%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 03:49:16 EDT 2022

% Result   : Theorem 3.09s 1.37s
% Output   : Proof 4.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.37  % Computer : n027.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Sat Jun 18 01:03:22 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.63/0.63          ____       _                          
% 0.63/0.63    ___  / __ \_____(_)___  ________  __________
% 0.63/0.63   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.63  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.63/0.63  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.63/0.63  
% 0.63/0.63  A Theorem Prover for First-Order Logic
% 0.63/0.63  (ePrincess v.1.0)
% 0.63/0.63  
% 0.63/0.63  (c) Philipp Rümmer, 2009-2015
% 0.63/0.63  (c) Peter Backeman, 2014-2015
% 0.63/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.63  Bug reports to peter@backeman.se
% 0.63/0.63  
% 0.63/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.63  
% 0.63/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.75/1.00  Prover 0: Preprocessing ...
% 2.70/1.26  Prover 0: Warning: ignoring some quantifiers
% 2.70/1.30  Prover 0: Constructing countermodel ...
% 3.09/1.37  Prover 0: proved (693ms)
% 3.09/1.37  
% 3.09/1.37  No countermodel exists, formula is valid
% 3.09/1.37  % SZS status Theorem for theBenchmark
% 3.09/1.37  
% 3.09/1.37  Generating proof ... Warning: ignoring some quantifiers
% 4.45/1.65  found it (size 4)
% 4.45/1.65  
% 4.45/1.65  % SZS output start Proof for theBenchmark
% 4.45/1.65  Assumed formulas after preprocessing and simplification: 
% 4.45/1.65  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (incident_point_and_line(v3, v0) & distinct_points(v2, v3) & distinct_points(v1, v3) & before_on_line(v0, v2, v3) & before_on_line(v0, v1, v2) & left_apart_point(v4, v0) &  ~ before_on_line(v0, v1, v3) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (reverse_line(v8) = v10) |  ~ (reverse_line(v7) = v9) |  ~ distinct_lines(v7, v8) |  ~ distinct_points(v5, v6) | left_apart_point(v6, v10) | left_apart_point(v6, v9) | left_apart_point(v6, v8) | left_apart_point(v6, v7) | left_apart_point(v5, v10) | left_apart_point(v5, v9) | left_apart_point(v5, v8) | left_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ unequally_directed_lines(v5, v8) |  ~ unequally_directed_lines(v5, v6) | unequally_directed_lines(v6, v9) | unequally_directed_lines(v5, v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ unequally_directed_lines(v5, v8) |  ~ unequally_directed_lines(v5, v6) | unequally_directed_lines(v6, v9) | unequally_directed_lines(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ unequally_directed_lines(v5, v8) |  ~ unequally_directed_lines(v5, v6) | unequally_directed_lines(v6, v7) | unequally_directed_lines(v5, v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (reverse_line(v7) = v9) |  ~ (reverse_line(v6) = v8) |  ~ unequally_directed_lines(v5, v8) |  ~ unequally_directed_lines(v5, v6) | unequally_directed_lines(v6, v7) | unequally_directed_lines(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (parallel_through_point(v8, v7) = v6) |  ~ (parallel_through_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection_point(v8, v7) = v6) |  ~ (intersection_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (line_connecting(v8, v7) = v6) |  ~ (line_connecting(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ incident_point_and_line(v7, v5) |  ~ incident_point_and_line(v6, v5) |  ~ distinct_points(v6, v7) |  ~ equally_directed_lines(v5, v8) | before_on_line(v5, v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ before_on_line(v5, v6, v7) | incident_point_and_line(v7, v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ before_on_line(v5, v6, v7) | incident_point_and_line(v6, v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ before_on_line(v5, v6, v7) | distinct_points(v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ before_on_line(v5, v6, v7) | equally_directed_lines(v5, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v5, v6) = v8) |  ~ distinct_points(v5, v6) |  ~ left_apart_point(v5, v7) | left_convergent_lines(v8, v7) | left_apart_point(v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (reverse_line(v7) = v8) |  ~ left_apart_point(v5, v6) |  ~ unequally_directed_lines(v6, v7) | distinct_lines(v6, v7) | left_apart_point(v5, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ between_on_line(v5, v6, v7, v8) | before_on_line(v5, v8, v7) | before_on_line(v5, v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ between_on_line(v5, v6, v7, v8) | before_on_line(v5, v8, v7) | before_on_line(v5, v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ between_on_line(v5, v6, v7, v8) | before_on_line(v5, v7, v8) | before_on_line(v5, v7, v6)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ between_on_line(v5, v6, v7, v8) | before_on_line(v5, v7, v6) | before_on_line(v5, v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ before_on_line(v5, v8, v7) |  ~ before_on_line(v5, v7, v6) | between_on_line(v5, v6, v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ before_on_line(v5, v7, v8) |  ~ before_on_line(v5, v6, v7) | between_on_line(v5, v6, v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (reverse_line(v7) = v6) |  ~ (reverse_line(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) |  ~ apart_point_and_line(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | equally_directed_lines(v7, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) |  ~ line(v5) |  ~ point(v6) | line(v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection_point(v5, v6) = v7) |  ~ line(v6) |  ~ line(v5) |  ~ unequally_directed_lines(v5, v6) | point(v7) |  ? [v8] : (reverse_line(v6) = v8 &  ~ unequally_directed_lines(v5, v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection_point(v5, v6) = v7) |  ~ apart_point_and_line(v7, v6) |  ~ unequally_directed_lines(v5, v6) |  ? [v8] : (reverse_line(v6) = v8 &  ~ unequally_directed_lines(v5, v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection_point(v5, v6) = v7) |  ~ apart_point_and_line(v7, v5) |  ~ unequally_directed_lines(v5, v6) |  ? [v8] : (reverse_line(v6) = v8 &  ~ unequally_directed_lines(v5, v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v6, v5) = v7) |  ~ distinct_points(v5, v6) |  ? [v8] :  ? [v9] : (line_connecting(v5, v6) = v8 & reverse_line(v7) = v9 & equally_directed_lines(v8, v9))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ~ point(v6) |  ~ point(v5) |  ~ distinct_points(v5, v6) | line(v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ~ distinct_points(v5, v6) |  ~ apart_point_and_line(v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ~ distinct_points(v5, v6) |  ~ apart_point_and_line(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (line_connecting(v5, v6) = v7) |  ~ distinct_points(v5, v6) |  ? [v8] :  ? [v9] : (line_connecting(v6, v5) = v8 & reverse_line(v8) = v9 & equally_directed_lines(v7, v9))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ left_convergent_lines(v5, v7) | right_convergent_lines(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ left_convergent_lines(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ right_convergent_lines(v5, v6) | left_convergent_lines(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ left_apart_point(v5, v7) | right_apart_point(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ left_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ right_apart_point(v5, v6) | left_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ unequally_directed_lines(v5, v7) |  ~ unequally_directed_lines(v5, v6) | left_convergent_lines(v5, v7) | left_convergent_lines(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ unequally_directed_lines(v5, v7) | unequally_directed_opposite_lines(v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) |  ~ unequally_directed_opposite_lines(v5, v6) | unequally_directed_lines(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ divides_points(v7, v5, v6) | left_apart_point(v6, v7) | left_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ divides_points(v7, v5, v6) | left_apart_point(v6, v7) | right_apart_point(v6, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ divides_points(v7, v5, v6) | left_apart_point(v5, v7) | right_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ divides_points(v7, v5, v6) | right_apart_point(v6, v7) | right_apart_point(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ left_apart_point(v6, v7) |  ~ right_apart_point(v5, v7) | divides_points(v7, v5, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ left_apart_point(v5, v7) |  ~ right_apart_point(v6, v7) | divides_points(v7, v5, v6)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ (reverse_line(v6) = v7) | unequally_directed_lines(v5, v7) | unequally_directed_lines(v5, v6)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ distinct_lines(v6, v7) | distinct_lines(v7, v5) | distinct_lines(v6, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ distinct_points(v6, v7) | distinct_points(v7, v5) | distinct_points(v6, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ left_convergent_lines(v6, v7) | left_convergent_lines(v6, v5) | unequally_directed_lines(v7, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ left_apart_point(v6, v7) | distinct_points(v6, v5) | left_apart_point(v5, v7)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ unequally_directed_lines(v6, v7) | unequally_directed_lines(v7, v5) | unequally_directed_lines(v6, v5)) &  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ line(v5) | line(v6)) &  ! [v5] :  ! [v6] : ( ~ (reverse_line(v5) = v6) |  ~ distinct_lines(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ convergent_lines(v5, v6) | unequally_directed_lines(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ convergent_lines(v5, v6) | unequally_directed_opposite_lines(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ apart_point_and_line(v5, v6) | left_apart_point(v5, v6) | right_apart_point(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ equally_directed_opposite_lines(v5, v6) |  ~ unequally_directed_opposite_lines(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ equally_directed_lines(v5, v6) |  ~ unequally_directed_lines(v5, v6)) &  ! [v5] :  ! [v6] :  ~ left_convergent_lines(v5, v6) &  ! [v5] :  ! [v6] : ( ~ left_apart_point(v5, v6) | apart_point_and_line(v5, v6)) &  ! [v5] :  ! [v6] :  ~ left_apart_point(v5, v6) &  ! [v5] :  ! [v6] : ( ~ right_apart_point(v5, v6) | apart_point_and_line(v5, v6)) &  ! [v5] :  ! [v6] : ( ~ unequally_directed_lines(v5, v6) |  ~ unequally_directed_opposite_lines(v5, v6) | convergent_lines(v5, v6)) &  ! [v5] :  ~ distinct_lines(v5, v5) &  ! [v5] :  ~ distinct_points(v5, v5) &  ? [v5] :  ? [v6] : (equally_directed_opposite_lines(v5, v6) | unequally_directed_opposite_lines(v5, v6)) &  ? [v5] :  ? [v6] : (equally_directed_lines(v5, v6) | unequally_directed_lines(v5, v6)) &  ? [v5] : equally_directed_lines(v5, v5))
% 4.70/1.71  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.70/1.71  | (1) incident_point_and_line(all_0_1_1, all_0_4_4) & distinct_points(all_0_2_2, all_0_1_1) & distinct_points(all_0_3_3, all_0_1_1) & before_on_line(all_0_4_4, all_0_2_2, all_0_1_1) & before_on_line(all_0_4_4, all_0_3_3, all_0_2_2) & left_apart_point(all_0_0_0, all_0_4_4) &  ~ before_on_line(all_0_4_4, all_0_3_3, 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] : ( ~ (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(v1, v2) = v3) |  ~ incident_point_and_line(v2, v0) |  ~ incident_point_and_line(v1, v0) |  ~ distinct_points(v1, v2) |  ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3)) &  ! [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) |  ~ left_apart_point(v0, v1) |  ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3)) &  ! [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) |  ~ apart_point_and_line(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ~ line(v0) |  ~ point(v1) | 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) |  ~ apart_point_and_line(v2, v1) |  ~ unequally_directed_lines(v0, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ apart_point_and_line(v2, v0) |  ~ unequally_directed_lines(v0, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ~ distinct_points(v0, v1) |  ? [v3] :  ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_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) |  ~ distinct_points(v0, v1) |  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2) | right_apart_point(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ right_apart_point(v0, v1) | left_apart_point(v0, v2)) &  ! [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_opposite_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) |  ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v0, v2) |  ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1)) &  ? [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] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ line(v0) | line(v1)) &  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ distinct_lines(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) |  ~ unequally_directed_opposite_lines(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ equally_directed_lines(v0, v1) |  ~ unequally_directed_lines(v0, v1)) &  ! [v0] :  ! [v1] :  ~ left_convergent_lines(v0, v1) &  ! [v0] :  ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1)) &  ! [v0] :  ! [v1] :  ~ left_apart_point(v0, v1) &  ! [v0] :  ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ unequally_directed_lines(v0, v1) |  ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1)) &  ! [v0] :  ~ distinct_lines(v0, v0) &  ! [v0] :  ~ distinct_points(v0, v0) &  ? [v0] :  ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1)) &  ? [v0] :  ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1)) &  ? [v0] : equally_directed_lines(v0, v0)
% 4.70/1.73  |
% 4.70/1.73  | Applying alpha-rule on (1) yields:
% 4.70/1.74  | (2)  ! [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))
% 4.70/1.74  | (3)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ distinct_lines(v0, v1))
% 4.70/1.74  | (4)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 4.70/1.74  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | right_apart_point(v1, v2))
% 4.70/1.74  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ apart_point_and_line(v2, v1) |  ~ unequally_directed_lines(v0, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3)))
% 4.70/1.74  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v1, v2))
% 4.70/1.74  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v1, v0) = v2) |  ~ distinct_points(v0, v1) |  ? [v3] :  ? [v4] : (line_connecting(v0, v1) = v3 & reverse_line(v2) = v4 & equally_directed_lines(v3, v4)))
% 4.70/1.74  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | incident_point_and_line(v2, v0))
% 4.70/1.74  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (reverse_line(v2) = v1) |  ~ (reverse_line(v2) = v0))
% 4.70/1.74  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ~ line(v0) |  ~ point(v1) | line(v2))
% 4.70/1.74  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 4.70/1.74  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (reverse_line(v2) = v3) |  ~ left_apart_point(v0, v1) |  ~ unequally_directed_lines(v1, v2) | distinct_lines(v1, v2) | left_apart_point(v0, v3))
% 4.70/1.74  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ? [v3] :  ? [v4] : (line_connecting(v1, v0) = v3 & reverse_line(v3) = v4 & equally_directed_lines(v2, v4)))
% 4.70/1.74  | (15)  ! [v0] :  ! [v1] : ( ~ apart_point_and_line(v0, v1) | left_apart_point(v0, v1) | right_apart_point(v0, v1))
% 4.70/1.74  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_opposite_lines(v0, v1) | unequally_directed_lines(v0, v2))
% 4.70/1.74  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ unequally_directed_lines(v0, v2) | unequally_directed_opposite_lines(v0, v1))
% 4.70/1.74  | (18)  ! [v0] :  ! [v1] : ( ~ equally_directed_opposite_lines(v0, v1) |  ~ unequally_directed_opposite_lines(v0, v1))
% 4.70/1.74  | (19)  ! [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))
% 4.70/1.74  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ right_convergent_lines(v0, v1) | left_convergent_lines(v0, v2))
% 4.70/1.74  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2) | right_convergent_lines(v0, v1))
% 4.70/1.74  | (22)  ? [v0] :  ? [v1] : (equally_directed_opposite_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.70/1.74  | (23)  ! [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))
% 4.70/1.74  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ point(v1) |  ~ point(v0) |  ~ distinct_points(v0, v1) | line(v2))
% 4.70/1.75  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) |  ~ right_apart_point(v0, v2) | divides_points(v2, v0, v1))
% 4.70/1.75  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v3, v2) |  ~ before_on_line(v0, v2, v1) | between_on_line(v0, v1, v2, v3))
% 4.70/1.75  | (27)  ! [v0] :  ~ distinct_lines(v0, v0)
% 4.70/1.75  | (28)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_convergent_lines(v1, v2) | left_convergent_lines(v1, v0) | unequally_directed_lines(v2, v0))
% 4.70/1.75  | (29)  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.70/1.75  | (30)  ! [v0] :  ! [v1] : ( ~ right_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.70/1.75  | (31)  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | unequally_directed_opposite_lines(v0, v1))
% 4.70/1.75  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ before_on_line(v0, v2, v3) |  ~ before_on_line(v0, v1, v2) | between_on_line(v0, v1, v2, v3))
% 4.70/1.75  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2))
% 4.70/1.75  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v1, v2))
% 4.70/1.75  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ apart_point_and_line(v2, v0) |  ~ unequally_directed_lines(v0, v1) |  ? [v3] : (reverse_line(v1) = v3 &  ~ unequally_directed_lines(v0, v3)))
% 4.70/1.75  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | equally_directed_lines(v0, v3))
% 4.70/1.75  | (37)  ! [v0] :  ! [v1] :  ~ left_convergent_lines(v0, v1)
% 4.70/1.75  | (38)  ! [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))
% 4.70/1.75  | (39)  ? [v0] :  ? [v1] : (equally_directed_lines(v0, v1) | unequally_directed_lines(v0, v1))
% 4.70/1.75  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v0, v2) |  ~ right_apart_point(v1, v2) | divides_points(v2, v0, v1))
% 4.70/1.75  | (41)  ! [v0] :  ! [v1] : ( ~ (reverse_line(v0) = v1) |  ~ line(v0) | line(v1))
% 4.70/1.75  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 4.70/1.75  | (43)  ! [v0] :  ! [v1] : ( ~ equally_directed_lines(v0, v1) |  ~ unequally_directed_lines(v0, v1))
% 4.70/1.75  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v1, v2) | left_apart_point(v0, v2))
% 4.70/1.75  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | right_apart_point(v1, v2) | right_apart_point(v0, v2))
% 4.70/1.75  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 4.70/1.75  | (47) before_on_line(all_0_4_4, all_0_2_2, all_0_1_1)
% 4.70/1.75  | (48)  ! [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))
% 4.70/1.75  | (49) incident_point_and_line(all_0_1_1, all_0_4_4)
% 4.70/1.75  | (50)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) | unequally_directed_lines(v0, v2) | unequally_directed_lines(v0, v1))
% 4.70/1.75  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ incident_point_and_line(v2, v0) |  ~ incident_point_and_line(v1, v0) |  ~ distinct_points(v1, v2) |  ~ equally_directed_lines(v0, v3) | before_on_line(v0, v1, v2))
% 4.70/1.75  | (52) distinct_points(all_0_3_3, all_0_1_1)
% 4.70/1.76  | (53)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ unequally_directed_lines(v1, v2) | unequally_directed_lines(v2, v0) | unequally_directed_lines(v1, v0))
% 4.70/1.76  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v3, v2) | before_on_line(v0, v2, v3))
% 4.70/1.76  | (55)  ! [v0] :  ~ distinct_points(v0, v0)
% 4.70/1.76  | (56)  ! [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))
% 4.70/1.76  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | incident_point_and_line(v1, v0))
% 4.70/1.76  | (58) distinct_points(all_0_2_2, all_0_1_1)
% 4.70/1.76  | (59)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ divides_points(v2, v0, v1) | left_apart_point(v0, v2) | right_apart_point(v0, v2))
% 4.70/1.76  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v1) | before_on_line(v0, v1, v2))
% 4.70/1.76  | (61)  ? [v0] : equally_directed_lines(v0, v0)
% 4.70/1.76  | (62) before_on_line(all_0_4_4, all_0_3_3, all_0_2_2)
% 4.70/1.76  | (63)  ! [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)))
% 4.70/1.76  | (64)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 4.70/1.76  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v1, v2) = v3) |  ~ before_on_line(v0, v1, v2) | distinct_points(v1, v2))
% 4.70/1.76  | (66)  ~ before_on_line(all_0_4_4, all_0_3_3, all_0_1_1)
% 4.70/1.76  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ right_apart_point(v0, v1) | left_apart_point(v0, v2))
% 4.70/1.76  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_apart_point(v0, v2) | right_apart_point(v0, v1))
% 4.70/1.76  | (69)  ! [v0] :  ! [v1] :  ~ left_apart_point(v0, v1)
% 4.70/1.76  | (70) left_apart_point(all_0_0_0, all_0_4_4)
% 4.70/1.76  | (71)  ! [v0] :  ! [v1] : ( ~ left_apart_point(v0, v1) | apart_point_and_line(v0, v1))
% 4.70/1.76  | (72)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ left_apart_point(v1, v2) | distinct_points(v1, v0) | left_apart_point(v0, v2))
% 4.70/1.76  | (73)  ! [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))
% 4.70/1.76  | (74)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (reverse_line(v1) = v2) |  ~ left_convergent_lines(v0, v2))
% 4.70/1.76  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ between_on_line(v0, v1, v2, v3) | before_on_line(v0, v2, v3) | before_on_line(v0, v2, v1))
% 4.70/1.76  | (76)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ apart_point_and_line(v0, v2))
% 4.70/1.76  | (77)  ! [v0] :  ! [v1] : ( ~ unequally_directed_lines(v0, v1) |  ~ unequally_directed_opposite_lines(v0, v1) | convergent_lines(v0, v1))
% 4.70/1.76  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ distinct_points(v0, v1) |  ~ apart_point_and_line(v0, v2))
% 4.70/1.76  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1))
% 4.70/1.77  |
% 4.70/1.77  | Instantiating formula (69) with all_0_4_4, all_0_0_0 and discharging atoms left_apart_point(all_0_0_0, all_0_4_4), yields:
% 4.70/1.77  | (80) $false
% 4.70/1.77  |
% 4.70/1.77  |-The branch is then unsatisfiable
% 4.70/1.77  % SZS output end Proof for theBenchmark
% 4.70/1.77  
% 4.70/1.77  1126ms
%------------------------------------------------------------------------------