TSTP Solution File: GEO255+3 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : GEO255+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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  : 300s
% DateTime : Wed Jul 27 12:55:04 EDT 2022

% Result   : Theorem 6.97s 7.16s
% Output   : Refutation 6.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   28 (  15 unt;   8 nHn;  19 RR)
%            Number of literals    :   45 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   32 (   4 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    ( ~ e_qually_directed_lines(A,B)
    | ~ une_qually_directed_lines(A,B) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ before_on_line(A,B,C)
    | distinct_points(B,C) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ before_on_line(A,B,C)
    | e_qually_directed_lines(A,line_connecting(B,C)) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(36,axiom,
    ( ~ une_qually_directed_lines(A,B)
    | une_qually_directed_lines(A,C)
    | une_qually_directed_lines(B,C) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ une_qually_directed_lines(A,B)
    | ~ une_qually_directed_lines(A,reverse_line(B))
    | left_convergent_lines(A,B)
    | left_convergent_lines(A,reverse_line(B)) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(41,axiom,
    ~ left_convergent_lines(A,B),
    file('GEO255+3.p',unknown),
    [] ).

cnf(52,axiom,
    ( ~ distinct_points(A,B)
    | e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(61,plain,
    ( ~ une_qually_directed_lines(A,A)
    | une_qually_directed_lines(A,B) ),
    inference(factor,[status(thm)],[36]),
    [iquote('factor,36.2.3')] ).

cnf(63,axiom,
    ( e_qually_directed_lines(A,B)
    | une_qually_directed_lines(A,B) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(66,axiom,
    ( une_qually_directed_lines(A,B)
    | une_qually_directed_lines(A,reverse_line(B)) ),
    file('GEO255+3.p',unknown),
    [] ).

cnf(68,axiom,
    before_on_line(dollar_c3,dollar_c2,dollar_c1),
    file('GEO255+3.p',unknown),
    [] ).

cnf(69,axiom,
    before_on_line(dollar_c3,dollar_c1,dollar_c2),
    file('GEO255+3.p',unknown),
    [] ).

cnf(71,plain,
    ( e_qually_directed_lines(A,B)
    | une_qually_directed_lines(A,C)
    | une_qually_directed_lines(B,C) ),
    inference(hyper,[status(thm)],[63,36]),
    [iquote('hyper,63,36')] ).

cnf(73,plain,
    e_qually_directed_lines(dollar_c3,line_connecting(dollar_c2,dollar_c1)),
    inference(hyper,[status(thm)],[68,24]),
    [iquote('hyper,68,24')] ).

cnf(76,plain,
    distinct_points(dollar_c2,dollar_c1),
    inference(hyper,[status(thm)],[68,21]),
    [iquote('hyper,68,21')] ).

cnf(79,plain,
    e_qually_directed_lines(line_connecting(dollar_c2,dollar_c1),reverse_line(line_connecting(dollar_c1,dollar_c2))),
    inference(hyper,[status(thm)],[76,52]),
    [iquote('hyper,76,52')] ).

cnf(83,plain,
    e_qually_directed_lines(dollar_c3,line_connecting(dollar_c1,dollar_c2)),
    inference(hyper,[status(thm)],[69,24]),
    [iquote('hyper,69,24')] ).

cnf(86,plain,
    une_qually_directed_lines(A,reverse_line(A)),
    inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[66,61])]),
    [iquote('hyper,66,61,factor_simp')] ).

cnf(100,plain,
    ( une_qually_directed_lines(A,B)
    | une_qually_directed_lines(reverse_line(A),B) ),
    inference(hyper,[status(thm)],[86,36]),
    [iquote('hyper,86,36')] ).

cnf(108,plain,
    une_qually_directed_lines(dollar_c3,reverse_line(line_connecting(dollar_c1,dollar_c2))),
    inference(hyper,[status(thm)],[83,7,66]),
    [iquote('hyper,83,7,66')] ).

cnf(117,plain,
    ( e_qually_directed_lines(A,B)
    | une_qually_directed_lines(B,A) ),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[71,39,86]),41,41]),
    [iquote('hyper,71,39,86,unit_del,41,41')] ).

cnf(133,plain,
    ( e_qually_directed_lines(A,dollar_c3)
    | une_qually_directed_lines(A,line_connecting(dollar_c2,dollar_c1)) ),
    inference(hyper,[status(thm)],[71,7,73]),
    [iquote('hyper,71,7,73')] ).

cnf(215,plain,
    e_qually_directed_lines(line_connecting(dollar_c1,dollar_c2),dollar_c3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[117,39,108]),41,41]),
    [iquote('hyper,117,39,108,unit_del,41,41')] ).

cnf(223,plain,
    e_qually_directed_lines(reverse_line(line_connecting(dollar_c1,dollar_c2)),line_connecting(dollar_c2,dollar_c1)),
    inference(hyper,[status(thm)],[117,7,79]),
    [iquote('hyper,117,7,79')] ).

cnf(227,plain,
    une_qually_directed_lines(line_connecting(dollar_c1,dollar_c2),reverse_line(dollar_c3)),
    inference(hyper,[status(thm)],[215,7,66]),
    [iquote('hyper,215,7,66')] ).

cnf(401,plain,
    une_qually_directed_lines(reverse_line(line_connecting(dollar_c1,dollar_c2)),dollar_c3),
    inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[100,39,227]),41,41]),
    [iquote('hyper,100,39,227,unit_del,41,41')] ).

cnf(3542,plain,
    e_qually_directed_lines(reverse_line(line_connecting(dollar_c1,dollar_c2)),dollar_c3),
    inference(hyper,[status(thm)],[223,7,133]),
    [iquote('hyper,223,7,133')] ).

cnf(3574,plain,
    $false,
    inference(hyper,[status(thm)],[3542,7,401]),
    [iquote('hyper,3542,7,401')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO255+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 07:44:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 2.00/2.19  ----- Otter 3.3f, August 2004 -----
% 2.00/2.19  The process was started by sandbox on n023.cluster.edu,
% 2.00/2.19  Wed Jul 27 07:44:48 2022
% 2.00/2.19  The command was "./otter".  The process ID is 10823.
% 2.00/2.19  
% 2.00/2.19  set(prolog_style_variables).
% 2.00/2.19  set(auto).
% 2.00/2.19     dependent: set(auto1).
% 2.00/2.19     dependent: set(process_input).
% 2.00/2.19     dependent: clear(print_kept).
% 2.00/2.19     dependent: clear(print_new_demod).
% 2.00/2.19     dependent: clear(print_back_demod).
% 2.00/2.19     dependent: clear(print_back_sub).
% 2.00/2.19     dependent: set(control_memory).
% 2.00/2.19     dependent: assign(max_mem, 12000).
% 2.00/2.19     dependent: assign(pick_given_ratio, 4).
% 2.00/2.19     dependent: assign(stats_level, 1).
% 2.00/2.19     dependent: assign(max_seconds, 10800).
% 2.00/2.19  clear(print_given).
% 2.00/2.19  
% 2.00/2.19  formula_list(usable).
% 2.00/2.19  all X Y (une_qually_directed_opposite_lines(X,Y)<->une_qually_directed_lines(X,reverse_line(Y))).
% 2.00/2.19  all X Y (right_apart_point(X,Y)<->left_apart_point(X,reverse_line(Y))).
% 2.00/2.19  all X Y (right_convergent_lines(X,Y)<->left_convergent_lines(X,reverse_line(Y))).
% 2.00/2.19  all X Y (e_qually_directed_lines(X,Y)<-> -une_qually_directed_lines(X,Y)).
% 2.00/2.19  all X Y (e_qually_directed_opposite_lines(X,Y)<-> -une_qually_directed_opposite_lines(X,Y)).
% 2.00/2.19  all A L (apart_point_and_line(A,L)<->left_apart_point(A,L)|right_apart_point(A,L)).
% 2.00/2.19  all L M (convergent_lines(L,M)<->une_qually_directed_lines(L,M)&une_qually_directed_opposite_lines(L,M)).
% 2.00/2.19  all A B L (divides_points(L,A,B)<->left_apart_point(A,L)&right_apart_point(B,L)|right_apart_point(A,L)&left_apart_point(B,L)).
% 2.00/2.19  all L A B (before_on_line(L,A,B)<->distinct_points(A,B)&incident_point_and_line(A,L)&incident_point_and_line(B,L)&e_qually_directed_lines(L,line_connecting(A,B))).
% 2.00/2.19  all L A B C (between_on_line(L,A,B,C)<->before_on_line(L,A,B)&before_on_line(L,B,C)|before_on_line(L,C,B)&before_on_line(L,B,A)).
% 2.00/2.19  all A (-distinct_points(A,A)).
% 2.00/2.19  all A B C (distinct_points(A,B)->distinct_points(A,C)|distinct_points(B,C)).
% 2.00/2.19  all L (-distinct_lines(L,L)).
% 2.00/2.19  all L M N (distinct_lines(L,M)->distinct_lines(L,N)|distinct_lines(M,N)).
% 2.00/2.19  all L e_qually_directed_lines(L,L).
% 2.00/2.19  all L M N (une_qually_directed_lines(L,M)->une_qually_directed_lines(L,N)|une_qually_directed_lines(M,N)).
% 2.00/2.19  all L M N (une_qually_directed_lines(L,M)&une_qually_directed_lines(L,reverse_line(M))->une_qually_directed_lines(L,N)&une_qually_directed_lines(L,reverse_line(N))|une_qually_directed_lines(M,N)&une_qually_directed_lines(M,reverse_line(N))).
% 2.00/2.19  all L M (une_qually_directed_lines(L,M)|une_qually_directed_lines(L,reverse_line(M))).
% 2.00/2.19  all L M (une_qually_directed_lines(L,M)&une_qually_directed_lines(L,reverse_line(M))->left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M))).
% 2.00/2.19  all A L (-(left_apart_point(A,L)|left_apart_point(A,reverse_line(L)))).
% 2.00/2.19  all L M (-(left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M)))).
% 2.00/2.19  all A B (point(A)&point(B)&distinct_points(A,B)->line(line_connecting(A,B))).
% 2.00/2.19  all L M (line(L)&line(M)&une_qually_directed_lines(L,M)&une_qually_directed_lines(L,reverse_line(M))->point(intersection_point(L,M))).
% 2.00/2.19  all L A (point(A)&line(L)->line(parallel_through_point(L,A))).
% 2.00/2.19  all L (line(L)->line(reverse_line(L))).
% 2.00/2.19  all A B (distinct_points(A,B)-> -apart_point_and_line(A,line_connecting(A,B))& -apart_point_and_line(B,line_connecting(A,B))).
% 2.00/2.19  all L M (une_qually_directed_lines(L,M)&une_qually_directed_lines(L,reverse_line(M))-> -apart_point_and_line(intersection_point(L,M),L)& -apart_point_and_line(intersection_point(L,M),M)).
% 2.00/2.19  all A L (-apart_point_and_line(A,parallel_through_point(L,A))).
% 2.00/2.19  all L (-distinct_lines(L,reverse_line(L))).
% 2.00/2.19  all A B (distinct_points(A,B)->e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))).
% 2.00/2.19  all A L e_qually_directed_lines(parallel_through_point(L,A),L).
% 2.00/2.19  all A B L M (distinct_points(A,B)&distinct_lines(L,M)->left_apart_point(A,L)|left_apart_point(B,L)|left_apart_point(A,M)|left_apart_point(B,M)|left_apart_point(A,reverse_line(L))|left_apart_point(B,reverse_line(L))|left_apart_point(A,reverse_line(M))|left_apart_point(B,reverse_line(M))).
% 2.00/2.19  all A B L (distinct_points(A,B)&left_apart_point(A,L)->left_apart_point(B,L)|left_convergent_lines(line_connecting(A,B),L)).
% 2.00/2.19  all A B L (left_apart_point(A,L)->distinct_points(A,B)|left_apart_point(B,L)).
% 2.00/2.19  all A L M (left_apart_point(A,L)&une_qually_directed_lines(L,M)->distinct_lines(L,M)|left_apart_point(A,reverse_line(M))).
% 2.00/2.19  all L M N (left_convergent_lines(L,M)->une_qually_directed_lines(M,N)|left_convergent_lines(L,N)).
% 2.00/2.19  -(all L A B (-(before_on_line(L,A,B)&before_on_line(L,B,A)))).
% 2.00/2.19  end_of_list.
% 2.00/2.19  
% 2.00/2.19  -------> usable clausifies to:
% 2.00/2.19  
% 2.00/2.19  list(usable).
% 2.00/2.19  0 [] -une_qually_directed_opposite_lines(X,Y)|une_qually_directed_lines(X,reverse_line(Y)).
% 2.00/2.19  0 [] une_qually_directed_opposite_lines(X,Y)| -une_qually_directed_lines(X,reverse_line(Y)).
% 2.00/2.19  0 [] -right_apart_point(X,Y)|left_apart_point(X,reverse_line(Y)).
% 2.00/2.19  0 [] right_apart_point(X,Y)| -left_apart_point(X,reverse_line(Y)).
% 2.00/2.19  0 [] -right_convergent_lines(X,Y)|left_convergent_lines(X,reverse_line(Y)).
% 2.00/2.19  0 [] right_convergent_lines(X,Y)| -left_convergent_lines(X,reverse_line(Y)).
% 2.00/2.19  0 [] -e_qually_directed_lines(X,Y)| -une_qually_directed_lines(X,Y).
% 2.00/2.19  0 [] e_qually_directed_lines(X,Y)|une_qually_directed_lines(X,Y).
% 2.00/2.19  0 [] -e_qually_directed_opposite_lines(X,Y)| -une_qually_directed_opposite_lines(X,Y).
% 2.00/2.19  0 [] e_qually_directed_opposite_lines(X,Y)|une_qually_directed_opposite_lines(X,Y).
% 2.00/2.19  0 [] -apart_point_and_line(A,L)|left_apart_point(A,L)|right_apart_point(A,L).
% 2.00/2.19  0 [] apart_point_and_line(A,L)| -left_apart_point(A,L).
% 2.00/2.19  0 [] apart_point_and_line(A,L)| -right_apart_point(A,L).
% 2.00/2.19  0 [] -convergent_lines(L,M)|une_qually_directed_lines(L,M).
% 2.00/2.19  0 [] -convergent_lines(L,M)|une_qually_directed_opposite_lines(L,M).
% 2.00/2.19  0 [] convergent_lines(L,M)| -une_qually_directed_lines(L,M)| -une_qually_directed_opposite_lines(L,M).
% 2.00/2.19  0 [] -divides_points(L,A,B)|left_apart_point(A,L)|right_apart_point(A,L).
% 2.00/2.19  0 [] -divides_points(L,A,B)|left_apart_point(A,L)|left_apart_point(B,L).
% 2.00/2.19  0 [] -divides_points(L,A,B)|right_apart_point(B,L)|right_apart_point(A,L).
% 2.00/2.19  0 [] -divides_points(L,A,B)|right_apart_point(B,L)|left_apart_point(B,L).
% 2.00/2.19  0 [] divides_points(L,A,B)| -left_apart_point(A,L)| -right_apart_point(B,L).
% 2.00/2.19  0 [] divides_points(L,A,B)| -right_apart_point(A,L)| -left_apart_point(B,L).
% 2.00/2.19  0 [] -before_on_line(L,A,B)|distinct_points(A,B).
% 2.00/2.19  0 [] -before_on_line(L,A,B)|incident_point_and_line(A,L).
% 2.00/2.19  0 [] -before_on_line(L,A,B)|incident_point_and_line(B,L).
% 2.00/2.19  0 [] -before_on_line(L,A,B)|e_qually_directed_lines(L,line_connecting(A,B)).
% 2.00/2.19  0 [] before_on_line(L,A,B)| -distinct_points(A,B)| -incident_point_and_line(A,L)| -incident_point_and_line(B,L)| -e_qually_directed_lines(L,line_connecting(A,B)).
% 2.00/2.19  0 [] -between_on_line(L,A,B,C)|before_on_line(L,A,B)|before_on_line(L,C,B).
% 2.00/2.19  0 [] -between_on_line(L,A,B,C)|before_on_line(L,A,B)|before_on_line(L,B,A).
% 2.00/2.19  0 [] -between_on_line(L,A,B,C)|before_on_line(L,B,C)|before_on_line(L,C,B).
% 2.00/2.19  0 [] -between_on_line(L,A,B,C)|before_on_line(L,B,C)|before_on_line(L,B,A).
% 2.00/2.19  0 [] between_on_line(L,A,B,C)| -before_on_line(L,A,B)| -before_on_line(L,B,C).
% 2.00/2.19  0 [] between_on_line(L,A,B,C)| -before_on_line(L,C,B)| -before_on_line(L,B,A).
% 2.00/2.19  0 [] -distinct_points(A,A).
% 2.00/2.19  0 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 2.00/2.19  0 [] -distinct_lines(L,L).
% 2.00/2.19  0 [] -distinct_lines(L,M)|distinct_lines(L,N)|distinct_lines(M,N).
% 2.00/2.19  0 [] e_qually_directed_lines(L,L).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)|une_qually_directed_lines(L,N)|une_qually_directed_lines(M,N).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|une_qually_directed_lines(L,N)|une_qually_directed_lines(M,N).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|une_qually_directed_lines(L,N)|une_qually_directed_lines(M,reverse_line(N)).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|une_qually_directed_lines(L,reverse_line(N))|une_qually_directed_lines(M,N).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|une_qually_directed_lines(L,reverse_line(N))|une_qually_directed_lines(M,reverse_line(N)).
% 2.00/2.19  0 [] une_qually_directed_lines(L,M)|une_qually_directed_lines(L,reverse_line(M)).
% 2.00/2.19  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M)).
% 2.00/2.19  0 [] -left_apart_point(A,L).
% 2.00/2.19  0 [] -left_apart_point(A,reverse_line(L)).
% 2.00/2.20  0 [] -left_convergent_lines(L,M).
% 2.00/2.20  0 [] -left_convergent_lines(L,reverse_line(M)).
% 2.00/2.20  0 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 2.00/2.20  0 [] -line(L)| -line(M)| -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|point(intersection_point(L,M)).
% 2.00/2.20  0 [] -point(A)| -line(L)|line(parallel_through_point(L,A)).
% 2.00/2.20  0 [] -line(L)|line(reverse_line(L)).
% 2.00/2.20  0 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 2.00/2.20  0 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 2.00/2.20  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))| -apart_point_and_line(intersection_point(L,M),L).
% 2.00/2.20  0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))| -apart_point_and_line(intersection_point(L,M),M).
% 2.00/2.20  0 [] -apart_point_and_line(A,parallel_through_point(L,A)).
% 2.00/2.20  0 [] -distinct_lines(L,reverse_line(L)).
% 2.00/2.20  0 [] -distinct_points(A,B)|e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))).
% 2.00/2.20  0 [] e_qually_directed_lines(parallel_through_point(L,A),L).
% 2.00/2.20  0 [] -distinct_points(A,B)| -distinct_lines(L,M)|left_apart_point(A,L)|left_apart_point(B,L)|left_apart_point(A,M)|left_apart_point(B,M)|left_apart_point(A,reverse_line(L))|left_apart_point(B,reverse_line(L))|left_apart_point(A,reverse_line(M))|left_apart_point(B,reverse_line(M)).
% 2.00/2.20  0 [] -distinct_points(A,B)| -left_apart_point(A,L)|left_apart_point(B,L)|left_convergent_lines(line_connecting(A,B),L).
% 2.00/2.20  0 [] -left_apart_point(A,L)|distinct_points(A,B)|left_apart_point(B,L).
% 2.00/2.20  0 [] -left_apart_point(A,L)| -une_qually_directed_lines(L,M)|distinct_lines(L,M)|left_apart_point(A,reverse_line(M)).
% 2.00/2.20  0 [] -left_convergent_lines(L,M)|une_qually_directed_lines(M,N)|left_convergent_lines(L,N).
% 2.00/2.20  0 [] before_on_line($c3,$c2,$c1).
% 2.00/2.20  0 [] before_on_line($c3,$c1,$c2).
% 2.00/2.20  end_of_list.
% 2.00/2.20  
% 2.00/2.20  SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=10.
% 2.00/2.20  
% 2.00/2.20  This is a non-Horn set without equality.  The strategy will
% 2.00/2.20  be ordered hyper_res, unit deletion, and factoring, with
% 2.00/2.20  satellites in sos and with nuclei in usable.
% 2.00/2.20  
% 2.00/2.20     dependent: set(hyper_res).
% 2.00/2.20     dependent: set(factor).
% 2.00/2.20     dependent: set(unit_deletion).
% 2.00/2.20  
% 2.00/2.20  ------------> process usable:
% 2.00/2.20  ** KEPT (pick-wt=7): 1 [] -une_qually_directed_opposite_lines(A,B)|une_qually_directed_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=7): 2 [] une_qually_directed_opposite_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=7): 3 [] -right_apart_point(A,B)|left_apart_point(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=7): 4 [] right_apart_point(A,B)| -left_apart_point(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=7): 5 [] -right_convergent_lines(A,B)|left_convergent_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=7): 6 [] right_convergent_lines(A,B)| -left_convergent_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=6): 7 [] -e_qually_directed_lines(A,B)| -une_qually_directed_lines(A,B).
% 2.00/2.20  ** KEPT (pick-wt=6): 8 [] -e_qually_directed_opposite_lines(A,B)| -une_qually_directed_opposite_lines(A,B).
% 2.00/2.20  ** KEPT (pick-wt=9): 9 [] -apart_point_and_line(A,B)|left_apart_point(A,B)|right_apart_point(A,B).
% 2.00/2.20  ** KEPT (pick-wt=6): 10 [] apart_point_and_line(A,B)| -left_apart_point(A,B).
% 2.00/2.20  ** KEPT (pick-wt=6): 11 [] apart_point_and_line(A,B)| -right_apart_point(A,B).
% 2.00/2.20  ** KEPT (pick-wt=6): 12 [] -convergent_lines(A,B)|une_qually_directed_lines(A,B).
% 2.00/2.20  ** KEPT (pick-wt=6): 13 [] -convergent_lines(A,B)|une_qually_directed_opposite_lines(A,B).
% 2.00/2.20  ** KEPT (pick-wt=9): 14 [] convergent_lines(A,B)| -une_qually_directed_lines(A,B)| -une_qually_directed_opposite_lines(A,B).
% 2.00/2.20  ** KEPT (pick-wt=10): 15 [] -divides_points(A,B,C)|left_apart_point(B,A)|right_apart_point(B,A).
% 2.00/2.20  ** KEPT (pick-wt=10): 16 [] -divides_points(A,B,C)|left_apart_point(B,A)|left_apart_point(C,A).
% 2.00/2.20  ** KEPT (pick-wt=10): 17 [] -divides_points(A,B,C)|right_apart_point(C,A)|right_apart_point(B,A).
% 2.00/2.20  ** KEPT (pick-wt=10): 18 [] -divides_points(A,B,C)|right_apart_point(C,A)|left_apart_point(C,A).
% 2.00/2.20  ** KEPT (pick-wt=10): 19 [] divides_points(A,B,C)| -left_apart_point(B,A)| -right_apart_point(C,A).
% 2.00/2.20  ** KEPT (pick-wt=10): 20 [] divides_points(A,B,C)| -right_apart_point(B,A)| -left_apart_point(C,A).
% 2.00/2.20  ** KEPT (pick-wt=7): 21 [] -before_on_line(A,B,C)|distinct_points(B,C).
% 2.00/2.20  ** KEPT (pick-wt=7): 22 [] -before_on_line(A,B,C)|incident_point_and_line(B,A).
% 2.00/2.20  ** KEPT (pick-wt=7): 23 [] -before_on_line(A,B,C)|incident_point_and_line(C,A).
% 2.00/2.20  ** KEPT (pick-wt=9): 24 [] -before_on_line(A,B,C)|e_qually_directed_lines(A,line_connecting(B,C)).
% 2.00/2.20  ** KEPT (pick-wt=18): 25 [] before_on_line(A,B,C)| -distinct_points(B,C)| -incident_point_and_line(B,A)| -incident_point_and_line(C,A)| -e_qually_directed_lines(A,line_connecting(B,C)).
% 2.00/2.20  ** KEPT (pick-wt=13): 26 [] -between_on_line(A,B,C,D)|before_on_line(A,B,C)|before_on_line(A,D,C).
% 2.00/2.20  ** KEPT (pick-wt=13): 27 [] -between_on_line(A,B,C,D)|before_on_line(A,B,C)|before_on_line(A,C,B).
% 2.00/2.20  ** KEPT (pick-wt=13): 28 [] -between_on_line(A,B,C,D)|before_on_line(A,C,D)|before_on_line(A,D,C).
% 2.00/2.20  ** KEPT (pick-wt=13): 29 [] -between_on_line(A,B,C,D)|before_on_line(A,C,D)|before_on_line(A,C,B).
% 2.00/2.20  ** KEPT (pick-wt=13): 30 [] between_on_line(A,B,C,D)| -before_on_line(A,B,C)| -before_on_line(A,C,D).
% 2.00/2.20  ** KEPT (pick-wt=13): 31 [] between_on_line(A,B,C,D)| -before_on_line(A,D,C)| -before_on_line(A,C,B).
% 2.00/2.20  ** KEPT (pick-wt=3): 32 [] -distinct_points(A,A).
% 2.00/2.20  ** KEPT (pick-wt=9): 33 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 2.00/2.20  ** KEPT (pick-wt=3): 34 [] -distinct_lines(A,A).
% 2.00/2.20  ** KEPT (pick-wt=9): 35 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 2.00/2.20  ** KEPT (pick-wt=9): 36 [] -une_qually_directed_lines(A,B)|une_qually_directed_lines(A,C)|une_qually_directed_lines(B,C).
% 2.00/2.20    Following clause subsumed by 36 during input processing: 0 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|une_qually_directed_lines(A,C)|une_qually_directed_lines(B,C).
% 2.00/2.20  ** KEPT (pick-wt=14): 37 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|une_qually_directed_lines(A,C)|une_qually_directed_lines(B,reverse_line(C)).
% 2.00/2.20  ** KEPT (pick-wt=14): 38 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|une_qually_directed_lines(A,reverse_line(C))|une_qually_directed_lines(B,C).
% 2.00/2.20    Following clause subsumed by 36 during input processing: 0 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|une_qually_directed_lines(A,reverse_line(C))|une_qually_directed_lines(B,reverse_line(C)).
% 2.00/2.20  ** KEPT (pick-wt=14): 39 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|left_convergent_lines(A,B)|left_convergent_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=3): 40 [] -left_apart_point(A,B).
% 2.00/2.20    Following clause subsumed by 40 during input processing: 0 [] -left_apart_point(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=3): 41 [] -left_convergent_lines(A,B).
% 2.00/2.20    Following clause subsumed by 41 during input processing: 0 [] -left_convergent_lines(A,reverse_line(B)).
% 2.00/2.20  ** KEPT (pick-wt=11): 42 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 2.00/2.20  ** KEPT (pick-wt=15): 43 [] -line(A)| -line(B)| -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))|point(intersection_point(A,B)).
% 2.00/2.20  ** KEPT (pick-wt=8): 44 [] -point(A)| -line(B)|line(parallel_through_point(B,A)).
% 2.00/2.20  ** KEPT (pick-wt=5): 45 [] -line(A)|line(reverse_line(A)).
% 2.00/2.20  ** KEPT (pick-wt=8): 46 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 2.00/2.20  ** KEPT (pick-wt=8): 47 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 2.00/2.20  ** KEPT (pick-wt=12): 48 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))| -apart_point_and_line(intersection_point(A,B),A).
% 2.00/2.20  ** KEPT (pick-wt=12): 49 [] -une_qually_directed_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B))| -apart_point_and_line(intersection_point(A,B),B).
% 2.00/2.20  ** KEPT (pick-wt=5): 50 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 2.00/2.20  ** KEPT (pick-wt=4): 51 [] -distinct_lines(A,reverse_line(A)).
% 2.00/2.20  ** KEPT (pick-wt=11): 52 [] -distinct_points(A,B)|e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))).
% 2.00/2.20  ** KEPT (pick-wt=6): 54 [copy,53,unit_del,40,40,40,40,40,40,40,40] -distinct_points(A,B)| -distinct_lines(C,D).
% 6.97/7.16    Following clause subsumed by 40 during input processing: 0 [unit_del,40,41] -distinct_points(A,B)| -left_apart_point(A,C).
% 6.97/7.16    Following clause subsumed by 40 during input processing: 0 [unit_del,40] -left_apart_point(A,B)|distinct_points(A,C).
% 6.97/7.16    Following clause subsumed by 40 during input processing: 0 [unit_del,40] -left_apart_point(A,B)| -une_qually_directed_lines(B,C)|distinct_lines(B,C).
% 6.97/7.16    Following clause subsumed by 41 during input processing: 0 [unit_del,41] -left_convergent_lines(A,B)|une_qually_directed_lines(B,C).
% 6.97/7.16  40 back subsumes 20.
% 6.97/7.16  40 back subsumes 19.
% 6.97/7.16  40 back subsumes 10.
% 6.97/7.16  40 back subsumes 4.
% 6.97/7.16  41 back subsumes 6.
% 6.97/7.16  
% 6.97/7.16  ------------> process sos:
% 6.97/7.16  ** KEPT (pick-wt=6): 63 [] e_qually_directed_lines(A,B)|une_qually_directed_lines(A,B).
% 6.97/7.16  ** KEPT (pick-wt=6): 64 [] e_qually_directed_opposite_lines(A,B)|une_qually_directed_opposite_lines(A,B).
% 6.97/7.16  ** KEPT (pick-wt=3): 65 [] e_qually_directed_lines(A,A).
% 6.97/7.16  ** KEPT (pick-wt=7): 66 [] une_qually_directed_lines(A,B)|une_qually_directed_lines(A,reverse_line(B)).
% 6.97/7.16  ** KEPT (pick-wt=5): 67 [] e_qually_directed_lines(parallel_through_point(A,B),A).
% 6.97/7.16  ** KEPT (pick-wt=4): 68 [] before_on_line($c3,$c2,$c1).
% 6.97/7.16  ** KEPT (pick-wt=4): 69 [] before_on_line($c3,$c1,$c2).
% 6.97/7.16  
% 6.97/7.16  ======= end of input processing =======
% 6.97/7.16  
% 6.97/7.16  =========== start of search ===========
% 6.97/7.16  
% 6.97/7.16  -------- PROOF -------- 
% 6.97/7.16  
% 6.97/7.16  -----> EMPTY CLAUSE at   4.97 sec ----> 3574 [hyper,3542,7,401] $F.
% 6.97/7.16  
% 6.97/7.16  Length of proof is 16.  Level of proof is 6.
% 6.97/7.16  
% 6.97/7.16  ---------------- PROOF ----------------
% 6.97/7.16  % SZS status Theorem
% 6.97/7.16  % SZS output start Refutation
% See solution above
% 6.97/7.16  ------------ end of proof -------------
% 6.97/7.16  
% 6.97/7.16  
% 6.97/7.16  Search stopped by max_proofs option.
% 6.97/7.16  
% 6.97/7.16  
% 6.97/7.16  Search stopped by max_proofs option.
% 6.97/7.16  
% 6.97/7.16  ============ end of search ============
% 6.97/7.16  
% 6.97/7.16  -------------- statistics -------------
% 6.97/7.16  clauses given                190
% 6.97/7.16  clauses generated          27148
% 6.97/7.16  clauses kept                3572
% 6.97/7.16  clauses forward subsumed   23643
% 6.97/7.16  clauses back subsumed        169
% 6.97/7.16  Kbytes malloced             3906
% 6.97/7.16  
% 6.97/7.16  ----------- times (seconds) -----------
% 6.97/7.16  user CPU time          4.97          (0 hr, 0 min, 4 sec)
% 6.97/7.16  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 6.97/7.16  wall-clock time        7             (0 hr, 0 min, 7 sec)
% 6.97/7.16  
% 6.97/7.16  That finishes the proof of the theorem.
% 6.97/7.16  
% 6.97/7.16  Process 10823 finished Wed Jul 27 07:44:55 2022
% 6.97/7.16  Otter interrupted
% 6.97/7.16  PROOF FOUND
%------------------------------------------------------------------------------