TSTP Solution File: GEO216+2 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 03:48:50 EDT 2022

% Result   : Theorem 3.87s 1.56s
% Output   : Proof 5.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 03:24:01 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.72/0.94  Prover 0: Preprocessing ...
% 2.10/1.09  Prover 0: Warning: ignoring some quantifiers
% 2.10/1.11  Prover 0: Constructing countermodel ...
% 3.28/1.42  Prover 0: gave up
% 3.28/1.42  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.28/1.45  Prover 1: Preprocessing ...
% 3.74/1.53  Prover 1: Constructing countermodel ...
% 3.87/1.55  Prover 1: proved (131ms)
% 3.87/1.55  
% 3.87/1.56  No countermodel exists, formula is valid
% 3.87/1.56  % SZS status Theorem for theBenchmark
% 3.87/1.56  
% 3.87/1.56  Generating proof ... found it (size 8)
% 4.55/1.77  
% 4.55/1.77  % SZS output start Proof for theBenchmark
% 4.55/1.77  Assumed formulas after preprocessing and simplification: 
% 4.55/1.77  | (0)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & unorthogonal_lines(v0, v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 | v5 = 0 |  ~ (unorthogonal_lines(v2, v4) = v6) |  ~ (unorthogonal_lines(v2, v3) = v5) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v3, v4) = v7)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (intersection_point(v2, v3) = v5) |  ~ (distinct_points(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v4, v3) = v9 & apart_point_and_line(v4, v2) = v8 & convergent_lines(v2, v3) = v7 & ( ~ (v7 = 0) | ( ~ (v9 = 0) &  ~ (v8 = 0))))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (unorthogonal_lines(v2, v4) = v6) |  ~ (unorthogonal_lines(v2, v3) = v5) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (unorthogonal_lines(v3, v4) = v10 & convergent_lines(v3, v4) = v9 & convergent_lines(v2, v4) = v8 & convergent_lines(v2, v3) = v7 & ( ~ (v10 = 0) |  ~ (v9 = 0) | (v8 = 0 & v6 = 0) | (v7 = 0 & v5 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_lines(v2, v4) = v5) |  ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_points(v2, v4) = v5) |  ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (unorthogonal_lines(v5, v4) = v3) |  ~ (unorthogonal_lines(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] : (v3 = v2 |  ~ (apart_point_and_line(v5, v4) = v3) |  ~ (apart_point_and_line(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (convergent_lines(v5, v4) = v3) |  ~ (convergent_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_lines(v5, v4) = v3) |  ~ (distinct_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_points(v5, v4) = v3) |  ~ (distinct_points(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v2, v3) = v5) |  ~ (apart_point_and_line(v4, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (distinct_points(v4, v3) = v8 & distinct_points(v4, v2) = v7 & distinct_points(v2, v3) = v6 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) |  ~ (distinct_points(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v3, v5) = v9 & apart_point_and_line(v3, v4) = v8 & apart_point_and_line(v2, v5) = v7 & apart_point_and_line(v2, v4) = v6 & (v9 = 0 | v8 = 0 | v7 = 0 | v6 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (distinct_lines(v2, v3) = v4) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5)) &  ! [v2] :  ~ (convergent_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_points(v2, v2) = 0))
% 4.97/1.80  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 4.97/1.80  | (1)  ~ (all_0_0_0 = 0) & unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(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] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.97/1.81  |
% 4.97/1.81  | Applying alpha-rule on (1) yields:
% 4.97/1.81  | (2) unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0
% 4.97/1.81  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 4.97/1.82  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0)))))
% 4.97/1.82  | (5)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 4.97/1.82  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 4.97/1.82  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 4.97/1.82  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 4.97/1.82  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.97/1.82  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 4.97/1.82  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 4.97/1.82  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 4.97/1.82  | (13)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 4.97/1.82  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 4.97/1.82  | (15)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.97/1.82  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 4.97/1.82  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 4.97/1.82  | (18)  ~ (all_0_0_0 = 0)
% 4.97/1.82  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 4.97/1.82  | (20)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 4.97/1.82  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 4.97/1.82  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 5.14/1.82  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 5.14/1.82  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (unorthogonal_lines(v1, v2) = v8 & convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) |  ~ (v7 = 0) | (v6 = 0 & v4 = 0) | (v5 = 0 & v3 = 0))))
% 5.14/1.83  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 5.14/1.83  |
% 5.14/1.83  | Instantiating formula (20) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 5.14/1.83  | (26) all_0_0_0 = 0 | convergent_lines(all_0_1_1, all_0_1_1) = 0
% 5.14/1.83  |
% 5.14/1.83  +-Applying beta-rule and splitting (26), into two cases.
% 5.14/1.83  |-Branch one:
% 5.14/1.83  | (27) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 5.14/1.83  |
% 5.14/1.83  	| Instantiating formula (13) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 5.14/1.83  	| (28) $false
% 5.14/1.83  	|
% 5.14/1.83  	|-The branch is then unsatisfiable
% 5.14/1.83  |-Branch two:
% 5.14/1.83  | (29)  ~ (convergent_lines(all_0_1_1, all_0_1_1) = 0)
% 5.14/1.83  | (30) all_0_0_0 = 0
% 5.14/1.83  |
% 5.14/1.83  	| Equations (30) can reduce 18 to:
% 5.14/1.83  	| (31) $false
% 5.14/1.83  	|
% 5.14/1.83  	|-The branch is then unsatisfiable
% 5.14/1.83  % SZS output end Proof for theBenchmark
% 5.14/1.83  
% 5.14/1.83  1244ms
%------------------------------------------------------------------------------