-Applying beta-rule and splitting (159), into two cases.
% 25.79/7.18  																	|-Branch one:
% 25.79/7.18  																	| (173) all_0_0_0 = 0
% 25.79/7.18  																	|
% 25.79/7.18  																		| Equations (173) can reduce 96 to:
% 25.79/7.18  																		| (174) $false
% 25.79/7.18  																		|
% 25.79/7.18  																		|-The branch is then unsatisfiable
% 25.79/7.18  																	|-Branch two:
% 25.79/7.18  																	| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  																	| (236) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  																	|
% 25.79/7.18  																		+-Applying beta-rule and splitting (160), into two cases.
% 25.79/7.18  																		|-Branch one:
% 25.79/7.18  																		| (173) all_0_0_0 = 0
% 25.79/7.18  																		|
% 25.79/7.18  																			| Equations (173) can reduce 96 to:
% 25.79/7.18  																			| (174) $false
% 25.79/7.18  																			|
% 25.79/7.18  																			|-The branch is then unsatisfiable
% 25.79/7.18  																		|-Branch two:
% 25.79/7.18  																		| (96)  ~ (all_0_0_0 = 0)
% 25.79/7.18  																		| (240) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.18  																		|
% 25.79/7.18  																			+-Applying beta-rule and splitting (224), into two cases.
% 25.79/7.18  																			|-Branch one:
% 25.79/7.18  																			| (177) all_0_1_1 = 0
% 25.79/7.18  																			|
% 25.79/7.18  																				| Equations (177) can reduce 18 to:
% 25.79/7.18  																				| (174) $false
% 25.79/7.18  																				|
% 25.79/7.18  																				|-The branch is then unsatisfiable
% 25.79/7.18  																			|-Branch two:
% 25.79/7.18  																			| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  																			| (244)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  																			|
% 25.79/7.18  																				+-Applying beta-rule and splitting (228), into two cases.
% 25.79/7.18  																				|-Branch one:
% 25.79/7.18  																				| (177) all_0_1_1 = 0
% 25.79/7.18  																				|
% 25.79/7.18  																					| Equations (177) can reduce 18 to:
% 25.79/7.18  																					| (174) $false
% 25.79/7.18  																					|
% 25.79/7.18  																					|-The branch is then unsatisfiable
% 25.79/7.18  																				|-Branch two:
% 25.79/7.18  																				| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  																				| (248)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.18  																				|
% 25.79/7.18  																					+-Applying beta-rule and splitting (232), into two cases.
% 25.79/7.18  																					|-Branch one:
% 25.79/7.18  																					| (177) all_0_1_1 = 0
% 25.79/7.18  																					|
% 25.79/7.18  																						| Equations (177) can reduce 18 to:
% 25.79/7.18  																						| (174) $false
% 25.79/7.18  																						|
% 25.79/7.18  																						|-The branch is then unsatisfiable
% 25.79/7.18  																					|-Branch two:
% 25.79/7.18  																					| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  																					| (252)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  																					|
% 25.79/7.18  																						+-Applying beta-rule and splitting (236), into two cases.
% 25.79/7.18  																						|-Branch one:
% 25.79/7.18  																						| (177) all_0_1_1 = 0
% 25.79/7.18  																						|
% 25.79/7.18  																							| Equations (177) can reduce 18 to:
% 25.79/7.18  																							| (174) $false
% 25.79/7.18  																							|
% 25.79/7.18  																							|-The branch is then unsatisfiable
% 25.79/7.18  																						|-Branch two:
% 25.79/7.18  																						| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.18  																						| (256)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0))
% 25.79/7.18  																						|
% 25.79/7.19  																							+-Applying beta-rule and splitting (240), into two cases.
% 25.79/7.19  																							|-Branch one:
% 25.79/7.19  																							| (177) all_0_1_1 = 0
% 25.79/7.19  																							|
% 25.79/7.19  																								| Equations (177) can reduce 18 to:
% 25.79/7.19  																								| (174) $false
% 25.79/7.19  																								|
% 25.79/7.19  																								|-The branch is then unsatisfiable
% 25.79/7.19  																							|-Branch two:
% 25.79/7.19  																							| (18)  ~ (all_0_1_1 = 0)
% 25.79/7.19  																							| (260)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0))
% 25.79/7.19  																							|
% 25.79/7.19  																								| Instantiating (260) with all_177_0_122 yields:
% 25.79/7.19  																								| (261) (all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_177_0_122 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_177_0_122)
% 25.79/7.19  																								|
% 25.79/7.19  																								+-Applying beta-rule and splitting (261), into two cases.
% 25.79/7.19  																								|-Branch one:
% 25.79/7.19  																								| (262) (all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0)
% 25.79/7.19  																								|
% 25.79/7.19  																									+-Applying beta-rule and splitting (262), into two cases.
% 25.79/7.19  																									|-Branch one:
% 25.79/7.19  																									| (263) all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 25.79/7.19  																									|
% 25.79/7.19  																										| Applying alpha-rule on (263) yields:
% 25.79/7.19  																										| (264) all_177_0_122 = 0
% 25.79/7.19  																										| (265) apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 25.79/7.19  																										|
% 25.79/7.19  																										| Instantiating formula (127) with all_0_2_2, all_0_3_3, 0, all_66_0_81 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_66_0_81, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 25.79/7.19  																										| (266) all_66_0_81 = 0
% 25.79/7.19  																										|
% 25.79/7.19  																										| Equations (266) can reduce 168 to:
% 25.79/7.19  																										| (174) $false
% 25.79/7.19  																										|
% 25.79/7.19  																										|-The branch is then unsatisfiable
% 25.79/7.19  																									|-Branch two:
% 25.79/7.19  																									| (268) all_177_0_122 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 25.79/7.19  																									|
% 25.79/7.19  																										| Applying alpha-rule on (268) yields:
% 25.79/7.19  																										| (264) all_177_0_122 = 0
% 25.79/7.19  																										| (270) apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 25.79/7.19  																										|
% 25.79/7.19  																										| Instantiating formula (127) with all_0_2_2, all_0_4_4, 0, all_65_0_80 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields:
% 25.79/7.19  																										| (271) all_65_0_80 = 0
% 25.79/7.19  																										|
% 25.79/7.19  																										| Equations (271) can reduce 171 to:
% 25.79/7.19  																										| (174) $false
% 25.79/7.19  																										|
% 25.79/7.19  																										|-The branch is then unsatisfiable
% 25.79/7.19  																								|-Branch two:
% 25.79/7.19  																								| (273)  ~ (all_177_0_122 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_177_0_122
% 25.79/7.19  																								|
% 25.79/7.19  																									| Applying alpha-rule on (273) yields:
% 25.79/7.19  																									| (274)  ~ (all_177_0_122 = 0)
% 25.79/7.19  																									| (275) distinct_lines(all_0_3_3, all_0_4_4) = all_177_0_122
% 25.79/7.19  																									|
% 25.79/7.19  																									| Instantiating formula (15) with all_177_0_122, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_4_4) = all_177_0_122, yields:
% 25.79/7.19  																									| (276) all_177_0_122 = 0 | convergent_lines(all_0_4_4, all_0_4_4) = 0
% 25.79/7.19  																									|
% 25.79/7.19  																									+-Applying beta-rule and splitting (276), into two cases.
% 25.79/7.19  																									|-Branch one:
% 25.79/7.19  																									| (277) convergent_lines(all_0_4_4, all_0_4_4) = 0
% 25.79/7.19  																									|
% 25.79/7.19  																										| Instantiating formula (85) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields:
% 25.79/7.19  																										| (278) $false
% 25.79/7.19  																										|
% 25.79/7.19  																										|-The branch is then unsatisfiable
% 25.79/7.19  																									|-Branch two:
% 25.79/7.19  																									| (279)  ~ (convergent_lines(all_0_4_4, all_0_4_4) = 0)
% 25.79/7.19  																									| (264) all_177_0_122 = 0
% 25.79/7.19  																									|
% 25.79/7.19  																										| Equations (264) can reduce 274 to:
% 25.79/7.19  																										| (174) $false
% 25.79/7.19  																										|
% 25.79/7.19  																										|-The branch is then unsatisfiable
% 25.79/7.19  	|-Branch two:
% 25.79/7.19  	| (282)  ~ (all_65_0_80 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_65_0_80
% 25.79/7.19  	|
% 25.79/7.19  		| Applying alpha-rule on (282) yields:
% 25.79/7.19  		| (171)  ~ (all_65_0_80 = 0)
% 25.79/7.19  		| (284) convergent_lines(all_0_4_4, all_0_3_3) = all_65_0_80
% 25.79/7.19  		|
% 25.79/7.19  		| Instantiating formula (122) with all_0_4_4, all_0_3_3, all_65_0_80, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_65_0_80, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 25.79/7.19  		| (271) all_65_0_80 = 0
% 25.79/7.19  		|
% 25.79/7.19  		| Equations (271) can reduce 171 to:
% 25.79/7.19  		| (174) $false
% 25.79/7.19  		|
% 25.79/7.19  		|-The branch is then unsatisfiable
% 25.79/7.19  |-Branch two:
% 25.79/7.19  | (287)  ~ (all_66_0_81 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_66_0_81
% 25.79/7.19  |
% 25.79/7.19  	| Applying alpha-rule on (287) yields:
% 25.79/7.19  	| (168)  ~ (all_66_0_81 = 0)
% 25.79/7.19  	| (289) convergent_lines(all_0_4_4, all_0_3_3) = all_66_0_81
% 25.79/7.19  	|
% 25.79/7.19  	| Instantiating formula (122) with all_0_4_4, all_0_3_3, all_66_0_81, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_66_0_81, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields:
% 25.79/7.19  	| (266) all_66_0_81 = 0
% 25.79/7.19  	|
% 25.79/7.19  	| Equations (266) can reduce 168 to:
% 25.79/7.19  	| (174) $false
% 25.79/7.19  	|
% 25.79/7.19  	|-The branch is then unsatisfiable
% 25.79/7.19  % SZS output end Proof for theBenchmark
% 25.79/7.19  
% 25.79/7.19  6597ms
%------------------------------------------------------------------------------