%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO194+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n005.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 03:48:30 EDT 2022

% Result   : Theorem 5.21s 1.96s
% Output   : Proof 26.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO194+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 11:27:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.59/0.59          ____       _                          
% 0.59/0.59    ___  / __ \_____(_)___  ________  __________
% 0.59/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.59  
% 0.59/0.59  A Theorem Prover for First-Order Logic
% 0.59/0.59  (ePrincess v.1.0)
% 0.59/0.59  
% 0.59/0.59  (c) Philipp Rümmer, 2009-2015
% 0.59/0.59  (c) Peter Backeman, 2014-2015
% 0.59/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.59  Bug reports to peter@backeman.se
% 0.59/0.59  
% 0.59/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.59  
% 0.59/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.94  Prover 0: Preprocessing ...
% 1.89/1.07  Prover 0: Warning: ignoring some quantifiers
% 2.02/1.09  Prover 0: Constructing countermodel ...
% 2.94/1.40  Prover 0: gave up
% 2.94/1.40  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.15/1.42  Prover 1: Preprocessing ...
% 3.41/1.50  Prover 1: Constructing countermodel ...
% 3.41/1.54  Prover 1: gave up
% 3.41/1.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.75/1.56  Prover 2: Preprocessing ...
% 4.13/1.66  Prover 2: Warning: ignoring some quantifiers
% 4.13/1.67  Prover 2: Constructing countermodel ...
% 5.21/1.96  Prover 2: proved (423ms)
% 5.21/1.96  
% 5.21/1.96  No countermodel exists, formula is valid
% 5.21/1.96  % SZS status Theorem for theBenchmark
% 5.21/1.96  
% 5.21/1.96  Generating proof ... Warning: ignoring some quantifiers
% 25.40/7.95  found it (size 497)
% 25.40/7.95  
% 25.40/7.95  % SZS output start Proof for theBenchmark
% 25.40/7.95  Assumed formulas after preprocessing and simplification: 
% 25.40/7.95  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & intersection_point(v0, v2) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v1) = 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)
% 25.61/8.00  | 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:
% 25.61/8.00  | (1)  ~ (all_0_0_0 = 0) & intersection_point(all_0_5_5, all_0_3_3) = 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_4_4) = 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
% 25.61/8.02  |
% 25.61/8.02  | Applying alpha-rule on (1) yields:
% 25.61/8.02  | (2)  ! [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))
% 25.61/8.02  | (3)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 25.61/8.02  | (4)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 25.61/8.02  | (5)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 25.61/8.02  | (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)
% 25.61/8.02  | (7) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2
% 25.61/8.02  | (8)  ! [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)
% 25.61/8.02  | (9)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 25.61/8.02  | (10) convergent_lines(all_0_5_5, all_0_3_3) = 0
% 25.61/8.02  | (11)  ! [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)))
% 25.61/8.03  | (12)  ! [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)
% 25.61/8.03  | (13) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 25.61/8.03  | (14) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 25.61/8.03  | (15)  ! [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)
% 25.61/8.03  | (16)  ! [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)))
% 25.61/8.03  | (17)  ! [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)))
% 25.61/8.03  | (18)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 25.61/8.03  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 25.61/8.03  | (20)  ! [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))
% 25.61/8.03  | (21)  ! [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))
% 25.61/8.03  | (22)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 25.61/8.03  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 25.61/8.03  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 25.61/8.03  | (25)  ! [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)))
% 25.61/8.03  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 25.61/8.03  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.61/8.03  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 25.61/8.03  | (29)  ! [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)))
% 25.61/8.03  | (30)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 25.61/8.03  | (31)  ! [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)))
% 25.61/8.03  | (32)  ! [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)))
% 25.61/8.03  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 25.61/8.03  | (34) apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 25.61/8.04  | (35)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 25.61/8.04  | (36)  ! [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)))
% 25.61/8.04  | (37)  ! [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))
% 25.61/8.04  | (38)  ~ (all_0_0_0 = 0)
% 25.61/8.04  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 25.61/8.04  | (40)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 25.61/8.04  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 25.61/8.04  | (42)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 25.61/8.04  | (43)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 25.61/8.04  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 25.61/8.04  | (45)  ! [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))
% 25.61/8.04  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 25.61/8.04  | (47)  ! [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)))
% 25.61/8.04  | (48)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 25.61/8.04  | (49) intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1
% 25.61/8.04  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.61/8.04  | (51)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 25.61/8.04  | (52)  ! [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)))
% 25.61/8.04  | (53)  ! [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))
% 25.61/8.04  | (54) apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0
% 25.61/8.04  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 25.61/8.04  | (56)  ! [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)))
% 25.61/8.04  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 25.61/8.04  |
% 25.61/8.04  | Instantiating formula (32) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 25.61/8.04  | (58)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 25.61/8.04  |
% 25.61/8.04  | Instantiating formula (56) with all_0_1_1, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_1_1, yields:
% 25.61/8.04  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (32) 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:
% 25.61/8.05  | (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))
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (56) 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:
% 25.61/8.05  | (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))
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (31) with all_0_0_0, all_0_0_0, 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_0_0_0, yields:
% 25.61/8.05  | (62) all_0_0_0 = 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))
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (51) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (35) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (51) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (35) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (51) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating formula (35) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (68) with all_20_0_24, all_20_1_25 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (69) yields:
% 25.61/8.05  | (70)  ~ (all_20_0_24 = 0)
% 25.61/8.05  | (71) intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25
% 25.61/8.05  | (72) apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (65) with all_22_0_26, all_22_1_27 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (73) yields:
% 25.61/8.05  | (74)  ~ (all_22_0_26 = 0)
% 25.61/8.05  | (75) intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27
% 25.61/8.05  | (76) apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (64) with all_24_0_28, all_24_1_29 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (77) yields:
% 25.61/8.05  | (78)  ~ (all_24_0_28 = 0)
% 25.61/8.05  | (79) intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29
% 25.61/8.05  | (80) apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (63) with all_26_0_30, all_26_1_31 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (81) yields:
% 25.61/8.05  | (82)  ~ (all_26_0_30 = 0)
% 25.61/8.05  | (83) intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31
% 25.61/8.05  | (84) apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (67) with all_28_0_32, all_28_1_33 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (85) yields:
% 25.61/8.05  | (86)  ~ (all_28_0_32 = 0)
% 25.61/8.05  | (87) intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33
% 25.61/8.05  | (88) apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (61) with all_30_0_34 yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (60) with all_31_0_35 yields:
% 25.61/8.05  | (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)
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (66) with all_32_0_36, all_32_1_37 yields:
% 25.61/8.05  | (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
% 25.61/8.05  |
% 25.61/8.05  | Applying alpha-rule on (91) yields:
% 25.61/8.05  | (92)  ~ (all_32_0_36 = 0)
% 25.61/8.05  | (93) intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37
% 25.61/8.05  | (94) apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36
% 25.61/8.05  |
% 25.61/8.05  | Instantiating (59) with all_34_0_38 yields:
% 25.61/8.05  | (95) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38)
% 25.61/8.06  |
% 25.61/8.06  | Instantiating (58) with all_35_0_39 yields:
% 25.61/8.06  | (96) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39)
% 25.61/8.06  |
% 25.61/8.06  +-Applying beta-rule and splitting (96), into two cases.
% 25.61/8.06  |-Branch one:
% 25.61/8.06  | (97)  ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_35_0_39
% 25.61/8.06  |
% 25.61/8.06  	| Applying alpha-rule on (97) yields:
% 25.61/8.06  	| (98)  ~ (all_35_0_39 = 0)
% 25.61/8.06  	| (99) apart_point_and_line(all_0_1_1, all_0_3_3) = all_35_0_39
% 25.61/8.06  	|
% 25.61/8.06  	+-Applying beta-rule and splitting (62), into two cases.
% 25.61/8.06  	|-Branch one:
% 25.61/8.06  	| (100) all_0_0_0 = 0
% 25.61/8.06  	|
% 25.61/8.06  		| Equations (100) can reduce 38 to:
% 25.61/8.06  		| (101) $false
% 25.61/8.06  		|
% 25.61/8.06  		|-The branch is then unsatisfiable
% 25.61/8.06  	|-Branch two:
% 25.61/8.06  	| (38)  ~ (all_0_0_0 = 0)
% 25.61/8.06  	| (103)  ? [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))
% 25.61/8.06  	|
% 25.61/8.06  		+-Applying beta-rule and splitting (89), into two cases.
% 25.61/8.06  		|-Branch one:
% 25.61/8.06  		| (104)  ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 25.61/8.06  		|
% 25.61/8.06  			| Applying alpha-rule on (104) yields:
% 25.61/8.06  			| (105)  ~ (all_30_0_34 = 0)
% 25.61/8.06  			| (106) apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 25.61/8.06  			|
% 25.61/8.06  			+-Applying beta-rule and splitting (95), into two cases.
% 25.61/8.06  			|-Branch one:
% 25.61/8.06  			| (107)  ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_34_0_38
% 25.61/8.06  			|
% 25.61/8.06  				| Applying alpha-rule on (107) yields:
% 25.61/8.06  				| (108)  ~ (all_34_0_38 = 0)
% 25.61/8.06  				| (109) apart_point_and_line(all_0_1_1, all_0_5_5) = all_34_0_38
% 25.61/8.06  				|
% 25.61/8.06  				+-Applying beta-rule and splitting (90), into two cases.
% 25.61/8.06  				|-Branch one:
% 25.61/8.06  				| (110)  ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 26.00/8.06  				|
% 26.00/8.06  					| Applying alpha-rule on (110) yields:
% 26.00/8.06  					| (111)  ~ (all_31_0_35 = 0)
% 26.00/8.06  					| (112) apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (24) 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:
% 26.00/8.06  					| (113) all_26_1_31 = all_24_1_29
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (24) with all_0_5_5, all_0_3_3, all_32_1_37, all_0_1_1 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_0_1_1, yields:
% 26.00/8.06  					| (114) all_32_1_37 = all_0_1_1
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (24) 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:
% 26.00/8.06  					| (115) all_32_1_37 = all_22_1_27
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (24) 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:
% 26.00/8.06  					| (116) all_28_1_33 = all_0_2_2
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (24) 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:
% 26.00/8.06  					| (117) all_28_1_33 = all_20_1_25
% 26.00/8.06  					|
% 26.00/8.06  					| Combining equations (115,114) yields a new equation:
% 26.00/8.06  					| (118) all_22_1_27 = all_0_1_1
% 26.00/8.06  					|
% 26.00/8.06  					| Simplifying 118 yields:
% 26.00/8.06  					| (119) all_22_1_27 = all_0_1_1
% 26.00/8.06  					|
% 26.00/8.06  					| Combining equations (116,117) yields a new equation:
% 26.00/8.06  					| (120) all_20_1_25 = all_0_2_2
% 26.00/8.06  					|
% 26.00/8.06  					| Combining equations (120,117) yields a new equation:
% 26.00/8.06  					| (116) all_28_1_33 = all_0_2_2
% 26.00/8.06  					|
% 26.00/8.06  					| From (114) and (94) follows:
% 26.00/8.06  					| (122) apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36
% 26.00/8.06  					|
% 26.00/8.06  					| From (116) and (88) follows:
% 26.00/8.06  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 26.00/8.06  					|
% 26.00/8.06  					| From (113) and (84) follows:
% 26.00/8.06  					| (124) apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30
% 26.00/8.06  					|
% 26.00/8.06  					| From (119) and (76) follows:
% 26.00/8.06  					| (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_22_0_26
% 26.00/8.06  					|
% 26.00/8.06  					| From (120) and (72) follows:
% 26.00/8.06  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (28) with all_0_1_1, all_0_3_3, all_22_0_26, all_35_0_39 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_35_0_39, apart_point_and_line(all_0_1_1, all_0_3_3) = all_22_0_26, yields:
% 26.00/8.06  					| (127) all_35_0_39 = all_22_0_26
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (28) with all_0_1_1, all_0_5_5, all_32_0_36, all_34_0_38 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_34_0_38, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.00/8.06  					| (128) all_34_0_38 = all_32_0_36
% 26.00/8.06  					|
% 26.00/8.06  					| Instantiating formula (28) 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:
% 26.00/8.07  					| (129) all_31_0_35 = all_28_0_32
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (28) 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:
% 26.00/8.07  					| (130) all_30_0_34 = all_20_0_24
% 26.00/8.07  					|
% 26.00/8.07  					| Equations (127) can reduce 98 to:
% 26.00/8.07  					| (74)  ~ (all_22_0_26 = 0)
% 26.00/8.07  					|
% 26.00/8.07  					| Equations (128) can reduce 108 to:
% 26.00/8.07  					| (92)  ~ (all_32_0_36 = 0)
% 26.00/8.07  					|
% 26.00/8.07  					| Equations (129) can reduce 111 to:
% 26.00/8.07  					| (86)  ~ (all_28_0_32 = 0)
% 26.00/8.07  					|
% 26.00/8.07  					| Equations (130) can reduce 105 to:
% 26.00/8.07  					| (70)  ~ (all_20_0_24 = 0)
% 26.00/8.07  					|
% 26.00/8.07  					| From (127) and (99) follows:
% 26.00/8.07  					| (125) apart_point_and_line(all_0_1_1, all_0_3_3) = all_22_0_26
% 26.00/8.07  					|
% 26.00/8.07  					| From (128) and (109) follows:
% 26.00/8.07  					| (122) apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36
% 26.00/8.07  					|
% 26.00/8.07  					| From (129) and (112) follows:
% 26.00/8.07  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 26.00/8.07  					|
% 26.00/8.07  					| From (130) and (106) follows:
% 26.00/8.07  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_24_0_28, all_0_0_0, all_0_3_3, all_0_4_4, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (139) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_0_0_0, all_24_0_28, all_0_4_4, all_0_3_3, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (140) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (17) with all_24_0_28, all_0_0_0, all_0_4_4, all_0_3_3, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (141) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (17) with all_0_0_0, all_24_0_28, all_0_3_3, all_0_4_4, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (142) all_24_0_28 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_24_0_28, all_24_0_28, all_0_3_3, all_0_3_3, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, yields:
% 26.00/8.07  					| (143) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_26_0_30, all_0_0_0, all_0_4_4, all_0_4_4, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (144) all_26_0_30 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_24_1_29) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_0_0_0, all_26_0_30, all_0_4_4, all_0_4_4, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.00/8.07  					| (145) all_26_0_30 = 0 | all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_26_0_30, all_24_0_28, all_0_4_4, all_0_3_3, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 26.00/8.07  					| (146) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.00/8.07  					|
% 26.00/8.07  					| Instantiating formula (31) with all_24_0_28, all_26_0_30, all_0_3_3, all_0_4_4, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 26.00/8.07  					| (147) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_26_0_30, all_26_0_30, all_0_4_4, all_0_4_4, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 26.08/8.08  					| (148) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_22_0_26, all_0_0_0, 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_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.08/8.08  					| (149) all_22_0_26 = 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_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))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_0_0_0, all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, yields:
% 26.08/8.08  					| (150) all_22_0_26 = 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_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))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (12) with all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 26.08/8.08  					| (151) all_22_0_26 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_22_0_26, all_24_0_28, all_0_3_3, all_0_3_3, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_3_3) = all_22_0_26, yields:
% 26.08/8.08  					| (152) all_24_0_28 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (17) with all_26_0_30, all_22_0_26, all_0_3_3, all_0_4_4, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_3_3) = all_22_0_26, yields:
% 26.08/8.08  					| (153) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_22_0_26, all_22_0_26, 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_22_0_26, yields:
% 26.08/8.08  					| (154) all_22_0_26 = 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))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_32_0_36, all_0_0_0, 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_0_0_0, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.08  					| (155) all_32_0_36 = 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))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_0_0_0, all_32_0_36, 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_0_0_0, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.08  					| (156) all_32_0_36 = 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))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_32_0_36, all_24_0_28, all_0_5_5, all_0_3_3, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.08  					| (157) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (31) with all_24_0_28, all_32_0_36, all_0_3_3, all_0_5_5, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.08  					| (158) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (17) with all_32_0_36, all_24_0_28, all_0_3_3, all_0_5_5, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.08  					| (159) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.08  					|
% 26.08/8.08  					| Instantiating formula (17) with all_24_0_28, all_32_0_36, all_0_5_5, all_0_3_3, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (160) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_32_0_36, all_26_0_30, all_0_5_5, all_0_4_4, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (161) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_26_0_30, all_32_0_36, all_0_4_4, all_0_5_5, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (162) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_24_1_29) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (17) with all_32_0_36, all_26_0_30, all_0_4_4, all_0_5_5, all_0_1_1, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (163) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (17) with all_26_0_30, all_32_0_36, all_0_5_5, all_0_4_4, all_24_1_29, all_0_1_1 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (164) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_24_1_29) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_22_0_26, all_32_0_36, 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_22_0_26, apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, yields:
% 26.08/8.09  					| (165) all_32_0_36 = 0 | all_22_0_26 = 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))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_32_0_36, all_32_0_36, 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_32_0_36, yields:
% 26.08/8.09  					| (166) all_32_0_36 = 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))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_28_0_32, all_0_0_0, 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_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.09  					| (167) 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_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))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_28_0_32, all_24_0_28, all_0_4_4, all_0_3_3, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.09  					| (168) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_24_0_28, all_28_0_32, all_0_3_3, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.09  					| (169) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (17) with all_28_0_32, all_24_0_28, all_0_3_3, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.09  					| (170) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.09  					|
% 26.08/8.09  					| Instantiating formula (31) with all_28_0_32, all_26_0_30, all_0_4_4, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.10  					| (171) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_28_0_32, all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (172) all_28_0_32 = 0 | all_22_0_26 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (173) all_28_0_32 = 0 | all_22_0_26 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (17) with all_28_0_32, all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (174) all_28_0_32 = 0 | all_22_0_26 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_28_0_32, all_32_0_36, 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_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (175) all_32_0_36 = 0 | all_28_0_32 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_32_0_36, 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_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (176) all_32_0_36 = 0 | all_28_0_32 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (17) with all_28_0_32, all_32_0_36, 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_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 26.08/8.10  					| (177) all_32_0_36 = 0 | all_28_0_32 = 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) 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:
% 26.08/8.10  					| (178) 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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_20_0_24, 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_4_4) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.10  					| (179) 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_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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_0_0_0, 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_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.10  					| (180) 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_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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (17) with all_20_0_24, 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_4_4) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.10  					| (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_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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (17) with all_0_0_0, 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_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.10  					| (182) 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_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))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_20_0_24, all_24_0_28, all_0_5_5, all_0_3_3, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.10  					| (183) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (31) with all_24_0_28, all_20_0_24, all_0_3_3, all_0_5_5, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.10  					| (184) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.10  					|
% 26.08/8.10  					| Instantiating formula (17) with all_20_0_24, all_24_0_28, all_0_3_3, all_0_5_5, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (185) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (17) with all_24_0_28, all_20_0_24, all_0_5_5, all_0_3_3, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (186) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_20_0_24, all_26_0_30, all_0_5_5, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (187) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_26_0_30, all_20_0_24, all_0_4_4, all_0_5_5, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (188) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (17) with all_20_0_24, all_26_0_30, all_0_4_4, all_0_5_5, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (189) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (17) with all_26_0_30, all_20_0_24, all_0_5_5, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, 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:
% 26.08/8.11  					| (190) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_20_0_24, all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.11  					| (191) all_22_0_26 = 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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.11  					| (192) all_22_0_26 = 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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (17) with all_20_0_24, all_22_0_26, 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_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.11  					| (193) all_22_0_26 = 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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_20_0_24, all_32_0_36, 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_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.11  					| (194) all_32_0_36 = 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_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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) with all_32_0_36, all_20_0_24, all_0_5_5, 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_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 26.08/8.11  					| (195) all_32_0_36 = 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_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_1_1) = v0))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) 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:
% 26.08/8.11  					| (196) 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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) 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:
% 26.08/8.11  					| (197) 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))
% 26.08/8.11  					|
% 26.08/8.11  					| Instantiating formula (31) 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:
% 26.08/8.11  					| (198) 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))
% 26.08/8.11  					|
% 26.08/8.11  					+-Applying beta-rule and splitting (148), into two cases.
% 26.08/8.11  					|-Branch one:
% 26.08/8.11  					| (199) all_26_0_30 = 0
% 26.08/8.11  					|
% 26.08/8.11  						| Equations (199) can reduce 82 to:
% 26.08/8.11  						| (101) $false
% 26.08/8.11  						|
% 26.08/8.11  						|-The branch is then unsatisfiable
% 26.08/8.11  					|-Branch two:
% 26.08/8.11  					| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.11  					| (202)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.11  					|
% 26.08/8.11  						+-Applying beta-rule and splitting (178), into two cases.
% 26.08/8.11  						|-Branch one:
% 26.08/8.11  						| (203) all_28_0_32 = 0
% 26.08/8.11  						|
% 26.08/8.11  							| Equations (203) can reduce 86 to:
% 26.08/8.11  							| (101) $false
% 26.08/8.11  							|
% 26.08/8.11  							|-The branch is then unsatisfiable
% 26.08/8.11  						|-Branch two:
% 26.08/8.11  						| (86)  ~ (all_28_0_32 = 0)
% 26.08/8.11  						| (206)  ? [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))
% 26.08/8.11  						|
% 26.08/8.11  							+-Applying beta-rule and splitting (145), into two cases.
% 26.08/8.11  							|-Branch one:
% 26.08/8.11  							| (199) all_26_0_30 = 0
% 26.08/8.11  							|
% 26.08/8.11  								| Equations (199) can reduce 82 to:
% 26.08/8.11  								| (101) $false
% 26.08/8.12  								|
% 26.08/8.12  								|-The branch is then unsatisfiable
% 26.08/8.12  							|-Branch two:
% 26.08/8.12  							| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.12  							| (210) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.08/8.12  							|
% 26.08/8.12  								+-Applying beta-rule and splitting (140), into two cases.
% 26.08/8.12  								|-Branch one:
% 26.08/8.12  								| (211) all_24_0_28 = 0
% 26.08/8.12  								|
% 26.08/8.12  									| Equations (211) can reduce 78 to:
% 26.08/8.12  									| (101) $false
% 26.08/8.12  									|
% 26.08/8.12  									|-The branch is then unsatisfiable
% 26.08/8.12  								|-Branch two:
% 26.08/8.12  								| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.12  								| (214) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.12  								|
% 26.08/8.12  									+-Applying beta-rule and splitting (141), into two cases.
% 26.08/8.12  									|-Branch one:
% 26.08/8.12  									| (211) all_24_0_28 = 0
% 26.08/8.12  									|
% 26.08/8.12  										| Equations (211) can reduce 78 to:
% 26.08/8.12  										| (101) $false
% 26.08/8.12  										|
% 26.08/8.12  										|-The branch is then unsatisfiable
% 26.08/8.12  									|-Branch two:
% 26.08/8.12  									| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.12  									| (218) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.12  									|
% 26.08/8.12  										+-Applying beta-rule and splitting (146), into two cases.
% 26.08/8.12  										|-Branch one:
% 26.08/8.12  										| (199) all_26_0_30 = 0
% 26.08/8.12  										|
% 26.08/8.12  											| Equations (199) can reduce 82 to:
% 26.08/8.12  											| (101) $false
% 26.08/8.12  											|
% 26.08/8.12  											|-The branch is then unsatisfiable
% 26.08/8.12  										|-Branch two:
% 26.08/8.12  										| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.12  										| (222) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.12  										|
% 26.08/8.12  											+-Applying beta-rule and splitting (151), into two cases.
% 26.08/8.12  											|-Branch one:
% 26.08/8.12  											| (223) distinct_points(all_0_2_2, all_0_1_1) = 0
% 26.08/8.12  											|
% 26.08/8.12  												+-Applying beta-rule and splitting (166), into two cases.
% 26.08/8.12  												|-Branch one:
% 26.08/8.12  												| (224) all_32_0_36 = 0
% 26.08/8.12  												|
% 26.08/8.12  													| Equations (224) can reduce 92 to:
% 26.08/8.12  													| (101) $false
% 26.08/8.12  													|
% 26.08/8.12  													|-The branch is then unsatisfiable
% 26.08/8.12  												|-Branch two:
% 26.08/8.12  												| (92)  ~ (all_32_0_36 = 0)
% 26.08/8.12  												| (227)  ? [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))
% 26.08/8.12  												|
% 26.08/8.12  													+-Applying beta-rule and splitting (147), into two cases.
% 26.08/8.12  													|-Branch one:
% 26.08/8.12  													| (199) all_26_0_30 = 0
% 26.08/8.12  													|
% 26.08/8.12  														| Equations (199) can reduce 82 to:
% 26.08/8.12  														| (101) $false
% 26.08/8.12  														|
% 26.08/8.12  														|-The branch is then unsatisfiable
% 26.08/8.12  													|-Branch two:
% 26.08/8.12  													| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.12  													| (231) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.12  													|
% 26.08/8.12  														+-Applying beta-rule and splitting (152), into two cases.
% 26.08/8.12  														|-Branch one:
% 26.08/8.12  														| (211) all_24_0_28 = 0
% 26.08/8.12  														|
% 26.08/8.12  															| Equations (211) can reduce 78 to:
% 26.08/8.12  															| (101) $false
% 26.08/8.12  															|
% 26.08/8.12  															|-The branch is then unsatisfiable
% 26.08/8.12  														|-Branch two:
% 26.08/8.12  														| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.12  														| (235) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.12  														|
% 26.08/8.12  															+-Applying beta-rule and splitting (185), into two cases.
% 26.08/8.12  															|-Branch one:
% 26.08/8.12  															| (211) all_24_0_28 = 0
% 26.08/8.12  															|
% 26.08/8.12  																| Equations (211) can reduce 78 to:
% 26.08/8.12  																| (101) $false
% 26.08/8.12  																|
% 26.08/8.12  																|-The branch is then unsatisfiable
% 26.08/8.12  															|-Branch two:
% 26.08/8.12  															| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.12  															| (239) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.12  															|
% 26.08/8.12  																+-Applying beta-rule and splitting (149), into two cases.
% 26.08/8.12  																|-Branch one:
% 26.08/8.12  																| (240) all_22_0_26 = 0
% 26.08/8.12  																|
% 26.08/8.12  																	| Equations (240) can reduce 74 to:
% 26.08/8.12  																	| (101) $false
% 26.08/8.12  																	|
% 26.08/8.12  																	|-The branch is then unsatisfiable
% 26.08/8.12  																|-Branch two:
% 26.08/8.12  																| (74)  ~ (all_22_0_26 = 0)
% 26.08/8.12  																| (243) 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_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))
% 26.08/8.12  																|
% 26.08/8.12  																	+-Applying beta-rule and splitting (150), into two cases.
% 26.08/8.12  																	|-Branch one:
% 26.08/8.12  																	| (240) all_22_0_26 = 0
% 26.08/8.12  																	|
% 26.08/8.12  																		| Equations (240) can reduce 74 to:
% 26.08/8.12  																		| (101) $false
% 26.08/8.12  																		|
% 26.08/8.12  																		|-The branch is then unsatisfiable
% 26.08/8.12  																	|-Branch two:
% 26.08/8.12  																	| (74)  ~ (all_22_0_26 = 0)
% 26.08/8.12  																	| (247) 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_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))
% 26.08/8.12  																	|
% 26.08/8.12  																		+-Applying beta-rule and splitting (186), into two cases.
% 26.08/8.12  																		|-Branch one:
% 26.08/8.12  																		| (211) all_24_0_28 = 0
% 26.08/8.12  																		|
% 26.08/8.12  																			| Equations (211) can reduce 78 to:
% 26.08/8.12  																			| (101) $false
% 26.08/8.12  																			|
% 26.08/8.12  																			|-The branch is then unsatisfiable
% 26.08/8.12  																		|-Branch two:
% 26.08/8.12  																		| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.12  																		| (251) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.12  																		|
% 26.08/8.12  																			+-Applying beta-rule and splitting (182), into two cases.
% 26.08/8.12  																			|-Branch one:
% 26.08/8.12  																			| (252) all_20_0_24 = 0
% 26.08/8.12  																			|
% 26.08/8.12  																				| Equations (252) can reduce 70 to:
% 26.08/8.12  																				| (101) $false
% 26.08/8.12  																				|
% 26.08/8.12  																				|-The branch is then unsatisfiable
% 26.08/8.12  																			|-Branch two:
% 26.08/8.12  																			| (70)  ~ (all_20_0_24 = 0)
% 26.08/8.12  																			| (255) 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_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))
% 26.08/8.12  																			|
% 26.08/8.12  																				+-Applying beta-rule and splitting (187), into two cases.
% 26.08/8.12  																				|-Branch one:
% 26.08/8.12  																				| (199) all_26_0_30 = 0
% 26.08/8.12  																				|
% 26.08/8.12  																					| Equations (199) can reduce 82 to:
% 26.08/8.12  																					| (101) $false
% 26.08/8.12  																					|
% 26.08/8.12  																					|-The branch is then unsatisfiable
% 26.08/8.12  																				|-Branch two:
% 26.08/8.12  																				| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.12  																				| (259) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.12  																				|
% 26.08/8.12  																					+-Applying beta-rule and splitting (188), into two cases.
% 26.08/8.12  																					|-Branch one:
% 26.08/8.12  																					| (199) all_26_0_30 = 0
% 26.08/8.12  																					|
% 26.08/8.12  																						| Equations (199) can reduce 82 to:
% 26.08/8.12  																						| (101) $false
% 26.08/8.12  																						|
% 26.08/8.12  																						|-The branch is then unsatisfiable
% 26.08/8.12  																					|-Branch two:
% 26.08/8.12  																					| (82)  ~ (all_26_0_30 = 0)
% 26.08/8.12  																					| (263) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.12  																					|
% 26.08/8.12  																						+-Applying beta-rule and splitting (210), into two cases.
% 26.08/8.12  																						|-Branch one:
% 26.08/8.12  																						| (100) all_0_0_0 = 0
% 26.08/8.12  																						|
% 26.08/8.12  																							| Equations (100) can reduce 38 to:
% 26.08/8.12  																							| (101) $false
% 26.08/8.12  																							|
% 26.08/8.12  																							|-The branch is then unsatisfiable
% 26.08/8.12  																						|-Branch two:
% 26.08/8.12  																						| (38)  ~ (all_0_0_0 = 0)
% 26.08/8.12  																						| (267)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.08/8.12  																						|
% 26.08/8.12  																							+-Applying beta-rule and splitting (214), into two cases.
% 26.08/8.12  																							|-Branch one:
% 26.08/8.12  																							| (100) all_0_0_0 = 0
% 26.08/8.12  																							|
% 26.08/8.12  																								| Equations (100) can reduce 38 to:
% 26.08/8.12  																								| (101) $false
% 26.08/8.12  																								|
% 26.08/8.12  																								|-The branch is then unsatisfiable
% 26.08/8.12  																							|-Branch two:
% 26.08/8.12  																							| (38)  ~ (all_0_0_0 = 0)
% 26.08/8.12  																							| (271)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.08/8.13  																							|
% 26.08/8.13  																								+-Applying beta-rule and splitting (218), into two cases.
% 26.08/8.13  																								|-Branch one:
% 26.08/8.13  																								| (100) all_0_0_0 = 0
% 26.08/8.13  																								|
% 26.08/8.13  																									| Equations (100) can reduce 38 to:
% 26.08/8.13  																									| (101) $false
% 26.08/8.13  																									|
% 26.08/8.13  																									|-The branch is then unsatisfiable
% 26.08/8.13  																								|-Branch two:
% 26.08/8.13  																								| (38)  ~ (all_0_0_0 = 0)
% 26.08/8.13  																								| (275)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.13  																								|
% 26.08/8.13  																									+-Applying beta-rule and splitting (222), into two cases.
% 26.08/8.13  																									|-Branch one:
% 26.08/8.13  																									| (211) all_24_0_28 = 0
% 26.08/8.13  																									|
% 26.08/8.13  																										| Equations (211) can reduce 78 to:
% 26.08/8.13  																										| (101) $false
% 26.08/8.13  																										|
% 26.08/8.13  																										|-The branch is then unsatisfiable
% 26.08/8.13  																									|-Branch two:
% 26.08/8.13  																									| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.13  																									| (279)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.08/8.13  																									|
% 26.08/8.13  																										+-Applying beta-rule and splitting (183), into two cases.
% 26.08/8.13  																										|-Branch one:
% 26.08/8.13  																										| (211) all_24_0_28 = 0
% 26.08/8.13  																										|
% 26.08/8.13  																											| Equations (211) can reduce 78 to:
% 26.08/8.13  																											| (101) $false
% 26.08/8.13  																											|
% 26.08/8.13  																											|-The branch is then unsatisfiable
% 26.08/8.13  																										|-Branch two:
% 26.08/8.13  																										| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.13  																										| (283) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.08/8.13  																										|
% 26.08/8.13  																											+-Applying beta-rule and splitting (184), into two cases.
% 26.08/8.13  																											|-Branch one:
% 26.08/8.13  																											| (211) all_24_0_28 = 0
% 26.08/8.13  																											|
% 26.08/8.13  																												| Equations (211) can reduce 78 to:
% 26.08/8.13  																												| (101) $false
% 26.08/8.13  																												|
% 26.08/8.13  																												|-The branch is then unsatisfiable
% 26.08/8.13  																											|-Branch two:
% 26.08/8.13  																											| (78)  ~ (all_24_0_28 = 0)
% 26.08/8.13  																											| (287) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.08/8.13  																											|
% 26.08/8.13  																												+-Applying beta-rule and splitting (181), into two cases.
% 26.08/8.13  																												|-Branch one:
% 26.08/8.13  																												| (252) all_20_0_24 = 0
% 26.08/8.13  																												|
% 26.08/8.13  																													| Equations (252) can reduce 70 to:
% 26.08/8.13  																													| (101) $false
% 26.08/8.13  																													|
% 26.08/8.13  																													|-The branch is then unsatisfiable
% 26.08/8.13  																												|-Branch two:
% 26.08/8.13  																												| (70)  ~ (all_20_0_24 = 0)
% 26.08/8.13  																												| (291) 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_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))
% 26.08/8.13  																												|
% 26.08/8.13  																													+-Applying beta-rule and splitting (154), into two cases.
% 26.08/8.13  																													|-Branch one:
% 26.08/8.13  																													| (240) all_22_0_26 = 0
% 26.08/8.13  																													|
% 26.08/8.13  																														| Equations (240) can reduce 74 to:
% 26.08/8.13  																														| (101) $false
% 26.08/8.13  																														|
% 26.08/8.13  																														|-The branch is then unsatisfiable
% 26.08/8.13  																													|-Branch two:
% 26.08/8.13  																													| (74)  ~ (all_22_0_26 = 0)
% 26.08/8.13  																													| (295)  ? [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))
% 26.08/8.13  																													|
% 26.08/8.13  																														+-Applying beta-rule and splitting (198), into two cases.
% 26.08/8.13  																														|-Branch one:
% 26.08/8.13  																														| (252) all_20_0_24 = 0
% 26.08/8.13  																														|
% 26.08/8.13  																															| Equations (252) can reduce 70 to:
% 26.08/8.13  																															| (101) $false
% 26.08/8.13  																															|
% 26.08/8.13  																															|-The branch is then unsatisfiable
% 26.08/8.13  																														|-Branch two:
% 26.08/8.13  																														| (70)  ~ (all_20_0_24 = 0)
% 26.08/8.13  																														| (299)  ? [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))
% 26.08/8.13  																														|
% 26.08/8.13  																															+-Applying beta-rule and splitting (197), into two cases.
% 26.08/8.13  																															|-Branch one:
% 26.08/8.13  																															| (203) all_28_0_32 = 0
% 26.08/8.13  																															|
% 26.08/8.13  																																| Equations (203) can reduce 86 to:
% 26.08/8.13  																																| (101) $false
% 26.08/8.13  																																|
% 26.08/8.13  																																|-The branch is then unsatisfiable
% 26.08/8.13  																															|-Branch two:
% 26.08/8.13  																															| (86)  ~ (all_28_0_32 = 0)
% 26.08/8.13  																															| (303) 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))
% 26.08/8.13  																															|
% 26.08/8.13  																																+-Applying beta-rule and splitting (155), into two cases.
% 26.08/8.13  																																|-Branch one:
% 26.08/8.13  																																| (224) all_32_0_36 = 0
% 26.08/8.13  																																|
% 26.08/8.13  																																	| Equations (224) can reduce 92 to:
% 26.08/8.13  																																	| (101) $false
% 26.08/8.13  																																	|
% 26.08/8.13  																																	|-The branch is then unsatisfiable
% 26.08/8.13  																																|-Branch two:
% 26.08/8.13  																																| (92)  ~ (all_32_0_36 = 0)
% 26.08/8.13  																																| (307) 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))
% 26.35/8.13  																																|
% 26.35/8.13  																																	+-Applying beta-rule and splitting (156), into two cases.
% 26.35/8.13  																																	|-Branch one:
% 26.35/8.13  																																	| (224) all_32_0_36 = 0
% 26.35/8.13  																																	|
% 26.35/8.13  																																		| Equations (224) can reduce 92 to:
% 26.35/8.13  																																		| (101) $false
% 26.35/8.13  																																		|
% 26.35/8.13  																																		|-The branch is then unsatisfiable
% 26.35/8.13  																																	|-Branch two:
% 26.35/8.13  																																	| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																	| (311) 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))
% 26.35/8.13  																																	|
% 26.35/8.13  																																		+-Applying beta-rule and splitting (161), into two cases.
% 26.35/8.13  																																		|-Branch one:
% 26.35/8.13  																																		| (224) all_32_0_36 = 0
% 26.35/8.13  																																		|
% 26.35/8.13  																																			| Equations (224) can reduce 92 to:
% 26.35/8.13  																																			| (101) $false
% 26.35/8.13  																																			|
% 26.35/8.13  																																			|-The branch is then unsatisfiable
% 26.35/8.13  																																		|-Branch two:
% 26.35/8.13  																																		| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																		| (315) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.35/8.13  																																		|
% 26.35/8.13  																																			+-Applying beta-rule and splitting (162), into two cases.
% 26.35/8.13  																																			|-Branch one:
% 26.35/8.13  																																			| (224) all_32_0_36 = 0
% 26.35/8.13  																																			|
% 26.35/8.13  																																				| Equations (224) can reduce 92 to:
% 26.35/8.13  																																				| (101) $false
% 26.35/8.13  																																				|
% 26.35/8.13  																																				|-The branch is then unsatisfiable
% 26.35/8.13  																																			|-Branch two:
% 26.35/8.13  																																			| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																			| (319) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_24_1_29) = v0))
% 26.35/8.13  																																			|
% 26.35/8.13  																																				+-Applying beta-rule and splitting (157), into two cases.
% 26.35/8.13  																																				|-Branch one:
% 26.35/8.13  																																				| (224) all_32_0_36 = 0
% 26.35/8.13  																																				|
% 26.35/8.13  																																					| Equations (224) can reduce 92 to:
% 26.35/8.13  																																					| (101) $false
% 26.35/8.13  																																					|
% 26.35/8.13  																																					|-The branch is then unsatisfiable
% 26.35/8.13  																																				|-Branch two:
% 26.35/8.13  																																				| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																				| (323) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.35/8.13  																																				|
% 26.35/8.13  																																					+-Applying beta-rule and splitting (180), into two cases.
% 26.35/8.13  																																					|-Branch one:
% 26.35/8.13  																																					| (252) all_20_0_24 = 0
% 26.35/8.13  																																					|
% 26.35/8.13  																																						| Equations (252) can reduce 70 to:
% 26.35/8.13  																																						| (101) $false
% 26.35/8.13  																																						|
% 26.35/8.13  																																						|-The branch is then unsatisfiable
% 26.35/8.13  																																					|-Branch two:
% 26.35/8.13  																																					| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.13  																																					| (327) 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_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))
% 26.35/8.13  																																					|
% 26.35/8.13  																																						+-Applying beta-rule and splitting (158), into two cases.
% 26.35/8.13  																																						|-Branch one:
% 26.35/8.13  																																						| (224) all_32_0_36 = 0
% 26.35/8.13  																																						|
% 26.35/8.13  																																							| Equations (224) can reduce 92 to:
% 26.35/8.13  																																							| (101) $false
% 26.35/8.13  																																							|
% 26.35/8.13  																																							|-The branch is then unsatisfiable
% 26.35/8.13  																																						|-Branch two:
% 26.35/8.13  																																						| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																						| (331) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.13  																																						|
% 26.35/8.13  																																							+-Applying beta-rule and splitting (159), into two cases.
% 26.35/8.13  																																							|-Branch one:
% 26.35/8.13  																																							| (224) all_32_0_36 = 0
% 26.35/8.13  																																							|
% 26.35/8.13  																																								| Equations (224) can reduce 92 to:
% 26.35/8.13  																																								| (101) $false
% 26.35/8.13  																																								|
% 26.35/8.13  																																								|-The branch is then unsatisfiable
% 26.35/8.13  																																							|-Branch two:
% 26.35/8.13  																																							| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																							| (335) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.35/8.13  																																							|
% 26.35/8.13  																																								+-Applying beta-rule and splitting (160), into two cases.
% 26.35/8.13  																																								|-Branch one:
% 26.35/8.13  																																								| (224) all_32_0_36 = 0
% 26.35/8.13  																																								|
% 26.35/8.13  																																									| Equations (224) can reduce 92 to:
% 26.35/8.13  																																									| (101) $false
% 26.35/8.13  																																									|
% 26.35/8.13  																																									|-The branch is then unsatisfiable
% 26.35/8.13  																																								|-Branch two:
% 26.35/8.13  																																								| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																								| (339) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.13  																																								|
% 26.35/8.13  																																									+-Applying beta-rule and splitting (163), into two cases.
% 26.35/8.13  																																									|-Branch one:
% 26.35/8.13  																																									| (224) all_32_0_36 = 0
% 26.35/8.13  																																									|
% 26.35/8.13  																																										| Equations (224) can reduce 92 to:
% 26.35/8.13  																																										| (101) $false
% 26.35/8.13  																																										|
% 26.35/8.13  																																										|-The branch is then unsatisfiable
% 26.35/8.13  																																									|-Branch two:
% 26.35/8.13  																																									| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.13  																																									| (343) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.35/8.13  																																									|
% 26.35/8.13  																																										+-Applying beta-rule and splitting (164), into two cases.
% 26.35/8.13  																																										|-Branch one:
% 26.35/8.13  																																										| (224) all_32_0_36 = 0
% 26.35/8.13  																																										|
% 26.35/8.14  																																											| Equations (224) can reduce 92 to:
% 26.35/8.14  																																											| (101) $false
% 26.35/8.14  																																											|
% 26.35/8.14  																																											|-The branch is then unsatisfiable
% 26.35/8.14  																																										|-Branch two:
% 26.35/8.14  																																										| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.14  																																										| (347) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_24_1_29) = v0))
% 26.35/8.14  																																										|
% 26.35/8.14  																																											+-Applying beta-rule and splitting (196), into two cases.
% 26.35/8.14  																																											|-Branch one:
% 26.35/8.14  																																											| (203) all_28_0_32 = 0
% 26.35/8.14  																																											|
% 26.35/8.14  																																												| Equations (203) can reduce 86 to:
% 26.35/8.14  																																												| (101) $false
% 26.35/8.14  																																												|
% 26.35/8.14  																																												|-The branch is then unsatisfiable
% 26.35/8.14  																																											|-Branch two:
% 26.35/8.14  																																											| (86)  ~ (all_28_0_32 = 0)
% 26.35/8.14  																																											| (351) 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))
% 26.35/8.14  																																											|
% 26.35/8.14  																																												+-Applying beta-rule and splitting (167), into two cases.
% 26.35/8.14  																																												|-Branch one:
% 26.35/8.14  																																												| (203) all_28_0_32 = 0
% 26.35/8.14  																																												|
% 26.35/8.14  																																													| Equations (203) can reduce 86 to:
% 26.35/8.14  																																													| (101) $false
% 26.35/8.14  																																													|
% 26.35/8.14  																																													|-The branch is then unsatisfiable
% 26.35/8.14  																																												|-Branch two:
% 26.35/8.14  																																												| (86)  ~ (all_28_0_32 = 0)
% 26.35/8.14  																																												| (355) 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_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))
% 26.35/8.14  																																												|
% 26.35/8.14  																																													+-Applying beta-rule and splitting (231), into two cases.
% 26.35/8.14  																																													|-Branch one:
% 26.35/8.14  																																													| (211) all_24_0_28 = 0
% 26.35/8.14  																																													|
% 26.35/8.14  																																														| Equations (211) can reduce 78 to:
% 26.35/8.14  																																														| (101) $false
% 26.35/8.14  																																														|
% 26.35/8.14  																																														|-The branch is then unsatisfiable
% 26.35/8.14  																																													|-Branch two:
% 26.35/8.14  																																													| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.14  																																													| (359)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.35/8.14  																																													|
% 26.35/8.14  																																														+-Applying beta-rule and splitting (235), into two cases.
% 26.35/8.14  																																														|-Branch one:
% 26.35/8.14  																																														| (240) all_22_0_26 = 0
% 26.35/8.14  																																														|
% 26.35/8.14  																																															| Equations (240) can reduce 74 to:
% 26.35/8.14  																																															| (101) $false
% 26.35/8.14  																																															|
% 26.35/8.14  																																															|-The branch is then unsatisfiable
% 26.35/8.14  																																														|-Branch two:
% 26.35/8.14  																																														| (74)  ~ (all_22_0_26 = 0)
% 26.35/8.14  																																														| (363)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.35/8.14  																																														|
% 26.35/8.14  																																															+-Applying beta-rule and splitting (239), into two cases.
% 26.35/8.14  																																															|-Branch one:
% 26.35/8.14  																																															| (252) all_20_0_24 = 0
% 26.35/8.14  																																															|
% 26.35/8.14  																																																| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																| (101) $false
% 26.35/8.14  																																																|
% 26.35/8.14  																																																|-The branch is then unsatisfiable
% 26.35/8.14  																																															|-Branch two:
% 26.35/8.14  																																															| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																															| (367)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.35/8.14  																																															|
% 26.35/8.14  																																																+-Applying beta-rule and splitting (243), into two cases.
% 26.35/8.14  																																																|-Branch one:
% 26.35/8.14  																																																| (100) all_0_0_0 = 0
% 26.35/8.14  																																																|
% 26.35/8.14  																																																	| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																	| (101) $false
% 26.35/8.14  																																																	|
% 26.35/8.14  																																																	|-The branch is then unsatisfiable
% 26.35/8.14  																																																|-Branch two:
% 26.35/8.14  																																																| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																| (371)  ? [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))
% 26.35/8.14  																																																|
% 26.35/8.14  																																																	+-Applying beta-rule and splitting (247), into two cases.
% 26.35/8.14  																																																	|-Branch one:
% 26.35/8.14  																																																	| (100) all_0_0_0 = 0
% 26.35/8.14  																																																	|
% 26.35/8.14  																																																		| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																		| (101) $false
% 26.35/8.14  																																																		|
% 26.35/8.14  																																																		|-The branch is then unsatisfiable
% 26.35/8.14  																																																	|-Branch two:
% 26.35/8.14  																																																	| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																	| (375)  ? [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))
% 26.35/8.14  																																																	|
% 26.35/8.14  																																																		+-Applying beta-rule and splitting (251), into two cases.
% 26.35/8.14  																																																		|-Branch one:
% 26.35/8.14  																																																		| (252) all_20_0_24 = 0
% 26.35/8.14  																																																		|
% 26.35/8.14  																																																			| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																			| (101) $false
% 26.35/8.14  																																																			|
% 26.35/8.14  																																																			|-The branch is then unsatisfiable
% 26.35/8.14  																																																		|-Branch two:
% 26.35/8.14  																																																		| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																																		| (379)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.14  																																																		|
% 26.35/8.14  																																																			+-Applying beta-rule and splitting (259), into two cases.
% 26.35/8.14  																																																			|-Branch one:
% 26.35/8.14  																																																			| (252) all_20_0_24 = 0
% 26.35/8.14  																																																			|
% 26.35/8.14  																																																				| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																				| (101) $false
% 26.35/8.14  																																																				|
% 26.35/8.14  																																																				|-The branch is then unsatisfiable
% 26.35/8.14  																																																			|-Branch two:
% 26.35/8.14  																																																			| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																																			| (383)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.35/8.14  																																																			|
% 26.35/8.14  																																																				+-Applying beta-rule and splitting (263), into two cases.
% 26.35/8.14  																																																				|-Branch one:
% 26.35/8.14  																																																				| (252) all_20_0_24 = 0
% 26.35/8.14  																																																				|
% 26.35/8.14  																																																					| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																					| (101) $false
% 26.35/8.14  																																																					|
% 26.35/8.14  																																																					|-The branch is then unsatisfiable
% 26.35/8.14  																																																				|-Branch two:
% 26.35/8.14  																																																				| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																																				| (387)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.14  																																																				|
% 26.35/8.14  																																																					+-Applying beta-rule and splitting (287), into two cases.
% 26.35/8.14  																																																					|-Branch one:
% 26.35/8.14  																																																					| (252) all_20_0_24 = 0
% 26.35/8.14  																																																					|
% 26.35/8.14  																																																						| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																						| (101) $false
% 26.35/8.14  																																																						|
% 26.35/8.14  																																																						|-The branch is then unsatisfiable
% 26.35/8.14  																																																					|-Branch two:
% 26.35/8.14  																																																					| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																																					| (391)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.14  																																																					|
% 26.35/8.14  																																																						+-Applying beta-rule and splitting (291), into two cases.
% 26.35/8.14  																																																						|-Branch one:
% 26.35/8.14  																																																						| (100) all_0_0_0 = 0
% 26.35/8.14  																																																						|
% 26.35/8.14  																																																							| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																							| (101) $false
% 26.35/8.14  																																																							|
% 26.35/8.14  																																																							|-The branch is then unsatisfiable
% 26.35/8.14  																																																						|-Branch two:
% 26.35/8.14  																																																						| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																						| (395)  ? [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))
% 26.35/8.14  																																																						|
% 26.35/8.14  																																																							+-Applying beta-rule and splitting (303), into two cases.
% 26.35/8.14  																																																							|-Branch one:
% 26.35/8.14  																																																							| (252) all_20_0_24 = 0
% 26.35/8.14  																																																							|
% 26.35/8.14  																																																								| Equations (252) can reduce 70 to:
% 26.35/8.14  																																																								| (101) $false
% 26.35/8.14  																																																								|
% 26.35/8.14  																																																								|-The branch is then unsatisfiable
% 26.35/8.14  																																																							|-Branch two:
% 26.35/8.14  																																																							| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.14  																																																							| (399)  ? [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))
% 26.35/8.14  																																																							|
% 26.35/8.14  																																																								+-Applying beta-rule and splitting (307), into two cases.
% 26.35/8.14  																																																								|-Branch one:
% 26.35/8.14  																																																								| (100) all_0_0_0 = 0
% 26.35/8.14  																																																								|
% 26.35/8.14  																																																									| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																									| (101) $false
% 26.35/8.14  																																																									|
% 26.35/8.14  																																																									|-The branch is then unsatisfiable
% 26.35/8.14  																																																								|-Branch two:
% 26.35/8.14  																																																								| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																								| (403)  ? [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))
% 26.35/8.14  																																																								|
% 26.35/8.14  																																																									+-Applying beta-rule and splitting (311), into two cases.
% 26.35/8.14  																																																									|-Branch one:
% 26.35/8.14  																																																									| (100) all_0_0_0 = 0
% 26.35/8.14  																																																									|
% 26.35/8.14  																																																										| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																										| (101) $false
% 26.35/8.14  																																																										|
% 26.35/8.14  																																																										|-The branch is then unsatisfiable
% 26.35/8.14  																																																									|-Branch two:
% 26.35/8.14  																																																									| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																									| (407)  ? [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))
% 26.35/8.14  																																																									|
% 26.35/8.14  																																																										+-Applying beta-rule and splitting (323), into two cases.
% 26.35/8.14  																																																										|-Branch one:
% 26.35/8.14  																																																										| (211) all_24_0_28 = 0
% 26.35/8.14  																																																										|
% 26.35/8.14  																																																											| Equations (211) can reduce 78 to:
% 26.35/8.14  																																																											| (101) $false
% 26.35/8.14  																																																											|
% 26.35/8.14  																																																											|-The branch is then unsatisfiable
% 26.35/8.14  																																																										|-Branch two:
% 26.35/8.14  																																																										| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.14  																																																										| (411)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.35/8.14  																																																										|
% 26.35/8.14  																																																											+-Applying beta-rule and splitting (327), into two cases.
% 26.35/8.14  																																																											|-Branch one:
% 26.35/8.14  																																																											| (100) all_0_0_0 = 0
% 26.35/8.14  																																																											|
% 26.35/8.14  																																																												| Equations (100) can reduce 38 to:
% 26.35/8.14  																																																												| (101) $false
% 26.35/8.14  																																																												|
% 26.35/8.14  																																																												|-The branch is then unsatisfiable
% 26.35/8.14  																																																											|-Branch two:
% 26.35/8.14  																																																											| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.14  																																																											| (415)  ? [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))
% 26.35/8.14  																																																											|
% 26.35/8.14  																																																												+-Applying beta-rule and splitting (331), into two cases.
% 26.35/8.14  																																																												|-Branch one:
% 26.35/8.14  																																																												| (211) all_24_0_28 = 0
% 26.35/8.14  																																																												|
% 26.35/8.14  																																																													| Equations (211) can reduce 78 to:
% 26.35/8.14  																																																													| (101) $false
% 26.35/8.14  																																																													|
% 26.35/8.14  																																																													|-The branch is then unsatisfiable
% 26.35/8.14  																																																												|-Branch two:
% 26.35/8.14  																																																												| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.14  																																																												| (419)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.14  																																																												|
% 26.35/8.14  																																																													+-Applying beta-rule and splitting (335), into two cases.
% 26.35/8.14  																																																													|-Branch one:
% 26.35/8.14  																																																													| (211) all_24_0_28 = 0
% 26.35/8.14  																																																													|
% 26.35/8.14  																																																														| Equations (211) can reduce 78 to:
% 26.35/8.14  																																																														| (101) $false
% 26.35/8.14  																																																														|
% 26.35/8.14  																																																														|-The branch is then unsatisfiable
% 26.35/8.14  																																																													|-Branch two:
% 26.35/8.14  																																																													| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.14  																																																													| (423)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.35/8.14  																																																													|
% 26.35/8.15  																																																														+-Applying beta-rule and splitting (355), into two cases.
% 26.35/8.15  																																																														|-Branch one:
% 26.35/8.15  																																																														| (100) all_0_0_0 = 0
% 26.35/8.15  																																																														|
% 26.35/8.15  																																																															| Equations (100) can reduce 38 to:
% 26.35/8.15  																																																															| (101) $false
% 26.35/8.15  																																																															|
% 26.35/8.15  																																																															|-The branch is then unsatisfiable
% 26.35/8.15  																																																														|-Branch two:
% 26.35/8.15  																																																														| (38)  ~ (all_0_0_0 = 0)
% 26.35/8.15  																																																														| (427)  ? [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))
% 26.35/8.15  																																																														|
% 26.35/8.15  																																																															+-Applying beta-rule and splitting (143), into two cases.
% 26.35/8.15  																																																															|-Branch one:
% 26.35/8.15  																																																															| (211) all_24_0_28 = 0
% 26.35/8.15  																																																															|
% 26.35/8.15  																																																																| Equations (211) can reduce 78 to:
% 26.35/8.15  																																																																| (101) $false
% 26.35/8.15  																																																																|
% 26.35/8.15  																																																																|-The branch is then unsatisfiable
% 26.35/8.15  																																																															|-Branch two:
% 26.35/8.15  																																																															| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.15  																																																															| (431)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 26.35/8.15  																																																															|
% 26.35/8.15  																																																																+-Applying beta-rule and splitting (139), into two cases.
% 26.35/8.15  																																																																|-Branch one:
% 26.35/8.15  																																																																| (211) all_24_0_28 = 0
% 26.35/8.15  																																																																|
% 26.35/8.15  																																																																	| Equations (211) can reduce 78 to:
% 26.35/8.15  																																																																	| (101) $false
% 26.35/8.15  																																																																	|
% 26.35/8.15  																																																																	|-The branch is then unsatisfiable
% 26.35/8.15  																																																																|-Branch two:
% 26.35/8.15  																																																																| (78)  ~ (all_24_0_28 = 0)
% 26.35/8.15  																																																																| (435) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.15  																																																																|
% 26.35/8.15  																																																																	+-Applying beta-rule and splitting (144), into two cases.
% 26.35/8.15  																																																																	|-Branch one:
% 26.35/8.15  																																																																	| (199) all_26_0_30 = 0
% 26.35/8.15  																																																																	|
% 26.35/8.15  																																																																		| Equations (199) can reduce 82 to:
% 26.35/8.15  																																																																		| (101) $false
% 26.35/8.15  																																																																		|
% 26.35/8.15  																																																																		|-The branch is then unsatisfiable
% 26.35/8.15  																																																																	|-Branch two:
% 26.35/8.15  																																																																	| (82)  ~ (all_26_0_30 = 0)
% 26.35/8.15  																																																																	| (439) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_24_1_29) = v0))
% 26.35/8.15  																																																																	|
% 26.35/8.15  																																																																		+-Applying beta-rule and splitting (177), into two cases.
% 26.35/8.15  																																																																		|-Branch one:
% 26.35/8.15  																																																																		| (224) all_32_0_36 = 0
% 26.35/8.15  																																																																		|
% 26.35/8.15  																																																																			| Equations (224) can reduce 92 to:
% 26.35/8.15  																																																																			| (101) $false
% 26.35/8.15  																																																																			|
% 26.35/8.15  																																																																			|-The branch is then unsatisfiable
% 26.35/8.15  																																																																		|-Branch two:
% 26.35/8.15  																																																																		| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.15  																																																																		| (443) all_28_0_32 = 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))
% 26.35/8.15  																																																																		|
% 26.35/8.15  																																																																			+-Applying beta-rule and splitting (168), into two cases.
% 26.35/8.15  																																																																			|-Branch one:
% 26.35/8.15  																																																																			| (203) all_28_0_32 = 0
% 26.35/8.15  																																																																			|
% 26.35/8.15  																																																																				| Equations (203) can reduce 86 to:
% 26.35/8.15  																																																																				| (101) $false
% 26.35/8.15  																																																																				|
% 26.35/8.15  																																																																				|-The branch is then unsatisfiable
% 26.35/8.15  																																																																			|-Branch two:
% 26.35/8.15  																																																																			| (86)  ~ (all_28_0_32 = 0)
% 26.35/8.15  																																																																			| (447) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.35/8.15  																																																																			|
% 26.35/8.15  																																																																				+-Applying beta-rule and splitting (169), into two cases.
% 26.35/8.15  																																																																				|-Branch one:
% 26.35/8.15  																																																																				| (203) all_28_0_32 = 0
% 26.35/8.15  																																																																				|
% 26.35/8.15  																																																																					| Equations (203) can reduce 86 to:
% 26.35/8.15  																																																																					| (101) $false
% 26.35/8.15  																																																																					|
% 26.35/8.15  																																																																					|-The branch is then unsatisfiable
% 26.35/8.15  																																																																				|-Branch two:
% 26.35/8.15  																																																																				| (86)  ~ (all_28_0_32 = 0)
% 26.35/8.15  																																																																				| (451) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.35/8.15  																																																																				|
% 26.35/8.15  																																																																					+-Applying beta-rule and splitting (175), into two cases.
% 26.35/8.15  																																																																					|-Branch one:
% 26.35/8.15  																																																																					| (224) all_32_0_36 = 0
% 26.35/8.15  																																																																					|
% 26.35/8.15  																																																																						| Equations (224) can reduce 92 to:
% 26.35/8.15  																																																																						| (101) $false
% 26.35/8.15  																																																																						|
% 26.35/8.15  																																																																						|-The branch is then unsatisfiable
% 26.35/8.15  																																																																					|-Branch two:
% 26.35/8.15  																																																																					| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.15  																																																																					| (455) all_28_0_32 = 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))
% 26.35/8.15  																																																																					|
% 26.35/8.15  																																																																						+-Applying beta-rule and splitting (176), into two cases.
% 26.35/8.15  																																																																						|-Branch one:
% 26.35/8.15  																																																																						| (224) all_32_0_36 = 0
% 26.35/8.15  																																																																						|
% 26.35/8.15  																																																																							| Equations (224) can reduce 92 to:
% 26.35/8.15  																																																																							| (101) $false
% 26.35/8.15  																																																																							|
% 26.35/8.15  																																																																							|-The branch is then unsatisfiable
% 26.35/8.15  																																																																						|-Branch two:
% 26.35/8.15  																																																																						| (92)  ~ (all_32_0_36 = 0)
% 26.35/8.15  																																																																						| (459) all_28_0_32 = 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))
% 26.35/8.15  																																																																						|
% 26.35/8.15  																																																																							+-Applying beta-rule and splitting (179), into two cases.
% 26.35/8.15  																																																																							|-Branch one:
% 26.35/8.15  																																																																							| (252) all_20_0_24 = 0
% 26.35/8.15  																																																																							|
% 26.35/8.15  																																																																								| Equations (252) can reduce 70 to:
% 26.35/8.15  																																																																								| (101) $false
% 26.35/8.15  																																																																								|
% 26.35/8.15  																																																																								|-The branch is then unsatisfiable
% 26.35/8.15  																																																																							|-Branch two:
% 26.35/8.15  																																																																							| (70)  ~ (all_20_0_24 = 0)
% 26.35/8.15  																																																																							| (463) 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_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))
% 26.35/8.15  																																																																							|
% 26.35/8.15  																																																																								+-Applying beta-rule and splitting (315), into two cases.
% 26.35/8.15  																																																																								|-Branch one:
% 26.35/8.15  																																																																								| (199) all_26_0_30 = 0
% 26.35/8.15  																																																																								|
% 26.35/8.15  																																																																									| Equations (199) can reduce 82 to:
% 26.35/8.15  																																																																									| (101) $false
% 26.35/8.15  																																																																									|
% 26.35/8.15  																																																																									|-The branch is then unsatisfiable
% 26.35/8.15  																																																																								|-Branch two:
% 26.35/8.15  																																																																								| (82)  ~ (all_26_0_30 = 0)
% 26.35/8.15  																																																																								| (467)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 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_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_1_1) = v0))
% 26.35/8.15  																																																																								|
% 26.35/8.15  																																																																									+-Applying beta-rule and splitting (319), into two cases.
% 26.35/8.15  																																																																									|-Branch one:
% 26.35/8.15  																																																																									| (199) all_26_0_30 = 0
% 26.35/8.15  																																																																									|
% 26.35/8.15  																																																																										| Equations (199) can reduce 82 to:
% 26.35/8.15  																																																																										| (101) $false
% 26.35/8.15  																																																																										|
% 26.35/8.15  																																																																										|-The branch is then unsatisfiable
% 26.35/8.15  																																																																									|-Branch two:
% 26.35/8.15  																																																																									| (82)  ~ (all_26_0_30 = 0)
% 26.35/8.15  																																																																									| (471)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, 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_24_1_29) = v0))
% 26.35/8.15  																																																																									|
% 26.35/8.15  																																																																										+-Applying beta-rule and splitting (153), into two cases.
% 26.35/8.15  																																																																										|-Branch one:
% 26.35/8.15  																																																																										| (199) all_26_0_30 = 0
% 26.35/8.15  																																																																										|
% 26.35/8.15  																																																																											| Equations (199) can reduce 82 to:
% 26.35/8.15  																																																																											| (101) $false
% 26.35/8.15  																																																																											|
% 26.35/8.15  																																																																											|-The branch is then unsatisfiable
% 26.35/8.15  																																																																										|-Branch two:
% 26.45/8.15  																																																																										| (82)  ~ (all_26_0_30 = 0)
% 26.45/8.15  																																																																										| (475) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.45/8.15  																																																																										|
% 26.45/8.15  																																																																											+-Applying beta-rule and splitting (165), into two cases.
% 26.45/8.15  																																																																											|-Branch one:
% 26.45/8.15  																																																																											| (224) all_32_0_36 = 0
% 26.45/8.15  																																																																											|
% 26.45/8.15  																																																																												| Equations (224) can reduce 92 to:
% 26.45/8.15  																																																																												| (101) $false
% 26.45/8.15  																																																																												|
% 26.45/8.15  																																																																												|-The branch is then unsatisfiable
% 26.45/8.15  																																																																											|-Branch two:
% 26.45/8.15  																																																																											| (92)  ~ (all_32_0_36 = 0)
% 26.45/8.15  																																																																											| (479) all_22_0_26 = 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))
% 26.45/8.15  																																																																											|
% 26.45/8.15  																																																																												+-Applying beta-rule and splitting (142), into two cases.
% 26.45/8.15  																																																																												|-Branch one:
% 26.45/8.15  																																																																												| (211) all_24_0_28 = 0
% 26.45/8.15  																																																																												|
% 26.45/8.15  																																																																													| Equations (211) can reduce 78 to:
% 26.45/8.15  																																																																													| (101) $false
% 26.45/8.15  																																																																													|
% 26.45/8.15  																																																																													|-The branch is then unsatisfiable
% 26.45/8.15  																																																																												|-Branch two:
% 26.45/8.15  																																																																												| (78)  ~ (all_24_0_28 = 0)
% 26.45/8.15  																																																																												| (483) all_0_0_0 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.45/8.15  																																																																												|
% 26.45/8.15  																																																																													+-Applying beta-rule and splitting (172), into two cases.
% 26.45/8.15  																																																																													|-Branch one:
% 26.45/8.15  																																																																													| (203) all_28_0_32 = 0
% 26.45/8.15  																																																																													|
% 26.45/8.15  																																																																														| Equations (203) can reduce 86 to:
% 26.45/8.15  																																																																														| (101) $false
% 26.45/8.15  																																																																														|
% 26.45/8.15  																																																																														|-The branch is then unsatisfiable
% 26.45/8.15  																																																																													|-Branch two:
% 26.45/8.15  																																																																													| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.15  																																																																													| (487) all_22_0_26 = 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))
% 26.45/8.15  																																																																													|
% 26.45/8.15  																																																																														+-Applying beta-rule and splitting (173), into two cases.
% 26.45/8.15  																																																																														|-Branch one:
% 26.45/8.15  																																																																														| (203) all_28_0_32 = 0
% 26.45/8.15  																																																																														|
% 26.45/8.15  																																																																															| Equations (203) can reduce 86 to:
% 26.45/8.15  																																																																															| (101) $false
% 26.45/8.15  																																																																															|
% 26.45/8.15  																																																																															|-The branch is then unsatisfiable
% 26.45/8.15  																																																																														|-Branch two:
% 26.45/8.15  																																																																														| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.15  																																																																														| (491) all_22_0_26 = 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))
% 26.45/8.15  																																																																														|
% 26.45/8.15  																																																																															+-Applying beta-rule and splitting (170), into two cases.
% 26.45/8.15  																																																																															|-Branch one:
% 26.45/8.15  																																																																															| (203) all_28_0_32 = 0
% 26.45/8.15  																																																																															|
% 26.45/8.16  																																																																																| Equations (203) can reduce 86 to:
% 26.45/8.16  																																																																																| (101) $false
% 26.45/8.16  																																																																																|
% 26.45/8.16  																																																																																|-The branch is then unsatisfiable
% 26.45/8.16  																																																																															|-Branch two:
% 26.45/8.16  																																																																															| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.16  																																																																															| (495) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.45/8.16  																																																																															|
% 26.45/8.16  																																																																																+-Applying beta-rule and splitting (171), into two cases.
% 26.45/8.16  																																																																																|-Branch one:
% 26.45/8.16  																																																																																| (203) all_28_0_32 = 0
% 26.45/8.16  																																																																																|
% 26.45/8.16  																																																																																	| Equations (203) can reduce 86 to:
% 26.45/8.16  																																																																																	| (101) $false
% 26.45/8.16  																																																																																	|
% 26.45/8.16  																																																																																	|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																|-Branch two:
% 26.45/8.16  																																																																																| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.16  																																																																																| (499) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.45/8.16  																																																																																|
% 26.45/8.16  																																																																																	+-Applying beta-rule and splitting (193), into two cases.
% 26.45/8.16  																																																																																	|-Branch one:
% 26.45/8.16  																																																																																	| (240) all_22_0_26 = 0
% 26.45/8.16  																																																																																	|
% 26.45/8.16  																																																																																		| Equations (240) can reduce 74 to:
% 26.45/8.16  																																																																																		| (101) $false
% 26.45/8.16  																																																																																		|
% 26.45/8.16  																																																																																		|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																	|-Branch two:
% 26.45/8.16  																																																																																	| (74)  ~ (all_22_0_26 = 0)
% 26.45/8.16  																																																																																	| (503) 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))
% 26.45/8.16  																																																																																	|
% 26.45/8.16  																																																																																		+-Applying beta-rule and splitting (189), into two cases.
% 26.45/8.16  																																																																																		|-Branch one:
% 26.45/8.16  																																																																																		| (199) all_26_0_30 = 0
% 26.45/8.16  																																																																																		|
% 26.45/8.16  																																																																																			| Equations (199) can reduce 82 to:
% 26.45/8.16  																																																																																			| (101) $false
% 26.45/8.16  																																																																																			|
% 26.45/8.16  																																																																																			|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																		|-Branch two:
% 26.45/8.16  																																																																																		| (82)  ~ (all_26_0_30 = 0)
% 26.45/8.16  																																																																																		| (507) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.45/8.16  																																																																																		|
% 26.45/8.16  																																																																																			+-Applying beta-rule and splitting (190), into two cases.
% 26.45/8.16  																																																																																			|-Branch one:
% 26.45/8.16  																																																																																			| (199) all_26_0_30 = 0
% 26.45/8.16  																																																																																			|
% 26.45/8.16  																																																																																				| Equations (199) can reduce 82 to:
% 26.45/8.16  																																																																																				| (101) $false
% 26.45/8.16  																																																																																				|
% 26.45/8.16  																																																																																				|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																			|-Branch two:
% 26.45/8.16  																																																																																			| (82)  ~ (all_26_0_30 = 0)
% 26.45/8.16  																																																																																			| (511) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.45/8.16  																																																																																			|
% 26.45/8.16  																																																																																				+-Applying beta-rule and splitting (191), into two cases.
% 26.45/8.16  																																																																																				|-Branch one:
% 26.45/8.16  																																																																																				| (240) all_22_0_26 = 0
% 26.45/8.16  																																																																																				|
% 26.45/8.16  																																																																																					| Equations (240) can reduce 74 to:
% 26.45/8.16  																																																																																					| (101) $false
% 26.45/8.16  																																																																																					|
% 26.45/8.16  																																																																																					|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																				|-Branch two:
% 26.45/8.16  																																																																																				| (74)  ~ (all_22_0_26 = 0)
% 26.45/8.16  																																																																																				| (515) 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))
% 26.45/8.16  																																																																																				|
% 26.45/8.16  																																																																																					+-Applying beta-rule and splitting (192), into two cases.
% 26.45/8.16  																																																																																					|-Branch one:
% 26.45/8.16  																																																																																					| (240) all_22_0_26 = 0
% 26.45/8.16  																																																																																					|
% 26.45/8.16  																																																																																						| Equations (240) can reduce 74 to:
% 26.45/8.16  																																																																																						| (101) $false
% 26.45/8.16  																																																																																						|
% 26.45/8.16  																																																																																						|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																					|-Branch two:
% 26.45/8.16  																																																																																					| (74)  ~ (all_22_0_26 = 0)
% 26.45/8.16  																																																																																					| (519) 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))
% 26.45/8.16  																																																																																					|
% 26.45/8.16  																																																																																						+-Applying beta-rule and splitting (194), into two cases.
% 26.45/8.16  																																																																																						|-Branch one:
% 26.45/8.16  																																																																																						| (224) all_32_0_36 = 0
% 26.45/8.16  																																																																																						|
% 26.45/8.16  																																																																																							| Equations (224) can reduce 92 to:
% 26.45/8.16  																																																																																							| (101) $false
% 26.45/8.16  																																																																																							|
% 26.45/8.16  																																																																																							|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																						|-Branch two:
% 26.45/8.16  																																																																																						| (92)  ~ (all_32_0_36 = 0)
% 26.45/8.16  																																																																																						| (523) 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_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))
% 26.45/8.16  																																																																																						|
% 26.45/8.16  																																																																																							+-Applying beta-rule and splitting (195), into two cases.
% 26.45/8.16  																																																																																							|-Branch one:
% 26.45/8.16  																																																																																							| (224) all_32_0_36 = 0
% 26.45/8.16  																																																																																							|
% 26.45/8.16  																																																																																								| Equations (224) can reduce 92 to:
% 26.45/8.16  																																																																																								| (101) $false
% 26.45/8.16  																																																																																								|
% 26.45/8.16  																																																																																								|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																							|-Branch two:
% 26.45/8.16  																																																																																							| (92)  ~ (all_32_0_36 = 0)
% 26.45/8.16  																																																																																							| (527) 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_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_1_1) = v0))
% 26.45/8.16  																																																																																							|
% 26.45/8.16  																																																																																								+-Applying beta-rule and splitting (174), into two cases.
% 26.45/8.16  																																																																																								|-Branch one:
% 26.45/8.16  																																																																																								| (203) all_28_0_32 = 0
% 26.45/8.16  																																																																																								|
% 26.45/8.16  																																																																																									| Equations (203) can reduce 86 to:
% 26.45/8.16  																																																																																									| (101) $false
% 26.45/8.16  																																																																																									|
% 26.45/8.16  																																																																																									|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																								|-Branch two:
% 26.45/8.16  																																																																																								| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.16  																																																																																								| (531) all_22_0_26 = 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))
% 26.45/8.16  																																																																																								|
% 26.45/8.16  																																																																																									+-Applying beta-rule and splitting (255), into two cases.
% 26.45/8.16  																																																																																									|-Branch one:
% 26.45/8.16  																																																																																									| (100) all_0_0_0 = 0
% 26.45/8.16  																																																																																									|
% 26.45/8.16  																																																																																										| Equations (100) can reduce 38 to:
% 26.45/8.16  																																																																																										| (101) $false
% 26.45/8.16  																																																																																										|
% 26.45/8.16  																																																																																										|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																									|-Branch two:
% 26.45/8.16  																																																																																									| (38)  ~ (all_0_0_0 = 0)
% 26.45/8.16  																																																																																									| (535)  ? [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))
% 26.45/8.16  																																																																																									|
% 26.45/8.16  																																																																																										| Instantiating (535) with all_393_0_3637 yields:
% 26.45/8.16  																																																																																										| (536) (all_393_0_3637 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_393_0_3637 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_393_0_3637 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637) | ( ~ (all_393_0_3637 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_393_0_3637)
% 26.45/8.16  																																																																																										|
% 26.45/8.16  																																																																																										+-Applying beta-rule and splitting (283), into two cases.
% 26.45/8.16  																																																																																										|-Branch one:
% 26.45/8.16  																																																																																										| (252) all_20_0_24 = 0
% 26.45/8.16  																																																																																										|
% 26.45/8.16  																																																																																											| Equations (252) can reduce 70 to:
% 26.45/8.16  																																																																																											| (101) $false
% 26.45/8.16  																																																																																											|
% 26.45/8.16  																																																																																											|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																										|-Branch two:
% 26.45/8.16  																																																																																										| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.16  																																																																																										| (540)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.45/8.16  																																																																																										|
% 26.45/8.16  																																																																																											+-Applying beta-rule and splitting (351), into two cases.
% 26.45/8.16  																																																																																											|-Branch one:
% 26.45/8.16  																																																																																											| (252) all_20_0_24 = 0
% 26.45/8.16  																																																																																											|
% 26.45/8.16  																																																																																												| Equations (252) can reduce 70 to:
% 26.45/8.16  																																																																																												| (101) $false
% 26.45/8.16  																																																																																												|
% 26.45/8.16  																																																																																												|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																											|-Branch two:
% 26.45/8.16  																																																																																											| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.16  																																																																																											| (544)  ? [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))
% 26.45/8.16  																																																																																											|
% 26.45/8.16  																																																																																												+-Applying beta-rule and splitting (463), into two cases.
% 26.45/8.16  																																																																																												|-Branch one:
% 26.45/8.16  																																																																																												| (100) all_0_0_0 = 0
% 26.45/8.16  																																																																																												|
% 26.45/8.16  																																																																																													| Equations (100) can reduce 38 to:
% 26.45/8.16  																																																																																													| (101) $false
% 26.45/8.16  																																																																																													|
% 26.45/8.16  																																																																																													|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																												|-Branch two:
% 26.45/8.16  																																																																																												| (38)  ~ (all_0_0_0 = 0)
% 26.45/8.16  																																																																																												| (548)  ? [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))
% 26.45/8.16  																																																																																												|
% 26.45/8.16  																																																																																													+-Applying beta-rule and splitting (536), into two cases.
% 26.45/8.16  																																																																																													|-Branch one:
% 26.45/8.16  																																																																																													| (549) (all_393_0_3637 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_393_0_3637 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_393_0_3637 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637)
% 26.45/8.16  																																																																																													|
% 26.45/8.16  																																																																																														+-Applying beta-rule and splitting (549), into two cases.
% 26.45/8.16  																																																																																														|-Branch one:
% 26.45/8.16  																																																																																														| (550) (all_393_0_3637 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_393_0_3637 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0)
% 26.45/8.16  																																																																																														|
% 26.45/8.16  																																																																																															+-Applying beta-rule and splitting (550), into two cases.
% 26.45/8.16  																																																																																															|-Branch one:
% 26.45/8.16  																																																																																															| (551) all_393_0_3637 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 26.45/8.16  																																																																																															|
% 26.45/8.16  																																																																																																| Applying alpha-rule on (551) yields:
% 26.45/8.16  																																																																																																| (552) all_393_0_3637 = 0
% 26.45/8.16  																																																																																																| (553) apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																| Instantiating formula (28) with all_0_1_1, all_0_5_5, 0, all_32_0_36 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields:
% 26.45/8.16  																																																																																																| (224) all_32_0_36 = 0
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																| Equations (224) can reduce 92 to:
% 26.45/8.16  																																																																																																| (101) $false
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																															|-Branch two:
% 26.45/8.16  																																																																																															| (556) all_393_0_3637 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 26.45/8.16  																																																																																															|
% 26.45/8.16  																																																																																																| Applying alpha-rule on (556) yields:
% 26.45/8.16  																																																																																																| (552) all_393_0_3637 = 0
% 26.45/8.16  																																																																																																| (558) apart_point_and_line(all_0_2_2, all_0_4_4) = 0
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																+-Applying beta-rule and splitting (443), into two cases.
% 26.45/8.16  																																																																																																|-Branch one:
% 26.45/8.16  																																																																																																| (203) all_28_0_32 = 0
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																	| Equations (203) can reduce 86 to:
% 26.45/8.16  																																																																																																	| (101) $false
% 26.45/8.16  																																																																																																	|
% 26.45/8.16  																																																																																																	|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																																|-Branch two:
% 26.45/8.16  																																																																																																| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.16  																																																																																																| (562)  ? [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))
% 26.45/8.16  																																																																																																|
% 26.45/8.16  																																																																																																	+-Applying beta-rule and splitting (455), into two cases.
% 26.45/8.16  																																																																																																	|-Branch one:
% 26.45/8.16  																																																																																																	| (203) all_28_0_32 = 0
% 26.45/8.16  																																																																																																	|
% 26.45/8.16  																																																																																																		| Equations (203) can reduce 86 to:
% 26.45/8.16  																																																																																																		| (101) $false
% 26.45/8.16  																																																																																																		|
% 26.45/8.16  																																																																																																		|-The branch is then unsatisfiable
% 26.45/8.16  																																																																																																	|-Branch two:
% 26.45/8.16  																																																																																																	| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.17  																																																																																																	| (566)  ? [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))
% 26.45/8.17  																																																																																																	|
% 26.45/8.17  																																																																																																		+-Applying beta-rule and splitting (459), into two cases.
% 26.45/8.17  																																																																																																		|-Branch one:
% 26.45/8.17  																																																																																																		| (203) all_28_0_32 = 0
% 26.45/8.17  																																																																																																		|
% 26.45/8.17  																																																																																																			| Equations (203) can reduce 86 to:
% 26.45/8.17  																																																																																																			| (101) $false
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																			|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																		|-Branch two:
% 26.45/8.17  																																																																																																		| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.17  																																																																																																		| (570)  ? [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))
% 26.45/8.17  																																																																																																		|
% 26.45/8.17  																																																																																																			| Instantiating formula (28) 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:
% 26.45/8.17  																																																																																																			| (203) all_28_0_32 = 0
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																			| Equations (203) can reduce 86 to:
% 26.45/8.17  																																																																																																			| (101) $false
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																			|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																														|-Branch two:
% 26.45/8.17  																																																																																														| (573)  ~ (all_393_0_3637 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637
% 26.45/8.17  																																																																																														|
% 26.45/8.17  																																																																																															| Applying alpha-rule on (573) yields:
% 26.45/8.17  																																																																																															| (574)  ~ (all_393_0_3637 = 0)
% 26.45/8.17  																																																																																															| (575) distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637
% 26.45/8.17  																																																																																															|
% 26.45/8.17  																																																																																															+-Applying beta-rule and splitting (435), into two cases.
% 26.45/8.17  																																																																																															|-Branch one:
% 26.45/8.17  																																																																																															| (100) all_0_0_0 = 0
% 26.45/8.17  																																																																																															|
% 26.45/8.17  																																																																																																| Equations (100) can reduce 38 to:
% 26.45/8.17  																																																																																																| (101) $false
% 26.45/8.17  																																																																																																|
% 26.45/8.17  																																																																																																|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																															|-Branch two:
% 26.45/8.17  																																																																																															| (38)  ~ (all_0_0_0 = 0)
% 26.45/8.17  																																																																																															| (579)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.45/8.17  																																																																																															|
% 26.45/8.17  																																																																																																+-Applying beta-rule and splitting (439), into two cases.
% 26.45/8.17  																																																																																																|-Branch one:
% 26.45/8.17  																																																																																																| (100) all_0_0_0 = 0
% 26.45/8.17  																																																																																																|
% 26.45/8.17  																																																																																																	| Equations (100) can reduce 38 to:
% 26.45/8.17  																																																																																																	| (101) $false
% 26.45/8.17  																																																																																																	|
% 26.45/8.17  																																																																																																	|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																|-Branch two:
% 26.45/8.17  																																																																																																| (38)  ~ (all_0_0_0 = 0)
% 26.45/8.17  																																																																																																| (583)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 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_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_24_1_29) = v0))
% 26.45/8.17  																																																																																																|
% 26.45/8.17  																																																																																																	+-Applying beta-rule and splitting (443), into two cases.
% 26.45/8.17  																																																																																																	|-Branch one:
% 26.45/8.17  																																																																																																	| (203) all_28_0_32 = 0
% 26.45/8.17  																																																																																																	|
% 26.45/8.17  																																																																																																		| Equations (203) can reduce 86 to:
% 26.45/8.17  																																																																																																		| (101) $false
% 26.45/8.17  																																																																																																		|
% 26.45/8.17  																																																																																																		|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																	|-Branch two:
% 26.45/8.17  																																																																																																	| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.17  																																																																																																	| (562)  ? [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))
% 26.45/8.17  																																																																																																	|
% 26.45/8.17  																																																																																																		+-Applying beta-rule and splitting (455), into two cases.
% 26.45/8.17  																																																																																																		|-Branch one:
% 26.45/8.17  																																																																																																		| (203) all_28_0_32 = 0
% 26.45/8.17  																																																																																																		|
% 26.45/8.17  																																																																																																			| Equations (203) can reduce 86 to:
% 26.45/8.17  																																																																																																			| (101) $false
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																			|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																		|-Branch two:
% 26.45/8.17  																																																																																																		| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.17  																																																																																																		| (566)  ? [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))
% 26.45/8.17  																																																																																																		|
% 26.45/8.17  																																																																																																			+-Applying beta-rule and splitting (459), into two cases.
% 26.45/8.17  																																																																																																			|-Branch one:
% 26.45/8.17  																																																																																																			| (203) all_28_0_32 = 0
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																				| Equations (203) can reduce 86 to:
% 26.45/8.17  																																																																																																				| (101) $false
% 26.45/8.17  																																																																																																				|
% 26.45/8.17  																																																																																																				|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																			|-Branch two:
% 26.45/8.17  																																																																																																			| (86)  ~ (all_28_0_32 = 0)
% 26.45/8.17  																																																																																																			| (570)  ? [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))
% 26.45/8.17  																																																																																																			|
% 26.45/8.17  																																																																																																				| Instantiating (570) with all_455_0_3716 yields:
% 26.45/8.17  																																																																																																				| (596) (all_455_0_3716 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_455_0_3716 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_455_0_3716 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_455_0_3716) | ( ~ (all_455_0_3716 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_455_0_3716)
% 26.45/8.17  																																																																																																				|
% 26.45/8.17  																																																																																																				+-Applying beta-rule and splitting (483), into two cases.
% 26.45/8.17  																																																																																																				|-Branch one:
% 26.45/8.17  																																																																																																				| (100) all_0_0_0 = 0
% 26.45/8.17  																																																																																																				|
% 26.45/8.17  																																																																																																					| Equations (100) can reduce 38 to:
% 26.45/8.17  																																																																																																					| (101) $false
% 26.45/8.17  																																																																																																					|
% 26.45/8.17  																																																																																																					|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																				|-Branch two:
% 26.45/8.17  																																																																																																				| (38)  ~ (all_0_0_0 = 0)
% 26.45/8.17  																																																																																																				| (600)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_1_1) = v0))
% 26.45/8.17  																																																																																																				|
% 26.45/8.17  																																																																																																					+-Applying beta-rule and splitting (503), into two cases.
% 26.45/8.17  																																																																																																					|-Branch one:
% 26.45/8.17  																																																																																																					| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																					|
% 26.45/8.17  																																																																																																						| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																						| (101) $false
% 26.45/8.17  																																																																																																						|
% 26.45/8.17  																																																																																																						|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																					|-Branch two:
% 26.45/8.17  																																																																																																					| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																					| (604)  ? [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))
% 26.45/8.17  																																																																																																					|
% 26.45/8.17  																																																																																																						+-Applying beta-rule and splitting (507), into two cases.
% 26.45/8.17  																																																																																																						|-Branch one:
% 26.45/8.17  																																																																																																						| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																						|
% 26.45/8.17  																																																																																																							| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																							| (101) $false
% 26.45/8.17  																																																																																																							|
% 26.45/8.17  																																																																																																							|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																						|-Branch two:
% 26.45/8.17  																																																																																																						| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																						| (608)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29, all_0_2_2) = v0))
% 26.45/8.17  																																																																																																						|
% 26.45/8.17  																																																																																																							+-Applying beta-rule and splitting (511), into two cases.
% 26.45/8.17  																																																																																																							|-Branch one:
% 26.45/8.17  																																																																																																							| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																							|
% 26.45/8.17  																																																																																																								| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																								| (101) $false
% 26.45/8.17  																																																																																																								|
% 26.45/8.17  																																																																																																								|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																							|-Branch two:
% 26.45/8.17  																																																																																																							| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																							| (612)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, 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_24_1_29) = v0))
% 26.45/8.17  																																																																																																							|
% 26.45/8.17  																																																																																																								+-Applying beta-rule and splitting (515), into two cases.
% 26.45/8.17  																																																																																																								|-Branch one:
% 26.45/8.17  																																																																																																								| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																								|
% 26.45/8.17  																																																																																																									| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																									| (101) $false
% 26.45/8.17  																																																																																																									|
% 26.45/8.17  																																																																																																									|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																								|-Branch two:
% 26.45/8.17  																																																																																																								| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																								| (616)  ? [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))
% 26.45/8.17  																																																																																																								|
% 26.45/8.17  																																																																																																									+-Applying beta-rule and splitting (523), into two cases.
% 26.45/8.17  																																																																																																									|-Branch one:
% 26.45/8.17  																																																																																																									| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																									|
% 26.45/8.17  																																																																																																										| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																										| (101) $false
% 26.45/8.17  																																																																																																										|
% 26.45/8.17  																																																																																																										|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																									|-Branch two:
% 26.45/8.17  																																																																																																									| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																									| (620)  ? [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))
% 26.45/8.17  																																																																																																									|
% 26.45/8.17  																																																																																																										+-Applying beta-rule and splitting (596), into two cases.
% 26.45/8.17  																																																																																																										|-Branch one:
% 26.45/8.17  																																																																																																										| (621) (all_455_0_3716 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_455_0_3716 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_455_0_3716 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_455_0_3716)
% 26.45/8.17  																																																																																																										|
% 26.45/8.17  																																																																																																											+-Applying beta-rule and splitting (621), into two cases.
% 26.45/8.17  																																																																																																											|-Branch one:
% 26.45/8.17  																																																																																																											| (622) (all_455_0_3716 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_455_0_3716 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0)
% 26.45/8.17  																																																																																																											|
% 26.45/8.17  																																																																																																												+-Applying beta-rule and splitting (622), into two cases.
% 26.45/8.17  																																																																																																												|-Branch one:
% 26.45/8.17  																																																																																																												| (623) all_455_0_3716 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 26.45/8.17  																																																																																																												|
% 26.45/8.17  																																																																																																													| Applying alpha-rule on (623) yields:
% 26.45/8.17  																																																																																																													| (624) all_455_0_3716 = 0
% 26.45/8.17  																																																																																																													| (625) apart_point_and_line(all_0_1_1, all_0_4_4) = 0
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																													| Instantiating formula (28) with all_0_1_1, all_0_4_4, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_0_0_0, apart_point_and_line(all_0_1_1, all_0_4_4) = 0, yields:
% 26.45/8.17  																																																																																																													| (100) all_0_0_0 = 0
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																													| Equations (100) can reduce 38 to:
% 26.45/8.17  																																																																																																													| (101) $false
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																													|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																												|-Branch two:
% 26.45/8.17  																																																																																																												| (628) all_455_0_3716 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 26.45/8.17  																																																																																																												|
% 26.45/8.17  																																																																																																													| Applying alpha-rule on (628) yields:
% 26.45/8.17  																																																																																																													| (624) all_455_0_3716 = 0
% 26.45/8.17  																																																																																																													| (630) apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																													+-Applying beta-rule and splitting (519), into two cases.
% 26.45/8.17  																																																																																																													|-Branch one:
% 26.45/8.17  																																																																																																													| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																														| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																														| (101) $false
% 26.45/8.17  																																																																																																														|
% 26.45/8.17  																																																																																																														|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																													|-Branch two:
% 26.45/8.17  																																																																																																													| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																													| (634)  ? [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))
% 26.45/8.17  																																																																																																													|
% 26.45/8.17  																																																																																																														+-Applying beta-rule and splitting (527), into two cases.
% 26.45/8.17  																																																																																																														|-Branch one:
% 26.45/8.17  																																																																																																														| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																														|
% 26.45/8.17  																																																																																																															| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																															| (101) $false
% 26.45/8.17  																																																																																																															|
% 26.45/8.17  																																																																																																															|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																														|-Branch two:
% 26.45/8.17  																																																																																																														| (70)  ~ (all_20_0_24 = 0)
% 26.45/8.17  																																																																																																														| (638)  ? [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_2_2, all_0_1_1) = v0))
% 26.45/8.17  																																																																																																														|
% 26.45/8.17  																																																																																																															| Instantiating formula (28) with all_0_2_2, all_0_5_5, 0, all_20_0_24 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, apart_point_and_line(all_0_2_2, all_0_5_5) = 0, yields:
% 26.45/8.17  																																																																																																															| (252) all_20_0_24 = 0
% 26.45/8.17  																																																																																																															|
% 26.45/8.17  																																																																																																															| Equations (252) can reduce 70 to:
% 26.45/8.17  																																																																																																															| (101) $false
% 26.45/8.17  																																																																																																															|
% 26.45/8.17  																																																																																																															|-The branch is then unsatisfiable
% 26.45/8.17  																																																																																																											|-Branch two:
% 26.45/8.17  																																																																																																											| (641)  ~ (all_455_0_3716 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_455_0_3716
% 26.45/8.17  																																																																																																											|
% 26.45/8.17  																																																																																																												| Applying alpha-rule on (641) yields:
% 26.45/8.17  																																																																																																												| (642)  ~ (all_455_0_3716 = 0)
% 26.45/8.17  																																																																																																												| (643) distinct_lines(all_0_4_4, all_0_5_5) = all_455_0_3716
% 26.45/8.17  																																																																																																												|
% 26.45/8.17  																																																																																																												| Instantiating formula (26) with all_0_4_4, all_0_5_5, all_393_0_3637, all_455_0_3716 and discharging atoms distinct_lines(all_0_4_4, all_0_5_5) = all_455_0_3716, distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637, yields:
% 26.45/8.17  																																																																																																												| (644) all_455_0_3716 = all_393_0_3637
% 26.45/8.17  																																																																																																												|
% 26.45/8.17  																																																																																																												| Equations (644) can reduce 642 to:
% 26.45/8.17  																																																																																																												| (574)  ~ (all_393_0_3637 = 0)
% 26.45/8.18  																																																																																																												|
% 26.45/8.18  																																																																																																												| From (644) and (643) follows:
% 26.45/8.18  																																																																																																												| (575) distinct_lines(all_0_4_4, all_0_5_5) = all_393_0_3637
% 26.45/8.18  																																																																																																												|
% 26.45/8.18  																																																																																																												| Instantiating formula (19) with all_393_0_3637, 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_393_0_3637, yields:
% 26.45/8.18  																																																																																																												| (647) all_393_0_3637 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0
% 26.45/8.18  																																																																																																												|
% 26.45/8.18  																																																																																																												+-Applying beta-rule and splitting (647), into two cases.
% 26.45/8.18  																																																																																																												|-Branch one:
% 26.45/8.18  																																																																																																												| (648) convergent_lines(all_0_5_5, all_0_5_5) = 0
% 26.45/8.18  																																																																																																												|
% 26.45/8.18  																																																																																																													| Instantiating formula (43) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields:
% 26.45/8.18  																																																																																																													| (649) $false
% 26.45/8.18  																																																																																																													|
% 26.45/8.18  																																																																																																													|-The branch is then unsatisfiable
% 26.45/8.18  																																																																																																												|-Branch two:
% 26.45/8.18  																																																																																																												| (650)  ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0)
% 26.45/8.18  																																																																																																												| (552) all_393_0_3637 = 0
% 26.45/8.18  																																																																																																												|
% 26.45/8.18  																																																																																																													| Equations (552) can reduce 574 to:
% 26.45/8.18  																																																																																																													| (101) $false
% 26.45/8.18  																																																																																																													|
% 26.45/8.18  																																																																																																													|-The branch is then unsatisfiable
% 26.45/8.18  																																																																																																										|-Branch two:
% 26.45/8.18  																																																																																																										| (653)  ~ (all_455_0_3716 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_455_0_3716
% 26.45/8.18  																																																																																																										|
% 26.45/8.18  																																																																																																											| Applying alpha-rule on (653) yields:
% 26.45/8.18  																																																																																																											| (642)  ~ (all_455_0_3716 = 0)
% 26.45/8.18  																																																																																																											| (655) distinct_points(all_0_2_2, all_0_1_1) = all_455_0_3716
% 26.45/8.18  																																																																																																											|
% 26.45/8.18  																																																																																																											| Instantiating formula (23) with all_0_2_2, all_0_1_1, 0, all_455_0_3716 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_455_0_3716, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 26.45/8.18  																																																																																																											| (624) all_455_0_3716 = 0
% 26.45/8.18  																																																																																																											|
% 26.45/8.18  																																																																																																											| Equations (624) can reduce 642 to:
% 26.45/8.18  																																																																																																											| (101) $false
% 26.45/8.18  																																																																																																											|
% 26.45/8.18  																																																																																																											|-The branch is then unsatisfiable
% 26.45/8.18  																																																																																													|-Branch two:
% 26.45/8.18  																																																																																													| (658)  ~ (all_393_0_3637 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_393_0_3637
% 26.45/8.18  																																																																																													|
% 26.45/8.18  																																																																																														| Applying alpha-rule on (658) yields:
% 26.45/8.18  																																																																																														| (574)  ~ (all_393_0_3637 = 0)
% 26.45/8.18  																																																																																														| (660) distinct_points(all_0_2_2, all_0_1_1) = all_393_0_3637
% 26.45/8.18  																																																																																														|
% 26.45/8.18  																																																																																														| Instantiating formula (23) with all_0_2_2, all_0_1_1, 0, all_393_0_3637 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_393_0_3637, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 26.45/8.18  																																																																																														| (552) all_393_0_3637 = 0
% 26.45/8.18  																																																																																														|
% 26.45/8.18  																																																																																														| Equations (552) can reduce 574 to:
% 26.45/8.18  																																																																																														| (101) $false
% 26.45/8.18  																																																																																														|
% 26.45/8.18  																																																																																														|-The branch is then unsatisfiable
% 26.45/8.18  											|-Branch two:
% 26.45/8.18  											| (663)  ~ (distinct_points(all_0_2_2, all_0_1_1) = 0)
% 26.45/8.18  											| (240) all_22_0_26 = 0
% 26.45/8.18  											|
% 26.45/8.18  												| Equations (240) can reduce 74 to:
% 26.45/8.18  												| (101) $false
% 26.45/8.18  												|
% 26.45/8.18  												|-The branch is then unsatisfiable
% 26.45/8.18  				|-Branch two:
% 26.45/8.18  				| (666)  ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 26.45/8.18  				|
% 26.45/8.18  					| Applying alpha-rule on (666) yields:
% 26.45/8.18  					| (111)  ~ (all_31_0_35 = 0)
% 26.45/8.18  					| (668) convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 26.45/8.18  					|
% 26.45/8.18  					| Instantiating formula (46) 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:
% 26.45/8.18  					| (669) all_31_0_35 = 0
% 26.45/8.18  					|
% 26.45/8.18  					| Equations (669) can reduce 111 to:
% 26.45/8.18  					| (101) $false
% 26.45/8.18  					|
% 26.45/8.18  					|-The branch is then unsatisfiable
% 26.45/8.18  			|-Branch two:
% 26.45/8.18  			| (671)  ~ (all_34_0_38 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38
% 26.45/8.18  			|
% 26.45/8.18  				| Applying alpha-rule on (671) yields:
% 26.45/8.18  				| (108)  ~ (all_34_0_38 = 0)
% 26.45/8.18  				| (673) convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38
% 26.45/8.18  				|
% 26.45/8.18  				| Instantiating formula (46) with all_0_5_5, all_0_3_3, all_34_0_38, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 26.45/8.18  				| (674) all_34_0_38 = 0
% 26.45/8.18  				|
% 26.45/8.18  				| Equations (674) can reduce 108 to:
% 26.45/8.18  				| (101) $false
% 26.45/8.18  				|
% 26.45/8.18  				|-The branch is then unsatisfiable
% 26.45/8.18  		|-Branch two:
% 26.45/8.18  		| (676)  ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 26.45/8.18  		|
% 26.45/8.18  			| Applying alpha-rule on (676) yields:
% 26.45/8.18  			| (105)  ~ (all_30_0_34 = 0)
% 26.45/8.18  			| (678) convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 26.45/8.18  			|
% 26.45/8.18  			| Instantiating formula (46) 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:
% 26.45/8.18  			| (679) all_30_0_34 = 0
% 26.45/8.18  			|
% 26.45/8.18  			| Equations (679) can reduce 105 to:
% 26.45/8.18  			| (101) $false
% 26.45/8.18  			|
% 26.45/8.18  			|-The branch is then unsatisfiable
% 26.45/8.18  |-Branch two:
% 26.45/8.18  | (681)  ~ (all_35_0_39 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39
% 26.45/8.18  |
% 26.45/8.18  	| Applying alpha-rule on (681) yields:
% 26.45/8.18  	| (98)  ~ (all_35_0_39 = 0)
% 26.45/8.18  	| (683) convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39
% 26.45/8.18  	|
% 26.45/8.18  	| Instantiating formula (46) with all_0_5_5, all_0_3_3, all_35_0_39, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 26.45/8.18  	| (684) all_35_0_39 = 0
% 26.45/8.18  	|
% 26.45/8.18  	| Equations (684) can reduce 98 to:
% 26.45/8.18  	| (101) $false
% 26.45/8.18  	|
% 26.45/8.18  	|-The branch is then unsatisfiable
% 26.45/8.18  % SZS output end Proof for theBenchmark
% 26.45/8.18  
% 26.45/8.18  7579ms
%------------------------------------------------------------------------------