%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO232+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n032.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 03:49:01 EDT 2022

% Result   : Theorem 2.46s 1.15s
% Output   : Proof 4.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : GEO232+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.00/0.10  % Command  : ePrincess-casc -timeout=%d %s
% 0.10/0.28  % Computer : n032.cluster.edu
% 0.10/0.28  % Model    : x86_64 x86_64
% 0.10/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28  % Memory   : 8042.1875MB
% 0.10/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28  % CPULimit : 300
% 0.10/0.28  % WCLimit  : 600
% 0.10/0.28  % DateTime : Sat Jun 18 12:51:32 EDT 2022
% 0.10/0.28  % CPUTime  : 
% 0.14/0.46          ____       _                          
% 0.14/0.46    ___  / __ \_____(_)___  ________  __________
% 0.14/0.46   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.46  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.14/0.46  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.14/0.46  
% 0.14/0.46  A Theorem Prover for First-Order Logic
% 0.14/0.46  (ePrincess v.1.0)
% 0.14/0.46  
% 0.14/0.46  (c) Philipp Rümmer, 2009-2015
% 0.14/0.46  (c) Peter Backeman, 2014-2015
% 0.14/0.46  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.46  Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.46  Bug reports to peter@backeman.se
% 0.14/0.46  
% 0.14/0.46  For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.46  
% 0.14/0.46  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.51  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.23/0.77  Prover 0: Preprocessing ...
% 2.17/1.01  Prover 0: Warning: ignoring some quantifiers
% 2.17/1.04  Prover 0: Constructing countermodel ...
% 2.46/1.15  Prover 0: proved (643ms)
% 2.46/1.15  
% 2.46/1.15  No countermodel exists, formula is valid
% 2.46/1.15  % SZS status Theorem for theBenchmark
% 2.46/1.15  
% 2.46/1.15  Generating proof ... Warning: ignoring some quantifiers
% 3.76/1.38  found it (size 5)
% 3.76/1.38  
% 3.76/1.38  % SZS output start Proof for theBenchmark
% 3.76/1.38  Assumed formulas after preprocessing and simplification: 
% 3.76/1.38  | (0)  ? [v0] :  ? [v1] : (reverse_line(v0) = v1 & line(v0) &  ~ unequally_directed_lines(v0, v1) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v5) = v7) |  ~ (reverse_line(v4) = v6) |  ~ distinct_lines(v4, v5) |  ~ distinct_points(v2, v3) | left_apart_point(v3, v7) | left_apart_point(v3, v6) | left_apart_point(v3, v5) | left_apart_point(v3, v4) | left_apart_point(v2, v7) | left_apart_point(v2, v6) | left_apart_point(v2, v5) | left_apart_point(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ distinct_points(v3, v4) | before_on_line(v2, v3, v4) | unequally_directed_lines(v2, v6) | left_apart_point(v4, v5) | left_apart_point(v4, v2) | left_apart_point(v3, v5) | left_apart_point(v3, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) |  ~ unequally_directed_lines(v2, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) |  ~ left_apart_point(v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) |  ~ left_apart_point(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) |  ~ left_apart_point(v3, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) |  ~ left_apart_point(v3, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ (reverse_line(v2) = v5) |  ~ before_on_line(v2, v3, v4) | distinct_points(v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v4) = v6) |  ~ (reverse_line(v3) = v5) |  ~ unequally_directed_lines(v2, v5) |  ~ unequally_directed_lines(v2, v3) | unequally_directed_lines(v3, v6) | unequally_directed_lines(v2, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v4) = v6) |  ~ (reverse_line(v3) = v5) |  ~ unequally_directed_lines(v2, v5) |  ~ unequally_directed_lines(v2, v3) | unequally_directed_lines(v3, v6) | unequally_directed_lines(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v4) = v6) |  ~ (reverse_line(v3) = v5) |  ~ unequally_directed_lines(v2, v5) |  ~ unequally_directed_lines(v2, v3) | unequally_directed_lines(v3, v4) | unequally_directed_lines(v2, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v4) = v6) |  ~ (reverse_line(v3) = v5) |  ~ unequally_directed_lines(v2, v5) |  ~ unequally_directed_lines(v2, v3) | unequally_directed_lines(v3, v4) | unequally_directed_lines(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (parallel_through_point(v5, v4) = v3) |  ~ (parallel_through_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (intersection_point(v5, v4) = v3) |  ~ (intersection_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (line_connecting(v5, v4) = v3) |  ~ (line_connecting(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v2, v3) = v5) |  ~ distinct_points(v2, v3) |  ~ left_apart_point(v2, v4) | left_convergent_lines(v5, v4) | left_apart_point(v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ divides_points(v4, v2, v3) | left_apart_point(v3, v5) | left_apart_point(v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ divides_points(v4, v2, v3) | left_apart_point(v3, v5) | left_apart_point(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ divides_points(v4, v2, v3) | left_apart_point(v3, v4) | left_apart_point(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ divides_points(v4, v2, v3) | left_apart_point(v2, v5) | left_apart_point(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ unequally_directed_lines(v3, v4) |  ~ left_apart_point(v2, v3) | distinct_lines(v3, v4) | left_apart_point(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_apart_point(v3, v5) |  ~ left_apart_point(v2, v4) | divides_points(v4, v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_apart_point(v3, v4) |  ~ left_apart_point(v2, v5) | divides_points(v4, v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ between_on_line(v2, v3, v4, v5) | before_on_line(v2, v5, v4) | before_on_line(v2, v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ between_on_line(v2, v3, v4, v5) | before_on_line(v2, v5, v4) | before_on_line(v2, v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ between_on_line(v2, v3, v4, v5) | before_on_line(v2, v4, v5) | before_on_line(v2, v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ between_on_line(v2, v3, v4, v5) | before_on_line(v2, v4, v3) | before_on_line(v2, v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ before_on_line(v2, v5, v4) |  ~ before_on_line(v2, v4, v3) | between_on_line(v2, v3, v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ before_on_line(v2, v4, v5) |  ~ before_on_line(v2, v3, v4) | between_on_line(v2, v3, v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (reverse_line(v4) = v3) |  ~ (reverse_line(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ~ unequally_directed_lines(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ~ apart_point_and_line(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v2, v3) = v4) |  ~ point(v3) |  ~ line(v2) | line(v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ~ line(v3) |  ~ line(v2) |  ~ unequally_directed_lines(v2, v3) | point(v4) |  ? [v5] : (reverse_line(v3) = v5 &  ~ unequally_directed_lines(v2, v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ~ unequally_directed_lines(v2, v3) |  ~ apart_point_and_line(v4, v3) |  ? [v5] : (reverse_line(v3) = v5 &  ~ unequally_directed_lines(v2, v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection_point(v2, v3) = v4) |  ~ unequally_directed_lines(v2, v3) |  ~ apart_point_and_line(v4, v2) |  ? [v5] : (reverse_line(v3) = v5 &  ~ unequally_directed_lines(v2, v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v3, v2) = v4) |  ? [v5] :  ? [v6] : (line_connecting(v2, v3) = v5 & reverse_line(v4) = v6 &  ~ unequally_directed_lines(v5, v6))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ~ point(v3) |  ~ point(v2) |  ~ distinct_points(v2, v3) | line(v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ~ distinct_points(v2, v3) |  ~ apart_point_and_line(v3, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ~ distinct_points(v2, v3) |  ~ apart_point_and_line(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v2, v3) = v4) |  ? [v5] :  ? [v6] : (line_connecting(v3, v2) = v5 & reverse_line(v5) = v6 &  ~ unequally_directed_lines(v4, v6))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ left_convergent_lines(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ line(v3) |  ~ line(v2) | unequally_directed_lines(v2, v4) | unequally_directed_lines(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ unequally_directed_lines(v2, v4) |  ~ unequally_directed_lines(v2, v3) | left_convergent_lines(v2, v4) | left_convergent_lines(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ unequally_directed_lines(v2, v4) |  ~ unequally_directed_lines(v2, v3) | convergent_lines(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ convergent_lines(v2, v3) | unequally_directed_lines(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ convergent_lines(v2, v3) | unequally_directed_lines(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ left_apart_point(v2, v4) | apart_point_and_line(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ left_apart_point(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ left_apart_point(v2, v3) | apart_point_and_line(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ apart_point_and_line(v2, v3) | left_apart_point(v2, v4) | left_apart_point(v2, v3)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ left_convergent_lines(v3, v4) | left_convergent_lines(v3, v2) | unequally_directed_lines(v4, v2)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ distinct_lines(v3, v4) | distinct_lines(v4, v2) | distinct_lines(v3, v2)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ distinct_points(v3, v4) | distinct_points(v4, v2) | distinct_points(v3, v2)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v2) | unequally_directed_lines(v3, v2)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ left_apart_point(v3, v4) | distinct_points(v3, v2) | left_apart_point(v2, v4)) &  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ line(v2) | line(v3)) &  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ distinct_lines(v2, v3)) &  ! [v2] :  ! [v3] :  ~ left_convergent_lines(v2, v3) &  ! [v2] :  ! [v3] :  ~ left_apart_point(v2, v3) &  ! [v2] :  ~ distinct_lines(v2, v2) &  ! [v2] :  ~ distinct_points(v2, v2) &  ! [v2] :  ~ unequally_directed_lines(v2, v2))
% 3.76/1.44  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 3.76/1.44  | (1) reverse_line(all_0_1_1) = all_0_0_0 & line(all_0_1_1) &  ~ unequally_directed_lines(all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v3) = v5) |  ~ (reverse_line(v2) = v4) |  ~ distinct_lines(v2, v3) |  ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ distinct_points(v1, v2) | before_on_line(v0, v1, v2) | unequally_directed_lines(v0, v4) | left_apart_point(v2, v3) | left_apart_point(v2, v0) | left_apart_point(v1, v3) | left_apart_point(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ unequally_directed_lines(v0, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v1, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ distinct_points(v0, v1) |  ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ unequally_directed_lines(v1, v2) |  ~ left_apart_point(v0, v1) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v3) |  ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v2) |  ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v3, v2) |  ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v2, v3) |  ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ unequally_directed_lines(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ apart_point_and_line(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ~ point(v1) |  ~ line(v0) | line(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ line(v1) |  ~ line(v0) |  ~ unequally_directed_lines(v0, v1) | point(v2) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ unequally_directed_lines(v0, v1) |  ~ apart_point_and_line(v2, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ unequally_directed_lines(v0, v1) |  ~ apart_point_and_line(v2, v0) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 &  ~ unequally_directed_lines(v3, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ point(v1) |  ~ point(v0) |  ~ distinct_points(v0, v1) | line(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 &  ~ unequally_directed_lines(v2, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ line(v1) |  ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) |  ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) |  ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ line(v0) | line(v1)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ distinct_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ~ left_convergent_lines(v0, v1) &  ! [v0] :  ! [v1] :  ~ left_apart_point(v0, v1) &  ! [v0] :  ~ distinct_lines(v0, v0) &  ! [v0] :  ~ distinct_points(v0, v0) &  ! [v0] :  ~ unequally_directed_lines(v0, v0)
% 3.76/1.46  |
% 3.76/1.46  | Applying alpha-rule on (1) yields:
% 3.76/1.46  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 3.76/1.46  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v4))
% 3.76/1.46  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2))
% 3.76/1.46  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v4))
% 3.76/1.46  | (6)  ! [v0] :  ~ unequally_directed_lines(v0, v0)
% 3.76/1.46  | (7)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 3.76/1.46  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ unequally_directed_lines(v2, v1))
% 3.76/1.46  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2))
% 3.76/1.46  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2))
% 3.76/1.47  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 3.76/1.47  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ unequally_directed_lines(v0, v4))
% 3.76/1.47  | (13)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ line(v0) | line(v1))
% 3.76/1.47  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 3.76/1.47  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ unequally_directed_lines(v1, v2) |  ~ left_apart_point(v0, v1) | distinct_lines(v1, v2) | left_apart_point(v0, v3))
% 3.76/1.47  | (16)  ~ unequally_directed_lines(all_0_1_1, all_0_0_0)
% 3.76/1.47  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ line(v1) |  ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 3.76/1.47  | (18)  ! [v0] :  ! [v1] :  ~ left_convergent_lines(v0, v1)
% 3.76/1.47  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 &  ~ unequally_directed_lines(v2, v4)))
% 3.76/1.47  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v3, v2) |  ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 3.76/1.47  | (21) line(all_0_1_1)
% 3.76/1.47  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ~ point(v1) |  ~ line(v0) | line(v2))
% 3.76/1.47  | (23)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 3.76/1.47  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ line(v1) |  ~ line(v0) |  ~ unequally_directed_lines(v0, v1) | point(v2) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3)))
% 3.76/1.47  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 3.76/1.47  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 3.76/1.47  | (27)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 3.76/1.47  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v1, v3))
% 3.76/1.47  | (29)  ! [v0] :  ~ distinct_lines(v0, v0)
% 3.76/1.47  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1))
% 3.76/1.47  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3))
% 3.76/1.47  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v3) |  ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 3.76/1.47  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v3) = v5) |  ~ (reverse_line(v2) = v4) |  ~ distinct_lines(v2, v3) |  ~ distinct_points(v0, v1) | left_apart_point(v1, v5) | left_apart_point(v1, v4) | left_apart_point(v1, v3) | left_apart_point(v1, v2) | left_apart_point(v0, v5) | left_apart_point(v0, v4) | left_apart_point(v0, v3) | left_apart_point(v0, v2))
% 4.13/1.48  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ distinct_points(v0, v1) |  ~ left_apart_point(v0, v2) | left_convergent_lines(v3, v2) | left_apart_point(v1, v2))
% 4.13/1.48  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.13/1.48  | (36) reverse_line(all_0_1_1) = all_0_0_0
% 4.13/1.48  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 4.13/1.48  | (38)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v1, v2))
% 4.13/1.48  | (39)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v0, v2))
% 4.13/1.48  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v1, v0))
% 4.13/1.48  | (41)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.13/1.48  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.13/1.48  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 &  ~ unequally_directed_lines(v3, v4)))
% 4.13/1.48  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v2) | unequally_directed_lines(v0, v2))
% 4.13/1.48  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ distinct_points(v1, v2) | before_on_line(v0, v1, v2) | unequally_directed_lines(v0, v4) | left_apart_point(v2, v3) | left_apart_point(v2, v0) | left_apart_point(v1, v3) | left_apart_point(v1, v0))
% 4.13/1.48  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ unequally_directed_lines(v0, v1) |  ~ apart_point_and_line(v2, v0) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3)))
% 4.13/1.48  | (47)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ distinct_lines(v0, v1))
% 4.13/1.48  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v2, v3) |  ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.13/1.48  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ point(v1) |  ~ point(v0) |  ~ distinct_points(v0, v1) | line(v2))
% 4.13/1.48  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.13/1.48  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v2, v3))
% 4.13/1.48  | (52)  ! [v0] :  ! [v1] :  ~ left_apart_point(v0, v1)
% 4.13/1.48  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v2) |  ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1))
% 4.13/1.48  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (reverse_line(v2) = v4) |  ~ (reverse_line(v1) = v3) |  ~ unequally_directed_lines(v0, v3) |  ~ unequally_directed_lines(v0, v1) | unequally_directed_lines(v1, v4) | unequally_directed_lines(v0, v2))
% 4.13/1.49  | (55)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) |  ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1))
% 4.13/1.49  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2))
% 4.13/1.49  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.13/1.49  | (58)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ apart_point_and_line(v0, v2))
% 4.13/1.49  | (59)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.13/1.49  | (60)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.13/1.49  | (61)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) |  ~ unequally_directed_lines(v0, v1) | left_convergent_lines(v0, v2) | left_convergent_lines(v0, v1))
% 4.13/1.49  | (62)  ! [v0] :  ~ distinct_points(v0, v0)
% 4.13/1.49  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ unequally_directed_lines(v0, v1) |  ~ apart_point_and_line(v2, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3)))
% 4.13/1.49  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1))
% 4.13/1.49  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) |  ~ left_apart_point(v2, v0))
% 4.13/1.49  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.13/1.49  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.13/1.49  |
% 4.13/1.49  | Instantiating formula (17) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms reverse_line(all_0_1_1) = all_0_0_0, line(all_0_1_1),  ~ unequally_directed_lines(all_0_1_1, all_0_0_0), yields:
% 4.13/1.49  | (68) unequally_directed_lines(all_0_1_1, all_0_1_1)
% 4.13/1.49  |
% 4.13/1.49  | Instantiating formula (6) with all_0_1_1 and discharging atoms unequally_directed_lines(all_0_1_1, all_0_1_1), yields:
% 4.13/1.49  | (69) $false
% 4.13/1.49  |
% 4.13/1.49  |-The branch is then unsatisfiable
% 4.13/1.49  % SZS output end Proof for theBenchmark
% 4.13/1.49  
% 4.13/1.49  1021ms
%------------------------------------------------------------------------------