%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 03:48:57 EDT 2022

% Result   : Theorem 27.56s 7.10s
% Output   : Proof 53.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jun 17 15:47:04 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.49/0.59          ____       _                          
% 0.49/0.59    ___  / __ \_____(_)___  ________  __________
% 0.49/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.49/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.49/0.59  
% 0.49/0.59  A Theorem Prover for First-Order Logic
% 0.49/0.59  (ePrincess v.1.0)
% 0.49/0.59  
% 0.49/0.59  (c) Philipp Rümmer, 2009-2015
% 0.49/0.59  (c) Peter Backeman, 2014-2015
% 0.49/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.59  Bug reports to peter@backeman.se
% 0.49/0.59  
% 0.49/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.59  
% 0.49/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/0.98  Prover 0: Preprocessing ...
% 2.42/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.42/1.22  Prover 0: Constructing countermodel ...
% 12.63/3.64  Prover 0: gave up
% 12.63/3.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 12.63/3.68  Prover 1: Preprocessing ...
% 13.45/3.80  Prover 1: Constructing countermodel ...
% 13.45/3.82  Prover 1: gave up
% 13.45/3.82  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 13.45/3.85  Prover 2: Preprocessing ...
% 14.46/4.02  Prover 2: Warning: ignoring some quantifiers
% 14.46/4.03  Prover 2: Constructing countermodel ...
% 14.78/4.09  Prover 2: gave up
% 14.78/4.09  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.78/4.12  Prover 3: Preprocessing ...
% 14.78/4.13  Prover 3: Warning: ignoring some quantifiers
% 14.78/4.14  Prover 3: Constructing countermodel ...
% 21.98/5.80  Prover 3: gave up
% 21.98/5.80  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 21.98/5.83  Prover 4: Preprocessing ...
% 22.33/5.94  Prover 4: Warning: ignoring some quantifiers
% 22.33/5.94  Prover 4: Constructing countermodel ...
% 25.87/6.75  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 25.87/6.78  Prover 5: Preprocessing ...
% 26.25/6.84  Prover 5: Constructing countermodel ...
% 27.56/7.10  Prover 5: proved (349ms)
% 27.56/7.10  Prover 4: stopped
% 27.56/7.10  
% 27.56/7.10  No countermodel exists, formula is valid
% 27.56/7.10  % SZS status Theorem for theBenchmark
% 27.56/7.10  
% 27.56/7.10  Generating proof ... found it (size 137)
% 53.23/17.79  
% 53.23/17.79  % SZS output start Proof for theBenchmark
% 53.23/17.79  Assumed formulas after preprocessing and simplification: 
% 53.23/17.79  | (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] :  ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [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] :  ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [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] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [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] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [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] :  ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) &  ! [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] :  ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] :  ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0))) &  ! [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] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [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] :  ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 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] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 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] :  ? [v4] :  ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [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] : ( ~ (point(v1) = 0) |  ~ (point(v0) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) &  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (line(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0))) &  ! [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] :  ? [v4] :  ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v5 = 0))) &  ! [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] : ( ~ (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] :  ? [v4] :  ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v5 = 0))) &  ! [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] : ( ~ (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] : (point(v0) = 0 & line(v1) = 0 &  ! [v2] : ( ~ (incident_point_and_line(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & point(v2) = v3)) &  ! [v2] : ( ~ (point(v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v2, v1) = v3)))
% 53.43/17.87  | Applying alpha-rule on (0) yields:
% 53.43/17.87  | (1)  ! [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))
% 53.43/17.87  | (2)  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.43/17.87  | (3)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 53.43/17.87  | (4)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 53.43/17.87  | (5)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 53.43/17.87  | (6)  ! [v0] :  ! [v1] : ( ~ (line(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (point(v3) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 53.43/17.88  | (7)  ! [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)
% 53.43/17.88  | (8)  ! [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)
% 53.43/17.88  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) | v6 = 0)))
% 53.43/17.88  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 53.43/17.88  | (11)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 53.43/17.88  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 53.43/17.88  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 53.43/17.88  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 53.43/17.88  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 53.43/17.88  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ~ (v3 = 0) | v6 = 0)))
% 53.43/17.88  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 53.43/17.88  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] :  ? [v6] : (apart_point_and_line(v0, v1) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 53.43/17.88  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 53.43/17.88  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 53.43/17.88  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 53.43/17.88  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 53.43/17.88  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 53.43/17.88  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 53.43/17.88  | (25)  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.43/17.88  | (26)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 53.43/17.88  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] :  ? [v6] : (convergent_lines(v1, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 53.43/17.88  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 53.43/17.88  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 53.43/17.88  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v2, v0) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 53.43/17.88  | (31)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 53.43/17.88  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v2, v1) = v4 & convergent_lines(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 53.43/17.89  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 53.43/17.89  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 53.43/17.89  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 53.43/17.89  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 53.43/17.89  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 53.43/17.89  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 53.43/17.89  | (39)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 53.43/17.89  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 53.43/17.89  | (41)  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.43/17.89  | (42)  ! [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))
% 53.43/17.89  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 53.43/17.89  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 53.43/17.89  | (45)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 53.43/17.89  | (46)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 53.43/17.89  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 53.43/17.89  | (48)  ! [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] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 53.43/17.89  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (point(v1) = v4 & line(v2) = v5 & line(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = 0)))
% 53.43/17.89  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 53.43/17.89  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 53.43/17.89  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 53.43/17.89  | (53)  ! [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))
% 53.43/17.89  | (54)  ! [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] :  ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 53.43/17.89  | (55)  ! [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)
% 53.43/17.89  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 53.43/17.89  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 53.43/17.89  | (58)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 53.43/17.89  | (59)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 53.43/17.90  | (60)  ! [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))
% 53.43/17.90  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 53.43/17.90  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 53.43/17.90  | (63)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 53.43/17.90  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 53.43/17.90  | (65)  ! [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))
% 53.43/17.90  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 53.43/17.90  | (67)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & line_connecting(v0, v1) = v4 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v5 = 0)))
% 53.43/17.90  | (68)  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2))
% 53.43/17.90  | (69)  ? [v0] :  ? [v1] : (point(v0) = 0 & line(v1) = 0 &  ! [v2] : ( ~ (incident_point_and_line(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & point(v2) = v3)) &  ! [v2] : ( ~ (point(v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & incident_point_and_line(v2, v1) = v3)))
% 53.43/17.90  | (70)  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (point(v0) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (line(v3) = v4 & line_connecting(v0, v1) = v3 & distinct_points(v0, v1) = v2 & ( ~ (v2 = 0) | v4 = 0)))
% 53.43/17.90  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v0, v2) = v5 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 53.43/17.90  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0) | (v6 = 0 & v5 = 0))))
% 53.43/17.90  | (73)  ! [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))
% 53.43/17.90  | (74)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 53.43/17.90  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v1) = v5 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 53.43/17.90  | (76)  ! [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))
% 53.43/17.90  | (77)  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2))
% 53.43/17.90  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 53.82/17.90  | (79)  ! [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] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 53.82/17.90  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] :  ? [v6] : (apart_point_and_line(v0, v2) = v6 & distinct_lines(v1, v2) = v5 & ( ~ (v5 = 0) | v6 = 0)))
% 53.82/17.90  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v7 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 53.82/17.91  | (82)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 53.82/17.91  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v6 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 53.82/17.91  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v2, v3) = v8 & apart_point_and_line(v0, v1) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.82/17.91  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 53.82/17.91  | (86)  ! [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)
% 53.82/17.91  | (87)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 53.82/17.91  | (88)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 53.82/17.91  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v1) = v6 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 53.82/17.91  | (90)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 53.82/17.91  | (91)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 53.82/17.91  | (92)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 53.82/17.91  | (93)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 53.82/17.91  | (94)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 53.82/17.91  | (95)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 53.82/17.91  | (96)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v1, v2) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.82/17.91  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 53.82/17.91  | (98)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v1) = v5 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v7 = 0) | (v6 = 0 & v3 = 0) | (v5 = 0 & v4 = 0))))
% 53.82/17.91  | (99)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 53.82/17.91  | (100)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 53.82/17.91  | (101)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 53.82/17.91  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v0, v2) = v6 & unorthogonal_lines(v0, v1) = v4 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v5 & ( ~ (v7 = 0) | (v6 = 0 & v5 = 0) | (v4 = 0 & v3 = 0))))
% 53.82/17.91  | (103)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 53.82/17.91  | (104)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 53.82/17.91  | (105)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 53.82/17.91  | (106)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 53.82/17.91  | (107)  ! [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] :  ? [v7] : (unorthogonal_lines(v1, v3) = v7 & apart_point_and_line(v0, v1) = v6 & (v7 = 0 | v6 = 0)))
% 53.82/17.92  | (108)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 53.82/17.92  | (109)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 53.82/17.92  | (110)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 53.82/17.92  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : (apart_point_and_line(v0, v1) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 53.82/17.92  | (112)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 53.82/17.92  | (113)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 53.82/17.92  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 53.82/17.92  | (115)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 53.82/17.92  | (116)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 53.82/17.92  | (117)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 53.82/17.92  | (118)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 53.82/17.92  | (119)  ! [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] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 53.82/17.92  | (120)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 53.82/17.92  | (121)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 53.82/17.92  | (122)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & unorthogonal_lines(v0, v2) = v5 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 53.82/17.92  | (123)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v0, v1) = v6 & convergent_lines(v1, v2) = v8 & convergent_lines(v0, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v8 = 0 & v4 = 0) | (v7 = 0 & v3 = 0))))
% 53.82/17.92  | (124)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 53.82/17.92  | (125)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (point(v4) = v5 & line(v1) = v3 & line(v0) = v2 & intersection_point(v0, v1) = v4 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v5 = 0)))
% 53.82/17.92  | (126)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 53.82/17.92  | (127)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & unorthogonal_lines(v0, v2) = v6 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 53.82/17.92  |
% 53.82/17.92  | Instantiating (69) with all_1_0_0, all_1_1_1 yields:
% 53.82/17.92  | (128) point(all_1_1_1) = 0 & line(all_1_0_0) = 0 &  ! [v0] : ( ~ (incident_point_and_line(v0, all_1_0_0) = 0) |  ? [v1] : ( ~ (v1 = 0) & point(v0) = v1)) &  ! [v0] : ( ~ (point(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_1_0_0) = v1))
% 53.82/17.92  |
% 53.82/17.92  | Applying alpha-rule on (128) yields:
% 53.82/17.92  | (129) point(all_1_1_1) = 0
% 53.82/17.92  | (130) line(all_1_0_0) = 0
% 53.82/17.92  | (131)  ! [v0] : ( ~ (incident_point_and_line(v0, all_1_0_0) = 0) |  ? [v1] : ( ~ (v1 = 0) & point(v0) = v1))
% 53.82/17.92  | (132)  ! [v0] : ( ~ (point(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & incident_point_and_line(v0, all_1_0_0) = v1))
% 53.82/17.92  |
% 53.82/17.92  | Instantiating formula (132) with all_1_1_1 and discharging atoms point(all_1_1_1) = 0, yields:
% 53.82/17.92  | (133)  ? [v0] : ( ~ (v0 = 0) & incident_point_and_line(all_1_1_1, all_1_0_0) = v0)
% 53.82/17.92  |
% 53.82/17.92  | Instantiating formula (68) with all_1_1_1, all_1_0_0 and discharging atoms point(all_1_1_1) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.92  | (134)  ? [v0] : (line(v0) = 0 & orthogonal_through_point(all_1_0_0, all_1_1_1) = v0)
% 53.82/17.92  |
% 53.82/17.92  | Instantiating formula (77) with all_1_1_1, all_1_0_0 and discharging atoms point(all_1_1_1) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.92  | (135)  ? [v0] : (line(v0) = 0 & parallel_through_point(all_1_0_0, all_1_1_1) = v0)
% 53.82/17.92  |
% 53.82/17.92  | Instantiating formula (6) with all_1_0_0, all_1_0_0 and discharging atoms line(all_1_0_0) = 0, yields:
% 53.82/17.92  | (136)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_1_0_0, all_1_0_0) = v1 & convergent_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.92  |
% 53.82/17.92  | Instantiating (136) with all_9_0_2, all_9_1_3, all_9_2_4 yields:
% 53.82/17.92  | (137) point(all_9_1_3) = all_9_0_2 & intersection_point(all_1_0_0, all_1_0_0) = all_9_1_3 & convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4 & ( ~ (all_9_2_4 = 0) | all_9_0_2 = 0)
% 53.82/17.92  |
% 53.82/17.92  | Applying alpha-rule on (137) yields:
% 53.82/17.92  | (138) point(all_9_1_3) = all_9_0_2
% 53.82/17.92  | (139) intersection_point(all_1_0_0, all_1_0_0) = all_9_1_3
% 53.82/17.92  | (140) convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4
% 53.82/17.92  | (141)  ~ (all_9_2_4 = 0) | all_9_0_2 = 0
% 53.82/17.92  |
% 53.82/17.92  | Instantiating (135) with all_11_0_5 yields:
% 53.82/17.92  | (142) line(all_11_0_5) = 0 & parallel_through_point(all_1_0_0, all_1_1_1) = all_11_0_5
% 53.82/17.92  |
% 53.82/17.92  | Applying alpha-rule on (142) yields:
% 53.82/17.92  | (143) line(all_11_0_5) = 0
% 53.82/17.92  | (144) parallel_through_point(all_1_0_0, all_1_1_1) = all_11_0_5
% 53.82/17.92  |
% 53.82/17.92  | Instantiating (133) with all_13_0_6 yields:
% 53.82/17.92  | (145)  ~ (all_13_0_6 = 0) & incident_point_and_line(all_1_1_1, all_1_0_0) = all_13_0_6
% 53.82/17.92  |
% 53.82/17.92  | Applying alpha-rule on (145) yields:
% 53.82/17.92  | (146)  ~ (all_13_0_6 = 0)
% 53.82/17.92  | (147) incident_point_and_line(all_1_1_1, all_1_0_0) = all_13_0_6
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (134) with all_17_0_10 yields:
% 53.82/17.93  | (148) line(all_17_0_10) = 0 & orthogonal_through_point(all_1_0_0, all_1_1_1) = all_17_0_10
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (148) yields:
% 53.82/17.93  | (149) line(all_17_0_10) = 0
% 53.82/17.93  | (150) orthogonal_through_point(all_1_0_0, all_1_1_1) = all_17_0_10
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (95) with all_1_0_0 yields:
% 53.82/17.93  | (151)  ~ (convergent_lines(all_1_0_0, all_1_0_0) = 0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (59) with all_13_0_6, all_1_0_0, all_1_1_1 and discharging atoms incident_point_and_line(all_1_1_1, all_1_0_0) = all_13_0_6, yields:
% 53.82/17.93  | (152) all_13_0_6 = 0 | apart_point_and_line(all_1_1_1, all_1_0_0) = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (6) with all_17_0_10, all_1_0_0 and discharging atoms line(all_17_0_10) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.93  | (153)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_1_0_0, all_17_0_10) = v1 & convergent_lines(all_1_0_0, all_17_0_10) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (6) with all_1_0_0, all_17_0_10 and discharging atoms line(all_17_0_10) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.93  | (154)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_17_0_10, all_1_0_0) = v1 & convergent_lines(all_17_0_10, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (6) with all_11_0_5, all_1_0_0 and discharging atoms line(all_11_0_5) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.93  | (155)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_1_0_0, all_11_0_5) = v1 & convergent_lines(all_1_0_0, all_11_0_5) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (6) with all_1_0_0, all_11_0_5 and discharging atoms line(all_11_0_5) = 0, line(all_1_0_0) = 0, yields:
% 53.82/17.93  | (156)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_11_0_5, all_1_0_0) = v1 & convergent_lines(all_11_0_5, all_1_0_0) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (6) with all_11_0_5, all_17_0_10 and discharging atoms line(all_17_0_10) = 0, line(all_11_0_5) = 0, yields:
% 53.82/17.93  | (157)  ? [v0] :  ? [v1] :  ? [v2] : (point(v1) = v2 & intersection_point(all_17_0_10, all_11_0_5) = v1 & convergent_lines(all_17_0_10, all_11_0_5) = v0 & ( ~ (v0 = 0) | v2 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (101) with all_17_0_10, all_1_0_0, all_1_1_1 and discharging atoms orthogonal_through_point(all_1_0_0, all_1_1_1) = all_17_0_10, yields:
% 53.82/17.93  | (158)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_17_0_10, all_1_0_0) = v0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (74) with all_11_0_5, all_1_0_0, all_1_1_1 and discharging atoms parallel_through_point(all_1_0_0, all_1_1_1) = all_11_0_5, yields:
% 53.82/17.93  | (159)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_1_1, all_11_0_5) = v0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (82) with all_11_0_5, all_1_0_0, all_1_1_1 and discharging atoms parallel_through_point(all_1_0_0, all_1_1_1) = all_11_0_5, yields:
% 53.82/17.93  | (160)  ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_11_0_5, all_1_0_0) = v0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (32) with all_9_1_3, all_1_0_0, all_1_0_0 and discharging atoms intersection_point(all_1_0_0, all_1_0_0) = all_9_1_3, yields:
% 53.82/17.93  | (161)  ? [v0] :  ? [v1] : (apart_point_and_line(all_9_1_3, all_1_0_0) = v1 & convergent_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (81) with all_9_2_4, all_9_2_4, all_1_0_0, all_1_0_0, all_1_0_0 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4, yields:
% 53.82/17.93  | (162)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_0_0, all_1_0_0) = v3 & unorthogonal_lines(all_1_0_0, all_1_0_0) = v2 & unorthogonal_lines(all_1_0_0, all_1_0_0) = v1 & convergent_lines(all_1_0_0, all_1_0_0) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | (v3 = 0 & all_9_2_4 = 0) | (v2 = 0 & all_9_2_4 = 0)))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating formula (21) with all_9_2_4, all_9_2_4, all_1_0_0, all_1_0_0, all_1_0_0 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4, yields:
% 53.82/17.93  | (163)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_0_0, all_1_0_0) = v3 & unorthogonal_lines(all_1_0_0, all_1_0_0) = v1 & unorthogonal_lines(all_1_0_0, all_1_0_0) = v0 & convergent_lines(all_1_0_0, all_1_0_0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) | (v1 = 0 & all_9_2_4 = 0) | (v0 = 0 & all_9_2_4 = 0)))
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (163) with all_32_0_11, all_32_1_12, all_32_2_13, all_32_3_14 yields:
% 53.82/17.93  | (164) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_0_11 & unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_2_13 & unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_3_14 & convergent_lines(all_1_0_0, all_1_0_0) = all_32_1_12 & ( ~ (all_32_0_11 = 0) |  ~ (all_32_1_12 = 0) | (all_32_2_13 = 0 & all_9_2_4 = 0) | (all_32_3_14 = 0 & all_9_2_4 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (164) yields:
% 53.82/17.93  | (165)  ~ (all_32_0_11 = 0) |  ~ (all_32_1_12 = 0) | (all_32_2_13 = 0 & all_9_2_4 = 0) | (all_32_3_14 = 0 & all_9_2_4 = 0)
% 53.82/17.93  | (166) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_0_11
% 53.82/17.93  | (167) convergent_lines(all_1_0_0, all_1_0_0) = all_32_1_12
% 53.82/17.93  | (168) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_2_13
% 53.82/17.93  | (169) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_32_3_14
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (162) with all_34_0_15, all_34_1_16, all_34_2_17, all_34_3_18 yields:
% 53.82/17.93  | (170) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_0_15 & unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_1_16 & unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_2_17 & convergent_lines(all_1_0_0, all_1_0_0) = all_34_3_18 & ( ~ (all_34_2_17 = 0) |  ~ (all_34_3_18 = 0) | (all_34_0_15 = 0 & all_9_2_4 = 0) | (all_34_1_16 = 0 & all_9_2_4 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (170) yields:
% 53.82/17.93  | (171) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_1_16
% 53.82/17.93  | (172) convergent_lines(all_1_0_0, all_1_0_0) = all_34_3_18
% 53.82/17.93  | (173) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_2_17
% 53.82/17.93  | (174) unorthogonal_lines(all_1_0_0, all_1_0_0) = all_34_0_15
% 53.82/17.93  | (175)  ~ (all_34_2_17 = 0) |  ~ (all_34_3_18 = 0) | (all_34_0_15 = 0 & all_9_2_4 = 0) | (all_34_1_16 = 0 & all_9_2_4 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (161) with all_38_0_21, all_38_1_22 yields:
% 53.82/17.93  | (176) apart_point_and_line(all_9_1_3, all_1_0_0) = all_38_0_21 & convergent_lines(all_1_0_0, all_1_0_0) = all_38_1_22 & ( ~ (all_38_0_21 = 0) |  ~ (all_38_1_22 = 0))
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (176) yields:
% 53.82/17.93  | (177) apart_point_and_line(all_9_1_3, all_1_0_0) = all_38_0_21
% 53.82/17.93  | (178) convergent_lines(all_1_0_0, all_1_0_0) = all_38_1_22
% 53.82/17.93  | (179)  ~ (all_38_0_21 = 0) |  ~ (all_38_1_22 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (157) with all_40_0_23, all_40_1_24, all_40_2_25 yields:
% 53.82/17.93  | (180) point(all_40_1_24) = all_40_0_23 & intersection_point(all_17_0_10, all_11_0_5) = all_40_1_24 & convergent_lines(all_17_0_10, all_11_0_5) = all_40_2_25 & ( ~ (all_40_2_25 = 0) | all_40_0_23 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (180) yields:
% 53.82/17.93  | (181) point(all_40_1_24) = all_40_0_23
% 53.82/17.93  | (182) intersection_point(all_17_0_10, all_11_0_5) = all_40_1_24
% 53.82/17.93  | (183) convergent_lines(all_17_0_10, all_11_0_5) = all_40_2_25
% 53.82/17.93  | (184)  ~ (all_40_2_25 = 0) | all_40_0_23 = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (155) with all_42_0_26, all_42_1_27, all_42_2_28 yields:
% 53.82/17.93  | (185) point(all_42_1_27) = all_42_0_26 & intersection_point(all_1_0_0, all_11_0_5) = all_42_1_27 & convergent_lines(all_1_0_0, all_11_0_5) = all_42_2_28 & ( ~ (all_42_2_28 = 0) | all_42_0_26 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (185) yields:
% 53.82/17.93  | (186) point(all_42_1_27) = all_42_0_26
% 53.82/17.93  | (187) intersection_point(all_1_0_0, all_11_0_5) = all_42_1_27
% 53.82/17.93  | (188) convergent_lines(all_1_0_0, all_11_0_5) = all_42_2_28
% 53.82/17.93  | (189)  ~ (all_42_2_28 = 0) | all_42_0_26 = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (156) with all_50_0_32, all_50_1_33, all_50_2_34 yields:
% 53.82/17.93  | (190) point(all_50_1_33) = all_50_0_32 & intersection_point(all_11_0_5, all_1_0_0) = all_50_1_33 & convergent_lines(all_11_0_5, all_1_0_0) = all_50_2_34 & ( ~ (all_50_2_34 = 0) | all_50_0_32 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (190) yields:
% 53.82/17.93  | (191) point(all_50_1_33) = all_50_0_32
% 53.82/17.93  | (192) intersection_point(all_11_0_5, all_1_0_0) = all_50_1_33
% 53.82/17.93  | (193) convergent_lines(all_11_0_5, all_1_0_0) = all_50_2_34
% 53.82/17.93  | (194)  ~ (all_50_2_34 = 0) | all_50_0_32 = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (154) with all_56_0_39, all_56_1_40, all_56_2_41 yields:
% 53.82/17.93  | (195) point(all_56_1_40) = all_56_0_39 & intersection_point(all_17_0_10, all_1_0_0) = all_56_1_40 & convergent_lines(all_17_0_10, all_1_0_0) = all_56_2_41 & ( ~ (all_56_2_41 = 0) | all_56_0_39 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (195) yields:
% 53.82/17.93  | (196) point(all_56_1_40) = all_56_0_39
% 53.82/17.93  | (197) intersection_point(all_17_0_10, all_1_0_0) = all_56_1_40
% 53.82/17.93  | (198) convergent_lines(all_17_0_10, all_1_0_0) = all_56_2_41
% 53.82/17.93  | (199)  ~ (all_56_2_41 = 0) | all_56_0_39 = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (153) with all_58_0_42, all_58_1_43, all_58_2_44 yields:
% 53.82/17.93  | (200) point(all_58_1_43) = all_58_0_42 & intersection_point(all_1_0_0, all_17_0_10) = all_58_1_43 & convergent_lines(all_1_0_0, all_17_0_10) = all_58_2_44 & ( ~ (all_58_2_44 = 0) | all_58_0_42 = 0)
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (200) yields:
% 53.82/17.93  | (201) point(all_58_1_43) = all_58_0_42
% 53.82/17.93  | (202) intersection_point(all_1_0_0, all_17_0_10) = all_58_1_43
% 53.82/17.93  | (203) convergent_lines(all_1_0_0, all_17_0_10) = all_58_2_44
% 53.82/17.93  | (204)  ~ (all_58_2_44 = 0) | all_58_0_42 = 0
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (158) with all_62_0_46 yields:
% 53.82/17.93  | (205)  ~ (all_62_0_46 = 0) & unorthogonal_lines(all_17_0_10, all_1_0_0) = all_62_0_46
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (205) yields:
% 53.82/17.93  | (206)  ~ (all_62_0_46 = 0)
% 53.82/17.93  | (207) unorthogonal_lines(all_17_0_10, all_1_0_0) = all_62_0_46
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (160) with all_64_0_47 yields:
% 53.82/17.93  | (208)  ~ (all_64_0_47 = 0) & convergent_lines(all_11_0_5, all_1_0_0) = all_64_0_47
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (208) yields:
% 53.82/17.93  | (209)  ~ (all_64_0_47 = 0)
% 53.82/17.93  | (210) convergent_lines(all_11_0_5, all_1_0_0) = all_64_0_47
% 53.82/17.93  |
% 53.82/17.93  | Instantiating (159) with all_66_0_48 yields:
% 53.82/17.93  | (211)  ~ (all_66_0_48 = 0) & apart_point_and_line(all_1_1_1, all_11_0_5) = all_66_0_48
% 53.82/17.93  |
% 53.82/17.93  | Applying alpha-rule on (211) yields:
% 53.82/17.93  | (212)  ~ (all_66_0_48 = 0)
% 53.82/17.93  | (213) apart_point_and_line(all_1_1_1, all_11_0_5) = all_66_0_48
% 53.82/17.93  |
% 53.82/17.93  +-Applying beta-rule and splitting (152), into two cases.
% 53.82/17.93  |-Branch one:
% 53.82/17.93  | (214) apart_point_and_line(all_1_1_1, all_1_0_0) = 0
% 53.82/17.93  |
% 53.82/17.93  	| Instantiating formula (95) with all_17_0_10 yields:
% 53.82/17.93  	| (215)  ~ (convergent_lines(all_17_0_10, all_17_0_10) = 0)
% 53.82/17.93  	|
% 53.82/17.93  	| Instantiating formula (37) with all_11_0_5, all_1_0_0, all_50_2_34, all_56_2_41 and discharging atoms convergent_lines(all_11_0_5, all_1_0_0) = all_50_2_34, yields:
% 53.82/17.93  	| (216) all_56_2_41 = all_50_2_34 |  ~ (convergent_lines(all_11_0_5, all_1_0_0) = all_56_2_41)
% 53.82/17.93  	|
% 53.82/17.93  	| Instantiating formula (37) with all_11_0_5, all_1_0_0, all_50_2_34, all_64_0_47 and discharging atoms convergent_lines(all_11_0_5, all_1_0_0) = all_64_0_47, convergent_lines(all_11_0_5, all_1_0_0) = all_50_2_34, yields:
% 53.82/17.93  	| (217) all_64_0_47 = all_50_2_34
% 53.82/17.93  	|
% 53.82/17.94  	| Instantiating formula (37) with all_1_0_0, all_1_0_0, all_38_1_22, all_9_2_4 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_38_1_22, convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4, yields:
% 53.82/17.94  	| (218) all_38_1_22 = all_9_2_4
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (37) with all_1_0_0, all_1_0_0, all_34_3_18, all_38_1_22 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_38_1_22, convergent_lines(all_1_0_0, all_1_0_0) = all_34_3_18, yields:
% 53.82/17.94  	| (219) all_38_1_22 = all_34_3_18
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (37) with all_1_0_0, all_1_0_0, all_32_1_12, all_34_3_18 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_34_3_18, convergent_lines(all_1_0_0, all_1_0_0) = all_32_1_12, yields:
% 53.82/17.94  	| (220) all_34_3_18 = all_32_1_12
% 53.82/17.94  	|
% 53.82/17.94  	| Using (167) and (151) yields:
% 53.82/17.94  	| (221)  ~ (all_32_1_12 = 0)
% 53.82/17.94  	|
% 53.82/17.94  	| Combining equations (219,218) yields a new equation:
% 53.82/17.94  	| (222) all_34_3_18 = all_9_2_4
% 53.82/17.94  	|
% 53.82/17.94  	| Simplifying 222 yields:
% 53.82/17.94  	| (223) all_34_3_18 = all_9_2_4
% 53.82/17.94  	|
% 53.82/17.94  	| Combining equations (223,220) yields a new equation:
% 53.82/17.94  	| (224) all_32_1_12 = all_9_2_4
% 53.82/17.94  	|
% 53.82/17.94  	| Equations (217) can reduce 209 to:
% 53.82/17.94  	| (225)  ~ (all_50_2_34 = 0)
% 53.82/17.94  	|
% 53.82/17.94  	| Equations (224) can reduce 221 to:
% 53.82/17.94  	| (226)  ~ (all_9_2_4 = 0)
% 53.82/17.94  	|
% 53.82/17.94  	| From (224) and (167) follows:
% 53.82/17.94  	| (140) convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (100) with all_62_0_46, all_1_0_0, all_17_0_10 and discharging atoms unorthogonal_lines(all_17_0_10, all_1_0_0) = all_62_0_46, yields:
% 53.82/17.94  	| (228) all_62_0_46 = 0 | convergent_lines(all_17_0_10, all_1_0_0) = 0
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (7) with all_66_0_48, all_11_0_5, all_1_0_0, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_11_0_5) = all_66_0_48, apart_point_and_line(all_1_1_1, all_1_0_0) = 0, yields:
% 53.82/17.94  	| (229) all_66_0_48 = 0 | distinct_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (108) with all_40_2_25, all_11_0_5, all_1_0_0, all_17_0_10 and discharging atoms convergent_lines(all_17_0_10, all_11_0_5) = all_40_2_25, yields:
% 53.82/17.94  	| (230) all_40_2_25 = 0 |  ~ (convergent_lines(all_17_0_10, all_1_0_0) = 0) | convergent_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (85) with all_58_2_44, all_17_0_10, all_1_0_0, all_17_0_10 and discharging atoms convergent_lines(all_1_0_0, all_17_0_10) = all_58_2_44,  ~ (convergent_lines(all_17_0_10, all_17_0_10) = 0), yields:
% 53.82/17.94  	| (231) all_58_2_44 = 0 |  ~ (convergent_lines(all_17_0_10, all_1_0_0) = 0)
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (78) with all_62_0_46, all_17_0_10, all_1_0_0, all_17_0_10 and discharging atoms unorthogonal_lines(all_17_0_10, all_1_0_0) = all_62_0_46, yields:
% 53.82/17.94  	| (232) all_62_0_46 = 0 |  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0) | unorthogonal_lines(all_17_0_10, all_17_0_10) = 0
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (85) with all_56_2_41, all_1_0_0, all_17_0_10, all_1_0_0 and discharging atoms convergent_lines(all_17_0_10, all_1_0_0) = all_56_2_41,  ~ (convergent_lines(all_1_0_0, all_1_0_0) = 0), yields:
% 53.82/17.94  	| (233) all_56_2_41 = 0 |  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (125) with all_17_0_10, all_1_0_0 yields:
% 53.82/17.94  	| (234)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0) |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_17_0_10) = v1 & line(all_1_0_0) = v0 & intersection_point(all_1_0_0, all_17_0_10) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (39) with all_17_0_10, all_1_0_0 yields:
% 53.82/17.94  	| (235)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0) |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_0_0, all_17_0_10) = v0 & apart_point_and_line(v0, all_17_0_10) = v1)
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (3) with all_17_0_10, all_1_0_0 yields:
% 53.82/17.94  	| (236)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0) |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_0_0, all_17_0_10) = v0 & apart_point_and_line(v0, all_1_0_0) = v1)
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (4) with all_17_0_10, all_1_0_0 yields:
% 53.82/17.94  	| (237)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0) |  ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_0_0, all_17_0_10) = v0)
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (108) with all_9_2_4, all_1_0_0, all_11_0_5, all_1_0_0 and discharging atoms convergent_lines(all_1_0_0, all_1_0_0) = all_9_2_4, yields:
% 53.82/17.94  	| (238) all_9_2_4 = 0 |  ~ (convergent_lines(all_1_0_0, all_11_0_5) = 0) | convergent_lines(all_11_0_5, all_1_0_0) = 0
% 53.82/17.94  	|
% 53.82/17.94  	| Instantiating formula (43) with all_42_2_28, all_11_0_5, all_1_0_0 and discharging atoms convergent_lines(all_1_0_0, all_11_0_5) = all_42_2_28, yields:
% 53.82/17.94  	| (239) all_42_2_28 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_0_0, all_11_0_5) = v0)
% 53.82/17.94  	|
% 53.82/17.94  	+-Applying beta-rule and splitting (228), into two cases.
% 53.82/17.94  	|-Branch one:
% 53.82/17.94  	| (240) convergent_lines(all_17_0_10, all_1_0_0) = 0
% 53.82/17.94  	|
% 53.82/17.94  		+-Applying beta-rule and splitting (231), into two cases.
% 53.82/17.94  		|-Branch one:
% 53.82/17.94  		| (241)  ~ (convergent_lines(all_17_0_10, all_1_0_0) = 0)
% 53.82/17.94  		|
% 53.82/17.94  			| Using (240) and (241) yields:
% 53.82/17.94  			| (242) $false
% 53.82/17.94  			|
% 53.82/17.94  			|-The branch is then unsatisfiable
% 53.82/17.94  		|-Branch two:
% 53.82/17.94  		| (240) convergent_lines(all_17_0_10, all_1_0_0) = 0
% 53.82/17.94  		| (244) all_58_2_44 = 0
% 53.82/17.94  		|
% 53.82/17.94  			| From (244) and (203) follows:
% 53.82/17.94  			| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  			|
% 53.82/17.94  			+-Applying beta-rule and splitting (229), into two cases.
% 53.82/17.94  			|-Branch one:
% 53.82/17.94  			| (246) distinct_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.94  			|
% 53.82/17.94  				+-Applying beta-rule and splitting (232), into two cases.
% 53.82/17.94  				|-Branch one:
% 53.82/17.94  				| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  				|
% 53.82/17.94  					| Using (245) and (247) yields:
% 53.82/17.94  					| (242) $false
% 53.82/17.94  					|
% 53.82/17.94  					|-The branch is then unsatisfiable
% 53.82/17.94  				|-Branch two:
% 53.82/17.94  				| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  				| (250) all_62_0_46 = 0 | unorthogonal_lines(all_17_0_10, all_17_0_10) = 0
% 53.82/17.94  				|
% 53.82/17.94  					+-Applying beta-rule and splitting (235), into two cases.
% 53.82/17.94  					|-Branch one:
% 53.82/17.94  					| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  					|
% 53.82/17.94  						| Using (245) and (247) yields:
% 53.82/17.94  						| (242) $false
% 53.82/17.94  						|
% 53.82/17.94  						|-The branch is then unsatisfiable
% 53.82/17.94  					|-Branch two:
% 53.82/17.94  					| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  					| (254)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_0_0, all_17_0_10) = v0 & apart_point_and_line(v0, all_17_0_10) = v1)
% 53.82/17.94  					|
% 53.82/17.94  						+-Applying beta-rule and splitting (237), into two cases.
% 53.82/17.94  						|-Branch one:
% 53.82/17.94  						| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  						|
% 53.82/17.94  							| Using (245) and (247) yields:
% 53.82/17.94  							| (242) $false
% 53.82/17.94  							|
% 53.82/17.94  							|-The branch is then unsatisfiable
% 53.82/17.94  						|-Branch two:
% 53.82/17.94  						| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  						| (258)  ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_0_0, all_17_0_10) = v0)
% 53.82/17.94  						|
% 53.82/17.94  							+-Applying beta-rule and splitting (236), into two cases.
% 53.82/17.94  							|-Branch one:
% 53.82/17.94  							| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  							|
% 53.82/17.94  								| Using (245) and (247) yields:
% 53.82/17.94  								| (242) $false
% 53.82/17.94  								|
% 53.82/17.94  								|-The branch is then unsatisfiable
% 53.82/17.94  							|-Branch two:
% 53.82/17.94  							| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  							| (262)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_0_0, all_17_0_10) = v0 & apart_point_and_line(v0, all_1_0_0) = v1)
% 53.82/17.94  							|
% 53.82/17.94  								+-Applying beta-rule and splitting (234), into two cases.
% 53.82/17.94  								|-Branch one:
% 53.82/17.94  								| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  								|
% 53.82/17.94  									| Using (245) and (247) yields:
% 53.82/17.94  									| (242) $false
% 53.82/17.94  									|
% 53.82/17.94  									|-The branch is then unsatisfiable
% 53.82/17.94  								|-Branch two:
% 53.82/17.94  								| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  								| (266)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_17_0_10) = v1 & line(all_1_0_0) = v0 & intersection_point(all_1_0_0, all_17_0_10) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 53.82/17.94  								|
% 53.82/17.94  									+-Applying beta-rule and splitting (233), into two cases.
% 53.82/17.94  									|-Branch one:
% 53.82/17.94  									| (247)  ~ (convergent_lines(all_1_0_0, all_17_0_10) = 0)
% 53.82/17.94  									|
% 53.82/17.94  										| Using (245) and (247) yields:
% 53.82/17.94  										| (242) $false
% 53.82/17.94  										|
% 53.82/17.94  										|-The branch is then unsatisfiable
% 53.82/17.94  									|-Branch two:
% 53.82/17.94  									| (245) convergent_lines(all_1_0_0, all_17_0_10) = 0
% 53.82/17.94  									| (270) all_56_2_41 = 0
% 53.82/17.94  									|
% 53.82/17.94  										| From (270) and (198) follows:
% 53.82/17.94  										| (240) convergent_lines(all_17_0_10, all_1_0_0) = 0
% 53.82/17.94  										|
% 53.82/17.94  										+-Applying beta-rule and splitting (199), into two cases.
% 53.82/17.94  										|-Branch one:
% 53.82/17.94  										| (272)  ~ (all_56_2_41 = 0)
% 53.82/17.94  										|
% 53.82/17.94  											| Equations (270) can reduce 272 to:
% 53.82/17.94  											| (273) $false
% 53.82/17.94  											|
% 53.82/17.94  											|-The branch is then unsatisfiable
% 53.82/17.94  										|-Branch two:
% 53.82/17.94  										| (270) all_56_2_41 = 0
% 53.82/17.94  										| (275) all_56_0_39 = 0
% 53.82/17.94  										|
% 53.82/17.94  											+-Applying beta-rule and splitting (238), into two cases.
% 53.82/17.94  											|-Branch one:
% 53.82/17.94  											| (276)  ~ (convergent_lines(all_1_0_0, all_11_0_5) = 0)
% 53.82/17.94  											|
% 53.82/17.94  												+-Applying beta-rule and splitting (230), into two cases.
% 53.82/17.94  												|-Branch one:
% 53.82/17.94  												| (241)  ~ (convergent_lines(all_17_0_10, all_1_0_0) = 0)
% 53.82/17.94  												|
% 53.82/17.94  													| Using (240) and (241) yields:
% 53.82/17.94  													| (242) $false
% 53.82/17.94  													|
% 53.82/17.94  													|-The branch is then unsatisfiable
% 53.82/17.94  												|-Branch two:
% 53.82/17.94  												| (240) convergent_lines(all_17_0_10, all_1_0_0) = 0
% 53.82/17.95  												| (280) all_40_2_25 = 0 | convergent_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.95  												|
% 53.82/17.95  													+-Applying beta-rule and splitting (280), into two cases.
% 53.82/17.95  													|-Branch one:
% 53.82/17.95  													| (281) convergent_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.95  													|
% 53.82/17.95  														| Using (281) and (276) yields:
% 53.82/17.95  														| (242) $false
% 53.82/17.95  														|
% 53.82/17.95  														|-The branch is then unsatisfiable
% 53.82/17.95  													|-Branch two:
% 53.82/17.95  													| (276)  ~ (convergent_lines(all_1_0_0, all_11_0_5) = 0)
% 53.82/17.95  													| (284) all_40_2_25 = 0
% 53.82/17.95  													|
% 53.82/17.95  														+-Applying beta-rule and splitting (239), into two cases.
% 53.82/17.95  														|-Branch one:
% 53.82/17.95  														| (285) all_42_2_28 = 0
% 53.82/17.95  														|
% 53.82/17.95  															| From (285) and (188) follows:
% 53.82/17.95  															| (281) convergent_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.95  															|
% 53.82/17.95  															| Using (281) and (276) yields:
% 53.82/17.95  															| (242) $false
% 53.82/17.95  															|
% 53.82/17.95  															|-The branch is then unsatisfiable
% 53.82/17.95  														|-Branch two:
% 53.82/17.95  														| (288)  ~ (all_42_2_28 = 0)
% 53.82/17.95  														| (289)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_0_0, all_11_0_5) = v0)
% 53.82/17.95  														|
% 53.82/17.95  															| Instantiating (289) with all_631_0_580 yields:
% 53.82/17.95  															| (290)  ~ (all_631_0_580 = 0) & distinct_lines(all_1_0_0, all_11_0_5) = all_631_0_580
% 53.82/17.95  															|
% 53.82/17.95  															| Applying alpha-rule on (290) yields:
% 53.82/17.95  															| (291)  ~ (all_631_0_580 = 0)
% 53.82/17.95  															| (292) distinct_lines(all_1_0_0, all_11_0_5) = all_631_0_580
% 53.82/17.95  															|
% 53.82/17.95  															| Instantiating formula (57) with all_1_0_0, all_11_0_5, all_631_0_580, 0 and discharging atoms distinct_lines(all_1_0_0, all_11_0_5) = all_631_0_580, distinct_lines(all_1_0_0, all_11_0_5) = 0, yields:
% 53.82/17.95  															| (293) all_631_0_580 = 0
% 53.82/17.95  															|
% 53.82/17.95  															| Equations (293) can reduce 291 to:
% 53.82/17.95  															| (273) $false
% 53.82/17.95  															|
% 53.82/17.95  															|-The branch is then unsatisfiable
% 53.82/17.95  											|-Branch two:
% 53.82/17.95  											| (281) convergent_lines(all_1_0_0, all_11_0_5) = 0
% 53.82/17.95  											| (296) all_9_2_4 = 0 | convergent_lines(all_11_0_5, all_1_0_0) = 0
% 53.82/17.95  											|
% 53.82/17.95  												+-Applying beta-rule and splitting (296), into two cases.
% 53.82/17.95  												|-Branch one:
% 53.82/17.95  												| (297) convergent_lines(all_11_0_5, all_1_0_0) = 0
% 53.82/17.95  												|
% 53.82/17.95  													+-Applying beta-rule and splitting (216), into two cases.
% 53.82/17.95  													|-Branch one:
% 53.82/17.95  													| (298)  ~ (convergent_lines(all_11_0_5, all_1_0_0) = all_56_2_41)
% 53.82/17.95  													|
% 53.82/17.95  														| From (270) and (298) follows:
% 53.82/17.95  														| (299)  ~ (convergent_lines(all_11_0_5, all_1_0_0) = 0)
% 53.82/17.95  														|
% 53.82/17.95  														| Using (297) and (299) yields:
% 53.82/17.95  														| (242) $false
% 53.82/17.95  														|
% 53.82/17.95  														|-The branch is then unsatisfiable
% 53.82/17.95  													|-Branch two:
% 53.82/17.95  													| (301) convergent_lines(all_11_0_5, all_1_0_0) = all_56_2_41
% 53.82/17.95  													| (302) all_56_2_41 = all_50_2_34
% 53.82/17.95  													|
% 53.82/17.95  														| Combining equations (302,270) yields a new equation:
% 53.82/17.95  														| (303) all_50_2_34 = 0
% 53.82/17.95  														|
% 53.82/17.95  														| Simplifying 303 yields:
% 53.82/17.95  														| (304) all_50_2_34 = 0
% 53.82/17.95  														|
% 53.82/17.95  														| Equations (304) can reduce 225 to:
% 53.82/17.95  														| (273) $false
% 53.82/17.95  														|
% 53.82/17.95  														|-The branch is then unsatisfiable
% 53.82/17.95  												|-Branch two:
% 53.82/17.95  												| (299)  ~ (convergent_lines(all_11_0_5, all_1_0_0) = 0)
% 53.82/17.95  												| (307) all_9_2_4 = 0
% 53.82/17.95  												|
% 53.82/17.95  													| Equations (307) can reduce 226 to:
% 53.82/17.95  													| (273) $false
% 53.82/17.95  													|
% 53.82/17.95  													|-The branch is then unsatisfiable
% 53.82/17.95  			|-Branch two:
% 53.82/17.95  			| (309)  ~ (distinct_lines(all_1_0_0, all_11_0_5) = 0)
% 53.82/17.95  			| (310) all_66_0_48 = 0
% 53.82/17.95  			|
% 53.82/17.95  				| Equations (310) can reduce 212 to:
% 53.82/17.95  				| (273) $false
% 53.82/17.95  				|
% 53.82/17.95  				|-The branch is then unsatisfiable
% 53.82/17.95  	|-Branch two:
% 53.82/17.95  	| (241)  ~ (convergent_lines(all_17_0_10, all_1_0_0) = 0)
% 53.82/17.95  	| (313) all_62_0_46 = 0
% 53.82/17.95  	|
% 53.82/17.95  		| Equations (313) can reduce 206 to:
% 53.82/17.95  		| (273) $false
% 53.82/17.95  		|
% 53.82/17.95  		|-The branch is then unsatisfiable
% 53.82/17.95  |-Branch two:
% 53.82/17.95  | (315)  ~ (apart_point_and_line(all_1_1_1, all_1_0_0) = 0)
% 53.82/17.95  | (316) all_13_0_6 = 0
% 53.82/17.95  |
% 53.82/17.95  	| Equations (316) can reduce 146 to:
% 53.82/17.95  	| (273) $false
% 53.82/17.95  	|
% 53.82/17.95  	|-The branch is then unsatisfiable
% 53.82/17.95  % SZS output end Proof for theBenchmark
% 53.82/17.95  
% 53.82/17.95  17348ms
%------------------------------------------------------------------------------