%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:54:41 EDT 2022
% Result : Theorem 18.10s 18.30s
% Output : Refutation 18.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of clauses : 53 ( 18 unt; 30 nHn; 22 RR)
% Number of literals : 115 ( 0 equ; 27 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ distinct_points(A,A),
file('GEO186+3.p',unknown),
[] ).
cnf(2,axiom,
~ distinct_lines(A,A),
file('GEO186+3.p',unknown),
[] ).
cnf(3,axiom,
~ convergent_lines(A,A),
file('GEO186+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ distinct_lines(A,B)
| distinct_lines(A,C)
| distinct_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ convergent_lines(A,B)
| convergent_lines(A,C)
| convergent_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(9,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(intersection_point(A,B),A) ),
file('GEO186+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ convergent_lines(A,B)
| ~ apart_point_and_line(intersection_point(A,B),B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ distinct_points(A,B)
| ~ distinct_lines(C,D)
| apart_point_and_line(A,C)
| apart_point_and_line(A,D)
| apart_point_and_line(B,C)
| apart_point_and_line(B,D) ),
file('GEO186+3.p',unknown),
[] ).
cnf(14,axiom,
( ~ convergent_lines(A,B)
| distinct_lines(B,C)
| convergent_lines(A,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(15,axiom,
( ~ distinct_lines(A,B)
| convergent_lines(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ convergent_lines(A,B)
| ~ unorthogonal_lines(A,B)
| convergent_lines(A,C)
| unorthogonal_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(21,axiom,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
file('GEO186+3.p',unknown),
[] ).
cnf(24,axiom,
( convergent_lines(A,B)
| convergent_lines(A,C)
| ~ convergent_lines(B,C)
| ~ unorthogonal_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(26,axiom,
( unorthogonal_lines(A,B)
| convergent_lines(A,C)
| ~ convergent_lines(B,C)
| ~ unorthogonal_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(28,axiom,
( unorthogonal_lines(A,B)
| unorthogonal_lines(A,C)
| ~ convergent_lines(B,C) ),
file('GEO186+3.p',unknown),
[] ).
cnf(36,axiom,
( ~ incident_point_and_line(A,B)
| ~ apart_point_and_line(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(37,axiom,
( ~ orthogonal_lines(A,B)
| ~ unorthogonal_lines(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(38,axiom,
~ e_qual_points(dollar_c4,intersection_point(dollar_c2,dollar_c1)),
file('GEO186+3.p',unknown),
[] ).
cnf(39,axiom,
( convergent_lines(A,B)
| unorthogonal_lines(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(40,axiom,
( e_qual_points(A,B)
| distinct_points(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(44,axiom,
( orthogonal_lines(A,B)
| unorthogonal_lines(A,B) ),
file('GEO186+3.p',unknown),
[] ).
cnf(46,axiom,
convergent_lines(dollar_c2,dollar_c1),
file('GEO186+3.p',unknown),
[] ).
cnf(47,axiom,
incident_point_and_line(dollar_c4,dollar_c2),
file('GEO186+3.p',unknown),
[] ).
cnf(48,axiom,
incident_point_and_line(dollar_c4,dollar_c1),
file('GEO186+3.p',unknown),
[] ).
cnf(49,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(hyper,[status(thm)],[39,21]),
[iquote('hyper,39,21')] ).
cnf(52,plain,
( distinct_lines(dollar_c1,A)
| convergent_lines(dollar_c2,A) ),
inference(hyper,[status(thm)],[46,14]),
[iquote('hyper,46,14')] ).
cnf(54,plain,
distinct_points(dollar_c4,intersection_point(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[40,38]),
[iquote('hyper,40,38')] ).
cnf(55,plain,
( unorthogonal_lines(A,orthogonal_through_point(B,C))
| unorthogonal_lines(A,B) ),
inference(hyper,[status(thm)],[49,28]),
[iquote('hyper,49,28')] ).
cnf(57,plain,
( convergent_lines(orthogonal_through_point(A,B),C)
| convergent_lines(A,C) ),
inference(hyper,[status(thm)],[49,6]),
[iquote('hyper,49,6')] ).
cnf(58,plain,
( distinct_points(dollar_c4,A)
| distinct_points(intersection_point(dollar_c2,dollar_c1),A) ),
inference(hyper,[status(thm)],[54,4]),
[iquote('hyper,54,4')] ).
cnf(65,plain,
orthogonal_lines(orthogonal_through_point(A,B),A),
inference(hyper,[status(thm)],[44,21]),
[iquote('hyper,44,21')] ).
cnf(87,plain,
( convergent_lines(dollar_c2,A)
| distinct_lines(dollar_c1,B)
| distinct_lines(A,B) ),
inference(hyper,[status(thm)],[52,5]),
[iquote('hyper,52,5')] ).
cnf(129,plain,
unorthogonal_lines(orthogonal_through_point(A,B),orthogonal_through_point(A,C)),
inference(hyper,[status(thm)],[55,37,65]),
[iquote('hyper,55,37,65')] ).
cnf(193,plain,
( convergent_lines(A,B)
| unorthogonal_lines(C,orthogonal_through_point(A,D))
| convergent_lines(C,B)
| orthogonal_lines(orthogonal_through_point(A,D),B) ),
inference(hyper,[status(thm)],[57,26,44]),
[iquote('hyper,57,26,44')] ).
cnf(199,plain,
convergent_lines(A,orthogonal_through_point(A,B)),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[57,24,129])])]),
[iquote('hyper,57,24,129,factor_simp,factor_simp')] ).
cnf(277,plain,
( convergent_lines(A,B)
| unorthogonal_lines(A,orthogonal_through_point(A,C))
| orthogonal_lines(orthogonal_through_point(A,C),B) ),
inference(factor,[status(thm)],[193]),
[iquote('factor,193.1.3')] ).
cnf(306,plain,
( convergent_lines(A,B)
| unorthogonal_lines(orthogonal_through_point(A,C),B)
| orthogonal_lines(A,orthogonal_through_point(A,C)) ),
inference(hyper,[status(thm)],[199,18,44]),
[iquote('hyper,199,18,44')] ).
cnf(314,plain,
distinct_points(intersection_point(dollar_c2,dollar_c1),dollar_c4),
inference(hyper,[status(thm)],[58,1]),
[iquote('hyper,58,1')] ).
cnf(607,plain,
( convergent_lines(dollar_c2,A)
| distinct_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[87,2]),
[iquote('hyper,87,2')] ).
cnf(609,plain,
( convergent_lines(dollar_c2,A)
| distinct_lines(dollar_c1,B)
| convergent_lines(A,B) ),
inference(hyper,[status(thm)],[87,15]),
[iquote('hyper,87,15')] ).
cnf(624,plain,
distinct_lines(dollar_c1,dollar_c2),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[609]),3]),
[iquote('factor,609.1.3,unit_del,3')] ).
cnf(688,plain,
( apart_point_and_line(intersection_point(dollar_c2,dollar_c1),dollar_c1)
| apart_point_and_line(intersection_point(dollar_c2,dollar_c1),dollar_c2)
| apart_point_and_line(dollar_c4,dollar_c1)
| apart_point_and_line(dollar_c4,dollar_c2) ),
inference(hyper,[status(thm)],[624,11,314]),
[iquote('hyper,624,11,314')] ).
cnf(698,plain,
( convergent_lines(dollar_c2,A)
| convergent_lines(A,dollar_c1) ),
inference(hyper,[status(thm)],[607,15]),
[iquote('hyper,607,15')] ).
cnf(781,plain,
( convergent_lines(A,dollar_c1)
| unorthogonal_lines(B,dollar_c2)
| unorthogonal_lines(B,A) ),
inference(hyper,[status(thm)],[698,28]),
[iquote('hyper,698,28')] ).
cnf(5651,plain,
orthogonal_lines(A,orthogonal_through_point(A,B)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[306,37,65]),3]),
[iquote('hyper,306,37,65,unit_del,3')] ).
cnf(5667,plain,
( convergent_lines(A,B)
| orthogonal_lines(orthogonal_through_point(A,C),B) ),
inference(hyper,[status(thm)],[5651,37,277]),
[iquote('hyper,5651,37,277')] ).
cnf(5692,plain,
( convergent_lines(A,B)
| convergent_lines(B,dollar_c1)
| unorthogonal_lines(orthogonal_through_point(A,C),dollar_c2) ),
inference(hyper,[status(thm)],[5667,37,781]),
[iquote('hyper,5667,37,781')] ).
cnf(5924,plain,
( convergent_lines(A,B)
| convergent_lines(B,dollar_c1)
| convergent_lines(A,dollar_c2) ),
inference(hyper,[status(thm)],[5692,37,5667]),
[iquote('hyper,5692,37,5667')] ).
cnf(5990,plain,
( apart_point_and_line(intersection_point(dollar_c2,dollar_c1),dollar_c2)
| apart_point_and_line(dollar_c4,dollar_c1)
| apart_point_and_line(dollar_c4,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[688,10,5924]),3,3]),
[iquote('hyper,688,10,5924,unit_del,3,3')] ).
cnf(6000,plain,
( apart_point_and_line(dollar_c4,dollar_c1)
| apart_point_and_line(dollar_c4,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5990,9,5924]),3,3]),
[iquote('hyper,5990,9,5924,unit_del,3,3')] ).
cnf(6003,plain,
apart_point_and_line(dollar_c4,dollar_c2),
inference(hyper,[status(thm)],[6000,36,48]),
[iquote('hyper,6000,36,48')] ).
cnf(6005,plain,
$false,
inference(hyper,[status(thm)],[6003,36,47]),
[iquote('hyper,6003,36,47')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 07:06:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.56/2.14 ----- Otter 3.3f, August 2004 -----
% 1.56/2.14 The process was started by sandbox on n015.cluster.edu,
% 1.56/2.14 Wed Jul 27 07:06:57 2022
% 1.56/2.14 The command was "./otter". The process ID is 4829.
% 1.56/2.14
% 1.56/2.14 set(prolog_style_variables).
% 1.56/2.14 set(auto).
% 1.56/2.14 dependent: set(auto1).
% 1.56/2.14 dependent: set(process_input).
% 1.56/2.14 dependent: clear(print_kept).
% 1.56/2.14 dependent: clear(print_new_demod).
% 1.56/2.14 dependent: clear(print_back_demod).
% 1.56/2.14 dependent: clear(print_back_sub).
% 1.56/2.14 dependent: set(control_memory).
% 1.56/2.14 dependent: assign(max_mem, 12000).
% 1.56/2.14 dependent: assign(pick_given_ratio, 4).
% 1.56/2.14 dependent: assign(stats_level, 1).
% 1.56/2.14 dependent: assign(max_seconds, 10800).
% 1.56/2.14 clear(print_given).
% 1.56/2.14
% 1.56/2.14 formula_list(usable).
% 1.56/2.14 all X (-distinct_points(X,X)).
% 1.56/2.14 all X (-distinct_lines(X,X)).
% 1.56/2.14 all X (-convergent_lines(X,X)).
% 1.56/2.14 all X Y Z (distinct_points(X,Y)->distinct_points(X,Z)|distinct_points(Y,Z)).
% 1.56/2.14 all X Y Z (distinct_lines(X,Y)->distinct_lines(X,Z)|distinct_lines(Y,Z)).
% 1.56/2.14 all X Y Z (convergent_lines(X,Y)->convergent_lines(X,Z)|convergent_lines(Y,Z)).
% 1.56/2.14 all X Y (distinct_points(X,Y)-> -apart_point_and_line(X,line_connecting(X,Y))).
% 1.56/2.14 all X Y (distinct_points(X,Y)-> -apart_point_and_line(Y,line_connecting(X,Y))).
% 1.56/2.14 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),X)).
% 1.56/2.14 all X Y (convergent_lines(X,Y)-> -apart_point_and_line(intersection_point(X,Y),Y)).
% 1.56/2.14 all X Y U V (distinct_points(X,Y)&distinct_lines(U,V)->apart_point_and_line(X,U)|apart_point_and_line(X,V)|apart_point_and_line(Y,U)|apart_point_and_line(Y,V)).
% 1.56/2.14 all X Y Z (apart_point_and_line(X,Y)->distinct_points(X,Z)|apart_point_and_line(Z,Y)).
% 1.56/2.14 all X Y Z (apart_point_and_line(X,Y)->distinct_lines(Y,Z)|apart_point_and_line(X,Z)).
% 1.56/2.14 all X Y Z (convergent_lines(X,Y)->distinct_lines(Y,Z)|convergent_lines(X,Z)).
% 1.56/2.14 all X Y (distinct_lines(X,Y)->convergent_lines(X,Y)).
% 1.56/2.14 all X Y (-convergent_lines(parallel_through_point(Y,X),Y)).
% 1.56/2.14 all X Y (-apart_point_and_line(X,parallel_through_point(Y,X))).
% 1.56/2.14 all X Y Z (distinct_lines(Y,Z)->apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z)).
% 1.56/2.14 all L M (convergent_lines(L,M)|unorthogonal_lines(L,M)).
% 1.56/2.14 all L M N (convergent_lines(L,M)&unorthogonal_lines(L,M)->convergent_lines(L,N)&unorthogonal_lines(L,N)|convergent_lines(M,N)&unorthogonal_lines(M,N)).
% 1.56/2.14 all A L (-unorthogonal_lines(orthogonal_through_point(L,A),L)).
% 1.56/2.14 all A L (-apart_point_and_line(A,orthogonal_through_point(L,A))).
% 1.56/2.14 all A L M N (distinct_lines(L,M)->apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N)).
% 1.56/2.14 all L M (-(-convergent_lines(L,M)& -unorthogonal_lines(L,M))).
% 1.56/2.14 all L M N ((-convergent_lines(L,M)| -unorthogonal_lines(L,M))& (-convergent_lines(L,N)| -unorthogonal_lines(L,N))-> -convergent_lines(M,N)| -unorthogonal_lines(M,N)).
% 1.56/2.14 all L M N (-unorthogonal_lines(L,M)& -unorthogonal_lines(L,N)-> -convergent_lines(M,N)).
% 1.56/2.14 all A B (point(A)&point(B)&distinct_points(A,B)->line(line_connecting(A,B))).
% 1.56/2.14 all L M (line(L)&line(M)&convergent_lines(L,M)->point(intersection_point(L,M))).
% 1.56/2.14 all L A (line(L)&point(A)->line(parallel_through_point(L,A))).
% 1.56/2.14 all L A (line(L)&point(A)->line(orthogonal_through_point(L,A))).
% 1.56/2.14 all X Y (e_qual_points(X,Y)<-> -distinct_points(X,Y)).
% 1.56/2.14 all X Y (e_qual_lines(X,Y)<-> -distinct_lines(X,Y)).
% 1.56/2.14 all X Y (parallel_lines(X,Y)<-> -convergent_lines(X,Y)).
% 1.56/2.14 all X Y (incident_point_and_line(X,Y)<-> -apart_point_and_line(X,Y)).
% 1.56/2.14 all X Y (orthogonal_lines(X,Y)<-> -unorthogonal_lines(X,Y)).
% 1.56/2.14 -(all X Y U V (distinct_points(X,Y)&convergent_lines(U,V)&incident_point_and_line(X,U)&incident_point_and_line(X,V)->e_qual_points(X,intersection_point(U,V)))).
% 1.56/2.14 end_of_list.
% 1.56/2.14
% 1.56/2.14 -------> usable clausifies to:
% 1.56/2.14
% 1.56/2.14 list(usable).
% 1.56/2.14 0 [] -distinct_points(X,X).
% 1.56/2.14 0 [] -distinct_lines(X,X).
% 1.56/2.14 0 [] -convergent_lines(X,X).
% 1.56/2.14 0 [] -distinct_points(X,Y)|distinct_points(X,Z)|distinct_points(Y,Z).
% 1.56/2.14 0 [] -distinct_lines(X,Y)|distinct_lines(X,Z)|distinct_lines(Y,Z).
% 1.56/2.14 0 [] -convergent_lines(X,Y)|convergent_lines(X,Z)|convergent_lines(Y,Z).
% 1.56/2.14 0 [] -distinct_points(X,Y)| -apart_point_and_line(X,line_connecting(X,Y)).
% 1.56/2.14 0 [] -distinct_points(X,Y)| -apart_point_and_line(Y,line_connecting(X,Y)).
% 1.56/2.14 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),X).
% 1.56/2.14 0 [] -convergent_lines(X,Y)| -apart_point_and_line(intersection_point(X,Y),Y).
% 1.56/2.14 0 [] -distinct_points(X,Y)| -distinct_lines(U,V)|apart_point_and_line(X,U)|apart_point_and_line(X,V)|apart_point_and_line(Y,U)|apart_point_and_line(Y,V).
% 1.56/2.14 0 [] -apart_point_and_line(X,Y)|distinct_points(X,Z)|apart_point_and_line(Z,Y).
% 1.56/2.14 0 [] -apart_point_and_line(X,Y)|distinct_lines(Y,Z)|apart_point_and_line(X,Z).
% 1.56/2.14 0 [] -convergent_lines(X,Y)|distinct_lines(Y,Z)|convergent_lines(X,Z).
% 1.56/2.14 0 [] -distinct_lines(X,Y)|convergent_lines(X,Y).
% 1.56/2.14 0 [] -convergent_lines(parallel_through_point(Y,X),Y).
% 1.56/2.14 0 [] -apart_point_and_line(X,parallel_through_point(Y,X)).
% 1.56/2.14 0 [] -distinct_lines(Y,Z)|apart_point_and_line(X,Y)|apart_point_and_line(X,Z)|convergent_lines(Y,Z).
% 1.56/2.14 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.56/2.14 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|convergent_lines(M,N).
% 1.56/2.14 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|convergent_lines(L,N)|unorthogonal_lines(M,N).
% 1.56/2.14 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|convergent_lines(M,N).
% 1.56/2.14 0 [] -convergent_lines(L,M)| -unorthogonal_lines(L,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 1.56/2.14 0 [] -unorthogonal_lines(orthogonal_through_point(L,A),L).
% 1.56/2.14 0 [] -apart_point_and_line(A,orthogonal_through_point(L,A)).
% 1.56/2.14 0 [] -distinct_lines(L,M)|apart_point_and_line(A,L)|apart_point_and_line(A,M)|unorthogonal_lines(L,N)|unorthogonal_lines(M,N).
% 1.56/2.14 0 [] convergent_lines(L,M)|unorthogonal_lines(L,M).
% 1.56/2.14 0 [] convergent_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.56/2.14 0 [] convergent_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.56/2.14 0 [] unorthogonal_lines(L,M)|convergent_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.56/2.14 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N)| -unorthogonal_lines(M,N).
% 1.56/2.14 0 [] unorthogonal_lines(L,M)|unorthogonal_lines(L,N)| -convergent_lines(M,N).
% 1.56/2.14 0 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.56/2.14 0 [] -line(L)| -line(M)| -convergent_lines(L,M)|point(intersection_point(L,M)).
% 1.56/2.14 0 [] -line(L)| -point(A)|line(parallel_through_point(L,A)).
% 1.56/2.14 0 [] -line(L)| -point(A)|line(orthogonal_through_point(L,A)).
% 1.56/2.14 0 [] -e_qual_points(X,Y)| -distinct_points(X,Y).
% 1.56/2.14 0 [] e_qual_points(X,Y)|distinct_points(X,Y).
% 1.56/2.14 0 [] -e_qual_lines(X,Y)| -distinct_lines(X,Y).
% 1.56/2.14 0 [] e_qual_lines(X,Y)|distinct_lines(X,Y).
% 1.56/2.14 0 [] -parallel_lines(X,Y)| -convergent_lines(X,Y).
% 1.56/2.14 0 [] parallel_lines(X,Y)|convergent_lines(X,Y).
% 1.56/2.14 0 [] -incident_point_and_line(X,Y)| -apart_point_and_line(X,Y).
% 1.56/2.14 0 [] incident_point_and_line(X,Y)|apart_point_and_line(X,Y).
% 1.56/2.14 0 [] -orthogonal_lines(X,Y)| -unorthogonal_lines(X,Y).
% 1.56/2.14 0 [] orthogonal_lines(X,Y)|unorthogonal_lines(X,Y).
% 1.56/2.14 0 [] distinct_points($c4,$c3).
% 1.56/2.14 0 [] convergent_lines($c2,$c1).
% 1.56/2.14 0 [] incident_point_and_line($c4,$c2).
% 1.56/2.14 0 [] incident_point_and_line($c4,$c1).
% 1.56/2.14 0 [] -e_qual_points($c4,intersection_point($c2,$c1)).
% 1.56/2.14 end_of_list.
% 1.56/2.14
% 1.56/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.56/2.14
% 1.56/2.14 This is a non-Horn set without equality. The strategy will
% 1.56/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.56/2.14 satellites in sos and with nuclei in usable.
% 1.56/2.14
% 1.56/2.14 dependent: set(hyper_res).
% 1.56/2.14 dependent: set(factor).
% 1.56/2.14 dependent: set(unit_deletion).
% 1.56/2.14
% 1.56/2.14 ------------> process usable:
% 1.56/2.14 ** KEPT (pick-wt=3): 1 [] -distinct_points(A,A).
% 1.56/2.14 ** KEPT (pick-wt=3): 2 [] -distinct_lines(A,A).
% 1.56/2.14 ** KEPT (pick-wt=3): 3 [] -convergent_lines(A,A).
% 1.56/2.14 ** KEPT (pick-wt=9): 4 [] -distinct_points(A,B)|distinct_points(A,C)|distinct_points(B,C).
% 1.56/2.14 ** KEPT (pick-wt=9): 5 [] -distinct_lines(A,B)|distinct_lines(A,C)|distinct_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=9): 6 [] -convergent_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=8): 7 [] -distinct_points(A,B)| -apart_point_and_line(A,line_connecting(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=8): 8 [] -distinct_points(A,B)| -apart_point_and_line(B,line_connecting(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=8): 9 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),A).
% 1.56/2.14 ** KEPT (pick-wt=8): 10 [] -convergent_lines(A,B)| -apart_point_and_line(intersection_point(A,B),B).
% 1.56/2.14 ** KEPT (pick-wt=18): 11 [] -distinct_points(A,B)| -distinct_lines(C,D)|apart_point_and_line(A,C)|apart_point_and_line(A,D)|apart_point_and_line(B,C)|apart_point_and_line(B,D).
% 1.56/2.14 ** KEPT (pick-wt=9): 12 [] -apart_point_and_line(A,B)|distinct_points(A,C)|apart_point_and_line(C,B).
% 1.56/2.14 ** KEPT (pick-wt=9): 13 [] -apart_point_and_line(A,B)|distinct_lines(B,C)|apart_point_and_line(A,C).
% 1.56/2.14 ** KEPT (pick-wt=9): 14 [] -convergent_lines(A,B)|distinct_lines(B,C)|convergent_lines(A,C).
% 1.56/2.14 ** KEPT (pick-wt=6): 15 [] -distinct_lines(A,B)|convergent_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=5): 16 [] -convergent_lines(parallel_through_point(A,B),A).
% 1.56/2.14 ** KEPT (pick-wt=5): 17 [] -apart_point_and_line(A,parallel_through_point(B,A)).
% 1.56/2.14 Following clause subsumed by 15 during input processing: 0 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|convergent_lines(A,B).
% 1.56/2.14 Following clause subsumed by 6 during input processing: 0 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|convergent_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 18 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|convergent_lines(A,C)|unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 19 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|convergent_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 20 [] -convergent_lines(A,B)| -unorthogonal_lines(A,B)|unorthogonal_lines(A,C)|unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=5): 21 [] -unorthogonal_lines(orthogonal_through_point(A,B),A).
% 1.56/2.14 ** KEPT (pick-wt=5): 22 [] -apart_point_and_line(A,orthogonal_through_point(B,A)).
% 1.56/2.14 ** KEPT (pick-wt=15): 23 [] -distinct_lines(A,B)|apart_point_and_line(C,A)|apart_point_and_line(C,B)|unorthogonal_lines(A,D)|unorthogonal_lines(B,D).
% 1.56/2.14 ** KEPT (pick-wt=12): 24 [] convergent_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 25 [] convergent_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 26 [] unorthogonal_lines(A,B)|convergent_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=12): 27 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C)| -unorthogonal_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=9): 28 [] unorthogonal_lines(A,B)|unorthogonal_lines(A,C)| -convergent_lines(B,C).
% 1.56/2.14 ** KEPT (pick-wt=11): 29 [] -point(A)| -point(B)| -distinct_points(A,B)|line(line_connecting(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=11): 30 [] -line(A)| -line(B)| -convergent_lines(A,B)|point(intersection_point(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=8): 31 [] -line(A)| -point(B)|line(parallel_through_point(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=8): 32 [] -line(A)| -point(B)|line(orthogonal_through_point(A,B)).
% 1.56/2.14 ** KEPT (pick-wt=6): 33 [] -e_qual_points(A,B)| -distinct_points(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 34 [] -e_qual_lines(A,B)| -distinct_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 35 [] -parallel_lines(A,B)| -convergent_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 36 [] -incident_point_and_line(A,B)| -apart_point_and_line(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 37 [] -orthogonal_lines(A,B)| -unorthogonal_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=5): 38 [] -e_qual_points($c4,intersection_point($c2,$c1)).
% 1.56/2.14 28 back subsumes 27.
% 1.56/2.14
% 1.56/2.14 ------------> process sos:
% 1.56/2.14 ** KEPT (pick-wt=6): 39 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 1.56/2.14 Following clause subsumed by 39 during input processing: 0 [] convergent_lines(A,B)|unorthogonal_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 40 [] e_qual_points(A,B)|distinct_points(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 41 [] e_qual_lines(A,B)|distinct_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 42 [] parallel_lines(A,B)|convergent_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 43 [] incident_point_and_line(A,B)|apart_point_and_line(A,B).
% 1.56/2.14 ** KEPT (pick-wt=6): 44 [] orthogonal_lines(A,B)|unorthogonal_lines(A,B).
% 1.56/2.14 ** KEPT (pick-wt=3): 45 [] distinct_points($c4,$c3).
% 1.56/2.14 ** KEPT (pick-wt=3): 46 [] convergent_lines($c2,$c1).
% 1.56/2.14 ** KEPT (pick-wt=3): 47 [] incident_point_and_line($c4,$c2).
% 1.56/2.14 ** KEPT (pick-wt=3): 48 [] incident_point_and_line($c4,$c1).
% 1.56/2.14
% 1.56/2.14 ======= end of input processing =======
% 1.56/2.14
% 1.56/2.14 =========== start of search ===========
% 18.10/18.30
% 18.10/18.30
% 18.10/18.30 Resetting weight limit to 11.
% 18.10/18.30
% 18.10/18.30
% 18.10/18.30 Resetting weight limit to 11.
% 18.10/18.30
% 18.10/18.30 sos_size=3847
% 18.10/18.30
% 18.10/18.30 -- HEY sandbox, WE HAVE A PROOF!! --
% 18.10/18.30
% 18.10/18.30 -----> EMPTY CLAUSE at 16.15 sec ----> 6005 [hyper,6003,36,47] $F.
% 18.10/18.30
% 18.10/18.30 Length of proof is 27. Level of proof is 12.
% 18.10/18.30
% 18.10/18.30 ---------------- PROOF ----------------
% 18.10/18.30 % SZS status Theorem
% 18.10/18.30 % SZS output start Refutation
% See solution above
% 18.10/18.30 ------------ end of proof -------------
% 18.10/18.30
% 18.10/18.30
% 18.10/18.30 Search stopped by max_proofs option.
% 18.10/18.30
% 18.10/18.30
% 18.10/18.30 Search stopped by max_proofs option.
% 18.10/18.30
% 18.10/18.30 ============ end of search ============
% 18.10/18.30
% 18.10/18.30 -------------- statistics -------------
% 18.10/18.30 clauses given 1078
% 18.10/18.30 clauses generated 598050
% 18.10/18.30 clauses kept 6004
% 18.10/18.30 clauses forward subsumed 32406
% 18.10/18.30 clauses back subsumed 3321
% 18.10/18.30 Kbytes malloced 4882
% 18.10/18.30
% 18.10/18.30 ----------- times (seconds) -----------
% 18.10/18.30 user CPU time 16.15 (0 hr, 0 min, 16 sec)
% 18.10/18.30 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 18.10/18.30 wall-clock time 17 (0 hr, 0 min, 17 sec)
% 18.10/18.30
% 18.10/18.30 That finishes the proof of the theorem.
% 18.10/18.30
% 18.10/18.30 Process 4829 finished Wed Jul 27 07:07:14 2022
% 18.10/18.30 Otter interrupted
% 18.10/18.30 PROOF FOUND
%------------------------------------------------------------------------------