%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 03:48:58 EDT 2022

% Result   : Theorem 2.85s 1.38s
% Output   : Proof 4.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.13/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jun 18 18:52:33 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.51/0.61          ____       _                          
% 0.51/0.61    ___  / __ \_____(_)___  ________  __________
% 0.51/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.61  
% 0.51/0.61  A Theorem Prover for First-Order Logic
% 0.51/0.62  (ePrincess v.1.0)
% 0.51/0.62  
% 0.51/0.62  (c) Philipp Rümmer, 2009-2015
% 0.51/0.62  (c) Peter Backeman, 2014-2015
% 0.51/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.62  Bug reports to peter@backeman.se
% 0.51/0.62  
% 0.51/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.62  
% 0.51/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.98  Prover 0: Preprocessing ...
% 2.52/1.24  Prover 0: Warning: ignoring some quantifiers
% 2.52/1.27  Prover 0: Constructing countermodel ...
% 2.85/1.38  Prover 0: proved (711ms)
% 2.85/1.38  
% 2.85/1.38  No countermodel exists, formula is valid
% 2.85/1.38  % SZS status Theorem for theBenchmark
% 2.85/1.38  
% 2.85/1.38  Generating proof ... Warning: ignoring some quantifiers
% 3.96/1.59  found it (size 4)
% 3.96/1.59  
% 3.96/1.59  % SZS output start Proof for theBenchmark
% 3.96/1.59  Assumed formulas after preprocessing and simplification: 
% 3.96/1.59  | (0)  ? [v0] :  ? [v1] :  ? [v2] : (reverse_line(v1) = v2 & line(v1) & line(v0) &  ~ unequally_directed_lines(v0, v2) &  ~ unequally_directed_lines(v0, v1) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (reverse_line(v6) = v8) |  ~ (reverse_line(v5) = v7) |  ~ distinct_lines(v5, v6) |  ~ distinct_points(v3, v4) | left_apart_point(v4, v8) | left_apart_point(v4, v7) | left_apart_point(v4, v6) | left_apart_point(v4, v5) | left_apart_point(v3, v8) | left_apart_point(v3, v7) | left_apart_point(v3, v6) | left_apart_point(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ distinct_points(v4, v5) | before_on_line(v3, v4, v5) | unequally_directed_lines(v3, v7) | left_apart_point(v5, v6) | left_apart_point(v5, v3) | left_apart_point(v4, v6) | left_apart_point(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) |  ~ unequally_directed_lines(v3, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) |  ~ left_apart_point(v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) |  ~ left_apart_point(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) |  ~ left_apart_point(v4, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) |  ~ left_apart_point(v4, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (reverse_line(v3) = v6) |  ~ before_on_line(v3, v4, v5) | distinct_points(v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v5) = v7) |  ~ (reverse_line(v4) = v6) |  ~ unequally_directed_lines(v3, v6) |  ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v7) | unequally_directed_lines(v3, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v5) = v7) |  ~ (reverse_line(v4) = v6) |  ~ unequally_directed_lines(v3, v6) |  ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v7) | unequally_directed_lines(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v5) = v7) |  ~ (reverse_line(v4) = v6) |  ~ unequally_directed_lines(v3, v6) |  ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v5) | unequally_directed_lines(v3, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v5) = v7) |  ~ (reverse_line(v4) = v6) |  ~ unequally_directed_lines(v3, v6) |  ~ unequally_directed_lines(v3, v4) | unequally_directed_lines(v4, v5) | unequally_directed_lines(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (parallel_through_point(v6, v5) = v4) |  ~ (parallel_through_point(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (intersection_point(v6, v5) = v4) |  ~ (intersection_point(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (line_connecting(v6, v5) = v4) |  ~ (line_connecting(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v3, v4) = v6) |  ~ distinct_points(v3, v4) |  ~ left_apart_point(v3, v5) | left_convergent_lines(v6, v5) | left_apart_point(v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ divides_points(v5, v3, v4) | left_apart_point(v4, v6) | left_apart_point(v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ divides_points(v5, v3, v4) | left_apart_point(v4, v6) | left_apart_point(v3, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ divides_points(v5, v3, v4) | left_apart_point(v4, v5) | left_apart_point(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ divides_points(v5, v3, v4) | left_apart_point(v3, v6) | left_apart_point(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ unequally_directed_lines(v4, v5) |  ~ left_apart_point(v3, v4) | distinct_lines(v4, v5) | left_apart_point(v3, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ left_apart_point(v4, v6) |  ~ left_apart_point(v3, v5) | divides_points(v5, v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ left_apart_point(v4, v5) |  ~ left_apart_point(v3, v6) | divides_points(v5, v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v6, v5) | before_on_line(v3, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v6, v5) | before_on_line(v3, v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v5, v6) | before_on_line(v3, v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ between_on_line(v3, v4, v5, v6) | before_on_line(v3, v5, v4) | before_on_line(v3, v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ before_on_line(v3, v6, v5) |  ~ before_on_line(v3, v5, v4) | between_on_line(v3, v4, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ before_on_line(v3, v5, v6) |  ~ before_on_line(v3, v4, v5) | between_on_line(v3, v4, v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (reverse_line(v5) = v4) |  ~ (reverse_line(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) |  ~ unequally_directed_lines(v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v4, v3) = v5) |  ~ apart_point_and_line(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (parallel_through_point(v3, v4) = v5) |  ~ point(v4) |  ~ line(v3) | line(v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ~ line(v4) |  ~ line(v3) |  ~ unequally_directed_lines(v3, v4) | point(v5) |  ? [v6] : (reverse_line(v4) = v6 &  ~ unequally_directed_lines(v3, v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ~ unequally_directed_lines(v3, v4) |  ~ apart_point_and_line(v5, v4) |  ? [v6] : (reverse_line(v4) = v6 &  ~ unequally_directed_lines(v3, v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection_point(v3, v4) = v5) |  ~ unequally_directed_lines(v3, v4) |  ~ apart_point_and_line(v5, v3) |  ? [v6] : (reverse_line(v4) = v6 &  ~ unequally_directed_lines(v3, v6))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v4, v3) = v5) |  ? [v6] :  ? [v7] : (line_connecting(v3, v4) = v6 & reverse_line(v5) = v7 &  ~ unequally_directed_lines(v6, v7))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ~ point(v4) |  ~ point(v3) |  ~ distinct_points(v3, v4) | line(v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ~ distinct_points(v3, v4) |  ~ apart_point_and_line(v4, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ~ distinct_points(v3, v4) |  ~ apart_point_and_line(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v3, v4) = v5) |  ? [v6] :  ? [v7] : (line_connecting(v4, v3) = v6 & reverse_line(v6) = v7 &  ~ unequally_directed_lines(v5, v7))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_convergent_lines(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ line(v4) |  ~ line(v3) | unequally_directed_lines(v3, v5) | unequally_directed_lines(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ unequally_directed_lines(v3, v5) |  ~ unequally_directed_lines(v3, v4) | left_convergent_lines(v3, v5) | left_convergent_lines(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ unequally_directed_lines(v3, v5) |  ~ unequally_directed_lines(v3, v4) | convergent_lines(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ convergent_lines(v3, v4) | unequally_directed_lines(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ convergent_lines(v3, v4) | unequally_directed_lines(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_apart_point(v3, v5) | apart_point_and_line(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_apart_point(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ left_apart_point(v3, v4) | apart_point_and_line(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (reverse_line(v4) = v5) |  ~ apart_point_and_line(v3, v4) | left_apart_point(v3, v5) | left_apart_point(v3, v4)) &  ? [v3] :  ! [v4] :  ! [v5] : ( ~ left_convergent_lines(v4, v5) | left_convergent_lines(v4, v3) | unequally_directed_lines(v5, v3)) &  ? [v3] :  ! [v4] :  ! [v5] : ( ~ distinct_lines(v4, v5) | distinct_lines(v5, v3) | distinct_lines(v4, v3)) &  ? [v3] :  ! [v4] :  ! [v5] : ( ~ distinct_points(v4, v5) | distinct_points(v5, v3) | distinct_points(v4, v3)) &  ? [v3] :  ! [v4] :  ! [v5] : ( ~ unequally_directed_lines(v4, v5) | unequally_directed_lines(v5, v3) | unequally_directed_lines(v4, v3)) &  ? [v3] :  ! [v4] :  ! [v5] : ( ~ left_apart_point(v4, v5) | distinct_points(v4, v3) | left_apart_point(v3, v5)) &  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ line(v3) | line(v4)) &  ! [v3] :  ! [v4] : ( ~ (reverse_line(v3) = v4) |  ~ distinct_lines(v3, v4)) &  ! [v3] :  ! [v4] :  ~ left_convergent_lines(v3, v4) &  ! [v3] :  ! [v4] :  ~ left_apart_point(v3, v4) &  ! [v3] :  ~ distinct_lines(v3, v3) &  ! [v3] :  ~ distinct_points(v3, v3) &  ! [v3] :  ~ unequally_directed_lines(v3, v3))
% 4.21/1.65  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 4.21/1.65  | (1) reverse_line(all_0_1_1) = all_0_0_0 & line(all_0_1_1) & line(all_0_2_2) &  ~ unequally_directed_lines(all_0_2_2, all_0_0_0) &  ~ unequally_directed_lines(all_0_2_2, all_0_1_1) &  ! [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)
% 4.21/1.67  |
% 4.21/1.67  | Applying alpha-rule on (1) yields:
% 4.21/1.67  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.21/1.67  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.21/1.67  | (4)  ! [v0] :  ~ unequally_directed_lines(v0, v0)
% 4.21/1.67  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) |  ~ unequally_directed_lines(v0, v1) | convergent_lines(v0, v1))
% 4.21/1.67  | (6)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.21/1.67  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 &  ~ unequally_directed_lines(v2, v4)))
% 4.21/1.67  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.21/1.67  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v1, v2))
% 4.21/1.67  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ point(v1) |  ~ point(v0) |  ~ distinct_points(v0, v1) | line(v2))
% 4.21/1.67  | (11)  ! [v0] :  ! [v1] :  ~ left_convergent_lines(v0, v1)
% 4.21/1.67  | (12)  ! [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))
% 4.21/1.67  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v3, v2) |  ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.21/1.67  | (14)  ! [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)))
% 4.21/1.67  | (15)  ! [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)))
% 4.21/1.67  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ line(v1) |  ~ line(v0) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.21/1.67  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v2) | left_apart_point(v0, v1))
% 4.21/1.67  | (18)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.21/1.67  | (19)  ! [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))
% 4.21/1.68  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ apart_point_and_line(v0, v2))
% 4.21/1.68  | (21)  ! [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))
% 4.21/1.68  | (22)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.21/1.68  | (23)  ! [v0] :  ~ distinct_lines(v0, v0)
% 4.21/1.68  | (24)  ! [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))
% 4.21/1.68  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.21/1.68  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v3) |  ~ left_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.21/1.68  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v0, v3) | left_apart_point(v0, v2))
% 4.21/1.68  | (28) line(all_0_2_2)
% 4.21/1.68  | (29)  ! [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))
% 4.21/1.68  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v0, v3))
% 4.21/1.68  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2) | apart_point_and_line(v0, v1))
% 4.21/1.68  | (32)  ! [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))
% 4.21/1.68  | (33)  ! [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))
% 4.21/1.68  | (34)  ! [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))
% 4.21/1.68  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 4.21/1.69  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ unequally_directed_lines(v2, v1))
% 4.21/1.69  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2))
% 4.21/1.69  | (38)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.21/1.69  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v1, v2) |  ~ left_apart_point(v0, v3) | divides_points(v2, v0, v1))
% 4.21/1.69  | (40)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ distinct_lines(v0, v1))
% 4.21/1.69  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v3) | left_apart_point(v1, v2))
% 4.21/1.69  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v0, v2))
% 4.21/1.69  | (43)  ! [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))
% 4.21/1.69  | (44)  ~ unequally_directed_lines(all_0_2_2, all_0_1_1)
% 4.21/1.69  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v2, v3) |  ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.21/1.69  | (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)))
% 4.21/1.69  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (line_connecting(v1, v2) = v4) |  ~ (reverse_line(v0) = v3) |  ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.21/1.69  | (48)  ! [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))
% 4.21/1.69  | (49)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ~ point(v1) |  ~ line(v0) | line(v2))
% 4.21/1.69  | (50)  ! [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))
% 4.21/1.69  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.21/1.69  | (52) line(all_0_1_1)
% 4.21/1.69  | (53)  ! [v0] :  ! [v1] :  ~ left_apart_point(v0, v1)
% 4.21/1.69  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 4.21/1.70  | (55) reverse_line(all_0_1_1) = all_0_0_0
% 4.21/1.70  | (56)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.21/1.70  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 4.21/1.70  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.21/1.70  | (59)  ! [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))
% 4.21/1.70  | (60)  ~ unequally_directed_lines(all_0_2_2, all_0_0_0)
% 4.21/1.70  | (61)  ! [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))
% 4.21/1.70  | (62)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ line(v0) | line(v1))
% 4.21/1.70  | (63)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.21/1.70  | (64)  ! [v0] :  ~ distinct_points(v0, v0)
% 4.21/1.70  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ? [v3] :  ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 &  ~ unequally_directed_lines(v3, v4)))
% 4.21/1.70  | (66)  ! [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))
% 4.21/1.70  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 4.21/1.70  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2))
% 4.21/1.70  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.21/1.70  |
% 4.21/1.70  | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms reverse_line(all_0_1_1) = all_0_0_0, line(all_0_1_1), line(all_0_2_2),  ~ unequally_directed_lines(all_0_2_2, all_0_0_0),  ~ unequally_directed_lines(all_0_2_2, all_0_1_1), yields:
% 4.21/1.71  | (70) $false
% 4.21/1.71  |
% 4.21/1.71  |-The branch is then unsatisfiable
% 4.21/1.71  % SZS output end Proof for theBenchmark
% 4.21/1.71  
% 4.21/1.71  1082ms
%------------------------------------------------------------------------------