%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.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 03:48:58 EDT 2022

% Result   : Theorem 17.75s 5.01s
% Output   : Proof 20.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO226+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jun 18 02:51:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.57/0.62          ____       _                          
% 0.57/0.62    ___  / __ \_____(_)___  ________  __________
% 0.57/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.62  
% 0.57/0.62  A Theorem Prover for First-Order Logic
% 0.57/0.63  (ePrincess v.1.0)
% 0.57/0.63  
% 0.57/0.63  (c) Philipp Rümmer, 2009-2015
% 0.57/0.63  (c) Peter Backeman, 2014-2015
% 0.57/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.63  Bug reports to peter@backeman.se
% 0.57/0.63  
% 0.57/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.63  
% 0.65/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.69  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/1.04  Prover 0: Preprocessing ...
% 2.49/1.25  Prover 0: Warning: ignoring some quantifiers
% 2.49/1.27  Prover 0: Constructing countermodel ...
% 15.62/4.55  Prover 0: gave up
% 15.62/4.55  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 15.62/4.59  Prover 1: Preprocessing ...
% 16.43/4.71  Prover 1: Constructing countermodel ...
% 16.43/4.73  Prover 1: gave up
% 16.43/4.73  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 16.62/4.76  Prover 2: Preprocessing ...
% 17.38/4.92  Prover 2: Warning: ignoring some quantifiers
% 17.38/4.93  Prover 2: Constructing countermodel ...
% 17.75/5.01  Prover 2: proved (279ms)
% 17.75/5.01  
% 17.75/5.01  No countermodel exists, formula is valid
% 17.75/5.01  % SZS status Theorem for theBenchmark
% 17.75/5.01  
% 17.75/5.01  Generating proof ... Warning: ignoring some quantifiers
% 19.70/5.46  found it (size 49)
% 19.70/5.46  
% 19.70/5.46  % SZS output start Proof for theBenchmark
% 19.70/5.46  Assumed formulas after preprocessing and simplification: 
% 19.70/5.46  | (0)  ? [v0] :  ? [v1] : (line(v1) = 0 & line(v0) = 0 & convergent_lines(v0, v1) = 0 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v4, v5) = v7) |  ~ (apart_point_and_line(v2, v4) = v6) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v8] : ((v8 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v3) = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v4, v5) = v7) |  ~ (apart_point_and_line(v2, v3) = v6) |  ? [v8] : ((v8 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (apart_point_and_line(v2, v4) = v6) |  ? [v8] : ((v8 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (apart_point_and_line(v2, v3) = v6) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v8] : ((v8 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (apart_point_and_line(v3, v4) = v6) |  ~ (distinct_points(v2, v3) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v2, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (apart_point_and_line(v2, v5) = v6) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (apart_point_and_line(v2, v4) = v6) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v4) = v7) |  ~ (apart_point_and_line(v2, v5) = v6) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v4) = v7) |  ~ (apart_point_and_line(v2, v4) = v6) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v2, v5) = 0) | ( ~ (v8 = 0) & distinct_points(v2, v3) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v2, v5) = v7) |  ~ (apart_point_and_line(v2, v4) = v6) |  ~ (distinct_points(v2, v3) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | (v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (unorthogonal_lines(v2, v4) = v6) |  ~ (unorthogonal_lines(v2, v3) = v5) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (apart_point_and_line(v4, v3) = v6) |  ~ (distinct_points(v2, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (apart_point_and_line(v2, v4) = v6) |  ~ (apart_point_and_line(v2, v3) = v5) |  ? [v7] : ((v7 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (apart_point_and_line(v2, v4) = v6) |  ~ (distinct_lines(v3, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (apart_point_and_line(v2, v4) = v5) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v7] : ((v7 = 0 & apart_point_and_line(v2, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (apart_point_and_line(v2, v3) = v5) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v7] : ((v7 = 0 & apart_point_and_line(v2, v4) = 0) | ( ~ (v7 = 0) & distinct_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (convergent_lines(v3, v4) = v6) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (convergent_lines(v2, v4) = v6) |  ~ (distinct_lines(v3, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_lines(v3, v4) = v6) |  ~ (distinct_lines(v2, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (distinct_points(v3, v4) = v6) |  ~ (distinct_points(v2, v4) = v5) |  ? [v7] : ( ~ (v7 = 0) & distinct_points(v2, v3) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) |  ~ (unorthogonal_lines(v2, v4) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v6) |  ~ (unorthogonal_lines(v2, v3) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v6) |  ~ (convergent_lines(v2, v3) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & convergent_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (convergent_lines(v2, v4) = v6) |  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v3, v4) = v6) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v2, v3) = v7) | ( ~ (v7 = 0) & convergent_lines(v2, v3) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v2, v4) = v6) |  ~ (convergent_lines(v2, v3) = v5) |  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0) | (v7 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (convergent_lines(v3, v4) = 0) | unorthogonal_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (convergent_lines(v3, v4) = 0) | unorthogonal_lines(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v4, v3) = v5) |  ~ (apart_point_and_line(v2, v3) = 0) | distinct_points(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v4) = v5) |  ~ (apart_point_and_line(v2, v3) = 0) | distinct_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v4) = v5) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v2, v3) = 0) | (v6 = 0 & convergent_lines(v3, v4) = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = v5) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v2, v4) = 0) | (v6 = 0 & convergent_lines(v3, v4) = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v3, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v2, v3) = 0) |  ~ (distinct_lines(v3, v4) = v5) | convergent_lines(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_lines(v3, v4) = v5) |  ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_lines(v2, v4) = v5) |  ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_points(v3, v4) = v5) |  ~ (distinct_points(v2, v3) = 0) | distinct_points(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_points(v2, v4) = v5) |  ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (orthogonal_lines(v5, v4) = v3) |  ~ (orthogonal_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (incident_point_and_line(v5, v4) = v3) |  ~ (incident_point_and_line(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (parallel_lines(v5, v4) = v3) |  ~ (parallel_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (equal_lines(v5, v4) = v3) |  ~ (equal_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (equal_points(v5, v4) = v3) |  ~ (equal_points(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (orthogonal_through_point(v5, v4) = v3) |  ~ (orthogonal_through_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (unorthogonal_lines(v5, v4) = v3) |  ~ (unorthogonal_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (parallel_through_point(v5, v4) = v3) |  ~ (parallel_through_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (intersection_point(v5, v4) = v3) |  ~ (intersection_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (line_connecting(v5, v4) = v3) |  ~ (line_connecting(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (apart_point_and_line(v5, v4) = v3) |  ~ (apart_point_and_line(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (convergent_lines(v5, v4) = v3) |  ~ (convergent_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_lines(v5, v4) = v3) |  ~ (distinct_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_points(v5, v4) = v3) |  ~ (distinct_points(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = v5) |  ~ (unorthogonal_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (unorthogonal_lines(v2, v4) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (unorthogonal_lines(v2, v3) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (convergent_lines(v2, v3) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (unorthogonal_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & convergent_lines(v2, v3) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = 0) |  ~ (convergent_lines(v3, v4) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v3) = 0) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & convergent_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v3, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v3, v4) = 0) |  ~ (convergent_lines(v2, v4) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v3) = 0 & convergent_lines(v2, v3) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v3, v4) = 0) |  ~ (convergent_lines(v2, v3) = v5) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v2, v4) = 0 & convergent_lines(v2, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v3) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v3, v4) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] : ((v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v6 = 0 & v5 = 0 & unorthogonal_lines(v2, v4) = 0) | ( ~ (v6 = 0) & unorthogonal_lines(v2, v3) = v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) |  ~ (distinct_points(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v3, v5) = 0) | (v6 = 0 & apart_point_and_line(v3, v4) = 0) | (v6 = 0 & apart_point_and_line(v2, v5) = 0) | (v6 = 0 & apart_point_and_line(v2, v4) = 0))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (orthogonal_lines(v2, v3) = v4) | unorthogonal_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (incident_point_and_line(v2, v3) = v4) | apart_point_and_line(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (parallel_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equal_lines(v2, v3) = v4) | distinct_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (equal_points(v2, v3) = v4) | distinct_points(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v4) | orthogonal_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (apart_point_and_line(v2, v3) = v4) | incident_point_and_line(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (convergent_lines(v2, v3) = v4) | parallel_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (convergent_lines(v2, v3) = v4) | unorthogonal_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (convergent_lines(v2, v3) = v4) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v2, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (distinct_lines(v2, v3) = v4) | equal_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (distinct_points(v2, v3) = v4) | equal_points(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (point(v4) = v3) |  ~ (point(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (line(v4) = v3) |  ~ (line(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & unorthogonal_lines(v4, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (orthogonal_through_point(v2, v3) = v4) |  ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v4, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) |  ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ? [v5] : ((v5 = 0 & point(v4) = 0) | ( ~ (v5 = 0) & line(v3) = v5) | ( ~ (v5 = 0) & line(v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v3) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v4, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ? [v5] : ((v5 = 0 & line(v4) = 0) | ( ~ (v5 = 0) & point(v3) = v5) | ( ~ (v5 = 0) & point(v2) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & apart_point_and_line(v2, v4) = v5) | ( ~ (v5 = 0) & distinct_points(v2, v3) = v5))) &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (point(v2) = v3)) &  ! [v2] :  ! [v3] : ( ~ (orthogonal_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & unorthogonal_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (incident_point_and_line(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & apart_point_and_line(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (parallel_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & convergent_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (equal_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & distinct_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (equal_points(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & distinct_points(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & orthogonal_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & incident_point_and_line(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v3) = v5)) &  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v3) = v4 & apart_point_and_line(v4, v2) = v5)) &  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & point(v4) = 0 & intersection_point(v2, v3) = v4) | ( ~ (v4 = 0) & line(v3) = v4) | ( ~ (v4 = 0) & line(v2) = v4))) &  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & parallel_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | convergent_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & equal_lines(v2, v3) = v4)) &  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v3) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v3, v4) = v5)) &  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v3) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & line_connecting(v2, v3) = v4 & apart_point_and_line(v2, v4) = v5)) &  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & line(v4) = 0 & line_connecting(v2, v3) = v4) | ( ~ (v4 = 0) & point(v3) = v4) | ( ~ (v4 = 0) & point(v2) = v4))) &  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & equal_points(v2, v3) = v4)) &  ! [v2] : ( ~ (incident_point_and_line(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v2, v0) = v3)) &  ! [v2] : ( ~ (incident_point_and_line(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v2, v1) = v3)) &  ! [v2] :  ~ (convergent_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_points(v2, v2) = 0) &  ? [v2] :  ? [v3] :  ? [v4] : orthogonal_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : incident_point_and_line(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : parallel_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : equal_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : equal_points(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : orthogonal_through_point(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : unorthogonal_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : parallel_through_point(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : intersection_point(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : line_connecting(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : apart_point_and_line(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : convergent_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : distinct_lines(v3, v2) = v4 &  ? [v2] :  ? [v3] :  ? [v4] : distinct_points(v3, v2) = v4 &  ? [v2] :  ? [v3] : point(v2) = v3 &  ? [v2] :  ? [v3] : line(v2) = v3)
% 20.06/5.53  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 20.06/5.53  | (1) line(all_0_0_0) = 0 & line(all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 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] : (v1 = 0 |  ~ (point(v0) = v1)) &  ! [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] : ( ~ (incident_point_and_line(v0, all_0_0_0) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_0_1_1) = v1)) &  ! [v0] : ( ~ (incident_point_and_line(v0, all_0_1_1) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_0_0_0) = v1)) &  ! [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
% 20.06/5.57  |
% 20.06/5.57  | Applying alpha-rule on (1) yields:
% 20.06/5.57  | (2)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 20.06/5.57  | (3)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 20.06/5.57  | (4)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 20.06/5.57  | (5)  ! [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)))
% 20.06/5.57  | (6)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 20.06/5.57  | (7)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 20.06/5.57  | (8)  ! [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)))
% 20.06/5.57  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 20.06/5.57  | (10)  ! [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)))
% 20.06/5.57  | (11)  ! [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)))
% 20.06/5.57  | (12)  ! [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))
% 20.06/5.57  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 20.06/5.57  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 20.06/5.57  | (15)  ! [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)))
% 20.06/5.57  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 20.06/5.57  | (17)  ! [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)))
% 20.06/5.57  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 20.06/5.57  | (19)  ! [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))
% 20.06/5.57  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 20.06/5.57  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 20.06/5.57  | (22)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 20.06/5.57  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 20.06/5.57  | (24)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 20.06/5.57  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 20.06/5.58  | (26)  ! [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)))
% 20.46/5.58  | (27) line(all_0_0_0) = 0
% 20.46/5.58  | (28)  ! [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)))
% 20.46/5.58  | (29)  ! [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)))
% 20.46/5.58  | (30)  ! [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)))
% 20.46/5.58  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 20.46/5.58  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 20.46/5.58  | (33)  ! [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)))
% 20.46/5.58  | (34)  ! [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)))
% 20.46/5.58  | (35)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 20.46/5.58  | (36)  ! [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)))
% 20.46/5.58  | (37)  ! [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)))
% 20.46/5.58  | (38)  ! [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)))
% 20.46/5.58  | (39)  ! [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)))
% 20.46/5.58  | (40)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 20.46/5.58  | (41)  ! [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)))
% 20.46/5.58  | (42)  ! [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)))
% 20.46/5.58  | (43)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2
% 20.46/5.58  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 20.46/5.58  | (45)  ! [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)))
% 20.46/5.58  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 20.46/5.58  | (47)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 20.46/5.58  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 20.46/5.58  | (49)  ! [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)))
% 20.46/5.58  | (50)  ! [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))
% 20.46/5.58  | (51)  ! [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)))
% 20.46/5.58  | (52)  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2
% 20.46/5.58  | (53)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 20.46/5.58  | (54)  ! [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)))
% 20.46/5.58  | (55)  ! [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)))
% 20.46/5.58  | (56)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 20.46/5.58  | (57)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 20.46/5.58  | (58)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 20.46/5.58  | (59)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 20.46/5.58  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 20.46/5.58  | (61)  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2
% 20.46/5.58  | (62)  ! [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)
% 20.46/5.58  | (63)  ! [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)))
% 20.46/5.58  | (64)  ! [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)))
% 20.46/5.58  | (65)  ! [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)))
% 20.46/5.58  | (66)  ? [v0] :  ? [v1] : point(v0) = v1
% 20.46/5.58  | (67)  ! [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)))
% 20.46/5.58  | (68)  ! [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)))
% 20.46/5.58  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 20.46/5.58  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 20.46/5.58  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 20.46/5.58  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.46/5.58  | (73)  ! [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))
% 20.46/5.58  | (74)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 20.46/5.58  | (75)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 20.46/5.59  | (76)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 20.46/5.59  | (77)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 20.46/5.59  | (78)  ! [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)))
% 20.46/5.59  | (79)  ! [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)))
% 20.46/5.59  | (80)  ! [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)))
% 20.46/5.59  | (81)  ! [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))
% 20.46/5.59  | (82)  ! [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)))
% 20.46/5.59  | (83)  ! [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)
% 20.46/5.59  | (84)  ! [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)
% 20.46/5.59  | (85)  ! [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)))
% 20.46/5.59  | (86)  ! [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)))
% 20.46/5.59  | (87)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 20.46/5.59  | (88) convergent_lines(all_0_1_1, all_0_0_0) = 0
% 20.46/5.59  | (89)  ! [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)))
% 20.46/5.59  | (90)  ! [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))
% 20.46/5.59  | (91)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 20.46/5.59  | (92)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 20.46/5.59  | (93)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (point(v0) = v1))
% 20.46/5.59  | (94)  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2
% 20.46/5.59  | (95)  ! [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)))
% 20.46/5.59  | (96)  ! [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)))
% 20.46/5.59  | (97)  ? [v0] :  ? [v1] : line(v0) = v1
% 20.46/5.59  | (98)  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2
% 20.46/5.59  | (99)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 20.46/5.59  | (100)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 20.46/5.59  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 20.46/5.59  | (102)  ! [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))
% 20.46/5.59  | (103)  ! [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)))
% 20.46/5.59  | (104)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 20.46/5.59  | (105)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 20.46/5.59  | (106)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 20.46/5.59  | (107)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 20.46/5.59  | (108)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 20.46/5.59  | (109)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 20.46/5.59  | (110)  ! [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)))
% 20.46/5.59  | (111) line(all_0_1_1) = 0
% 20.46/5.59  | (112)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 20.46/5.59  | (113)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 20.46/5.59  | (114)  ! [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)))
% 20.46/5.59  | (115)  ! [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)))
% 20.46/5.59  | (116)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 20.46/5.59  | (117)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 20.46/5.59  | (118)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 20.46/5.59  | (119)  ! [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)))
% 20.46/5.59  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 20.46/5.59  | (121)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 20.46/5.59  | (122)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 20.46/5.59  | (123)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 20.46/5.59  | (124)  ! [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)))
% 20.46/5.59  | (125)  ! [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)))
% 20.46/5.59  | (126)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 20.46/5.59  | (127)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 20.46/5.59  | (128)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 20.46/5.59  | (129)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 20.46/5.59  | (130)  ! [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)))
% 20.46/5.59  | (131)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 20.46/5.59  | (132)  ! [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)))
% 20.46/5.59  | (133)  ! [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)))
% 20.46/5.59  | (134)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 20.46/5.59  | (135)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 20.46/5.59  | (136)  ! [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)))
% 20.46/5.59  | (137)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 20.46/5.59  | (138)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 20.55/5.59  | (139)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 20.55/5.60  | (140)  ! [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)
% 20.55/5.60  | (141)  ! [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)))
% 20.55/5.60  | (142)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 20.55/5.60  | (143)  ! [v0] : ( ~ (incident_point_and_line(v0, all_0_1_1) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_0_0_0) = v1))
% 20.55/5.60  | (144)  ! [v0] : ( ~ (incident_point_and_line(v0, all_0_0_0) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_0_1_1) = v1))
% 20.55/5.60  | (145)  ! [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)))
% 20.55/5.60  |
% 20.55/5.60  | Instantiating formula (129) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 20.55/5.60  | (146)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_0_0) = v1)
% 20.55/5.60  |
% 20.55/5.60  | Instantiating formula (117) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 20.55/5.60  | (147)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_1_1, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_1_1) = v1)
% 20.55/5.60  |
% 20.55/5.60  | Instantiating formula (136) with all_0_0_0, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_0_0) = 0, yields:
% 20.55/5.60  | (148)  ? [v0] :  ? [v1] : ((v1 = 0 & point(v0) = 0 & intersection_point(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & line(all_0_0_0) = v0) | ( ~ (v0 = 0) & line(all_0_1_1) = v0))
% 20.55/5.60  |
% 20.55/5.60  | Instantiating (148) with all_46_0_49, all_46_1_50 yields:
% 20.55/5.60  | (149) (all_46_0_49 = 0 & point(all_46_1_50) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_46_1_50) | ( ~ (all_46_1_50 = 0) & line(all_0_0_0) = all_46_1_50) | ( ~ (all_46_1_50 = 0) & line(all_0_1_1) = all_46_1_50)
% 20.55/5.60  |
% 20.55/5.60  | Instantiating (147) with all_47_0_51, all_47_1_52 yields:
% 20.55/5.60  | (150)  ~ (all_47_0_51 = 0) & intersection_point(all_0_1_1, all_0_0_0) = all_47_1_52 & apart_point_and_line(all_47_1_52, all_0_1_1) = all_47_0_51
% 20.55/5.60  |
% 20.55/5.60  | Applying alpha-rule on (150) yields:
% 20.55/5.60  | (151)  ~ (all_47_0_51 = 0)
% 20.55/5.60  | (152) intersection_point(all_0_1_1, all_0_0_0) = all_47_1_52
% 20.55/5.60  | (153) apart_point_and_line(all_47_1_52, all_0_1_1) = all_47_0_51
% 20.55/5.60  |
% 20.55/5.60  | Instantiating (146) with all_49_0_53, all_49_1_54 yields:
% 20.55/5.60  | (154)  ~ (all_49_0_53 = 0) & intersection_point(all_0_1_1, all_0_0_0) = all_49_1_54 & apart_point_and_line(all_49_1_54, all_0_0_0) = all_49_0_53
% 20.55/5.60  |
% 20.55/5.60  | Applying alpha-rule on (154) yields:
% 20.55/5.60  | (155)  ~ (all_49_0_53 = 0)
% 20.55/5.60  | (156) intersection_point(all_0_1_1, all_0_0_0) = all_49_1_54
% 20.55/5.60  | (157) apart_point_and_line(all_49_1_54, all_0_0_0) = all_49_0_53
% 20.55/5.60  |
% 20.55/5.60  +-Applying beta-rule and splitting (149), into two cases.
% 20.55/5.60  |-Branch one:
% 20.55/5.60  | (158) (all_46_0_49 = 0 & point(all_46_1_50) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_46_1_50) | ( ~ (all_46_1_50 = 0) & line(all_0_0_0) = all_46_1_50)
% 20.55/5.60  |
% 20.55/5.60  	+-Applying beta-rule and splitting (158), into two cases.
% 20.55/5.60  	|-Branch one:
% 20.55/5.60  	| (159) all_46_0_49 = 0 & point(all_46_1_50) = 0 & intersection_point(all_0_1_1, all_0_0_0) = all_46_1_50
% 20.55/5.60  	|
% 20.55/5.60  		| Applying alpha-rule on (159) yields:
% 20.55/5.60  		| (160) all_46_0_49 = 0
% 20.55/5.60  		| (161) point(all_46_1_50) = 0
% 20.55/5.60  		| (162) intersection_point(all_0_1_1, all_0_0_0) = all_46_1_50
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (121) with all_0_1_1, all_0_0_0, all_47_1_52, all_49_1_54 and discharging atoms intersection_point(all_0_1_1, all_0_0_0) = all_49_1_54, intersection_point(all_0_1_1, all_0_0_0) = all_47_1_52, yields:
% 20.55/5.60  		| (163) all_49_1_54 = all_47_1_52
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (121) with all_0_1_1, all_0_0_0, all_46_1_50, all_49_1_54 and discharging atoms intersection_point(all_0_1_1, all_0_0_0) = all_49_1_54, intersection_point(all_0_1_1, all_0_0_0) = all_46_1_50, yields:
% 20.55/5.60  		| (164) all_49_1_54 = all_46_1_50
% 20.55/5.60  		|
% 20.55/5.60  		| Combining equations (163,164) yields a new equation:
% 20.55/5.60  		| (165) all_47_1_52 = all_46_1_50
% 20.55/5.60  		|
% 20.55/5.60  		| Simplifying 165 yields:
% 20.55/5.60  		| (166) all_47_1_52 = all_46_1_50
% 20.55/5.60  		|
% 20.55/5.60  		| From (164) and (157) follows:
% 20.55/5.60  		| (167) apart_point_and_line(all_46_1_50, all_0_0_0) = all_49_0_53
% 20.55/5.60  		|
% 20.55/5.60  		| From (166) and (153) follows:
% 20.55/5.60  		| (168) apart_point_and_line(all_46_1_50, all_0_1_1) = all_47_0_51
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (104) with all_49_0_53, all_0_0_0, all_46_1_50 and discharging atoms apart_point_and_line(all_46_1_50, all_0_0_0) = all_49_0_53, yields:
% 20.55/5.60  		| (169) all_49_0_53 = 0 | incident_point_and_line(all_46_1_50, all_0_0_0) = 0
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (55) with all_49_0_53, all_47_0_51, all_0_0_0, all_0_1_1, all_46_1_50 and discharging atoms apart_point_and_line(all_46_1_50, all_0_0_0) = all_49_0_53, apart_point_and_line(all_46_1_50, all_0_1_1) = all_47_0_51, yields:
% 20.55/5.60  		| (170) all_49_0_53 = 0 | all_47_0_51 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (78) with all_47_0_51, all_49_0_53, all_0_1_1, all_0_0_0, all_46_1_50, all_46_1_50 and discharging atoms apart_point_and_line(all_46_1_50, all_0_0_0) = all_49_0_53, apart_point_and_line(all_46_1_50, all_0_1_1) = all_47_0_51, yields:
% 20.55/5.60  		| (171) all_49_0_53 = 0 | all_47_0_51 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_46_1_50, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_46_1_50, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_46_1_50, all_46_1_50) = v0))
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (104) with all_47_0_51, all_0_1_1, all_46_1_50 and discharging atoms apart_point_and_line(all_46_1_50, all_0_1_1) = all_47_0_51, yields:
% 20.55/5.60  		| (172) all_47_0_51 = 0 | incident_point_and_line(all_46_1_50, all_0_1_1) = 0
% 20.55/5.60  		|
% 20.55/5.60  		+-Applying beta-rule and splitting (172), into two cases.
% 20.55/5.60  		|-Branch one:
% 20.55/5.60  		| (173) incident_point_and_line(all_46_1_50, all_0_1_1) = 0
% 20.55/5.60  		|
% 20.55/5.60  			+-Applying beta-rule and splitting (170), into two cases.
% 20.55/5.60  			|-Branch one:
% 20.55/5.60  			| (174) all_49_0_53 = 0
% 20.55/5.60  			|
% 20.55/5.60  				| Equations (174) can reduce 155 to:
% 20.55/5.60  				| (175) $false
% 20.55/5.60  				|
% 20.55/5.60  				|-The branch is then unsatisfiable
% 20.55/5.60  			|-Branch two:
% 20.55/5.60  			| (155)  ~ (all_49_0_53 = 0)
% 20.55/5.60  			| (177) all_47_0_51 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 20.55/5.60  			|
% 20.55/5.60  				+-Applying beta-rule and splitting (171), into two cases.
% 20.55/5.60  				|-Branch one:
% 20.55/5.60  				| (174) all_49_0_53 = 0
% 20.55/5.60  				|
% 20.55/5.60  					| Equations (174) can reduce 155 to:
% 20.55/5.60  					| (175) $false
% 20.55/5.60  					|
% 20.55/5.60  					|-The branch is then unsatisfiable
% 20.55/5.60  				|-Branch two:
% 20.55/5.60  				| (155)  ~ (all_49_0_53 = 0)
% 20.55/5.60  				| (181) all_47_0_51 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_46_1_50, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_46_1_50, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_46_1_50, all_46_1_50) = v0))
% 20.55/5.60  				|
% 20.55/5.60  					+-Applying beta-rule and splitting (169), into two cases.
% 20.55/5.60  					|-Branch one:
% 20.55/5.60  					| (182) incident_point_and_line(all_46_1_50, all_0_0_0) = 0
% 20.55/5.60  					|
% 20.55/5.60  						| Instantiating formula (143) with all_46_1_50 and discharging atoms incident_point_and_line(all_46_1_50, all_0_1_1) = 0, yields:
% 20.55/5.60  						| (183)  ? [v0] : ( ~ (v0 = 0) & incident_point_and_line(all_46_1_50, all_0_0_0) = v0)
% 20.55/5.60  						|
% 20.55/5.60  						| Instantiating (183) with all_142_0_85 yields:
% 20.55/5.60  						| (184)  ~ (all_142_0_85 = 0) & incident_point_and_line(all_46_1_50, all_0_0_0) = all_142_0_85
% 20.55/5.60  						|
% 20.55/5.60  						| Applying alpha-rule on (184) yields:
% 20.55/5.60  						| (185)  ~ (all_142_0_85 = 0)
% 20.55/5.60  						| (186) incident_point_and_line(all_46_1_50, all_0_0_0) = all_142_0_85
% 20.55/5.60  						|
% 20.55/5.60  						| Instantiating formula (69) with all_46_1_50, all_0_0_0, all_142_0_85, 0 and discharging atoms incident_point_and_line(all_46_1_50, all_0_0_0) = all_142_0_85, incident_point_and_line(all_46_1_50, all_0_0_0) = 0, yields:
% 20.55/5.60  						| (187) all_142_0_85 = 0
% 20.55/5.60  						|
% 20.55/5.60  						| Equations (187) can reduce 185 to:
% 20.55/5.60  						| (175) $false
% 20.55/5.60  						|
% 20.55/5.60  						|-The branch is then unsatisfiable
% 20.55/5.60  					|-Branch two:
% 20.55/5.60  					| (189)  ~ (incident_point_and_line(all_46_1_50, all_0_0_0) = 0)
% 20.55/5.60  					| (174) all_49_0_53 = 0
% 20.55/5.60  					|
% 20.55/5.60  						| Equations (174) can reduce 155 to:
% 20.55/5.60  						| (175) $false
% 20.55/5.60  						|
% 20.55/5.60  						|-The branch is then unsatisfiable
% 20.55/5.60  		|-Branch two:
% 20.55/5.60  		| (192)  ~ (incident_point_and_line(all_46_1_50, all_0_1_1) = 0)
% 20.55/5.60  		| (193) all_47_0_51 = 0
% 20.55/5.60  		|
% 20.55/5.60  			| Equations (193) can reduce 151 to:
% 20.55/5.60  			| (175) $false
% 20.55/5.60  			|
% 20.55/5.60  			|-The branch is then unsatisfiable
% 20.55/5.60  	|-Branch two:
% 20.55/5.60  	| (195)  ~ (all_46_1_50 = 0) & line(all_0_0_0) = all_46_1_50
% 20.55/5.60  	|
% 20.55/5.60  		| Applying alpha-rule on (195) yields:
% 20.55/5.60  		| (196)  ~ (all_46_1_50 = 0)
% 20.55/5.60  		| (197) line(all_0_0_0) = all_46_1_50
% 20.55/5.60  		|
% 20.55/5.60  		| Instantiating formula (106) with all_0_0_0, all_46_1_50, 0 and discharging atoms line(all_0_0_0) = all_46_1_50, line(all_0_0_0) = 0, yields:
% 20.55/5.60  		| (198) all_46_1_50 = 0
% 20.55/5.60  		|
% 20.55/5.60  		| Equations (198) can reduce 196 to:
% 20.55/5.60  		| (175) $false
% 20.55/5.60  		|
% 20.55/5.60  		|-The branch is then unsatisfiable
% 20.55/5.60  |-Branch two:
% 20.55/5.60  | (200)  ~ (all_46_1_50 = 0) & line(all_0_1_1) = all_46_1_50
% 20.55/5.60  |
% 20.55/5.60  	| Applying alpha-rule on (200) yields:
% 20.55/5.60  	| (196)  ~ (all_46_1_50 = 0)
% 20.55/5.61  	| (202) line(all_0_1_1) = all_46_1_50
% 20.55/5.61  	|
% 20.55/5.61  	| Instantiating formula (106) with all_0_1_1, all_46_1_50, 0 and discharging atoms line(all_0_1_1) = all_46_1_50, line(all_0_1_1) = 0, yields:
% 20.55/5.61  	| (198) all_46_1_50 = 0
% 20.55/5.61  	|
% 20.55/5.61  	| Equations (198) can reduce 196 to:
% 20.55/5.61  	| (175) $false
% 20.55/5.61  	|
% 20.55/5.61  	|-The branch is then unsatisfiable
% 20.55/5.61  % SZS output end Proof for theBenchmark
% 20.55/5.61  
% 20.55/5.61  4962ms
%------------------------------------------------------------------------------