%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n025.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 03:48:41 EDT 2022

% Result   : Theorem 12.18s 3.52s
% Output   : Proof 26.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 16:10:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.57  (ePrincess v.1.0)
% 0.19/0.57  
% 0.19/0.57  (c) Philipp Rümmer, 2009-2015
% 0.19/0.57  (c) Peter Backeman, 2014-2015
% 0.19/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57  Bug reports to peter@backeman.se
% 0.19/0.57  
% 0.19/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57  
% 0.19/0.57  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.69/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.95  Prover 0: Preprocessing ...
% 1.86/1.08  Prover 0: Warning: ignoring some quantifiers
% 2.05/1.10  Prover 0: Constructing countermodel ...
% 2.56/1.32  Prover 0: gave up
% 2.90/1.32  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.90/1.35  Prover 1: Preprocessing ...
% 3.18/1.43  Prover 1: Constructing countermodel ...
% 3.52/1.50  Prover 1: gave up
% 3.52/1.50  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.52/1.52  Prover 2: Preprocessing ...
% 4.10/1.63  Prover 2: Warning: ignoring some quantifiers
% 4.10/1.64  Prover 2: Constructing countermodel ...
% 4.43/1.76  Prover 2: gave up
% 4.43/1.76  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.85/1.78  Prover 3: Preprocessing ...
% 4.85/1.80  Prover 3: Warning: ignoring some quantifiers
% 4.85/1.80  Prover 3: Constructing countermodel ...
% 5.05/1.83  Prover 3: gave up
% 5.05/1.83  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 5.05/1.85  Prover 4: Preprocessing ...
% 5.44/1.91  Prover 4: Warning: ignoring some quantifiers
% 5.44/1.92  Prover 4: Constructing countermodel ...
% 10.00/3.05  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 10.00/3.07  Prover 5: Preprocessing ...
% 10.43/3.15  Prover 5: Constructing countermodel ...
% 12.18/3.51  Prover 5: proved (466ms)
% 12.18/3.52  Prover 4: stopped
% 12.18/3.52  
% 12.18/3.52  No countermodel exists, formula is valid
% 12.18/3.52  % SZS status Theorem for theBenchmark
% 12.18/3.52  
% 12.18/3.52  Generating proof ... found it (size 582)
% 25.21/6.67  
% 25.21/6.67  % SZS output start Proof for theBenchmark
% 25.21/6.67  Assumed formulas after preprocessing and simplification: 
% 25.21/6.67  | (0)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (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 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v0, v1) = v4) |  ~ (apart_point_and_line(v2, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) &  ~ (v3 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v0, v1) = v4) |  ~ (apart_point_and_line(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) &  ~ (v3 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (distinct_points(v2, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (distinct_points(v2, v0) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) |  ~ (apart_point_and_line(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) &  ~ (v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (distinct_points(v2, v1) = v4) |  ~ (distinct_points(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) |  ~ (v5 = 0))) | (v4 = 0 & v3 = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, 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 |  ~ (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] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) &  ~ (v3 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) &  ~ (v3 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v1) = v3) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v0) = v3) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v3 = 0) & intersection_point(v0, v2) = v6 & intersection_point(v0, v1) = v5 & convergent_lines(v0, v2) = v4 & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v3 & distinct_points(v5, v6) = v7 & ( ~ (v4 = 0) | v7 = 0))
% 25.65/6.73  | Applying alpha-rule on (0) yields:
% 25.65/6.73  | (1)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v1) = v3) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 25.65/6.73  | (2)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 25.65/6.73  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 25.65/6.73  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 25.65/6.73  | (5)  ! [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))
% 25.65/6.73  | (6)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 25.65/6.73  | (7)  ! [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))
% 25.65/6.73  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 25.65/6.73  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 25.65/6.73  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 25.65/6.73  | (11)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v3 = 0) & intersection_point(v0, v2) = v6 & intersection_point(v0, v1) = v5 & convergent_lines(v0, v2) = v4 & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v3 & distinct_points(v5, v6) = v7 & ( ~ (v4 = 0) | v7 = 0))
% 25.65/6.73  | (12)  ! [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)
% 25.65/6.73  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (apart_point_and_line(v2, v1) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v0) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) &  ~ (v3 = 0)))))
% 25.65/6.73  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 25.65/6.73  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (distinct_points(v2, v0) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v1) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 25.65/6.73  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 25.65/6.73  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0)))))
% 25.65/6.74  | (18)  ! [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))
% 25.65/6.74  | (19)  ! [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)
% 25.65/6.74  | (20)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 25.65/6.74  | (21)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 25.65/6.74  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v2) = v9 & apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 25.65/6.74  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 25.65/6.74  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 25.65/6.74  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 25.65/6.74  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 25.65/6.74  | (27)  ! [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))
% 25.65/6.74  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (distinct_points(v2, v1) = v4) |  ~ (distinct_points(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (line_connecting(v0, v1) = v6 & apart_point_and_line(v2, v6) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v7 = 0) |  ~ (v5 = 0))) | (v4 = 0 & v3 = 0))
% 25.65/6.74  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v0, v1) = v4) |  ~ (apart_point_and_line(v2, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) &  ~ (v3 = 0)))))
% 25.65/6.74  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v0, v1) = v4) |  ~ (apart_point_and_line(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v4) = v7 & ( ~ (v5 = 0) | v7 = 0 | ( ~ (v6 = 0) &  ~ (v3 = 0)))))
% 25.65/6.74  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_points(v2, v0) = v3) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (line_connecting(v0, v1) = v4 & apart_point_and_line(v2, v4) = v5 & distinct_points(v2, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v3 = 0))))
% 25.65/6.74  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.65/6.74  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (distinct_points(v2, v1) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v3) = v6 & distinct_points(v2, v0) = v7 & distinct_points(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | (v7 = 0 & v4 = 0))))
% 25.65/6.74  | (34)  ! [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)
% 25.65/6.74  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v2) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 25.65/6.74  | (36)  ! [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))
% 25.65/6.74  | (37)  ! [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)
% 25.65/6.74  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 25.65/6.75  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) |  ~ (v6 = 0) | v9 = 0 | v8 = 0)))
% 25.65/6.75  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0)))
% 25.65/6.75  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (apart_point_and_line(v2, v1) = v4) |  ~ (apart_point_and_line(v2, v0) = v3) |  ? [v5] :  ? [v6] :  ? [v7] : (intersection_point(v0, v1) = v6 & convergent_lines(v0, v1) = v5 & distinct_points(v2, v6) = v7 & ( ~ (v5 = 0) | v7 = 0)) | ( ~ (v4 = 0) &  ~ (v3 = 0)))
% 25.65/6.75  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 25.65/6.75  | (43)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 25.65/6.75  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 25.65/6.75  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 25.65/6.75  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (apart_point_and_line(v2, v0) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (intersection_point(v0, v1) = v5 & apart_point_and_line(v2, v1) = v4 & distinct_points(v2, v5) = v6 & (v6 = 0 | ( ~ (v4 = 0) &  ~ (v3 = 0)))))
% 25.65/6.75  |
% 25.65/6.75  | Instantiating (11) with all_1_0_0, all_1_1_1, all_1_2_2, all_1_3_3, all_1_4_4, all_1_5_5, all_1_6_6, all_1_7_7 yields:
% 25.65/6.75  | (47)  ~ (all_1_4_4 = 0) & intersection_point(all_1_7_7, all_1_5_5) = all_1_1_1 & intersection_point(all_1_7_7, all_1_6_6) = all_1_2_2 & convergent_lines(all_1_7_7, all_1_5_5) = all_1_3_3 & convergent_lines(all_1_7_7, all_1_6_6) = 0 & distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4 & distinct_points(all_1_2_2, all_1_1_1) = all_1_0_0 & ( ~ (all_1_3_3 = 0) | all_1_0_0 = 0)
% 25.65/6.75  |
% 25.65/6.75  | Applying alpha-rule on (47) yields:
% 25.65/6.75  | (48) convergent_lines(all_1_7_7, all_1_5_5) = all_1_3_3
% 25.65/6.75  | (49) intersection_point(all_1_7_7, all_1_5_5) = all_1_1_1
% 25.65/6.75  | (50) distinct_points(all_1_2_2, all_1_1_1) = all_1_0_0
% 25.65/6.75  | (51)  ~ (all_1_3_3 = 0) | all_1_0_0 = 0
% 25.65/6.75  | (52) distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4
% 25.65/6.75  | (53) intersection_point(all_1_7_7, all_1_6_6) = all_1_2_2
% 25.65/6.75  | (54) convergent_lines(all_1_7_7, all_1_6_6) = 0
% 25.65/6.75  | (55)  ~ (all_1_4_4 = 0)
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (2) with all_1_5_5, all_1_7_7 yields:
% 25.65/6.75  | (56)  ~ (convergent_lines(all_1_7_7, all_1_5_5) = 0) | distinct_lines(all_1_7_7, all_1_5_5) = 0
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (45) with all_1_3_3, all_1_5_5, all_1_6_6, all_1_7_7 and discharging atoms convergent_lines(all_1_7_7, all_1_5_5) = all_1_3_3, convergent_lines(all_1_7_7, all_1_6_6) = 0, yields:
% 25.65/6.75  | (57) all_1_3_3 = 0 | convergent_lines(all_1_6_6, all_1_5_5) = 0
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (2) with all_1_6_6, all_1_7_7 and discharging atoms convergent_lines(all_1_7_7, all_1_6_6) = 0, yields:
% 25.65/6.75  | (58) distinct_lines(all_1_7_7, all_1_6_6) = 0
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (5) with all_1_4_4, all_1_4_4, all_1_5_5, all_1_6_6, all_1_6_6 and discharging atoms distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4, yields:
% 25.65/6.75  | (59) all_1_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_6_6, all_1_6_6) = v0)
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (43) with all_1_4_4, all_1_5_5, all_1_6_6 and discharging atoms distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4, yields:
% 25.65/6.75  | (60) all_1_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_6_6, all_1_5_5) = v0)
% 25.65/6.75  |
% 25.65/6.75  | Instantiating formula (1) with 0, all_1_2_2, all_1_1_1, all_1_2_2 yields:
% 25.65/6.75  | (61)  ~ (distinct_points(all_1_2_2, all_1_1_1) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(all_1_2_2, v0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 25.65/6.75  |
% 25.65/6.75  +-Applying beta-rule and splitting (59), into two cases.
% 25.65/6.75  |-Branch one:
% 25.65/6.75  | (62) all_1_4_4 = 0
% 25.65/6.75  |
% 25.65/6.76  	| Equations (62) can reduce 55 to:
% 25.65/6.76  	| (63) $false
% 25.65/6.76  	|
% 25.65/6.76  	|-The branch is then unsatisfiable
% 25.65/6.76  |-Branch two:
% 25.65/6.76  | (55)  ~ (all_1_4_4 = 0)
% 25.65/6.76  | (65)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_1_6_6, all_1_6_6) = v0)
% 25.65/6.76  |
% 25.65/6.76  	+-Applying beta-rule and splitting (60), into two cases.
% 25.65/6.76  	|-Branch one:
% 25.65/6.76  	| (62) all_1_4_4 = 0
% 25.65/6.76  	|
% 25.65/6.76  		| Equations (62) can reduce 55 to:
% 25.65/6.76  		| (63) $false
% 25.65/6.76  		|
% 25.65/6.76  		|-The branch is then unsatisfiable
% 25.65/6.76  	|-Branch two:
% 25.65/6.76  	| (55)  ~ (all_1_4_4 = 0)
% 25.65/6.76  	| (69)  ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_1_6_6, all_1_5_5) = v0)
% 25.65/6.76  	|
% 25.65/6.76  		| Instantiating (69) with all_26_0_9 yields:
% 25.65/6.76  		| (70)  ~ (all_26_0_9 = 0) & convergent_lines(all_1_6_6, all_1_5_5) = all_26_0_9
% 25.65/6.76  		|
% 25.65/6.76  		| Applying alpha-rule on (70) yields:
% 25.65/6.76  		| (71)  ~ (all_26_0_9 = 0)
% 25.65/6.76  		| (72) convergent_lines(all_1_6_6, all_1_5_5) = all_26_0_9
% 25.65/6.76  		|
% 25.65/6.76  		+-Applying beta-rule and splitting (57), into two cases.
% 25.65/6.76  		|-Branch one:
% 25.65/6.76  		| (73) convergent_lines(all_1_6_6, all_1_5_5) = 0
% 25.65/6.76  		|
% 25.65/6.76  			| Instantiating formula (3) with all_1_6_6, all_1_5_5, 0, all_26_0_9 and discharging atoms convergent_lines(all_1_6_6, all_1_5_5) = all_26_0_9, convergent_lines(all_1_6_6, all_1_5_5) = 0, yields:
% 25.65/6.76  			| (74) all_26_0_9 = 0
% 25.65/6.76  			|
% 25.65/6.76  			| Equations (74) can reduce 71 to:
% 25.65/6.76  			| (63) $false
% 25.65/6.76  			|
% 25.65/6.76  			|-The branch is then unsatisfiable
% 25.65/6.76  		|-Branch two:
% 25.65/6.76  		| (76)  ~ (convergent_lines(all_1_6_6, all_1_5_5) = 0)
% 25.65/6.76  		| (77) all_1_3_3 = 0
% 25.65/6.76  		|
% 25.65/6.76  			| From (77) and (48) follows:
% 25.65/6.76  			| (78) convergent_lines(all_1_7_7, all_1_5_5) = 0
% 25.65/6.76  			|
% 25.65/6.76  			+-Applying beta-rule and splitting (51), into two cases.
% 25.65/6.76  			|-Branch one:
% 25.65/6.76  			| (79)  ~ (all_1_3_3 = 0)
% 25.65/6.76  			|
% 25.65/6.76  				| Equations (77) can reduce 79 to:
% 25.65/6.76  				| (63) $false
% 25.65/6.76  				|
% 25.65/6.76  				|-The branch is then unsatisfiable
% 25.65/6.76  			|-Branch two:
% 25.65/6.76  			| (77) all_1_3_3 = 0
% 25.65/6.76  			| (82) all_1_0_0 = 0
% 25.65/6.76  			|
% 25.65/6.76  				| From (82) and (50) follows:
% 25.65/6.76  				| (83) distinct_points(all_1_2_2, all_1_1_1) = 0
% 25.65/6.76  				|
% 25.65/6.76  				+-Applying beta-rule and splitting (56), into two cases.
% 25.65/6.76  				|-Branch one:
% 25.65/6.76  				| (84)  ~ (convergent_lines(all_1_7_7, all_1_5_5) = 0)
% 25.65/6.76  				|
% 25.65/6.76  					| Using (78) and (84) yields:
% 25.65/6.76  					| (85) $false
% 25.65/6.76  					|
% 25.65/6.76  					|-The branch is then unsatisfiable
% 25.65/6.76  				|-Branch two:
% 25.65/6.76  				| (78) convergent_lines(all_1_7_7, all_1_5_5) = 0
% 25.65/6.76  				| (87) distinct_lines(all_1_7_7, all_1_5_5) = 0
% 25.65/6.76  				|
% 25.65/6.76  					+-Applying beta-rule and splitting (61), into two cases.
% 25.65/6.76  					|-Branch one:
% 25.65/6.76  					| (88)  ~ (distinct_points(all_1_2_2, all_1_1_1) = 0)
% 25.65/6.76  					|
% 25.65/6.76  						| Using (83) and (88) yields:
% 25.65/6.76  						| (85) $false
% 25.65/6.76  						|
% 25.65/6.76  						|-The branch is then unsatisfiable
% 25.65/6.76  					|-Branch two:
% 25.65/6.76  					| (83) distinct_points(all_1_2_2, all_1_1_1) = 0
% 25.65/6.76  					| (91)  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(all_1_2_2, v0) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 25.65/6.76  					|
% 25.65/6.76  						| Instantiating (91) with all_44_0_10, all_44_1_11, all_44_2_12 yields:
% 25.65/6.76  						| (92) line_connecting(all_1_2_2, all_1_1_1) = all_44_2_12 & apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11 & distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10 & ( ~ (all_44_1_11 = 0) | all_44_0_10 = 0)
% 25.65/6.76  						|
% 25.65/6.76  						| Applying alpha-rule on (92) yields:
% 25.65/6.76  						| (93) line_connecting(all_1_2_2, all_1_1_1) = all_44_2_12
% 25.65/6.76  						| (94) apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11
% 25.65/6.76  						| (95) distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10
% 25.65/6.76  						| (96)  ~ (all_44_1_11 = 0) | all_44_0_10 = 0
% 25.65/6.76  						|
% 25.65/6.76  						| Instantiating formula (6) with all_1_2_2 yields:
% 25.65/6.76  						| (97)  ~ (distinct_points(all_1_2_2, all_1_2_2) = 0)
% 25.65/6.76  						|
% 25.65/6.76  						| Using (95) and (97) yields:
% 25.65/6.76  						| (98)  ~ (all_44_0_10 = 0)
% 25.65/6.76  						|
% 25.65/6.76  						+-Applying beta-rule and splitting (96), into two cases.
% 25.65/6.76  						|-Branch one:
% 25.65/6.76  						| (99)  ~ (all_44_1_11 = 0)
% 25.65/6.76  						|
% 25.65/6.76  							| Instantiating formula (22) with all_44_1_11, all_44_1_11, all_44_2_12, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 25.65/6.76  							| (100) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_44_2_12, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 25.65/6.76  							|
% 25.65/6.76  							| Instantiating formula (25) with all_44_1_11, all_44_1_11, all_44_2_12, all_44_2_12, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 25.65/6.76  							| (101) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_lines(all_44_2_12, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 25.65/6.76  							|
% 25.65/6.76  							| Instantiating formula (44) with all_1_5_5, all_1_7_7, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_7_7, all_1_5_5) = 0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 25.65/6.76  							| (102)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v3 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 25.65/6.76  							|
% 25.65/6.76  							| Instantiating formula (44) with all_1_6_6, all_1_7_7, all_1_1_1, all_1_2_2 and discharging atoms distinct_lines(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 25.65/6.76  							| (103)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_6_6) = v3 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v0 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating formula (9) with all_44_0_10, all_1_2_2, all_1_1_1, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10, yields:
% 25.65/6.77  							| (104) all_44_0_10 = 0 | distinct_points(all_1_1_1, all_1_2_2) = 0
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating formula (28) with all_44_0_10, 0, all_1_2_2, all_1_2_2, all_1_1_1 and discharging atoms distinct_points(all_1_2_2, all_1_1_1) = 0, distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10, yields:
% 25.65/6.77  							| (105) all_44_0_10 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_1_1, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0)))
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating formula (28) with all_44_0_10, all_44_0_10, all_1_2_2, all_1_2_2, all_1_2_2 and discharging atoms distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10, yields:
% 25.65/6.77  							| (106) all_44_0_10 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_2_2, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0)))
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating formula (17) with all_44_0_10, all_1_2_2, all_1_2_2, all_1_6_6, all_1_7_7 and discharging atoms intersection_point(all_1_7_7, all_1_6_6) = all_1_2_2, distinct_points(all_1_2_2, all_1_2_2) = all_44_0_10, yields:
% 25.65/6.77  							| (107) all_44_0_10 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & convergent_lines(all_1_7_7, all_1_6_6) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0))))
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating (103) with all_63_0_13, all_63_1_14, all_63_2_15, all_63_3_16 yields:
% 25.65/6.77  							| (108) apart_point_and_line(all_1_1_1, all_1_6_6) = all_63_0_13 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14 & apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15 & apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16 & (all_63_0_13 = 0 | all_63_1_14 = 0 | all_63_2_15 = 0 | all_63_3_16 = 0)
% 25.65/6.77  							|
% 25.65/6.77  							| Applying alpha-rule on (108) yields:
% 25.65/6.77  							| (109) apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14
% 25.65/6.77  							| (110) all_63_0_13 = 0 | all_63_1_14 = 0 | all_63_2_15 = 0 | all_63_3_16 = 0
% 25.65/6.77  							| (111) apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16
% 25.65/6.77  							| (112) apart_point_and_line(all_1_1_1, all_1_6_6) = all_63_0_13
% 25.65/6.77  							| (113) apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15
% 25.65/6.77  							|
% 25.65/6.77  							| Instantiating (102) with all_65_0_17, all_65_1_18, all_65_2_19, all_65_3_20 yields:
% 25.65/6.77  							| (114) apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_65_1_18 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_65_2_19 & apart_point_and_line(all_1_2_2, all_1_7_7) = all_65_3_20 & (all_65_0_17 = 0 | all_65_1_18 = 0 | all_65_2_19 = 0 | all_65_3_20 = 0)
% 25.65/6.77  							|
% 25.65/6.77  							| Applying alpha-rule on (114) yields:
% 25.65/6.77  							| (115) all_65_0_17 = 0 | all_65_1_18 = 0 | all_65_2_19 = 0 | all_65_3_20 = 0
% 25.65/6.77  							| (116) apart_point_and_line(all_1_2_2, all_1_7_7) = all_65_3_20
% 25.65/6.77  							| (117) apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17
% 25.65/6.77  							| (118) apart_point_and_line(all_1_2_2, all_1_5_5) = all_65_2_19
% 25.65/6.77  							| (119) apart_point_and_line(all_1_1_1, all_1_7_7) = all_65_1_18
% 25.65/6.77  							|
% 25.65/6.77  							+-Applying beta-rule and splitting (104), into two cases.
% 25.65/6.77  							|-Branch one:
% 25.65/6.77  							| (120) distinct_points(all_1_1_1, all_1_2_2) = 0
% 25.65/6.77  							|
% 25.65/6.77  								+-Applying beta-rule and splitting (107), into two cases.
% 25.65/6.77  								|-Branch one:
% 25.65/6.77  								| (121) all_44_0_10 = 0
% 25.65/6.77  								|
% 25.65/6.77  									| Equations (121) can reduce 98 to:
% 25.65/6.77  									| (63) $false
% 25.65/6.77  									|
% 25.65/6.77  									|-The branch is then unsatisfiable
% 25.65/6.77  								|-Branch two:
% 25.65/6.77  								| (98)  ~ (all_44_0_10 = 0)
% 25.65/6.77  								| (124)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & convergent_lines(all_1_7_7, all_1_6_6) = v0 & ( ~ (v0 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0))))
% 25.65/6.77  								|
% 25.65/6.77  									| Instantiating (124) with all_75_0_21, all_75_1_22, all_75_2_23 yields:
% 25.65/6.77  									| (125) apart_point_and_line(all_1_2_2, all_1_6_6) = all_75_0_21 & apart_point_and_line(all_1_2_2, all_1_7_7) = all_75_1_22 & convergent_lines(all_1_7_7, all_1_6_6) = all_75_2_23 & ( ~ (all_75_2_23 = 0) | ( ~ (all_75_0_21 = 0) &  ~ (all_75_1_22 = 0)))
% 25.65/6.77  									|
% 25.65/6.77  									| Applying alpha-rule on (125) yields:
% 25.65/6.77  									| (126) apart_point_and_line(all_1_2_2, all_1_6_6) = all_75_0_21
% 25.65/6.77  									| (127) apart_point_and_line(all_1_2_2, all_1_7_7) = all_75_1_22
% 25.65/6.77  									| (128) convergent_lines(all_1_7_7, all_1_6_6) = all_75_2_23
% 25.65/6.77  									| (129)  ~ (all_75_2_23 = 0) | ( ~ (all_75_0_21 = 0) &  ~ (all_75_1_22 = 0))
% 25.65/6.77  									|
% 25.65/6.77  									+-Applying beta-rule and splitting (100), into two cases.
% 25.65/6.77  									|-Branch one:
% 25.65/6.77  									| (130) all_44_1_11 = 0
% 25.65/6.77  									|
% 25.65/6.77  										| Equations (130) can reduce 99 to:
% 25.65/6.77  										| (63) $false
% 25.65/6.77  										|
% 25.65/6.77  										|-The branch is then unsatisfiable
% 25.65/6.77  									|-Branch two:
% 25.65/6.77  									| (99)  ~ (all_44_1_11 = 0)
% 25.65/6.77  									| (133)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_44_2_12, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 25.65/6.77  									|
% 25.65/6.77  										| Instantiating (133) with all_81_0_24, all_81_1_25, all_81_2_26, all_81_3_27 yields:
% 25.65/6.77  										| (134) apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_0_24 & apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_1_25 & distinct_lines(all_44_2_12, all_44_2_12) = all_81_2_26 & distinct_points(all_1_2_2, all_1_2_2) = all_81_3_27 & ( ~ (all_81_2_26 = 0) |  ~ (all_81_3_27 = 0) | all_81_0_24 = 0 | all_81_1_25 = 0)
% 25.65/6.77  										|
% 25.65/6.77  										| Applying alpha-rule on (134) yields:
% 25.65/6.77  										| (135) apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_1_25
% 25.65/6.77  										| (136) apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_0_24
% 25.65/6.77  										| (137)  ~ (all_81_2_26 = 0) |  ~ (all_81_3_27 = 0) | all_81_0_24 = 0 | all_81_1_25 = 0
% 25.65/6.77  										| (138) distinct_lines(all_44_2_12, all_44_2_12) = all_81_2_26
% 25.65/6.77  										| (139) distinct_points(all_1_2_2, all_1_2_2) = all_81_3_27
% 25.65/6.77  										|
% 25.65/6.77  										+-Applying beta-rule and splitting (101), into two cases.
% 25.65/6.77  										|-Branch one:
% 25.65/6.77  										| (130) all_44_1_11 = 0
% 25.65/6.77  										|
% 25.65/6.77  											| Equations (130) can reduce 99 to:
% 25.65/6.77  											| (63) $false
% 25.65/6.77  											|
% 25.65/6.77  											|-The branch is then unsatisfiable
% 25.65/6.77  										|-Branch two:
% 25.65/6.77  										| (99)  ~ (all_44_1_11 = 0)
% 25.65/6.77  										| (143)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_lines(all_44_2_12, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 25.65/6.78  										|
% 25.65/6.78  											+-Applying beta-rule and splitting (106), into two cases.
% 25.65/6.78  											|-Branch one:
% 25.65/6.78  											| (121) all_44_0_10 = 0
% 25.65/6.78  											|
% 25.65/6.78  												| Equations (121) can reduce 98 to:
% 25.65/6.78  												| (63) $false
% 25.65/6.78  												|
% 25.65/6.78  												|-The branch is then unsatisfiable
% 25.65/6.78  											|-Branch two:
% 25.65/6.78  											| (98)  ~ (all_44_0_10 = 0)
% 25.65/6.78  											| (147)  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_2_2, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0)))
% 25.65/6.78  											|
% 25.65/6.78  												+-Applying beta-rule and splitting (105), into two cases.
% 25.65/6.78  												|-Branch one:
% 25.65/6.78  												| (121) all_44_0_10 = 0
% 25.65/6.78  												|
% 25.65/6.78  													| Equations (121) can reduce 98 to:
% 25.65/6.78  													| (63) $false
% 25.65/6.78  													|
% 25.65/6.78  													|-The branch is then unsatisfiable
% 25.65/6.78  												|-Branch two:
% 25.65/6.78  												| (98)  ~ (all_44_0_10 = 0)
% 25.65/6.78  												| (151)  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_1_1, all_1_2_2) = v1 & apart_point_and_line(all_1_2_2, v1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0)))
% 25.65/6.78  												|
% 25.65/6.78  													| Instantiating (151) with all_96_0_34, all_96_1_35, all_96_2_36 yields:
% 25.65/6.78  													| (152) line_connecting(all_1_1_1, all_1_2_2) = all_96_1_35 & apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34 & distinct_points(all_1_1_1, all_1_2_2) = all_96_2_36 & ( ~ (all_96_0_34 = 0) |  ~ (all_96_2_36 = 0))
% 25.65/6.78  													|
% 25.65/6.78  													| Applying alpha-rule on (152) yields:
% 25.65/6.78  													| (153) line_connecting(all_1_1_1, all_1_2_2) = all_96_1_35
% 25.65/6.78  													| (154) apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34
% 25.65/6.78  													| (155) distinct_points(all_1_1_1, all_1_2_2) = all_96_2_36
% 25.65/6.78  													| (156)  ~ (all_96_0_34 = 0) |  ~ (all_96_2_36 = 0)
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_63_1_14, all_65_1_18 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_65_1_18, apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, yields:
% 25.65/6.78  													| (157) all_65_1_18 = all_63_1_14
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_2_2, all_44_2_12, all_81_0_24, all_44_1_11 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_0_24, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 25.65/6.78  													| (158) all_81_0_24 = all_44_1_11
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_2_2, all_44_2_12, all_81_1_25, all_81_0_24 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_0_24, apart_point_and_line(all_1_2_2, all_44_2_12) = all_81_1_25, yields:
% 25.65/6.78  													| (159) all_81_0_24 = all_81_1_25
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_2_2, all_1_6_6, all_63_2_15, all_75_0_21 and discharging atoms apart_point_and_line(all_1_2_2, all_1_6_6) = all_75_0_21, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 25.65/6.78  													| (160) all_75_0_21 = all_63_2_15
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_2_2, all_1_7_7, all_65_3_20, all_75_1_22 and discharging atoms apart_point_and_line(all_1_2_2, all_1_7_7) = all_75_1_22, apart_point_and_line(all_1_2_2, all_1_7_7) = all_65_3_20, yields:
% 25.65/6.78  													| (161) all_75_1_22 = all_65_3_20
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (26) with all_1_2_2, all_1_7_7, all_63_3_16, all_75_1_22 and discharging atoms apart_point_and_line(all_1_2_2, all_1_7_7) = all_75_1_22, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 25.65/6.78  													| (162) all_75_1_22 = all_63_3_16
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (3) with all_1_7_7, all_1_6_6, all_75_2_23, 0 and discharging atoms convergent_lines(all_1_7_7, all_1_6_6) = all_75_2_23, convergent_lines(all_1_7_7, all_1_6_6) = 0, yields:
% 25.65/6.78  													| (163) all_75_2_23 = 0
% 25.65/6.78  													|
% 25.65/6.78  													| Instantiating formula (23) with all_1_1_1, all_1_2_2, 0, all_96_2_36 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = all_96_2_36, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 25.65/6.78  													| (164) all_96_2_36 = 0
% 25.65/6.78  													|
% 25.65/6.78  													| Combining equations (159,158) yields a new equation:
% 25.65/6.78  													| (165) all_81_1_25 = all_44_1_11
% 25.65/6.78  													|
% 25.65/6.78  													| Simplifying 165 yields:
% 25.65/6.78  													| (166) all_81_1_25 = all_44_1_11
% 25.65/6.78  													|
% 25.65/6.78  													| Combining equations (162,161) yields a new equation:
% 25.65/6.78  													| (167) all_65_3_20 = all_63_3_16
% 25.65/6.78  													|
% 25.65/6.78  													| Combining equations (167,161) yields a new equation:
% 25.65/6.78  													| (162) all_75_1_22 = all_63_3_16
% 25.65/6.78  													|
% 25.65/6.78  													| From (157) and (119) follows:
% 25.65/6.78  													| (109) apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14
% 25.65/6.78  													|
% 25.65/6.78  													| From (166) and (135) follows:
% 25.65/6.78  													| (94) apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11
% 25.65/6.78  													|
% 25.65/6.78  													| From (160) and (126) follows:
% 25.65/6.78  													| (113) apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15
% 25.65/6.78  													|
% 25.65/6.78  													| From (167) and (116) follows:
% 25.65/6.78  													| (111) apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16
% 25.65/6.78  													|
% 25.65/6.78  													| From (164) and (155) follows:
% 25.65/6.78  													| (120) distinct_points(all_1_1_1, all_1_2_2) = 0
% 25.65/6.78  													|
% 25.65/6.78  													+-Applying beta-rule and splitting (129), into two cases.
% 25.65/6.78  													|-Branch one:
% 25.65/6.78  													| (174)  ~ (all_75_2_23 = 0)
% 25.65/6.78  													|
% 25.65/6.78  														| Equations (163) can reduce 174 to:
% 25.65/6.78  														| (63) $false
% 25.65/6.78  														|
% 25.65/6.78  														|-The branch is then unsatisfiable
% 25.65/6.78  													|-Branch two:
% 25.65/6.78  													| (163) all_75_2_23 = 0
% 25.65/6.78  													| (177)  ~ (all_75_0_21 = 0) &  ~ (all_75_1_22 = 0)
% 25.65/6.78  													|
% 25.65/6.78  														| Applying alpha-rule on (177) yields:
% 25.65/6.78  														| (178)  ~ (all_75_0_21 = 0)
% 25.65/6.78  														| (179)  ~ (all_75_1_22 = 0)
% 25.65/6.78  														|
% 25.65/6.78  														| Equations (160) can reduce 178 to:
% 25.65/6.78  														| (180)  ~ (all_63_2_15 = 0)
% 25.65/6.78  														|
% 25.65/6.78  														| Equations (162) can reduce 179 to:
% 25.65/6.78  														| (181)  ~ (all_63_3_16 = 0)
% 25.65/6.78  														|
% 25.65/6.78  														+-Applying beta-rule and splitting (156), into two cases.
% 25.65/6.78  														|-Branch one:
% 25.65/6.78  														| (182)  ~ (all_96_0_34 = 0)
% 25.65/6.78  														|
% 25.65/6.78  															| Instantiating formula (22) with all_65_0_17, all_44_1_11, all_1_5_5, all_44_2_12, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 25.65/6.78  															| (183) all_65_0_17 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_44_2_12, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 25.65/6.78  															|
% 25.65/6.78  															| Instantiating formula (36) with all_65_0_17, all_1_4_4, all_1_5_5, all_1_6_6, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4, yields:
% 25.65/6.78  															| (184) all_65_0_17 = 0 | all_1_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_1_1, all_1_6_6) = v0)
% 25.65/6.78  															|
% 25.65/6.78  															| Instantiating formula (29) with all_1_1_1, all_65_0_17, all_1_1_1, all_1_5_5, all_1_7_7 and discharging atoms intersection_point(all_1_7_7, all_1_5_5) = all_1_1_1, apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, yields:
% 25.65/6.79  															| (185)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & convergent_lines(all_1_7_7, all_1_5_5) = v0 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) &  ~ (all_65_0_17 = 0))))
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (13) with all_65_0_17, all_1_1_1, all_1_5_5, all_1_7_7 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, convergent_lines(all_1_7_7, all_1_5_5) = 0, yields:
% 25.65/6.79  															| (186)  ? [v0] :  ? [v1] :  ? [v2] : (intersection_point(all_1_7_7, all_1_5_5) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v0 & distinct_points(all_1_1_1, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) &  ~ (all_65_0_17 = 0))))
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (12) with all_65_0_17, all_1_5_5, all_1_6_6, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, yields:
% 25.65/6.79  															| (187) all_65_0_17 = 0 |  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0) | distinct_lines(all_1_6_6, all_1_5_5) = 0
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (19) with all_1_4_4, all_1_5_5, all_1_6_6, all_1_1_1 and discharging atoms distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4, yields:
% 25.65/6.79  															| (188) all_1_4_4 = 0 |  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0) | apart_point_and_line(all_1_1_1, all_1_5_5) = 0
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (39) with all_65_0_17, all_63_1_14, all_1_7_7, all_1_5_5, all_1_1_1, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, yields:
% 25.65/6.79  															| (189) all_65_0_17 = 0 | all_63_1_14 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v3 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (12) with all_63_1_14, all_1_7_7, all_1_6_6, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, yields:
% 25.65/6.79  															| (190) all_63_1_14 = 0 |  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0) | distinct_lines(all_1_6_6, all_1_7_7) = 0
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (30) with all_1_1_1, all_63_1_14, all_1_1_1, all_1_5_5, all_1_7_7 and discharging atoms intersection_point(all_1_7_7, all_1_5_5) = all_1_1_1, apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, yields:
% 25.65/6.79  															| (191)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & convergent_lines(all_1_7_7, all_1_5_5) = v0 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v0 = 0) | v2 = 0 | ( ~ (v1 = 0) &  ~ (all_63_1_14 = 0))))
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (46) with all_63_1_14, all_1_1_1, all_1_5_5, all_1_7_7 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, convergent_lines(all_1_7_7, all_1_5_5) = 0, yields:
% 25.65/6.79  															| (192)  ? [v0] :  ? [v1] :  ? [v2] : (intersection_point(all_1_7_7, all_1_5_5) = v1 & apart_point_and_line(all_1_1_1, all_1_5_5) = v0 & distinct_points(all_1_1_1, v1) = v2 & (v2 = 0 | ( ~ (v0 = 0) &  ~ (all_63_1_14 = 0))))
% 25.65/6.79  															|
% 25.65/6.79  															| Instantiating formula (22) with all_96_0_34, all_44_1_11, all_96_1_35, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 25.65/6.79  															| (193) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (22) with all_44_1_11, all_96_0_34, all_44_2_12, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 26.11/6.79  															| (194) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (39) with all_96_0_34, all_44_1_11, all_44_2_12, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 26.11/6.79  															| (195) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (39) with all_44_1_11, all_96_0_34, all_96_1_35, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, yields:
% 26.11/6.79  															| (196) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (22) with all_65_0_17, all_96_0_34, all_1_5_5, all_96_1_35, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, yields:
% 26.11/6.79  															| (197) all_96_0_34 = 0 | all_65_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_96_1_35, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (39) with all_65_0_17, all_96_0_34, all_96_1_35, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, yields:
% 26.11/6.79  															| (198) all_96_0_34 = 0 | all_65_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (22) with all_96_0_34, all_96_0_34, all_96_1_35, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, yields:
% 26.11/6.79  															| (199) all_96_0_34 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & distinct_lines(all_96_1_35, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (35) with all_65_2_19, all_65_0_17, all_1_5_5, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_1_5_5) = all_65_2_19, distinct_lines(all_1_7_7, all_1_5_5) = 0, yields:
% 26.11/6.79  															| (200) all_65_0_17 = 0 | all_65_2_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (35) with all_65_0_17, all_65_2_19, all_1_5_5, all_1_7_7, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_1_5_5) = all_65_2_19, distinct_lines(all_1_7_7, all_1_5_5) = 0, yields:
% 26.11/6.79  															| (201) all_65_0_17 = 0 | all_65_2_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.11/6.79  															|
% 26.11/6.79  															| Instantiating formula (22) with all_63_2_15, all_44_1_11, all_1_6_6, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.11/6.79  															| (202) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.80  															|
% 26.11/6.80  															| Instantiating formula (22) with all_44_1_11, all_63_2_15, all_44_2_12, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.11/6.80  															| (203) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.80  															|
% 26.11/6.80  															| Instantiating formula (39) with all_63_2_15, all_44_1_11, all_44_2_12, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.11/6.80  															| (204) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.11/6.80  															|
% 26.11/6.80  															| Instantiating formula (39) with all_44_1_11, all_63_2_15, all_1_6_6, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.11/6.80  															| (205) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (35) with all_63_2_15, all_63_0_13, all_1_6_6, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_63_0_13, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, distinct_lines(all_1_7_7, all_1_6_6) = 0, yields:
% 26.15/6.80  															| (206) all_63_0_13 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (22) with all_63_2_15, all_96_0_34, all_1_6_6, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.15/6.80  															| (207) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (22) with all_96_0_34, all_63_2_15, all_96_1_35, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.15/6.80  															| (208) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (39) with all_63_2_15, all_96_0_34, all_96_1_35, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.15/6.80  															| (209) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (39) with all_96_0_34, all_63_2_15, all_1_6_6, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, yields:
% 26.15/6.80  															| (210) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (22) with all_63_3_16, all_44_1_11, all_1_7_7, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.15/6.80  															| (211) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_44_2_12, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (22) with all_44_1_11, all_63_3_16, all_44_2_12, all_1_7_7, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.15/6.80  															| (212) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (39) with all_63_3_16, all_44_1_11, all_44_2_12, all_1_7_7, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.15/6.80  															| (213) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (39) with all_44_1_11, all_63_3_16, all_1_7_7, all_44_2_12, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.15/6.80  															| (214) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_44_2_12, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (22) with all_63_3_16, all_65_0_17, all_1_7_7, all_1_5_5, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.15/6.80  															| (215) all_65_0_17 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.15/6.80  															|
% 26.15/6.80  															| Instantiating formula (39) with all_65_0_17, all_63_3_16, all_1_7_7, all_1_5_5, all_1_1_1, all_1_2_2 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.80  															| (216) all_65_0_17 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.80  															|
% 26.17/6.80  															| Instantiating formula (22) with all_63_3_16, all_96_0_34, all_1_7_7, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.80  															| (217) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.80  															|
% 26.17/6.80  															| Instantiating formula (22) with all_96_0_34, all_63_3_16, all_96_1_35, all_1_7_7, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.80  															| (218) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.80  															|
% 26.17/6.80  															| Instantiating formula (39) with all_63_3_16, all_96_0_34, all_96_1_35, all_1_7_7, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.80  															| (219) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.80  															|
% 26.17/6.80  															| Instantiating formula (39) with all_96_0_34, all_63_3_16, all_1_7_7, all_96_1_35, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.80  															| (220) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (22) with all_63_3_16, all_63_2_15, all_1_7_7, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.81  															| (221) all_63_2_15 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (39) with all_63_2_15, all_63_3_16, all_1_7_7, all_1_6_6, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.81  															| (222) all_63_2_15 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (22) with all_63_3_16, all_63_3_16, all_1_7_7, all_1_7_7, all_1_2_2, all_1_2_2 and discharging atoms apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, yields:
% 26.17/6.81  															| (223) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (31) with 0, all_1_1_1, all_1_1_1, all_1_2_2 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = 0, distinct_points(all_1_2_2, all_1_1_1) = 0, yields:
% 26.17/6.81  															| (224)  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_2_2, all_1_1_1) = v0 & apart_point_and_line(all_1_1_1, v0) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (1) with 0, all_1_1_1, all_1_2_2, all_1_1_1 and discharging atoms distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (225)  ? [v0] :  ? [v1] :  ? [v2] : (line_connecting(all_1_1_1, all_1_2_2) = v0 & apart_point_and_line(all_1_1_1, v0) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v2 & ( ~ (v1 = 0) | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (15) with 0, all_44_2_12, all_1_1_1, all_1_1_1, all_1_2_2 and discharging atoms line_connecting(all_1_2_2, all_1_1_1) = all_44_2_12, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (226)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v2 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (33) with 0, all_96_1_35, all_1_1_1, all_1_2_2, all_1_1_1 and discharging atoms line_connecting(all_1_1_1, all_1_2_2) = all_96_1_35, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (227)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_44_1_11, all_96_0_34, all_44_2_12, all_96_1_35, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (228) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_44_1_11, all_63_2_15, all_44_2_12, all_1_6_6, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (229) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_44_1_11, all_63_3_16, all_44_2_12, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (230) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (25) with all_65_0_17, all_65_0_17, all_1_5_5, all_1_5_5, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (231) all_65_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (25) with all_65_0_17, all_63_1_14, all_1_5_5, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_1_1, all_1_5_5) = all_65_0_17, apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (232) all_65_0_17 = 0 | all_63_1_14 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_96_0_34, all_44_1_11, all_96_1_35, all_44_2_12, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (233) all_96_0_34 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_lines(all_44_2_12, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_96_0_34, all_96_0_34, all_96_1_35, all_96_1_35, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (234) all_96_0_34 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & distinct_lines(all_96_1_35, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_96_0_34, all_63_2_15, all_96_1_35, all_1_6_6, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (235) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_96_0_34, all_63_3_16, all_96_1_35, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (236) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_2_15, all_44_1_11, all_1_6_6, all_44_2_12, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (237) all_63_2_15 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_2_15, all_96_0_34, all_1_6_6, all_96_1_35, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (238) all_96_0_34 = 0 | all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_3_16, all_44_1_11, all_1_7_7, all_44_2_12, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_44_2_12) = all_44_1_11, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (239) all_63_3_16 = 0 | all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_44_2_12, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_3_16, all_96_0_34, all_1_7_7, all_96_1_35, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_96_1_35) = all_96_0_34, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (240) all_96_0_34 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_3_16, all_63_2_15, all_1_7_7, all_1_6_6, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_1_6_6) = all_63_2_15, apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (241) all_63_2_15 = 0 | all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (14) with all_63_3_16, all_63_3_16, all_1_7_7, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms apart_point_and_line(all_1_2_2, all_1_7_7) = all_63_3_16, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.81  															| (242) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.81  															|
% 26.17/6.81  															| Instantiating formula (44) with all_1_5_5, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms distinct_lines(all_1_7_7, all_1_5_5) = 0, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.82  															| (243)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v0 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating formula (44) with all_1_6_6, all_1_7_7, all_1_2_2, all_1_1_1 and discharging atoms distinct_lines(all_1_7_7, all_1_6_6) = 0, distinct_points(all_1_1_1, all_1_2_2) = 0, yields:
% 26.17/6.82  															| (244)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v0 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & (v3 = 0 | v2 = 0 | v1 = 0 | v0 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (244) with all_129_0_39, all_129_1_40, all_129_2_41, all_129_3_42 yields:
% 26.17/6.82  															| (245) apart_point_and_line(all_1_1_1, all_1_6_6) = all_129_2_41 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_129_3_42 & apart_point_and_line(all_1_2_2, all_1_6_6) = all_129_0_39 & apart_point_and_line(all_1_2_2, all_1_7_7) = all_129_1_40 & (all_129_0_39 = 0 | all_129_1_40 = 0 | all_129_2_41 = 0 | all_129_3_42 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (245) yields:
% 26.17/6.82  															| (246) all_129_0_39 = 0 | all_129_1_40 = 0 | all_129_2_41 = 0 | all_129_3_42 = 0
% 26.17/6.82  															| (247) apart_point_and_line(all_1_2_2, all_1_6_6) = all_129_0_39
% 26.17/6.82  															| (248) apart_point_and_line(all_1_1_1, all_1_6_6) = all_129_2_41
% 26.17/6.82  															| (249) apart_point_and_line(all_1_1_1, all_1_7_7) = all_129_3_42
% 26.17/6.82  															| (250) apart_point_and_line(all_1_2_2, all_1_7_7) = all_129_1_40
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (243) with all_131_0_43, all_131_1_44, all_131_2_45, all_131_3_46 yields:
% 26.17/6.82  															| (251) apart_point_and_line(all_1_1_1, all_1_5_5) = all_131_2_45 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_131_3_46 & apart_point_and_line(all_1_2_2, all_1_5_5) = all_131_0_43 & apart_point_and_line(all_1_2_2, all_1_7_7) = all_131_1_44 & (all_131_0_43 = 0 | all_131_1_44 = 0 | all_131_2_45 = 0 | all_131_3_46 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (251) yields:
% 26.17/6.82  															| (252) all_131_0_43 = 0 | all_131_1_44 = 0 | all_131_2_45 = 0 | all_131_3_46 = 0
% 26.17/6.82  															| (253) apart_point_and_line(all_1_1_1, all_1_7_7) = all_131_3_46
% 26.17/6.82  															| (254) apart_point_and_line(all_1_2_2, all_1_7_7) = all_131_1_44
% 26.17/6.82  															| (255) apart_point_and_line(all_1_1_1, all_1_5_5) = all_131_2_45
% 26.17/6.82  															| (256) apart_point_and_line(all_1_2_2, all_1_5_5) = all_131_0_43
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (192) with all_133_0_47, all_133_1_48, all_133_2_49 yields:
% 26.17/6.82  															| (257) intersection_point(all_1_7_7, all_1_5_5) = all_133_1_48 & apart_point_and_line(all_1_1_1, all_1_5_5) = all_133_2_49 & distinct_points(all_1_1_1, all_133_1_48) = all_133_0_47 & (all_133_0_47 = 0 | ( ~ (all_133_2_49 = 0) &  ~ (all_63_1_14 = 0)))
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (257) yields:
% 26.17/6.82  															| (258) intersection_point(all_1_7_7, all_1_5_5) = all_133_1_48
% 26.17/6.82  															| (259) apart_point_and_line(all_1_1_1, all_1_5_5) = all_133_2_49
% 26.17/6.82  															| (260) distinct_points(all_1_1_1, all_133_1_48) = all_133_0_47
% 26.17/6.82  															| (261) all_133_0_47 = 0 | ( ~ (all_133_2_49 = 0) &  ~ (all_63_1_14 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (186) with all_135_0_50, all_135_1_51, all_135_2_52 yields:
% 26.17/6.82  															| (262) intersection_point(all_1_7_7, all_1_5_5) = all_135_1_51 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_135_2_52 & distinct_points(all_1_1_1, all_135_1_51) = all_135_0_50 & (all_135_0_50 = 0 | ( ~ (all_135_2_52 = 0) &  ~ (all_65_0_17 = 0)))
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (262) yields:
% 26.17/6.82  															| (263) intersection_point(all_1_7_7, all_1_5_5) = all_135_1_51
% 26.17/6.82  															| (264) apart_point_and_line(all_1_1_1, all_1_7_7) = all_135_2_52
% 26.17/6.82  															| (265) distinct_points(all_1_1_1, all_135_1_51) = all_135_0_50
% 26.17/6.82  															| (266) all_135_0_50 = 0 | ( ~ (all_135_2_52 = 0) &  ~ (all_65_0_17 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (185) with all_137_0_53, all_137_1_54, all_137_2_55 yields:
% 26.17/6.82  															| (267) apart_point_and_line(all_1_1_1, all_1_7_7) = all_137_1_54 & convergent_lines(all_1_7_7, all_1_5_5) = all_137_2_55 & distinct_points(all_1_1_1, all_1_1_1) = all_137_0_53 & ( ~ (all_137_2_55 = 0) | all_137_0_53 = 0 | ( ~ (all_137_1_54 = 0) &  ~ (all_65_0_17 = 0)))
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (267) yields:
% 26.17/6.82  															| (268) apart_point_and_line(all_1_1_1, all_1_7_7) = all_137_1_54
% 26.17/6.82  															| (269) convergent_lines(all_1_7_7, all_1_5_5) = all_137_2_55
% 26.17/6.82  															| (270) distinct_points(all_1_1_1, all_1_1_1) = all_137_0_53
% 26.17/6.82  															| (271)  ~ (all_137_2_55 = 0) | all_137_0_53 = 0 | ( ~ (all_137_1_54 = 0) &  ~ (all_65_0_17 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (191) with all_139_0_56, all_139_1_57, all_139_2_58 yields:
% 26.17/6.82  															| (272) apart_point_and_line(all_1_1_1, all_1_5_5) = all_139_1_57 & convergent_lines(all_1_7_7, all_1_5_5) = all_139_2_58 & distinct_points(all_1_1_1, all_1_1_1) = all_139_0_56 & ( ~ (all_139_2_58 = 0) | all_139_0_56 = 0 | ( ~ (all_139_1_57 = 0) &  ~ (all_63_1_14 = 0)))
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (272) yields:
% 26.17/6.82  															| (273) apart_point_and_line(all_1_1_1, all_1_5_5) = all_139_1_57
% 26.17/6.82  															| (274) convergent_lines(all_1_7_7, all_1_5_5) = all_139_2_58
% 26.17/6.82  															| (275) distinct_points(all_1_1_1, all_1_1_1) = all_139_0_56
% 26.17/6.82  															| (276)  ~ (all_139_2_58 = 0) | all_139_0_56 = 0 | ( ~ (all_139_1_57 = 0) &  ~ (all_63_1_14 = 0))
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (226) with all_141_0_59, all_141_1_60, all_141_2_61 yields:
% 26.17/6.82  															| (277) apart_point_and_line(all_1_1_1, all_44_2_12) = all_141_1_60 & distinct_points(all_1_1_1, all_1_1_1) = all_141_0_59 & distinct_points(all_1_2_2, all_1_1_1) = all_141_2_61 & ( ~ (all_141_1_60 = 0) |  ~ (all_141_2_61 = 0) | all_141_0_59 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (277) yields:
% 26.17/6.82  															| (278) apart_point_and_line(all_1_1_1, all_44_2_12) = all_141_1_60
% 26.17/6.82  															| (279) distinct_points(all_1_1_1, all_1_1_1) = all_141_0_59
% 26.17/6.82  															| (280) distinct_points(all_1_2_2, all_1_1_1) = all_141_2_61
% 26.17/6.82  															| (281)  ~ (all_141_1_60 = 0) |  ~ (all_141_2_61 = 0) | all_141_0_59 = 0
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (225) with all_143_0_62, all_143_1_63, all_143_2_64 yields:
% 26.17/6.82  															| (282) line_connecting(all_1_1_1, all_1_2_2) = all_143_2_64 & apart_point_and_line(all_1_1_1, all_143_2_64) = all_143_1_63 & distinct_points(all_1_1_1, all_1_1_1) = all_143_0_62 & ( ~ (all_143_1_63 = 0) | all_143_0_62 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (282) yields:
% 26.17/6.82  															| (283) line_connecting(all_1_1_1, all_1_2_2) = all_143_2_64
% 26.17/6.82  															| (284) apart_point_and_line(all_1_1_1, all_143_2_64) = all_143_1_63
% 26.17/6.82  															| (285) distinct_points(all_1_1_1, all_1_1_1) = all_143_0_62
% 26.17/6.82  															| (286)  ~ (all_143_1_63 = 0) | all_143_0_62 = 0
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (227) with all_147_0_68, all_147_1_69, all_147_2_70 yields:
% 26.17/6.82  															| (287) apart_point_and_line(all_1_1_1, all_96_1_35) = all_147_1_69 & distinct_points(all_1_1_1, all_1_1_1) = all_147_0_68 & distinct_points(all_1_1_1, all_1_2_2) = all_147_2_70 & ( ~ (all_147_1_69 = 0) |  ~ (all_147_2_70 = 0) | all_147_0_68 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (287) yields:
% 26.17/6.82  															| (288) apart_point_and_line(all_1_1_1, all_96_1_35) = all_147_1_69
% 26.17/6.82  															| (289) distinct_points(all_1_1_1, all_1_1_1) = all_147_0_68
% 26.17/6.82  															| (290) distinct_points(all_1_1_1, all_1_2_2) = all_147_2_70
% 26.17/6.82  															| (291)  ~ (all_147_1_69 = 0) |  ~ (all_147_2_70 = 0) | all_147_0_68 = 0
% 26.17/6.82  															|
% 26.17/6.82  															| Instantiating (224) with all_149_0_71, all_149_1_72, all_149_2_73 yields:
% 26.17/6.82  															| (292) line_connecting(all_1_2_2, all_1_1_1) = all_149_2_73 & apart_point_and_line(all_1_1_1, all_149_2_73) = all_149_1_72 & distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71 & ( ~ (all_149_1_72 = 0) | all_149_0_71 = 0)
% 26.17/6.82  															|
% 26.17/6.82  															| Applying alpha-rule on (292) yields:
% 26.17/6.82  															| (293) line_connecting(all_1_2_2, all_1_1_1) = all_149_2_73
% 26.17/6.82  															| (294) apart_point_and_line(all_1_1_1, all_149_2_73) = all_149_1_72
% 26.17/6.82  															| (295) distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71
% 26.17/6.82  															| (296)  ~ (all_149_1_72 = 0) | all_149_0_71 = 0
% 26.17/6.82  															|
% 26.17/6.82  															+-Applying beta-rule and splitting (234), into two cases.
% 26.17/6.82  															|-Branch one:
% 26.17/6.82  															| (297) all_96_0_34 = 0
% 26.17/6.82  															|
% 26.17/6.82  																| Equations (297) can reduce 182 to:
% 26.17/6.82  																| (63) $false
% 26.17/6.82  																|
% 26.17/6.82  																|-The branch is then unsatisfiable
% 26.17/6.82  															|-Branch two:
% 26.17/6.82  															| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.82  															| (300)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & distinct_lines(all_96_1_35, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.82  															|
% 26.17/6.82  																+-Applying beta-rule and splitting (199), into two cases.
% 26.17/6.82  																|-Branch one:
% 26.17/6.82  																| (297) all_96_0_34 = 0
% 26.17/6.82  																|
% 26.17/6.82  																	| Equations (297) can reduce 182 to:
% 26.17/6.82  																	| (63) $false
% 26.17/6.82  																	|
% 26.17/6.82  																	|-The branch is then unsatisfiable
% 26.17/6.82  																|-Branch two:
% 26.17/6.82  																| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.82  																| (304)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & distinct_lines(all_96_1_35, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.82  																|
% 26.17/6.82  																	+-Applying beta-rule and splitting (223), into two cases.
% 26.17/6.82  																	|-Branch one:
% 26.17/6.82  																	| (305) all_63_3_16 = 0
% 26.17/6.82  																	|
% 26.17/6.82  																		| Equations (305) can reduce 181 to:
% 26.17/6.82  																		| (63) $false
% 26.17/6.82  																		|
% 26.17/6.82  																		|-The branch is then unsatisfiable
% 26.17/6.82  																	|-Branch two:
% 26.17/6.82  																	| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.82  																	| (308)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.82  																	|
% 26.17/6.82  																		+-Applying beta-rule and splitting (242), into two cases.
% 26.17/6.82  																		|-Branch one:
% 26.17/6.82  																		| (305) all_63_3_16 = 0
% 26.17/6.82  																		|
% 26.17/6.82  																			| Equations (305) can reduce 181 to:
% 26.17/6.82  																			| (63) $false
% 26.17/6.82  																			|
% 26.17/6.82  																			|-The branch is then unsatisfiable
% 26.17/6.82  																		|-Branch two:
% 26.17/6.82  																		| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.82  																		| (312)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.82  																		|
% 26.17/6.82  																			| Instantiating (312) with all_170_0_85, all_170_1_86, all_170_2_87 yields:
% 26.17/6.82  																			| (313) apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_0_85 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_1_86 & distinct_lines(all_1_7_7, all_1_7_7) = all_170_2_87 & ( ~ (all_170_2_87 = 0) | all_170_0_85 = 0 | all_170_1_86 = 0)
% 26.17/6.82  																			|
% 26.17/6.82  																			| Applying alpha-rule on (313) yields:
% 26.17/6.82  																			| (314) apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_0_85
% 26.17/6.82  																			| (315) apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_1_86
% 26.17/6.83  																			| (316) distinct_lines(all_1_7_7, all_1_7_7) = all_170_2_87
% 26.17/6.83  																			| (317)  ~ (all_170_2_87 = 0) | all_170_0_85 = 0 | all_170_1_86 = 0
% 26.17/6.83  																			|
% 26.17/6.83  																			+-Applying beta-rule and splitting (237), into two cases.
% 26.17/6.83  																			|-Branch one:
% 26.17/6.83  																			| (318) all_63_2_15 = 0
% 26.17/6.83  																			|
% 26.17/6.83  																				| Equations (318) can reduce 180 to:
% 26.17/6.83  																				| (63) $false
% 26.17/6.83  																				|
% 26.17/6.83  																				|-The branch is then unsatisfiable
% 26.17/6.83  																			|-Branch two:
% 26.17/6.83  																			| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																			| (321) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																			|
% 26.17/6.83  																				+-Applying beta-rule and splitting (229), into two cases.
% 26.17/6.83  																				|-Branch one:
% 26.17/6.83  																				| (318) all_63_2_15 = 0
% 26.17/6.83  																				|
% 26.17/6.83  																					| Equations (318) can reduce 180 to:
% 26.17/6.83  																					| (63) $false
% 26.17/6.83  																					|
% 26.17/6.83  																					|-The branch is then unsatisfiable
% 26.17/6.83  																				|-Branch two:
% 26.17/6.83  																				| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																				| (325) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																				|
% 26.17/6.83  																					+-Applying beta-rule and splitting (202), into two cases.
% 26.17/6.83  																					|-Branch one:
% 26.17/6.83  																					| (318) all_63_2_15 = 0
% 26.17/6.83  																					|
% 26.17/6.83  																						| Equations (318) can reduce 180 to:
% 26.17/6.83  																						| (63) $false
% 26.17/6.83  																						|
% 26.17/6.83  																						|-The branch is then unsatisfiable
% 26.17/6.83  																					|-Branch two:
% 26.17/6.83  																					| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																					| (329) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																					|
% 26.17/6.83  																						+-Applying beta-rule and splitting (222), into two cases.
% 26.17/6.83  																						|-Branch one:
% 26.17/6.83  																						| (318) all_63_2_15 = 0
% 26.17/6.83  																						|
% 26.17/6.83  																							| Equations (318) can reduce 180 to:
% 26.17/6.83  																							| (63) $false
% 26.17/6.83  																							|
% 26.17/6.83  																							|-The branch is then unsatisfiable
% 26.17/6.83  																						|-Branch two:
% 26.17/6.83  																						| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																						| (333) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																						|
% 26.17/6.83  																							+-Applying beta-rule and splitting (221), into two cases.
% 26.17/6.83  																							|-Branch one:
% 26.17/6.83  																							| (318) all_63_2_15 = 0
% 26.17/6.83  																							|
% 26.17/6.83  																								| Equations (318) can reduce 180 to:
% 26.17/6.83  																								| (63) $false
% 26.17/6.83  																								|
% 26.17/6.83  																								|-The branch is then unsatisfiable
% 26.17/6.83  																							|-Branch two:
% 26.17/6.83  																							| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																							| (337) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																							|
% 26.17/6.83  																								+-Applying beta-rule and splitting (193), into two cases.
% 26.17/6.83  																								|-Branch one:
% 26.17/6.83  																								| (297) all_96_0_34 = 0
% 26.17/6.83  																								|
% 26.17/6.83  																									| Equations (297) can reduce 182 to:
% 26.17/6.83  																									| (63) $false
% 26.17/6.83  																									|
% 26.17/6.83  																									|-The branch is then unsatisfiable
% 26.17/6.83  																								|-Branch two:
% 26.17/6.83  																								| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																								| (341) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																								|
% 26.17/6.83  																									+-Applying beta-rule and splitting (233), into two cases.
% 26.17/6.83  																									|-Branch one:
% 26.17/6.83  																									| (297) all_96_0_34 = 0
% 26.17/6.83  																									|
% 26.17/6.83  																										| Equations (297) can reduce 182 to:
% 26.17/6.83  																										| (63) $false
% 26.17/6.83  																										|
% 26.17/6.83  																										|-The branch is then unsatisfiable
% 26.17/6.83  																									|-Branch two:
% 26.17/6.83  																									| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																									| (345) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_lines(all_44_2_12, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																									|
% 26.17/6.83  																										+-Applying beta-rule and splitting (194), into two cases.
% 26.17/6.83  																										|-Branch one:
% 26.17/6.83  																										| (297) all_96_0_34 = 0
% 26.17/6.83  																										|
% 26.17/6.83  																											| Equations (297) can reduce 182 to:
% 26.17/6.83  																											| (63) $false
% 26.17/6.83  																											|
% 26.17/6.83  																											|-The branch is then unsatisfiable
% 26.17/6.83  																										|-Branch two:
% 26.17/6.83  																										| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																										| (349) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																										|
% 26.17/6.83  																											+-Applying beta-rule and splitting (195), into two cases.
% 26.17/6.83  																											|-Branch one:
% 26.17/6.83  																											| (297) all_96_0_34 = 0
% 26.17/6.83  																											|
% 26.17/6.83  																												| Equations (297) can reduce 182 to:
% 26.17/6.83  																												| (63) $false
% 26.17/6.83  																												|
% 26.17/6.83  																												|-The branch is then unsatisfiable
% 26.17/6.83  																											|-Branch two:
% 26.17/6.83  																											| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																											| (353) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																											|
% 26.17/6.83  																												+-Applying beta-rule and splitting (196), into two cases.
% 26.17/6.83  																												|-Branch one:
% 26.17/6.83  																												| (297) all_96_0_34 = 0
% 26.17/6.83  																												|
% 26.17/6.83  																													| Equations (297) can reduce 182 to:
% 26.17/6.83  																													| (63) $false
% 26.17/6.83  																													|
% 26.17/6.83  																													|-The branch is then unsatisfiable
% 26.17/6.83  																												|-Branch two:
% 26.17/6.83  																												| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																												| (357) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																												|
% 26.17/6.83  																													+-Applying beta-rule and splitting (228), into two cases.
% 26.17/6.83  																													|-Branch one:
% 26.17/6.83  																													| (297) all_96_0_34 = 0
% 26.17/6.83  																													|
% 26.17/6.83  																														| Equations (297) can reduce 182 to:
% 26.17/6.83  																														| (63) $false
% 26.17/6.83  																														|
% 26.17/6.83  																														|-The branch is then unsatisfiable
% 26.17/6.83  																													|-Branch two:
% 26.17/6.83  																													| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																													| (361) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																													|
% 26.17/6.83  																														+-Applying beta-rule and splitting (203), into two cases.
% 26.17/6.83  																														|-Branch one:
% 26.17/6.83  																														| (318) all_63_2_15 = 0
% 26.17/6.83  																														|
% 26.17/6.83  																															| Equations (318) can reduce 180 to:
% 26.17/6.83  																															| (63) $false
% 26.17/6.83  																															|
% 26.17/6.83  																															|-The branch is then unsatisfiable
% 26.17/6.83  																														|-Branch two:
% 26.17/6.83  																														| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																														| (365) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																														|
% 26.17/6.83  																															+-Applying beta-rule and splitting (204), into two cases.
% 26.17/6.83  																															|-Branch one:
% 26.17/6.83  																															| (318) all_63_2_15 = 0
% 26.17/6.83  																															|
% 26.17/6.83  																																| Equations (318) can reduce 180 to:
% 26.17/6.83  																																| (63) $false
% 26.17/6.83  																																|
% 26.17/6.83  																																|-The branch is then unsatisfiable
% 26.17/6.83  																															|-Branch two:
% 26.17/6.83  																															| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																															| (369) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																															|
% 26.17/6.83  																																+-Applying beta-rule and splitting (205), into two cases.
% 26.17/6.83  																																|-Branch one:
% 26.17/6.83  																																| (318) all_63_2_15 = 0
% 26.17/6.83  																																|
% 26.17/6.83  																																	| Equations (318) can reduce 180 to:
% 26.17/6.83  																																	| (63) $false
% 26.17/6.83  																																	|
% 26.17/6.83  																																	|-The branch is then unsatisfiable
% 26.17/6.83  																																|-Branch two:
% 26.17/6.83  																																| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.83  																																| (373) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																																|
% 26.17/6.83  																																	+-Applying beta-rule and splitting (209), into two cases.
% 26.17/6.83  																																	|-Branch one:
% 26.17/6.83  																																	| (297) all_96_0_34 = 0
% 26.17/6.83  																																	|
% 26.17/6.83  																																		| Equations (297) can reduce 182 to:
% 26.17/6.83  																																		| (63) $false
% 26.17/6.83  																																		|
% 26.17/6.83  																																		|-The branch is then unsatisfiable
% 26.17/6.83  																																	|-Branch two:
% 26.17/6.83  																																	| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																																	| (377) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																																	|
% 26.17/6.83  																																		+-Applying beta-rule and splitting (210), into two cases.
% 26.17/6.83  																																		|-Branch one:
% 26.17/6.83  																																		| (297) all_96_0_34 = 0
% 26.17/6.83  																																		|
% 26.17/6.83  																																			| Equations (297) can reduce 182 to:
% 26.17/6.83  																																			| (63) $false
% 26.17/6.83  																																			|
% 26.17/6.83  																																			|-The branch is then unsatisfiable
% 26.17/6.83  																																		|-Branch two:
% 26.17/6.83  																																		| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																																		| (381) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.83  																																		|
% 26.17/6.83  																																			+-Applying beta-rule and splitting (238), into two cases.
% 26.17/6.83  																																			|-Branch one:
% 26.17/6.83  																																			| (297) all_96_0_34 = 0
% 26.17/6.83  																																			|
% 26.17/6.83  																																				| Equations (297) can reduce 182 to:
% 26.17/6.83  																																				| (63) $false
% 26.17/6.83  																																				|
% 26.17/6.83  																																				|-The branch is then unsatisfiable
% 26.17/6.83  																																			|-Branch two:
% 26.17/6.83  																																			| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																																			| (385) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																																			|
% 26.17/6.83  																																				+-Applying beta-rule and splitting (235), into two cases.
% 26.17/6.83  																																				|-Branch one:
% 26.17/6.83  																																				| (297) all_96_0_34 = 0
% 26.17/6.83  																																				|
% 26.17/6.83  																																					| Equations (297) can reduce 182 to:
% 26.17/6.83  																																					| (63) $false
% 26.17/6.83  																																					|
% 26.17/6.83  																																					|-The branch is then unsatisfiable
% 26.17/6.83  																																				|-Branch two:
% 26.17/6.83  																																				| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																																				| (389) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.83  																																				|
% 26.17/6.83  																																					+-Applying beta-rule and splitting (207), into two cases.
% 26.17/6.83  																																					|-Branch one:
% 26.17/6.83  																																					| (297) all_96_0_34 = 0
% 26.17/6.83  																																					|
% 26.17/6.83  																																						| Equations (297) can reduce 182 to:
% 26.17/6.83  																																						| (63) $false
% 26.17/6.83  																																						|
% 26.17/6.83  																																						|-The branch is then unsatisfiable
% 26.17/6.83  																																					|-Branch two:
% 26.17/6.83  																																					| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.83  																																					| (393) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																					|
% 26.17/6.84  																																						+-Applying beta-rule and splitting (208), into two cases.
% 26.17/6.84  																																						|-Branch one:
% 26.17/6.84  																																						| (297) all_96_0_34 = 0
% 26.17/6.84  																																						|
% 26.17/6.84  																																							| Equations (297) can reduce 182 to:
% 26.17/6.84  																																							| (63) $false
% 26.17/6.84  																																							|
% 26.17/6.84  																																							|-The branch is then unsatisfiable
% 26.17/6.84  																																						|-Branch two:
% 26.17/6.84  																																						| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																						| (397) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																						|
% 26.17/6.84  																																							+-Applying beta-rule and splitting (240), into two cases.
% 26.17/6.84  																																							|-Branch one:
% 26.17/6.84  																																							| (297) all_96_0_34 = 0
% 26.17/6.84  																																							|
% 26.17/6.84  																																								| Equations (297) can reduce 182 to:
% 26.17/6.84  																																								| (63) $false
% 26.17/6.84  																																								|
% 26.17/6.84  																																								|-The branch is then unsatisfiable
% 26.17/6.84  																																							|-Branch two:
% 26.17/6.84  																																							| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																							| (401) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																							|
% 26.17/6.84  																																								+-Applying beta-rule and splitting (236), into two cases.
% 26.17/6.84  																																								|-Branch one:
% 26.17/6.84  																																								| (297) all_96_0_34 = 0
% 26.17/6.84  																																								|
% 26.17/6.84  																																									| Equations (297) can reduce 182 to:
% 26.17/6.84  																																									| (63) $false
% 26.17/6.84  																																									|
% 26.17/6.84  																																									|-The branch is then unsatisfiable
% 26.17/6.84  																																								|-Branch two:
% 26.17/6.84  																																								| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																								| (405) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																								|
% 26.17/6.84  																																									+-Applying beta-rule and splitting (217), into two cases.
% 26.17/6.84  																																									|-Branch one:
% 26.17/6.84  																																									| (297) all_96_0_34 = 0
% 26.17/6.84  																																									|
% 26.17/6.84  																																										| Equations (297) can reduce 182 to:
% 26.17/6.84  																																										| (63) $false
% 26.17/6.84  																																										|
% 26.17/6.84  																																										|-The branch is then unsatisfiable
% 26.17/6.84  																																									|-Branch two:
% 26.17/6.84  																																									| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																									| (409) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																									|
% 26.17/6.84  																																										+-Applying beta-rule and splitting (220), into two cases.
% 26.17/6.84  																																										|-Branch one:
% 26.17/6.84  																																										| (297) all_96_0_34 = 0
% 26.17/6.84  																																										|
% 26.17/6.84  																																											| Equations (297) can reduce 182 to:
% 26.17/6.84  																																											| (63) $false
% 26.17/6.84  																																											|
% 26.17/6.84  																																											|-The branch is then unsatisfiable
% 26.17/6.84  																																										|-Branch two:
% 26.17/6.84  																																										| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																										| (413) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																										|
% 26.17/6.84  																																											+-Applying beta-rule and splitting (218), into two cases.
% 26.17/6.84  																																											|-Branch one:
% 26.17/6.84  																																											| (297) all_96_0_34 = 0
% 26.17/6.84  																																											|
% 26.17/6.84  																																												| Equations (297) can reduce 182 to:
% 26.17/6.84  																																												| (63) $false
% 26.17/6.84  																																												|
% 26.17/6.84  																																												|-The branch is then unsatisfiable
% 26.17/6.84  																																											|-Branch two:
% 26.17/6.84  																																											| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																											| (417) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																											|
% 26.17/6.84  																																												+-Applying beta-rule and splitting (219), into two cases.
% 26.17/6.84  																																												|-Branch one:
% 26.17/6.84  																																												| (297) all_96_0_34 = 0
% 26.17/6.84  																																												|
% 26.17/6.84  																																													| Equations (297) can reduce 182 to:
% 26.17/6.84  																																													| (63) $false
% 26.17/6.84  																																													|
% 26.17/6.84  																																													|-The branch is then unsatisfiable
% 26.17/6.84  																																												|-Branch two:
% 26.17/6.84  																																												| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.84  																																												| (421) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																												|
% 26.17/6.84  																																													+-Applying beta-rule and splitting (212), into two cases.
% 26.17/6.84  																																													|-Branch one:
% 26.17/6.84  																																													| (305) all_63_3_16 = 0
% 26.17/6.84  																																													|
% 26.17/6.84  																																														| Equations (305) can reduce 181 to:
% 26.17/6.84  																																														| (63) $false
% 26.17/6.84  																																														|
% 26.17/6.84  																																														|-The branch is then unsatisfiable
% 26.17/6.84  																																													|-Branch two:
% 26.17/6.84  																																													| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																													| (425) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																													|
% 26.17/6.84  																																														+-Applying beta-rule and splitting (213), into two cases.
% 26.17/6.84  																																														|-Branch one:
% 26.17/6.84  																																														| (305) all_63_3_16 = 0
% 26.17/6.84  																																														|
% 26.17/6.84  																																															| Equations (305) can reduce 181 to:
% 26.17/6.84  																																															| (63) $false
% 26.17/6.84  																																															|
% 26.17/6.84  																																															|-The branch is then unsatisfiable
% 26.17/6.84  																																														|-Branch two:
% 26.17/6.84  																																														| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																														| (429) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																														|
% 26.17/6.84  																																															+-Applying beta-rule and splitting (239), into two cases.
% 26.17/6.84  																																															|-Branch one:
% 26.17/6.84  																																															| (305) all_63_3_16 = 0
% 26.17/6.84  																																															|
% 26.17/6.84  																																																| Equations (305) can reduce 181 to:
% 26.17/6.84  																																																| (63) $false
% 26.17/6.84  																																																|
% 26.17/6.84  																																																|-The branch is then unsatisfiable
% 26.17/6.84  																																															|-Branch two:
% 26.17/6.84  																																															| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																															| (433) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_44_2_12, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																															|
% 26.17/6.84  																																																+-Applying beta-rule and splitting (230), into two cases.
% 26.17/6.84  																																																|-Branch one:
% 26.17/6.84  																																																| (305) all_63_3_16 = 0
% 26.17/6.84  																																																|
% 26.17/6.84  																																																	| Equations (305) can reduce 181 to:
% 26.17/6.84  																																																	| (63) $false
% 26.17/6.84  																																																	|
% 26.17/6.84  																																																	|-The branch is then unsatisfiable
% 26.17/6.84  																																																|-Branch two:
% 26.17/6.84  																																																| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																																| (437) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																																|
% 26.17/6.84  																																																	+-Applying beta-rule and splitting (211), into two cases.
% 26.17/6.84  																																																	|-Branch one:
% 26.17/6.84  																																																	| (305) all_63_3_16 = 0
% 26.17/6.84  																																																	|
% 26.17/6.84  																																																		| Equations (305) can reduce 181 to:
% 26.17/6.84  																																																		| (63) $false
% 26.17/6.84  																																																		|
% 26.17/6.84  																																																		|-The branch is then unsatisfiable
% 26.17/6.84  																																																	|-Branch two:
% 26.17/6.84  																																																	| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																																	| (441) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_44_2_12, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																																	|
% 26.17/6.84  																																																		+-Applying beta-rule and splitting (214), into two cases.
% 26.17/6.84  																																																		|-Branch one:
% 26.17/6.84  																																																		| (305) all_63_3_16 = 0
% 26.17/6.84  																																																		|
% 26.17/6.84  																																																			| Equations (305) can reduce 181 to:
% 26.17/6.84  																																																			| (63) $false
% 26.17/6.84  																																																			|
% 26.17/6.84  																																																			|-The branch is then unsatisfiable
% 26.17/6.84  																																																		|-Branch two:
% 26.17/6.84  																																																		| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.84  																																																		| (445) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_44_2_12, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.84  																																																		|
% 26.17/6.84  																																																			+-Applying beta-rule and splitting (241), into two cases.
% 26.17/6.84  																																																			|-Branch one:
% 26.17/6.84  																																																			| (318) all_63_2_15 = 0
% 26.17/6.84  																																																			|
% 26.17/6.84  																																																				| Equations (318) can reduce 180 to:
% 26.17/6.84  																																																				| (63) $false
% 26.17/6.84  																																																				|
% 26.17/6.84  																																																				|-The branch is then unsatisfiable
% 26.17/6.84  																																																			|-Branch two:
% 26.17/6.84  																																																			| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.84  																																																			| (449) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																																			|
% 26.17/6.84  																																																				+-Applying beta-rule and splitting (321), into two cases.
% 26.17/6.84  																																																				|-Branch one:
% 26.17/6.84  																																																				| (130) all_44_1_11 = 0
% 26.17/6.84  																																																				|
% 26.17/6.84  																																																					| Equations (130) can reduce 99 to:
% 26.17/6.84  																																																					| (63) $false
% 26.17/6.84  																																																					|
% 26.17/6.84  																																																					|-The branch is then unsatisfiable
% 26.17/6.84  																																																				|-Branch two:
% 26.17/6.84  																																																				| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.84  																																																				| (453)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																																				|
% 26.17/6.84  																																																					| Instantiating (453) with all_280_0_89, all_280_1_90, all_280_2_91 yields:
% 26.17/6.84  																																																					| (454) apart_point_and_line(all_1_1_1, all_44_2_12) = all_280_1_90 & apart_point_and_line(all_1_1_1, all_1_6_6) = all_280_0_89 & distinct_lines(all_44_2_12, all_1_6_6) = all_280_2_91 & ( ~ (all_280_2_91 = 0) | all_280_0_89 = 0 | all_280_1_90 = 0)
% 26.17/6.84  																																																					|
% 26.17/6.84  																																																					| Applying alpha-rule on (454) yields:
% 26.17/6.84  																																																					| (455) apart_point_and_line(all_1_1_1, all_44_2_12) = all_280_1_90
% 26.17/6.84  																																																					| (456) apart_point_and_line(all_1_1_1, all_1_6_6) = all_280_0_89
% 26.17/6.84  																																																					| (457) distinct_lines(all_44_2_12, all_1_6_6) = all_280_2_91
% 26.17/6.84  																																																					| (458)  ~ (all_280_2_91 = 0) | all_280_0_89 = 0 | all_280_1_90 = 0
% 26.17/6.84  																																																					|
% 26.17/6.84  																																																					+-Applying beta-rule and splitting (325), into two cases.
% 26.17/6.84  																																																					|-Branch one:
% 26.17/6.84  																																																					| (130) all_44_1_11 = 0
% 26.17/6.84  																																																					|
% 26.17/6.84  																																																						| Equations (130) can reduce 99 to:
% 26.17/6.84  																																																						| (63) $false
% 26.17/6.84  																																																						|
% 26.17/6.84  																																																						|-The branch is then unsatisfiable
% 26.17/6.84  																																																					|-Branch two:
% 26.17/6.84  																																																					| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.84  																																																					| (462)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.84  																																																					|
% 26.17/6.84  																																																						| Instantiating (462) with all_285_0_92, all_285_1_93, all_285_2_94 yields:
% 26.17/6.84  																																																						| (463) apart_point_and_line(all_1_1_1, all_44_2_12) = all_285_0_92 & apart_point_and_line(all_1_1_1, all_1_6_6) = all_285_1_93 & distinct_lines(all_1_6_6, all_44_2_12) = all_285_2_94 & ( ~ (all_285_2_94 = 0) | all_285_0_92 = 0 | all_285_1_93 = 0)
% 26.17/6.84  																																																						|
% 26.17/6.84  																																																						| Applying alpha-rule on (463) yields:
% 26.17/6.84  																																																						| (464) apart_point_and_line(all_1_1_1, all_44_2_12) = all_285_0_92
% 26.17/6.84  																																																						| (465) apart_point_and_line(all_1_1_1, all_1_6_6) = all_285_1_93
% 26.17/6.84  																																																						| (466) distinct_lines(all_1_6_6, all_44_2_12) = all_285_2_94
% 26.17/6.84  																																																						| (467)  ~ (all_285_2_94 = 0) | all_285_0_92 = 0 | all_285_1_93 = 0
% 26.17/6.84  																																																						|
% 26.17/6.84  																																																						+-Applying beta-rule and splitting (329), into two cases.
% 26.17/6.84  																																																						|-Branch one:
% 26.17/6.84  																																																						| (130) all_44_1_11 = 0
% 26.17/6.84  																																																						|
% 26.17/6.84  																																																							| Equations (130) can reduce 99 to:
% 26.17/6.84  																																																							| (63) $false
% 26.17/6.84  																																																							|
% 26.17/6.84  																																																							|-The branch is then unsatisfiable
% 26.17/6.84  																																																						|-Branch two:
% 26.17/6.84  																																																						| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.84  																																																						| (471)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																						|
% 26.17/6.85  																																																							+-Applying beta-rule and splitting (333), into two cases.
% 26.17/6.85  																																																							|-Branch one:
% 26.17/6.85  																																																							| (305) all_63_3_16 = 0
% 26.17/6.85  																																																							|
% 26.17/6.85  																																																								| Equations (305) can reduce 181 to:
% 26.17/6.85  																																																								| (63) $false
% 26.17/6.85  																																																								|
% 26.17/6.85  																																																								|-The branch is then unsatisfiable
% 26.17/6.85  																																																							|-Branch two:
% 26.17/6.85  																																																							| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.85  																																																							| (475)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																							|
% 26.17/6.85  																																																								+-Applying beta-rule and splitting (337), into two cases.
% 26.17/6.85  																																																								|-Branch one:
% 26.17/6.85  																																																								| (305) all_63_3_16 = 0
% 26.17/6.85  																																																								|
% 26.17/6.85  																																																									| Equations (305) can reduce 181 to:
% 26.17/6.85  																																																									| (63) $false
% 26.17/6.85  																																																									|
% 26.17/6.85  																																																									|-The branch is then unsatisfiable
% 26.17/6.85  																																																								|-Branch two:
% 26.17/6.85  																																																								| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.85  																																																								| (479)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																								|
% 26.17/6.85  																																																									+-Applying beta-rule and splitting (341), into two cases.
% 26.17/6.85  																																																									|-Branch one:
% 26.17/6.85  																																																									| (130) all_44_1_11 = 0
% 26.17/6.85  																																																									|
% 26.17/6.85  																																																										| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																										| (63) $false
% 26.17/6.85  																																																										|
% 26.17/6.85  																																																										|-The branch is then unsatisfiable
% 26.17/6.85  																																																									|-Branch two:
% 26.17/6.85  																																																									| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																									| (483)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																									|
% 26.17/6.85  																																																										+-Applying beta-rule and splitting (345), into two cases.
% 26.17/6.85  																																																										|-Branch one:
% 26.17/6.85  																																																										| (130) all_44_1_11 = 0
% 26.17/6.85  																																																										|
% 26.17/6.85  																																																											| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																											| (63) $false
% 26.17/6.85  																																																											|
% 26.17/6.85  																																																											|-The branch is then unsatisfiable
% 26.17/6.85  																																																										|-Branch two:
% 26.17/6.85  																																																										| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																										| (487)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & distinct_lines(all_44_2_12, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.85  																																																										|
% 26.17/6.85  																																																											+-Applying beta-rule and splitting (349), into two cases.
% 26.17/6.85  																																																											|-Branch one:
% 26.17/6.85  																																																											| (130) all_44_1_11 = 0
% 26.17/6.85  																																																											|
% 26.17/6.85  																																																												| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																												| (63) $false
% 26.17/6.85  																																																												|
% 26.17/6.85  																																																												|-The branch is then unsatisfiable
% 26.17/6.85  																																																											|-Branch two:
% 26.17/6.85  																																																											| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																											| (491)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																											|
% 26.17/6.85  																																																												+-Applying beta-rule and splitting (353), into two cases.
% 26.17/6.85  																																																												|-Branch one:
% 26.17/6.85  																																																												| (130) all_44_1_11 = 0
% 26.17/6.85  																																																												|
% 26.17/6.85  																																																													| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																													| (63) $false
% 26.17/6.85  																																																													|
% 26.17/6.85  																																																													|-The branch is then unsatisfiable
% 26.17/6.85  																																																												|-Branch two:
% 26.17/6.85  																																																												| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																												| (495)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & distinct_lines(all_96_1_35, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																												|
% 26.17/6.85  																																																													+-Applying beta-rule and splitting (357), into two cases.
% 26.17/6.85  																																																													|-Branch one:
% 26.17/6.85  																																																													| (130) all_44_1_11 = 0
% 26.17/6.85  																																																													|
% 26.17/6.85  																																																														| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																														| (63) $false
% 26.17/6.85  																																																														|
% 26.17/6.85  																																																														|-The branch is then unsatisfiable
% 26.17/6.85  																																																													|-Branch two:
% 26.17/6.85  																																																													| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																													| (499)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & distinct_lines(all_44_2_12, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																													|
% 26.17/6.85  																																																														+-Applying beta-rule and splitting (361), into two cases.
% 26.17/6.85  																																																														|-Branch one:
% 26.17/6.85  																																																														| (130) all_44_1_11 = 0
% 26.17/6.85  																																																														|
% 26.17/6.85  																																																															| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																															| (63) $false
% 26.17/6.85  																																																															|
% 26.17/6.85  																																																															|-The branch is then unsatisfiable
% 26.17/6.85  																																																														|-Branch two:
% 26.17/6.85  																																																														| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																														| (503)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & distinct_lines(all_96_1_35, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.85  																																																														|
% 26.17/6.85  																																																															+-Applying beta-rule and splitting (365), into two cases.
% 26.17/6.85  																																																															|-Branch one:
% 26.17/6.85  																																																															| (130) all_44_1_11 = 0
% 26.17/6.85  																																																															|
% 26.17/6.85  																																																																| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																																| (63) $false
% 26.17/6.85  																																																																|
% 26.17/6.85  																																																																|-The branch is then unsatisfiable
% 26.17/6.85  																																																															|-Branch two:
% 26.17/6.85  																																																															| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																															| (507)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																															|
% 26.17/6.85  																																																																+-Applying beta-rule and splitting (369), into two cases.
% 26.17/6.85  																																																																|-Branch one:
% 26.17/6.85  																																																																| (130) all_44_1_11 = 0
% 26.17/6.85  																																																																|
% 26.17/6.85  																																																																	| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																																	| (63) $false
% 26.17/6.85  																																																																	|
% 26.17/6.85  																																																																	|-The branch is then unsatisfiable
% 26.17/6.85  																																																																|-Branch two:
% 26.17/6.85  																																																																| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																																| (511)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																|
% 26.17/6.85  																																																																	+-Applying beta-rule and splitting (373), into two cases.
% 26.17/6.85  																																																																	|-Branch one:
% 26.17/6.85  																																																																	| (130) all_44_1_11 = 0
% 26.17/6.85  																																																																	|
% 26.17/6.85  																																																																		| Equations (130) can reduce 99 to:
% 26.17/6.85  																																																																		| (63) $false
% 26.17/6.85  																																																																		|
% 26.17/6.85  																																																																		|-The branch is then unsatisfiable
% 26.17/6.85  																																																																	|-Branch two:
% 26.17/6.85  																																																																	| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.85  																																																																	| (515)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_44_2_12, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																	|
% 26.17/6.85  																																																																		+-Applying beta-rule and splitting (377), into two cases.
% 26.17/6.85  																																																																		|-Branch one:
% 26.17/6.85  																																																																		| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																		|
% 26.17/6.85  																																																																			| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																			| (63) $false
% 26.17/6.85  																																																																			|
% 26.17/6.85  																																																																			|-The branch is then unsatisfiable
% 26.17/6.85  																																																																		|-Branch two:
% 26.17/6.85  																																																																		| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																		| (519)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																		|
% 26.17/6.85  																																																																			+-Applying beta-rule and splitting (381), into two cases.
% 26.17/6.85  																																																																			|-Branch one:
% 26.17/6.85  																																																																			| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																			|
% 26.17/6.85  																																																																				| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																				| (63) $false
% 26.17/6.85  																																																																				|
% 26.17/6.85  																																																																				|-The branch is then unsatisfiable
% 26.17/6.85  																																																																			|-Branch two:
% 26.17/6.85  																																																																			| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																			| (523)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																			|
% 26.17/6.85  																																																																				+-Applying beta-rule and splitting (385), into two cases.
% 26.17/6.85  																																																																				|-Branch one:
% 26.17/6.85  																																																																				| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																				|
% 26.17/6.85  																																																																					| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																					| (63) $false
% 26.17/6.85  																																																																					|
% 26.17/6.85  																																																																					|-The branch is then unsatisfiable
% 26.17/6.85  																																																																				|-Branch two:
% 26.17/6.85  																																																																				| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																				| (527)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.85  																																																																				|
% 26.17/6.85  																																																																					| Instantiating (527) with all_360_0_149, all_360_1_150, all_360_2_151 yields:
% 26.17/6.85  																																																																					| (528) apart_point_and_line(all_1_1_1, all_96_1_35) = all_360_1_150 & apart_point_and_line(all_1_1_1, all_1_6_6) = all_360_0_149 & distinct_lines(all_96_1_35, all_1_6_6) = all_360_2_151 & ( ~ (all_360_2_151 = 0) | all_360_0_149 = 0 | all_360_1_150 = 0)
% 26.17/6.85  																																																																					|
% 26.17/6.85  																																																																					| Applying alpha-rule on (528) yields:
% 26.17/6.85  																																																																					| (529) apart_point_and_line(all_1_1_1, all_96_1_35) = all_360_1_150
% 26.17/6.85  																																																																					| (530) apart_point_and_line(all_1_1_1, all_1_6_6) = all_360_0_149
% 26.17/6.85  																																																																					| (531) distinct_lines(all_96_1_35, all_1_6_6) = all_360_2_151
% 26.17/6.85  																																																																					| (532)  ~ (all_360_2_151 = 0) | all_360_0_149 = 0 | all_360_1_150 = 0
% 26.17/6.85  																																																																					|
% 26.17/6.85  																																																																					+-Applying beta-rule and splitting (389), into two cases.
% 26.17/6.85  																																																																					|-Branch one:
% 26.17/6.85  																																																																					| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																					|
% 26.17/6.85  																																																																						| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																						| (63) $false
% 26.17/6.85  																																																																						|
% 26.17/6.85  																																																																						|-The branch is then unsatisfiable
% 26.17/6.85  																																																																					|-Branch two:
% 26.17/6.85  																																																																					| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																					| (536)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & distinct_lines(all_1_6_6, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.85  																																																																					|
% 26.17/6.85  																																																																						| Instantiating (536) with all_365_0_152, all_365_1_153, all_365_2_154 yields:
% 26.17/6.85  																																																																						| (537) apart_point_and_line(all_1_1_1, all_96_1_35) = all_365_0_152 & apart_point_and_line(all_1_1_1, all_1_6_6) = all_365_1_153 & distinct_lines(all_1_6_6, all_96_1_35) = all_365_2_154 & ( ~ (all_365_2_154 = 0) | all_365_0_152 = 0 | all_365_1_153 = 0)
% 26.17/6.85  																																																																						|
% 26.17/6.85  																																																																						| Applying alpha-rule on (537) yields:
% 26.17/6.85  																																																																						| (538) apart_point_and_line(all_1_1_1, all_96_1_35) = all_365_0_152
% 26.17/6.85  																																																																						| (539) apart_point_and_line(all_1_1_1, all_1_6_6) = all_365_1_153
% 26.17/6.85  																																																																						| (540) distinct_lines(all_1_6_6, all_96_1_35) = all_365_2_154
% 26.17/6.85  																																																																						| (541)  ~ (all_365_2_154 = 0) | all_365_0_152 = 0 | all_365_1_153 = 0
% 26.17/6.85  																																																																						|
% 26.17/6.85  																																																																						+-Applying beta-rule and splitting (393), into two cases.
% 26.17/6.85  																																																																						|-Branch one:
% 26.17/6.85  																																																																						| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																						|
% 26.17/6.85  																																																																							| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																							| (63) $false
% 26.17/6.85  																																																																							|
% 26.17/6.85  																																																																							|-The branch is then unsatisfiable
% 26.17/6.85  																																																																						|-Branch two:
% 26.17/6.85  																																																																						| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																						| (545)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_6_6) = v2 & distinct_lines(all_96_1_35, all_1_6_6) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																						|
% 26.17/6.85  																																																																							+-Applying beta-rule and splitting (397), into two cases.
% 26.17/6.85  																																																																							|-Branch one:
% 26.17/6.85  																																																																							| (318) all_63_2_15 = 0
% 26.17/6.85  																																																																							|
% 26.17/6.85  																																																																								| Equations (318) can reduce 180 to:
% 26.17/6.85  																																																																								| (63) $false
% 26.17/6.85  																																																																								|
% 26.17/6.85  																																																																								|-The branch is then unsatisfiable
% 26.17/6.85  																																																																							|-Branch two:
% 26.17/6.85  																																																																							| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.85  																																																																							| (549)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_6_6) = v3 & distinct_lines(all_1_6_6, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.85  																																																																							|
% 26.17/6.85  																																																																								+-Applying beta-rule and splitting (401), into two cases.
% 26.17/6.85  																																																																								|-Branch one:
% 26.17/6.85  																																																																								| (305) all_63_3_16 = 0
% 26.17/6.85  																																																																								|
% 26.17/6.86  																																																																									| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																									| (63) $false
% 26.17/6.86  																																																																									|
% 26.17/6.86  																																																																									|-The branch is then unsatisfiable
% 26.17/6.86  																																																																								|-Branch two:
% 26.17/6.86  																																																																								| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																								| (553)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.86  																																																																								|
% 26.17/6.86  																																																																									| Instantiating (553) with all_380_0_163, all_380_1_164, all_380_2_165 yields:
% 26.17/6.86  																																																																									| (554) apart_point_and_line(all_1_1_1, all_96_1_35) = all_380_1_164 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_380_0_163 & distinct_lines(all_96_1_35, all_1_7_7) = all_380_2_165 & ( ~ (all_380_2_165 = 0) | all_380_0_163 = 0 | all_380_1_164 = 0)
% 26.17/6.86  																																																																									|
% 26.17/6.86  																																																																									| Applying alpha-rule on (554) yields:
% 26.17/6.86  																																																																									| (555) apart_point_and_line(all_1_1_1, all_96_1_35) = all_380_1_164
% 26.17/6.86  																																																																									| (556) apart_point_and_line(all_1_1_1, all_1_7_7) = all_380_0_163
% 26.17/6.86  																																																																									| (557) distinct_lines(all_96_1_35, all_1_7_7) = all_380_2_165
% 26.17/6.86  																																																																									| (558)  ~ (all_380_2_165 = 0) | all_380_0_163 = 0 | all_380_1_164 = 0
% 26.17/6.86  																																																																									|
% 26.17/6.86  																																																																									+-Applying beta-rule and splitting (405), into two cases.
% 26.17/6.86  																																																																									|-Branch one:
% 26.17/6.86  																																																																									| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																									|
% 26.17/6.86  																																																																										| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																										| (63) $false
% 26.17/6.86  																																																																										|
% 26.17/6.86  																																																																										|-The branch is then unsatisfiable
% 26.17/6.86  																																																																									|-Branch two:
% 26.17/6.86  																																																																									| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																									| (562)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_96_1_35) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.86  																																																																									|
% 26.17/6.86  																																																																										| Instantiating (562) with all_385_0_166, all_385_1_167, all_385_2_168 yields:
% 26.17/6.86  																																																																										| (563) apart_point_and_line(all_1_1_1, all_96_1_35) = all_385_0_166 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_385_1_167 & distinct_lines(all_1_7_7, all_96_1_35) = all_385_2_168 & ( ~ (all_385_2_168 = 0) | all_385_0_166 = 0 | all_385_1_167 = 0)
% 26.17/6.86  																																																																										|
% 26.17/6.86  																																																																										| Applying alpha-rule on (563) yields:
% 26.17/6.86  																																																																										| (564) apart_point_and_line(all_1_1_1, all_96_1_35) = all_385_0_166
% 26.17/6.86  																																																																										| (565) apart_point_and_line(all_1_1_1, all_1_7_7) = all_385_1_167
% 26.17/6.86  																																																																										| (566) distinct_lines(all_1_7_7, all_96_1_35) = all_385_2_168
% 26.17/6.86  																																																																										| (567)  ~ (all_385_2_168 = 0) | all_385_0_166 = 0 | all_385_1_167 = 0
% 26.17/6.86  																																																																										|
% 26.17/6.86  																																																																										+-Applying beta-rule and splitting (409), into two cases.
% 26.17/6.86  																																																																										|-Branch one:
% 26.17/6.86  																																																																										| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																										|
% 26.17/6.86  																																																																											| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																											| (63) $false
% 26.17/6.86  																																																																											|
% 26.17/6.86  																																																																											|-The branch is then unsatisfiable
% 26.17/6.86  																																																																										|-Branch two:
% 26.17/6.86  																																																																										| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																										| (571)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																										|
% 26.17/6.86  																																																																											+-Applying beta-rule and splitting (413), into two cases.
% 26.17/6.86  																																																																											|-Branch one:
% 26.17/6.86  																																																																											| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																											|
% 26.17/6.86  																																																																												| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																												| (63) $false
% 26.17/6.86  																																																																												|
% 26.17/6.86  																																																																												|-The branch is then unsatisfiable
% 26.17/6.86  																																																																											|-Branch two:
% 26.17/6.86  																																																																											| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																											| (575)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_96_1_35, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																											|
% 26.17/6.86  																																																																												+-Applying beta-rule and splitting (417), into two cases.
% 26.17/6.86  																																																																												|-Branch one:
% 26.17/6.86  																																																																												| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																												|
% 26.17/6.86  																																																																													| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																													| (63) $false
% 26.17/6.86  																																																																													|
% 26.17/6.86  																																																																													|-The branch is then unsatisfiable
% 26.17/6.86  																																																																												|-Branch two:
% 26.17/6.86  																																																																												| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																												| (579)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																												|
% 26.17/6.86  																																																																													+-Applying beta-rule and splitting (421), into two cases.
% 26.17/6.86  																																																																													|-Branch one:
% 26.17/6.86  																																																																													| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																													|
% 26.17/6.86  																																																																														| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																														| (63) $false
% 26.17/6.86  																																																																														|
% 26.17/6.86  																																																																														|-The branch is then unsatisfiable
% 26.17/6.86  																																																																													|-Branch two:
% 26.17/6.86  																																																																													| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																													| (583)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																													|
% 26.17/6.86  																																																																														+-Applying beta-rule and splitting (425), into two cases.
% 26.17/6.86  																																																																														|-Branch one:
% 26.17/6.86  																																																																														| (130) all_44_1_11 = 0
% 26.17/6.86  																																																																														|
% 26.17/6.86  																																																																															| Equations (130) can reduce 99 to:
% 26.17/6.86  																																																																															| (63) $false
% 26.17/6.86  																																																																															|
% 26.17/6.86  																																																																															|-The branch is then unsatisfiable
% 26.17/6.86  																																																																														|-Branch two:
% 26.17/6.86  																																																																														| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.86  																																																																														| (587)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v3 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																														|
% 26.17/6.86  																																																																															+-Applying beta-rule and splitting (429), into two cases.
% 26.17/6.86  																																																																															|-Branch one:
% 26.17/6.86  																																																																															| (130) all_44_1_11 = 0
% 26.17/6.86  																																																																															|
% 26.17/6.86  																																																																																| Equations (130) can reduce 99 to:
% 26.17/6.86  																																																																																| (63) $false
% 26.17/6.86  																																																																																|
% 26.17/6.86  																																																																																|-The branch is then unsatisfiable
% 26.17/6.86  																																																																															|-Branch two:
% 26.17/6.86  																																																																															| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.86  																																																																															| (591)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_2_2, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_lines(all_1_7_7, all_44_2_12) = v1 & distinct_points(all_1_2_2, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.86  																																																																															|
% 26.17/6.86  																																																																																+-Applying beta-rule and splitting (433), into two cases.
% 26.17/6.86  																																																																																|-Branch one:
% 26.17/6.86  																																																																																| (130) all_44_1_11 = 0
% 26.17/6.86  																																																																																|
% 26.17/6.86  																																																																																	| Equations (130) can reduce 99 to:
% 26.17/6.86  																																																																																	| (63) $false
% 26.17/6.86  																																																																																	|
% 26.17/6.86  																																																																																	|-The branch is then unsatisfiable
% 26.17/6.86  																																																																																|-Branch two:
% 26.17/6.86  																																																																																| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.86  																																																																																| (595)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_44_2_12, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.86  																																																																																|
% 26.17/6.86  																																																																																	| Instantiating (595) with all_420_0_193, all_420_1_194, all_420_2_195 yields:
% 26.17/6.86  																																																																																	| (596) apart_point_and_line(all_1_1_1, all_44_2_12) = all_420_1_194 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_420_0_193 & distinct_lines(all_44_2_12, all_1_7_7) = all_420_2_195 & ( ~ (all_420_2_195 = 0) | all_420_0_193 = 0 | all_420_1_194 = 0)
% 26.17/6.86  																																																																																	|
% 26.17/6.86  																																																																																	| Applying alpha-rule on (596) yields:
% 26.17/6.86  																																																																																	| (597) apart_point_and_line(all_1_1_1, all_44_2_12) = all_420_1_194
% 26.17/6.86  																																																																																	| (598) apart_point_and_line(all_1_1_1, all_1_7_7) = all_420_0_193
% 26.17/6.86  																																																																																	| (599) distinct_lines(all_44_2_12, all_1_7_7) = all_420_2_195
% 26.17/6.86  																																																																																	| (600)  ~ (all_420_2_195 = 0) | all_420_0_193 = 0 | all_420_1_194 = 0
% 26.17/6.86  																																																																																	|
% 26.17/6.86  																																																																																	+-Applying beta-rule and splitting (437), into two cases.
% 26.17/6.86  																																																																																	|-Branch one:
% 26.17/6.86  																																																																																	| (130) all_44_1_11 = 0
% 26.17/6.86  																																																																																	|
% 26.17/6.86  																																																																																		| Equations (130) can reduce 99 to:
% 26.17/6.86  																																																																																		| (63) $false
% 26.17/6.86  																																																																																		|
% 26.17/6.86  																																																																																		|-The branch is then unsatisfiable
% 26.17/6.86  																																																																																	|-Branch two:
% 26.17/6.86  																																																																																	| (99)  ~ (all_44_1_11 = 0)
% 26.17/6.86  																																																																																	| (604)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_44_2_12) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.86  																																																																																	|
% 26.17/6.86  																																																																																		| Instantiating (604) with all_425_0_196, all_425_1_197, all_425_2_198 yields:
% 26.17/6.86  																																																																																		| (605) apart_point_and_line(all_1_1_1, all_44_2_12) = all_425_0_196 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_425_1_197 & distinct_lines(all_1_7_7, all_44_2_12) = all_425_2_198 & ( ~ (all_425_2_198 = 0) | all_425_0_196 = 0 | all_425_1_197 = 0)
% 26.17/6.86  																																																																																		|
% 26.17/6.86  																																																																																		| Applying alpha-rule on (605) yields:
% 26.17/6.86  																																																																																		| (606) apart_point_and_line(all_1_1_1, all_44_2_12) = all_425_0_196
% 26.17/6.86  																																																																																		| (607) apart_point_and_line(all_1_1_1, all_1_7_7) = all_425_1_197
% 26.17/6.86  																																																																																		| (608) distinct_lines(all_1_7_7, all_44_2_12) = all_425_2_198
% 26.17/6.86  																																																																																		| (609)  ~ (all_425_2_198 = 0) | all_425_0_196 = 0 | all_425_1_197 = 0
% 26.17/6.86  																																																																																		|
% 26.17/6.86  																																																																																		+-Applying beta-rule and splitting (449), into two cases.
% 26.17/6.86  																																																																																		|-Branch one:
% 26.17/6.86  																																																																																		| (305) all_63_3_16 = 0
% 26.17/6.86  																																																																																		|
% 26.17/6.86  																																																																																			| Equations (305) can reduce 181 to:
% 26.17/6.86  																																																																																			| (63) $false
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			|-The branch is then unsatisfiable
% 26.17/6.86  																																																																																		|-Branch two:
% 26.17/6.86  																																																																																		| (181)  ~ (all_63_3_16 = 0)
% 26.17/6.86  																																																																																		| (613)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_6_6) = v1 & apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & distinct_lines(all_1_6_6, all_1_7_7) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.86  																																																																																		|
% 26.17/6.86  																																																																																			| Instantiating (613) with all_440_0_207, all_440_1_208, all_440_2_209 yields:
% 26.17/6.86  																																																																																			| (614) apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208 & apart_point_and_line(all_1_1_1, all_1_7_7) = all_440_0_207 & distinct_lines(all_1_6_6, all_1_7_7) = all_440_2_209 & ( ~ (all_440_2_209 = 0) | all_440_0_207 = 0 | all_440_1_208 = 0)
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Applying alpha-rule on (614) yields:
% 26.17/6.86  																																																																																			| (615) apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208
% 26.17/6.86  																																																																																			| (616) apart_point_and_line(all_1_1_1, all_1_7_7) = all_440_0_207
% 26.17/6.86  																																																																																			| (617) distinct_lines(all_1_6_6, all_1_7_7) = all_440_2_209
% 26.17/6.86  																																																																																			| (618)  ~ (all_440_2_209 = 0) | all_440_0_207 = 0 | all_440_1_208 = 0
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (4) with all_1_7_7, all_1_5_5, all_135_1_51, all_1_1_1 and discharging atoms intersection_point(all_1_7_7, all_1_5_5) = all_135_1_51, intersection_point(all_1_7_7, all_1_5_5) = all_1_1_1, yields:
% 26.17/6.86  																																																																																			| (619) all_135_1_51 = all_1_1_1
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (4) with all_1_7_7, all_1_5_5, all_133_1_48, all_135_1_51 and discharging atoms intersection_point(all_1_7_7, all_1_5_5) = all_135_1_51, intersection_point(all_1_7_7, all_1_5_5) = all_133_1_48, yields:
% 26.17/6.86  																																																																																			| (620) all_135_1_51 = all_133_1_48
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_365_1_153, all_440_1_208 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208, apart_point_and_line(all_1_1_1, all_1_6_6) = all_365_1_153, yields:
% 26.17/6.86  																																																																																			| (621) all_440_1_208 = all_365_1_153
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_360_0_149, all_440_1_208 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208, apart_point_and_line(all_1_1_1, all_1_6_6) = all_360_0_149, yields:
% 26.17/6.86  																																																																																			| (622) all_440_1_208 = all_360_0_149
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_285_1_93, all_440_1_208 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208, apart_point_and_line(all_1_1_1, all_1_6_6) = all_285_1_93, yields:
% 26.17/6.86  																																																																																			| (623) all_440_1_208 = all_285_1_93
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_280_0_89, all_63_0_13 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_280_0_89, apart_point_and_line(all_1_1_1, all_1_6_6) = all_63_0_13, yields:
% 26.17/6.86  																																																																																			| (624) all_280_0_89 = all_63_0_13
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_280_0_89, all_285_1_93 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_285_1_93, apart_point_and_line(all_1_1_1, all_1_6_6) = all_280_0_89, yields:
% 26.17/6.86  																																																																																			| (625) all_285_1_93 = all_280_0_89
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_6_6, all_129_2_41, all_440_1_208 and discharging atoms apart_point_and_line(all_1_1_1, all_1_6_6) = all_440_1_208, apart_point_and_line(all_1_1_1, all_1_6_6) = all_129_2_41, yields:
% 26.17/6.86  																																																																																			| (626) all_440_1_208 = all_129_2_41
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_385_1_167, all_440_0_207 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_440_0_207, apart_point_and_line(all_1_1_1, all_1_7_7) = all_385_1_167, yields:
% 26.17/6.86  																																																																																			| (627) all_440_0_207 = all_385_1_167
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_385_1_167, all_425_1_197 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_425_1_197, apart_point_and_line(all_1_1_1, all_1_7_7) = all_385_1_167, yields:
% 26.17/6.86  																																																																																			| (628) all_425_1_197 = all_385_1_167
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_380_0_163, all_440_0_207 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_440_0_207, apart_point_and_line(all_1_1_1, all_1_7_7) = all_380_0_163, yields:
% 26.17/6.86  																																																																																			| (629) all_440_0_207 = all_380_0_163
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_170_0_85, all_440_0_207 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_440_0_207, apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_0_85, yields:
% 26.17/6.86  																																																																																			| (630) all_440_0_207 = all_170_0_85
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_170_1_86, all_170_0_85 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_0_85, apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_1_86, yields:
% 26.17/6.86  																																																																																			| (631) all_170_0_85 = all_170_1_86
% 26.17/6.86  																																																																																			|
% 26.17/6.86  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_137_1_54, all_425_1_197 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_425_1_197, apart_point_and_line(all_1_1_1, all_1_7_7) = all_137_1_54, yields:
% 26.17/6.87  																																																																																			| (632) all_425_1_197 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_135_2_52, all_63_1_14 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_135_2_52, apart_point_and_line(all_1_1_1, all_1_7_7) = all_63_1_14, yields:
% 26.17/6.87  																																																																																			| (633) all_135_2_52 = all_63_1_14
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_135_2_52, all_420_0_193 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_420_0_193, apart_point_and_line(all_1_1_1, all_1_7_7) = all_135_2_52, yields:
% 26.17/6.87  																																																																																			| (634) all_420_0_193 = all_135_2_52
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_135_2_52, all_170_1_86 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_1_86, apart_point_and_line(all_1_1_1, all_1_7_7) = all_135_2_52, yields:
% 26.17/6.87  																																																																																			| (635) all_170_1_86 = all_135_2_52
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_131_3_46, all_170_1_86 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_170_1_86, apart_point_and_line(all_1_1_1, all_1_7_7) = all_131_3_46, yields:
% 26.17/6.87  																																																																																			| (636) all_170_1_86 = all_131_3_46
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (26) with all_1_1_1, all_1_7_7, all_129_3_42, all_420_0_193 and discharging atoms apart_point_and_line(all_1_1_1, all_1_7_7) = all_420_0_193, apart_point_and_line(all_1_1_1, all_1_7_7) = all_129_3_42, yields:
% 26.17/6.87  																																																																																			| (637) all_420_0_193 = all_129_3_42
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (3) with all_1_7_7, all_1_5_5, all_139_2_58, 0 and discharging atoms convergent_lines(all_1_7_7, all_1_5_5) = all_139_2_58, convergent_lines(all_1_7_7, all_1_5_5) = 0, yields:
% 26.17/6.87  																																																																																			| (638) all_139_2_58 = 0
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (3) with all_1_7_7, all_1_5_5, all_137_2_55, all_139_2_58 and discharging atoms convergent_lines(all_1_7_7, all_1_5_5) = all_139_2_58, convergent_lines(all_1_7_7, all_1_5_5) = all_137_2_55, yields:
% 26.17/6.87  																																																																																			| (639) all_139_2_58 = all_137_2_55
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_149_0_71, all_133_0_47 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71, yields:
% 26.17/6.87  																																																																																			| (640) all_149_0_71 = all_133_0_47 |  ~ (distinct_points(all_1_1_1, all_1_1_1) = all_133_0_47)
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (6) with all_1_1_1 yields:
% 26.17/6.87  																																																																																			| (641)  ~ (distinct_points(all_1_1_1, all_1_1_1) = 0)
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_143_0_62, all_149_0_71 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71, distinct_points(all_1_1_1, all_1_1_1) = all_143_0_62, yields:
% 26.17/6.87  																																																																																			| (642) all_149_0_71 = all_143_0_62
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_141_0_59, all_135_0_50 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_141_0_59, yields:
% 26.17/6.87  																																																																																			| (643) all_141_0_59 = all_135_0_50 |  ~ (distinct_points(all_1_1_1, all_1_1_1) = all_135_0_50)
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_141_0_59, all_149_0_71 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71, distinct_points(all_1_1_1, all_1_1_1) = all_141_0_59, yields:
% 26.17/6.87  																																																																																			| (644) all_149_0_71 = all_141_0_59
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_141_0_59, all_147_0_68 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_147_0_68, distinct_points(all_1_1_1, all_1_1_1) = all_141_0_59, yields:
% 26.17/6.87  																																																																																			| (645) all_147_0_68 = all_141_0_59
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_139_0_56, all_147_0_68 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_147_0_68, distinct_points(all_1_1_1, all_1_1_1) = all_139_0_56, yields:
% 26.17/6.87  																																																																																			| (646) all_147_0_68 = all_139_0_56
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Instantiating formula (23) with all_1_1_1, all_1_1_1, all_137_0_53, all_149_0_71 and discharging atoms distinct_points(all_1_1_1, all_1_1_1) = all_149_0_71, distinct_points(all_1_1_1, all_1_1_1) = all_137_0_53, yields:
% 26.17/6.87  																																																																																			| (647) all_149_0_71 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (627,629) yields a new equation:
% 26.17/6.87  																																																																																			| (648) all_385_1_167 = all_380_0_163
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 648 yields:
% 26.17/6.87  																																																																																			| (649) all_385_1_167 = all_380_0_163
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (630,629) yields a new equation:
% 26.17/6.87  																																																																																			| (650) all_380_0_163 = all_170_0_85
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (623,621) yields a new equation:
% 26.17/6.87  																																																																																			| (651) all_365_1_153 = all_285_1_93
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (626,621) yields a new equation:
% 26.17/6.87  																																																																																			| (652) all_365_1_153 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (622,621) yields a new equation:
% 26.17/6.87  																																																																																			| (653) all_365_1_153 = all_360_0_149
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (628,632) yields a new equation:
% 26.17/6.87  																																																																																			| (654) all_385_1_167 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 654 yields:
% 26.17/6.87  																																																																																			| (655) all_385_1_167 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (634,637) yields a new equation:
% 26.17/6.87  																																																																																			| (656) all_135_2_52 = all_129_3_42
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 656 yields:
% 26.17/6.87  																																																																																			| (657) all_135_2_52 = all_129_3_42
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (649,655) yields a new equation:
% 26.17/6.87  																																																																																			| (658) all_380_0_163 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 658 yields:
% 26.17/6.87  																																																																																			| (659) all_380_0_163 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (650,659) yields a new equation:
% 26.17/6.87  																																																																																			| (660) all_170_0_85 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 660 yields:
% 26.17/6.87  																																																																																			| (661) all_170_0_85 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (651,653) yields a new equation:
% 26.17/6.87  																																																																																			| (662) all_360_0_149 = all_285_1_93
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (652,653) yields a new equation:
% 26.17/6.87  																																																																																			| (663) all_360_0_149 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (662,663) yields a new equation:
% 26.17/6.87  																																																																																			| (664) all_285_1_93 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 664 yields:
% 26.17/6.87  																																																																																			| (665) all_285_1_93 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (625,665) yields a new equation:
% 26.17/6.87  																																																																																			| (666) all_280_0_89 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 666 yields:
% 26.17/6.87  																																																																																			| (667) all_280_0_89 = all_129_2_41
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (624,667) yields a new equation:
% 26.17/6.87  																																																																																			| (668) all_129_2_41 = all_63_0_13
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (631,661) yields a new equation:
% 26.17/6.87  																																																																																			| (669) all_170_1_86 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 669 yields:
% 26.17/6.87  																																																																																			| (670) all_170_1_86 = all_137_1_54
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (635,670) yields a new equation:
% 26.17/6.87  																																																																																			| (671) all_137_1_54 = all_135_2_52
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (636,670) yields a new equation:
% 26.17/6.87  																																																																																			| (672) all_137_1_54 = all_131_3_46
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (644,642) yields a new equation:
% 26.17/6.87  																																																																																			| (673) all_143_0_62 = all_141_0_59
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (647,642) yields a new equation:
% 26.17/6.87  																																																																																			| (674) all_143_0_62 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (645,646) yields a new equation:
% 26.17/6.87  																																																																																			| (675) all_141_0_59 = all_139_0_56
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 675 yields:
% 26.17/6.87  																																																																																			| (676) all_141_0_59 = all_139_0_56
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (673,674) yields a new equation:
% 26.17/6.87  																																																																																			| (677) all_141_0_59 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 677 yields:
% 26.17/6.87  																																																																																			| (678) all_141_0_59 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (678,676) yields a new equation:
% 26.17/6.87  																																																																																			| (679) all_139_0_56 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (638,639) yields a new equation:
% 26.17/6.87  																																																																																			| (680) all_137_2_55 = 0
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (671,672) yields a new equation:
% 26.17/6.87  																																																																																			| (681) all_135_2_52 = all_131_3_46
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 681 yields:
% 26.17/6.87  																																																																																			| (682) all_135_2_52 = all_131_3_46
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (620,619) yields a new equation:
% 26.17/6.87  																																																																																			| (683) all_133_1_48 = all_1_1_1
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Simplifying 683 yields:
% 26.17/6.87  																																																																																			| (684) all_133_1_48 = all_1_1_1
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (657,682) yields a new equation:
% 26.17/6.87  																																																																																			| (685) all_131_3_46 = all_129_3_42
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (633,682) yields a new equation:
% 26.17/6.87  																																																																																			| (686) all_131_3_46 = all_63_1_14
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (686,685) yields a new equation:
% 26.17/6.87  																																																																																			| (687) all_129_3_42 = all_63_1_14
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (687,685) yields a new equation:
% 26.17/6.87  																																																																																			| (686) all_131_3_46 = all_63_1_14
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (686,672) yields a new equation:
% 26.17/6.87  																																																																																			| (689) all_137_1_54 = all_63_1_14
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (679,676) yields a new equation:
% 26.17/6.87  																																																																																			| (678) all_141_0_59 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| Combining equations (674,642) yields a new equation:
% 26.17/6.87  																																																																																			| (647) all_149_0_71 = all_137_0_53
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| From (668) and (248) follows:
% 26.17/6.87  																																																																																			| (112) apart_point_and_line(all_1_1_1, all_1_6_6) = all_63_0_13
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| From (619) and (265) follows:
% 26.17/6.87  																																																																																			| (693) distinct_points(all_1_1_1, all_1_1_1) = all_135_0_50
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			| From (684) and (260) follows:
% 26.17/6.87  																																																																																			| (694) distinct_points(all_1_1_1, all_1_1_1) = all_133_0_47
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																			+-Applying beta-rule and splitting (640), into two cases.
% 26.17/6.87  																																																																																			|-Branch one:
% 26.17/6.87  																																																																																			| (695)  ~ (distinct_points(all_1_1_1, all_1_1_1) = all_133_0_47)
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																				| Using (694) and (695) yields:
% 26.17/6.87  																																																																																				| (85) $false
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																				|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																			|-Branch two:
% 26.17/6.87  																																																																																			| (694) distinct_points(all_1_1_1, all_1_1_1) = all_133_0_47
% 26.17/6.87  																																																																																			| (698) all_149_0_71 = all_133_0_47
% 26.17/6.87  																																																																																			|
% 26.17/6.87  																																																																																				| Combining equations (647,698) yields a new equation:
% 26.17/6.87  																																																																																				| (699) all_137_0_53 = all_133_0_47
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																				| Simplifying 699 yields:
% 26.17/6.87  																																																																																				| (700) all_137_0_53 = all_133_0_47
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																				| Combining equations (700,678) yields a new equation:
% 26.17/6.87  																																																																																				| (701) all_141_0_59 = all_133_0_47
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																				+-Applying beta-rule and splitting (643), into two cases.
% 26.17/6.87  																																																																																				|-Branch one:
% 26.17/6.87  																																																																																				| (702)  ~ (distinct_points(all_1_1_1, all_1_1_1) = all_135_0_50)
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																					| Using (693) and (702) yields:
% 26.17/6.87  																																																																																					| (85) $false
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																					|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																				|-Branch two:
% 26.17/6.87  																																																																																				| (693) distinct_points(all_1_1_1, all_1_1_1) = all_135_0_50
% 26.17/6.87  																																																																																				| (705) all_141_0_59 = all_135_0_50
% 26.17/6.87  																																																																																				|
% 26.17/6.87  																																																																																					| Combining equations (705,701) yields a new equation:
% 26.17/6.87  																																																																																					| (706) all_135_0_50 = all_133_0_47
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																					| Simplifying 706 yields:
% 26.17/6.87  																																																																																					| (707) all_135_0_50 = all_133_0_47
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																					| From (707) and (693) follows:
% 26.17/6.87  																																																																																					| (694) distinct_points(all_1_1_1, all_1_1_1) = all_133_0_47
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																					| Using (694) and (641) yields:
% 26.17/6.87  																																																																																					| (709)  ~ (all_133_0_47 = 0)
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																					+-Applying beta-rule and splitting (271), into two cases.
% 26.17/6.87  																																																																																					|-Branch one:
% 26.17/6.87  																																																																																					| (710)  ~ (all_137_2_55 = 0)
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																						| Equations (680) can reduce 710 to:
% 26.17/6.87  																																																																																						| (63) $false
% 26.17/6.87  																																																																																						|
% 26.17/6.87  																																																																																						|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																					|-Branch two:
% 26.17/6.87  																																																																																					| (680) all_137_2_55 = 0
% 26.17/6.87  																																																																																					| (713) all_137_0_53 = 0 | ( ~ (all_137_1_54 = 0) &  ~ (all_65_0_17 = 0))
% 26.17/6.87  																																																																																					|
% 26.17/6.87  																																																																																						+-Applying beta-rule and splitting (713), into two cases.
% 26.17/6.87  																																																																																						|-Branch one:
% 26.17/6.87  																																																																																						| (714) all_137_0_53 = 0
% 26.17/6.87  																																																																																						|
% 26.17/6.87  																																																																																							| Combining equations (700,714) yields a new equation:
% 26.17/6.87  																																																																																							| (715) all_133_0_47 = 0
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																							| Simplifying 715 yields:
% 26.17/6.87  																																																																																							| (716) all_133_0_47 = 0
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																							| Equations (716) can reduce 709 to:
% 26.17/6.87  																																																																																							| (63) $false
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																							|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																						|-Branch two:
% 26.17/6.87  																																																																																						| (718)  ~ (all_137_0_53 = 0)
% 26.17/6.87  																																																																																						| (719)  ~ (all_137_1_54 = 0) &  ~ (all_65_0_17 = 0)
% 26.17/6.87  																																																																																						|
% 26.17/6.87  																																																																																							| Applying alpha-rule on (719) yields:
% 26.17/6.87  																																																																																							| (720)  ~ (all_137_1_54 = 0)
% 26.17/6.87  																																																																																							| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																							| Equations (689) can reduce 720 to:
% 26.17/6.87  																																																																																							| (722)  ~ (all_63_1_14 = 0)
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																							+-Applying beta-rule and splitting (206), into two cases.
% 26.17/6.87  																																																																																							|-Branch one:
% 26.17/6.87  																																																																																							| (723) all_63_0_13 = 0
% 26.17/6.87  																																																																																							|
% 26.17/6.87  																																																																																								| From (723) and (112) follows:
% 26.17/6.87  																																																																																								| (724) apart_point_and_line(all_1_1_1, all_1_6_6) = 0
% 26.17/6.87  																																																																																								|
% 26.17/6.87  																																																																																								+-Applying beta-rule and splitting (115), into two cases.
% 26.17/6.87  																																																																																								|-Branch one:
% 26.17/6.87  																																																																																								| (725) all_65_0_17 = 0
% 26.17/6.87  																																																																																								|
% 26.17/6.87  																																																																																									| Equations (725) can reduce 721 to:
% 26.17/6.87  																																																																																									| (63) $false
% 26.17/6.87  																																																																																									|
% 26.17/6.87  																																																																																									|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																								|-Branch two:
% 26.17/6.87  																																																																																								| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.87  																																																																																								| (728) all_65_1_18 = 0 | all_65_2_19 = 0 | all_65_3_20 = 0
% 26.17/6.87  																																																																																								|
% 26.17/6.87  																																																																																									+-Applying beta-rule and splitting (184), into two cases.
% 26.17/6.87  																																																																																									|-Branch one:
% 26.17/6.87  																																																																																									| (725) all_65_0_17 = 0
% 26.17/6.87  																																																																																									|
% 26.17/6.87  																																																																																										| Equations (725) can reduce 721 to:
% 26.17/6.87  																																																																																										| (63) $false
% 26.17/6.87  																																																																																										|
% 26.17/6.87  																																																																																										|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																									|-Branch two:
% 26.17/6.87  																																																																																									| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.87  																																																																																									| (732) all_1_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_1_1, all_1_6_6) = v0)
% 26.17/6.87  																																																																																									|
% 26.17/6.87  																																																																																										+-Applying beta-rule and splitting (732), into two cases.
% 26.17/6.87  																																																																																										|-Branch one:
% 26.17/6.87  																																																																																										| (62) all_1_4_4 = 0
% 26.17/6.87  																																																																																										|
% 26.17/6.87  																																																																																											| Equations (62) can reduce 55 to:
% 26.17/6.87  																																																																																											| (63) $false
% 26.17/6.87  																																																																																											|
% 26.17/6.87  																																																																																											|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																										|-Branch two:
% 26.17/6.87  																																																																																										| (55)  ~ (all_1_4_4 = 0)
% 26.17/6.87  																																																																																										| (736)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_1_1_1, all_1_6_6) = v0)
% 26.17/6.87  																																																																																										|
% 26.17/6.87  																																																																																											+-Applying beta-rule and splitting (200), into two cases.
% 26.17/6.87  																																																																																											|-Branch one:
% 26.17/6.87  																																																																																											| (725) all_65_0_17 = 0
% 26.17/6.87  																																																																																											|
% 26.17/6.87  																																																																																												| Equations (725) can reduce 721 to:
% 26.17/6.87  																																																																																												| (63) $false
% 26.17/6.87  																																																																																												|
% 26.17/6.87  																																																																																												|-The branch is then unsatisfiable
% 26.17/6.87  																																																																																											|-Branch two:
% 26.17/6.87  																																																																																											| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.87  																																																																																											| (740) all_65_2_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.87  																																																																																											|
% 26.17/6.88  																																																																																												+-Applying beta-rule and splitting (216), into two cases.
% 26.17/6.88  																																																																																												|-Branch one:
% 26.17/6.88  																																																																																												| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																												|
% 26.17/6.88  																																																																																													| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																													| (63) $false
% 26.17/6.88  																																																																																													|
% 26.17/6.88  																																																																																													|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																												|-Branch two:
% 26.17/6.88  																																																																																												| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																												| (744) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																												|
% 26.17/6.88  																																																																																													+-Applying beta-rule and splitting (201), into two cases.
% 26.17/6.88  																																																																																													|-Branch one:
% 26.17/6.88  																																																																																													| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																													|
% 26.17/6.88  																																																																																														| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																														| (63) $false
% 26.17/6.88  																																																																																														|
% 26.17/6.88  																																																																																														|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																													|-Branch two:
% 26.17/6.88  																																																																																													| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																													| (748) all_65_2_19 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.88  																																																																																													|
% 26.17/6.88  																																																																																														+-Applying beta-rule and splitting (198), into two cases.
% 26.17/6.88  																																																																																														|-Branch one:
% 26.17/6.88  																																																																																														| (297) all_96_0_34 = 0
% 26.17/6.88  																																																																																														|
% 26.17/6.88  																																																																																															| Equations (297) can reduce 182 to:
% 26.17/6.88  																																																																																															| (63) $false
% 26.17/6.88  																																																																																															|
% 26.17/6.88  																																																																																															|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																														|-Branch two:
% 26.17/6.88  																																																																																														| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.88  																																																																																														| (752) all_65_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																														|
% 26.17/6.88  																																																																																															+-Applying beta-rule and splitting (752), into two cases.
% 26.17/6.88  																																																																																															|-Branch one:
% 26.17/6.88  																																																																																															| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																															|
% 26.17/6.88  																																																																																																| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																| (63) $false
% 26.17/6.88  																																																																																																|
% 26.17/6.88  																																																																																																|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																															|-Branch two:
% 26.17/6.88  																																																																																															| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																															| (756)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_1_5_5, all_96_1_35) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																															|
% 26.17/6.88  																																																																																																+-Applying beta-rule and splitting (231), into two cases.
% 26.17/6.88  																																																																																																|-Branch one:
% 26.17/6.88  																																																																																																| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																|
% 26.17/6.88  																																																																																																	| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																	| (63) $false
% 26.17/6.88  																																																																																																	|
% 26.17/6.88  																																																																																																	|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																|-Branch two:
% 26.17/6.88  																																																																																																| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																| (760)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v1 & distinct_lines(all_1_5_5, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.88  																																																																																																|
% 26.17/6.88  																																																																																																	+-Applying beta-rule and splitting (183), into two cases.
% 26.17/6.88  																																																																																																	|-Branch one:
% 26.17/6.88  																																																																																																	| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																	|
% 26.17/6.88  																																																																																																		| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																		| (63) $false
% 26.17/6.88  																																																																																																		|
% 26.17/6.88  																																																																																																		|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																	|-Branch two:
% 26.17/6.88  																																																																																																	| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																	| (764) all_44_1_11 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_44_2_12) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_44_2_12, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																																	|
% 26.17/6.88  																																																																																																		+-Applying beta-rule and splitting (232), into two cases.
% 26.17/6.88  																																																																																																		|-Branch one:
% 26.17/6.88  																																																																																																		| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																		|
% 26.17/6.88  																																																																																																			| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																			| (63) $false
% 26.17/6.88  																																																																																																			|
% 26.17/6.88  																																																																																																			|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																		|-Branch two:
% 26.17/6.88  																																																																																																		| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																		| (768) all_63_1_14 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & apart_point_and_line(all_1_2_2, all_1_7_7) = v1 & distinct_lines(all_1_7_7, all_1_5_5) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.88  																																																																																																		|
% 26.17/6.88  																																																																																																			+-Applying beta-rule and splitting (189), into two cases.
% 26.17/6.88  																																																																																																			|-Branch one:
% 26.17/6.88  																																																																																																			| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																			|
% 26.17/6.88  																																																																																																				| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																				| (63) $false
% 26.17/6.88  																																																																																																				|
% 26.17/6.88  																																																																																																				|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																			|-Branch two:
% 26.17/6.88  																																																																																																			| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																			| (772) all_63_1_14 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_5_5) = v2 & apart_point_and_line(all_1_1_1, all_1_7_7) = v3 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_1_1, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																																			|
% 26.17/6.88  																																																																																																				+-Applying beta-rule and splitting (197), into two cases.
% 26.17/6.88  																																																																																																				|-Branch one:
% 26.17/6.88  																																																																																																				| (297) all_96_0_34 = 0
% 26.17/6.88  																																																																																																				|
% 26.17/6.88  																																																																																																					| Equations (297) can reduce 182 to:
% 26.17/6.88  																																																																																																					| (63) $false
% 26.17/6.88  																																																																																																					|
% 26.17/6.88  																																																																																																					|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																				|-Branch two:
% 26.17/6.88  																																																																																																				| (182)  ~ (all_96_0_34 = 0)
% 26.17/6.88  																																																																																																				| (776) all_65_0_17 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_96_1_35, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																																				|
% 26.17/6.88  																																																																																																					+-Applying beta-rule and splitting (215), into two cases.
% 26.17/6.88  																																																																																																					|-Branch one:
% 26.17/6.88  																																																																																																					| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																					|
% 26.17/6.88  																																																																																																						| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																						| (63) $false
% 26.17/6.88  																																																																																																						|
% 26.17/6.88  																																																																																																						|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																					|-Branch two:
% 26.17/6.88  																																																																																																					| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																					| (780) all_63_3_16 = 0 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v2 & apart_point_and_line(all_1_2_2, all_1_5_5) = v3 & distinct_lines(all_1_5_5, all_1_7_7) = v1 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																																					|
% 26.17/6.88  																																																																																																						+-Applying beta-rule and splitting (776), into two cases.
% 26.17/6.88  																																																																																																						|-Branch one:
% 26.17/6.88  																																																																																																						| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																						|
% 26.17/6.88  																																																																																																							| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																							| (63) $false
% 26.17/6.88  																																																																																																							|
% 26.17/6.88  																																																																																																							|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																						|-Branch two:
% 26.17/6.88  																																																																																																						| (721)  ~ (all_65_0_17 = 0)
% 26.17/6.88  																																																																																																						| (784)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (apart_point_and_line(all_1_1_1, all_96_1_35) = v3 & apart_point_and_line(all_1_2_2, all_1_5_5) = v2 & distinct_lines(all_96_1_35, all_1_5_5) = v1 & distinct_points(all_1_2_2, all_1_1_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | v3 = 0 | v2 = 0))
% 26.17/6.88  																																																																																																						|
% 26.17/6.88  																																																																																																							+-Applying beta-rule and splitting (188), into two cases.
% 26.17/6.88  																																																																																																							|-Branch one:
% 26.17/6.88  																																																																																																							| (785)  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0)
% 26.17/6.88  																																																																																																							|
% 26.17/6.88  																																																																																																								| Using (724) and (785) yields:
% 26.17/6.88  																																																																																																								| (85) $false
% 26.17/6.88  																																																																																																								|
% 26.17/6.88  																																																																																																								|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																							|-Branch two:
% 26.17/6.88  																																																																																																							| (724) apart_point_and_line(all_1_1_1, all_1_6_6) = 0
% 26.17/6.88  																																																																																																							| (788) all_1_4_4 = 0 | apart_point_and_line(all_1_1_1, all_1_5_5) = 0
% 26.17/6.88  																																																																																																							|
% 26.17/6.88  																																																																																																								+-Applying beta-rule and splitting (190), into two cases.
% 26.17/6.88  																																																																																																								|-Branch one:
% 26.17/6.88  																																																																																																								| (785)  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0)
% 26.17/6.88  																																																																																																								|
% 26.17/6.88  																																																																																																									| Using (724) and (785) yields:
% 26.17/6.88  																																																																																																									| (85) $false
% 26.17/6.88  																																																																																																									|
% 26.17/6.88  																																																																																																									|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																								|-Branch two:
% 26.17/6.88  																																																																																																								| (724) apart_point_and_line(all_1_1_1, all_1_6_6) = 0
% 26.17/6.88  																																																																																																								| (792) all_63_1_14 = 0 | distinct_lines(all_1_6_6, all_1_7_7) = 0
% 26.17/6.88  																																																																																																								|
% 26.17/6.88  																																																																																																									+-Applying beta-rule and splitting (187), into two cases.
% 26.17/6.88  																																																																																																									|-Branch one:
% 26.17/6.88  																																																																																																									| (785)  ~ (apart_point_and_line(all_1_1_1, all_1_6_6) = 0)
% 26.17/6.88  																																																																																																									|
% 26.17/6.88  																																																																																																										| Using (724) and (785) yields:
% 26.17/6.88  																																																																																																										| (85) $false
% 26.17/6.88  																																																																																																										|
% 26.17/6.88  																																																																																																										|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																									|-Branch two:
% 26.17/6.88  																																																																																																									| (724) apart_point_and_line(all_1_1_1, all_1_6_6) = 0
% 26.17/6.88  																																																																																																									| (796) all_65_0_17 = 0 | distinct_lines(all_1_6_6, all_1_5_5) = 0
% 26.17/6.88  																																																																																																									|
% 26.17/6.88  																																																																																																										+-Applying beta-rule and splitting (796), into two cases.
% 26.17/6.88  																																																																																																										|-Branch one:
% 26.17/6.88  																																																																																																										| (797) distinct_lines(all_1_6_6, all_1_5_5) = 0
% 26.17/6.88  																																																																																																										|
% 26.17/6.88  																																																																																																											| Instantiating formula (16) with all_1_6_6, all_1_5_5, 0, all_1_4_4 and discharging atoms distinct_lines(all_1_6_6, all_1_5_5) = all_1_4_4, distinct_lines(all_1_6_6, all_1_5_5) = 0, yields:
% 26.17/6.88  																																																																																																											| (62) all_1_4_4 = 0
% 26.17/6.88  																																																																																																											|
% 26.17/6.88  																																																																																																											| Equations (62) can reduce 55 to:
% 26.17/6.88  																																																																																																											| (63) $false
% 26.17/6.88  																																																																																																											|
% 26.17/6.88  																																																																																																											|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																																										|-Branch two:
% 26.17/6.88  																																																																																																										| (800)  ~ (distinct_lines(all_1_6_6, all_1_5_5) = 0)
% 26.17/6.88  																																																																																																										| (725) all_65_0_17 = 0
% 26.17/6.88  																																																																																																										|
% 26.17/6.88  																																																																																																											| Equations (725) can reduce 721 to:
% 26.17/6.88  																																																																																																											| (63) $false
% 26.17/6.88  																																																																																																											|
% 26.17/6.88  																																																																																																											|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																							|-Branch two:
% 26.17/6.88  																																																																																							| (803)  ~ (all_63_0_13 = 0)
% 26.17/6.88  																																																																																							| (804) all_63_2_15 = 0 |  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.88  																																																																																							|
% 26.17/6.88  																																																																																								+-Applying beta-rule and splitting (110), into two cases.
% 26.17/6.88  																																																																																								|-Branch one:
% 26.17/6.88  																																																																																								| (723) all_63_0_13 = 0
% 26.17/6.88  																																																																																								|
% 26.17/6.88  																																																																																									| Equations (723) can reduce 803 to:
% 26.17/6.88  																																																																																									| (63) $false
% 26.17/6.88  																																																																																									|
% 26.17/6.88  																																																																																									|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																								|-Branch two:
% 26.17/6.88  																																																																																								| (803)  ~ (all_63_0_13 = 0)
% 26.17/6.88  																																																																																								| (808) all_63_1_14 = 0 | all_63_2_15 = 0 | all_63_3_16 = 0
% 26.17/6.88  																																																																																								|
% 26.17/6.88  																																																																																									+-Applying beta-rule and splitting (808), into two cases.
% 26.17/6.88  																																																																																									|-Branch one:
% 26.17/6.88  																																																																																									| (809) all_63_1_14 = 0
% 26.17/6.88  																																																																																									|
% 26.17/6.88  																																																																																										| Equations (809) can reduce 722 to:
% 26.17/6.88  																																																																																										| (63) $false
% 26.17/6.88  																																																																																										|
% 26.17/6.88  																																																																																										|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																									|-Branch two:
% 26.17/6.88  																																																																																									| (722)  ~ (all_63_1_14 = 0)
% 26.17/6.88  																																																																																									| (812) all_63_2_15 = 0 | all_63_3_16 = 0
% 26.17/6.88  																																																																																									|
% 26.17/6.88  																																																																																										+-Applying beta-rule and splitting (804), into two cases.
% 26.17/6.88  																																																																																										|-Branch one:
% 26.17/6.88  																																																																																										| (318) all_63_2_15 = 0
% 26.17/6.88  																																																																																										|
% 26.17/6.88  																																																																																											| Equations (318) can reduce 180 to:
% 26.17/6.88  																																																																																											| (63) $false
% 26.17/6.88  																																																																																											|
% 26.17/6.88  																																																																																											|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																										|-Branch two:
% 26.17/6.88  																																																																																										| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.88  																																																																																										| (816)  ? [v0] :  ? [v1] :  ? [v2] : (apart_point_and_line(all_1_1_1, all_1_7_7) = v1 & apart_point_and_line(all_1_2_2, all_1_7_7) = v2 & distinct_points(all_1_1_1, all_1_2_2) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 = 0))
% 26.17/6.88  																																																																																										|
% 26.17/6.88  																																																																																											+-Applying beta-rule and splitting (812), into two cases.
% 26.17/6.88  																																																																																											|-Branch one:
% 26.17/6.88  																																																																																											| (318) all_63_2_15 = 0
% 26.17/6.88  																																																																																											|
% 26.17/6.88  																																																																																												| Equations (318) can reduce 180 to:
% 26.17/6.88  																																																																																												| (63) $false
% 26.17/6.88  																																																																																												|
% 26.17/6.88  																																																																																												|-The branch is then unsatisfiable
% 26.17/6.88  																																																																																											|-Branch two:
% 26.17/6.88  																																																																																											| (180)  ~ (all_63_2_15 = 0)
% 26.17/6.88  																																																																																											| (305) all_63_3_16 = 0
% 26.17/6.88  																																																																																											|
% 26.17/6.88  																																																																																												| Equations (305) can reduce 181 to:
% 26.17/6.88  																																																																																												| (63) $false
% 26.17/6.88  																																																																																												|
% 26.17/6.88  																																																																																												|-The branch is then unsatisfiable
% 26.17/6.88  														|-Branch two:
% 26.17/6.88  														| (297) all_96_0_34 = 0
% 26.17/6.88  														| (823)  ~ (all_96_2_36 = 0)
% 26.17/6.88  														|
% 26.17/6.88  															| Equations (164) can reduce 823 to:
% 26.17/6.88  															| (63) $false
% 26.17/6.88  															|
% 26.17/6.88  															|-The branch is then unsatisfiable
% 26.17/6.88  							|-Branch two:
% 26.17/6.88  							| (825)  ~ (distinct_points(all_1_1_1, all_1_2_2) = 0)
% 26.17/6.88  							| (121) all_44_0_10 = 0
% 26.17/6.88  							|
% 26.17/6.88  								| Equations (121) can reduce 98 to:
% 26.17/6.88  								| (63) $false
% 26.17/6.88  								|
% 26.17/6.88  								|-The branch is then unsatisfiable
% 26.17/6.88  						|-Branch two:
% 26.17/6.88  						| (130) all_44_1_11 = 0
% 26.17/6.88  						| (121) all_44_0_10 = 0
% 26.17/6.88  						|
% 26.17/6.88  							| Equations (121) can reduce 98 to:
% 26.17/6.88  							| (63) $false
% 26.17/6.88  							|
% 26.17/6.88  							|-The branch is then unsatisfiable
% 26.17/6.88  % SZS output end Proof for theBenchmark
% 26.17/6.89  
% 26.17/6.89  6305ms
%------------------------------------------------------------------------------