%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO199+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n019.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 03:48:35 EDT 2022

% Result   : Theorem 47.88s 14.64s
% Output   : Proof 70.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO199+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 18:07:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.48/0.59          ____       _                          
% 0.48/0.59    ___  / __ \_____(_)___  ________  __________
% 0.48/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.48/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.48/0.59  
% 0.48/0.59  A Theorem Prover for First-Order Logic
% 0.48/0.59  (ePrincess v.1.0)
% 0.48/0.59  
% 0.48/0.59  (c) Philipp Rümmer, 2009-2015
% 0.48/0.59  (c) Peter Backeman, 2014-2015
% 0.48/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.59  Bug reports to peter@backeman.se
% 0.48/0.59  
% 0.48/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.59  
% 0.48/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.84/1.00  Prover 0: Preprocessing ...
% 2.31/1.23  Prover 0: Warning: ignoring some quantifiers
% 2.53/1.26  Prover 0: Constructing countermodel ...
% 20.69/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 20.76/5.99  Prover 1: Preprocessing ...
% 21.82/6.17  Prover 1: Constructing countermodel ...
% 22.15/6.25  Prover 1: gave up
% 22.15/6.25  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 22.15/6.28  Prover 2: Preprocessing ...
% 22.83/6.46  Prover 2: Warning: ignoring some quantifiers
% 23.19/6.47  Prover 2: Constructing countermodel ...
% 29.57/7.99  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 29.78/8.04  Prover 3: Preprocessing ...
% 29.84/8.08  Prover 3: Warning: ignoring some quantifiers
% 29.84/8.08  Prover 3: Constructing countermodel ...
% 40.14/12.33  Prover 3: gave up
% 40.14/12.33  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 40.42/12.35  Prover 4: Preprocessing ...
% 40.92/12.46  Prover 4: Warning: ignoring some quantifiers
% 40.92/12.47  Prover 4: Constructing countermodel ...
% 45.67/13.95  Prover 0: stopped
% 45.98/14.15  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 46.03/14.19  Prover 5: Preprocessing ...
% 46.59/14.28  Prover 5: Constructing countermodel ...
% 47.88/14.64  Prover 5: proved (498ms)
% 47.88/14.64  Prover 2: stopped
% 47.88/14.64  Prover 4: stopped
% 47.88/14.64  
% 47.88/14.64  No countermodel exists, formula is valid
% 47.88/14.64  % SZS status Theorem for theBenchmark
% 47.88/14.64  
% 47.88/14.64  Generating proof ... found it (size 703)
% 68.72/21.56  
% 68.72/21.56  % SZS output start Proof for theBenchmark
% 68.72/21.56  Assumed formulas after preprocessing and simplification: 
% 68.72/21.56  | (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] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v4, v2) = v5 & incident_point_and_line(v3, v2) = 0 & intersection_point(v1, v0) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 69.03/21.65  | Applying alpha-rule on (0) yields:
% 69.03/21.65  | (1)  ! [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)))
% 69.03/21.65  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 69.03/21.65  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 69.03/21.65  | (4)  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & orthogonal_through_point(v0, v1) = v2))
% 69.03/21.65  | (5)  ! [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)))
% 69.03/21.66  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 69.03/21.66  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 69.03/21.66  | (8)  ! [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)))
% 69.03/21.66  | (9)  ! [v0] :  ! [v1] : ( ~ (point(v1) = 0) |  ~ (line(v0) = 0) |  ? [v2] : (line(v2) = 0 & parallel_through_point(v0, v1) = v2))
% 69.03/21.66  | (10)  ! [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))))
% 69.03/21.66  | (11)  ! [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))))
% 69.03/21.66  | (12)  ! [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))))
% 69.03/21.66  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 69.03/21.66  | (14)  ! [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))))
% 69.03/21.66  | (15)  ! [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))
% 69.03/21.66  | (16)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 69.03/21.66  | (17)  ! [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)))
% 69.03/21.66  | (18)  ! [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))))
% 69.03/21.66  | (19)  ! [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))))
% 69.03/21.66  | (20)  ! [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))))
% 69.03/21.66  | (21)  ! [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))))
% 69.03/21.66  | (22)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 69.03/21.66  | (23)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 69.03/21.66  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 69.03/21.66  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 69.03/21.66  | (26)  ! [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))))
% 69.03/21.67  | (27)  ! [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)))
% 69.03/21.67  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 69.03/21.67  | (29)  ! [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))))
% 69.03/21.67  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 69.03/21.67  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 69.03/21.67  | (32)  ! [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)))
% 69.03/21.67  | (33)  ! [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)))
% 69.03/21.67  | (34)  ! [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))))
% 69.03/21.67  | (35)  ! [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))))
% 69.03/21.67  | (36)  ! [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)
% 69.03/21.67  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 69.03/21.67  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 69.03/21.67  | (39)  ! [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))
% 69.03/21.67  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 69.03/21.67  | (41)  ! [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))))
% 69.03/21.67  | (42)  ! [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))
% 69.03/21.67  | (43)  ! [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)))
% 69.03/21.67  | (44)  ! [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))))
% 69.03/21.67  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 69.03/21.67  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 69.03/21.67  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 69.03/21.67  | (48)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 69.23/21.67  | (49)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 69.23/21.67  | (50)  ! [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)))
% 69.23/21.68  | (51)  ! [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)))
% 69.23/21.68  | (52)  ! [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))))
% 69.23/21.68  | (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))
% 69.23/21.68  | (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)))
% 69.23/21.68  | (55)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 69.23/21.68  | (56)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 69.23/21.68  | (57)  ! [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))))
% 69.23/21.68  | (58)  ! [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))))
% 69.23/21.68  | (59)  ! [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))))
% 69.23/21.68  | (60)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 69.23/21.68  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 69.23/21.68  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 69.23/21.68  | (63)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 69.23/21.68  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 69.23/21.68  | (65)  ! [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)))
% 69.23/21.68  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 69.23/21.68  | (67)  ! [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)))
% 69.23/21.68  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 69.23/21.68  | (69)  ! [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))))
% 69.23/21.68  | (70)  ! [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)
% 69.23/21.68  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 69.23/21.68  | (72)  ! [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))
% 69.23/21.69  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 69.23/21.69  | (74)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 69.23/21.69  | (75)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 69.23/21.69  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 69.23/21.69  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 69.23/21.69  | (78)  ! [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)))
% 69.23/21.69  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 69.23/21.69  | (80)  ! [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)))
% 69.23/21.69  | (81)  ! [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))))
% 69.23/21.69  | (82)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 69.23/21.69  | (83)  ! [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))))
% 69.23/21.69  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 69.23/21.69  | (85)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 69.23/21.69  | (86)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 69.23/21.69  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 69.23/21.69  | (88)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 69.23/21.69  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 69.23/21.69  | (90)  ! [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))))
% 69.23/21.69  | (91)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 69.23/21.69  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 69.23/21.69  | (93)  ! [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)))
% 69.23/21.69  | (94)  ! [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)))
% 69.23/21.69  | (95)  ! [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))))
% 69.23/21.69  | (96)  ! [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)))
% 69.23/21.70  | (97)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 69.23/21.70  | (98)  ! [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))))
% 69.23/21.70  | (99)  ! [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))
% 69.23/21.70  | (100)  ! [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)
% 69.23/21.70  | (101)  ! [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))))
% 69.23/21.70  | (102)  ! [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)))
% 69.23/21.70  | (103)  ! [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)))
% 69.23/21.70  | (104)  ! [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))
% 69.23/21.70  | (105)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 69.23/21.70  | (106)  ! [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))))
% 69.23/21.70  | (107)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 69.23/21.70  | (108)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 69.23/21.70  | (109)  ! [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)))
% 69.23/21.70  | (110)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 69.23/21.70  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 69.23/21.70  | (112)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 69.23/21.70  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 69.23/21.70  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 69.23/21.70  | (115)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 69.23/21.70  | (116)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 69.23/21.70  | (117)  ! [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)))
% 69.23/21.70  | (118)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & incident_point_and_line(v4, v2) = v5 & incident_point_and_line(v3, v2) = 0 & intersection_point(v1, v0) = v4 & intersection_point(v0, v1) = v3 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0)
% 69.23/21.70  | (119)  ! [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))))
% 69.23/21.70  | (120)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 69.23/21.70  | (121)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 69.23/21.70  | (122)  ! [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)))
% 69.23/21.70  | (123)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 69.23/21.71  | (124)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 69.23/21.71  | (125)  ! [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))))
% 69.23/21.71  | (126)  ! [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)
% 69.23/21.71  | (127)  ! [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)))
% 69.23/21.71  |
% 69.23/21.71  | Instantiating (118) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5 yields:
% 69.23/21.71  | (128)  ~ (all_1_0_0 = 0) & incident_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0 & incident_point_and_line(all_1_2_2, all_1_3_3) = 0 & intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1 & intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2 & convergent_lines(all_1_3_3, all_1_4_4) = 0 & convergent_lines(all_1_5_5, all_1_3_3) = 0 & convergent_lines(all_1_5_5, all_1_4_4) = 0
% 69.23/21.71  |
% 69.23/21.71  | Applying alpha-rule on (128) yields:
% 69.23/21.71  | (129) incident_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0
% 69.23/21.71  | (130)  ~ (all_1_0_0 = 0)
% 69.23/21.71  | (131) intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1
% 69.23/21.71  | (132) convergent_lines(all_1_3_3, all_1_4_4) = 0
% 69.23/21.71  | (133) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 69.23/21.71  | (134) intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2
% 69.23/21.71  | (135) incident_point_and_line(all_1_2_2, all_1_3_3) = 0
% 69.23/21.71  | (136) convergent_lines(all_1_5_5, all_1_3_3) = 0
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (97) with all_1_4_4 yields:
% 69.23/21.71  | (137)  ~ (convergent_lines(all_1_4_4, all_1_4_4) = 0)
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (97) with all_1_5_5 yields:
% 69.23/21.71  | (138)  ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0)
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (3) with all_1_0_0, all_1_3_3, all_1_1_1 and discharging atoms incident_point_and_line(all_1_1_1, all_1_3_3) = all_1_0_0, yields:
% 69.23/21.71  | (139) all_1_0_0 = 0 | apart_point_and_line(all_1_1_1, all_1_3_3) = 0
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (124) with all_1_3_3, all_1_2_2 and discharging atoms incident_point_and_line(all_1_2_2, all_1_3_3) = 0, yields:
% 69.23/21.71  | (140)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_2_2, all_1_3_3) = v0)
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (127) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 69.23/21.71  | (141)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(all_1_1_1) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (29) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 69.23/21.71  | (142)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (44) with all_1_1_1, all_1_5_5, all_1_4_4 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 69.23/21.71  | (143)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & convergent_lines(all_1_4_4, all_1_5_5) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 69.23/21.71  |
% 69.23/21.71  | Instantiating formula (127) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 69.23/21.71  | (144)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(all_1_2_2) = v3 & line(all_1_4_4) = v1 & line(all_1_5_5) = v0 & convergent_lines(all_1_5_5, all_1_4_4) = v2 & ( ~ (v2 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (29) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 69.23/21.72  | (145)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (44) with all_1_2_2, all_1_4_4, all_1_5_5 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 69.23/21.72  | (146)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_4_4) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (58) with 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (147)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v0 & unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | v1 = 0 | (v3 = 0 & v2 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (19) with 0, all_1_4_4, all_1_3_3, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (148)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_3_3) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v2 & convergent_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v3 = 0) | v2 = 0 | (v1 = 0 & v0 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (11) with 0, 0, all_1_4_4, all_1_3_3, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (149)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_3_3) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v2 & convergent_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (18) with 0, 0, all_1_4_4, all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (150)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v1 & unorthogonal_lines(all_1_3_3, all_1_4_4) = v0 & unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v1 = 0 | v0 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (67) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (151)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_1_3_3) = v0 & line(all_1_4_4) = v1 & intersection_point(all_1_3_3, all_1_4_4) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (88) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (152)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (56) with all_1_4_4, all_1_3_3 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, yields:
% 69.23/21.72  | (153)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_3_3, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_3_3) = v1)
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (125) with 0, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (154)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & convergent_lines(all_1_5_5, all_1_4_4) = v1 & ( ~ (v3 = 0) | v0 = 0 | (v2 = 0 & v1 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (58) with 0, all_1_3_3, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (155)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v1 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & convergent_lines(all_1_3_3, all_1_3_3) = v2 & ( ~ (v0 = 0) | v1 = 0 | (v3 = 0 & v2 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (19) with 0, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (156)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v3 = 0) | v2 = 0 | (v1 = 0 & v0 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (11) with 0, 0, all_1_3_3, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (157)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (18) with 0, 0, all_1_3_3, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (158)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_3_3) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v1 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & convergent_lines(all_1_3_3, all_1_3_3) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v1 = 0 | v0 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (34) with 0, all_1_4_4, all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_3_3, all_1_4_4) = 0, convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (159)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_3_3, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_3_3) = v0 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & convergent_lines(all_1_5_5, all_1_4_4) = v1 & ( ~ (v0 = 0) | v3 = 0 | (v2 = 0 & v1 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (67) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (160)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_1_3_3) = v1 & line(all_1_5_5) = v0 & intersection_point(all_1_5_5, all_1_3_3) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (88) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (161)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(v0, all_1_3_3) = v1)
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (56) with all_1_3_3, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_3_3) = 0, yields:
% 69.23/21.72  | (162)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_3_3) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (58) with 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.72  | (163)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v1 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v0 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v0 = 0) | v1 = 0 | (v3 = 0 & v2 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (19) with 0, all_1_4_4, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.72  | (164)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v3 = 0) | v2 = 0 | (v1 = 0 & v0 = 0)))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (11) with 0, 0, all_1_4_4, all_1_5_5, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.72  | (165)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_5_5, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v2 & unorthogonal_lines(all_1_5_5, all_1_5_5) = v1 & convergent_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.23/21.72  |
% 69.23/21.72  | Instantiating formula (18) with 0, 0, all_1_4_4, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.72  | (166)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (unorthogonal_lines(all_1_4_4, all_1_4_4) = v3 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v1 & unorthogonal_lines(all_1_5_5, all_1_4_4) = v0 & convergent_lines(all_1_4_4, all_1_4_4) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0) | v1 = 0 | v0 = 0))
% 69.23/21.73  |
% 69.23/21.73  | Instantiating formula (67) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.73  | (167)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_1_4_4) = v1 & line(all_1_5_5) = v0 & intersection_point(all_1_5_5, all_1_4_4) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.23/21.73  |
% 69.23/21.73  | Instantiating formula (88) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.73  | (168)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 69.23/21.73  |
% 69.23/21.73  | Instantiating formula (56) with all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.23/21.73  | (169)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_5_5, all_1_4_4) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (169) with all_18_0_7, all_18_1_8 yields:
% 69.23/21.73  | (170)  ~ (all_18_0_7 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_18_1_8 & apart_point_and_line(all_18_1_8, all_1_5_5) = all_18_0_7
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (170) yields:
% 69.23/21.73  | (171)  ~ (all_18_0_7 = 0)
% 69.23/21.73  | (172) intersection_point(all_1_5_5, all_1_4_4) = all_18_1_8
% 69.23/21.73  | (173) apart_point_and_line(all_18_1_8, all_1_5_5) = all_18_0_7
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (153) with all_24_0_17, all_24_1_18 yields:
% 69.23/21.73  | (174)  ~ (all_24_0_17 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_24_1_18 & apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (174) yields:
% 69.23/21.73  | (175)  ~ (all_24_0_17 = 0)
% 69.23/21.73  | (176) intersection_point(all_1_3_3, all_1_4_4) = all_24_1_18
% 69.23/21.73  | (177) apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (152) with all_26_0_19, all_26_1_20 yields:
% 69.23/21.73  | (178)  ~ (all_26_0_19 = 0) & intersection_point(all_1_3_3, all_1_4_4) = all_26_1_20 & apart_point_and_line(all_26_1_20, all_1_4_4) = all_26_0_19
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (178) yields:
% 69.23/21.73  | (179)  ~ (all_26_0_19 = 0)
% 69.23/21.73  | (180) intersection_point(all_1_3_3, all_1_4_4) = all_26_1_20
% 69.23/21.73  | (181) apart_point_and_line(all_26_1_20, all_1_4_4) = all_26_0_19
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (151) with all_28_0_21, all_28_1_22, all_28_2_23, all_28_3_24 yields:
% 69.23/21.73  | (182) point(all_28_1_22) = all_28_0_21 & line(all_1_3_3) = all_28_3_24 & line(all_1_4_4) = all_28_2_23 & intersection_point(all_1_3_3, all_1_4_4) = all_28_1_22 & ( ~ (all_28_2_23 = 0) |  ~ (all_28_3_24 = 0) | all_28_0_21 = 0)
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (182) yields:
% 69.23/21.73  | (183) line(all_1_3_3) = all_28_3_24
% 69.23/21.73  | (184) intersection_point(all_1_3_3, all_1_4_4) = all_28_1_22
% 69.23/21.73  | (185) point(all_28_1_22) = all_28_0_21
% 69.23/21.73  | (186) line(all_1_4_4) = all_28_2_23
% 69.23/21.73  | (187)  ~ (all_28_2_23 = 0) |  ~ (all_28_3_24 = 0) | all_28_0_21 = 0
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (145) with all_30_0_25, all_30_1_26 yields:
% 69.23/21.73  | (188) apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25 & convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_26 & ( ~ (all_30_0_25 = 0) |  ~ (all_30_1_26 = 0))
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (188) yields:
% 69.23/21.73  | (189) apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25
% 69.23/21.73  | (190) convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_26
% 69.23/21.73  | (191)  ~ (all_30_0_25 = 0) |  ~ (all_30_1_26 = 0)
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (144) with all_32_0_27, all_32_1_28, all_32_2_29, all_32_3_30 yields:
% 69.23/21.73  | (192) point(all_1_2_2) = all_32_0_27 & line(all_1_4_4) = all_32_2_29 & line(all_1_5_5) = all_32_3_30 & convergent_lines(all_1_5_5, all_1_4_4) = all_32_1_28 & ( ~ (all_32_1_28 = 0) |  ~ (all_32_2_29 = 0) |  ~ (all_32_3_30 = 0) | all_32_0_27 = 0)
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (192) yields:
% 69.23/21.73  | (193) convergent_lines(all_1_5_5, all_1_4_4) = all_32_1_28
% 69.23/21.73  | (194) line(all_1_5_5) = all_32_3_30
% 69.23/21.73  | (195) point(all_1_2_2) = all_32_0_27
% 69.23/21.73  | (196) line(all_1_4_4) = all_32_2_29
% 69.23/21.73  | (197)  ~ (all_32_1_28 = 0) |  ~ (all_32_2_29 = 0) |  ~ (all_32_3_30 = 0) | all_32_0_27 = 0
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (150) with all_34_0_31, all_34_1_32, all_34_2_33, all_34_3_34 yields:
% 69.23/21.73  | (198) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_34_2_33 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_34_3_34 & unorthogonal_lines(all_1_4_4, all_1_4_4) = all_34_0_31 & convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32 & ( ~ (all_34_0_31 = 0) |  ~ (all_34_1_32 = 0) | all_34_2_33 = 0 | all_34_3_34 = 0)
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (198) yields:
% 69.23/21.73  | (199) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_34_0_31
% 69.23/21.73  | (200) convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32
% 69.23/21.73  | (201) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_34_3_34
% 69.23/21.73  | (202)  ~ (all_34_0_31 = 0) |  ~ (all_34_1_32 = 0) | all_34_2_33 = 0 | all_34_3_34 = 0
% 69.23/21.73  | (203) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_34_2_33
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (162) with all_44_0_48, all_44_1_49 yields:
% 69.23/21.73  | (204)  ~ (all_44_0_48 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_44_1_49 & apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (204) yields:
% 69.23/21.73  | (205)  ~ (all_44_0_48 = 0)
% 69.23/21.73  | (206) intersection_point(all_1_5_5, all_1_3_3) = all_44_1_49
% 69.23/21.73  | (207) apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (161) with all_46_0_50, all_46_1_51 yields:
% 69.23/21.73  | (208)  ~ (all_46_0_50 = 0) & intersection_point(all_1_5_5, all_1_3_3) = all_46_1_51 & apart_point_and_line(all_46_1_51, all_1_3_3) = all_46_0_50
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (208) yields:
% 69.23/21.73  | (209)  ~ (all_46_0_50 = 0)
% 69.23/21.73  | (210) intersection_point(all_1_5_5, all_1_3_3) = all_46_1_51
% 69.23/21.73  | (211) apart_point_and_line(all_46_1_51, all_1_3_3) = all_46_0_50
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (141) with all_48_0_52, all_48_1_53, all_48_2_54, all_48_3_55 yields:
% 69.23/21.73  | (212) point(all_1_1_1) = all_48_0_52 & line(all_1_4_4) = all_48_3_55 & line(all_1_5_5) = all_48_2_54 & convergent_lines(all_1_4_4, all_1_5_5) = all_48_1_53 & ( ~ (all_48_1_53 = 0) |  ~ (all_48_2_54 = 0) |  ~ (all_48_3_55 = 0) | all_48_0_52 = 0)
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (212) yields:
% 69.23/21.73  | (213) point(all_1_1_1) = all_48_0_52
% 69.23/21.73  | (214)  ~ (all_48_1_53 = 0) |  ~ (all_48_2_54 = 0) |  ~ (all_48_3_55 = 0) | all_48_0_52 = 0
% 69.23/21.73  | (215) line(all_1_4_4) = all_48_3_55
% 69.23/21.73  | (216) convergent_lines(all_1_4_4, all_1_5_5) = all_48_1_53
% 69.23/21.73  | (217) line(all_1_5_5) = all_48_2_54
% 69.23/21.73  |
% 69.23/21.73  | Instantiating (140) with all_50_0_56 yields:
% 69.23/21.73  | (218)  ~ (all_50_0_56 = 0) & apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56
% 69.23/21.73  |
% 69.23/21.73  | Applying alpha-rule on (218) yields:
% 69.23/21.73  | (219)  ~ (all_50_0_56 = 0)
% 69.23/21.73  | (220) apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56
% 69.23/21.74  |
% 69.23/21.74  | Instantiating (143) with all_52_0_57, all_52_1_58 yields:
% 69.23/21.74  | (221) apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57 & convergent_lines(all_1_4_4, all_1_5_5) = all_52_1_58 & ( ~ (all_52_0_57 = 0) |  ~ (all_52_1_58 = 0))
% 69.23/21.74  |
% 69.23/21.74  | Applying alpha-rule on (221) yields:
% 69.23/21.74  | (222) apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57
% 69.23/21.74  | (223) convergent_lines(all_1_4_4, all_1_5_5) = all_52_1_58
% 69.23/21.74  | (224)  ~ (all_52_0_57 = 0) |  ~ (all_52_1_58 = 0)
% 69.23/21.74  |
% 69.23/21.74  | Instantiating (149) with all_54_0_59, all_54_1_60, all_54_2_61, all_54_3_62 yields:
% 69.23/21.74  | (225) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_54_2_61 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_0_59 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_1_60 & convergent_lines(all_1_3_3, all_1_3_3) = all_54_3_62 & ( ~ (all_54_2_61 = 0) |  ~ (all_54_3_62 = 0) | all_54_0_59 = 0 | all_54_1_60 = 0)
% 69.23/21.74  |
% 69.23/21.74  | Applying alpha-rule on (225) yields:
% 69.23/21.74  | (226)  ~ (all_54_2_61 = 0) |  ~ (all_54_3_62 = 0) | all_54_0_59 = 0 | all_54_1_60 = 0
% 69.23/21.74  | (227) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_0_59
% 69.23/21.74  | (228) convergent_lines(all_1_3_3, all_1_3_3) = all_54_3_62
% 69.23/21.74  | (229) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_54_2_61
% 69.23/21.74  | (230) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_54_1_60
% 69.23/21.74  |
% 69.23/21.74  | Instantiating (148) with all_56_0_63, all_56_1_64, all_56_2_65, all_56_3_66 yields:
% 69.23/21.74  | (231) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_56_2_65 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_56_0_63 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_56_1_64 & convergent_lines(all_1_3_3, all_1_3_3) = all_56_3_66 & ( ~ (all_56_0_63 = 0) | all_56_1_64 = 0 | (all_56_2_65 = 0 & all_56_3_66 = 0))
% 69.23/21.74  |
% 69.23/21.74  | Applying alpha-rule on (231) yields:
% 69.23/21.74  | (232) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_56_1_64
% 69.23/21.74  | (233) convergent_lines(all_1_3_3, all_1_3_3) = all_56_3_66
% 69.23/21.74  | (234)  ~ (all_56_0_63 = 0) | all_56_1_64 = 0 | (all_56_2_65 = 0 & all_56_3_66 = 0)
% 69.23/21.74  | (235) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_56_0_63
% 69.23/21.74  | (236) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_56_2_65
% 69.23/21.74  |
% 69.23/21.74  | Instantiating (147) with all_58_0_67, all_58_1_68, all_58_2_69, all_58_3_70 yields:
% 69.23/21.74  | (237) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_58_2_69 & unorthogonal_lines(all_1_3_3, all_1_4_4) = all_58_3_70 & unorthogonal_lines(all_1_4_4, all_1_4_4) = all_58_0_67 & convergent_lines(all_1_4_4, all_1_4_4) = all_58_1_68 & ( ~ (all_58_3_70 = 0) | all_58_2_69 = 0 | (all_58_0_67 = 0 & all_58_1_68 = 0))
% 69.23/21.74  |
% 69.23/21.74  | Applying alpha-rule on (237) yields:
% 69.23/21.74  | (238) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_58_2_69
% 69.23/21.74  | (239) convergent_lines(all_1_4_4, all_1_4_4) = all_58_1_68
% 69.23/21.74  | (240) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_58_3_70
% 69.55/21.74  | (241) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_58_0_67
% 69.55/21.74  | (242)  ~ (all_58_3_70 = 0) | all_58_2_69 = 0 | (all_58_0_67 = 0 & all_58_1_68 = 0)
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (142) with all_60_0_71, all_60_1_72 yields:
% 69.55/21.74  | (243) apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71 & convergent_lines(all_1_4_4, all_1_5_5) = all_60_1_72 & ( ~ (all_60_0_71 = 0) |  ~ (all_60_1_72 = 0))
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (243) yields:
% 69.55/21.74  | (244) apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71
% 69.55/21.74  | (245) convergent_lines(all_1_4_4, all_1_5_5) = all_60_1_72
% 69.55/21.74  | (246)  ~ (all_60_0_71 = 0) |  ~ (all_60_1_72 = 0)
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (168) with all_62_0_73, all_62_1_74 yields:
% 69.55/21.74  | (247)  ~ (all_62_0_73 = 0) & intersection_point(all_1_5_5, all_1_4_4) = all_62_1_74 & apart_point_and_line(all_62_1_74, all_1_4_4) = all_62_0_73
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (247) yields:
% 69.55/21.74  | (248)  ~ (all_62_0_73 = 0)
% 69.55/21.74  | (249) intersection_point(all_1_5_5, all_1_4_4) = all_62_1_74
% 69.55/21.74  | (250) apart_point_and_line(all_62_1_74, all_1_4_4) = all_62_0_73
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (167) with all_64_0_75, all_64_1_76, all_64_2_77, all_64_3_78 yields:
% 69.55/21.74  | (251) point(all_64_1_76) = all_64_0_75 & line(all_1_4_4) = all_64_2_77 & line(all_1_5_5) = all_64_3_78 & intersection_point(all_1_5_5, all_1_4_4) = all_64_1_76 & ( ~ (all_64_2_77 = 0) |  ~ (all_64_3_78 = 0) | all_64_0_75 = 0)
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (251) yields:
% 69.55/21.74  | (252)  ~ (all_64_2_77 = 0) |  ~ (all_64_3_78 = 0) | all_64_0_75 = 0
% 69.55/21.74  | (253) line(all_1_5_5) = all_64_3_78
% 69.55/21.74  | (254) intersection_point(all_1_5_5, all_1_4_4) = all_64_1_76
% 69.55/21.74  | (255) line(all_1_4_4) = all_64_2_77
% 69.55/21.74  | (256) point(all_64_1_76) = all_64_0_75
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (160) with all_68_0_83, all_68_1_84, all_68_2_85, all_68_3_86 yields:
% 69.55/21.74  | (257) point(all_68_1_84) = all_68_0_83 & line(all_1_3_3) = all_68_2_85 & line(all_1_5_5) = all_68_3_86 & intersection_point(all_1_5_5, all_1_3_3) = all_68_1_84 & ( ~ (all_68_2_85 = 0) |  ~ (all_68_3_86 = 0) | all_68_0_83 = 0)
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (257) yields:
% 69.55/21.74  | (258) intersection_point(all_1_5_5, all_1_3_3) = all_68_1_84
% 69.55/21.74  | (259)  ~ (all_68_2_85 = 0) |  ~ (all_68_3_86 = 0) | all_68_0_83 = 0
% 69.55/21.74  | (260) line(all_1_5_5) = all_68_3_86
% 69.55/21.74  | (261) point(all_68_1_84) = all_68_0_83
% 69.55/21.74  | (262) line(all_1_3_3) = all_68_2_85
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (159) with all_70_0_87, all_70_1_88, all_70_2_89, all_70_3_90 yields:
% 69.55/21.74  | (263) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_70_0_87 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_70_3_90 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_70_1_88 & convergent_lines(all_1_5_5, all_1_4_4) = all_70_2_89 & ( ~ (all_70_3_90 = 0) | all_70_0_87 = 0 | (all_70_1_88 = 0 & all_70_2_89 = 0))
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (263) yields:
% 69.55/21.74  | (264) convergent_lines(all_1_5_5, all_1_4_4) = all_70_2_89
% 69.55/21.74  | (265) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_70_0_87
% 69.55/21.74  | (266)  ~ (all_70_3_90 = 0) | all_70_0_87 = 0 | (all_70_1_88 = 0 & all_70_2_89 = 0)
% 69.55/21.74  | (267) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_70_1_88
% 69.55/21.74  | (268) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_70_3_90
% 69.55/21.74  |
% 69.55/21.74  | Instantiating (156) with all_72_0_91, all_72_1_92, all_72_2_93, all_72_3_94 yields:
% 69.55/21.74  | (269) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_72_0_91 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_72_1_92 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_72_2_93 & convergent_lines(all_1_5_5, all_1_5_5) = all_72_3_94 & ( ~ (all_72_0_91 = 0) | all_72_1_92 = 0 | (all_72_2_93 = 0 & all_72_3_94 = 0))
% 69.55/21.74  |
% 69.55/21.74  | Applying alpha-rule on (269) yields:
% 69.55/21.74  | (270)  ~ (all_72_0_91 = 0) | all_72_1_92 = 0 | (all_72_2_93 = 0 & all_72_3_94 = 0)
% 69.55/21.75  | (271) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_72_1_92
% 69.55/21.75  | (272) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_72_2_93
% 69.55/21.75  | (273) convergent_lines(all_1_5_5, all_1_5_5) = all_72_3_94
% 69.55/21.75  | (274) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_72_0_91
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (155) with all_74_0_95, all_74_1_96, all_74_2_97, all_74_3_98 yields:
% 69.55/21.75  | (275) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_74_0_95 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_74_2_97 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_74_3_98 & convergent_lines(all_1_3_3, all_1_3_3) = all_74_1_96 & ( ~ (all_74_3_98 = 0) | all_74_2_97 = 0 | (all_74_0_95 = 0 & all_74_1_96 = 0))
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (275) yields:
% 69.55/21.75  | (276) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_74_3_98
% 69.55/21.75  | (277) convergent_lines(all_1_3_3, all_1_3_3) = all_74_1_96
% 69.55/21.75  | (278) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_74_0_95
% 69.55/21.75  | (279)  ~ (all_74_3_98 = 0) | all_74_2_97 = 0 | (all_74_0_95 = 0 & all_74_1_96 = 0)
% 69.55/21.75  | (280) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_74_2_97
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (154) with all_76_0_99, all_76_1_100, all_76_2_101, all_76_3_102 yields:
% 69.55/21.75  | (281) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_0_99 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_76_3_102 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_76_1_100 & convergent_lines(all_1_5_5, all_1_4_4) = all_76_2_101 & ( ~ (all_76_0_99 = 0) | all_76_3_102 = 0 | (all_76_1_100 = 0 & all_76_2_101 = 0))
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (281) yields:
% 69.55/21.75  | (282) unorthogonal_lines(all_1_3_3, all_1_4_4) = all_76_0_99
% 69.55/21.75  | (283) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_76_3_102
% 69.55/21.75  | (284) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_76_1_100
% 69.55/21.75  | (285)  ~ (all_76_0_99 = 0) | all_76_3_102 = 0 | (all_76_1_100 = 0 & all_76_2_101 = 0)
% 69.55/21.75  | (286) convergent_lines(all_1_5_5, all_1_4_4) = all_76_2_101
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (158) with all_78_0_103, all_78_1_104, all_78_2_105, all_78_3_106 yields:
% 69.55/21.75  | (287) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_78_0_103 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_2_105 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_3_106 & convergent_lines(all_1_3_3, all_1_3_3) = all_78_1_104 & ( ~ (all_78_0_103 = 0) |  ~ (all_78_1_104 = 0) | all_78_2_105 = 0 | all_78_3_106 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (287) yields:
% 69.55/21.75  | (288) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_2_105
% 69.55/21.75  | (289)  ~ (all_78_0_103 = 0) |  ~ (all_78_1_104 = 0) | all_78_2_105 = 0 | all_78_3_106 = 0
% 69.55/21.75  | (290) convergent_lines(all_1_3_3, all_1_3_3) = all_78_1_104
% 69.55/21.75  | (291) unorthogonal_lines(all_1_3_3, all_1_3_3) = all_78_0_103
% 69.55/21.75  | (292) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_78_3_106
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (157) with all_82_0_108, all_82_1_109, all_82_2_110, all_82_3_111 yields:
% 69.55/21.75  | (293) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_82_0_108 & unorthogonal_lines(all_1_5_5, all_1_3_3) = all_82_1_109 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_82_2_110 & convergent_lines(all_1_5_5, all_1_5_5) = all_82_3_111 & ( ~ (all_82_2_110 = 0) |  ~ (all_82_3_111 = 0) | all_82_0_108 = 0 | all_82_1_109 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (293) yields:
% 69.55/21.75  | (294) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_82_2_110
% 69.55/21.75  | (295) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_82_1_109
% 69.55/21.75  | (296) unorthogonal_lines(all_1_5_5, all_1_3_3) = all_82_0_108
% 69.55/21.75  | (297) convergent_lines(all_1_5_5, all_1_5_5) = all_82_3_111
% 69.55/21.75  | (298)  ~ (all_82_2_110 = 0) |  ~ (all_82_3_111 = 0) | all_82_0_108 = 0 | all_82_1_109 = 0
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (146) with all_84_0_112, all_84_1_113 yields:
% 69.55/21.75  | (299) apart_point_and_line(all_1_2_2, all_1_5_5) = all_84_0_112 & convergent_lines(all_1_5_5, all_1_4_4) = all_84_1_113 & ( ~ (all_84_0_112 = 0) |  ~ (all_84_1_113 = 0))
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (299) yields:
% 69.55/21.75  | (300) apart_point_and_line(all_1_2_2, all_1_5_5) = all_84_0_112
% 69.55/21.75  | (301) convergent_lines(all_1_5_5, all_1_4_4) = all_84_1_113
% 69.55/21.75  | (302)  ~ (all_84_0_112 = 0) |  ~ (all_84_1_113 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (165) with all_86_0_114, all_86_1_115, all_86_2_116, all_86_3_117 yields:
% 69.55/21.75  | (303) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_86_0_114 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_86_1_115 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_86_2_116 & convergent_lines(all_1_5_5, all_1_5_5) = all_86_3_117 & ( ~ (all_86_2_116 = 0) |  ~ (all_86_3_117 = 0) | all_86_0_114 = 0 | all_86_1_115 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (303) yields:
% 69.55/21.75  | (304) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_86_2_116
% 69.55/21.75  | (305) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_86_0_114
% 69.55/21.75  | (306) convergent_lines(all_1_5_5, all_1_5_5) = all_86_3_117
% 69.55/21.75  | (307) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_86_1_115
% 69.55/21.75  | (308)  ~ (all_86_2_116 = 0) |  ~ (all_86_3_117 = 0) | all_86_0_114 = 0 | all_86_1_115 = 0
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (163) with all_88_0_118, all_88_1_119, all_88_2_120, all_88_3_121 yields:
% 69.55/21.75  | (309) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_88_0_118 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_88_2_120 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_88_3_121 & convergent_lines(all_1_4_4, all_1_4_4) = all_88_1_119 & ( ~ (all_88_3_121 = 0) | all_88_2_120 = 0 | (all_88_0_118 = 0 & all_88_1_119 = 0))
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (309) yields:
% 69.55/21.75  | (310) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_88_0_118
% 69.55/21.75  | (311) convergent_lines(all_1_4_4, all_1_4_4) = all_88_1_119
% 69.55/21.75  | (312) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_88_2_120
% 69.55/21.75  | (313) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_88_3_121
% 69.55/21.75  | (314)  ~ (all_88_3_121 = 0) | all_88_2_120 = 0 | (all_88_0_118 = 0 & all_88_1_119 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (164) with all_92_0_126, all_92_1_127, all_92_2_128, all_92_3_129 yields:
% 69.55/21.75  | (315) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_92_0_126 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_92_1_127 & unorthogonal_lines(all_1_5_5, all_1_5_5) = all_92_2_128 & convergent_lines(all_1_5_5, all_1_5_5) = all_92_3_129 & ( ~ (all_92_0_126 = 0) | all_92_1_127 = 0 | (all_92_2_128 = 0 & all_92_3_129 = 0))
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (315) yields:
% 69.55/21.75  | (316) convergent_lines(all_1_5_5, all_1_5_5) = all_92_3_129
% 69.55/21.75  | (317) unorthogonal_lines(all_1_5_5, all_1_5_5) = all_92_2_128
% 69.55/21.75  | (318) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_92_1_127
% 69.55/21.75  | (319)  ~ (all_92_0_126 = 0) | all_92_1_127 = 0 | (all_92_2_128 = 0 & all_92_3_129 = 0)
% 69.55/21.75  | (320) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_92_0_126
% 69.55/21.75  |
% 69.55/21.75  | Instantiating (166) with all_96_0_134, all_96_1_135, all_96_2_136, all_96_3_137 yields:
% 69.55/21.75  | (321) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_96_0_134 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_96_2_136 & unorthogonal_lines(all_1_5_5, all_1_4_4) = all_96_3_137 & convergent_lines(all_1_4_4, all_1_4_4) = all_96_1_135 & ( ~ (all_96_0_134 = 0) |  ~ (all_96_1_135 = 0) | all_96_2_136 = 0 | all_96_3_137 = 0)
% 69.55/21.75  |
% 69.55/21.75  | Applying alpha-rule on (321) yields:
% 69.55/21.75  | (322) unorthogonal_lines(all_1_4_4, all_1_4_4) = all_96_0_134
% 69.55/21.75  | (323)  ~ (all_96_0_134 = 0) |  ~ (all_96_1_135 = 0) | all_96_2_136 = 0 | all_96_3_137 = 0
% 69.55/21.75  | (324) convergent_lines(all_1_4_4, all_1_4_4) = all_96_1_135
% 69.55/21.75  | (325) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_96_3_137
% 69.55/21.75  | (326) unorthogonal_lines(all_1_5_5, all_1_4_4) = all_96_2_136
% 69.55/21.75  |
% 69.55/21.75  +-Applying beta-rule and splitting (139), into two cases.
% 69.55/21.75  |-Branch one:
% 69.55/21.75  | (327) apart_point_and_line(all_1_1_1, all_1_3_3) = 0
% 69.55/21.75  |
% 69.55/21.75  	| Instantiating formula (114) with all_1_3_3, all_1_4_4, all_26_1_20, all_28_1_22 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_28_1_22, intersection_point(all_1_3_3, all_1_4_4) = all_26_1_20, yields:
% 69.55/21.75  	| (328) all_28_1_22 = all_26_1_20
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_3_3, all_1_4_4, all_24_1_18, all_28_1_22 and discharging atoms intersection_point(all_1_3_3, all_1_4_4) = all_28_1_22, intersection_point(all_1_3_3, all_1_4_4) = all_24_1_18, yields:
% 69.55/21.75  	| (329) all_28_1_22 = all_24_1_18
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_5_5, all_1_3_3, all_46_1_51, all_68_1_84 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_68_1_84, intersection_point(all_1_5_5, all_1_3_3) = all_46_1_51, yields:
% 69.55/21.75  	| (330) all_68_1_84 = all_46_1_51
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_5_5, all_1_3_3, all_44_1_49, all_68_1_84 and discharging atoms intersection_point(all_1_5_5, all_1_3_3) = all_68_1_84, intersection_point(all_1_5_5, all_1_3_3) = all_44_1_49, yields:
% 69.55/21.75  	| (331) all_68_1_84 = all_44_1_49
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_5_5, all_1_4_4, all_64_1_76, all_1_2_2 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_64_1_76, intersection_point(all_1_5_5, all_1_4_4) = all_1_2_2, yields:
% 69.55/21.75  	| (332) all_64_1_76 = all_1_2_2
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_5_5, all_1_4_4, all_62_1_74, all_64_1_76 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_64_1_76, intersection_point(all_1_5_5, all_1_4_4) = all_62_1_74, yields:
% 69.55/21.75  	| (333) all_64_1_76 = all_62_1_74
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (114) with all_1_5_5, all_1_4_4, all_18_1_8, all_64_1_76 and discharging atoms intersection_point(all_1_5_5, all_1_4_4) = all_64_1_76, intersection_point(all_1_5_5, all_1_4_4) = all_18_1_8, yields:
% 69.55/21.75  	| (334) all_64_1_76 = all_18_1_8
% 69.55/21.75  	|
% 69.55/21.75  	| Instantiating formula (13) with all_1_2_2, all_1_4_4, all_30_0_25, all_62_0_73 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, yields:
% 69.55/21.75  	| (335) all_62_0_73 = all_30_0_25 |  ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_62_0_73)
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_84_0_112, all_18_0_7 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_84_0_112, yields:
% 69.55/21.76  	| (336) all_84_0_112 = all_18_0_7 |  ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7)
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (97) with all_1_3_3 yields:
% 69.55/21.76  	| (337)  ~ (convergent_lines(all_1_3_3, all_1_3_3) = 0)
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_3_3, all_1_3_3, all_74_1_96, all_78_1_104 and discharging atoms convergent_lines(all_1_3_3, all_1_3_3) = all_78_1_104, convergent_lines(all_1_3_3, all_1_3_3) = all_74_1_96, yields:
% 69.55/21.76  	| (338) all_78_1_104 = all_74_1_96
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_3_3, all_1_3_3, all_56_3_66, all_74_1_96 and discharging atoms convergent_lines(all_1_3_3, all_1_3_3) = all_74_1_96, convergent_lines(all_1_3_3, all_1_3_3) = all_56_3_66, yields:
% 69.55/21.76  	| (339) all_74_1_96 = all_56_3_66
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_3_3, all_1_3_3, all_54_3_62, all_78_1_104 and discharging atoms convergent_lines(all_1_3_3, all_1_3_3) = all_78_1_104, convergent_lines(all_1_3_3, all_1_3_3) = all_54_3_62, yields:
% 69.55/21.76  	| (340) all_78_1_104 = all_54_3_62
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_4_4, all_1_4_4, all_88_1_119, all_96_1_135 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_96_1_135, convergent_lines(all_1_4_4, all_1_4_4) = all_88_1_119, yields:
% 69.55/21.76  	| (341) all_96_1_135 = all_88_1_119
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_4_4, all_1_4_4, all_58_1_68, all_96_1_135 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_96_1_135, convergent_lines(all_1_4_4, all_1_4_4) = all_58_1_68, yields:
% 69.55/21.76  	| (342) all_96_1_135 = all_58_1_68
% 69.55/21.76  	|
% 69.55/21.76  	| Using (239) and (137) yields:
% 69.55/21.76  	| (343)  ~ (all_58_1_68 = 0)
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_4_4, all_1_4_4, all_34_1_32, all_96_1_135 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_96_1_135, convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32, yields:
% 69.55/21.76  	| (344) all_96_1_135 = all_34_1_32
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_4_4, all_1_5_5, all_52_1_58, all_60_1_72 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_60_1_72, convergent_lines(all_1_4_4, all_1_5_5) = all_52_1_58, yields:
% 69.55/21.76  	| (345) all_60_1_72 = all_52_1_58
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_4_4, all_1_5_5, all_48_1_53, all_60_1_72 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_60_1_72, convergent_lines(all_1_4_4, all_1_5_5) = all_48_1_53, yields:
% 69.55/21.76  	| (346) all_60_1_72 = all_48_1_53
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_4_4, all_76_2_101, all_84_1_113 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_84_1_113, convergent_lines(all_1_5_5, all_1_4_4) = all_76_2_101, yields:
% 69.55/21.76  	| (347) all_84_1_113 = all_76_2_101
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_4_4, all_70_2_89, 0 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_70_2_89, convergent_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.55/21.76  	| (348) all_70_2_89 = 0
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_4_4, all_70_2_89, all_84_1_113 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_84_1_113, convergent_lines(all_1_5_5, all_1_4_4) = all_70_2_89, yields:
% 69.55/21.76  	| (349) all_84_1_113 = all_70_2_89
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_4_4, all_32_1_28, all_84_1_113 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_84_1_113, convergent_lines(all_1_5_5, all_1_4_4) = all_32_1_28, yields:
% 69.55/21.76  	| (350) all_84_1_113 = all_32_1_28
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_4_4, all_30_1_26, all_70_2_89 and discharging atoms convergent_lines(all_1_5_5, all_1_4_4) = all_70_2_89, convergent_lines(all_1_5_5, all_1_4_4) = all_30_1_26, yields:
% 69.55/21.76  	| (351) all_70_2_89 = all_30_1_26
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_5_5, all_86_3_117, all_92_3_129 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_92_3_129, convergent_lines(all_1_5_5, all_1_5_5) = all_86_3_117, yields:
% 69.55/21.76  	| (352) all_92_3_129 = all_86_3_117
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_5_5, all_82_3_111, all_92_3_129 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_92_3_129, convergent_lines(all_1_5_5, all_1_5_5) = all_82_3_111, yields:
% 69.55/21.76  	| (353) all_92_3_129 = all_82_3_111
% 69.55/21.76  	|
% 69.55/21.76  	| Using (297) and (138) yields:
% 69.55/21.76  	| (354)  ~ (all_82_3_111 = 0)
% 69.55/21.76  	|
% 69.55/21.76  	| Instantiating formula (25) with all_1_5_5, all_1_5_5, all_72_3_94, all_92_3_129 and discharging atoms convergent_lines(all_1_5_5, all_1_5_5) = all_92_3_129, convergent_lines(all_1_5_5, all_1_5_5) = all_72_3_94, yields:
% 69.55/21.76  	| (355) all_92_3_129 = all_72_3_94
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (342,341) yields a new equation:
% 69.55/21.76  	| (356) all_88_1_119 = all_58_1_68
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (344,341) yields a new equation:
% 69.55/21.76  	| (357) all_88_1_119 = all_34_1_32
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (355,352) yields a new equation:
% 69.55/21.76  	| (358) all_86_3_117 = all_72_3_94
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (353,352) yields a new equation:
% 69.55/21.76  	| (359) all_86_3_117 = all_82_3_111
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (356,357) yields a new equation:
% 69.55/21.76  	| (360) all_58_1_68 = all_34_1_32
% 69.55/21.76  	|
% 69.55/21.76  	| Simplifying 360 yields:
% 69.55/21.76  	| (361) all_58_1_68 = all_34_1_32
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (359,358) yields a new equation:
% 69.55/21.76  	| (362) all_82_3_111 = all_72_3_94
% 69.55/21.76  	|
% 69.55/21.76  	| Simplifying 362 yields:
% 69.55/21.76  	| (363) all_82_3_111 = all_72_3_94
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (349,347) yields a new equation:
% 69.55/21.76  	| (364) all_76_2_101 = all_70_2_89
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (350,347) yields a new equation:
% 69.55/21.76  	| (365) all_76_2_101 = all_32_1_28
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (338,340) yields a new equation:
% 69.55/21.76  	| (366) all_74_1_96 = all_54_3_62
% 69.55/21.76  	|
% 69.55/21.76  	| Simplifying 366 yields:
% 69.55/21.76  	| (367) all_74_1_96 = all_54_3_62
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (364,365) yields a new equation:
% 69.55/21.76  	| (368) all_70_2_89 = all_32_1_28
% 69.55/21.76  	|
% 69.55/21.76  	| Simplifying 368 yields:
% 69.55/21.76  	| (369) all_70_2_89 = all_32_1_28
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (339,367) yields a new equation:
% 69.55/21.76  	| (370) all_56_3_66 = all_54_3_62
% 69.55/21.76  	|
% 69.55/21.76  	| Simplifying 370 yields:
% 69.55/21.76  	| (371) all_56_3_66 = all_54_3_62
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (351,369) yields a new equation:
% 69.55/21.76  	| (372) all_32_1_28 = all_30_1_26
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (348,369) yields a new equation:
% 69.55/21.76  	| (373) all_32_1_28 = 0
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (331,330) yields a new equation:
% 69.55/21.76  	| (374) all_46_1_51 = all_44_1_49
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (334,333) yields a new equation:
% 69.55/21.76  	| (375) all_62_1_74 = all_18_1_8
% 69.55/21.76  	|
% 69.55/21.76  	| Combining equations (332,333) yields a new equation:
% 69.66/21.76  	| (376) all_62_1_74 = all_1_2_2
% 69.66/21.76  	|
% 69.66/21.76  	| Combining equations (375,376) yields a new equation:
% 69.66/21.76  	| (377) all_18_1_8 = all_1_2_2
% 69.66/21.76  	|
% 69.66/21.76  	| Simplifying 377 yields:
% 69.66/21.76  	| (378) all_18_1_8 = all_1_2_2
% 69.66/21.76  	|
% 69.66/21.76  	| Combining equations (346,345) yields a new equation:
% 69.66/21.76  	| (379) all_52_1_58 = all_48_1_53
% 69.66/21.76  	|
% 69.66/21.76  	| Combining equations (373,372) yields a new equation:
% 69.66/21.76  	| (380) all_30_1_26 = 0
% 69.66/21.76  	|
% 69.66/21.76  	| Combining equations (329,328) yields a new equation:
% 69.66/21.76  	| (381) all_26_1_20 = all_24_1_18
% 69.66/21.76  	|
% 69.66/21.76  	| Combining equations (379,345) yields a new equation:
% 69.66/21.76  	| (346) all_60_1_72 = all_48_1_53
% 69.66/21.76  	|
% 69.66/21.76  	| Equations (363) can reduce 354 to:
% 69.66/21.76  	| (383)  ~ (all_72_3_94 = 0)
% 69.66/21.76  	|
% 69.66/21.76  	| Equations (361) can reduce 343 to:
% 69.66/21.76  	| (384)  ~ (all_34_1_32 = 0)
% 69.66/21.76  	|
% 69.66/21.76  	| From (376) and (250) follows:
% 69.66/21.76  	| (385) apart_point_and_line(all_1_2_2, all_1_4_4) = all_62_0_73
% 69.66/21.76  	|
% 69.66/21.76  	| From (374) and (211) follows:
% 69.66/21.76  	| (386) apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50
% 69.66/21.76  	|
% 69.66/21.76  	| From (381) and (181) follows:
% 69.66/21.76  	| (387) apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19
% 69.66/21.76  	|
% 69.66/21.76  	| From (378) and (173) follows:
% 69.66/21.76  	| (388) apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7
% 69.66/21.76  	|
% 69.66/21.76  	| From (371) and (233) follows:
% 69.66/21.76  	| (228) convergent_lines(all_1_3_3, all_1_3_3) = all_54_3_62
% 69.66/21.76  	|
% 69.66/21.76  	| From (361) and (239) follows:
% 69.66/21.77  	| (200) convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32
% 69.66/21.77  	|
% 69.66/21.77  	| From (379) and (223) follows:
% 69.66/21.77  	| (216) convergent_lines(all_1_4_4, all_1_5_5) = all_48_1_53
% 69.66/21.77  	|
% 69.66/21.77  	| From (380) and (190) follows:
% 69.66/21.77  	| (133) convergent_lines(all_1_5_5, all_1_4_4) = 0
% 69.66/21.77  	|
% 69.66/21.77  	| From (363) and (297) follows:
% 69.66/21.77  	| (273) convergent_lines(all_1_5_5, all_1_5_5) = all_72_3_94
% 69.66/21.77  	|
% 69.66/21.77  	+-Applying beta-rule and splitting (336), into two cases.
% 69.66/21.77  	|-Branch one:
% 69.66/21.77  	| (394)  ~ (apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7)
% 69.66/21.77  	|
% 69.66/21.77  		| Using (388) and (394) yields:
% 69.66/21.77  		| (395) $false
% 69.66/21.77  		|
% 69.66/21.77  		|-The branch is then unsatisfiable
% 69.66/21.77  	|-Branch two:
% 69.66/21.77  	| (388) apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7
% 69.66/21.77  	| (397) all_84_0_112 = all_18_0_7
% 69.66/21.77  	|
% 69.66/21.77  		| From (397) and (300) follows:
% 69.66/21.77  		| (388) apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7
% 69.66/21.77  		|
% 69.66/21.77  		+-Applying beta-rule and splitting (335), into two cases.
% 69.66/21.77  		|-Branch one:
% 69.66/21.77  		| (399)  ~ (apart_point_and_line(all_1_2_2, all_1_4_4) = all_62_0_73)
% 69.66/21.77  		|
% 69.66/21.77  			| Using (385) and (399) yields:
% 69.66/21.77  			| (395) $false
% 69.66/21.77  			|
% 69.66/21.77  			|-The branch is then unsatisfiable
% 69.66/21.77  		|-Branch two:
% 69.66/21.77  		| (385) apart_point_and_line(all_1_2_2, all_1_4_4) = all_62_0_73
% 69.66/21.77  		| (402) all_62_0_73 = all_30_0_25
% 69.66/21.77  		|
% 69.66/21.77  			| Equations (402) can reduce 248 to:
% 69.66/21.77  			| (403)  ~ (all_30_0_25 = 0)
% 69.66/21.77  			|
% 69.66/21.77  			| From (402) and (385) follows:
% 69.66/21.77  			| (189) apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25
% 69.66/21.77  			|
% 69.66/21.77  			| Using (228) and (337) yields:
% 69.66/21.77  			| (405)  ~ (all_54_3_62 = 0)
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (109) with all_44_0_48, all_46_0_50, all_1_5_5, all_1_3_3, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (406) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (109) with all_46_0_50, all_44_0_48, all_1_3_3, all_1_5_5, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (407) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] : (convergent_lines(all_1_5_5, all_1_3_3) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_44_0_48, all_46_0_50, all_1_5_5, all_1_3_3, all_44_1_49, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (408) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_46_0_50, all_44_0_48, all_1_3_3, all_1_5_5, all_44_1_49, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (409) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (96) with all_44_0_48, all_46_0_50, all_1_3_3, all_1_5_5, all_44_1_49, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (410) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (96) with all_46_0_50, all_44_0_48, all_1_5_5, all_1_3_3, all_44_1_49, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (411) all_46_0_50 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_44_0_48, all_44_0_48, all_1_5_5, all_1_5_5, all_44_1_49, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, yields:
% 69.66/21.77  			| (412) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_24_0_17, all_46_0_50, all_1_3_3, all_1_3_3, all_24_1_18, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (413) all_46_0_50 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_46_0_50, all_24_0_17, all_1_3_3, all_1_3_3, all_44_1_49, all_24_1_18 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (414) all_46_0_50 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_24_0_17, all_44_0_48, all_1_3_3, all_1_5_5, all_24_1_18, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (415) all_44_0_48 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_44_0_48, all_24_0_17, all_1_5_5, all_1_3_3, all_44_1_49, all_24_1_18 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (416) all_44_0_48 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (96) with all_24_0_17, all_44_0_48, all_1_5_5, all_1_3_3, all_24_1_18, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (417) all_44_0_48 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (96) with all_44_0_48, all_24_0_17, all_1_3_3, all_1_5_5, all_44_1_49, all_24_1_18 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, yields:
% 69.66/21.77  			| (418) all_44_0_48 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_52_0_57, all_46_0_50, all_1_4_4, all_1_3_3, all_1_1_1, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.77  			| (419) all_52_0_57 = 0 | all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (1) with all_46_0_50, all_52_0_57, all_1_3_3, all_1_4_4, all_44_1_49, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.77  			| (420) all_52_0_57 = 0 | all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.77  			|
% 69.66/21.77  			| Instantiating formula (96) with all_52_0_57, all_46_0_50, all_1_3_3, all_1_4_4, all_1_1_1, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.77  			| (421) all_52_0_57 = 0 | all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_46_0_50, all_52_0_57, all_1_4_4, all_1_3_3, all_44_1_49, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (422) all_52_0_57 = 0 | all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_52_0_57, all_44_0_48, all_1_4_4, all_1_5_5, all_1_1_1, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (423) all_52_0_57 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_44_0_48, all_52_0_57, all_1_5_5, all_1_4_4, all_44_1_49, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (424) all_52_0_57 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_52_0_57, all_44_0_48, all_1_5_5, all_1_4_4, all_1_1_1, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (425) all_52_0_57 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_44_0_48, all_52_0_57, all_1_4_4, all_1_5_5, all_44_1_49, all_1_1_1 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (426) all_52_0_57 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_52_0_57, all_24_0_17, all_1_4_4, all_1_3_3, all_1_1_1, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (427) all_52_0_57 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_24_0_17, all_52_0_57, all_1_3_3, all_1_4_4, all_24_1_18, all_1_1_1 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (428) all_52_0_57 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_52_0_57, all_24_0_17, all_1_3_3, all_1_4_4, all_1_1_1, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (429) all_52_0_57 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_24_0_17, all_52_0_57, all_1_4_4, all_1_3_3, all_24_1_18, all_1_1_1 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (430) all_52_0_57 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_52_0_57, all_52_0_57, all_1_4_4, all_1_4_4, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.66/21.78  			| (431) all_52_0_57 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_60_0_71, all_26_0_19, all_1_5_5, all_1_4_4, all_1_1_1, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.66/21.78  			| (432) all_60_0_71 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_26_0_19, all_60_0_71, all_1_4_4, all_1_5_5, all_24_1_18, all_1_1_1 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.66/21.78  			| (433) all_60_0_71 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_60_0_71, all_26_0_19, all_1_4_4, all_1_5_5, all_1_1_1, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.66/21.78  			| (434) all_60_0_71 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_26_0_19, all_60_0_71, all_1_5_5, all_1_4_4, all_24_1_18, all_1_1_1 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.66/21.78  			| (435) all_60_0_71 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_60_0_71, all_52_0_57, all_1_5_5, all_1_4_4, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.66/21.78  			| (436) all_60_0_71 = 0 | all_52_0_57 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_50_0_56, all_44_0_48, all_1_3_3, all_1_5_5, all_1_2_2, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (437) all_50_0_56 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_44_0_48, all_50_0_56, all_1_5_5, all_1_3_3, all_44_1_49, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (438) all_50_0_56 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_50_0_56, all_44_0_48, all_1_5_5, all_1_3_3, all_1_2_2, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (439) all_50_0_56 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_44_0_48, all_50_0_56, all_1_3_3, all_1_5_5, all_44_1_49, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (440) all_50_0_56 = 0 | all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_50_0_56, all_24_0_17, all_1_3_3, all_1_3_3, all_1_2_2, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (441) all_50_0_56 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_24_0_17, all_50_0_56, all_1_3_3, all_1_3_3, all_24_1_18, all_1_2_2 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (442) all_50_0_56 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_50_0_56, all_26_0_19, all_1_3_3, all_1_4_4, all_1_2_2, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (443) all_50_0_56 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (1) with all_26_0_19, all_50_0_56, all_1_4_4, all_1_3_3, all_24_1_18, all_1_2_2 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (444) all_50_0_56 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.78  			|
% 69.66/21.78  			| Instantiating formula (96) with all_50_0_56, all_26_0_19, all_1_4_4, all_1_3_3, all_1_2_2, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.78  			| (445) all_50_0_56 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_26_0_19, all_50_0_56, all_1_3_3, all_1_4_4, all_24_1_18, all_1_2_2 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.79  			| (446) all_50_0_56 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (100) with all_50_0_56, all_1_2_2, all_1_3_3, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_3_3) = 0, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.79  			| (447) all_50_0_56 = 0 | distinct_points(all_1_1_1, all_1_2_2) = 0
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_60_0_71, all_50_0_56, all_1_3_3, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, yields:
% 69.66/21.79  			| (448) all_60_0_71 = 0 | all_50_0_56 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_30_0_25, all_24_0_17, all_1_4_4, all_1_3_3, all_1_2_2, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_3_3) = all_24_0_17, apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, yields:
% 69.66/21.79  			| (449) all_30_0_25 = 0 | all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_30_0_25, all_60_0_71, all_1_4_4, all_1_5_5, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, yields:
% 69.66/21.79  			| (450) all_60_0_71 = 0 | all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_30_0_25, all_50_0_56, all_1_4_4, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, yields:
% 69.66/21.79  			| (451) all_50_0_56 = 0 | all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_50_0_56, all_30_0_25, all_1_4_4, all_1_3_3, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, yields:
% 69.66/21.79  			| (452) all_50_0_56 = 0 | all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_18_0_7, all_46_0_50, all_1_5_5, all_1_3_3, all_1_2_2, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (453) all_46_0_50 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_46_0_50, all_18_0_7, all_1_3_3, all_1_5_5, all_44_1_49, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (454) all_46_0_50 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_18_0_7, all_46_0_50, all_1_3_3, all_1_5_5, all_1_2_2, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (455) all_46_0_50 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_46_0_50, all_18_0_7, all_1_5_5, all_1_3_3, all_44_1_49, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_49, all_1_3_3) = all_46_0_50, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (456) all_46_0_50 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_18_0_7, all_44_0_48, all_1_5_5, all_1_5_5, all_1_2_2, all_44_1_49 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (457) all_44_0_48 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_44_0_48, all_18_0_7, all_1_5_5, all_1_5_5, all_44_1_49, all_1_2_2 and discharging atoms apart_point_and_line(all_44_1_49, all_1_5_5) = all_44_0_48, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (458) all_44_0_48 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_18_0_7, all_52_0_57, all_1_4_4, all_1_5_5, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (459) all_52_0_57 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_30_0_25, all_18_0_7, all_1_4_4, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (460) all_30_0_25 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_18_0_7, all_30_0_25, all_1_4_4, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (461) all_30_0_25 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (96) with all_30_0_25, all_18_0_7, all_1_5_5, all_1_4_4, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (462) all_30_0_25 = 0 | all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (109) with all_18_0_7, all_18_0_7, all_1_5_5, all_1_5_5, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (463) all_18_0_7 = 0 |  ? [v0] :  ? [v1] : (convergent_lines(all_1_5_5, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (1) with all_18_0_7, all_18_0_7, all_1_5_5, all_1_5_5, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.66/21.79  			| (464) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (102) with all_54_3_62, all_50_0_56, all_1_3_3, all_1_3_3, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_3_3) = all_50_0_56, convergent_lines(all_1_3_3, all_1_3_3) = all_54_3_62, yields:
% 69.66/21.79  			| (465) all_54_3_62 = 0 | all_50_0_56 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (102) with all_34_1_32, all_26_0_19, all_1_4_4, all_1_4_4, all_24_1_18 and discharging atoms apart_point_and_line(all_24_1_18, all_1_4_4) = all_26_0_19, convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32, yields:
% 69.66/21.79  			| (466) all_34_1_32 = 0 | all_26_0_19 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (102) with all_34_1_32, all_52_0_57, all_1_4_4, all_1_4_4, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32, yields:
% 69.66/21.79  			| (467) all_52_0_57 = 0 | all_34_1_32 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (102) with all_34_1_32, all_30_0_25, all_1_4_4, all_1_4_4, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_4_4) = all_30_0_25, convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32, yields:
% 69.66/21.79  			| (468) all_34_1_32 = 0 | all_30_0_25 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (79) with all_48_1_53, all_1_5_5, all_1_4_4, all_1_5_5 and discharging atoms convergent_lines(all_1_4_4, all_1_5_5) = all_48_1_53, convergent_lines(all_1_5_5, all_1_4_4) = 0,  ~ (convergent_lines(all_1_5_5, all_1_5_5) = 0), yields:
% 69.66/21.79  			| (469) all_48_1_53 = 0
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (87) with all_34_1_32, all_1_4_4, all_1_5_5, all_1_4_4 and discharging atoms convergent_lines(all_1_4_4, all_1_4_4) = all_34_1_32, yields:
% 69.66/21.79  			| (470) all_34_1_32 = 0 |  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) | distinct_lines(all_1_5_5, all_1_4_4) = 0
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (67) with all_1_5_5, all_1_4_4 yields:
% 69.66/21.79  			| (471)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & intersection_point(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (88) with all_1_5_5, all_1_4_4 yields:
% 69.66/21.79  			| (472)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (56) with all_1_5_5, all_1_4_4 yields:
% 69.66/21.79  			| (473)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (85) with all_1_5_5, all_1_4_4 yields:
% 69.66/21.79  			| (474)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0) |  ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_4_4, all_1_5_5) = v0)
% 69.66/21.79  			|
% 69.66/21.79  			| Instantiating formula (102) with all_72_3_94, all_60_0_71, all_1_5_5, all_1_5_5, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, convergent_lines(all_1_5_5, all_1_5_5) = all_72_3_94, yields:
% 69.66/21.80  			| (475) all_72_3_94 = 0 | all_60_0_71 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  			|
% 69.66/21.80  			| Combining equations (469,379) yields a new equation:
% 69.66/21.80  			| (476) all_52_1_58 = 0
% 69.66/21.80  			|
% 69.66/21.80  			| Combining equations (469,346) yields a new equation:
% 69.66/21.80  			| (477) all_60_1_72 = 0
% 69.66/21.80  			|
% 69.66/21.80  			| From (469) and (216) follows:
% 69.66/21.80  			| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.66/21.80  			|
% 69.66/21.80  			+-Applying beta-rule and splitting (468), into two cases.
% 69.66/21.80  			|-Branch one:
% 69.66/21.80  			| (479) all_34_1_32 = 0
% 69.66/21.80  			|
% 69.66/21.80  				| Equations (479) can reduce 384 to:
% 69.66/21.80  				| (480) $false
% 69.66/21.80  				|
% 69.66/21.80  				|-The branch is then unsatisfiable
% 69.66/21.80  			|-Branch two:
% 69.66/21.80  			| (384)  ~ (all_34_1_32 = 0)
% 69.66/21.80  			| (482) all_30_0_25 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  			|
% 69.66/21.80  				+-Applying beta-rule and splitting (414), into two cases.
% 69.66/21.80  				|-Branch one:
% 69.66/21.80  				| (483) all_46_0_50 = 0
% 69.66/21.80  				|
% 69.66/21.80  					| Equations (483) can reduce 209 to:
% 69.66/21.80  					| (480) $false
% 69.66/21.80  					|
% 69.66/21.80  					|-The branch is then unsatisfiable
% 69.66/21.80  				|-Branch two:
% 69.66/21.80  				| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.80  				| (486) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  				|
% 69.66/21.80  					+-Applying beta-rule and splitting (413), into two cases.
% 69.66/21.80  					|-Branch one:
% 69.66/21.80  					| (483) all_46_0_50 = 0
% 69.66/21.80  					|
% 69.66/21.80  						| Equations (483) can reduce 209 to:
% 69.66/21.80  						| (480) $false
% 69.66/21.80  						|
% 69.66/21.80  						|-The branch is then unsatisfiable
% 69.66/21.80  					|-Branch two:
% 69.66/21.80  					| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.80  					| (490) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  					|
% 69.66/21.80  						+-Applying beta-rule and splitting (482), into two cases.
% 69.66/21.80  						|-Branch one:
% 69.66/21.80  						| (491) all_30_0_25 = 0
% 69.66/21.80  						|
% 69.66/21.80  							| Equations (491) can reduce 403 to:
% 69.66/21.80  							| (480) $false
% 69.66/21.80  							|
% 69.66/21.80  							|-The branch is then unsatisfiable
% 69.66/21.80  						|-Branch two:
% 69.66/21.80  						| (403)  ~ (all_30_0_25 = 0)
% 69.66/21.80  						| (494)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  						|
% 69.66/21.80  							+-Applying beta-rule and splitting (465), into two cases.
% 69.66/21.80  							|-Branch one:
% 69.66/21.80  							| (495) all_54_3_62 = 0
% 69.66/21.80  							|
% 69.66/21.80  								| Equations (495) can reduce 405 to:
% 69.66/21.80  								| (480) $false
% 69.66/21.80  								|
% 69.66/21.80  								|-The branch is then unsatisfiable
% 69.66/21.80  							|-Branch two:
% 69.66/21.80  							| (405)  ~ (all_54_3_62 = 0)
% 69.66/21.80  							| (498) all_50_0_56 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  							|
% 69.66/21.80  								+-Applying beta-rule and splitting (463), into two cases.
% 69.66/21.80  								|-Branch one:
% 69.66/21.80  								| (499) all_18_0_7 = 0
% 69.66/21.80  								|
% 69.66/21.80  									| Equations (499) can reduce 171 to:
% 69.66/21.80  									| (480) $false
% 69.66/21.80  									|
% 69.66/21.80  									|-The branch is then unsatisfiable
% 69.66/21.80  								|-Branch two:
% 69.66/21.80  								| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.80  								| (502)  ? [v0] :  ? [v1] : (convergent_lines(all_1_5_5, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  								|
% 69.66/21.80  									+-Applying beta-rule and splitting (460), into two cases.
% 69.66/21.80  									|-Branch one:
% 69.66/21.80  									| (491) all_30_0_25 = 0
% 69.66/21.80  									|
% 69.66/21.80  										| Equations (491) can reduce 403 to:
% 69.66/21.80  										| (480) $false
% 69.66/21.80  										|
% 69.66/21.80  										|-The branch is then unsatisfiable
% 69.66/21.80  									|-Branch two:
% 69.66/21.80  									| (403)  ~ (all_30_0_25 = 0)
% 69.66/21.80  									| (506) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  									|
% 69.66/21.80  										+-Applying beta-rule and splitting (461), into two cases.
% 69.66/21.80  										|-Branch one:
% 69.66/21.80  										| (491) all_30_0_25 = 0
% 69.66/21.80  										|
% 69.66/21.80  											| Equations (491) can reduce 403 to:
% 69.66/21.80  											| (480) $false
% 69.66/21.80  											|
% 69.66/21.80  											|-The branch is then unsatisfiable
% 69.66/21.80  										|-Branch two:
% 69.66/21.80  										| (403)  ~ (all_30_0_25 = 0)
% 69.66/21.80  										| (510) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  										|
% 69.66/21.80  											+-Applying beta-rule and splitting (498), into two cases.
% 69.66/21.80  											|-Branch one:
% 69.66/21.80  											| (511) all_50_0_56 = 0
% 69.66/21.80  											|
% 69.66/21.80  												| Equations (511) can reduce 219 to:
% 69.66/21.80  												| (480) $false
% 69.66/21.80  												|
% 69.66/21.80  												|-The branch is then unsatisfiable
% 69.66/21.80  											|-Branch two:
% 69.66/21.80  											| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.80  											| (514)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v1 & distinct_lines(all_1_3_3, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  											|
% 69.66/21.80  												+-Applying beta-rule and splitting (224), into two cases.
% 69.66/21.80  												|-Branch one:
% 69.66/21.80  												| (515)  ~ (all_52_0_57 = 0)
% 69.66/21.80  												|
% 69.66/21.80  													+-Applying beta-rule and splitting (246), into two cases.
% 69.66/21.80  													|-Branch one:
% 69.66/21.80  													| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.80  													|
% 69.66/21.80  														+-Applying beta-rule and splitting (406), into two cases.
% 69.66/21.80  														|-Branch one:
% 69.66/21.80  														| (483) all_46_0_50 = 0
% 69.66/21.80  														|
% 69.66/21.80  															| Equations (483) can reduce 209 to:
% 69.66/21.80  															| (480) $false
% 69.66/21.80  															|
% 69.66/21.80  															|-The branch is then unsatisfiable
% 69.66/21.80  														|-Branch two:
% 69.66/21.80  														| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.80  														| (520) all_44_0_48 = 0 |  ? [v0] :  ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  														|
% 69.66/21.80  															+-Applying beta-rule and splitting (407), into two cases.
% 69.66/21.80  															|-Branch one:
% 69.66/21.80  															| (483) all_46_0_50 = 0
% 69.66/21.80  															|
% 69.66/21.80  																| Equations (483) can reduce 209 to:
% 69.66/21.80  																| (480) $false
% 69.66/21.80  																|
% 69.66/21.80  																|-The branch is then unsatisfiable
% 69.66/21.80  															|-Branch two:
% 69.66/21.80  															| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.80  															| (524) all_44_0_48 = 0 |  ? [v0] :  ? [v1] : (convergent_lines(all_1_5_5, all_1_3_3) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.80  															|
% 69.66/21.80  																+-Applying beta-rule and splitting (412), into two cases.
% 69.66/21.80  																|-Branch one:
% 69.66/21.80  																| (525) all_44_0_48 = 0
% 69.66/21.80  																|
% 69.66/21.80  																	| Equations (525) can reduce 205 to:
% 69.66/21.80  																	| (480) $false
% 69.66/21.80  																	|
% 69.66/21.80  																	|-The branch is then unsatisfiable
% 69.66/21.80  																|-Branch two:
% 69.66/21.80  																| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.80  																| (528)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  																|
% 69.66/21.80  																	+-Applying beta-rule and splitting (464), into two cases.
% 69.66/21.80  																	|-Branch one:
% 69.66/21.80  																	| (499) all_18_0_7 = 0
% 69.66/21.80  																	|
% 69.66/21.80  																		| Equations (499) can reduce 171 to:
% 69.66/21.80  																		| (480) $false
% 69.66/21.80  																		|
% 69.66/21.80  																		|-The branch is then unsatisfiable
% 69.66/21.80  																	|-Branch two:
% 69.66/21.80  																	| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.80  																	| (532)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  																	|
% 69.66/21.80  																		| Instantiating (532) with all_597_0_843, all_597_1_844, all_597_2_845, all_597_3_846 yields:
% 69.66/21.80  																		| (533) apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_0_843 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_1_844 & distinct_lines(all_1_5_5, all_1_5_5) = all_597_2_845 & distinct_points(all_1_2_2, all_1_2_2) = all_597_3_846 & ( ~ (all_597_2_845 = 0) |  ~ (all_597_3_846 = 0) | all_597_0_843 = 0 | all_597_1_844 = 0)
% 69.66/21.80  																		|
% 69.66/21.80  																		| Applying alpha-rule on (533) yields:
% 69.66/21.80  																		| (534) apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_1_844
% 69.66/21.80  																		| (535) apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_0_843
% 69.66/21.80  																		| (536) distinct_points(all_1_2_2, all_1_2_2) = all_597_3_846
% 69.66/21.80  																		| (537) distinct_lines(all_1_5_5, all_1_5_5) = all_597_2_845
% 69.66/21.80  																		| (538)  ~ (all_597_2_845 = 0) |  ~ (all_597_3_846 = 0) | all_597_0_843 = 0 | all_597_1_844 = 0
% 69.66/21.80  																		|
% 69.66/21.80  																		+-Applying beta-rule and splitting (462), into two cases.
% 69.66/21.80  																		|-Branch one:
% 69.66/21.80  																		| (491) all_30_0_25 = 0
% 69.66/21.80  																		|
% 69.66/21.80  																			| Equations (491) can reduce 403 to:
% 69.66/21.80  																			| (480) $false
% 69.66/21.80  																			|
% 69.66/21.80  																			|-The branch is then unsatisfiable
% 69.66/21.80  																		|-Branch two:
% 69.66/21.80  																		| (403)  ~ (all_30_0_25 = 0)
% 69.66/21.80  																		| (542) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  																		|
% 69.66/21.80  																			+-Applying beta-rule and splitting (415), into two cases.
% 69.66/21.80  																			|-Branch one:
% 69.66/21.80  																			| (525) all_44_0_48 = 0
% 69.66/21.80  																			|
% 69.66/21.80  																				| Equations (525) can reduce 205 to:
% 69.66/21.80  																				| (480) $false
% 69.66/21.80  																				|
% 69.66/21.80  																				|-The branch is then unsatisfiable
% 69.66/21.80  																			|-Branch two:
% 69.66/21.80  																			| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.80  																			| (546) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  																			|
% 69.66/21.80  																				+-Applying beta-rule and splitting (418), into two cases.
% 69.66/21.80  																				|-Branch one:
% 69.66/21.80  																				| (525) all_44_0_48 = 0
% 69.66/21.80  																				|
% 69.66/21.80  																					| Equations (525) can reduce 205 to:
% 69.66/21.80  																					| (480) $false
% 69.66/21.80  																					|
% 69.66/21.80  																					|-The branch is then unsatisfiable
% 69.66/21.80  																				|-Branch two:
% 69.66/21.80  																				| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.80  																				| (550) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.80  																				|
% 69.66/21.80  																					+-Applying beta-rule and splitting (416), into two cases.
% 69.66/21.80  																					|-Branch one:
% 69.66/21.80  																					| (525) all_44_0_48 = 0
% 69.66/21.80  																					|
% 69.66/21.80  																						| Equations (525) can reduce 205 to:
% 69.66/21.80  																						| (480) $false
% 69.66/21.80  																						|
% 69.66/21.80  																						|-The branch is then unsatisfiable
% 69.66/21.80  																					|-Branch two:
% 69.66/21.80  																					| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																					| (554) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_24_1_18, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																					|
% 69.66/21.81  																						+-Applying beta-rule and splitting (417), into two cases.
% 69.66/21.81  																						|-Branch one:
% 69.66/21.81  																						| (525) all_44_0_48 = 0
% 69.66/21.81  																						|
% 69.66/21.81  																							| Equations (525) can reduce 205 to:
% 69.66/21.81  																							| (480) $false
% 69.66/21.81  																							|
% 69.66/21.81  																							|-The branch is then unsatisfiable
% 69.66/21.81  																						|-Branch two:
% 69.66/21.81  																						| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																						| (558) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																						|
% 69.66/21.81  																							+-Applying beta-rule and splitting (411), into two cases.
% 69.66/21.81  																							|-Branch one:
% 69.66/21.81  																							| (483) all_46_0_50 = 0
% 69.66/21.81  																							|
% 69.66/21.81  																								| Equations (483) can reduce 209 to:
% 69.66/21.81  																								| (480) $false
% 69.66/21.81  																								|
% 69.66/21.81  																								|-The branch is then unsatisfiable
% 69.66/21.81  																							|-Branch two:
% 69.66/21.81  																							| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.81  																							| (562) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																							|
% 69.66/21.81  																								+-Applying beta-rule and splitting (409), into two cases.
% 69.66/21.81  																								|-Branch one:
% 69.66/21.81  																								| (483) all_46_0_50 = 0
% 69.66/21.81  																								|
% 69.66/21.81  																									| Equations (483) can reduce 209 to:
% 69.66/21.81  																									| (480) $false
% 69.66/21.81  																									|
% 69.66/21.81  																									|-The branch is then unsatisfiable
% 69.66/21.81  																								|-Branch two:
% 69.66/21.81  																								| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.81  																								| (566) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																								|
% 69.66/21.81  																									+-Applying beta-rule and splitting (410), into two cases.
% 69.66/21.81  																									|-Branch one:
% 69.66/21.81  																									| (483) all_46_0_50 = 0
% 69.66/21.81  																									|
% 69.66/21.81  																										| Equations (483) can reduce 209 to:
% 69.66/21.81  																										| (480) $false
% 69.66/21.81  																										|
% 69.66/21.81  																										|-The branch is then unsatisfiable
% 69.66/21.81  																									|-Branch two:
% 69.66/21.81  																									| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.81  																									| (570) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																									|
% 69.66/21.81  																										+-Applying beta-rule and splitting (408), into two cases.
% 69.66/21.81  																										|-Branch one:
% 69.66/21.81  																										| (483) all_46_0_50 = 0
% 69.66/21.81  																										|
% 69.66/21.81  																											| Equations (483) can reduce 209 to:
% 69.66/21.81  																											| (480) $false
% 69.66/21.81  																											|
% 69.66/21.81  																											|-The branch is then unsatisfiable
% 69.66/21.81  																										|-Branch two:
% 69.66/21.81  																										| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.81  																										| (574) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																										|
% 69.66/21.81  																											+-Applying beta-rule and splitting (447), into two cases.
% 69.66/21.81  																											|-Branch one:
% 69.66/21.81  																											| (575) distinct_points(all_1_1_1, all_1_2_2) = 0
% 69.66/21.81  																											|
% 69.66/21.81  																												+-Applying beta-rule and splitting (444), into two cases.
% 69.66/21.81  																												|-Branch one:
% 69.66/21.81  																												| (511) all_50_0_56 = 0
% 69.66/21.81  																												|
% 69.66/21.81  																													| Equations (511) can reduce 219 to:
% 69.66/21.81  																													| (480) $false
% 69.66/21.81  																													|
% 69.66/21.81  																													|-The branch is then unsatisfiable
% 69.66/21.81  																												|-Branch two:
% 69.66/21.81  																												| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																												| (579) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																												|
% 69.66/21.81  																													+-Applying beta-rule and splitting (445), into two cases.
% 69.66/21.81  																													|-Branch one:
% 69.66/21.81  																													| (511) all_50_0_56 = 0
% 69.66/21.81  																													|
% 69.66/21.81  																														| Equations (511) can reduce 219 to:
% 69.66/21.81  																														| (480) $false
% 69.66/21.81  																														|
% 69.66/21.81  																														|-The branch is then unsatisfiable
% 69.66/21.81  																													|-Branch two:
% 69.66/21.81  																													| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																													| (583) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																													|
% 69.66/21.81  																														+-Applying beta-rule and splitting (443), into two cases.
% 69.66/21.81  																														|-Branch one:
% 69.66/21.81  																														| (511) all_50_0_56 = 0
% 69.66/21.81  																														|
% 69.66/21.81  																															| Equations (511) can reduce 219 to:
% 69.66/21.81  																															| (480) $false
% 69.66/21.81  																															|
% 69.66/21.81  																															|-The branch is then unsatisfiable
% 69.66/21.81  																														|-Branch two:
% 69.66/21.81  																														| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																														| (587) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																														|
% 69.66/21.81  																															+-Applying beta-rule and splitting (448), into two cases.
% 69.66/21.81  																															|-Branch one:
% 69.66/21.81  																															| (588) all_60_0_71 = 0
% 69.66/21.81  																															|
% 69.66/21.81  																																| Equations (588) can reduce 516 to:
% 69.66/21.81  																																| (480) $false
% 69.66/21.81  																																|
% 69.66/21.81  																																|-The branch is then unsatisfiable
% 69.66/21.81  																															|-Branch two:
% 69.66/21.81  																															| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.81  																															| (591) all_50_0_56 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																															|
% 69.66/21.81  																																+-Applying beta-rule and splitting (520), into two cases.
% 69.66/21.81  																																|-Branch one:
% 69.66/21.81  																																| (525) all_44_0_48 = 0
% 69.66/21.81  																																|
% 69.66/21.81  																																	| Equations (525) can reduce 205 to:
% 69.66/21.81  																																	| (480) $false
% 69.66/21.81  																																	|
% 69.66/21.81  																																	|-The branch is then unsatisfiable
% 69.66/21.81  																																|-Branch two:
% 69.66/21.81  																																| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																																| (595)  ? [v0] :  ? [v1] : (convergent_lines(all_1_3_3, all_1_5_5) = v1 & distinct_lines(all_1_3_3, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.81  																																|
% 69.66/21.81  																																	+-Applying beta-rule and splitting (524), into two cases.
% 69.66/21.81  																																	|-Branch one:
% 69.66/21.81  																																	| (525) all_44_0_48 = 0
% 69.66/21.81  																																	|
% 69.66/21.81  																																		| Equations (525) can reduce 205 to:
% 69.66/21.81  																																		| (480) $false
% 69.66/21.81  																																		|
% 69.66/21.81  																																		|-The branch is then unsatisfiable
% 69.66/21.81  																																	|-Branch two:
% 69.66/21.81  																																	| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																																	| (599)  ? [v0] :  ? [v1] : (convergent_lines(all_1_5_5, all_1_3_3) = v1 & distinct_lines(all_1_5_5, all_1_3_3) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.81  																																	|
% 69.66/21.81  																																		+-Applying beta-rule and splitting (542), into two cases.
% 69.66/21.81  																																		|-Branch one:
% 69.66/21.81  																																		| (499) all_18_0_7 = 0
% 69.66/21.81  																																		|
% 69.66/21.81  																																			| Equations (499) can reduce 171 to:
% 69.66/21.81  																																			| (480) $false
% 69.66/21.81  																																			|
% 69.66/21.81  																																			|-The branch is then unsatisfiable
% 69.66/21.81  																																		|-Branch two:
% 69.66/21.81  																																		| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.81  																																		| (603)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																		|
% 69.66/21.81  																																			| Instantiating (603) with all_659_0_851, all_659_1_852, all_659_2_853, all_659_3_854 yields:
% 69.66/21.81  																																			| (604) apart_point_and_line(all_1_2_2, all_1_4_4) = all_659_1_852 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_659_0_851 & distinct_lines(all_1_4_4, all_1_5_5) = all_659_2_853 & distinct_points(all_1_2_2, all_1_2_2) = all_659_3_854 & ( ~ (all_659_2_853 = 0) |  ~ (all_659_3_854 = 0) | all_659_0_851 = 0 | all_659_1_852 = 0)
% 69.66/21.81  																																			|
% 69.66/21.81  																																			| Applying alpha-rule on (604) yields:
% 69.66/21.81  																																			| (605) apart_point_and_line(all_1_2_2, all_1_4_4) = all_659_1_852
% 69.66/21.81  																																			| (606) distinct_points(all_1_2_2, all_1_2_2) = all_659_3_854
% 69.66/21.81  																																			| (607) distinct_lines(all_1_4_4, all_1_5_5) = all_659_2_853
% 69.66/21.81  																																			| (608)  ~ (all_659_2_853 = 0) |  ~ (all_659_3_854 = 0) | all_659_0_851 = 0 | all_659_1_852 = 0
% 69.66/21.81  																																			| (609) apart_point_and_line(all_1_2_2, all_1_5_5) = all_659_0_851
% 69.66/21.81  																																			|
% 69.66/21.81  																																			+-Applying beta-rule and splitting (562), into two cases.
% 69.66/21.81  																																			|-Branch one:
% 69.66/21.81  																																			| (525) all_44_0_48 = 0
% 69.66/21.81  																																			|
% 69.66/21.81  																																				| Equations (525) can reduce 205 to:
% 69.66/21.81  																																				| (480) $false
% 69.66/21.81  																																				|
% 69.66/21.81  																																				|-The branch is then unsatisfiable
% 69.66/21.81  																																			|-Branch two:
% 69.66/21.81  																																			| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																																			| (613)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																			|
% 69.66/21.81  																																				+-Applying beta-rule and splitting (570), into two cases.
% 69.66/21.81  																																				|-Branch one:
% 69.66/21.81  																																				| (525) all_44_0_48 = 0
% 69.66/21.81  																																				|
% 69.66/21.81  																																					| Equations (525) can reduce 205 to:
% 69.66/21.81  																																					| (480) $false
% 69.66/21.81  																																					|
% 69.66/21.81  																																					|-The branch is then unsatisfiable
% 69.66/21.81  																																				|-Branch two:
% 69.66/21.81  																																				| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																																				| (617)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																				|
% 69.66/21.81  																																					+-Applying beta-rule and splitting (574), into two cases.
% 69.66/21.81  																																					|-Branch one:
% 69.66/21.81  																																					| (525) all_44_0_48 = 0
% 69.66/21.81  																																					|
% 69.66/21.81  																																						| Equations (525) can reduce 205 to:
% 69.66/21.81  																																						| (480) $false
% 69.66/21.81  																																						|
% 69.66/21.81  																																						|-The branch is then unsatisfiable
% 69.66/21.81  																																					|-Branch two:
% 69.66/21.81  																																					| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.81  																																					| (621)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																					|
% 69.66/21.81  																																						+-Applying beta-rule and splitting (437), into two cases.
% 69.66/21.81  																																						|-Branch one:
% 69.66/21.81  																																						| (511) all_50_0_56 = 0
% 69.66/21.81  																																						|
% 69.66/21.81  																																							| Equations (511) can reduce 219 to:
% 69.66/21.81  																																							| (480) $false
% 69.66/21.81  																																							|
% 69.66/21.81  																																							|-The branch is then unsatisfiable
% 69.66/21.81  																																						|-Branch two:
% 69.66/21.81  																																						| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																																						| (625) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																						|
% 69.66/21.81  																																							+-Applying beta-rule and splitting (438), into two cases.
% 69.66/21.81  																																							|-Branch one:
% 69.66/21.81  																																							| (511) all_50_0_56 = 0
% 69.66/21.81  																																							|
% 69.66/21.81  																																								| Equations (511) can reduce 219 to:
% 69.66/21.81  																																								| (480) $false
% 69.66/21.81  																																								|
% 69.66/21.81  																																								|-The branch is then unsatisfiable
% 69.66/21.81  																																							|-Branch two:
% 69.66/21.81  																																							| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																																							| (629) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																							|
% 69.66/21.81  																																								+-Applying beta-rule and splitting (439), into two cases.
% 69.66/21.81  																																								|-Branch one:
% 69.66/21.81  																																								| (511) all_50_0_56 = 0
% 69.66/21.81  																																								|
% 69.66/21.81  																																									| Equations (511) can reduce 219 to:
% 69.66/21.81  																																									| (480) $false
% 69.66/21.81  																																									|
% 69.66/21.81  																																									|-The branch is then unsatisfiable
% 69.66/21.81  																																								|-Branch two:
% 69.66/21.81  																																								| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																																								| (633) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																								|
% 69.66/21.81  																																									+-Applying beta-rule and splitting (440), into two cases.
% 69.66/21.81  																																									|-Branch one:
% 69.66/21.81  																																									| (511) all_50_0_56 = 0
% 69.66/21.81  																																									|
% 69.66/21.81  																																										| Equations (511) can reduce 219 to:
% 69.66/21.81  																																										| (480) $false
% 69.66/21.81  																																										|
% 69.66/21.81  																																										|-The branch is then unsatisfiable
% 69.66/21.81  																																									|-Branch two:
% 69.66/21.81  																																									| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																																									| (637) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.81  																																									|
% 69.66/21.81  																																										+-Applying beta-rule and splitting (442), into two cases.
% 69.66/21.81  																																										|-Branch one:
% 69.66/21.81  																																										| (511) all_50_0_56 = 0
% 69.66/21.81  																																										|
% 69.66/21.81  																																											| Equations (511) can reduce 219 to:
% 69.66/21.81  																																											| (480) $false
% 69.66/21.81  																																											|
% 69.66/21.81  																																											|-The branch is then unsatisfiable
% 69.66/21.81  																																										|-Branch two:
% 69.66/21.81  																																										| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.81  																																										| (641) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																										|
% 69.66/21.82  																																											+-Applying beta-rule and splitting (441), into two cases.
% 69.66/21.82  																																											|-Branch one:
% 69.66/21.82  																																											| (511) all_50_0_56 = 0
% 69.66/21.82  																																											|
% 69.66/21.82  																																												| Equations (511) can reduce 219 to:
% 69.66/21.82  																																												| (480) $false
% 69.66/21.82  																																												|
% 69.66/21.82  																																												|-The branch is then unsatisfiable
% 69.66/21.82  																																											|-Branch two:
% 69.66/21.82  																																											| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.82  																																											| (645) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																											|
% 69.66/21.82  																																												+-Applying beta-rule and splitting (446), into two cases.
% 69.66/21.82  																																												|-Branch one:
% 69.66/21.82  																																												| (511) all_50_0_56 = 0
% 69.66/21.82  																																												|
% 69.66/21.82  																																													| Equations (511) can reduce 219 to:
% 69.66/21.82  																																													| (480) $false
% 69.66/21.82  																																													|
% 69.66/21.82  																																													|-The branch is then unsatisfiable
% 69.66/21.82  																																												|-Branch two:
% 69.66/21.82  																																												| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.82  																																												| (649) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																												|
% 69.66/21.82  																																													+-Applying beta-rule and splitting (451), into two cases.
% 69.66/21.82  																																													|-Branch one:
% 69.66/21.82  																																													| (511) all_50_0_56 = 0
% 69.66/21.82  																																													|
% 69.66/21.82  																																														| Equations (511) can reduce 219 to:
% 69.66/21.82  																																														| (480) $false
% 69.66/21.82  																																														|
% 69.66/21.82  																																														|-The branch is then unsatisfiable
% 69.66/21.82  																																													|-Branch two:
% 69.66/21.82  																																													| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.82  																																													| (653) all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																													|
% 69.66/21.82  																																														+-Applying beta-rule and splitting (452), into two cases.
% 69.66/21.82  																																														|-Branch one:
% 69.66/21.82  																																														| (511) all_50_0_56 = 0
% 69.66/21.82  																																														|
% 69.66/21.82  																																															| Equations (511) can reduce 219 to:
% 69.66/21.82  																																															| (480) $false
% 69.66/21.82  																																															|
% 69.66/21.82  																																															|-The branch is then unsatisfiable
% 69.66/21.82  																																														|-Branch two:
% 69.66/21.82  																																														| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.82  																																														| (657) all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																														|
% 69.66/21.82  																																															+-Applying beta-rule and splitting (457), into two cases.
% 69.66/21.82  																																															|-Branch one:
% 69.66/21.82  																																															| (525) all_44_0_48 = 0
% 69.66/21.82  																																															|
% 69.66/21.82  																																																| Equations (525) can reduce 205 to:
% 69.66/21.82  																																																| (480) $false
% 69.66/21.82  																																																|
% 69.66/21.82  																																																|-The branch is then unsatisfiable
% 69.66/21.82  																																															|-Branch two:
% 69.66/21.82  																																															| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.82  																																															| (661) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																															|
% 69.66/21.82  																																																+-Applying beta-rule and splitting (458), into two cases.
% 69.66/21.82  																																																|-Branch one:
% 69.66/21.82  																																																| (525) all_44_0_48 = 0
% 69.66/21.82  																																																|
% 69.66/21.82  																																																	| Equations (525) can reduce 205 to:
% 69.66/21.82  																																																	| (480) $false
% 69.66/21.82  																																																	|
% 69.66/21.82  																																																	|-The branch is then unsatisfiable
% 69.66/21.82  																																																|-Branch two:
% 69.66/21.82  																																																| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.82  																																																| (665) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																|
% 69.66/21.82  																																																	+-Applying beta-rule and splitting (453), into two cases.
% 69.66/21.82  																																																	|-Branch one:
% 69.66/21.82  																																																	| (483) all_46_0_50 = 0
% 69.66/21.82  																																																	|
% 69.66/21.82  																																																		| Equations (483) can reduce 209 to:
% 69.66/21.82  																																																		| (480) $false
% 69.66/21.82  																																																		|
% 69.66/21.82  																																																		|-The branch is then unsatisfiable
% 69.66/21.82  																																																	|-Branch two:
% 69.66/21.82  																																																	| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.82  																																																	| (669) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																	|
% 69.66/21.82  																																																		+-Applying beta-rule and splitting (456), into two cases.
% 69.66/21.82  																																																		|-Branch one:
% 69.66/21.82  																																																		| (483) all_46_0_50 = 0
% 69.66/21.82  																																																		|
% 69.66/21.82  																																																			| Equations (483) can reduce 209 to:
% 69.66/21.82  																																																			| (480) $false
% 69.66/21.82  																																																			|
% 69.66/21.82  																																																			|-The branch is then unsatisfiable
% 69.66/21.82  																																																		|-Branch two:
% 69.66/21.82  																																																		| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.82  																																																		| (673) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																		|
% 69.66/21.82  																																																			+-Applying beta-rule and splitting (454), into two cases.
% 69.66/21.82  																																																			|-Branch one:
% 69.66/21.82  																																																			| (483) all_46_0_50 = 0
% 69.66/21.82  																																																			|
% 69.66/21.82  																																																				| Equations (483) can reduce 209 to:
% 69.66/21.82  																																																				| (480) $false
% 69.66/21.82  																																																				|
% 69.66/21.82  																																																				|-The branch is then unsatisfiable
% 69.66/21.82  																																																			|-Branch two:
% 69.66/21.82  																																																			| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.82  																																																			| (677) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																			|
% 69.66/21.82  																																																				+-Applying beta-rule and splitting (455), into two cases.
% 69.66/21.82  																																																				|-Branch one:
% 69.66/21.82  																																																				| (483) all_46_0_50 = 0
% 69.66/21.82  																																																				|
% 69.66/21.82  																																																					| Equations (483) can reduce 209 to:
% 69.66/21.82  																																																					| (480) $false
% 69.66/21.82  																																																					|
% 69.66/21.82  																																																					|-The branch is then unsatisfiable
% 69.66/21.82  																																																				|-Branch two:
% 69.66/21.82  																																																				| (209)  ~ (all_46_0_50 = 0)
% 69.66/21.82  																																																				| (681) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																				|
% 69.66/21.82  																																																					+-Applying beta-rule and splitting (579), into two cases.
% 69.66/21.82  																																																					|-Branch one:
% 69.66/21.82  																																																					| (682) all_26_0_19 = 0
% 69.66/21.82  																																																					|
% 69.66/21.82  																																																						| Equations (682) can reduce 179 to:
% 69.66/21.82  																																																						| (480) $false
% 69.66/21.82  																																																						|
% 69.66/21.82  																																																						|-The branch is then unsatisfiable
% 69.66/21.82  																																																					|-Branch two:
% 69.66/21.82  																																																					| (179)  ~ (all_26_0_19 = 0)
% 69.66/21.82  																																																					| (685)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																					|
% 69.66/21.82  																																																						+-Applying beta-rule and splitting (583), into two cases.
% 69.66/21.82  																																																						|-Branch one:
% 69.66/21.82  																																																						| (682) all_26_0_19 = 0
% 69.66/21.82  																																																						|
% 69.66/21.82  																																																							| Equations (682) can reduce 179 to:
% 69.66/21.82  																																																							| (480) $false
% 69.66/21.82  																																																							|
% 69.66/21.82  																																																							|-The branch is then unsatisfiable
% 69.66/21.82  																																																						|-Branch two:
% 69.66/21.82  																																																						| (179)  ~ (all_26_0_19 = 0)
% 69.66/21.82  																																																						| (689)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																						|
% 69.66/21.82  																																																							+-Applying beta-rule and splitting (587), into two cases.
% 69.66/21.82  																																																							|-Branch one:
% 69.66/21.82  																																																							| (682) all_26_0_19 = 0
% 69.66/21.82  																																																							|
% 69.66/21.82  																																																								| Equations (682) can reduce 179 to:
% 69.66/21.82  																																																								| (480) $false
% 69.66/21.82  																																																								|
% 69.66/21.82  																																																								|-The branch is then unsatisfiable
% 69.66/21.82  																																																							|-Branch two:
% 69.66/21.82  																																																							| (179)  ~ (all_26_0_19 = 0)
% 69.66/21.82  																																																							| (693)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																							|
% 69.66/21.82  																																																								+-Applying beta-rule and splitting (591), into two cases.
% 69.66/21.82  																																																								|-Branch one:
% 69.66/21.82  																																																								| (511) all_50_0_56 = 0
% 69.66/21.82  																																																								|
% 69.66/21.82  																																																									| Equations (511) can reduce 219 to:
% 69.66/21.82  																																																									| (480) $false
% 69.66/21.82  																																																									|
% 69.66/21.82  																																																									|-The branch is then unsatisfiable
% 69.66/21.82  																																																								|-Branch two:
% 69.66/21.82  																																																								| (219)  ~ (all_50_0_56 = 0)
% 69.66/21.82  																																																								| (697)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																								|
% 69.66/21.82  																																																									| Instantiating (697) with all_748_0_883, all_748_1_884, all_748_2_885, all_748_3_886 yields:
% 69.66/21.82  																																																									| (698) apart_point_and_line(all_1_1_1, all_1_3_3) = all_748_0_883 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_748_1_884 & distinct_lines(all_1_5_5, all_1_3_3) = all_748_2_885 & distinct_points(all_1_2_2, all_1_1_1) = all_748_3_886 & ( ~ (all_748_2_885 = 0) |  ~ (all_748_3_886 = 0) | all_748_0_883 = 0 | all_748_1_884 = 0)
% 69.66/21.82  																																																									|
% 69.66/21.82  																																																									| Applying alpha-rule on (698) yields:
% 69.66/21.82  																																																									| (699) distinct_lines(all_1_5_5, all_1_3_3) = all_748_2_885
% 69.66/21.82  																																																									| (700)  ~ (all_748_2_885 = 0) |  ~ (all_748_3_886 = 0) | all_748_0_883 = 0 | all_748_1_884 = 0
% 69.66/21.82  																																																									| (701) apart_point_and_line(all_1_1_1, all_1_3_3) = all_748_0_883
% 69.66/21.82  																																																									| (702) apart_point_and_line(all_1_2_2, all_1_5_5) = all_748_1_884
% 69.66/21.82  																																																									| (703) distinct_points(all_1_2_2, all_1_1_1) = all_748_3_886
% 69.66/21.82  																																																									|
% 69.66/21.82  																																																									+-Applying beta-rule and splitting (629), into two cases.
% 69.66/21.82  																																																									|-Branch one:
% 69.66/21.82  																																																									| (525) all_44_0_48 = 0
% 69.66/21.82  																																																									|
% 69.66/21.82  																																																										| Equations (525) can reduce 205 to:
% 69.66/21.82  																																																										| (480) $false
% 69.66/21.82  																																																										|
% 69.66/21.82  																																																										|-The branch is then unsatisfiable
% 69.66/21.82  																																																									|-Branch two:
% 69.66/21.82  																																																									| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.82  																																																									| (707)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																									|
% 69.66/21.82  																																																										| Instantiating (707) with all_757_0_887, all_757_1_888, all_757_2_889, all_757_3_890 yields:
% 69.66/21.82  																																																										| (708) apart_point_and_line(all_44_1_49, all_1_3_3) = all_757_0_887 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_757_1_888 & distinct_lines(all_1_3_3, all_1_5_5) = all_757_2_889 & distinct_points(all_1_2_2, all_44_1_49) = all_757_3_890 & ( ~ (all_757_2_889 = 0) |  ~ (all_757_3_890 = 0) | all_757_0_887 = 0 | all_757_1_888 = 0)
% 69.66/21.82  																																																										|
% 69.66/21.82  																																																										| Applying alpha-rule on (708) yields:
% 69.66/21.82  																																																										| (709) apart_point_and_line(all_44_1_49, all_1_3_3) = all_757_0_887
% 69.66/21.82  																																																										| (710) apart_point_and_line(all_1_2_2, all_1_5_5) = all_757_1_888
% 69.66/21.82  																																																										| (711) distinct_points(all_1_2_2, all_44_1_49) = all_757_3_890
% 69.66/21.82  																																																										| (712) distinct_lines(all_1_3_3, all_1_5_5) = all_757_2_889
% 69.66/21.82  																																																										| (713)  ~ (all_757_2_889 = 0) |  ~ (all_757_3_890 = 0) | all_757_0_887 = 0 | all_757_1_888 = 0
% 69.66/21.82  																																																										|
% 69.66/21.82  																																																										+-Applying beta-rule and splitting (633), into two cases.
% 69.66/21.82  																																																										|-Branch one:
% 69.66/21.82  																																																										| (525) all_44_0_48 = 0
% 69.66/21.82  																																																										|
% 69.66/21.82  																																																											| Equations (525) can reduce 205 to:
% 69.66/21.82  																																																											| (480) $false
% 69.66/21.82  																																																											|
% 69.66/21.82  																																																											|-The branch is then unsatisfiable
% 69.66/21.82  																																																										|-Branch two:
% 69.66/21.82  																																																										| (205)  ~ (all_44_0_48 = 0)
% 69.66/21.82  																																																										| (717)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_3_3) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.82  																																																										|
% 69.66/21.82  																																																											| Instantiating (717) with all_762_0_891, all_762_1_892, all_762_2_893, all_762_3_894 yields:
% 69.66/21.82  																																																											| (718) apart_point_and_line(all_44_1_49, all_1_3_3) = all_762_1_892 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_762_0_891 & distinct_lines(all_1_3_3, all_1_5_5) = all_762_2_893 & distinct_points(all_44_1_49, all_1_2_2) = all_762_3_894 & ( ~ (all_762_2_893 = 0) |  ~ (all_762_3_894 = 0) | all_762_0_891 = 0 | all_762_1_892 = 0)
% 69.66/21.82  																																																											|
% 69.66/21.82  																																																											| Applying alpha-rule on (718) yields:
% 69.66/21.82  																																																											| (719) distinct_lines(all_1_3_3, all_1_5_5) = all_762_2_893
% 69.66/21.82  																																																											| (720) apart_point_and_line(all_44_1_49, all_1_3_3) = all_762_1_892
% 69.66/21.82  																																																											| (721) distinct_points(all_44_1_49, all_1_2_2) = all_762_3_894
% 69.66/21.82  																																																											| (722)  ~ (all_762_2_893 = 0) |  ~ (all_762_3_894 = 0) | all_762_0_891 = 0 | all_762_1_892 = 0
% 69.66/21.82  																																																											| (723) apart_point_and_line(all_1_2_2, all_1_5_5) = all_762_0_891
% 69.66/21.82  																																																											|
% 69.66/21.83  																																																											+-Applying beta-rule and splitting (661), into two cases.
% 69.66/21.83  																																																											|-Branch one:
% 69.66/21.83  																																																											| (499) all_18_0_7 = 0
% 69.66/21.83  																																																											|
% 69.66/21.83  																																																												| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																												| (480) $false
% 69.66/21.83  																																																												|
% 69.66/21.83  																																																												|-The branch is then unsatisfiable
% 69.66/21.83  																																																											|-Branch two:
% 69.66/21.83  																																																											| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																											| (727)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																											|
% 69.66/21.83  																																																												| Instantiating (727) with all_767_0_895, all_767_1_896, all_767_2_897, all_767_3_898 yields:
% 69.66/21.83  																																																												| (728) apart_point_and_line(all_44_1_49, all_1_5_5) = all_767_1_896 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_767_0_895 & distinct_lines(all_1_5_5, all_1_5_5) = all_767_2_897 & distinct_points(all_44_1_49, all_1_2_2) = all_767_3_898 & ( ~ (all_767_2_897 = 0) |  ~ (all_767_3_898 = 0) | all_767_0_895 = 0 | all_767_1_896 = 0)
% 69.66/21.83  																																																												|
% 69.66/21.83  																																																												| Applying alpha-rule on (728) yields:
% 69.66/21.83  																																																												| (729) apart_point_and_line(all_1_2_2, all_1_5_5) = all_767_0_895
% 69.66/21.83  																																																												| (730) distinct_points(all_44_1_49, all_1_2_2) = all_767_3_898
% 69.66/21.83  																																																												| (731) distinct_lines(all_1_5_5, all_1_5_5) = all_767_2_897
% 69.66/21.83  																																																												| (732) apart_point_and_line(all_44_1_49, all_1_5_5) = all_767_1_896
% 69.66/21.83  																																																												| (733)  ~ (all_767_2_897 = 0) |  ~ (all_767_3_898 = 0) | all_767_0_895 = 0 | all_767_1_896 = 0
% 69.66/21.83  																																																												|
% 69.66/21.83  																																																												+-Applying beta-rule and splitting (665), into two cases.
% 69.66/21.83  																																																												|-Branch one:
% 69.66/21.83  																																																												| (499) all_18_0_7 = 0
% 69.66/21.83  																																																												|
% 69.66/21.83  																																																													| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																													| (480) $false
% 69.66/21.83  																																																													|
% 69.66/21.83  																																																													|-The branch is then unsatisfiable
% 69.66/21.83  																																																												|-Branch two:
% 69.66/21.83  																																																												| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																												| (737)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																												|
% 69.66/21.83  																																																													| Instantiating (737) with all_772_0_899, all_772_1_900, all_772_2_901, all_772_3_902 yields:
% 69.66/21.83  																																																													| (738) apart_point_and_line(all_44_1_49, all_1_5_5) = all_772_0_899 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_772_1_900 & distinct_lines(all_1_5_5, all_1_5_5) = all_772_2_901 & distinct_points(all_1_2_2, all_44_1_49) = all_772_3_902 & ( ~ (all_772_2_901 = 0) |  ~ (all_772_3_902 = 0) | all_772_0_899 = 0 | all_772_1_900 = 0)
% 69.66/21.83  																																																													|
% 69.66/21.83  																																																													| Applying alpha-rule on (738) yields:
% 69.66/21.83  																																																													| (739)  ~ (all_772_2_901 = 0) |  ~ (all_772_3_902 = 0) | all_772_0_899 = 0 | all_772_1_900 = 0
% 69.66/21.83  																																																													| (740) distinct_lines(all_1_5_5, all_1_5_5) = all_772_2_901
% 69.66/21.83  																																																													| (741) apart_point_and_line(all_44_1_49, all_1_5_5) = all_772_0_899
% 69.66/21.83  																																																													| (742) distinct_points(all_1_2_2, all_44_1_49) = all_772_3_902
% 69.66/21.83  																																																													| (743) apart_point_and_line(all_1_2_2, all_1_5_5) = all_772_1_900
% 69.66/21.83  																																																													|
% 69.66/21.83  																																																													+-Applying beta-rule and splitting (669), into two cases.
% 69.66/21.83  																																																													|-Branch one:
% 69.66/21.83  																																																													| (499) all_18_0_7 = 0
% 69.66/21.83  																																																													|
% 69.66/21.83  																																																														| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																														| (480) $false
% 69.66/21.83  																																																														|
% 69.66/21.83  																																																														|-The branch is then unsatisfiable
% 69.66/21.83  																																																													|-Branch two:
% 69.66/21.83  																																																													| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																													| (747)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																													|
% 69.66/21.83  																																																														+-Applying beta-rule and splitting (673), into two cases.
% 69.66/21.83  																																																														|-Branch one:
% 69.66/21.83  																																																														| (499) all_18_0_7 = 0
% 69.66/21.83  																																																														|
% 69.66/21.83  																																																															| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																															| (480) $false
% 69.66/21.83  																																																															|
% 69.66/21.83  																																																															|-The branch is then unsatisfiable
% 69.66/21.83  																																																														|-Branch two:
% 69.66/21.83  																																																														| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																														| (751)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																														|
% 69.66/21.83  																																																															+-Applying beta-rule and splitting (677), into two cases.
% 69.66/21.83  																																																															|-Branch one:
% 69.66/21.83  																																																															| (499) all_18_0_7 = 0
% 69.66/21.83  																																																															|
% 69.66/21.83  																																																																| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																																| (480) $false
% 69.66/21.83  																																																																|
% 69.66/21.83  																																																																|-The branch is then unsatisfiable
% 69.66/21.83  																																																															|-Branch two:
% 69.66/21.83  																																																															| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																															| (755)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_3_3) = v2 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_1_2_2, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																															|
% 69.66/21.83  																																																																+-Applying beta-rule and splitting (681), into two cases.
% 69.66/21.83  																																																																|-Branch one:
% 69.66/21.83  																																																																| (499) all_18_0_7 = 0
% 69.66/21.83  																																																																|
% 69.66/21.83  																																																																	| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																																	| (480) $false
% 69.66/21.83  																																																																	|
% 69.66/21.83  																																																																	|-The branch is then unsatisfiable
% 69.66/21.83  																																																																|-Branch two:
% 69.66/21.83  																																																																| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																																| (759)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_5_5, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																																|
% 69.66/21.83  																																																																	+-Applying beta-rule and splitting (475), into two cases.
% 69.66/21.83  																																																																	|-Branch one:
% 69.66/21.83  																																																																	| (760) all_72_3_94 = 0
% 69.66/21.83  																																																																	|
% 69.66/21.83  																																																																		| Equations (760) can reduce 383 to:
% 69.66/21.83  																																																																		| (480) $false
% 69.66/21.83  																																																																		|
% 69.66/21.83  																																																																		|-The branch is then unsatisfiable
% 69.66/21.83  																																																																	|-Branch two:
% 69.66/21.83  																																																																	| (383)  ~ (all_72_3_94 = 0)
% 69.66/21.83  																																																																	| (763) all_60_0_71 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.83  																																																																	|
% 69.66/21.83  																																																																		+-Applying beta-rule and splitting (506), into two cases.
% 69.66/21.83  																																																																		|-Branch one:
% 69.66/21.83  																																																																		| (499) all_18_0_7 = 0
% 69.66/21.83  																																																																		|
% 69.66/21.83  																																																																			| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																																			| (480) $false
% 69.66/21.83  																																																																			|
% 69.66/21.83  																																																																			|-The branch is then unsatisfiable
% 69.66/21.83  																																																																		|-Branch two:
% 69.66/21.83  																																																																		| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																																		| (767)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																																		|
% 69.66/21.83  																																																																			| Instantiating (767) with all_801_0_919, all_801_1_920, all_801_2_921, all_801_3_922 yields:
% 69.66/21.83  																																																																			| (768) apart_point_and_line(all_1_2_2, all_1_4_4) = all_801_1_920 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_801_0_919 & distinct_lines(all_1_5_5, all_1_4_4) = all_801_2_921 & distinct_points(all_1_2_2, all_1_2_2) = all_801_3_922 & ( ~ (all_801_2_921 = 0) |  ~ (all_801_3_922 = 0) | all_801_0_919 = 0 | all_801_1_920 = 0)
% 69.66/21.83  																																																																			|
% 69.66/21.83  																																																																			| Applying alpha-rule on (768) yields:
% 69.66/21.83  																																																																			| (769) distinct_lines(all_1_5_5, all_1_4_4) = all_801_2_921
% 69.66/21.83  																																																																			| (770) distinct_points(all_1_2_2, all_1_2_2) = all_801_3_922
% 69.66/21.83  																																																																			| (771)  ~ (all_801_2_921 = 0) |  ~ (all_801_3_922 = 0) | all_801_0_919 = 0 | all_801_1_920 = 0
% 69.66/21.83  																																																																			| (772) apart_point_and_line(all_1_2_2, all_1_4_4) = all_801_1_920
% 69.66/21.83  																																																																			| (773) apart_point_and_line(all_1_2_2, all_1_5_5) = all_801_0_919
% 69.66/21.83  																																																																			|
% 69.66/21.83  																																																																			+-Applying beta-rule and splitting (510), into two cases.
% 69.66/21.83  																																																																			|-Branch one:
% 69.66/21.83  																																																																			| (499) all_18_0_7 = 0
% 69.66/21.83  																																																																			|
% 69.66/21.83  																																																																				| Equations (499) can reduce 171 to:
% 69.66/21.83  																																																																				| (480) $false
% 69.66/21.83  																																																																				|
% 69.66/21.83  																																																																				|-The branch is then unsatisfiable
% 69.66/21.83  																																																																			|-Branch two:
% 69.66/21.83  																																																																			| (171)  ~ (all_18_0_7 = 0)
% 69.66/21.83  																																																																			| (777)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.83  																																																																			|
% 69.66/21.83  																																																																				| Instantiating (777) with all_806_0_923, all_806_1_924, all_806_2_925, all_806_3_926 yields:
% 69.66/21.83  																																																																				| (778) apart_point_and_line(all_1_2_2, all_1_4_4) = all_806_0_923 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_806_1_924 & distinct_lines(all_1_5_5, all_1_4_4) = all_806_2_925 & distinct_points(all_1_2_2, all_1_2_2) = all_806_3_926 & ( ~ (all_806_2_925 = 0) |  ~ (all_806_3_926 = 0) | all_806_0_923 = 0 | all_806_1_924 = 0)
% 69.66/21.83  																																																																				|
% 69.66/21.83  																																																																				| Applying alpha-rule on (778) yields:
% 69.66/21.83  																																																																				| (779)  ~ (all_806_2_925 = 0) |  ~ (all_806_3_926 = 0) | all_806_0_923 = 0 | all_806_1_924 = 0
% 69.66/21.83  																																																																				| (780) apart_point_and_line(all_1_2_2, all_1_5_5) = all_806_1_924
% 69.66/21.83  																																																																				| (781) distinct_points(all_1_2_2, all_1_2_2) = all_806_3_926
% 69.66/21.83  																																																																				| (782) distinct_lines(all_1_5_5, all_1_4_4) = all_806_2_925
% 69.66/21.83  																																																																				| (783) apart_point_and_line(all_1_2_2, all_1_4_4) = all_806_0_923
% 69.66/21.83  																																																																				|
% 69.66/21.83  																																																																				+-Applying beta-rule and splitting (467), into two cases.
% 69.66/21.83  																																																																				|-Branch one:
% 69.66/21.83  																																																																				| (784) all_52_0_57 = 0
% 69.66/21.83  																																																																				|
% 69.66/21.83  																																																																					| Equations (784) can reduce 515 to:
% 69.66/21.83  																																																																					| (480) $false
% 69.66/21.83  																																																																					|
% 69.66/21.83  																																																																					|-The branch is then unsatisfiable
% 69.66/21.83  																																																																				|-Branch two:
% 69.66/21.83  																																																																				| (515)  ~ (all_52_0_57 = 0)
% 69.66/21.83  																																																																				| (787) all_34_1_32 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.83  																																																																				|
% 69.66/21.83  																																																																					+-Applying beta-rule and splitting (787), into two cases.
% 69.66/21.83  																																																																					|-Branch one:
% 69.66/21.83  																																																																					| (479) all_34_1_32 = 0
% 69.66/21.83  																																																																					|
% 69.66/21.83  																																																																						| Equations (479) can reduce 384 to:
% 69.66/21.83  																																																																						| (480) $false
% 69.66/21.83  																																																																						|
% 69.66/21.83  																																																																						|-The branch is then unsatisfiable
% 69.66/21.83  																																																																					|-Branch two:
% 69.66/21.83  																																																																					| (384)  ~ (all_34_1_32 = 0)
% 69.66/21.83  																																																																					| (791)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.83  																																																																					|
% 69.66/21.83  																																																																						+-Applying beta-rule and splitting (763), into two cases.
% 69.66/21.83  																																																																						|-Branch one:
% 69.66/21.83  																																																																						| (588) all_60_0_71 = 0
% 69.66/21.83  																																																																						|
% 69.66/21.83  																																																																							| Equations (588) can reduce 516 to:
% 69.66/21.83  																																																																							| (480) $false
% 69.66/21.83  																																																																							|
% 69.66/21.83  																																																																							|-The branch is then unsatisfiable
% 69.66/21.83  																																																																						|-Branch two:
% 69.66/21.83  																																																																						| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.83  																																																																						| (795)  ? [v0] :  ? [v1] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.83  																																																																						|
% 69.66/21.83  																																																																							| Instantiating (795) with all_827_0_930, all_827_1_931 yields:
% 69.66/21.83  																																																																							| (796) apart_point_and_line(all_1_1_1, all_1_5_5) = all_827_0_930 & distinct_lines(all_1_5_5, all_1_5_5) = all_827_1_931 & ( ~ (all_827_1_931 = 0) | all_827_0_930 = 0)
% 69.66/21.83  																																																																							|
% 69.66/21.83  																																																																							| Applying alpha-rule on (796) yields:
% 69.66/21.83  																																																																							| (797) apart_point_and_line(all_1_1_1, all_1_5_5) = all_827_0_930
% 69.66/21.83  																																																																							| (798) distinct_lines(all_1_5_5, all_1_5_5) = all_827_1_931
% 69.66/21.83  																																																																							| (799)  ~ (all_827_1_931 = 0) | all_827_0_930 = 0
% 69.66/21.83  																																																																							|
% 69.66/21.83  																																																																							+-Applying beta-rule and splitting (466), into two cases.
% 69.66/21.83  																																																																							|-Branch one:
% 69.66/21.83  																																																																							| (479) all_34_1_32 = 0
% 69.66/21.83  																																																																							|
% 69.66/21.83  																																																																								| Equations (479) can reduce 384 to:
% 69.66/21.83  																																																																								| (480) $false
% 69.66/21.83  																																																																								|
% 69.66/21.83  																																																																								|-The branch is then unsatisfiable
% 69.66/21.83  																																																																							|-Branch two:
% 69.66/21.83  																																																																							| (384)  ~ (all_34_1_32 = 0)
% 69.66/21.83  																																																																							| (803) all_26_0_19 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v1 & distinct_lines(all_1_4_4, all_1_4_4) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 69.66/21.83  																																																																							|
% 69.66/21.83  																																																																								+-Applying beta-rule and splitting (431), into two cases.
% 69.66/21.83  																																																																								|-Branch one:
% 69.66/21.83  																																																																								| (784) all_52_0_57 = 0
% 69.66/21.83  																																																																								|
% 69.66/21.83  																																																																									| Equations (784) can reduce 515 to:
% 69.66/21.83  																																																																									| (480) $false
% 69.66/21.83  																																																																									|
% 69.66/21.83  																																																																									|-The branch is then unsatisfiable
% 69.66/21.83  																																																																								|-Branch two:
% 69.66/21.83  																																																																								| (515)  ~ (all_52_0_57 = 0)
% 69.66/21.83  																																																																								| (807)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.84  																																																																								|
% 69.66/21.84  																																																																									| Instantiating (807) with all_883_0_940, all_883_1_941, all_883_2_942, all_883_3_943 yields:
% 69.66/21.84  																																																																									| (808) apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_0_940 & apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_1_941 & distinct_lines(all_1_4_4, all_1_4_4) = all_883_2_942 & distinct_points(all_1_1_1, all_1_1_1) = all_883_3_943 & ( ~ (all_883_2_942 = 0) |  ~ (all_883_3_943 = 0) | all_883_0_940 = 0 | all_883_1_941 = 0)
% 69.66/21.84  																																																																									|
% 69.66/21.84  																																																																									| Applying alpha-rule on (808) yields:
% 69.66/21.84  																																																																									| (809)  ~ (all_883_2_942 = 0) |  ~ (all_883_3_943 = 0) | all_883_0_940 = 0 | all_883_1_941 = 0
% 69.66/21.84  																																																																									| (810) distinct_points(all_1_1_1, all_1_1_1) = all_883_3_943
% 69.66/21.84  																																																																									| (811) distinct_lines(all_1_4_4, all_1_4_4) = all_883_2_942
% 69.66/21.84  																																																																									| (812) apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_1_941
% 69.66/21.84  																																																																									| (813) apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_0_940
% 69.66/21.84  																																																																									|
% 69.66/21.84  																																																																									+-Applying beta-rule and splitting (435), into two cases.
% 69.66/21.84  																																																																									|-Branch one:
% 69.66/21.84  																																																																									| (588) all_60_0_71 = 0
% 69.66/21.84  																																																																									|
% 69.66/21.84  																																																																										| Equations (588) can reduce 516 to:
% 69.66/21.84  																																																																										| (480) $false
% 69.66/21.84  																																																																										|
% 69.66/21.84  																																																																										|-The branch is then unsatisfiable
% 69.66/21.84  																																																																									|-Branch two:
% 69.66/21.84  																																																																									| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.84  																																																																									| (817) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.84  																																																																									|
% 69.66/21.84  																																																																										+-Applying beta-rule and splitting (433), into two cases.
% 69.66/21.84  																																																																										|-Branch one:
% 69.66/21.84  																																																																										| (588) all_60_0_71 = 0
% 69.66/21.84  																																																																										|
% 69.66/21.84  																																																																											| Equations (588) can reduce 516 to:
% 69.66/21.84  																																																																											| (480) $false
% 69.66/21.84  																																																																											|
% 69.66/21.84  																																																																											|-The branch is then unsatisfiable
% 69.66/21.84  																																																																										|-Branch two:
% 69.66/21.84  																																																																										| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.84  																																																																										| (821) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.84  																																																																										|
% 69.66/21.84  																																																																											+-Applying beta-rule and splitting (434), into two cases.
% 69.66/21.84  																																																																											|-Branch one:
% 69.66/21.84  																																																																											| (588) all_60_0_71 = 0
% 69.66/21.84  																																																																											|
% 69.66/21.84  																																																																												| Equations (588) can reduce 516 to:
% 69.66/21.84  																																																																												| (480) $false
% 69.66/21.84  																																																																												|
% 69.66/21.84  																																																																												|-The branch is then unsatisfiable
% 69.66/21.84  																																																																											|-Branch two:
% 69.66/21.84  																																																																											| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.84  																																																																											| (825) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.66/21.84  																																																																											|
% 69.66/21.84  																																																																												+-Applying beta-rule and splitting (432), into two cases.
% 69.66/21.84  																																																																												|-Branch one:
% 69.66/21.84  																																																																												| (588) all_60_0_71 = 0
% 69.66/21.84  																																																																												|
% 69.66/21.84  																																																																													| Equations (588) can reduce 516 to:
% 69.66/21.84  																																																																													| (480) $false
% 69.66/21.84  																																																																													|
% 69.66/21.84  																																																																													|-The branch is then unsatisfiable
% 69.66/21.84  																																																																												|-Branch two:
% 69.66/21.84  																																																																												| (516)  ~ (all_60_0_71 = 0)
% 69.66/21.84  																																																																												| (829) all_26_0_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																												|
% 69.99/21.84  																																																																													+-Applying beta-rule and splitting (424), into two cases.
% 69.99/21.84  																																																																													|-Branch one:
% 69.99/21.84  																																																																													| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																													|
% 69.99/21.84  																																																																														| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																														| (480) $false
% 69.99/21.84  																																																																														|
% 69.99/21.84  																																																																														|-The branch is then unsatisfiable
% 69.99/21.84  																																																																													|-Branch two:
% 69.99/21.84  																																																																													| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																													| (833) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																													|
% 69.99/21.84  																																																																														+-Applying beta-rule and splitting (425), into two cases.
% 69.99/21.84  																																																																														|-Branch one:
% 69.99/21.84  																																																																														| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																														|
% 69.99/21.84  																																																																															| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																															| (480) $false
% 69.99/21.84  																																																																															|
% 69.99/21.84  																																																																															|-The branch is then unsatisfiable
% 69.99/21.84  																																																																														|-Branch two:
% 69.99/21.84  																																																																														| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																														| (837) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																														|
% 69.99/21.84  																																																																															+-Applying beta-rule and splitting (428), into two cases.
% 69.99/21.84  																																																																															|-Branch one:
% 69.99/21.84  																																																																															| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																															|
% 69.99/21.84  																																																																																| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																| (480) $false
% 69.99/21.84  																																																																																|
% 69.99/21.84  																																																																																|-The branch is then unsatisfiable
% 69.99/21.84  																																																																															|-Branch two:
% 69.99/21.84  																																																																															| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																															| (841) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																															|
% 69.99/21.84  																																																																																+-Applying beta-rule and splitting (429), into two cases.
% 69.99/21.84  																																																																																|-Branch one:
% 69.99/21.84  																																																																																| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																|
% 69.99/21.84  																																																																																	| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																	| (480) $false
% 69.99/21.84  																																																																																	|
% 69.99/21.84  																																																																																	|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																|-Branch two:
% 69.99/21.84  																																																																																| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																| (845) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																|
% 69.99/21.84  																																																																																	+-Applying beta-rule and splitting (422), into two cases.
% 69.99/21.84  																																																																																	|-Branch one:
% 69.99/21.84  																																																																																	| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																	|
% 69.99/21.84  																																																																																		| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																		| (480) $false
% 69.99/21.84  																																																																																		|
% 69.99/21.84  																																																																																		|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																	|-Branch two:
% 69.99/21.84  																																																																																	| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																	| (849) all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																	|
% 69.99/21.84  																																																																																		+-Applying beta-rule and splitting (423), into two cases.
% 69.99/21.84  																																																																																		|-Branch one:
% 69.99/21.84  																																																																																		| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																		|
% 69.99/21.84  																																																																																			| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																			| (480) $false
% 69.99/21.84  																																																																																			|
% 69.99/21.84  																																																																																			|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																		|-Branch two:
% 69.99/21.84  																																																																																		| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																		| (853) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																		|
% 69.99/21.84  																																																																																			+-Applying beta-rule and splitting (420), into two cases.
% 69.99/21.84  																																																																																			|-Branch one:
% 69.99/21.84  																																																																																			| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																			|
% 69.99/21.84  																																																																																				| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																				| (480) $false
% 69.99/21.84  																																																																																				|
% 69.99/21.84  																																																																																				|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																			|-Branch two:
% 69.99/21.84  																																																																																			| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																			| (857) all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																			|
% 69.99/21.84  																																																																																				+-Applying beta-rule and splitting (421), into two cases.
% 69.99/21.84  																																																																																				|-Branch one:
% 69.99/21.84  																																																																																				| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																				|
% 69.99/21.84  																																																																																					| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																					| (480) $false
% 69.99/21.84  																																																																																					|
% 69.99/21.84  																																																																																					|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																				|-Branch two:
% 69.99/21.84  																																																																																				| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																				| (861) all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_4_4, all_1_3_3) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																				|
% 69.99/21.84  																																																																																					+-Applying beta-rule and splitting (427), into two cases.
% 69.99/21.84  																																																																																					|-Branch one:
% 69.99/21.84  																																																																																					| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																					|
% 69.99/21.84  																																																																																						| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																						| (480) $false
% 69.99/21.84  																																																																																						|
% 69.99/21.84  																																																																																						|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																					|-Branch two:
% 69.99/21.84  																																																																																					| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																					| (865) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																					|
% 69.99/21.84  																																																																																						+-Applying beta-rule and splitting (430), into two cases.
% 69.99/21.84  																																																																																						|-Branch one:
% 69.99/21.84  																																																																																						| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																						|
% 69.99/21.84  																																																																																							| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																							| (480) $false
% 69.99/21.84  																																																																																							|
% 69.99/21.84  																																																																																							|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																						|-Branch two:
% 69.99/21.84  																																																																																						| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																						| (869) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_3_3) = v2 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_24_1_18) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																						|
% 69.99/21.84  																																																																																							+-Applying beta-rule and splitting (426), into two cases.
% 69.99/21.84  																																																																																							|-Branch one:
% 69.99/21.84  																																																																																							| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																							|
% 69.99/21.84  																																																																																								| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																								| (480) $false
% 69.99/21.84  																																																																																								|
% 69.99/21.84  																																																																																								|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																							|-Branch two:
% 69.99/21.84  																																																																																							| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																							| (873) all_44_0_48 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																							|
% 69.99/21.84  																																																																																								+-Applying beta-rule and splitting (419), into two cases.
% 69.99/21.84  																																																																																								|-Branch one:
% 69.99/21.84  																																																																																								| (784) all_52_0_57 = 0
% 69.99/21.84  																																																																																								|
% 69.99/21.84  																																																																																									| Equations (784) can reduce 515 to:
% 69.99/21.84  																																																																																									| (480) $false
% 69.99/21.84  																																																																																									|
% 69.99/21.84  																																																																																									|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																								|-Branch two:
% 69.99/21.84  																																																																																								| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.84  																																																																																								| (877) all_46_0_50 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																								|
% 69.99/21.84  																																																																																									+-Applying beta-rule and splitting (825), into two cases.
% 69.99/21.84  																																																																																									|-Branch one:
% 69.99/21.84  																																																																																									| (682) all_26_0_19 = 0
% 69.99/21.84  																																																																																									|
% 69.99/21.84  																																																																																										| Equations (682) can reduce 179 to:
% 69.99/21.84  																																																																																										| (480) $false
% 69.99/21.84  																																																																																										|
% 69.99/21.84  																																																																																										|-The branch is then unsatisfiable
% 69.99/21.84  																																																																																									|-Branch two:
% 69.99/21.84  																																																																																									| (179)  ~ (all_26_0_19 = 0)
% 69.99/21.84  																																																																																									| (881)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.84  																																																																																									|
% 69.99/21.84  																																																																																										| Instantiating (881) with all_944_0_944, all_944_1_945, all_944_2_946, all_944_3_947 yields:
% 69.99/21.84  																																																																																										| (882) apart_point_and_line(all_24_1_18, all_1_5_5) = all_944_1_945 & apart_point_and_line(all_1_1_1, all_1_4_4) = all_944_0_944 & distinct_lines(all_1_5_5, all_1_4_4) = all_944_2_946 & distinct_points(all_24_1_18, all_1_1_1) = all_944_3_947 & ( ~ (all_944_2_946 = 0) |  ~ (all_944_3_947 = 0) | all_944_0_944 = 0 | all_944_1_945 = 0)
% 69.99/21.84  																																																																																										|
% 69.99/21.84  																																																																																										| Applying alpha-rule on (882) yields:
% 69.99/21.84  																																																																																										| (883) distinct_points(all_24_1_18, all_1_1_1) = all_944_3_947
% 69.99/21.85  																																																																																										| (884)  ~ (all_944_2_946 = 0) |  ~ (all_944_3_947 = 0) | all_944_0_944 = 0 | all_944_1_945 = 0
% 69.99/21.85  																																																																																										| (885) apart_point_and_line(all_24_1_18, all_1_5_5) = all_944_1_945
% 69.99/21.85  																																																																																										| (886) apart_point_and_line(all_1_1_1, all_1_4_4) = all_944_0_944
% 69.99/21.85  																																																																																										| (887) distinct_lines(all_1_5_5, all_1_4_4) = all_944_2_946
% 69.99/21.85  																																																																																										|
% 69.99/21.85  																																																																																										+-Applying beta-rule and splitting (829), into two cases.
% 69.99/21.85  																																																																																										|-Branch one:
% 69.99/21.85  																																																																																										| (682) all_26_0_19 = 0
% 69.99/21.85  																																																																																										|
% 69.99/21.85  																																																																																											| Equations (682) can reduce 179 to:
% 69.99/21.85  																																																																																											| (480) $false
% 69.99/21.85  																																																																																											|
% 69.99/21.85  																																																																																											|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																										|-Branch two:
% 69.99/21.85  																																																																																										| (179)  ~ (all_26_0_19 = 0)
% 69.99/21.85  																																																																																										| (891)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_24_1_18, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.85  																																																																																										|
% 69.99/21.85  																																																																																											| Instantiating (891) with all_949_0_948, all_949_1_949, all_949_2_950, all_949_3_951 yields:
% 69.99/21.85  																																																																																											| (892) apart_point_and_line(all_24_1_18, all_1_5_5) = all_949_1_949 & apart_point_and_line(all_1_1_1, all_1_4_4) = all_949_0_948 & distinct_lines(all_1_4_4, all_1_5_5) = all_949_2_950 & distinct_points(all_24_1_18, all_1_1_1) = all_949_3_951 & ( ~ (all_949_2_950 = 0) |  ~ (all_949_3_951 = 0) | all_949_0_948 = 0 | all_949_1_949 = 0)
% 69.99/21.85  																																																																																											|
% 69.99/21.85  																																																																																											| Applying alpha-rule on (892) yields:
% 69.99/21.85  																																																																																											| (893) apart_point_and_line(all_24_1_18, all_1_5_5) = all_949_1_949
% 69.99/21.85  																																																																																											| (894) apart_point_and_line(all_1_1_1, all_1_4_4) = all_949_0_948
% 69.99/21.85  																																																																																											| (895)  ~ (all_949_2_950 = 0) |  ~ (all_949_3_951 = 0) | all_949_0_948 = 0 | all_949_1_949 = 0
% 69.99/21.85  																																																																																											| (896) distinct_lines(all_1_4_4, all_1_5_5) = all_949_2_950
% 69.99/21.85  																																																																																											| (897) distinct_points(all_24_1_18, all_1_1_1) = all_949_3_951
% 69.99/21.85  																																																																																											|
% 69.99/21.85  																																																																																											+-Applying beta-rule and splitting (833), into two cases.
% 69.99/21.85  																																																																																											|-Branch one:
% 69.99/21.85  																																																																																											| (525) all_44_0_48 = 0
% 69.99/21.85  																																																																																											|
% 69.99/21.85  																																																																																												| Equations (525) can reduce 205 to:
% 69.99/21.85  																																																																																												| (480) $false
% 69.99/21.85  																																																																																												|
% 69.99/21.85  																																																																																												|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																											|-Branch two:
% 69.99/21.85  																																																																																											| (205)  ~ (all_44_0_48 = 0)
% 69.99/21.85  																																																																																											| (901)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_44_1_49) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.85  																																																																																											|
% 69.99/21.85  																																																																																												| Instantiating (901) with all_954_0_952, all_954_1_953, all_954_2_954, all_954_3_955 yields:
% 69.99/21.85  																																																																																												| (902) apart_point_and_line(all_44_1_49, all_1_4_4) = all_954_0_952 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_954_1_953 & distinct_lines(all_1_4_4, all_1_5_5) = all_954_2_954 & distinct_points(all_1_1_1, all_44_1_49) = all_954_3_955 & ( ~ (all_954_2_954 = 0) |  ~ (all_954_3_955 = 0) | all_954_0_952 = 0 | all_954_1_953 = 0)
% 69.99/21.85  																																																																																												|
% 69.99/21.85  																																																																																												| Applying alpha-rule on (902) yields:
% 69.99/21.85  																																																																																												| (903) apart_point_and_line(all_44_1_49, all_1_4_4) = all_954_0_952
% 69.99/21.85  																																																																																												| (904)  ~ (all_954_2_954 = 0) |  ~ (all_954_3_955 = 0) | all_954_0_952 = 0 | all_954_1_953 = 0
% 69.99/21.85  																																																																																												| (905) distinct_points(all_1_1_1, all_44_1_49) = all_954_3_955
% 69.99/21.85  																																																																																												| (906) apart_point_and_line(all_1_1_1, all_1_5_5) = all_954_1_953
% 69.99/21.85  																																																																																												| (907) distinct_lines(all_1_4_4, all_1_5_5) = all_954_2_954
% 69.99/21.85  																																																																																												|
% 69.99/21.85  																																																																																												+-Applying beta-rule and splitting (837), into two cases.
% 69.99/21.85  																																																																																												|-Branch one:
% 69.99/21.85  																																																																																												| (525) all_44_0_48 = 0
% 69.99/21.85  																																																																																												|
% 69.99/21.85  																																																																																													| Equations (525) can reduce 205 to:
% 69.99/21.85  																																																																																													| (480) $false
% 69.99/21.85  																																																																																													|
% 69.99/21.85  																																																																																													|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																												|-Branch two:
% 69.99/21.85  																																																																																												| (205)  ~ (all_44_0_48 = 0)
% 69.99/21.85  																																																																																												| (911)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.85  																																																																																												|
% 69.99/21.85  																																																																																													| Instantiating (911) with all_959_0_956, all_959_1_957, all_959_2_958, all_959_3_959 yields:
% 69.99/21.85  																																																																																													| (912) apart_point_and_line(all_44_1_49, all_1_4_4) = all_959_1_957 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_959_0_956 & distinct_lines(all_1_4_4, all_1_5_5) = all_959_2_958 & distinct_points(all_44_1_49, all_1_1_1) = all_959_3_959 & ( ~ (all_959_2_958 = 0) |  ~ (all_959_3_959 = 0) | all_959_0_956 = 0 | all_959_1_957 = 0)
% 69.99/21.85  																																																																																													|
% 69.99/21.85  																																																																																													| Applying alpha-rule on (912) yields:
% 69.99/21.85  																																																																																													| (913) distinct_lines(all_1_4_4, all_1_5_5) = all_959_2_958
% 69.99/21.85  																																																																																													| (914) apart_point_and_line(all_44_1_49, all_1_4_4) = all_959_1_957
% 69.99/21.85  																																																																																													| (915)  ~ (all_959_2_958 = 0) |  ~ (all_959_3_959 = 0) | all_959_0_956 = 0 | all_959_1_957 = 0
% 69.99/21.85  																																																																																													| (916) apart_point_and_line(all_1_1_1, all_1_5_5) = all_959_0_956
% 69.99/21.85  																																																																																													| (917) distinct_points(all_44_1_49, all_1_1_1) = all_959_3_959
% 69.99/21.85  																																																																																													|
% 69.99/21.85  																																																																																													+-Applying beta-rule and splitting (853), into two cases.
% 69.99/21.85  																																																																																													|-Branch one:
% 69.99/21.85  																																																																																													| (525) all_44_0_48 = 0
% 69.99/21.85  																																																																																													|
% 69.99/21.85  																																																																																														| Equations (525) can reduce 205 to:
% 69.99/21.85  																																																																																														| (480) $false
% 69.99/21.85  																																																																																														|
% 69.99/21.85  																																																																																														|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																													|-Branch two:
% 69.99/21.85  																																																																																													| (205)  ~ (all_44_0_48 = 0)
% 69.99/21.85  																																																																																													| (921)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_44_1_49, all_1_4_4) = v2 & apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_44_1_49, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.85  																																																																																													|
% 69.99/21.85  																																																																																														| Instantiating (921) with all_964_0_960, all_964_1_961, all_964_2_962, all_964_3_963 yields:
% 69.99/21.85  																																																																																														| (922) apart_point_and_line(all_44_1_49, all_1_4_4) = all_964_1_961 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_964_0_960 & distinct_lines(all_1_5_5, all_1_4_4) = all_964_2_962 & distinct_points(all_44_1_49, all_1_1_1) = all_964_3_963 & ( ~ (all_964_2_962 = 0) |  ~ (all_964_3_963 = 0) | all_964_0_960 = 0 | all_964_1_961 = 0)
% 69.99/21.85  																																																																																														|
% 69.99/21.85  																																																																																														| Applying alpha-rule on (922) yields:
% 69.99/21.85  																																																																																														| (923) apart_point_and_line(all_1_1_1, all_1_5_5) = all_964_0_960
% 69.99/21.85  																																																																																														| (924) apart_point_and_line(all_44_1_49, all_1_4_4) = all_964_1_961
% 69.99/21.85  																																																																																														| (925)  ~ (all_964_2_962 = 0) |  ~ (all_964_3_963 = 0) | all_964_0_960 = 0 | all_964_1_961 = 0
% 69.99/21.85  																																																																																														| (926) distinct_lines(all_1_5_5, all_1_4_4) = all_964_2_962
% 69.99/21.85  																																																																																														| (927) distinct_points(all_44_1_49, all_1_1_1) = all_964_3_963
% 69.99/21.85  																																																																																														|
% 69.99/21.85  																																																																																														+-Applying beta-rule and splitting (473), into two cases.
% 69.99/21.85  																																																																																														|-Branch one:
% 69.99/21.85  																																																																																														| (928)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 69.99/21.85  																																																																																														|
% 69.99/21.85  																																																																																															| Using (478) and (928) yields:
% 69.99/21.85  																																																																																															| (395) $false
% 69.99/21.85  																																																																																															|
% 69.99/21.85  																																																																																															|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																														|-Branch two:
% 69.99/21.85  																																																																																														| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.99/21.85  																																																																																														| (931)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_4_4) = v1)
% 69.99/21.85  																																																																																														|
% 69.99/21.85  																																																																																															| Instantiating (931) with all_997_0_970, all_997_1_971 yields:
% 69.99/21.85  																																																																																															| (932)  ~ (all_997_0_970 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_997_1_971 & apart_point_and_line(all_997_1_971, all_1_4_4) = all_997_0_970
% 69.99/21.85  																																																																																															|
% 69.99/21.85  																																																																																															| Applying alpha-rule on (932) yields:
% 69.99/21.85  																																																																																															| (933)  ~ (all_997_0_970 = 0)
% 69.99/21.85  																																																																																															| (934) intersection_point(all_1_4_4, all_1_5_5) = all_997_1_971
% 69.99/21.85  																																																																																															| (935) apart_point_and_line(all_997_1_971, all_1_4_4) = all_997_0_970
% 69.99/21.85  																																																																																															|
% 69.99/21.85  																																																																																															+-Applying beta-rule and splitting (474), into two cases.
% 69.99/21.85  																																																																																															|-Branch one:
% 69.99/21.85  																																																																																															| (928)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 69.99/21.85  																																																																																															|
% 69.99/21.85  																																																																																																| Using (478) and (928) yields:
% 69.99/21.85  																																																																																																| (395) $false
% 69.99/21.85  																																																																																																|
% 69.99/21.85  																																																																																																|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																															|-Branch two:
% 69.99/21.85  																																																																																															| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.99/21.85  																																																																																															| (939)  ? [v0] : ( ~ (v0 = 0) & parallel_lines(all_1_4_4, all_1_5_5) = v0)
% 69.99/21.85  																																																																																															|
% 69.99/21.85  																																																																																																+-Applying beta-rule and splitting (470), into two cases.
% 69.99/21.85  																																																																																																|-Branch one:
% 69.99/21.85  																																																																																																| (928)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 69.99/21.85  																																																																																																|
% 69.99/21.85  																																																																																																	| Using (478) and (928) yields:
% 69.99/21.85  																																																																																																	| (395) $false
% 69.99/21.85  																																																																																																	|
% 69.99/21.85  																																																																																																	|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																																|-Branch two:
% 69.99/21.85  																																																																																																| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.99/21.85  																																																																																																| (943) all_34_1_32 = 0 | distinct_lines(all_1_5_5, all_1_4_4) = 0
% 69.99/21.85  																																																																																																|
% 69.99/21.85  																																																																																																	+-Applying beta-rule and splitting (472), into two cases.
% 69.99/21.85  																																																																																																	|-Branch one:
% 69.99/21.85  																																																																																																	| (928)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 69.99/21.85  																																																																																																	|
% 69.99/21.85  																																																																																																		| Using (478) and (928) yields:
% 69.99/21.85  																																																																																																		| (395) $false
% 69.99/21.85  																																																																																																		|
% 69.99/21.85  																																																																																																		|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																																	|-Branch two:
% 69.99/21.85  																																																																																																	| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.99/21.85  																																																																																																	| (947)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_1_4_4, all_1_5_5) = v0 & apart_point_and_line(v0, all_1_5_5) = v1)
% 69.99/21.85  																																																																																																	|
% 69.99/21.85  																																																																																																		| Instantiating (947) with all_1011_0_973, all_1011_1_974 yields:
% 69.99/21.85  																																																																																																		| (948)  ~ (all_1011_0_973 = 0) & intersection_point(all_1_4_4, all_1_5_5) = all_1011_1_974 & apart_point_and_line(all_1011_1_974, all_1_5_5) = all_1011_0_973
% 69.99/21.85  																																																																																																		|
% 69.99/21.85  																																																																																																		| Applying alpha-rule on (948) yields:
% 69.99/21.85  																																																																																																		| (949)  ~ (all_1011_0_973 = 0)
% 69.99/21.85  																																																																																																		| (950) intersection_point(all_1_4_4, all_1_5_5) = all_1011_1_974
% 69.99/21.85  																																																																																																		| (951) apart_point_and_line(all_1011_1_974, all_1_5_5) = all_1011_0_973
% 69.99/21.85  																																																																																																		|
% 69.99/21.85  																																																																																																		+-Applying beta-rule and splitting (943), into two cases.
% 69.99/21.85  																																																																																																		|-Branch one:
% 69.99/21.85  																																																																																																		| (952) distinct_lines(all_1_5_5, all_1_4_4) = 0
% 69.99/21.85  																																																																																																		|
% 69.99/21.85  																																																																																																			+-Applying beta-rule and splitting (471), into two cases.
% 69.99/21.85  																																																																																																			|-Branch one:
% 69.99/21.85  																																																																																																			| (928)  ~ (convergent_lines(all_1_4_4, all_1_5_5) = 0)
% 69.99/21.85  																																																																																																			|
% 69.99/21.85  																																																																																																				| Using (478) and (928) yields:
% 69.99/21.85  																																																																																																				| (395) $false
% 69.99/21.85  																																																																																																				|
% 69.99/21.85  																																																																																																				|-The branch is then unsatisfiable
% 69.99/21.85  																																																																																																			|-Branch two:
% 69.99/21.85  																																																																																																			| (478) convergent_lines(all_1_4_4, all_1_5_5) = 0
% 69.99/21.85  																																																																																																			| (956)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (point(v2) = v3 & line(all_1_4_4) = v0 & line(all_1_5_5) = v1 & intersection_point(all_1_4_4, all_1_5_5) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0))
% 69.99/21.85  																																																																																																			|
% 69.99/21.85  																																																																																																				| Instantiating (956) with all_1026_0_976, all_1026_1_977, all_1026_2_978, all_1026_3_979 yields:
% 69.99/21.85  																																																																																																				| (957) point(all_1026_1_977) = all_1026_0_976 & line(all_1_4_4) = all_1026_3_979 & line(all_1_5_5) = all_1026_2_978 & intersection_point(all_1_4_4, all_1_5_5) = all_1026_1_977 & ( ~ (all_1026_2_978 = 0) |  ~ (all_1026_3_979 = 0) | all_1026_0_976 = 0)
% 69.99/21.85  																																																																																																				|
% 69.99/21.85  																																																																																																				| Applying alpha-rule on (957) yields:
% 69.99/21.85  																																																																																																				| (958) line(all_1_5_5) = all_1026_2_978
% 69.99/21.85  																																																																																																				| (959) intersection_point(all_1_4_4, all_1_5_5) = all_1026_1_977
% 69.99/21.85  																																																																																																				| (960) line(all_1_4_4) = all_1026_3_979
% 69.99/21.85  																																																																																																				| (961) point(all_1026_1_977) = all_1026_0_976
% 69.99/21.85  																																																																																																				| (962)  ~ (all_1026_2_978 = 0) |  ~ (all_1026_3_979 = 0) | all_1026_0_976 = 0
% 69.99/21.85  																																																																																																				|
% 69.99/21.85  																																																																																																				| Instantiating formula (114) with all_1_4_4, all_1_5_5, all_1026_1_977, all_1_1_1 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1026_1_977, intersection_point(all_1_4_4, all_1_5_5) = all_1_1_1, yields:
% 69.99/21.86  																																																																																																				| (963) all_1026_1_977 = all_1_1_1
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (114) with all_1_4_4, all_1_5_5, all_1011_1_974, all_1026_1_977 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1026_1_977, intersection_point(all_1_4_4, all_1_5_5) = all_1011_1_974, yields:
% 69.99/21.86  																																																																																																				| (964) all_1026_1_977 = all_1011_1_974
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (114) with all_1_4_4, all_1_5_5, all_997_1_971, all_1026_1_977 and discharging atoms intersection_point(all_1_4_4, all_1_5_5) = all_1026_1_977, intersection_point(all_1_4_4, all_1_5_5) = all_997_1_971, yields:
% 69.99/21.86  																																																																																																				| (965) all_1026_1_977 = all_997_1_971
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_944_0_944, all_949_0_948 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_949_0_948, apart_point_and_line(all_1_1_1, all_1_4_4) = all_944_0_944, yields:
% 69.99/21.86  																																																																																																				| (966) all_949_0_948 = all_944_0_944
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_883_0_940, all_52_0_57 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_0_940, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.99/21.86  																																																																																																				| (967) all_883_0_940 = all_52_0_57
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_883_0_940, all_997_0_970 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_0_940, yields:
% 69.99/21.86  																																																																																																				| (968) all_997_0_970 = all_883_0_940 |  ~ (apart_point_and_line(all_1_1_1, all_1_4_4) = all_997_0_970)
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_883_0_940, all_944_0_944 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_944_0_944, apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_0_940, yields:
% 69.99/21.86  																																																																																																				| (969) all_944_0_944 = all_883_0_940
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_883_1_941, all_949_0_948 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_949_0_948, apart_point_and_line(all_1_1_1, all_1_4_4) = all_883_1_941, yields:
% 69.99/21.86  																																																																																																				| (970) all_949_0_948 = all_883_1_941
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_5_5, all_964_0_960, all_1011_0_973 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_964_0_960, yields:
% 69.99/21.86  																																																																																																				| (971) all_1011_0_973 = all_964_0_960 |  ~ (apart_point_and_line(all_1_1_1, all_1_5_5) = all_1011_0_973)
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_5_5, all_959_0_956, all_964_0_960 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_964_0_960, apart_point_and_line(all_1_1_1, all_1_5_5) = all_959_0_956, yields:
% 69.99/21.86  																																																																																																				| (972) all_964_0_960 = all_959_0_956
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_5_5, all_954_1_953, all_60_0_71 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_954_1_953, apart_point_and_line(all_1_1_1, all_1_5_5) = all_60_0_71, yields:
% 69.99/21.86  																																																																																																				| (973) all_954_1_953 = all_60_0_71
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_5_5, all_954_1_953, all_959_0_956 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_959_0_956, apart_point_and_line(all_1_1_1, all_1_5_5) = all_954_1_953, yields:
% 69.99/21.86  																																																																																																				| (974) all_959_0_956 = all_954_1_953
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_1_1, all_1_5_5, all_827_0_930, all_964_0_960 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_964_0_960, apart_point_and_line(all_1_1_1, all_1_5_5) = all_827_0_930, yields:
% 69.99/21.86  																																																																																																				| (975) all_964_0_960 = all_827_0_930
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_801_0_919, all_806_1_924 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_806_1_924, apart_point_and_line(all_1_2_2, all_1_5_5) = all_801_0_919, yields:
% 69.99/21.86  																																																																																																				| (976) all_806_1_924 = all_801_0_919
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_772_1_900, all_801_0_919 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_801_0_919, apart_point_and_line(all_1_2_2, all_1_5_5) = all_772_1_900, yields:
% 69.99/21.86  																																																																																																				| (977) all_801_0_919 = all_772_1_900
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_767_0_895, all_772_1_900 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_772_1_900, apart_point_and_line(all_1_2_2, all_1_5_5) = all_767_0_895, yields:
% 69.99/21.86  																																																																																																				| (978) all_772_1_900 = all_767_0_895
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_762_0_891, all_767_0_895 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_767_0_895, apart_point_and_line(all_1_2_2, all_1_5_5) = all_762_0_891, yields:
% 69.99/21.86  																																																																																																				| (979) all_767_0_895 = all_762_0_891
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_757_1_888, all_762_0_891 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_762_0_891, apart_point_and_line(all_1_2_2, all_1_5_5) = all_757_1_888, yields:
% 69.99/21.86  																																																																																																				| (980) all_762_0_891 = all_757_1_888
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_748_1_884, all_757_1_888 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_757_1_888, apart_point_and_line(all_1_2_2, all_1_5_5) = all_748_1_884, yields:
% 69.99/21.86  																																																																																																				| (981) all_757_1_888 = all_748_1_884
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_659_0_851, all_748_1_884 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_748_1_884, apart_point_and_line(all_1_2_2, all_1_5_5) = all_659_0_851, yields:
% 69.99/21.86  																																																																																																				| (982) all_748_1_884 = all_659_0_851
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_597_0_843, all_18_0_7 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_0_843, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.99/21.86  																																																																																																				| (983) all_597_0_843 = all_18_0_7
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_597_0_843, all_659_0_851 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_659_0_851, apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_0_843, yields:
% 69.99/21.86  																																																																																																				| (984) all_659_0_851 = all_597_0_843
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_597_1_844, all_806_1_924 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_806_1_924, apart_point_and_line(all_1_2_2, all_1_5_5) = all_597_1_844, yields:
% 69.99/21.86  																																																																																																				| (985) all_806_1_924 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (45) with all_1_5_5, all_1_4_4, all_944_2_946, all_964_2_962 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_964_2_962, distinct_lines(all_1_5_5, all_1_4_4) = all_944_2_946, yields:
% 69.99/21.86  																																																																																																				| (986) all_964_2_962 = all_944_2_946
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (45) with all_1_5_5, all_1_4_4, all_806_2_925, all_964_2_962 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_964_2_962, distinct_lines(all_1_5_5, all_1_4_4) = all_806_2_925, yields:
% 69.99/21.86  																																																																																																				| (987) all_964_2_962 = all_806_2_925
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (45) with all_1_5_5, all_1_4_4, all_801_2_921, all_944_2_946 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_944_2_946, distinct_lines(all_1_5_5, all_1_4_4) = all_801_2_921, yields:
% 69.99/21.86  																																																																																																				| (988) all_944_2_946 = all_801_2_921
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Instantiating formula (45) with all_1_5_5, all_1_4_4, 0, all_944_2_946 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_944_2_946, distinct_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.99/21.86  																																																																																																				| (989) all_944_2_946 = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (965,964) yields a new equation:
% 69.99/21.86  																																																																																																				| (990) all_1011_1_974 = all_997_1_971
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (963,964) yields a new equation:
% 69.99/21.86  																																																																																																				| (991) all_1011_1_974 = all_1_1_1
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (991,990) yields a new equation:
% 69.99/21.86  																																																																																																				| (992) all_997_1_971 = all_1_1_1
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (972,975) yields a new equation:
% 69.99/21.86  																																																																																																				| (993) all_959_0_956 = all_827_0_930
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 993 yields:
% 69.99/21.86  																																																																																																				| (994) all_959_0_956 = all_827_0_930
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (986,987) yields a new equation:
% 69.99/21.86  																																																																																																				| (995) all_944_2_946 = all_806_2_925
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 995 yields:
% 69.99/21.86  																																																																																																				| (996) all_944_2_946 = all_806_2_925
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (974,994) yields a new equation:
% 69.99/21.86  																																																																																																				| (997) all_954_1_953 = all_827_0_930
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 997 yields:
% 69.99/21.86  																																																																																																				| (998) all_954_1_953 = all_827_0_930
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (973,998) yields a new equation:
% 69.99/21.86  																																																																																																				| (999) all_827_0_930 = all_60_0_71
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (966,970) yields a new equation:
% 69.99/21.86  																																																																																																				| (1000) all_944_0_944 = all_883_1_941
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1000 yields:
% 69.99/21.86  																																																																																																				| (1001) all_944_0_944 = all_883_1_941
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (969,1001) yields a new equation:
% 69.99/21.86  																																																																																																				| (1002) all_883_0_940 = all_883_1_941
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1002 yields:
% 69.99/21.86  																																																																																																				| (1003) all_883_0_940 = all_883_1_941
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (989,996) yields a new equation:
% 69.99/21.86  																																																																																																				| (1004) all_806_2_925 = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (988,996) yields a new equation:
% 69.99/21.86  																																																																																																				| (1005) all_806_2_925 = all_801_2_921
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (967,1003) yields a new equation:
% 69.99/21.86  																																																																																																				| (1006) all_883_1_941 = all_52_0_57
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (976,985) yields a new equation:
% 69.99/21.86  																																																																																																				| (1007) all_801_0_919 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1007 yields:
% 69.99/21.86  																																																																																																				| (1008) all_801_0_919 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (1005,1004) yields a new equation:
% 69.99/21.86  																																																																																																				| (1009) all_801_2_921 = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1009 yields:
% 69.99/21.86  																																																																																																				| (1010) all_801_2_921 = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (977,1008) yields a new equation:
% 69.99/21.86  																																																																																																				| (1011) all_772_1_900 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1011 yields:
% 69.99/21.86  																																																																																																				| (1012) all_772_1_900 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (978,1012) yields a new equation:
% 69.99/21.86  																																																																																																				| (1013) all_767_0_895 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1013 yields:
% 69.99/21.86  																																																																																																				| (1014) all_767_0_895 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (979,1014) yields a new equation:
% 69.99/21.86  																																																																																																				| (1015) all_762_0_891 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1015 yields:
% 69.99/21.86  																																																																																																				| (1016) all_762_0_891 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (980,1016) yields a new equation:
% 69.99/21.86  																																																																																																				| (1017) all_757_1_888 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1017 yields:
% 69.99/21.86  																																																																																																				| (1018) all_757_1_888 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (981,1018) yields a new equation:
% 69.99/21.86  																																																																																																				| (1019) all_748_1_884 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1019 yields:
% 69.99/21.86  																																																																																																				| (1020) all_748_1_884 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (982,1020) yields a new equation:
% 69.99/21.86  																																																																																																				| (1021) all_659_0_851 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1021 yields:
% 69.99/21.86  																																																																																																				| (1022) all_659_0_851 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (984,1022) yields a new equation:
% 69.99/21.86  																																																																																																				| (1023) all_597_0_843 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Simplifying 1023 yields:
% 69.99/21.86  																																																																																																				| (1024) all_597_0_843 = all_597_1_844
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (983,1024) yields a new equation:
% 69.99/21.86  																																																																																																				| (1025) all_597_1_844 = all_18_0_7
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (1006,1003) yields a new equation:
% 69.99/21.86  																																																																																																				| (967) all_883_0_940 = all_52_0_57
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (999,975) yields a new equation:
% 69.99/21.86  																																																																																																				| (1027) all_964_0_960 = all_60_0_71
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| Combining equations (992,990) yields a new equation:
% 69.99/21.86  																																																																																																				| (991) all_1011_1_974 = all_1_1_1
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| From (991) and (951) follows:
% 69.99/21.86  																																																																																																				| (1029) apart_point_and_line(all_1_1_1, all_1_5_5) = all_1011_0_973
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| From (992) and (935) follows:
% 69.99/21.86  																																																																																																				| (1030) apart_point_and_line(all_1_1_1, all_1_4_4) = all_997_0_970
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| From (1025) and (534) follows:
% 69.99/21.86  																																																																																																				| (388) apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				| From (1010) and (769) follows:
% 69.99/21.86  																																																																																																				| (952) distinct_lines(all_1_5_5, all_1_4_4) = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																				+-Applying beta-rule and splitting (449), into two cases.
% 69.99/21.86  																																																																																																				|-Branch one:
% 69.99/21.86  																																																																																																				| (491) all_30_0_25 = 0
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																					| Equations (491) can reduce 403 to:
% 69.99/21.86  																																																																																																					| (480) $false
% 69.99/21.86  																																																																																																					|
% 69.99/21.86  																																																																																																					|-The branch is then unsatisfiable
% 69.99/21.86  																																																																																																				|-Branch two:
% 69.99/21.86  																																																																																																				| (403)  ~ (all_30_0_25 = 0)
% 69.99/21.86  																																																																																																				| (1036) all_24_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_24_1_18, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_3_3) = v3 & distinct_lines(all_1_3_3, all_1_4_4) = v1 & distinct_points(all_24_1_18, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.86  																																																																																																				|
% 69.99/21.86  																																																																																																					+-Applying beta-rule and splitting (436), into two cases.
% 69.99/21.86  																																																																																																					|-Branch one:
% 69.99/21.86  																																																																																																					| (588) all_60_0_71 = 0
% 69.99/21.86  																																																																																																					|
% 69.99/21.86  																																																																																																						| Equations (588) can reduce 516 to:
% 69.99/21.86  																																																																																																						| (480) $false
% 69.99/21.86  																																																																																																						|
% 69.99/21.86  																																																																																																						|-The branch is then unsatisfiable
% 69.99/21.86  																																																																																																					|-Branch two:
% 69.99/21.86  																																																																																																					| (516)  ~ (all_60_0_71 = 0)
% 69.99/21.86  																																																																																																					| (1040) all_52_0_57 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																					|
% 69.99/21.87  																																																																																																						+-Applying beta-rule and splitting (1040), into two cases.
% 69.99/21.87  																																																																																																						|-Branch one:
% 69.99/21.87  																																																																																																						| (784) all_52_0_57 = 0
% 69.99/21.87  																																																																																																						|
% 69.99/21.87  																																																																																																							| Equations (784) can reduce 515 to:
% 69.99/21.87  																																																																																																							| (480) $false
% 69.99/21.87  																																																																																																							|
% 69.99/21.87  																																																																																																							|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																						|-Branch two:
% 69.99/21.87  																																																																																																						| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.87  																																																																																																						| (1044)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v3 & apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & distinct_lines(all_1_4_4, all_1_5_5) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																						|
% 69.99/21.87  																																																																																																							| Instantiating (1044) with all_1078_0_986, all_1078_1_987, all_1078_2_988, all_1078_3_989 yields:
% 69.99/21.87  																																																																																																							| (1045) apart_point_and_line(all_1_1_1, all_1_4_4) = all_1078_0_986 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_1078_1_987 & distinct_lines(all_1_4_4, all_1_5_5) = all_1078_2_988 & distinct_points(all_1_1_1, all_1_1_1) = all_1078_3_989 & ( ~ (all_1078_2_988 = 0) |  ~ (all_1078_3_989 = 0) | all_1078_0_986 = 0 | all_1078_1_987 = 0)
% 69.99/21.87  																																																																																																							|
% 69.99/21.87  																																																																																																							| Applying alpha-rule on (1045) yields:
% 69.99/21.87  																																																																																																							| (1046) distinct_points(all_1_1_1, all_1_1_1) = all_1078_3_989
% 69.99/21.87  																																																																																																							| (1047)  ~ (all_1078_2_988 = 0) |  ~ (all_1078_3_989 = 0) | all_1078_0_986 = 0 | all_1078_1_987 = 0
% 69.99/21.87  																																																																																																							| (1048) apart_point_and_line(all_1_1_1, all_1_4_4) = all_1078_0_986
% 69.99/21.87  																																																																																																							| (1049) apart_point_and_line(all_1_1_1, all_1_5_5) = all_1078_1_987
% 69.99/21.87  																																																																																																							| (1050) distinct_lines(all_1_4_4, all_1_5_5) = all_1078_2_988
% 69.99/21.87  																																																																																																							|
% 69.99/21.87  																																																																																																							+-Applying beta-rule and splitting (971), into two cases.
% 69.99/21.87  																																																																																																							|-Branch one:
% 69.99/21.87  																																																																																																							| (1051)  ~ (apart_point_and_line(all_1_1_1, all_1_5_5) = all_1011_0_973)
% 69.99/21.87  																																																																																																							|
% 69.99/21.87  																																																																																																								| Using (1029) and (1051) yields:
% 69.99/21.87  																																																																																																								| (395) $false
% 69.99/21.87  																																																																																																								|
% 69.99/21.87  																																																																																																								|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																							|-Branch two:
% 69.99/21.87  																																																																																																							| (1029) apart_point_and_line(all_1_1_1, all_1_5_5) = all_1011_0_973
% 69.99/21.87  																																																																																																							| (1054) all_1011_0_973 = all_964_0_960
% 69.99/21.87  																																																																																																							|
% 69.99/21.87  																																																																																																								| Combining equations (1027,1054) yields a new equation:
% 69.99/21.87  																																																																																																								| (1055) all_1011_0_973 = all_60_0_71
% 69.99/21.87  																																																																																																								|
% 69.99/21.87  																																																																																																								| Equations (1055) can reduce 949 to:
% 69.99/21.87  																																																																																																								| (516)  ~ (all_60_0_71 = 0)
% 69.99/21.87  																																																																																																								|
% 69.99/21.87  																																																																																																								+-Applying beta-rule and splitting (450), into two cases.
% 69.99/21.87  																																																																																																								|-Branch one:
% 69.99/21.87  																																																																																																								| (588) all_60_0_71 = 0
% 69.99/21.87  																																																																																																								|
% 69.99/21.87  																																																																																																									| Equations (588) can reduce 516 to:
% 69.99/21.87  																																																																																																									| (480) $false
% 69.99/21.87  																																																																																																									|
% 69.99/21.87  																																																																																																									|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																								|-Branch two:
% 69.99/21.87  																																																																																																								| (516)  ~ (all_60_0_71 = 0)
% 69.99/21.87  																																																																																																								| (1060) all_30_0_25 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																								|
% 69.99/21.87  																																																																																																									+-Applying beta-rule and splitting (1060), into two cases.
% 69.99/21.87  																																																																																																									|-Branch one:
% 69.99/21.87  																																																																																																									| (491) all_30_0_25 = 0
% 69.99/21.87  																																																																																																									|
% 69.99/21.87  																																																																																																										| Equations (491) can reduce 403 to:
% 69.99/21.87  																																																																																																										| (480) $false
% 69.99/21.87  																																																																																																										|
% 69.99/21.87  																																																																																																										|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																									|-Branch two:
% 69.99/21.87  																																																																																																									| (403)  ~ (all_30_0_25 = 0)
% 69.99/21.87  																																																																																																									| (1064)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_4_4) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																									|
% 69.99/21.87  																																																																																																										| Instantiating (1064) with all_1114_0_994, all_1114_1_995, all_1114_2_996, all_1114_3_997 yields:
% 69.99/21.87  																																																																																																										| (1065) apart_point_and_line(all_1_1_1, all_1_4_4) = all_1114_1_995 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_1114_0_994 & distinct_lines(all_1_5_5, all_1_4_4) = all_1114_2_996 & distinct_points(all_1_1_1, all_1_2_2) = all_1114_3_997 & ( ~ (all_1114_2_996 = 0) |  ~ (all_1114_3_997 = 0) | all_1114_0_994 = 0 | all_1114_1_995 = 0)
% 69.99/21.87  																																																																																																										|
% 69.99/21.87  																																																																																																										| Applying alpha-rule on (1065) yields:
% 69.99/21.87  																																																																																																										| (1066)  ~ (all_1114_2_996 = 0) |  ~ (all_1114_3_997 = 0) | all_1114_0_994 = 0 | all_1114_1_995 = 0
% 69.99/21.87  																																																																																																										| (1067) apart_point_and_line(all_1_2_2, all_1_5_5) = all_1114_0_994
% 69.99/21.87  																																																																																																										| (1068) distinct_points(all_1_1_1, all_1_2_2) = all_1114_3_997
% 69.99/21.87  																																																																																																										| (1069) distinct_lines(all_1_5_5, all_1_4_4) = all_1114_2_996
% 69.99/21.87  																																																																																																										| (1070) apart_point_and_line(all_1_1_1, all_1_4_4) = all_1114_1_995
% 69.99/21.87  																																																																																																										|
% 69.99/21.87  																																																																																																										+-Applying beta-rule and splitting (968), into two cases.
% 69.99/21.87  																																																																																																										|-Branch one:
% 69.99/21.87  																																																																																																										| (1071)  ~ (apart_point_and_line(all_1_1_1, all_1_4_4) = all_997_0_970)
% 69.99/21.87  																																																																																																										|
% 69.99/21.87  																																																																																																											| Using (1030) and (1071) yields:
% 69.99/21.87  																																																																																																											| (395) $false
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																										|-Branch two:
% 69.99/21.87  																																																																																																										| (1030) apart_point_and_line(all_1_1_1, all_1_4_4) = all_997_0_970
% 69.99/21.87  																																																																																																										| (1074) all_997_0_970 = all_883_0_940
% 69.99/21.87  																																																																																																										|
% 69.99/21.87  																																																																																																											| Combining equations (967,1074) yields a new equation:
% 69.99/21.87  																																																																																																											| (1075) all_997_0_970 = all_52_0_57
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Equations (1075) can reduce 933 to:
% 69.99/21.87  																																																																																																											| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| From (1075) and (1030) follows:
% 69.99/21.87  																																																																																																											| (222) apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_1114_1_995, all_52_0_57 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_1114_1_995, apart_point_and_line(all_1_1_1, all_1_4_4) = all_52_0_57, yields:
% 69.99/21.87  																																																																																																											| (1078) all_1114_1_995 = all_52_0_57
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Instantiating formula (13) with all_1_1_1, all_1_4_4, all_1078_0_986, all_1114_1_995 and discharging atoms apart_point_and_line(all_1_1_1, all_1_4_4) = all_1114_1_995, apart_point_and_line(all_1_1_1, all_1_4_4) = all_1078_0_986, yields:
% 69.99/21.87  																																																																																																											| (1079) all_1114_1_995 = all_1078_0_986
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Instantiating formula (13) with all_1_2_2, all_1_5_5, all_1114_0_994, all_18_0_7 and discharging atoms apart_point_and_line(all_1_2_2, all_1_5_5) = all_1114_0_994, apart_point_and_line(all_1_2_2, all_1_5_5) = all_18_0_7, yields:
% 69.99/21.87  																																																																																																											| (1080) all_1114_0_994 = all_18_0_7
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Instantiating formula (45) with all_1_5_5, all_1_4_4, all_1114_2_996, 0 and discharging atoms distinct_lines(all_1_5_5, all_1_4_4) = all_1114_2_996, distinct_lines(all_1_5_5, all_1_4_4) = 0, yields:
% 69.99/21.87  																																																																																																											| (1081) all_1114_2_996 = 0
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Instantiating formula (76) with all_1_1_1, all_1_2_2, all_1114_3_997, 0 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = all_1114_3_997, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 69.99/21.87  																																																																																																											| (1082) all_1114_3_997 = 0
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Combining equations (1078,1079) yields a new equation:
% 69.99/21.87  																																																																																																											| (1083) all_1078_0_986 = all_52_0_57
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											| Combining equations (1083,1079) yields a new equation:
% 69.99/21.87  																																																																																																											| (1078) all_1114_1_995 = all_52_0_57
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																											+-Applying beta-rule and splitting (459), into two cases.
% 69.99/21.87  																																																																																																											|-Branch one:
% 69.99/21.87  																																																																																																											| (784) all_52_0_57 = 0
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																												| Equations (784) can reduce 515 to:
% 69.99/21.87  																																																																																																												| (480) $false
% 69.99/21.87  																																																																																																												|
% 69.99/21.87  																																																																																																												|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																											|-Branch two:
% 69.99/21.87  																																																																																																											| (515)  ~ (all_52_0_57 = 0)
% 69.99/21.87  																																																																																																											| (1088) all_18_0_7 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																											|
% 69.99/21.87  																																																																																																												+-Applying beta-rule and splitting (1088), into two cases.
% 69.99/21.87  																																																																																																												|-Branch one:
% 69.99/21.87  																																																																																																												| (499) all_18_0_7 = 0
% 69.99/21.87  																																																																																																												|
% 69.99/21.87  																																																																																																													| Equations (499) can reduce 171 to:
% 69.99/21.87  																																																																																																													| (480) $false
% 69.99/21.87  																																																																																																													|
% 69.99/21.87  																																																																																																													|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																												|-Branch two:
% 69.99/21.87  																																																																																																												| (171)  ~ (all_18_0_7 = 0)
% 69.99/21.87  																																																																																																												| (1092)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_4_4) = v3 & distinct_lines(all_1_5_5, all_1_4_4) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 69.99/21.87  																																																																																																												|
% 69.99/21.87  																																																																																																													+-Applying beta-rule and splitting (1066), into two cases.
% 69.99/21.87  																																																																																																													|-Branch one:
% 69.99/21.87  																																																																																																													| (1093)  ~ (all_1114_2_996 = 0)
% 69.99/21.87  																																																																																																													|
% 69.99/21.87  																																																																																																														| Equations (1081) can reduce 1093 to:
% 69.99/21.87  																																																																																																														| (480) $false
% 69.99/21.87  																																																																																																														|
% 69.99/21.87  																																																																																																														|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																													|-Branch two:
% 69.99/21.87  																																																																																																													| (1081) all_1114_2_996 = 0
% 69.99/21.87  																																																																																																													| (1096)  ~ (all_1114_3_997 = 0) | all_1114_0_994 = 0 | all_1114_1_995 = 0
% 69.99/21.87  																																																																																																													|
% 69.99/21.87  																																																																																																														+-Applying beta-rule and splitting (1096), into two cases.
% 69.99/21.87  																																																																																																														|-Branch one:
% 69.99/21.87  																																																																																																														| (1097)  ~ (all_1114_3_997 = 0)
% 69.99/21.87  																																																																																																														|
% 69.99/21.87  																																																																																																															| Equations (1082) can reduce 1097 to:
% 69.99/21.87  																																																																																																															| (480) $false
% 69.99/21.87  																																																																																																															|
% 69.99/21.87  																																																																																																															|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																														|-Branch two:
% 69.99/21.87  																																																																																																														| (1082) all_1114_3_997 = 0
% 69.99/21.87  																																																																																																														| (1100) all_1114_0_994 = 0 | all_1114_1_995 = 0
% 69.99/21.87  																																																																																																														|
% 69.99/21.87  																																																																																																															+-Applying beta-rule and splitting (1100), into two cases.
% 69.99/21.87  																																																																																																															|-Branch one:
% 69.99/21.87  																																																																																																															| (1101) all_1114_0_994 = 0
% 69.99/21.87  																																																																																																															|
% 69.99/21.87  																																																																																																																| Combining equations (1101,1080) yields a new equation:
% 69.99/21.87  																																																																																																																| (499) all_18_0_7 = 0
% 69.99/21.87  																																																																																																																|
% 69.99/21.87  																																																																																																																| Equations (499) can reduce 171 to:
% 69.99/21.87  																																																																																																																| (480) $false
% 69.99/21.87  																																																																																																																|
% 69.99/21.87  																																																																																																																|-The branch is then unsatisfiable
% 69.99/21.87  																																																																																																															|-Branch two:
% 69.99/21.87  																																																																																																															| (1104)  ~ (all_1114_0_994 = 0)
% 69.99/21.87  																																																																																																															| (1105) all_1114_1_995 = 0
% 69.99/21.87  																																																																																																															|
% 69.99/21.87  																																																																																																																| Combining equations (1105,1078) yields a new equation:
% 70.15/21.87  																																																																																																																| (784) all_52_0_57 = 0
% 70.15/21.87  																																																																																																																|
% 70.15/21.87  																																																																																																																| Equations (784) can reduce 515 to:
% 70.15/21.87  																																																																																																																| (480) $false
% 70.15/21.87  																																																																																																																|
% 70.15/21.87  																																																																																																																|-The branch is then unsatisfiable
% 70.15/21.87  																																																																																																		|-Branch two:
% 70.15/21.87  																																																																																																		| (1108)  ~ (distinct_lines(all_1_5_5, all_1_4_4) = 0)
% 70.15/21.87  																																																																																																		| (479) all_34_1_32 = 0
% 70.15/21.87  																																																																																																		|
% 70.15/21.87  																																																																																																			| Equations (479) can reduce 384 to:
% 70.15/21.87  																																																																																																			| (480) $false
% 70.15/21.87  																																																																																																			|
% 70.15/21.87  																																																																																																			|-The branch is then unsatisfiable
% 70.15/21.88  																											|-Branch two:
% 70.15/21.88  																											| (1111)  ~ (distinct_points(all_1_1_1, all_1_2_2) = 0)
% 70.15/21.88  																											| (511) all_50_0_56 = 0
% 70.15/21.88  																											|
% 70.15/21.88  																												| Equations (511) can reduce 219 to:
% 70.15/21.88  																												| (480) $false
% 70.15/21.88  																												|
% 70.15/21.88  																												|-The branch is then unsatisfiable
% 70.15/21.88  													|-Branch two:
% 70.15/21.88  													| (588) all_60_0_71 = 0
% 70.15/21.88  													| (1115)  ~ (all_60_1_72 = 0)
% 70.15/21.88  													|
% 70.15/21.88  														| Equations (477) can reduce 1115 to:
% 70.15/21.88  														| (480) $false
% 70.15/21.88  														|
% 70.15/21.88  														|-The branch is then unsatisfiable
% 70.15/21.88  												|-Branch two:
% 70.15/21.88  												| (784) all_52_0_57 = 0
% 70.15/21.88  												| (1118)  ~ (all_52_1_58 = 0)
% 70.15/21.88  												|
% 70.15/21.88  													| Equations (476) can reduce 1118 to:
% 70.15/21.88  													| (480) $false
% 70.15/21.88  													|
% 70.15/21.88  													|-The branch is then unsatisfiable
% 70.15/21.88  |-Branch two:
% 70.15/21.88  | (1120)  ~ (apart_point_and_line(all_1_1_1, all_1_3_3) = 0)
% 70.15/21.88  | (1121) all_1_0_0 = 0
% 70.15/21.88  |
% 70.15/21.88  	| Equations (1121) can reduce 130 to:
% 70.15/21.88  	| (480) $false
% 70.15/21.88  	|
% 70.15/21.88  	|-The branch is then unsatisfiable
% 70.15/21.88  % SZS output end Proof for theBenchmark
% 70.15/21.88  
% 70.15/21.88  21278ms
%------------------------------------------------------------------------------