ePrincess---1.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n003.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 03:48:08 EDT 2022

% Result   : Theorem 19.70s 5.91s
% Output   : Proof 22.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n003.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 18:29:43 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.56/0.62          ____       _                          
% 0.56/0.62    ___  / __ \_____(_)___  ________  __________
% 0.56/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.62  
% 0.56/0.62  A Theorem Prover for First-Order Logic
% 0.56/0.62  (ePrincess v.1.0)
% 0.56/0.62  
% 0.56/0.62  (c) Philipp Rümmer, 2009-2015
% 0.56/0.62  (c) Peter Backeman, 2014-2015
% 0.56/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.62  Bug reports to peter@backeman.se
% 0.56/0.62  
% 0.56/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.62  
% 0.56/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.69  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.03  Prover 0: Preprocessing ...
% 2.48/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.48/1.27  Prover 0: Constructing countermodel ...
% 16.98/5.28  Prover 0: gave up
% 16.98/5.28  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 16.98/5.31  Prover 1: Preprocessing ...
% 17.88/5.44  Prover 1: Constructing countermodel ...
% 17.88/5.46  Prover 1: gave up
% 17.88/5.46  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.28/5.49  Prover 2: Preprocessing ...
% 18.80/5.66  Prover 2: Warning: ignoring some quantifiers
% 18.80/5.67  Prover 2: Constructing countermodel ...
% 19.70/5.91  Prover 2: proved (447ms)
% 19.70/5.91  
% 19.70/5.91  No countermodel exists, formula is valid
% 19.70/5.91  % SZS status Theorem for theBenchmark
% 19.70/5.91  
% 19.70/5.91  Generating proof ... Warning: ignoring some quantifiers
% 22.38/6.41  found it (size 39)
% 22.38/6.41  
% 22.38/6.41  % SZS output start Proof for theBenchmark
% 22.38/6.41  Assumed formulas after preprocessing and simplification: 
% 22.38/6.41  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v0, v1) = v2 &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (unorthogonal_lines(v5, v6) = v8) |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v9] : ((v9 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v4) = 0))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (unorthogonal_lines(v5, v6) = v8) |  ~ (apart_point_and_line(v3, v4) = v7) |  ? [v9] : ((v9 = 0 & unorthogonal_lines(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (unorthogonal_lines(v4, v6) = v8) |  ~ (apart_point_and_line(v3, v5) = v7) |  ? [v9] : ((v9 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (unorthogonal_lines(v4, v6) = v8) |  ~ (apart_point_and_line(v3, v4) = v7) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v9] : ((v9 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (apart_point_and_line(v4, v5) = v7) |  ~ (distinct_points(v3, v4) = 0) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v3, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (apart_point_and_line(v3, v6) = v7) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (apart_point_and_line(v3, v5) = v7) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | (v9 = 0 & apart_point_and_line(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v5) = v8) |  ~ (apart_point_and_line(v3, v6) = v7) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v5) = v8) |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v3, v6) = 0) | ( ~ (v9 = 0) & distinct_points(v3, v4) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v3, v6) = v8) |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (distinct_points(v3, v4) = 0) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | (v9 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (unorthogonal_lines(v3, v4) = v6) |  ? [v8] : ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v5, v4) = v7) |  ~ (distinct_points(v3, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (apart_point_and_line(v3, v4) = v6) |  ? [v8] : ((v8 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v7) |  ~ (distinct_lines(v4, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v6) |  ~ (convergent_lines(v4, v5) = v7) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v4) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (apart_point_and_line(v3, v4) = v6) |  ~ (convergent_lines(v4, v5) = v7) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v3, v5) = 0) | ( ~ (v8 = 0) & distinct_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (convergent_lines(v4, v5) = v7) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (convergent_lines(v3, v5) = v7) |  ~ (distinct_lines(v4, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (distinct_lines(v4, v5) = v7) |  ~ (distinct_lines(v3, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & distinct_lines(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (distinct_points(v4, v5) = v7) |  ~ (distinct_points(v3, v5) = v6) |  ? [v8] : ( ~ (v8 = 0) & distinct_points(v3, v4) = v8)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = v7) |  ~ (unorthogonal_lines(v3, v5) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = v7) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (unorthogonal_lines(v3, v4) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & convergent_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v3, v5) = v6) |  ~ (convergent_lines(v4, v5) = v7) |  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v3, v4) = v6) |  ~ (convergent_lines(v3, v5) = v7) |  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v4, v5) = v7) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v3, v4) = v8) | ( ~ (v8 = 0) & convergent_lines(v3, v4) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v3, v5) = v7) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0) | (v8 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (unorthogonal_lines(v3, v5) = v6) |  ~ (convergent_lines(v4, v5) = 0) | unorthogonal_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (unorthogonal_lines(v3, v4) = v6) |  ~ (convergent_lines(v4, v5) = 0) | unorthogonal_lines(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v5, v4) = v6) |  ~ (apart_point_and_line(v3, v4) = 0) | distinct_points(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v6) |  ~ (apart_point_and_line(v3, v4) = 0) | distinct_lines(v4, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v3, v5) = v6) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v7] : ((v7 = 0 & apart_point_and_line(v3, v4) = 0) | (v7 = 0 & convergent_lines(v4, v5) = 0))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v3, v4) = v6) |  ~ (distinct_lines(v4, v5) = 0) |  ? [v7] : ((v7 = 0 & apart_point_and_line(v3, v5) = 0) | (v7 = 0 & convergent_lines(v4, v5) = 0))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v3, v4) = 0) |  ~ (distinct_lines(v4, v5) = v6) | apart_point_and_line(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (apart_point_and_line(v3, v4) = 0) |  ~ (distinct_points(v3, v5) = v6) | apart_point_and_line(v5, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (convergent_lines(v4, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) | convergent_lines(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (convergent_lines(v3, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) | convergent_lines(v4, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (convergent_lines(v3, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) | distinct_lines(v4, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (convergent_lines(v3, v4) = 0) |  ~ (distinct_lines(v4, v5) = v6) | convergent_lines(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (distinct_lines(v4, v5) = v6) |  ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (distinct_lines(v3, v5) = v6) |  ~ (distinct_lines(v3, v4) = 0) | distinct_lines(v4, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (distinct_points(v4, v5) = v6) |  ~ (distinct_points(v3, v4) = 0) | distinct_points(v3, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (distinct_points(v3, v5) = v6) |  ~ (distinct_points(v3, v4) = 0) | distinct_points(v4, v5) = 0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (orthogonal_lines(v6, v5) = v4) |  ~ (orthogonal_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (incident_point_and_line(v6, v5) = v4) |  ~ (incident_point_and_line(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (parallel_lines(v6, v5) = v4) |  ~ (parallel_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (equal_lines(v6, v5) = v4) |  ~ (equal_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (equal_points(v6, v5) = v4) |  ~ (equal_points(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (orthogonal_through_point(v6, v5) = v4) |  ~ (orthogonal_through_point(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (unorthogonal_lines(v6, v5) = v4) |  ~ (unorthogonal_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (parallel_through_point(v6, v5) = v4) |  ~ (parallel_through_point(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (intersection_point(v6, v5) = v4) |  ~ (intersection_point(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (line_connecting(v6, v5) = v4) |  ~ (line_connecting(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (apart_point_and_line(v6, v5) = v4) |  ~ (apart_point_and_line(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (convergent_lines(v6, v5) = v4) |  ~ (convergent_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (distinct_lines(v6, v5) = v4) |  ~ (distinct_lines(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (distinct_points(v6, v5) = v4) |  ~ (distinct_points(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = v6) |  ~ (unorthogonal_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (unorthogonal_lines(v3, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (unorthogonal_lines(v3, v4) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) |  ~ (unorthogonal_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = v6) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & convergent_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (convergent_lines(v4, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v4, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v4, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v4, v5) = 0) |  ~ (convergent_lines(v3, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v4) = 0 & convergent_lines(v3, v4) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v4, v5) = 0) |  ~ (convergent_lines(v3, v4) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v3, v5) = 0 & convergent_lines(v3, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v4) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v4, v5) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (convergent_lines(v3, v5) = v6) |  ~ (convergent_lines(v3, v4) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v5) = 0 & convergent_lines(v4, v5) = 0) | (v7 = 0 & v6 = 0 & unorthogonal_lines(v3, v5) = 0) | ( ~ (v7 = 0) & unorthogonal_lines(v3, v4) = v7))) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (distinct_lines(v5, v6) = 0) |  ~ (distinct_points(v3, v4) = 0) |  ? [v7] : ((v7 = 0 & apart_point_and_line(v4, v6) = 0) | (v7 = 0 & apart_point_and_line(v4, v5) = 0) | (v7 = 0 & apart_point_and_line(v3, v6) = 0) | (v7 = 0 & apart_point_and_line(v3, v5) = 0))) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (orthogonal_lines(v3, v4) = v5) | unorthogonal_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (incident_point_and_line(v3, v4) = v5) | apart_point_and_line(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (parallel_lines(v3, v4) = v5) | convergent_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equal_lines(v3, v4) = v5) | distinct_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (equal_points(v3, v4) = v5) | distinct_points(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (unorthogonal_lines(v3, v4) = v5) | orthogonal_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (unorthogonal_lines(v3, v4) = v5) | convergent_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v3, v4) = v5) | incident_point_and_line(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v3, v4) = v5) | parallel_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v3, v4) = v5) | unorthogonal_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & distinct_lines(v3, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_lines(v3, v4) = v5) | equal_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_points(v3, v4) = v5) | equal_points(v3, v4) = 0) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (point(v5) = v4) |  ~ (point(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (line(v5) = v4) |  ~ (line(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (orthogonal_through_point(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & unorthogonal_lines(v5, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (orthogonal_through_point(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (orthogonal_through_point(v3, v4) = v5) |  ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) |  ? [v6] : ( ~ (v6 = 0) & convergent_lines(v5, v4) = v6)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v3, v4) = v5) |  ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ? [v6] : ((v6 = 0 & point(v5) = 0) | ( ~ (v6 = 0) & line(v4) = v6) | ( ~ (v6 = 0) & line(v3) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v5, v4) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v5, v3) = v6) | ( ~ (v6 = 0) & convergent_lines(v3, v4) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & point(v4) = v6) | ( ~ (v6 = 0) & point(v3) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v4, v5) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ? [v6] : (( ~ (v6 = 0) & apart_point_and_line(v3, v5) = v6) | ( ~ (v6 = 0) & distinct_points(v3, v4) = v6))) &  ! [v3] :  ! [v4] : ( ~ (orthogonal_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & unorthogonal_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (incident_point_and_line(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (parallel_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (equal_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (equal_points(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & orthogonal_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (apart_point_and_line(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & intersection_point(v3, v4) = v5 & apart_point_and_line(v5, v4) = v6)) &  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & intersection_point(v3, v4) = v5 & apart_point_and_line(v5, v3) = v6)) &  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & point(v5) = 0 & intersection_point(v3, v4) = v5) | ( ~ (v5 = 0) & line(v4) = v5) | ( ~ (v5 = 0) & line(v3) = v5))) &  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & parallel_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (distinct_lines(v3, v4) = 0) | convergent_lines(v3, v4) = 0) &  ! [v3] :  ! [v4] : ( ~ (distinct_lines(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & equal_lines(v3, v4) = v5)) &  ! [v3] :  ! [v4] : ( ~ (distinct_points(v3, v4) = 0) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & line_connecting(v3, v4) = v5 & apart_point_and_line(v4, v5) = v6)) &  ! [v3] :  ! [v4] : ( ~ (distinct_points(v3, v4) = 0) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & line_connecting(v3, v4) = v5 & apart_point_and_line(v3, v5) = v6)) &  ! [v3] :  ! [v4] : ( ~ (distinct_points(v3, v4) = 0) |  ? [v5] :  ? [v6] : ((v6 = 0 & line(v5) = 0 & line_connecting(v3, v4) = v5) | ( ~ (v5 = 0) & point(v4) = v5) | ( ~ (v5 = 0) & point(v3) = v5))) &  ! [v3] :  ! [v4] : ( ~ (distinct_points(v3, v4) = 0) |  ? [v5] : ( ~ (v5 = 0) & equal_points(v3, v4) = v5)) &  ! [v3] :  ~ (convergent_lines(v3, v3) = 0) &  ! [v3] :  ~ (distinct_lines(v3, v3) = 0) &  ! [v3] :  ~ (distinct_points(v3, v3) = 0) &  ? [v3] :  ? [v4] :  ? [v5] : orthogonal_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : incident_point_and_line(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : parallel_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : equal_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : equal_points(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : orthogonal_through_point(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : unorthogonal_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : parallel_through_point(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : intersection_point(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : line_connecting(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : apart_point_and_line(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : convergent_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : distinct_lines(v4, v3) = v5 &  ? [v3] :  ? [v4] :  ? [v5] : distinct_points(v4, v3) = v5 &  ? [v3] :  ? [v4] : point(v3) = v4 &  ? [v3] :  ? [v4] : line(v3) = v4)
% 22.38/6.47  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 22.38/6.47  | (1)  ~ (all_0_0_0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = 0 & distinct_lines(all_0_2_2, all_0_1_1) = all_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] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2 &  ? [v0] :  ? [v1] : point(v0) = v1 &  ? [v0] :  ? [v1] : line(v0) = v1
% 22.80/6.50  |
% 22.80/6.50  | Applying alpha-rule on (1) yields:
% 22.80/6.50  | (2)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 22.80/6.50  | (3)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 22.80/6.50  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 22.80/6.50  | (5)  ! [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)
% 22.80/6.50  | (6)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 22.80/6.50  | (7)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 22.80/6.50  | (8)  ? [v0] :  ? [v1] : line(v0) = v1
% 22.80/6.50  | (9)  ! [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)
% 22.80/6.50  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 22.80/6.50  | (11)  ! [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)))
% 22.80/6.50  | (12)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 22.80/6.50  | (13)  ! [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)
% 22.80/6.50  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 22.80/6.50  | (15)  ! [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)))
% 22.80/6.50  | (16)  ! [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)))
% 22.80/6.50  | (17)  ! [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)))
% 22.80/6.50  | (18)  ! [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)))
% 22.80/6.50  | (19)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 22.80/6.50  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 22.80/6.50  | (21)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.80/6.50  | (22)  ! [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)))
% 22.80/6.50  | (23)  ! [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)))
% 22.80/6.50  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 22.80/6.50  | (25)  ! [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)))
% 22.80/6.50  | (26)  ! [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)))
% 22.80/6.50  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 22.80/6.50  | (28)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 22.80/6.50  | (29)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 22.80/6.50  | (30)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 22.80/6.50  | (31)  ! [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)))
% 22.80/6.50  | (32)  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2
% 22.80/6.50  | (33)  ! [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)))
% 22.80/6.51  | (34)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 22.80/6.51  | (35)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 22.80/6.51  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.51  | (37)  ! [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)))
% 22.80/6.51  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 22.80/6.51  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.80/6.51  | (40)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 22.80/6.51  | (41)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 22.80/6.51  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 22.80/6.51  | (43)  ! [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))
% 22.80/6.51  | (44)  ! [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)))
% 22.80/6.51  | (45)  ! [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)))
% 22.80/6.51  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.80/6.51  | (47)  ! [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)))
% 22.80/6.51  | (48)  ! [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))
% 22.80/6.51  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 22.80/6.51  | (50)  ! [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)))
% 22.80/6.51  | (51)  ! [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)))
% 22.80/6.51  | (52)  ! [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)))
% 22.80/6.51  | (53)  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2
% 22.80/6.51  | (54)  ! [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)))
% 22.80/6.51  | (55)  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2
% 22.80/6.51  | (56)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 22.80/6.51  | (57)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 22.80/6.51  | (58)  ! [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))
% 22.80/6.51  | (59) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 22.80/6.51  | (60)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 22.80/6.51  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 22.80/6.51  | (62)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 22.80/6.51  | (63)  ! [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)))
% 22.80/6.51  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.80/6.51  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 22.80/6.51  | (66)  ! [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)))
% 22.80/6.51  | (67)  ! [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)))
% 22.80/6.51  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 22.80/6.51  | (69)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 22.80/6.51  | (70)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 22.80/6.51  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 22.80/6.51  | (72)  ! [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))
% 22.80/6.51  | (73)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 22.80/6.51  | (74)  ! [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)))
% 22.80/6.51  | (75)  ! [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)))
% 22.80/6.51  | (76)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 22.80/6.51  | (77)  ! [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)))
% 22.80/6.51  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 22.80/6.51  | (79)  ! [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)))
% 22.80/6.52  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.80/6.52  | (81)  ! [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))
% 22.80/6.52  | (82)  ! [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)))
% 22.80/6.52  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.80/6.52  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 22.80/6.52  | (85)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 22.80/6.52  | (86)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 22.80/6.52  | (87)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 22.80/6.52  | (88)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 22.80/6.52  | (89)  ! [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)))
% 22.80/6.52  | (90)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 22.80/6.52  | (91)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 22.80/6.52  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.52  | (93)  ! [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)))
% 22.80/6.52  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.80/6.52  | (95)  ! [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)))
% 22.80/6.52  | (96)  ! [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)))
% 22.80/6.52  | (97)  ! [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)))
% 22.80/6.52  | (98)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 22.80/6.52  | (99)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 22.80/6.52  | (100)  ! [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)))
% 22.80/6.52  | (101)  ! [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)
% 22.80/6.52  | (102)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.80/6.52  | (103)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.80/6.52  | (104)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 22.80/6.52  | (105)  ! [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)))
% 22.80/6.52  | (106)  ! [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)))
% 22.80/6.52  | (107)  ! [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)))
% 22.80/6.52  | (108)  ! [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)))
% 22.80/6.52  | (109)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2
% 22.80/6.52  | (110)  ? [v0] :  ? [v1] : point(v0) = v1
% 22.80/6.52  | (111)  ! [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))
% 22.80/6.52  | (112)  ~ (all_0_0_0 = 0)
% 22.80/6.52  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 22.80/6.52  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.80/6.52  | (115)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 22.80/6.52  | (116)  ! [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)))
% 22.80/6.52  | (117)  ! [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)))
% 22.80/6.52  | (118)  ! [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)))
% 22.80/6.52  | (119)  ! [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)))
% 22.80/6.52  | (120)  ! [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)))
% 22.80/6.53  | (121)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 22.80/6.53  | (122)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 22.80/6.53  | (123)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 22.80/6.53  | (124)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 22.80/6.53  | (125)  ! [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)))
% 22.80/6.53  | (126)  ! [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)))
% 22.80/6.53  | (127)  ! [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)))
% 22.80/6.53  | (128)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 22.80/6.53  | (129)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 22.80/6.53  | (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)))
% 22.80/6.53  | (131)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 22.80/6.53  | (132)  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2
% 22.80/6.53  | (133)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 22.80/6.53  | (134)  ! [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)))
% 22.80/6.53  | (135)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 22.80/6.53  | (136) distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0
% 22.80/6.53  | (137)  ! [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))
% 22.80/6.53  | (138)  ! [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)))
% 22.80/6.53  | (139)  ! [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)))
% 22.80/6.53  | (140)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 22.80/6.53  | (141)  ! [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)))
% 22.80/6.53  | (142)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 22.80/6.53  |
% 22.80/6.53  | Instantiating formula (21) with all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 22.80/6.53  | (143)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(v0, all_0_1_1) = v1)
% 22.80/6.53  |
% 22.80/6.53  | Instantiating formula (40) with all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 22.80/6.53  | (144)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 22.80/6.53  |
% 22.80/6.53  | Instantiating formula (48) with all_0_0_0, all_0_0_0, all_0_1_1, all_0_2_2, all_0_2_2 and discharging atoms distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.80/6.53  | (145) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)
% 22.80/6.53  |
% 22.80/6.53  | Instantiating (144) with all_42_0_50, all_42_1_51 yields:
% 22.80/6.53  | (146)  ~ (all_42_0_50 = 0) & intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51 & apart_point_and_line(all_42_1_51, all_0_2_2) = all_42_0_50
% 22.80/6.53  |
% 22.80/6.53  | Applying alpha-rule on (146) yields:
% 22.80/6.53  | (147)  ~ (all_42_0_50 = 0)
% 22.80/6.53  | (148) intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51
% 22.80/6.53  | (149) apart_point_and_line(all_42_1_51, all_0_2_2) = all_42_0_50
% 22.80/6.53  |
% 22.80/6.53  | Instantiating (143) with all_44_0_52, all_44_1_53 yields:
% 22.80/6.53  | (150)  ~ (all_44_0_52 = 0) & intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53 & apart_point_and_line(all_44_1_53, all_0_1_1) = all_44_0_52
% 22.80/6.53  |
% 22.80/6.53  | Applying alpha-rule on (150) yields:
% 22.80/6.53  | (151)  ~ (all_44_0_52 = 0)
% 22.80/6.53  | (152) intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53
% 22.80/6.53  | (153) apart_point_and_line(all_44_1_53, all_0_1_1) = all_44_0_52
% 22.80/6.53  |
% 22.80/6.53  +-Applying beta-rule and splitting (145), into two cases.
% 22.80/6.53  |-Branch one:
% 22.80/6.53  | (154) all_0_0_0 = 0
% 22.80/6.53  |
% 22.80/6.53  	| Equations (154) can reduce 112 to:
% 22.80/6.53  	| (155) $false
% 22.80/6.53  	|
% 22.80/6.53  	|-The branch is then unsatisfiable
% 22.80/6.53  |-Branch two:
% 22.80/6.53  | (112)  ~ (all_0_0_0 = 0)
% 22.80/6.53  | (157)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0)
% 22.80/6.53  |
% 22.80/6.53  	| Instantiating formula (42) with all_0_2_2, all_0_1_1, all_42_1_51, all_44_1_53 and discharging atoms intersection_point(all_0_2_2, all_0_1_1) = all_44_1_53, intersection_point(all_0_2_2, all_0_1_1) = all_42_1_51, yields:
% 22.80/6.53  	| (158) all_44_1_53 = all_42_1_51
% 22.80/6.53  	|
% 22.80/6.53  	| From (158) and (153) follows:
% 22.80/6.53  	| (159) apart_point_and_line(all_42_1_51, all_0_1_1) = all_44_0_52
% 22.80/6.53  	|
% 22.80/6.53  	| Instantiating formula (125) with all_44_0_52, all_44_0_52, all_0_1_1, all_0_1_1, all_42_1_51 and discharging atoms apart_point_and_line(all_42_1_51, all_0_1_1) = all_44_0_52, yields:
% 22.80/6.53  	| (160) all_44_0_52 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 22.80/6.53  	|
% 22.80/6.53  	+-Applying beta-rule and splitting (160), into two cases.
% 22.80/6.53  	|-Branch one:
% 22.80/6.53  	| (161) all_44_0_52 = 0
% 22.80/6.53  	|
% 22.80/6.53  		| Equations (161) can reduce 151 to:
% 22.80/6.53  		| (155) $false
% 22.80/6.53  		|
% 22.80/6.53  		|-The branch is then unsatisfiable
% 22.80/6.53  	|-Branch two:
% 22.80/6.53  	| (151)  ~ (all_44_0_52 = 0)
% 22.80/6.54  	| (164)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 22.80/6.54  	|
% 22.80/6.54  		| Instantiating (164) with all_100_0_81 yields:
% 22.80/6.54  		| (165) (all_100_0_81 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (all_100_0_81 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81)
% 22.80/6.54  		|
% 22.80/6.54  		+-Applying beta-rule and splitting (165), into two cases.
% 22.80/6.54  		|-Branch one:
% 22.80/6.54  		| (166) all_100_0_81 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 22.80/6.54  		|
% 22.80/6.54  			| Applying alpha-rule on (166) yields:
% 22.80/6.54  			| (167) all_100_0_81 = 0
% 22.80/6.54  			| (168) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 22.80/6.54  			|
% 22.80/6.54  			| Instantiating formula (34) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 22.80/6.54  			| (169) $false
% 22.80/6.54  			|
% 22.80/6.54  			|-The branch is then unsatisfiable
% 22.80/6.54  		|-Branch two:
% 22.80/6.54  		| (170)  ~ (all_100_0_81 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81
% 22.80/6.54  		|
% 22.80/6.54  			| Applying alpha-rule on (170) yields:
% 22.80/6.54  			| (171)  ~ (all_100_0_81 = 0)
% 22.80/6.54  			| (172) distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81
% 22.80/6.54  			|
% 22.80/6.54  			| Instantiating formula (48) with all_0_0_0, all_100_0_81, all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms distinct_lines(all_0_1_1, all_0_1_1) = all_100_0_81, distinct_lines(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 22.80/6.54  			| (173) all_100_0_81 = 0 | all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54  			|
% 22.80/6.54  			+-Applying beta-rule and splitting (173), into two cases.
% 22.80/6.54  			|-Branch one:
% 22.80/6.54  			| (167) all_100_0_81 = 0
% 22.80/6.54  			|
% 22.80/6.54  				| Equations (167) can reduce 171 to:
% 22.80/6.54  				| (155) $false
% 22.80/6.54  				|
% 22.80/6.54  				|-The branch is then unsatisfiable
% 22.80/6.54  			|-Branch two:
% 22.80/6.54  			| (171)  ~ (all_100_0_81 = 0)
% 22.80/6.54  			| (177) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54  			|
% 22.80/6.54  				+-Applying beta-rule and splitting (177), into two cases.
% 22.80/6.54  				|-Branch one:
% 22.80/6.54  				| (154) all_0_0_0 = 0
% 22.80/6.54  				|
% 22.80/6.54  					| Equations (154) can reduce 112 to:
% 22.80/6.54  					| (155) $false
% 22.80/6.54  					|
% 22.80/6.54  					|-The branch is then unsatisfiable
% 22.80/6.54  				|-Branch two:
% 22.80/6.54  				| (112)  ~ (all_0_0_0 = 0)
% 22.80/6.54  				| (181)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0)
% 22.80/6.54  				|
% 22.80/6.54  					| Instantiating (181) with all_211_0_94 yields:
% 22.80/6.54  					| (182)  ~ (all_211_0_94 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94
% 22.80/6.54  					|
% 22.80/6.54  					| Applying alpha-rule on (182) yields:
% 22.80/6.54  					| (183)  ~ (all_211_0_94 = 0)
% 22.80/6.54  					| (184) distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94
% 22.80/6.54  					|
% 22.80/6.54  					| Instantiating formula (114) with all_211_0_94, all_0_2_2, all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = 0, distinct_lines(all_0_1_1, all_0_2_2) = all_211_0_94, yields:
% 22.80/6.54  					| (185) all_211_0_94 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 22.80/6.54  					|
% 22.80/6.54  					+-Applying beta-rule and splitting (185), into two cases.
% 22.80/6.54  					|-Branch one:
% 22.80/6.54  					| (186) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 22.80/6.54  					|
% 22.80/6.54  						| Instantiating formula (34) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 22.80/6.54  						| (169) $false
% 22.80/6.54  						|
% 22.80/6.54  						|-The branch is then unsatisfiable
% 22.80/6.54  					|-Branch two:
% 22.80/6.54  					| (188)  ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 22.80/6.54  					| (189) all_211_0_94 = 0
% 22.80/6.54  					|
% 22.80/6.54  						| Equations (189) can reduce 183 to:
% 22.80/6.54  						| (155) $false
% 22.80/6.54  						|
% 22.80/6.54  						|-The branch is then unsatisfiable
% 22.80/6.54  % SZS output end Proof for theBenchmark
% 22.80/6.54  
% 22.80/6.54  5900ms
%------------------------------------------------------------------------------