%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO193+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 03:48:29 EDT 2022

% Result   : Theorem 5.69s 1.98s
% Output   : Proof 32.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem  : GEO193+1 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Fri Jun 17 18:52:57 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.53/0.62          ____       _                          
% 0.53/0.62    ___  / __ \_____(_)___  ________  __________
% 0.53/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.62  
% 0.53/0.62  A Theorem Prover for First-Order Logic
% 0.53/0.62  (ePrincess v.1.0)
% 0.53/0.62  
% 0.53/0.62  (c) Philipp Rümmer, 2009-2015
% 0.53/0.62  (c) Peter Backeman, 2014-2015
% 0.53/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.62  Bug reports to peter@backeman.se
% 0.53/0.62  
% 0.53/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.62  
% 0.53/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.95  Prover 0: Preprocessing ...
% 2.04/1.08  Prover 0: Warning: ignoring some quantifiers
% 2.04/1.10  Prover 0: Constructing countermodel ...
% 3.03/1.41  Prover 0: gave up
% 3.03/1.41  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.03/1.43  Prover 1: Preprocessing ...
% 3.56/1.51  Prover 1: Constructing countermodel ...
% 3.74/1.55  Prover 1: gave up
% 3.74/1.55  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.74/1.57  Prover 2: Preprocessing ...
% 4.39/1.68  Prover 2: Warning: ignoring some quantifiers
% 4.39/1.68  Prover 2: Constructing countermodel ...
% 5.69/1.98  Prover 2: proved (424ms)
% 5.69/1.98  
% 5.69/1.98  No countermodel exists, formula is valid
% 5.69/1.98  % SZS status Theorem for theBenchmark
% 5.69/1.98  
% 5.69/1.98  Generating proof ... Warning: ignoring some quantifiers
% 31.37/10.82  found it (size 438)
% 31.37/10.82  
% 31.37/10.82  % SZS output start Proof for theBenchmark
% 31.37/10.82  Assumed formulas after preprocessing and simplification: 
% 31.37/10.82  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v1) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v0) = v5 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (distinct_points(v6, v7) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v9) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (apart_point_and_line(v6, v9) = v10) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v6, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_points(v6, v7) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v8, v7) = v10) |  ~ (distinct_points(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v7, v8) = v10) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = v10) |  ~ (distinct_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_points(v7, v8) = v10) |  ~ (distinct_points(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v8, v7) = v9) |  ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v9) |  ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v7, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v6, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v7, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v6, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (intersection_point(v9, v8) = v7) |  ~ (intersection_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (line_connecting(v9, v8) = v7) |  ~ (line_connecting(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (apart_point_and_line(v9, v8) = v7) |  ~ (apart_point_and_line(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (convergent_lines(v9, v8) = v7) |  ~ (convergent_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_lines(v9, v8) = v7) |  ~ (distinct_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_points(v9, v8) = v7) |  ~ (distinct_points(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) |  ~ (distinct_points(v6, v7) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) &  ! [v6] :  ~ (convergent_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_points(v6, v6) = 0) &  ? [v6] :  ? [v7] :  ? [v8] : intersection_point(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : line_connecting(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : apart_point_and_line(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : convergent_lines(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : distinct_lines(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : distinct_points(v7, v6) = v8)
% 31.82/10.88  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 31.82/10.88  | (1)  ~ (all_0_0_0 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (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) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (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, 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 |  ~ (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] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (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] : ( ~ (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] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 31.82/10.89  |
% 31.82/10.89  | Applying alpha-rule on (1) yields:
% 31.82/10.90  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 31.82/10.90  | (3) apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0
% 31.82/10.90  | (4) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2
% 31.82/10.90  | (5) intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1
% 31.82/10.90  | (6)  ! [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)
% 31.82/10.90  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 31.82/10.90  | (8)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 31.82/10.90  | (9) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 31.82/10.90  | (10)  ! [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))
% 31.82/10.90  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 31.82/10.90  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 31.82/10.90  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.82/10.90  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 31.82/10.90  | (15) apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 31.82/10.90  | (16)  ! [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))
% 31.82/10.90  | (17)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 31.82/10.90  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 31.82/10.90  | (19)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 31.82/10.90  | (20) convergent_lines(all_0_5_5, all_0_3_3) = 0
% 31.82/10.90  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 31.82/10.90  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 31.82/10.90  | (23)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 31.82/10.90  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 31.82/10.90  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 31.82/10.90  | (26) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 31.82/10.90  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 31.82/10.90  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 31.82/10.90  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 31.82/10.91  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 31.82/10.91  | (31)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 31.82/10.91  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 31.82/10.91  | (33)  ! [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))
% 31.82/10.91  | (34)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 31.82/10.91  | (35)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 31.82/10.91  | (36)  ! [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))
% 31.82/10.91  | (37)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 31.82/10.91  | (38)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 31.82/10.91  | (39)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 31.82/10.91  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 31.82/10.91  | (41)  ! [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)
% 31.82/10.91  | (42)  ! [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)
% 31.82/10.91  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 31.82/10.91  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 31.82/10.91  | (45)  ! [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)
% 31.82/10.91  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 31.82/10.91  | (47)  ! [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))
% 31.82/10.91  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 31.82/10.91  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 31.82/10.91  | (50)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 31.82/10.91  | (51)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 31.82/10.91  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 31.82/10.91  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 31.82/10.91  | (54)  ! [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))
% 31.82/10.92  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 31.82/10.92  | (56)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 31.82/10.92  | (57)  ~ (all_0_0_0 = 0)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (52) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 31.82/10.92  | (58)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0))
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (7) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 31.82/10.92  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0))
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (52) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 31.82/10.92  | (60)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (7) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 31.82/10.92  | (61)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (14) with all_0_0_0, all_0_0_0, all_0_5_5, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 31.82/10.92  | (62) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (50) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 31.82/10.92  | (63)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (19) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 31.82/10.92  | (64)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (50) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 31.82/10.92  | (65)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (19) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 31.82/10.92  | (66)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (50) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 31.82/10.92  | (67)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating formula (19) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 31.82/10.92  | (68)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 31.82/10.92  |
% 31.82/10.92  | Instantiating (68) with all_20_0_24, all_20_1_25 yields:
% 31.82/10.92  | (69)  ~ (all_20_0_24 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24
% 31.82/10.92  |
% 32.09/10.92  | Applying alpha-rule on (69) yields:
% 32.09/10.92  | (70)  ~ (all_20_0_24 = 0)
% 32.09/10.92  | (71) intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25
% 32.09/10.92  | (72) apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24
% 32.09/10.92  |
% 32.09/10.92  | Instantiating (65) with all_22_0_26, all_22_1_27 yields:
% 32.09/10.92  | (73)  ~ (all_22_0_26 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27 & apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26
% 32.09/10.92  |
% 32.09/10.92  | Applying alpha-rule on (73) yields:
% 32.09/10.92  | (74)  ~ (all_22_0_26 = 0)
% 32.09/10.92  | (75) intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27
% 32.09/10.92  | (76) apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26
% 32.09/10.92  |
% 32.09/10.92  | Instantiating (64) with all_24_0_28, all_24_1_29 yields:
% 32.09/10.92  | (77)  ~ (all_24_0_28 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29 & apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28
% 32.09/10.92  |
% 32.09/10.92  | Applying alpha-rule on (77) yields:
% 32.09/10.92  | (78)  ~ (all_24_0_28 = 0)
% 32.09/10.92  | (79) intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29
% 32.09/10.92  | (80) apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28
% 32.09/10.92  |
% 32.09/10.92  | Instantiating (63) with all_26_0_30, all_26_1_31 yields:
% 32.09/10.92  | (81)  ~ (all_26_0_30 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31 & apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30
% 32.09/10.93  |
% 32.09/10.93  | Applying alpha-rule on (81) yields:
% 32.09/10.93  | (82)  ~ (all_26_0_30 = 0)
% 32.09/10.93  | (83) intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31
% 32.09/10.93  | (84) apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (67) with all_28_0_32, all_28_1_33 yields:
% 32.09/10.93  | (85)  ~ (all_28_0_32 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33 & apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32
% 32.09/10.93  |
% 32.09/10.93  | Applying alpha-rule on (85) yields:
% 32.09/10.93  | (86)  ~ (all_28_0_32 = 0)
% 32.09/10.93  | (87) intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33
% 32.09/10.93  | (88) apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (61) with all_30_0_34 yields:
% 32.09/10.93  | (89) ( ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34) | ( ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34)
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (60) with all_31_0_35 yields:
% 32.09/10.93  | (90) ( ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35) | ( ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35)
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (66) with all_32_0_36, all_32_1_37 yields:
% 32.09/10.93  | (91)  ~ (all_32_0_36 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37 & apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36
% 32.09/10.93  |
% 32.09/10.93  | Applying alpha-rule on (91) yields:
% 32.09/10.93  | (92)  ~ (all_32_0_36 = 0)
% 32.09/10.93  | (93) intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37
% 32.09/10.93  | (94) apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (59) with all_34_0_38 yields:
% 32.09/10.93  | (95) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38)
% 32.09/10.93  |
% 32.09/10.93  | Instantiating (58) with all_35_0_39 yields:
% 32.09/10.93  | (96) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39)
% 32.09/10.93  |
% 32.09/10.93  +-Applying beta-rule and splitting (96), into two cases.
% 32.09/10.93  |-Branch one:
% 32.09/10.93  | (97)  ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39
% 32.09/10.93  |
% 32.09/10.93  	| Applying alpha-rule on (97) yields:
% 32.09/10.93  	| (98)  ~ (all_35_0_39 = 0)
% 32.09/10.93  	| (99) apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39
% 32.09/10.93  	|
% 32.09/10.93  	+-Applying beta-rule and splitting (62), into two cases.
% 32.09/10.93  	|-Branch one:
% 32.09/10.93  	| (100) all_0_0_0 = 0
% 32.09/10.93  	|
% 32.09/10.93  		| Equations (100) can reduce 57 to:
% 32.09/10.93  		| (101) $false
% 32.09/10.93  		|
% 32.09/10.93  		|-The branch is then unsatisfiable
% 32.09/10.93  	|-Branch two:
% 32.09/10.93  	| (57)  ~ (all_0_0_0 = 0)
% 32.09/10.93  	| (103)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.93  	|
% 32.09/10.93  		+-Applying beta-rule and splitting (89), into two cases.
% 32.09/10.93  		|-Branch one:
% 32.09/10.93  		| (104)  ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 32.09/10.93  		|
% 32.09/10.93  			| Applying alpha-rule on (104) yields:
% 32.09/10.93  			| (105)  ~ (all_30_0_34 = 0)
% 32.09/10.93  			| (106) apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 32.09/10.93  			|
% 32.09/10.93  			+-Applying beta-rule and splitting (95), into two cases.
% 32.09/10.93  			|-Branch one:
% 32.09/10.93  			| (107)  ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38
% 32.09/10.93  			|
% 32.09/10.93  				| Applying alpha-rule on (107) yields:
% 32.09/10.93  				| (108)  ~ (all_34_0_38 = 0)
% 32.09/10.93  				| (109) apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38
% 32.09/10.93  				|
% 32.09/10.93  				+-Applying beta-rule and splitting (90), into two cases.
% 32.09/10.93  				|-Branch one:
% 32.09/10.93  				| (110)  ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 32.09/10.93  				|
% 32.09/10.93  					| Applying alpha-rule on (110) yields:
% 32.09/10.93  					| (111)  ~ (all_31_0_35 = 0)
% 32.09/10.93  					| (112) apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 32.09/10.93  					|
% 32.09/10.93  					| Instantiating formula (22) with all_0_3_3, all_0_4_4, all_26_1_31, all_0_1_1 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31, intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields:
% 32.09/10.93  					| (113) all_26_1_31 = all_0_1_1
% 32.09/10.93  					|
% 32.09/10.93  					| Instantiating formula (22) with all_0_3_3, all_0_4_4, all_24_1_29, all_26_1_31 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31, intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29, yields:
% 32.09/10.93  					| (114) all_26_1_31 = all_24_1_29
% 32.09/10.93  					|
% 32.09/10.93  					| Instantiating formula (22) with all_0_5_5, all_0_3_3, all_22_1_27, all_32_1_37 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37, intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27, yields:
% 32.09/10.93  					| (115) all_32_1_37 = all_22_1_27
% 32.09/10.93  					|
% 32.09/10.93  					| Instantiating formula (22) with all_0_5_5, all_0_4_4, all_28_1_33, all_0_2_2 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 32.09/10.93  					| (116) all_28_1_33 = all_0_2_2
% 32.09/10.93  					|
% 32.09/10.93  					| Instantiating formula (22) with all_0_5_5, all_0_4_4, all_20_1_25, all_28_1_33 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 32.09/10.93  					| (117) all_28_1_33 = all_20_1_25
% 32.09/10.93  					|
% 32.09/10.94  					| Combining equations (116,117) yields a new equation:
% 32.09/10.94  					| (118) all_20_1_25 = all_0_2_2
% 32.09/10.94  					|
% 32.09/10.94  					| Combining equations (114,113) yields a new equation:
% 32.09/10.94  					| (119) all_24_1_29 = all_0_1_1
% 32.09/10.94  					|
% 32.09/10.94  					| Simplifying 119 yields:
% 32.09/10.94  					| (120) all_24_1_29 = all_0_1_1
% 32.09/10.94  					|
% 32.09/10.94  					| Combining equations (118,117) yields a new equation:
% 32.09/10.94  					| (116) all_28_1_33 = all_0_2_2
% 32.09/10.94  					|
% 32.09/10.94  					| From (115) and (94) follows:
% 32.09/10.94  					| (122) apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36
% 32.09/10.94  					|
% 32.09/10.94  					| From (116) and (88) follows:
% 32.09/10.94  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 32.09/10.94  					|
% 32.09/10.94  					| From (113) and (84) follows:
% 32.09/10.94  					| (124) apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30
% 32.09/10.94  					|
% 32.09/10.94  					| From (120) and (80) follows:
% 32.09/10.94  					| (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28
% 32.09/10.94  					|
% 32.09/10.94  					| From (118) and (72) follows:
% 32.09/10.94  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (21) with all_0_1_1, all_0_3_3, all_24_0_28, all_34_0_38 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_34_0_38, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, yields:
% 32.09/10.94  					| (127) all_34_0_38 = all_24_0_28
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (21) with all_0_1_1, all_0_4_4, all_26_0_30, all_35_0_39 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_35_0_39, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.94  					| (128) all_35_0_39 = all_26_0_30
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (21) with all_0_2_2, all_0_4_4, all_28_0_32, all_31_0_35 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.94  					| (129) all_31_0_35 = all_28_0_32
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (21) with all_0_2_2, all_0_5_5, all_20_0_24, all_30_0_34 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.09/10.94  					| (130) all_30_0_34 = all_20_0_24
% 32.09/10.94  					|
% 32.09/10.94  					| Equations (128) can reduce 98 to:
% 32.09/10.94  					| (82)  ~ (all_26_0_30 = 0)
% 32.09/10.94  					|
% 32.09/10.94  					| Equations (127) can reduce 108 to:
% 32.09/10.94  					| (78)  ~ (all_24_0_28 = 0)
% 32.09/10.94  					|
% 32.09/10.94  					| Equations (129) can reduce 111 to:
% 32.09/10.94  					| (86)  ~ (all_28_0_32 = 0)
% 32.09/10.94  					|
% 32.09/10.94  					| Equations (130) can reduce 105 to:
% 32.09/10.94  					| (70)  ~ (all_20_0_24 = 0)
% 32.09/10.94  					|
% 32.09/10.94  					| From (127) and (109) follows:
% 32.09/10.94  					| (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28
% 32.09/10.94  					|
% 32.09/10.94  					| From (128) and (99) follows:
% 32.09/10.94  					| (124) apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30
% 32.09/10.94  					|
% 32.09/10.94  					| From (129) and (112) follows:
% 32.09/10.94  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 32.09/10.94  					|
% 32.09/10.94  					| From (130) and (106) follows:
% 32.09/10.94  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (14) with all_22_0_26, all_0_0_0, all_0_3_3, all_0_5_5, all_22_1_27, all_0_1_1 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.94  					| (139) all_22_0_26 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (14) with all_0_0_0, all_22_0_26, all_0_5_5, all_0_3_3, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.94  					| (140) all_22_0_26 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (44) with all_22_0_26, all_0_0_0, all_0_5_5, all_0_3_3, all_22_1_27, all_0_1_1 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.94  					| (141) all_22_0_26 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (44) with all_0_0_0, all_22_0_26, all_0_3_3, all_0_5_5, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.94  					| (142) all_22_0_26 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.94  					|
% 32.09/10.94  					| Instantiating formula (14) with all_22_0_26, all_22_0_26, all_0_3_3, all_0_3_3, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, yields:
% 32.09/10.94  					| (143) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_32_0_36, all_0_0_0, all_0_5_5, all_0_5_5, all_22_1_27, all_0_1_1 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (144) all_32_0_36 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_0_0_0, all_32_0_36, all_0_5_5, all_0_5_5, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (145) all_32_0_36 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_32_0_36, all_22_0_26, all_0_5_5, all_0_3_3, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields:
% 32.09/10.95  					| (146) all_32_0_36 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_22_0_26, all_32_0_36, all_0_3_3, all_0_5_5, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields:
% 32.09/10.95  					| (147) all_32_0_36 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_32_0_36, all_32_0_36, all_0_5_5, all_0_5_5, all_22_1_27, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, yields:
% 32.09/10.95  					| (148) all_32_0_36 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_24_0_28, all_0_0_0, all_0_3_3, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (149) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_0_0_0, all_24_0_28, all_0_5_5, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (150) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (42) with all_24_0_28, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 32.09/10.95  					| (151) all_24_0_28 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_24_0_28, all_22_0_26, all_0_3_3, all_0_3_3, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, yields:
% 32.09/10.95  					| (152) all_24_0_28 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_24_0_28, all_24_0_28, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, yields:
% 32.09/10.95  					| (153) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_26_0_30, all_0_0_0, all_0_4_4, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (154) all_26_0_30 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.95  					|
% 32.09/10.95  					| Instantiating formula (14) with all_0_0_0, all_26_0_30, all_0_5_5, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields:
% 32.09/10.95  					| (155) all_26_0_30 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_26_0_30, all_22_0_26, all_0_4_4, all_0_3_3, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (156) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_22_0_26, all_26_0_30, all_0_3_3, all_0_4_4, all_22_1_27, all_0_1_1 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (157) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (44) with all_26_0_30, all_22_0_26, all_0_3_3, all_0_4_4, all_0_1_1, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (158) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (44) with all_22_0_26, all_26_0_30, all_0_4_4, all_0_3_3, all_22_1_27, all_0_1_1 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (159) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_26_0_30, all_24_0_28, all_0_4_4, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (160) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_24_0_28, all_26_0_30, all_0_3_3, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (161) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_26_0_30, all_26_0_30, all_0_4_4, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, yields:
% 32.09/10.96  					| (162) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_28_0_32, all_0_0_0, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.96  					| (163) all_28_0_32 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (14) with all_0_0_0, all_28_0_32, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.96  					| (164) all_28_0_32 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (44) with all_28_0_32, all_0_0_0, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.96  					| (165) all_28_0_32 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.09/10.96  					|
% 32.09/10.96  					| Instantiating formula (44) with all_0_0_0, all_28_0_32, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.96  					| (166) all_28_0_32 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.09/10.97  					|
% 32.09/10.97  					| Instantiating formula (14) with all_28_0_32, all_22_0_26, all_0_4_4, all_0_3_3, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.97  					| (167) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.09/10.97  					|
% 32.09/10.97  					| Instantiating formula (14) with all_22_0_26, all_28_0_32, all_0_3_3, all_0_4_4, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.97  					| (168) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.09/10.97  					|
% 32.09/10.97  					| Instantiating formula (44) with all_28_0_32, all_22_0_26, all_0_3_3, all_0_4_4, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.97  					| (169) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.09/10.97  					|
% 32.09/10.97  					| Instantiating formula (44) with all_22_0_26, all_28_0_32, all_0_4_4, all_0_3_3, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.09/10.97  					| (170) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.09/10.97  					|
% 32.09/10.97  					| Instantiating formula (14) with all_28_0_32, all_32_0_36, all_0_4_4, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.97  					| (171) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/10.97  					|
% 32.33/10.97  					| Instantiating formula (14) with all_32_0_36, all_28_0_32, all_0_5_5, all_0_4_4, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.97  					| (172) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/10.97  					|
% 32.33/10.97  					| Instantiating formula (44) with all_28_0_32, all_32_0_36, all_0_5_5, all_0_4_4, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.97  					| (173) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/10.97  					|
% 32.33/10.97  					| Instantiating formula (44) with all_32_0_36, all_28_0_32, all_0_4_4, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.97  					| (174) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/10.97  					|
% 32.33/10.97  					| Instantiating formula (14) with all_28_0_32, all_24_0_28, all_0_4_4, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.97  					| (175) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_24_0_28, all_28_0_32, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.98  					| (176) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (44) with all_28_0_32, all_24_0_28, all_0_3_3, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.98  					| (177) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_28_0_32, all_26_0_30, all_0_4_4, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.98  					| (178) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_26_0_30, all_28_0_32, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.98  					| (179) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_28_0_32, all_28_0_32, all_0_4_4, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 32.33/10.98  					| (180) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_20_0_24, all_0_0_0, all_0_5_5, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (181) all_20_0_24 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (44) with all_20_0_24, all_22_0_26, all_0_3_3, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (182) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (44) with all_22_0_26, all_20_0_24, all_0_5_5, all_0_3_3, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (183) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_20_0_24, all_32_0_36, all_0_5_5, all_0_5_5, all_0_2_2, all_22_1_27 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (184) all_32_0_36 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_32_0_36, all_20_0_24, all_0_5_5, all_0_5_5, all_22_1_27, all_0_2_2 and discharging atoms apart_point_and_line(all_22_1_27, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (185) all_32_0_36 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_20_0_24, all_24_0_28, all_0_5_5, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (186) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_24_0_28, all_20_0_24, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (187) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (44) with all_20_0_24, all_24_0_28, all_0_3_3, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (188) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.98  					|
% 32.33/10.98  					| Instantiating formula (14) with all_20_0_24, all_26_0_30, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.98  					| (189) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (14) with all_26_0_30, all_20_0_24, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (190) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (44) with all_20_0_24, all_26_0_30, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (191) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (44) with all_26_0_30, all_20_0_24, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (192) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (14) with all_20_0_24, all_28_0_32, all_0_5_5, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (193) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (14) with all_28_0_32, all_20_0_24, all_0_4_4, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (194) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					| Instantiating formula (14) with all_20_0_24, all_20_0_24, all_0_5_5, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 32.33/10.99  					| (195) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/10.99  					|
% 32.33/10.99  					+-Applying beta-rule and splitting (148), into two cases.
% 32.33/10.99  					|-Branch one:
% 32.33/10.99  					| (196) all_32_0_36 = 0
% 32.33/10.99  					|
% 32.33/10.99  						| Equations (196) can reduce 92 to:
% 32.33/10.99  						| (101) $false
% 32.33/10.99  						|
% 32.33/10.99  						|-The branch is then unsatisfiable
% 32.33/10.99  					|-Branch two:
% 32.33/10.99  					| (92)  ~ (all_32_0_36 = 0)
% 32.33/10.99  					| (199)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/10.99  					|
% 32.33/10.99  						+-Applying beta-rule and splitting (180), into two cases.
% 32.33/10.99  						|-Branch one:
% 32.33/10.99  						| (200) all_28_0_32 = 0
% 32.33/10.99  						|
% 32.33/10.99  							| Equations (200) can reduce 86 to:
% 32.33/10.99  							| (101) $false
% 32.33/10.99  							|
% 32.33/10.99  							|-The branch is then unsatisfiable
% 32.33/10.99  						|-Branch two:
% 32.33/10.99  						| (86)  ~ (all_28_0_32 = 0)
% 32.33/10.99  						| (203)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/10.99  						|
% 32.33/10.99  							+-Applying beta-rule and splitting (145), into two cases.
% 32.33/10.99  							|-Branch one:
% 32.33/10.99  							| (196) all_32_0_36 = 0
% 32.33/10.99  							|
% 32.33/10.99  								| Equations (196) can reduce 92 to:
% 32.33/10.99  								| (101) $false
% 32.33/10.99  								|
% 32.33/10.99  								|-The branch is then unsatisfiable
% 32.33/10.99  							|-Branch two:
% 32.33/10.99  							| (92)  ~ (all_32_0_36 = 0)
% 32.33/10.99  							| (207) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/10.99  							|
% 32.33/10.99  								+-Applying beta-rule and splitting (140), into two cases.
% 32.33/10.99  								|-Branch one:
% 32.33/10.99  								| (208) all_22_0_26 = 0
% 32.33/10.99  								|
% 32.33/10.99  									| Equations (208) can reduce 74 to:
% 32.33/10.99  									| (101) $false
% 32.33/10.99  									|
% 32.33/10.99  									|-The branch is then unsatisfiable
% 32.33/10.99  								|-Branch two:
% 32.33/10.99  								| (74)  ~ (all_22_0_26 = 0)
% 32.33/10.99  								| (211) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/10.99  								|
% 32.33/10.99  									+-Applying beta-rule and splitting (141), into two cases.
% 32.33/10.99  									|-Branch one:
% 32.33/10.99  									| (208) all_22_0_26 = 0
% 32.33/10.99  									|
% 32.33/10.99  										| Equations (208) can reduce 74 to:
% 32.33/10.99  										| (101) $false
% 32.33/10.99  										|
% 32.33/10.99  										|-The branch is then unsatisfiable
% 32.33/10.99  									|-Branch two:
% 32.33/10.99  									| (74)  ~ (all_22_0_26 = 0)
% 32.33/10.99  									| (215) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/10.99  									|
% 32.33/10.99  										+-Applying beta-rule and splitting (146), into two cases.
% 32.33/10.99  										|-Branch one:
% 32.33/10.99  										| (196) all_32_0_36 = 0
% 32.33/10.99  										|
% 32.33/10.99  											| Equations (196) can reduce 92 to:
% 32.33/10.99  											| (101) $false
% 32.33/10.99  											|
% 32.33/10.99  											|-The branch is then unsatisfiable
% 32.33/10.99  										|-Branch two:
% 32.33/10.99  										| (92)  ~ (all_32_0_36 = 0)
% 32.33/10.99  										| (219) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/10.99  										|
% 32.33/10.99  											+-Applying beta-rule and splitting (151), into two cases.
% 32.33/10.99  											|-Branch one:
% 32.33/10.99  											| (220) distinct_points(all_0_2_2, all_0_1_1) = 0
% 32.33/10.99  											|
% 32.33/10.99  												+-Applying beta-rule and splitting (162), into two cases.
% 32.33/10.99  												|-Branch one:
% 32.33/10.99  												| (221) all_26_0_30 = 0
% 32.33/10.99  												|
% 32.33/10.99  													| Equations (221) can reduce 82 to:
% 32.33/10.99  													| (101) $false
% 32.33/10.99  													|
% 32.33/10.99  													|-The branch is then unsatisfiable
% 32.33/10.99  												|-Branch two:
% 32.33/10.99  												| (82)  ~ (all_26_0_30 = 0)
% 32.33/10.99  												| (224)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/10.99  												|
% 32.33/10.99  													+-Applying beta-rule and splitting (147), into two cases.
% 32.33/10.99  													|-Branch one:
% 32.33/10.99  													| (196) all_32_0_36 = 0
% 32.33/10.99  													|
% 32.33/10.99  														| Equations (196) can reduce 92 to:
% 32.33/10.99  														| (101) $false
% 32.33/10.99  														|
% 32.33/10.99  														|-The branch is then unsatisfiable
% 32.33/10.99  													|-Branch two:
% 32.33/10.99  													| (92)  ~ (all_32_0_36 = 0)
% 32.33/10.99  													| (228) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/10.99  													|
% 32.33/10.99  														+-Applying beta-rule and splitting (152), into two cases.
% 32.33/10.99  														|-Branch one:
% 32.33/10.99  														| (229) all_24_0_28 = 0
% 32.33/10.99  														|
% 32.33/10.99  															| Equations (229) can reduce 78 to:
% 32.33/10.99  															| (101) $false
% 32.33/10.99  															|
% 32.33/10.99  															|-The branch is then unsatisfiable
% 32.33/10.99  														|-Branch two:
% 32.33/10.99  														| (78)  ~ (all_24_0_28 = 0)
% 32.33/10.99  														| (232) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/10.99  														|
% 32.33/10.99  															+-Applying beta-rule and splitting (182), into two cases.
% 32.33/10.99  															|-Branch one:
% 32.33/10.99  															| (208) all_22_0_26 = 0
% 32.33/10.99  															|
% 32.33/10.99  																| Equations (208) can reduce 74 to:
% 32.33/10.99  																| (101) $false
% 32.33/10.99  																|
% 32.33/10.99  																|-The branch is then unsatisfiable
% 32.33/10.99  															|-Branch two:
% 32.33/10.99  															| (74)  ~ (all_22_0_26 = 0)
% 32.33/10.99  															| (236) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/10.99  															|
% 32.33/10.99  																+-Applying beta-rule and splitting (149), into two cases.
% 32.33/10.99  																|-Branch one:
% 32.33/10.99  																| (229) all_24_0_28 = 0
% 32.33/10.99  																|
% 32.33/10.99  																	| Equations (229) can reduce 78 to:
% 32.33/10.99  																	| (101) $false
% 32.33/10.99  																	|
% 32.33/10.99  																	|-The branch is then unsatisfiable
% 32.33/10.99  																|-Branch two:
% 32.33/10.99  																| (78)  ~ (all_24_0_28 = 0)
% 32.33/10.99  																| (240) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.00  																|
% 32.33/11.00  																	+-Applying beta-rule and splitting (150), into two cases.
% 32.33/11.00  																	|-Branch one:
% 32.33/11.00  																	| (229) all_24_0_28 = 0
% 32.33/11.00  																	|
% 32.33/11.00  																		| Equations (229) can reduce 78 to:
% 32.33/11.00  																		| (101) $false
% 32.33/11.00  																		|
% 32.33/11.00  																		|-The branch is then unsatisfiable
% 32.33/11.00  																	|-Branch two:
% 32.33/11.00  																	| (78)  ~ (all_24_0_28 = 0)
% 32.33/11.00  																	| (244) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.00  																	|
% 32.33/11.00  																		+-Applying beta-rule and splitting (183), into two cases.
% 32.33/11.00  																		|-Branch one:
% 32.33/11.00  																		| (208) all_22_0_26 = 0
% 32.33/11.00  																		|
% 32.33/11.00  																			| Equations (208) can reduce 74 to:
% 32.33/11.00  																			| (101) $false
% 32.33/11.00  																			|
% 32.33/11.00  																			|-The branch is then unsatisfiable
% 32.33/11.00  																		|-Branch two:
% 32.33/11.00  																		| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.00  																		| (248) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.00  																		|
% 32.33/11.00  																			+-Applying beta-rule and splitting (184), into two cases.
% 32.33/11.00  																			|-Branch one:
% 32.33/11.00  																			| (196) all_32_0_36 = 0
% 32.33/11.00  																			|
% 32.33/11.00  																				| Equations (196) can reduce 92 to:
% 32.33/11.00  																				| (101) $false
% 32.33/11.00  																				|
% 32.33/11.00  																				|-The branch is then unsatisfiable
% 32.33/11.00  																			|-Branch two:
% 32.33/11.00  																			| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.00  																			| (252) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.00  																			|
% 32.33/11.00  																				+-Applying beta-rule and splitting (185), into two cases.
% 32.33/11.00  																				|-Branch one:
% 32.33/11.00  																				| (196) all_32_0_36 = 0
% 32.33/11.00  																				|
% 32.33/11.00  																					| Equations (196) can reduce 92 to:
% 32.33/11.00  																					| (101) $false
% 32.33/11.00  																					|
% 32.33/11.00  																					|-The branch is then unsatisfiable
% 32.33/11.00  																				|-Branch two:
% 32.33/11.00  																				| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.00  																				| (256) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.00  																				|
% 32.33/11.00  																					+-Applying beta-rule and splitting (207), into two cases.
% 32.33/11.00  																					|-Branch one:
% 32.33/11.00  																					| (100) all_0_0_0 = 0
% 32.33/11.00  																					|
% 32.33/11.00  																						| Equations (100) can reduce 57 to:
% 32.33/11.00  																						| (101) $false
% 32.33/11.00  																						|
% 32.33/11.00  																						|-The branch is then unsatisfiable
% 32.33/11.00  																					|-Branch two:
% 32.33/11.00  																					| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.00  																					| (260)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.00  																					|
% 32.33/11.00  																						+-Applying beta-rule and splitting (211), into two cases.
% 32.33/11.00  																						|-Branch one:
% 32.33/11.00  																						| (100) all_0_0_0 = 0
% 32.33/11.00  																						|
% 32.33/11.00  																							| Equations (100) can reduce 57 to:
% 32.33/11.00  																							| (101) $false
% 32.33/11.00  																							|
% 32.33/11.00  																							|-The branch is then unsatisfiable
% 32.33/11.00  																						|-Branch two:
% 32.33/11.00  																						| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.00  																						| (264)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.00  																						|
% 32.33/11.00  																							+-Applying beta-rule and splitting (215), into two cases.
% 32.33/11.00  																							|-Branch one:
% 32.33/11.00  																							| (100) all_0_0_0 = 0
% 32.33/11.00  																							|
% 32.33/11.00  																								| Equations (100) can reduce 57 to:
% 32.33/11.00  																								| (101) $false
% 32.33/11.00  																								|
% 32.33/11.00  																								|-The branch is then unsatisfiable
% 32.33/11.00  																							|-Branch two:
% 32.33/11.00  																							| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.00  																							| (268)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.00  																							|
% 32.33/11.00  																								+-Applying beta-rule and splitting (219), into two cases.
% 32.33/11.00  																								|-Branch one:
% 32.33/11.00  																								| (208) all_22_0_26 = 0
% 32.33/11.00  																								|
% 32.33/11.00  																									| Equations (208) can reduce 74 to:
% 32.33/11.00  																									| (101) $false
% 32.33/11.00  																									|
% 32.33/11.00  																									|-The branch is then unsatisfiable
% 32.33/11.00  																								|-Branch two:
% 32.33/11.00  																								| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.00  																								| (272)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/11.00  																								|
% 32.33/11.00  																									+-Applying beta-rule and splitting (236), into two cases.
% 32.33/11.00  																									|-Branch one:
% 32.33/11.00  																									| (273) all_20_0_24 = 0
% 32.33/11.00  																									|
% 32.33/11.00  																										| Equations (273) can reduce 70 to:
% 32.33/11.00  																										| (101) $false
% 32.33/11.00  																										|
% 32.33/11.00  																										|-The branch is then unsatisfiable
% 32.33/11.00  																									|-Branch two:
% 32.33/11.00  																									| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.00  																									| (276)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.00  																									|
% 32.33/11.00  																										+-Applying beta-rule and splitting (143), into two cases.
% 32.33/11.00  																										|-Branch one:
% 32.33/11.00  																										| (208) all_22_0_26 = 0
% 32.33/11.00  																										|
% 32.33/11.00  																											| Equations (208) can reduce 74 to:
% 32.33/11.00  																											| (101) $false
% 32.33/11.00  																											|
% 32.33/11.00  																											|-The branch is then unsatisfiable
% 32.33/11.00  																										|-Branch two:
% 32.33/11.00  																										| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.00  																										| (280)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/11.00  																										|
% 32.33/11.00  																											+-Applying beta-rule and splitting (153), into two cases.
% 32.33/11.00  																											|-Branch one:
% 32.33/11.00  																											| (229) all_24_0_28 = 0
% 32.33/11.00  																											|
% 32.33/11.00  																												| Equations (229) can reduce 78 to:
% 32.33/11.00  																												| (101) $false
% 32.33/11.00  																												|
% 32.33/11.00  																												|-The branch is then unsatisfiable
% 32.33/11.00  																											|-Branch two:
% 32.33/11.00  																											| (78)  ~ (all_24_0_28 = 0)
% 32.33/11.00  																											| (284)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.00  																											|
% 32.33/11.00  																												+-Applying beta-rule and splitting (195), into two cases.
% 32.33/11.00  																												|-Branch one:
% 32.33/11.00  																												| (273) all_20_0_24 = 0
% 32.33/11.00  																												|
% 32.33/11.00  																													| Equations (273) can reduce 70 to:
% 32.33/11.00  																													| (101) $false
% 32.33/11.00  																													|
% 32.33/11.00  																													|-The branch is then unsatisfiable
% 32.33/11.00  																												|-Branch two:
% 32.33/11.00  																												| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.00  																												| (288)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/11.00  																												|
% 32.33/11.00  																													+-Applying beta-rule and splitting (186), into two cases.
% 32.33/11.00  																													|-Branch one:
% 32.33/11.00  																													| (229) all_24_0_28 = 0
% 32.33/11.00  																													|
% 32.33/11.00  																														| Equations (229) can reduce 78 to:
% 32.33/11.00  																														| (101) $false
% 32.33/11.00  																														|
% 32.33/11.00  																														|-The branch is then unsatisfiable
% 32.33/11.00  																													|-Branch two:
% 32.33/11.00  																													| (78)  ~ (all_24_0_28 = 0)
% 32.33/11.00  																													| (292) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.00  																													|
% 32.33/11.00  																														+-Applying beta-rule and splitting (187), into two cases.
% 32.33/11.00  																														|-Branch one:
% 32.33/11.00  																														| (229) all_24_0_28 = 0
% 32.33/11.00  																														|
% 32.33/11.00  																															| Equations (229) can reduce 78 to:
% 32.33/11.00  																															| (101) $false
% 32.33/11.00  																															|
% 32.33/11.00  																															|-The branch is then unsatisfiable
% 32.33/11.00  																														|-Branch two:
% 32.33/11.00  																														| (78)  ~ (all_24_0_28 = 0)
% 32.33/11.00  																														| (296) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.00  																														|
% 32.33/11.00  																															+-Applying beta-rule and splitting (188), into two cases.
% 32.33/11.00  																															|-Branch one:
% 32.33/11.00  																															| (229) all_24_0_28 = 0
% 32.33/11.00  																															|
% 32.33/11.00  																																| Equations (229) can reduce 78 to:
% 32.33/11.00  																																| (101) $false
% 32.33/11.00  																																|
% 32.33/11.00  																																|-The branch is then unsatisfiable
% 32.33/11.00  																															|-Branch two:
% 32.33/11.00  																															| (78)  ~ (all_24_0_28 = 0)
% 32.33/11.00  																															| (300) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.00  																															|
% 32.33/11.00  																																+-Applying beta-rule and splitting (191), into two cases.
% 32.33/11.00  																																|-Branch one:
% 32.33/11.00  																																| (221) all_26_0_30 = 0
% 32.33/11.00  																																|
% 32.33/11.00  																																	| Equations (221) can reduce 82 to:
% 32.33/11.00  																																	| (101) $false
% 32.33/11.00  																																	|
% 32.33/11.00  																																	|-The branch is then unsatisfiable
% 32.33/11.00  																																|-Branch two:
% 32.33/11.00  																																| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.00  																																| (304) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.00  																																|
% 32.33/11.00  																																	+-Applying beta-rule and splitting (189), into two cases.
% 32.33/11.00  																																	|-Branch one:
% 32.33/11.00  																																	| (221) all_26_0_30 = 0
% 32.33/11.00  																																	|
% 32.33/11.00  																																		| Equations (221) can reduce 82 to:
% 32.33/11.00  																																		| (101) $false
% 32.33/11.00  																																		|
% 32.33/11.00  																																		|-The branch is then unsatisfiable
% 32.33/11.00  																																	|-Branch two:
% 32.33/11.00  																																	| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.00  																																	| (308) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.00  																																	|
% 32.33/11.00  																																		+-Applying beta-rule and splitting (190), into two cases.
% 32.33/11.00  																																		|-Branch one:
% 32.33/11.00  																																		| (221) all_26_0_30 = 0
% 32.33/11.00  																																		|
% 32.33/11.00  																																			| Equations (221) can reduce 82 to:
% 32.33/11.00  																																			| (101) $false
% 32.33/11.00  																																			|
% 32.33/11.00  																																			|-The branch is then unsatisfiable
% 32.33/11.00  																																		|-Branch two:
% 32.33/11.00  																																		| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.00  																																		| (312) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.01  																																		|
% 32.33/11.01  																																			+-Applying beta-rule and splitting (160), into two cases.
% 32.33/11.01  																																			|-Branch one:
% 32.33/11.01  																																			| (221) all_26_0_30 = 0
% 32.33/11.01  																																			|
% 32.33/11.01  																																				| Equations (221) can reduce 82 to:
% 32.33/11.01  																																				| (101) $false
% 32.33/11.01  																																				|
% 32.33/11.01  																																				|-The branch is then unsatisfiable
% 32.33/11.01  																																			|-Branch two:
% 32.33/11.01  																																			| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.01  																																			| (316) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.01  																																			|
% 32.33/11.01  																																				+-Applying beta-rule and splitting (161), into two cases.
% 32.33/11.01  																																				|-Branch one:
% 32.33/11.01  																																				| (221) all_26_0_30 = 0
% 32.33/11.01  																																				|
% 32.33/11.01  																																					| Equations (221) can reduce 82 to:
% 32.33/11.01  																																					| (101) $false
% 32.33/11.01  																																					|
% 32.33/11.01  																																					|-The branch is then unsatisfiable
% 32.33/11.01  																																				|-Branch two:
% 32.33/11.01  																																				| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.01  																																				| (320) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.01  																																				|
% 32.33/11.01  																																					+-Applying beta-rule and splitting (172), into two cases.
% 32.33/11.01  																																					|-Branch one:
% 32.33/11.01  																																					| (196) all_32_0_36 = 0
% 32.33/11.01  																																					|
% 32.33/11.01  																																						| Equations (196) can reduce 92 to:
% 32.33/11.01  																																						| (101) $false
% 32.33/11.01  																																						|
% 32.33/11.01  																																						|-The branch is then unsatisfiable
% 32.33/11.01  																																					|-Branch two:
% 32.33/11.01  																																					| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.01  																																					| (324) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.01  																																					|
% 32.33/11.01  																																						+-Applying beta-rule and splitting (192), into two cases.
% 32.33/11.01  																																						|-Branch one:
% 32.33/11.01  																																						| (221) all_26_0_30 = 0
% 32.33/11.01  																																						|
% 32.33/11.01  																																							| Equations (221) can reduce 82 to:
% 32.33/11.01  																																							| (101) $false
% 32.33/11.01  																																							|
% 32.33/11.01  																																							|-The branch is then unsatisfiable
% 32.33/11.01  																																						|-Branch two:
% 32.33/11.01  																																						| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.01  																																						| (328) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.01  																																						|
% 32.33/11.01  																																							+-Applying beta-rule and splitting (167), into two cases.
% 32.33/11.01  																																							|-Branch one:
% 32.33/11.01  																																							| (200) all_28_0_32 = 0
% 32.33/11.01  																																							|
% 32.33/11.01  																																								| Equations (200) can reduce 86 to:
% 32.33/11.01  																																								| (101) $false
% 32.33/11.01  																																								|
% 32.33/11.01  																																								|-The branch is then unsatisfiable
% 32.33/11.01  																																							|-Branch two:
% 32.33/11.01  																																							| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.01  																																							| (332) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.01  																																							|
% 32.33/11.01  																																								+-Applying beta-rule and splitting (168), into two cases.
% 32.33/11.01  																																								|-Branch one:
% 32.33/11.01  																																								| (200) all_28_0_32 = 0
% 32.33/11.01  																																								|
% 32.33/11.01  																																									| Equations (200) can reduce 86 to:
% 32.33/11.01  																																									| (101) $false
% 32.33/11.01  																																									|
% 32.33/11.01  																																									|-The branch is then unsatisfiable
% 32.33/11.01  																																								|-Branch two:
% 32.33/11.01  																																								| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.01  																																								| (336) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.01  																																								|
% 32.33/11.01  																																									+-Applying beta-rule and splitting (169), into two cases.
% 32.33/11.01  																																									|-Branch one:
% 32.33/11.01  																																									| (200) all_28_0_32 = 0
% 32.33/11.01  																																									|
% 32.33/11.01  																																										| Equations (200) can reduce 86 to:
% 32.33/11.01  																																										| (101) $false
% 32.33/11.01  																																										|
% 32.33/11.01  																																										|-The branch is then unsatisfiable
% 32.33/11.01  																																									|-Branch two:
% 32.33/11.01  																																									| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.01  																																									| (340) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.01  																																									|
% 32.33/11.01  																																										+-Applying beta-rule and splitting (170), into two cases.
% 32.33/11.01  																																										|-Branch one:
% 32.33/11.01  																																										| (200) all_28_0_32 = 0
% 32.33/11.01  																																										|
% 32.33/11.01  																																											| Equations (200) can reduce 86 to:
% 32.33/11.01  																																											| (101) $false
% 32.33/11.01  																																											|
% 32.33/11.01  																																											|-The branch is then unsatisfiable
% 32.33/11.01  																																										|-Branch two:
% 32.33/11.01  																																										| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.01  																																										| (344) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.01  																																										|
% 32.33/11.01  																																											+-Applying beta-rule and splitting (173), into two cases.
% 32.33/11.01  																																											|-Branch one:
% 32.33/11.01  																																											| (196) all_32_0_36 = 0
% 32.33/11.01  																																											|
% 32.33/11.01  																																												| Equations (196) can reduce 92 to:
% 32.33/11.01  																																												| (101) $false
% 32.33/11.01  																																												|
% 32.33/11.01  																																												|-The branch is then unsatisfiable
% 32.33/11.01  																																											|-Branch two:
% 32.33/11.01  																																											| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.01  																																											| (348) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.01  																																											|
% 32.33/11.01  																																												+-Applying beta-rule and splitting (171), into two cases.
% 32.33/11.01  																																												|-Branch one:
% 32.33/11.01  																																												| (196) all_32_0_36 = 0
% 32.33/11.01  																																												|
% 32.33/11.01  																																													| Equations (196) can reduce 92 to:
% 32.33/11.01  																																													| (101) $false
% 32.33/11.01  																																													|
% 32.33/11.01  																																													|-The branch is then unsatisfiable
% 32.33/11.01  																																												|-Branch two:
% 32.33/11.01  																																												| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.01  																																												| (352) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.01  																																												|
% 32.33/11.01  																																													+-Applying beta-rule and splitting (174), into two cases.
% 32.33/11.01  																																													|-Branch one:
% 32.33/11.01  																																													| (196) all_32_0_36 = 0
% 32.33/11.01  																																													|
% 32.33/11.01  																																														| Equations (196) can reduce 92 to:
% 32.33/11.01  																																														| (101) $false
% 32.33/11.01  																																														|
% 32.33/11.01  																																														|-The branch is then unsatisfiable
% 32.33/11.01  																																													|-Branch two:
% 32.33/11.01  																																													| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.01  																																													| (356) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.01  																																													|
% 32.33/11.01  																																														+-Applying beta-rule and splitting (228), into two cases.
% 32.33/11.01  																																														|-Branch one:
% 32.33/11.01  																																														| (208) all_22_0_26 = 0
% 32.33/11.01  																																														|
% 32.33/11.01  																																															| Equations (208) can reduce 74 to:
% 32.33/11.01  																																															| (101) $false
% 32.33/11.01  																																															|
% 32.33/11.01  																																															|-The branch is then unsatisfiable
% 32.33/11.01  																																														|-Branch two:
% 32.33/11.01  																																														| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.01  																																														| (360)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_22_1_27) = v0))
% 32.33/11.01  																																														|
% 32.33/11.01  																																															+-Applying beta-rule and splitting (232), into two cases.
% 32.33/11.01  																																															|-Branch one:
% 32.33/11.01  																																															| (208) all_22_0_26 = 0
% 32.33/11.01  																																															|
% 32.33/11.01  																																																| Equations (208) can reduce 74 to:
% 32.33/11.01  																																																| (101) $false
% 32.33/11.01  																																																|
% 32.33/11.01  																																																|-The branch is then unsatisfiable
% 32.33/11.01  																																															|-Branch two:
% 32.33/11.01  																																															| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.01  																																															| (364)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.01  																																															|
% 32.33/11.01  																																																+-Applying beta-rule and splitting (240), into two cases.
% 32.33/11.01  																																																|-Branch one:
% 32.33/11.01  																																																| (100) all_0_0_0 = 0
% 32.33/11.01  																																																|
% 32.33/11.01  																																																	| Equations (100) can reduce 57 to:
% 32.33/11.01  																																																	| (101) $false
% 32.33/11.01  																																																	|
% 32.33/11.01  																																																	|-The branch is then unsatisfiable
% 32.33/11.01  																																																|-Branch two:
% 32.33/11.01  																																																| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.01  																																																| (368)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.01  																																																|
% 32.33/11.01  																																																	+-Applying beta-rule and splitting (244), into two cases.
% 32.33/11.01  																																																	|-Branch one:
% 32.33/11.01  																																																	| (100) all_0_0_0 = 0
% 32.33/11.01  																																																	|
% 32.33/11.01  																																																		| Equations (100) can reduce 57 to:
% 32.33/11.01  																																																		| (101) $false
% 32.33/11.01  																																																		|
% 32.33/11.01  																																																		|-The branch is then unsatisfiable
% 32.33/11.01  																																																	|-Branch two:
% 32.33/11.01  																																																	| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.01  																																																	| (372)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.01  																																																	|
% 32.33/11.01  																																																		+-Applying beta-rule and splitting (252), into two cases.
% 32.33/11.01  																																																		|-Branch one:
% 32.33/11.01  																																																		| (273) all_20_0_24 = 0
% 32.33/11.01  																																																		|
% 32.33/11.01  																																																			| Equations (273) can reduce 70 to:
% 32.33/11.01  																																																			| (101) $false
% 32.33/11.01  																																																			|
% 32.33/11.01  																																																			|-The branch is then unsatisfiable
% 32.33/11.01  																																																		|-Branch two:
% 32.33/11.01  																																																		| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.01  																																																		| (376)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.01  																																																		|
% 32.33/11.01  																																																			+-Applying beta-rule and splitting (256), into two cases.
% 32.33/11.01  																																																			|-Branch one:
% 32.33/11.01  																																																			| (273) all_20_0_24 = 0
% 32.33/11.01  																																																			|
% 32.33/11.01  																																																				| Equations (273) can reduce 70 to:
% 32.33/11.01  																																																				| (101) $false
% 32.33/11.01  																																																				|
% 32.33/11.01  																																																				|-The branch is then unsatisfiable
% 32.33/11.01  																																																			|-Branch two:
% 32.33/11.01  																																																			| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.01  																																																			| (380)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.01  																																																			|
% 32.33/11.01  																																																				+-Applying beta-rule and splitting (304), into two cases.
% 32.33/11.01  																																																				|-Branch one:
% 32.33/11.01  																																																				| (273) all_20_0_24 = 0
% 32.33/11.01  																																																				|
% 32.33/11.01  																																																					| Equations (273) can reduce 70 to:
% 32.33/11.01  																																																					| (101) $false
% 32.33/11.01  																																																					|
% 32.33/11.01  																																																					|-The branch is then unsatisfiable
% 32.33/11.01  																																																				|-Branch two:
% 32.33/11.01  																																																				| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.01  																																																				| (384)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.01  																																																				|
% 32.33/11.01  																																																					+-Applying beta-rule and splitting (308), into two cases.
% 32.33/11.01  																																																					|-Branch one:
% 32.33/11.01  																																																					| (273) all_20_0_24 = 0
% 32.33/11.01  																																																					|
% 32.33/11.02  																																																						| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																						| (101) $false
% 32.33/11.02  																																																						|
% 32.33/11.02  																																																						|-The branch is then unsatisfiable
% 32.33/11.02  																																																					|-Branch two:
% 32.33/11.02  																																																					| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																					| (388)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																					|
% 32.33/11.02  																																																						+-Applying beta-rule and splitting (336), into two cases.
% 32.33/11.02  																																																						|-Branch one:
% 32.33/11.02  																																																						| (208) all_22_0_26 = 0
% 32.33/11.02  																																																						|
% 32.33/11.02  																																																							| Equations (208) can reduce 74 to:
% 32.33/11.02  																																																							| (101) $false
% 32.33/11.02  																																																							|
% 32.33/11.02  																																																							|-The branch is then unsatisfiable
% 32.33/11.02  																																																						|-Branch two:
% 32.33/11.02  																																																						| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.02  																																																						| (392)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.02  																																																						|
% 32.33/11.02  																																																							+-Applying beta-rule and splitting (352), into two cases.
% 32.33/11.02  																																																							|-Branch one:
% 32.33/11.02  																																																							| (200) all_28_0_32 = 0
% 32.33/11.02  																																																							|
% 32.33/11.02  																																																								| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																								| (101) $false
% 32.33/11.02  																																																								|
% 32.33/11.02  																																																								|-The branch is then unsatisfiable
% 32.33/11.02  																																																							|-Branch two:
% 32.33/11.02  																																																							| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																							| (396)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.02  																																																							|
% 32.33/11.02  																																																								+-Applying beta-rule and splitting (356), into two cases.
% 32.33/11.02  																																																								|-Branch one:
% 32.33/11.02  																																																								| (200) all_28_0_32 = 0
% 32.33/11.02  																																																								|
% 32.33/11.02  																																																									| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																									| (101) $false
% 32.33/11.02  																																																									|
% 32.33/11.02  																																																									|-The branch is then unsatisfiable
% 32.33/11.02  																																																								|-Branch two:
% 32.33/11.02  																																																								| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																								| (400)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.02  																																																								|
% 32.33/11.02  																																																									+-Applying beta-rule and splitting (139), into two cases.
% 32.33/11.02  																																																									|-Branch one:
% 32.33/11.02  																																																									| (208) all_22_0_26 = 0
% 32.33/11.02  																																																									|
% 32.33/11.02  																																																										| Equations (208) can reduce 74 to:
% 32.33/11.02  																																																										| (101) $false
% 32.33/11.02  																																																										|
% 32.33/11.02  																																																										|-The branch is then unsatisfiable
% 32.33/11.02  																																																									|-Branch two:
% 32.33/11.02  																																																									| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.02  																																																									| (404) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.02  																																																									|
% 32.33/11.02  																																																										+-Applying beta-rule and splitting (144), into two cases.
% 32.33/11.02  																																																										|-Branch one:
% 32.33/11.02  																																																										| (196) all_32_0_36 = 0
% 32.33/11.02  																																																										|
% 32.33/11.02  																																																											| Equations (196) can reduce 92 to:
% 32.33/11.02  																																																											| (101) $false
% 32.33/11.02  																																																											|
% 32.33/11.02  																																																											|-The branch is then unsatisfiable
% 32.33/11.02  																																																										|-Branch two:
% 32.33/11.02  																																																										| (92)  ~ (all_32_0_36 = 0)
% 32.33/11.02  																																																										| (408) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.02  																																																										|
% 32.33/11.02  																																																											+-Applying beta-rule and splitting (165), into two cases.
% 32.33/11.02  																																																											|-Branch one:
% 32.33/11.02  																																																											| (200) all_28_0_32 = 0
% 32.33/11.02  																																																											|
% 32.33/11.02  																																																												| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																												| (101) $false
% 32.33/11.02  																																																												|
% 32.33/11.02  																																																												|-The branch is then unsatisfiable
% 32.33/11.02  																																																											|-Branch two:
% 32.33/11.02  																																																											| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																											| (412) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																											|
% 32.33/11.02  																																																												+-Applying beta-rule and splitting (177), into two cases.
% 32.33/11.02  																																																												|-Branch one:
% 32.33/11.02  																																																												| (200) all_28_0_32 = 0
% 32.33/11.02  																																																												|
% 32.33/11.02  																																																													| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																													| (101) $false
% 32.33/11.02  																																																													|
% 32.33/11.02  																																																													|-The branch is then unsatisfiable
% 32.33/11.02  																																																												|-Branch two:
% 32.33/11.02  																																																												| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																												| (416) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																												|
% 32.33/11.02  																																																													+-Applying beta-rule and splitting (175), into two cases.
% 32.33/11.02  																																																													|-Branch one:
% 32.33/11.02  																																																													| (200) all_28_0_32 = 0
% 32.33/11.02  																																																													|
% 32.33/11.02  																																																														| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																														| (101) $false
% 32.33/11.02  																																																														|
% 32.33/11.02  																																																														|-The branch is then unsatisfiable
% 32.33/11.02  																																																													|-Branch two:
% 32.33/11.02  																																																													| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																													| (420) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																													|
% 32.33/11.02  																																																														+-Applying beta-rule and splitting (176), into two cases.
% 32.33/11.02  																																																														|-Branch one:
% 32.33/11.02  																																																														| (200) all_28_0_32 = 0
% 32.33/11.02  																																																														|
% 32.33/11.02  																																																															| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																															| (101) $false
% 32.33/11.02  																																																															|
% 32.33/11.02  																																																															|-The branch is then unsatisfiable
% 32.33/11.02  																																																														|-Branch two:
% 32.33/11.02  																																																														| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																														| (424) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.02  																																																														|
% 32.33/11.02  																																																															+-Applying beta-rule and splitting (181), into two cases.
% 32.33/11.02  																																																															|-Branch one:
% 32.33/11.02  																																																															| (273) all_20_0_24 = 0
% 32.33/11.02  																																																															|
% 32.33/11.02  																																																																| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																																| (101) $false
% 32.33/11.02  																																																																|
% 32.33/11.02  																																																																|-The branch is then unsatisfiable
% 32.33/11.02  																																																															|-Branch two:
% 32.33/11.02  																																																															| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																															| (428) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																															|
% 32.33/11.02  																																																																+-Applying beta-rule and splitting (142), into two cases.
% 32.33/11.02  																																																																|-Branch one:
% 32.33/11.02  																																																																| (208) all_22_0_26 = 0
% 32.33/11.02  																																																																|
% 32.33/11.02  																																																																	| Equations (208) can reduce 74 to:
% 32.33/11.02  																																																																	| (101) $false
% 32.33/11.02  																																																																	|
% 32.33/11.02  																																																																	|-The branch is then unsatisfiable
% 32.33/11.02  																																																																|-Branch two:
% 32.33/11.02  																																																																| (74)  ~ (all_22_0_26 = 0)
% 32.33/11.02  																																																																| (432) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.02  																																																																|
% 32.33/11.02  																																																																	+-Applying beta-rule and splitting (292), into two cases.
% 32.33/11.02  																																																																	|-Branch one:
% 32.33/11.02  																																																																	| (273) all_20_0_24 = 0
% 32.33/11.02  																																																																	|
% 32.33/11.02  																																																																		| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																																		| (101) $false
% 32.33/11.02  																																																																		|
% 32.33/11.02  																																																																		|-The branch is then unsatisfiable
% 32.33/11.02  																																																																	|-Branch two:
% 32.33/11.02  																																																																	| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																																	| (436)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																																	|
% 32.33/11.02  																																																																		+-Applying beta-rule and splitting (296), into two cases.
% 32.33/11.02  																																																																		|-Branch one:
% 32.33/11.02  																																																																		| (273) all_20_0_24 = 0
% 32.33/11.02  																																																																		|
% 32.33/11.02  																																																																			| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																																			| (101) $false
% 32.33/11.02  																																																																			|
% 32.33/11.02  																																																																			|-The branch is then unsatisfiable
% 32.33/11.02  																																																																		|-Branch two:
% 32.33/11.02  																																																																		| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																																		| (440)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.02  																																																																		|
% 32.33/11.02  																																																																			+-Applying beta-rule and splitting (300), into two cases.
% 32.33/11.02  																																																																			|-Branch one:
% 32.33/11.02  																																																																			| (273) all_20_0_24 = 0
% 32.33/11.02  																																																																			|
% 32.33/11.02  																																																																				| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																																				| (101) $false
% 32.33/11.02  																																																																				|
% 32.33/11.02  																																																																				|-The branch is then unsatisfiable
% 32.33/11.02  																																																																			|-Branch two:
% 32.33/11.02  																																																																			| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																																			| (444)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.02  																																																																			|
% 32.33/11.02  																																																																				+-Applying beta-rule and splitting (324), into two cases.
% 32.33/11.02  																																																																				|-Branch one:
% 32.33/11.02  																																																																				| (200) all_28_0_32 = 0
% 32.33/11.02  																																																																				|
% 32.33/11.02  																																																																					| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																																					| (101) $false
% 32.33/11.02  																																																																					|
% 32.33/11.02  																																																																					|-The branch is then unsatisfiable
% 32.33/11.02  																																																																				|-Branch two:
% 32.33/11.02  																																																																				| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																																				| (448)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_22_1_27) = v0))
% 32.33/11.02  																																																																				|
% 32.33/11.02  																																																																					+-Applying beta-rule and splitting (328), into two cases.
% 32.33/11.02  																																																																					|-Branch one:
% 32.33/11.02  																																																																					| (273) all_20_0_24 = 0
% 32.33/11.02  																																																																					|
% 32.33/11.02  																																																																						| Equations (273) can reduce 70 to:
% 32.33/11.02  																																																																						| (101) $false
% 32.33/11.02  																																																																						|
% 32.33/11.02  																																																																						|-The branch is then unsatisfiable
% 32.33/11.02  																																																																					|-Branch two:
% 32.33/11.02  																																																																					| (70)  ~ (all_20_0_24 = 0)
% 32.33/11.02  																																																																					| (452)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.02  																																																																					|
% 32.33/11.02  																																																																						| Instantiating (452) with all_345_0_5202 yields:
% 32.33/11.02  																																																																						| (453) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202) | ( ~ (all_345_0_5202 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202)
% 32.33/11.02  																																																																						|
% 32.33/11.02  																																																																						+-Applying beta-rule and splitting (453), into two cases.
% 32.33/11.02  																																																																						|-Branch one:
% 32.33/11.02  																																																																						| (454) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202)
% 32.33/11.02  																																																																						|
% 32.33/11.02  																																																																							+-Applying beta-rule and splitting (454), into two cases.
% 32.33/11.02  																																																																							|-Branch one:
% 32.33/11.02  																																																																							| (455) (all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0)
% 32.33/11.02  																																																																							|
% 32.33/11.02  																																																																								+-Applying beta-rule and splitting (455), into two cases.
% 32.33/11.02  																																																																								|-Branch one:
% 32.33/11.02  																																																																								| (456) all_345_0_5202 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 32.33/11.02  																																																																								|
% 32.33/11.02  																																																																									| Applying alpha-rule on (456) yields:
% 32.33/11.02  																																																																									| (457) all_345_0_5202 = 0
% 32.33/11.02  																																																																									| (458) apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 32.33/11.02  																																																																									|
% 32.33/11.02  																																																																									+-Applying beta-rule and splitting (164), into two cases.
% 32.33/11.02  																																																																									|-Branch one:
% 32.33/11.02  																																																																									| (200) all_28_0_32 = 0
% 32.33/11.02  																																																																									|
% 32.33/11.02  																																																																										| Equations (200) can reduce 86 to:
% 32.33/11.02  																																																																										| (101) $false
% 32.33/11.02  																																																																										|
% 32.33/11.02  																																																																										|-The branch is then unsatisfiable
% 32.33/11.02  																																																																									|-Branch two:
% 32.33/11.02  																																																																									| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.02  																																																																									| (462) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.03  																																																																									|
% 32.33/11.03  																																																																										+-Applying beta-rule and splitting (163), into two cases.
% 32.33/11.03  																																																																										|-Branch one:
% 32.33/11.03  																																																																										| (200) all_28_0_32 = 0
% 32.33/11.03  																																																																										|
% 32.33/11.03  																																																																											| Equations (200) can reduce 86 to:
% 32.33/11.03  																																																																											| (101) $false
% 32.33/11.03  																																																																											|
% 32.33/11.03  																																																																											|-The branch is then unsatisfiable
% 32.33/11.03  																																																																										|-Branch two:
% 32.33/11.03  																																																																										| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.03  																																																																										| (466) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.03  																																																																										|
% 32.33/11.03  																																																																											+-Applying beta-rule and splitting (166), into two cases.
% 32.33/11.03  																																																																											|-Branch one:
% 32.33/11.03  																																																																											| (200) all_28_0_32 = 0
% 32.33/11.03  																																																																											|
% 32.33/11.03  																																																																												| Equations (200) can reduce 86 to:
% 32.33/11.03  																																																																												| (101) $false
% 32.33/11.03  																																																																												|
% 32.33/11.03  																																																																												|-The branch is then unsatisfiable
% 32.33/11.03  																																																																											|-Branch two:
% 32.33/11.03  																																																																											| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.03  																																																																											| (470) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.03  																																																																											|
% 32.33/11.03  																																																																												+-Applying beta-rule and splitting (156), into two cases.
% 32.33/11.03  																																																																												|-Branch one:
% 32.33/11.03  																																																																												| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																												|
% 32.33/11.03  																																																																													| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																													| (101) $false
% 32.33/11.03  																																																																													|
% 32.33/11.03  																																																																													|-The branch is then unsatisfiable
% 32.33/11.03  																																																																												|-Branch two:
% 32.33/11.03  																																																																												| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																												| (474) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.03  																																																																												|
% 32.33/11.03  																																																																													+-Applying beta-rule and splitting (157), into two cases.
% 32.33/11.03  																																																																													|-Branch one:
% 32.33/11.03  																																																																													| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																													|
% 32.33/11.03  																																																																														| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																														| (101) $false
% 32.33/11.03  																																																																														|
% 32.33/11.03  																																																																														|-The branch is then unsatisfiable
% 32.33/11.03  																																																																													|-Branch two:
% 32.33/11.03  																																																																													| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																													| (478) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.03  																																																																													|
% 32.33/11.03  																																																																														+-Applying beta-rule and splitting (158), into two cases.
% 32.33/11.03  																																																																														|-Branch one:
% 32.33/11.03  																																																																														| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																														|
% 32.33/11.03  																																																																															| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																															| (101) $false
% 32.33/11.03  																																																																															|
% 32.33/11.03  																																																																															|-The branch is then unsatisfiable
% 32.33/11.03  																																																																														|-Branch two:
% 32.33/11.03  																																																																														| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																														| (482) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.03  																																																																														|
% 32.33/11.03  																																																																															+-Applying beta-rule and splitting (159), into two cases.
% 32.33/11.03  																																																																															|-Branch one:
% 32.33/11.03  																																																																															| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																															|
% 32.33/11.03  																																																																																| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																																| (101) $false
% 32.33/11.03  																																																																																|
% 32.33/11.03  																																																																																|-The branch is then unsatisfiable
% 32.33/11.03  																																																																															|-Branch two:
% 32.33/11.03  																																																																															| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																															| (486) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.03  																																																																															|
% 32.33/11.03  																																																																																+-Applying beta-rule and splitting (154), into two cases.
% 32.33/11.03  																																																																																|-Branch one:
% 32.33/11.03  																																																																																| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																																|
% 32.33/11.03  																																																																																	| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																																	| (101) $false
% 32.33/11.03  																																																																																	|
% 32.33/11.03  																																																																																	|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																|-Branch two:
% 32.33/11.03  																																																																																| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																																| (490) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.03  																																																																																|
% 32.33/11.03  																																																																																	+-Applying beta-rule and splitting (155), into two cases.
% 32.33/11.03  																																																																																	|-Branch one:
% 32.33/11.03  																																																																																	| (221) all_26_0_30 = 0
% 32.33/11.03  																																																																																	|
% 32.33/11.03  																																																																																		| Equations (221) can reduce 82 to:
% 32.33/11.03  																																																																																		| (101) $false
% 32.33/11.03  																																																																																		|
% 32.33/11.03  																																																																																		|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																	|-Branch two:
% 32.33/11.03  																																																																																	| (82)  ~ (all_26_0_30 = 0)
% 32.33/11.03  																																																																																	| (494) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.03  																																																																																	|
% 32.33/11.03  																																																																																		+-Applying beta-rule and splitting (404), into two cases.
% 32.33/11.03  																																																																																		|-Branch one:
% 32.33/11.03  																																																																																		| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																		|
% 32.33/11.03  																																																																																			| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																			| (101) $false
% 32.33/11.03  																																																																																			|
% 32.33/11.03  																																																																																			|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																		|-Branch two:
% 32.33/11.03  																																																																																		| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																		| (498)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.03  																																																																																		|
% 32.33/11.03  																																																																																			+-Applying beta-rule and splitting (408), into two cases.
% 32.33/11.03  																																																																																			|-Branch one:
% 32.33/11.03  																																																																																			| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																			|
% 32.33/11.03  																																																																																				| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																				| (101) $false
% 32.33/11.03  																																																																																				|
% 32.33/11.03  																																																																																				|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																			|-Branch two:
% 32.33/11.03  																																																																																			| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																			| (502)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_22_1_27) = v0))
% 32.33/11.03  																																																																																			|
% 32.33/11.03  																																																																																				+-Applying beta-rule and splitting (412), into two cases.
% 32.33/11.03  																																																																																				|-Branch one:
% 32.33/11.03  																																																																																				| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																				|
% 32.33/11.03  																																																																																					| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																					| (101) $false
% 32.33/11.03  																																																																																					|
% 32.33/11.03  																																																																																					|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																				|-Branch two:
% 32.33/11.03  																																																																																				| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																				| (506)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.03  																																																																																				|
% 32.33/11.03  																																																																																					+-Applying beta-rule and splitting (428), into two cases.
% 32.33/11.03  																																																																																					|-Branch one:
% 32.33/11.03  																																																																																					| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																					|
% 32.33/11.03  																																																																																						| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																						| (101) $false
% 32.33/11.03  																																																																																						|
% 32.33/11.03  																																																																																						|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																					|-Branch two:
% 32.33/11.03  																																																																																					| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																					| (510)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.03  																																																																																					|
% 32.33/11.03  																																																																																						+-Applying beta-rule and splitting (432), into two cases.
% 32.33/11.03  																																																																																						|-Branch one:
% 32.33/11.03  																																																																																						| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																						|
% 32.33/11.03  																																																																																							| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																							| (101) $false
% 32.33/11.03  																																																																																							|
% 32.33/11.03  																																																																																							|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																						|-Branch two:
% 32.33/11.03  																																																																																						| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																						| (514)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_1_1) = v0))
% 32.33/11.03  																																																																																						|
% 32.33/11.03  																																																																																							+-Applying beta-rule and splitting (462), into two cases.
% 32.33/11.03  																																																																																							|-Branch one:
% 32.33/11.03  																																																																																							| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																							|
% 32.33/11.03  																																																																																								| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																								| (101) $false
% 32.33/11.03  																																																																																								|
% 32.33/11.03  																																																																																								|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																							|-Branch two:
% 32.33/11.03  																																																																																							| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																							| (518)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.03  																																																																																							|
% 32.33/11.03  																																																																																								+-Applying beta-rule and splitting (466), into two cases.
% 32.33/11.03  																																																																																								|-Branch one:
% 32.33/11.03  																																																																																								| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																								|
% 32.33/11.03  																																																																																									| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																									| (101) $false
% 32.33/11.03  																																																																																									|
% 32.33/11.03  																																																																																									|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																								|-Branch two:
% 32.33/11.03  																																																																																								| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																								| (522)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.03  																																																																																								|
% 32.33/11.03  																																																																																									+-Applying beta-rule and splitting (470), into two cases.
% 32.33/11.03  																																																																																									|-Branch one:
% 32.33/11.03  																																																																																									| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																									|
% 32.33/11.03  																																																																																										| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																										| (101) $false
% 32.33/11.03  																																																																																										|
% 32.33/11.03  																																																																																										|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																									|-Branch two:
% 32.33/11.03  																																																																																									| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																									| (526)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.03  																																																																																									|
% 32.33/11.03  																																																																																										+-Applying beta-rule and splitting (490), into two cases.
% 32.33/11.03  																																																																																										|-Branch one:
% 32.33/11.03  																																																																																										| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																										|
% 32.33/11.03  																																																																																											| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																											| (101) $false
% 32.33/11.03  																																																																																											|
% 32.33/11.03  																																																																																											|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																										|-Branch two:
% 32.33/11.03  																																																																																										| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																										| (530)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.03  																																																																																										|
% 32.33/11.03  																																																																																											+-Applying beta-rule and splitting (494), into two cases.
% 32.33/11.03  																																																																																											|-Branch one:
% 32.33/11.03  																																																																																											| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																											|
% 32.33/11.03  																																																																																												| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																												| (101) $false
% 32.33/11.03  																																																																																												|
% 32.33/11.03  																																																																																												|-The branch is then unsatisfiable
% 32.33/11.03  																																																																																											|-Branch two:
% 32.33/11.03  																																																																																											| (57)  ~ (all_0_0_0 = 0)
% 32.33/11.03  																																																																																											| (534)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 32.33/11.03  																																																																																											|
% 32.33/11.03  																																																																																												| Instantiating formula (21) with all_0_1_1, all_0_5_5, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields:
% 32.33/11.03  																																																																																												| (100) all_0_0_0 = 0
% 32.33/11.03  																																																																																												|
% 32.33/11.03  																																																																																												| Equations (100) can reduce 57 to:
% 32.33/11.03  																																																																																												| (101) $false
% 32.33/11.03  																																																																																												|
% 32.33/11.03  																																																																																												|-The branch is then unsatisfiable
% 32.33/11.03  																																																																								|-Branch two:
% 32.33/11.03  																																																																								| (537) all_345_0_5202 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 32.33/11.04  																																																																								|
% 32.33/11.04  																																																																									| Applying alpha-rule on (537) yields:
% 32.33/11.04  																																																																									| (457) all_345_0_5202 = 0
% 32.33/11.04  																																																																									| (539) apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 32.33/11.04  																																																																									|
% 32.33/11.04  																																																																									+-Applying beta-rule and splitting (164), into two cases.
% 32.33/11.04  																																																																									|-Branch one:
% 32.33/11.04  																																																																									| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																									|
% 32.33/11.04  																																																																										| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																										| (101) $false
% 32.33/11.04  																																																																										|
% 32.33/11.04  																																																																										|-The branch is then unsatisfiable
% 32.33/11.04  																																																																									|-Branch two:
% 32.33/11.04  																																																																									| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																									| (462) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.04  																																																																									|
% 32.33/11.04  																																																																										+-Applying beta-rule and splitting (163), into two cases.
% 32.33/11.04  																																																																										|-Branch one:
% 32.33/11.04  																																																																										| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																										|
% 32.33/11.04  																																																																											| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																											| (101) $false
% 32.33/11.04  																																																																											|
% 32.33/11.04  																																																																											|-The branch is then unsatisfiable
% 32.33/11.04  																																																																										|-Branch two:
% 32.33/11.04  																																																																										| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																										| (466) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.04  																																																																										|
% 32.33/11.04  																																																																											+-Applying beta-rule and splitting (166), into two cases.
% 32.33/11.04  																																																																											|-Branch one:
% 32.33/11.04  																																																																											| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																											|
% 32.33/11.04  																																																																												| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																												| (101) $false
% 32.33/11.04  																																																																												|
% 32.33/11.04  																																																																												|-The branch is then unsatisfiable
% 32.33/11.04  																																																																											|-Branch two:
% 32.33/11.04  																																																																											| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																											| (470) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.04  																																																																											|
% 32.33/11.04  																																																																												+-Applying beta-rule and splitting (178), into two cases.
% 32.33/11.04  																																																																												|-Branch one:
% 32.33/11.04  																																																																												| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																												|
% 32.33/11.04  																																																																													| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																													| (101) $false
% 32.33/11.04  																																																																													|
% 32.33/11.04  																																																																													|-The branch is then unsatisfiable
% 32.33/11.04  																																																																												|-Branch two:
% 32.33/11.04  																																																																												| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																												| (555) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 32.33/11.04  																																																																												|
% 32.33/11.04  																																																																													+-Applying beta-rule and splitting (179), into two cases.
% 32.33/11.04  																																																																													|-Branch one:
% 32.33/11.04  																																																																													| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																													|
% 32.33/11.04  																																																																														| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																														| (101) $false
% 32.33/11.04  																																																																														|
% 32.33/11.04  																																																																														|-The branch is then unsatisfiable
% 32.33/11.04  																																																																													|-Branch two:
% 32.33/11.04  																																																																													| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																													| (559) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 32.33/11.04  																																																																													|
% 32.33/11.04  																																																																														+-Applying beta-rule and splitting (193), into two cases.
% 32.33/11.04  																																																																														|-Branch one:
% 32.33/11.04  																																																																														| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																														|
% 32.33/11.04  																																																																															| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																															| (101) $false
% 32.33/11.04  																																																																															|
% 32.33/11.04  																																																																															|-The branch is then unsatisfiable
% 32.33/11.04  																																																																														|-Branch two:
% 32.33/11.04  																																																																														| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																														| (563) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/11.04  																																																																														|
% 32.33/11.04  																																																																															+-Applying beta-rule and splitting (194), into two cases.
% 32.33/11.04  																																																																															|-Branch one:
% 32.33/11.04  																																																																															| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																															|
% 32.33/11.04  																																																																																| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																																| (101) $false
% 32.33/11.04  																																																																																|
% 32.33/11.04  																																																																																|-The branch is then unsatisfiable
% 32.33/11.04  																																																																															|-Branch two:
% 32.33/11.04  																																																																															| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																															| (567) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 32.33/11.04  																																																																															|
% 32.33/11.04  																																																																																+-Applying beta-rule and splitting (348), into two cases.
% 32.33/11.04  																																																																																|-Branch one:
% 32.33/11.04  																																																																																| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																																|
% 32.33/11.04  																																																																																	| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																																	| (101) $false
% 32.33/11.04  																																																																																	|
% 32.33/11.04  																																																																																	|-The branch is then unsatisfiable
% 32.33/11.04  																																																																																|-Branch two:
% 32.33/11.04  																																																																																| (86)  ~ (all_28_0_32 = 0)
% 32.33/11.04  																																																																																| (571)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_22_1_27, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_22_1_27, all_0_2_2) = v0))
% 32.33/11.04  																																																																																|
% 32.33/11.04  																																																																																	| Instantiating formula (21) with all_0_2_2, all_0_4_4, 0, all_28_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields:
% 32.33/11.04  																																																																																	| (200) all_28_0_32 = 0
% 32.33/11.04  																																																																																	|
% 32.33/11.04  																																																																																	| Equations (200) can reduce 86 to:
% 32.33/11.04  																																																																																	| (101) $false
% 32.33/11.04  																																																																																	|
% 32.33/11.04  																																																																																	|-The branch is then unsatisfiable
% 32.33/11.04  																																																																							|-Branch two:
% 32.33/11.04  																																																																							| (574)  ~ (all_345_0_5202 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202
% 32.33/11.04  																																																																							|
% 32.33/11.04  																																																																								| Applying alpha-rule on (574) yields:
% 32.33/11.04  																																																																								| (575)  ~ (all_345_0_5202 = 0)
% 32.33/11.04  																																																																								| (576) distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202
% 32.33/11.04  																																																																								|
% 32.33/11.04  																																																																								| Instantiating formula (25) with all_345_0_5202, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_5_5) = all_345_0_5202, yields:
% 32.33/11.04  																																																																								| (577) all_345_0_5202 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0
% 32.33/11.04  																																																																								|
% 32.33/11.04  																																																																								+-Applying beta-rule and splitting (577), into two cases.
% 32.33/11.04  																																																																								|-Branch one:
% 32.33/11.04  																																																																								| (578) convergent_lines(all_0_5_5, all_0_5_5) = 0
% 32.33/11.04  																																																																								|
% 32.33/11.04  																																																																									| Instantiating formula (38) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields:
% 32.33/11.04  																																																																									| (579) $false
% 32.33/11.04  																																																																									|
% 32.33/11.04  																																																																									|-The branch is then unsatisfiable
% 32.33/11.04  																																																																								|-Branch two:
% 32.33/11.04  																																																																								| (580)  ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0)
% 32.33/11.04  																																																																								| (457) all_345_0_5202 = 0
% 32.33/11.04  																																																																								|
% 32.33/11.04  																																																																									| Equations (457) can reduce 575 to:
% 32.33/11.04  																																																																									| (101) $false
% 32.33/11.04  																																																																									|
% 32.33/11.04  																																																																									|-The branch is then unsatisfiable
% 32.33/11.04  																																																																						|-Branch two:
% 32.33/11.04  																																																																						| (583)  ~ (all_345_0_5202 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202
% 32.33/11.04  																																																																						|
% 32.33/11.04  																																																																							| Applying alpha-rule on (583) yields:
% 32.33/11.04  																																																																							| (575)  ~ (all_345_0_5202 = 0)
% 32.33/11.04  																																																																							| (585) distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202
% 32.33/11.04  																																																																							|
% 32.33/11.04  																																																																							| Instantiating formula (53) with all_0_2_2, all_0_1_1, 0, all_345_0_5202 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_345_0_5202, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 32.33/11.04  																																																																							| (457) all_345_0_5202 = 0
% 32.33/11.04  																																																																							|
% 32.33/11.04  																																																																							| Equations (457) can reduce 575 to:
% 32.33/11.04  																																																																							| (101) $false
% 32.33/11.04  																																																																							|
% 32.33/11.04  																																																																							|-The branch is then unsatisfiable
% 32.33/11.04  											|-Branch two:
% 32.33/11.04  											| (588)  ~ (distinct_points(all_0_2_2, all_0_1_1) = 0)
% 32.33/11.04  											| (229) all_24_0_28 = 0
% 32.33/11.04  											|
% 32.33/11.04  												| Equations (229) can reduce 78 to:
% 32.33/11.04  												| (101) $false
% 32.33/11.04  												|
% 32.33/11.04  												|-The branch is then unsatisfiable
% 32.33/11.04  				|-Branch two:
% 32.33/11.04  				| (591)  ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 32.33/11.04  				|
% 32.33/11.04  					| Applying alpha-rule on (591) yields:
% 32.33/11.04  					| (111)  ~ (all_31_0_35 = 0)
% 32.33/11.04  					| (593) convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 32.33/11.04  					|
% 32.33/11.04  					| Instantiating formula (18) with all_0_5_5, all_0_4_4, all_31_0_35, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 32.33/11.04  					| (594) all_31_0_35 = 0
% 32.33/11.04  					|
% 32.33/11.04  					| Equations (594) can reduce 111 to:
% 32.33/11.04  					| (101) $false
% 32.33/11.04  					|
% 32.33/11.04  					|-The branch is then unsatisfiable
% 32.33/11.04  			|-Branch two:
% 32.33/11.04  			| (596)  ~ (all_34_0_38 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38
% 32.33/11.05  			|
% 32.33/11.05  				| Applying alpha-rule on (596) yields:
% 32.33/11.05  				| (108)  ~ (all_34_0_38 = 0)
% 32.33/11.05  				| (598) convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38
% 32.33/11.05  				|
% 32.33/11.05  				| Instantiating formula (18) with all_0_3_3, all_0_4_4, all_34_0_38, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_34_0_38, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 32.33/11.05  				| (599) all_34_0_38 = 0
% 32.33/11.05  				|
% 32.33/11.05  				| Equations (599) can reduce 108 to:
% 32.33/11.05  				| (101) $false
% 32.33/11.05  				|
% 32.33/11.05  				|-The branch is then unsatisfiable
% 32.33/11.05  		|-Branch two:
% 32.33/11.05  		| (601)  ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 32.33/11.05  		|
% 32.33/11.05  			| Applying alpha-rule on (601) yields:
% 32.33/11.05  			| (105)  ~ (all_30_0_34 = 0)
% 32.33/11.05  			| (603) convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 32.67/11.05  			|
% 32.67/11.05  			| Instantiating formula (18) with all_0_5_5, all_0_4_4, all_30_0_34, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 32.67/11.05  			| (604) all_30_0_34 = 0
% 32.67/11.05  			|
% 32.67/11.05  			| Equations (604) can reduce 105 to:
% 32.67/11.05  			| (101) $false
% 32.67/11.05  			|
% 32.67/11.05  			|-The branch is then unsatisfiable
% 32.67/11.05  |-Branch two:
% 32.67/11.05  | (606)  ~ (all_35_0_39 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39
% 32.67/11.05  |
% 32.67/11.05  	| Applying alpha-rule on (606) yields:
% 32.67/11.05  	| (98)  ~ (all_35_0_39 = 0)
% 32.67/11.05  	| (608) convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39
% 32.67/11.05  	|
% 32.67/11.05  	| Instantiating formula (18) with all_0_3_3, all_0_4_4, all_35_0_39, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_35_0_39, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 32.67/11.05  	| (609) all_35_0_39 = 0
% 32.67/11.05  	|
% 32.67/11.05  	| Equations (609) can reduce 98 to:
% 32.67/11.05  	| (101) $false
% 32.67/11.05  	|
% 32.67/11.05  	|-The branch is then unsatisfiable
% 32.67/11.05  % SZS output end Proof for theBenchmark
% 32.67/11.05  
% 32.67/11.05  10416ms
%------------------------------------------------------------------------------