TSTP Solution File: GEO265+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 12:55:07 EDT 2022
% Result : Theorem 1.80s 1.97s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 15 ( 8 unt; 3 nHn; 13 RR)
% Number of literals : 25 ( 0 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ une_qually_directed_opposite_lines(A,B)
| une_qually_directed_lines(A,reverse_line(B)) ),
file('GEO265+3.p',unknown),
[] ).
cnf(7,axiom,
( ~ e_qually_directed_lines(A,B)
| ~ une_qually_directed_lines(A,B) ),
file('GEO265+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ convergent_lines(A,B)
| une_qually_directed_opposite_lines(A,B) ),
file('GEO265+3.p',unknown),
[] ).
cnf(14,axiom,
( convergent_lines(A,B)
| ~ une_qually_directed_lines(A,B)
| ~ une_qually_directed_opposite_lines(A,B) ),
file('GEO265+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('GEO265+3.p',unknown),
[] ).
cnf(41,axiom,
~ left_convergent_lines(A,B),
file('GEO265+3.p',unknown),
[] ).
cnf(55,axiom,
~ e_qually_directed_opposite_lines(dollar_c2,dollar_c1),
file('GEO265+3.p',unknown),
[] ).
cnf(65,axiom,
( e_qually_directed_opposite_lines(A,B)
| une_qually_directed_opposite_lines(A,B) ),
file('GEO265+3.p',unknown),
[] ).
cnf(67,axiom,
( une_qually_directed_lines(A,B)
| une_qually_directed_lines(A,reverse_line(B)) ),
file('GEO265+3.p',unknown),
[] ).
cnf(69,axiom,
e_qually_directed_lines(dollar_c2,reverse_line(dollar_c1)),
file('GEO265+3.p',unknown),
[] ).
cnf(86,plain,
une_qually_directed_lines(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[67,7,69]),
[iquote('hyper,67,7,69')] ).
cnf(90,plain,
convergent_lines(dollar_c2,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[86,14,65]),55]),
[iquote('hyper,86,14,65,unit_del,55')] ).
cnf(91,plain,
une_qually_directed_opposite_lines(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[90,13]),
[iquote('hyper,90,13')] ).
cnf(92,plain,
une_qually_directed_lines(dollar_c2,reverse_line(dollar_c1)),
inference(hyper,[status(thm)],[91,1]),
[iquote('hyper,91,1')] ).
cnf(102,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[92,39,86]),41,41]),
[iquote('hyper,92,39,86,unit_del,41,41')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO265+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 07:19:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.76/1.97 ----- Otter 3.3f, August 2004 -----
% 1.76/1.97 The process was started by sandbox2 on n027.cluster.edu,
% 1.76/1.97 Wed Jul 27 07:19:06 2022
% 1.76/1.97 The command was "./otter". The process ID is 23955.
% 1.76/1.97
% 1.76/1.97 set(prolog_style_variables).
% 1.76/1.97 set(auto).
% 1.76/1.97 dependent: set(auto1).
% 1.76/1.97 dependent: set(process_input).
% 1.76/1.97 dependent: clear(print_kept).
% 1.76/1.97 dependent: clear(print_new_demod).
% 1.76/1.97 dependent: clear(print_back_demod).
% 1.76/1.97 dependent: clear(print_back_sub).
% 1.76/1.97 dependent: set(control_memory).
% 1.76/1.97 dependent: assign(max_mem, 12000).
% 1.76/1.97 dependent: assign(pick_given_ratio, 4).
% 1.76/1.97 dependent: assign(stats_level, 1).
% 1.76/1.97 dependent: assign(max_seconds, 10800).
% 1.76/1.97 clear(print_given).
% 1.76/1.97
% 1.76/1.97 formula_list(usable).
% 1.76/1.97 all X Y (une_qually_directed_opposite_lines(X,Y)<->une_qually_directed_lines(X,reverse_line(Y))).
% 1.76/1.97 all X Y (right_apart_point(X,Y)<->left_apart_point(X,reverse_line(Y))).
% 1.76/1.97 all X Y (right_convergent_lines(X,Y)<->left_convergent_lines(X,reverse_line(Y))).
% 1.76/1.97 all X Y (e_qually_directed_lines(X,Y)<-> -une_qually_directed_lines(X,Y)).
% 1.76/1.97 all X Y (e_qually_directed_opposite_lines(X,Y)<-> -une_qually_directed_opposite_lines(X,Y)).
% 1.76/1.97 all A L (apart_point_and_line(A,L)<->left_apart_point(A,L)|right_apart_point(A,L)).
% 1.76/1.97 all L M (convergent_lines(L,M)<->une_qually_directed_lines(L,M)&une_qually_directed_opposite_lines(L,M)).
% 1.76/1.97 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)).
% 1.76/1.97 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))).
% 1.76/1.97 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)).
% 1.76/1.97 all A (-distinct_points(A,A)).
% 1.76/1.97 all A B C (distinct_points(A,B)->distinct_points(A,C)|distinct_points(B,C)).
% 1.76/1.97 all L (-distinct_lines(L,L)).
% 1.76/1.97 all L M N (distinct_lines(L,M)->distinct_lines(L,N)|distinct_lines(M,N)).
% 1.76/1.97 all L e_qually_directed_lines(L,L).
% 1.76/1.97 all L M N (une_qually_directed_lines(L,M)->une_qually_directed_lines(L,N)|une_qually_directed_lines(M,N)).
% 1.76/1.97 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))).
% 1.76/1.97 all L M (une_qually_directed_lines(L,M)|une_qually_directed_lines(L,reverse_line(M))).
% 1.76/1.97 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))).
% 1.76/1.97 all A L (-(left_apart_point(A,L)|left_apart_point(A,reverse_line(L)))).
% 1.76/1.97 all L M (-(left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M)))).
% 1.76/1.97 all A B (point(A)&point(B)&distinct_points(A,B)->line(line_connecting(A,B))).
% 1.76/1.97 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))).
% 1.76/1.97 all L A (point(A)&line(L)->line(parallel_through_point(L,A))).
% 1.76/1.97 all L (line(L)->line(reverse_line(L))).
% 1.76/1.97 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))).
% 1.76/1.97 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)).
% 1.76/1.97 all A L (-apart_point_and_line(A,parallel_through_point(L,A))).
% 1.76/1.97 all L (-distinct_lines(L,reverse_line(L))).
% 1.76/1.97 all A B (distinct_points(A,B)->e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))).
% 1.76/1.97 all A L e_qually_directed_lines(parallel_through_point(L,A),L).
% 1.76/1.97 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))).
% 1.76/1.97 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)).
% 1.76/1.97 all A B L (left_apart_point(A,L)->distinct_points(A,B)|left_apart_point(B,L)).
% 1.76/1.97 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))).
% 1.76/1.97 all L M N (left_convergent_lines(L,M)->une_qually_directed_lines(M,N)|left_convergent_lines(L,N)).
% 1.76/1.97 -(all L M (e_qually_directed_lines(L,reverse_line(M))->e_qually_directed_opposite_lines(L,M))).
% 1.76/1.97 end_of_list.
% 1.76/1.97
% 1.76/1.97 -------> usable clausifies to:
% 1.76/1.97
% 1.76/1.97 list(usable).
% 1.76/1.97 0 [] -une_qually_directed_opposite_lines(X,Y)|une_qually_directed_lines(X,reverse_line(Y)).
% 1.76/1.97 0 [] une_qually_directed_opposite_lines(X,Y)| -une_qually_directed_lines(X,reverse_line(Y)).
% 1.76/1.97 0 [] -right_apart_point(X,Y)|left_apart_point(X,reverse_line(Y)).
% 1.76/1.97 0 [] right_apart_point(X,Y)| -left_apart_point(X,reverse_line(Y)).
% 1.76/1.97 0 [] -right_convergent_lines(X,Y)|left_convergent_lines(X,reverse_line(Y)).
% 1.76/1.97 0 [] right_convergent_lines(X,Y)| -left_convergent_lines(X,reverse_line(Y)).
% 1.76/1.97 0 [] -e_qually_directed_lines(X,Y)| -une_qually_directed_lines(X,Y).
% 1.76/1.97 0 [] e_qually_directed_lines(X,Y)|une_qually_directed_lines(X,Y).
% 1.76/1.97 0 [] -e_qually_directed_opposite_lines(X,Y)| -une_qually_directed_opposite_lines(X,Y).
% 1.76/1.97 0 [] e_qually_directed_opposite_lines(X,Y)|une_qually_directed_opposite_lines(X,Y).
% 1.76/1.97 0 [] -apart_point_and_line(A,L)|left_apart_point(A,L)|right_apart_point(A,L).
% 1.76/1.97 0 [] apart_point_and_line(A,L)| -left_apart_point(A,L).
% 1.76/1.97 0 [] apart_point_and_line(A,L)| -right_apart_point(A,L).
% 1.76/1.97 0 [] -convergent_lines(L,M)|une_qually_directed_lines(L,M).
% 1.76/1.97 0 [] -convergent_lines(L,M)|une_qually_directed_opposite_lines(L,M).
% 1.76/1.97 0 [] convergent_lines(L,M)| -une_qually_directed_lines(L,M)| -une_qually_directed_opposite_lines(L,M).
% 1.76/1.97 0 [] -divides_points(L,A,B)|left_apart_point(A,L)|right_apart_point(A,L).
% 1.76/1.97 0 [] -divides_points(L,A,B)|left_apart_point(A,L)|left_apart_point(B,L).
% 1.76/1.97 0 [] -divides_points(L,A,B)|right_apart_point(B,L)|right_apart_point(A,L).
% 1.76/1.97 0 [] -divides_points(L,A,B)|right_apart_point(B,L)|left_apart_point(B,L).
% 1.76/1.97 0 [] divides_points(L,A,B)| -left_apart_point(A,L)| -right_apart_point(B,L).
% 1.76/1.97 0 [] divides_points(L,A,B)| -right_apart_point(A,L)| -left_apart_point(B,L).
% 1.76/1.97 0 [] -before_on_line(L,A,B)|distinct_points(A,B).
% 1.76/1.97 0 [] -before_on_line(L,A,B)|incident_point_and_line(A,L).
% 1.76/1.97 0 [] -before_on_line(L,A,B)|incident_point_and_line(B,L).
% 1.76/1.97 0 [] -before_on_line(L,A,B)|e_qually_directed_lines(L,line_connecting(A,B)).
% 1.76/1.97 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)).
% 1.76/1.97 0 [] -between_on_line(L,A,B,C)|before_on_line(L,A,B)|before_on_line(L,C,B).
% 1.76/1.97 0 [] -between_on_line(L,A,B,C)|before_on_line(L,A,B)|before_on_line(L,B,A).
% 1.76/1.97 0 [] -between_on_line(L,A,B,C)|before_on_line(L,B,C)|before_on_line(L,C,B).
% 1.76/1.97 0 [] -between_on_line(L,A,B,C)|before_on_line(L,B,C)|before_on_line(L,B,A).
% 1.76/1.97 0 [] between_on_line(L,A,B,C)| -before_on_line(L,A,B)| -before_on_line(L,B,C).
% 1.76/1.97 0 [] between_on_line(L,A,B,C)| -before_on_line(L,C,B)| -before_on_line(L,B,A).
% 1.76/1.97 0 [] -distinct_points(A,A).
% 1.76/1.97 0 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.76/1.97 0 [] -distinct_lines(L,L).
% 1.76/1.97 0 [] -distinct_lines(L,M)|distinct_lines(L,N)|distinct_lines(M,N).
% 1.76/1.97 0 [] e_qually_directed_lines(L,L).
% 1.76/1.97 0 [] -une_qually_directed_lines(L,M)|une_qually_directed_lines(L,N)|une_qually_directed_lines(M,N).
% 1.76/1.97 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).
% 1.76/1.97 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)).
% 1.76/1.97 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).
% 1.76/1.97 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)).
% 1.76/1.97 0 [] une_qually_directed_lines(L,M)|une_qually_directed_lines(L,reverse_line(M)).
% 1.76/1.97 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)).
% 1.76/1.97 0 [] -left_apart_point(A,L).
% 1.76/1.97 0 [] -left_apart_point(A,reverse_line(L)).
% 1.76/1.97 0 [] -left_convergent_lines(L,M).
% 1.76/1.97 0 [] -left_convergent_lines(L,reverse_line(M)).
% 1.76/1.97 0 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.76/1.97 0 [] -line(L)| -line(M)| -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))|point(intersection_point(L,M)).
% 1.76/1.97 0 [] -point(A)| -line(L)|line(parallel_through_point(L,A)).
% 1.76/1.97 0 [] -line(L)|line(reverse_line(L)).
% 1.76/1.97 0 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 1.76/1.97 0 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 1.76/1.97 0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))| -apart_point_and_line(intersection_point(L,M),L).
% 1.76/1.97 0 [] -une_qually_directed_lines(L,M)| -une_qually_directed_lines(L,reverse_line(M))| -apart_point_and_line(intersection_point(L,M),M).
% 1.76/1.97 0 [] -apart_point_and_line(A,parallel_through_point(L,A)).
% 1.76/1.97 0 [] -distinct_lines(L,reverse_line(L)).
% 1.76/1.97 0 [] -distinct_points(A,B)|e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))).
% 1.76/1.97 0 [] e_qually_directed_lines(parallel_through_point(L,A),L).
% 1.76/1.97 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)).
% 1.76/1.97 0 [] -distinct_points(A,B)| -left_apart_point(A,L)|left_apart_point(B,L)|left_convergent_lines(line_connecting(A,B),L).
% 1.76/1.97 0 [] -left_apart_point(A,L)|distinct_points(A,B)|left_apart_point(B,L).
% 1.76/1.97 0 [] -left_apart_point(A,L)| -une_qually_directed_lines(L,M)|distinct_lines(L,M)|left_apart_point(A,reverse_line(M)).
% 1.76/1.97 0 [] -left_convergent_lines(L,M)|une_qually_directed_lines(M,N)|left_convergent_lines(L,N).
% 1.76/1.97 0 [] e_qually_directed_lines($c2,reverse_line($c1)).
% 1.76/1.97 0 [] -e_qually_directed_opposite_lines($c2,$c1).
% 1.76/1.97 end_of_list.
% 1.76/1.97
% 1.76/1.97 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=10.
% 1.76/1.97
% 1.76/1.97 This is a non-Horn set without equality. The strategy will
% 1.76/1.97 be ordered hyper_res, unit deletion, and factoring, with
% 1.76/1.97 satellites in sos and with nuclei in usable.
% 1.76/1.97
% 1.76/1.97 dependent: set(hyper_res).
% 1.76/1.97 dependent: set(factor).
% 1.76/1.97 dependent: set(unit_deletion).
% 1.76/1.97
% 1.76/1.97 ------------> process usable:
% 1.76/1.97 ** KEPT (pick-wt=7): 1 [] -une_qually_directed_opposite_lines(A,B)|une_qually_directed_lines(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=7): 2 [] une_qually_directed_opposite_lines(A,B)| -une_qually_directed_lines(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=7): 3 [] -right_apart_point(A,B)|left_apart_point(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=7): 4 [] right_apart_point(A,B)| -left_apart_point(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=7): 5 [] -right_convergent_lines(A,B)|left_convergent_lines(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=7): 6 [] right_convergent_lines(A,B)| -left_convergent_lines(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=6): 7 [] -e_qually_directed_lines(A,B)| -une_qually_directed_lines(A,B).
% 1.76/1.97 ** KEPT (pick-wt=6): 8 [] -e_qually_directed_opposite_lines(A,B)| -une_qually_directed_opposite_lines(A,B).
% 1.76/1.97 ** KEPT (pick-wt=9): 9 [] -apart_point_and_line(A,B)|left_apart_point(A,B)|right_apart_point(A,B).
% 1.76/1.97 ** KEPT (pick-wt=6): 10 [] apart_point_and_line(A,B)| -left_apart_point(A,B).
% 1.76/1.97 ** KEPT (pick-wt=6): 11 [] apart_point_and_line(A,B)| -right_apart_point(A,B).
% 1.76/1.97 ** KEPT (pick-wt=6): 12 [] -convergent_lines(A,B)|une_qually_directed_lines(A,B).
% 1.76/1.97 ** KEPT (pick-wt=6): 13 [] -convergent_lines(A,B)|une_qually_directed_opposite_lines(A,B).
% 1.76/1.97 ** KEPT (pick-wt=9): 14 [] convergent_lines(A,B)| -une_qually_directed_lines(A,B)| -une_qually_directed_opposite_lines(A,B).
% 1.76/1.97 ** KEPT (pick-wt=10): 15 [] -divides_points(A,B,C)|left_apart_point(B,A)|right_apart_point(B,A).
% 1.76/1.97 ** KEPT (pick-wt=10): 16 [] -divides_points(A,B,C)|left_apart_point(B,A)|left_apart_point(C,A).
% 1.76/1.97 ** KEPT (pick-wt=10): 17 [] -divides_points(A,B,C)|right_apart_point(C,A)|right_apart_point(B,A).
% 1.76/1.97 ** KEPT (pick-wt=10): 18 [] -divides_points(A,B,C)|right_apart_point(C,A)|left_apart_point(C,A).
% 1.76/1.97 ** KEPT (pick-wt=10): 19 [] divides_points(A,B,C)| -left_apart_point(B,A)| -right_apart_point(C,A).
% 1.76/1.97 ** KEPT (pick-wt=10): 20 [] divides_points(A,B,C)| -right_apart_point(B,A)| -left_apart_point(C,A).
% 1.76/1.97 ** KEPT (pick-wt=7): 21 [] -before_on_line(A,B,C)|distinct_points(B,C).
% 1.76/1.97 ** KEPT (pick-wt=7): 22 [] -before_on_line(A,B,C)|incident_point_and_line(B,A).
% 1.76/1.97 ** KEPT (pick-wt=7): 23 [] -before_on_line(A,B,C)|incident_point_and_line(C,A).
% 1.76/1.97 ** KEPT (pick-wt=9): 24 [] -before_on_line(A,B,C)|e_qually_directed_lines(A,line_connecting(B,C)).
% 1.76/1.97 ** 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)).
% 1.76/1.97 ** KEPT (pick-wt=13): 26 [] -between_on_line(A,B,C,D)|before_on_line(A,B,C)|before_on_line(A,D,C).
% 1.76/1.97 ** KEPT (pick-wt=13): 27 [] -between_on_line(A,B,C,D)|before_on_line(A,B,C)|before_on_line(A,C,B).
% 1.76/1.97 ** KEPT (pick-wt=13): 28 [] -between_on_line(A,B,C,D)|before_on_line(A,C,D)|before_on_line(A,D,C).
% 1.76/1.97 ** KEPT (pick-wt=13): 29 [] -between_on_line(A,B,C,D)|before_on_line(A,C,D)|before_on_line(A,C,B).
% 1.76/1.97 ** KEPT (pick-wt=13): 30 [] between_on_line(A,B,C,D)| -before_on_line(A,B,C)| -before_on_line(A,C,D).
% 1.76/1.97 ** KEPT (pick-wt=13): 31 [] between_on_line(A,B,C,D)| -before_on_line(A,D,C)| -before_on_line(A,C,B).
% 1.76/1.97 ** KEPT (pick-wt=3): 32 [] -distinct_points(A,A).
% 1.76/1.97 ** KEPT (pick-wt=9): 33 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.76/1.97 ** KEPT (pick-wt=3): 34 [] -distinct_lines(A,A).
% 1.76/1.97 ** KEPT (pick-wt=9): 35 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.76/1.97 ** KEPT (pick-wt=9): 36 [] -une_qually_directed_lines(A,B)|une_qually_directed_lines(A,C)|une_qually_directed_lines(B,C).
% 1.76/1.97 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).
% 1.76/1.97 ** 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)).
% 1.76/1.97 ** 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).
% 1.76/1.97 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)).
% 1.76/1.97 ** 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)).
% 1.76/1.97 ** KEPT (pick-wt=3): 40 [] -left_apart_point(A,B).
% 1.76/1.97 Following clause subsumed by 40 during input processing: 0 [] -left_apart_point(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=3): 41 [] -left_convergent_lines(A,B).
% 1.76/1.97 Following clause subsumed by 41 during input processing: 0 [] -left_convergent_lines(A,reverse_line(B)).
% 1.76/1.97 ** KEPT (pick-wt=11): 42 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.76/1.97 ** 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)).
% 1.76/1.97 ** KEPT (pick-wt=8): 44 [] -point(A)| -line(B)|line(parallel_through_point(B,A)).
% 1.76/1.97 ** KEPT (pick-wt=5): 45 [] -line(A)|line(reverse_line(A)).
% 1.76/1.97 ** KEPT (pick-wt=8): 46 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 1.76/1.97 ** KEPT (pick-wt=8): 47 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 1.76/1.97 ** 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).
% 1.76/1.97 ** 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).
% 1.76/1.97 ** KEPT (pick-wt=5): 50 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.76/1.97 ** KEPT (pick-wt=4): 51 [] -distinct_lines(A,reverse_line(A)).
% 1.76/1.97 ** KEPT (pick-wt=11): 52 [] -distinct_points(A,B)|e_qually_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))).
% 1.80/1.97 ** 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).
% 1.80/1.97 Following clause subsumed by 40 during input processing: 0 [unit_del,40,41] -distinct_points(A,B)| -left_apart_point(A,C).
% 1.80/1.97 Following clause subsumed by 40 during input processing: 0 [unit_del,40] -left_apart_point(A,B)|distinct_points(A,C).
% 1.80/1.97 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).
% 1.80/1.97 Following clause subsumed by 41 during input processing: 0 [unit_del,41] -left_convergent_lines(A,B)|une_qually_directed_lines(B,C).
% 1.80/1.97 ** KEPT (pick-wt=3): 55 [] -e_qually_directed_opposite_lines($c2,$c1).
% 1.80/1.97 40 back subsumes 20.
% 1.80/1.97 40 back subsumes 19.
% 1.80/1.97 40 back subsumes 10.
% 1.80/1.97 40 back subsumes 4.
% 1.80/1.97 41 back subsumes 6.
% 1.80/1.97
% 1.80/1.97 ------------> process sos:
% 1.80/1.97 ** KEPT (pick-wt=6): 64 [] e_qually_directed_lines(A,B)|une_qually_directed_lines(A,B).
% 1.80/1.97 ** KEPT (pick-wt=6): 65 [] e_qually_directed_opposite_lines(A,B)|une_qually_directed_opposite_lines(A,B).
% 1.80/1.97 ** KEPT (pick-wt=3): 66 [] e_qually_directed_lines(A,A).
% 1.80/1.97 ** KEPT (pick-wt=7): 67 [] une_qually_directed_lines(A,B)|une_qually_directed_lines(A,reverse_line(B)).
% 1.80/1.97 ** KEPT (pick-wt=5): 68 [] e_qually_directed_lines(parallel_through_point(A,B),A).
% 1.80/1.97 ** KEPT (pick-wt=4): 69 [] e_qually_directed_lines($c2,reverse_line($c1)).
% 1.80/1.97
% 1.80/1.97 ======= end of input processing =======
% 1.80/1.97
% 1.80/1.97 =========== start of search ===========
% 1.80/1.97
% 1.80/1.97 -------- PROOF --------
% 1.80/1.97
% 1.80/1.97 -----> EMPTY CLAUSE at 0.01 sec ----> 102 [hyper,92,39,86,unit_del,41,41] $F.
% 1.80/1.97
% 1.80/1.97 Length of proof is 4. Level of proof is 4.
% 1.80/1.97
% 1.80/1.97 ---------------- PROOF ----------------
% 1.80/1.97 % SZS status Theorem
% 1.80/1.97 % SZS output start Refutation
% See solution above
% 1.80/1.97 ------------ end of proof -------------
% 1.80/1.97
% 1.80/1.97
% 1.80/1.97 Search stopped by max_proofs option.
% 1.80/1.97
% 1.80/1.97
% 1.80/1.97 Search stopped by max_proofs option.
% 1.80/1.97
% 1.80/1.97 ============ end of search ============
% 1.80/1.97
% 1.80/1.97 -------------- statistics -------------
% 1.80/1.97 clauses given 14
% 1.80/1.97 clauses generated 160
% 1.80/1.97 clauses kept 100
% 1.80/1.97 clauses forward subsumed 127
% 1.80/1.97 clauses back subsumed 5
% 1.80/1.97 Kbytes malloced 976
% 1.80/1.97
% 1.80/1.97 ----------- times (seconds) -----------
% 1.80/1.97 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.80/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/1.97
% 1.80/1.97 That finishes the proof of the theorem.
% 1.80/1.97
% 1.80/1.97 Process 23955 finished Wed Jul 27 07:19:08 2022
% 1.80/1.97 Otter interrupted
% 1.80/1.97 PROOF FOUND
%------------------------------------------------------------------------------